Dissertations / Theses: 'Mathematical modelling/biology'

1

Hunt, Gordon S. "Mathematical modelling of pattern formation in developmental biology." Thesis, Heriot-Watt University, 2013. http://hdl.handle.net/10399/2706.

Full text

Abstract:

The transformation from a single cell to the adult form is one of the remarkable wonders of nature. However, the fundamental mechanisms and interactions involved in this metamorphic change still remain elusive. Due to the complexity of the process, researchers have attempted to exploit simpler systems and, in particular, have focussed on the emergence of varied and spectacular patterns in nature. A number of mathematical models have been proposed to study this problem with one of the most well studied and prominent being the novel concept provided by A.M. Turing in 1952. Turing's simple yet elegant idea consisted of a system of interacting chemicals that reacted and di used such that, under certain conditions, spatial patterns can arise from near homogeneity. However, the implicit assumption that cells respond to respective chemical levels, di erentiating accordingly, is an oversimpli cation and may not capture the true extent of the biology. Here, we propose mathematical models that explicitly introduce cell dynamics into pattern formation mechanisms. The models presented are formulated based on Turing's classical mechanism and are used to gain insight into the signi cance and impact that cells may have in biological phenomena. The rst part of this work considers cell di erentiation and incorporates two conceptually di erent cell commitment processes: asymmetric precursor di erentiation and precursor speci cation. A variety of possible feedback mechanisms are considered with the results of direct activator upregulation suggesting a relaxation of the two species Turing Instability requirement of long range inhibition, short range activation. Moreover, the results also suggest that the type of feedback mechanism should be considered to explain observed biological results. In a separate model, cell signalling is investigated using a discrete mathematical model that is derived from Turing's classical continuous framework. Within this, two types of cell signalling are considered, namely autocrine and juxtacrine signalling, with both showing the attainability of a variety of wavelength patterns that are illustrated and explainable through individual cell activity levels of receptor, ligand and inhibitor. Together with the full system, a reduced two species system is investigated that permits a direct comparison to the classical activator-inhibitor model and the results produce pattern formation in systems considering both one and two di usible species together with an autocrine and/or juxtacrine signalling mechanism. Formulating the model in this way shows a greater applicability to biology with fundamental cell signalling and the interactions involved in Turing type patterning described using clear and concise variables.

APA, Harvard, Vancouver, ISO, and other styles

2

Nurtay, Anel. "Mathematical modelling of pathogen specialisation." Doctoral thesis, Universitat Autònoma de Barcelona, 2019. http://hdl.handle.net/10803/667178.

Full text

Abstract:

L’aparició de nous virus causants de malalties està estretament lligada a l’especialització de subpoblacions virals cap a nous tipus d’amfitrions. La modelització matemàtica proporciona un marc quantitatiu que pot ajudar amb la predicció de processos a llarg termini com pot ser l’especialització. A causa de la naturalesa complexa que presenten les interaccions intra i interespecífiques en els processos evolutius, cal aplicar eines matemàtiques complexes, com ara l’anàlisi de bifurcacions, al estudiar dinàmiques de població. Aquesta tesi desenvolupa una jerarquia de models de població per poder comprendre l’aparició i les dinàmiques d’especialització, i la seva dependència dels paràmetres del sistema. Utilitzant un model per a un virus de tipus salvatge i un virus mutat que competeixen pel mateix amfitrió, es determinen les condicions per a la supervivència únicament de la subpoblació mutant, juntament amb la seva coexistència amb el cep de tipus salvatge. Els diagrames d’estabilitat que representen regions de dinàmiques diferenciades es construeixen en termes de taxa d’infecció, virulència i taxa de mutació; els diagrames s’expliquen en base a les característiques biològiques de les subpoblacions. Per a paràmetres variables, s’observa i es descriu el fenomen d’intersecció i intercanvi d’estabilitat entre diferents solucions sistemàtiques i periòdiques en l’àmbit dels ceps de tipus salvatge i els ceps mutants en competència directa. En el cas de que diversos tipus d’amfitrions estiguin disponibles per a ser disputats per ceps especialitzats i generalistes existeixen regions de biestabilitat, i les probabilitats d’observar cada estat es calculen com funcions de les taxes d’infecció. S’ha trobat un rar atractor caòtic i s’ha analitzat amb l’ús d’exponents de Lyapunov. Això, combinat amb els diagrames d’estabilitat, mostra que la supervivència del cep generalista en un entorn estable és un fet improbable. A més, s’estudia el cas dels diversos ceps N>>1 que competeixen per diferents tipus de cèl·lules amfitriones. En aquest cas s’ha descobert una dependència no monotònica, contraria al que es preveia, del temps d’especialització sobre la mida inicial i la taxa de mutació, com a conseqüència de la realització d’un anàlisi de regressió sobre dades obtingudes numèricament. En general, aquest treball fa contribucions àmplies a la modelització matemàtica i anàlisi de la dinàmica dels patogens i els processos evolutius.
La aparición de nuevos virus causantes de enfermedades está estrechamente ligada a la especialización de las subpoblaciones virales hacia nuevos tipos de anfitriones. La modelizaci ón matemática proporciona un marco cuantitativo que puede ayudar a la predicción de procesos a largo plazo como la especialización. Debido a la naturaleza compleja que presentan las interacciones intra e interespecíficas en los procesos evolutivos, aplicar herramientas matemáticas complejas, tales como el análisis de bifurcación, al estudiar dinámicas de población. Esta tesis desarrolla una jerarquía de modelos de población para poder comprender la aparición y las dinámicas de especialización, y su dependencia de los parámetros del sistema. Utilizando un modelo para un virus de tipo salvaje y un virus mutado que compiten por el mismo anfitrión, se determinan las condiciones para la supervivencia únicamente de la subpoblación mutante, junto con su coexistencia con la cepa de tipo salvaje. Los diagramas de estabilidad que representan regiones de dinámicas diferenciadas se construyen en términos de tasa de infección, virulencia y tasa de mutación; los diagramas se explican en base a las características biológicas de las subpoblaciones. Para parámetros variables, se observa y se describe el fenómeno de intersección e intercambio de estabilidad entre diferentes soluciones sistemáticas y periódicas en el ámbito de las cepas de tipo salvaje y las cepas mutantes en competencia directa. En el caso de que varios tipos de anfitriones estén disponibles para ser disputados por cepas especializadas y generalistas existen regiones de biestabilidad, y las probabilidades de observar cada estado se calculan como funciones de las tasas de infección. Se ha encontrado un raro atractor caótico y se ha analizado con el uso de exponentes de Lyapunov. Esto, combinado con los diagramas de estabilidad, muestra que la supervivencia de la cepa generalista en un entorno estable es un hecho improbable. Además, se estudia el caso de los varias cepas N>> 1 que compiten por diferentes tipos de células anfitrionas. En este caso se ha descubierto una dependencia no monotónica, contraria a lo que se preveía, del tiempo de especialización sobre el tamaño inicial y la tasa de mutación, como consecuencia de la realización de un análisis de regresión sobre datos obtenidos numéricamente. En general, este trabajo hace contribuciones amplias a la modelización matemática y el análisis de la dinámica de los patógenos y los procesos evolutivos.
The occurrence of new disease-causing viruses is tightly linked to the specialisation of viral sub-populations towards new host types. Mathematical modelling provides a quantitative framework that can aid with the prediction of long-term processes such as specialisation. Due to the complex nature of intra- and interspecific interactions present in evolutionary processes, elaborate mathematical tools such as bifurcation analysis must be employed while studying population dynamics. In this thesis, a hierarchy of population models is developed to understand the onset and dynamics of specialisation and their dependence on the parameters of the system. Using a model for a wild-type and mutant virus that compete for the same host, conditions for the survival of only the mutant subpopulation, along with its coexistence with the wild-type strain, are determined. Stability diagrams that depict regions of distinct dynamics are constructed in terms of infection rates, virulence and the mutation rate; the diagrams are explained in terms of the biological characteristics of the sub-populations. For varying parameters, the phenomenon of intersection and exchange of stability between different periodic solutions of the system is observed and described in the scope of the competing wild-type and mutant strains. In the case of several types of hosts being available for competing specialist and generalist strains, regions of bistability exist, and the probabilities of observing each state are calculated as functions of the infection rates. A strange chaotic attractor is discovered and analysed with the use of Lyapunov exponents. This, combined with the stability diagrams, shows that the survival of the generalist in a stable environment is an unlikely event. Furthermore, the case of N=1 different strains competing for different types of host cells is studied. For this case, a counterintuitive and non-monotonic dependence of the specialisation time on the burst size and mutation rate is discovered as a result of carrying out a regression analysis on numerically obtained data. Overall, this work makes broad contributions to mathematical modelling and analysis of pathogen dynamics and evolutionary processes.

APA, Harvard, Vancouver, ISO, and other styles

3

Rata, Scott. "Mathematical modelling of mitotic controls." Thesis, University of Oxford, 2018. https://ora.ox.ac.uk/objects/uuid:7bef862c-2025-4494-a2bb-4fe93584d92a.

Full text

Abstract:

The mitotic cell cycle is fundamental to eukaryotic life. In mitosis, replicated chromosomes are segregated to form two new nuclei. This is essential to ensure the maintenance of chromosome number between parent and daughter cells. In higher eukaryotes, numerous cytological changes occur to facilitate the separation of the genetic material: the nuclear envelope breaks down, the mitotic spindle assembles, and the cell rounds-up. There is a well-conserved control network that regulates these processes to bring about the entry into mitosis, the separation of the genetic material, and the reversal of these processes during mitotic exit. To build a coherent model of these regulatory networks requires us to write the biochemical reactions in mathematical form. The work in this Thesis pertains to three fundamental switches: entry into mitosis, the metaphase-to-anaphase transition, and exit from mitosis. I present three studies from a systems-level perspective. The first investigates a novel bistable mechanism controlling mitotic entry/exit in vitro using purified proteins. Dephosphorylation of Greatwall kinase by the phosphatase PP2A-B55 creates a double negative feedback loop that gives a bistable system response with respect to cyclin-dependent kinase 1 (Cdk1) activity. The second looks at hysteresis between mitotic entry and mitotic exit in HeLa cells. Hysteresis persists when either of the regulatory loops of Cdk1 or its counter-acting phosphatase PP2A-B55 is removed, but is diminished when they are both removed. Finally, the regulation of separase in the metaphase-to-anaphase transition is analysed. Separase that is liberated from securin inhibition is isomerised by Pin1 into a conformation that can bind to cyclin B1. This binding peaks after separase has cleaved cohesin and initiated anaphase.

APA, Harvard, Vancouver, ISO, and other styles

4

Catt, Christopher Joseph. "Mathematical modelling of tissue metabolism and growth." Thesis, University of Southampton, 2010. https://eprints.soton.ac.uk/176447/.

Full text

Abstract:

The work presented in this thesis is concerned with modelling the growth of tissue constructs, with particular focus on the effects the local micro environment has on the cell cycle and metabolism. We consider two cases; multicellular tumour spheroids and orthopaedic tissue constructs. This thesis is divided into two parts. In the first part we will present a multispecies model of an avascular tumour that studies how a cell’s metabolism affects the cell cycle, spheroid growth and the mechanical forces that arise during growth. The second part consists of a study of the growth of an engineered cartilaginous tissue layer. Experimental observations will be compared to a model of the distribution of cells and extracellular matrix. The efficiency of cancer treatments such as radiotherapy and chemotherapy are sensitive to the local environment of a cell. Therefore an essential task in tumour biology is to understand the microenvironment within a tumour. Many mathematical models study the effects of nutrients and waste products, usually assuming growth is limited by the diffusion of a single nutrient. We will look in detail at the metabolic pathways from which cells obtain energy (ATP). A multispecies model is presented that considers the transition from aerobic to anaerobic respi- ration and includes relevant chemical and ionic buffering reactions and transport mechanisms. Results show that potential ATP production affects the cell cycle and consequently the rate of growth. This model is simplified using mathematical analysis and is integrated with a morphoelastic model to study the development of mechanical forces. The model shows that mechanical effects are particularly important during necrosis, where large tensile forces are shown to develop. A review of the equations governing nutrient conservation is given, by developing alternative macroscopic equations based on the microscopic features of a tumour using homogenization techniques. The second part of this thesis studies the growth of cartilaginous tissue. Bio-materials are being engineered in an attempt to replace dysfunctional tissue in the human body using cells extracted from living organisms. We model the growth of a cartilaginous tissue construct that has been grown from expanded chondrocytes seeded onto collagen coated filters. A model is developed to explain the distribution of cells and the concentration and distribution of collagen and GAGs. This is achieved by studying the local environment of the cells. Model predictions are compared to a range of experimental data and show most of the growth takes place in the upper region of the construct.

APA, Harvard, Vancouver, ISO, and other styles

5

Modhara, Sunny. "Mathematical modelling of vascular development in zebrafish." Thesis, University of Nottingham, 2015. http://eprints.nottingham.ac.uk/29125/.

Full text

Abstract:

The Notch signalling pathway is pivotal in ensuring that the processes of arterial specification, angiogenic sprouting and haematopoietic stem cell (HSC) specification are correctly carried out in the dorsal aorta (DA), a primary arterial blood vessel in developing vertebrate embryos. Using the zebrafish as a model organism, and additional experimental observations from mouse and cell line models to guide mathematical modelling, this thesis aims to better understand the mechanisms involved in the establishment of a healthy vasculature in the growing embryo. We begin by studying arterial and HSC specification in the zebrafish DA. Mathematical models are used to analyse the dose response of arterial and HSC genes to an input Notch signal. The models determine how distinct levels of Notch signalling may be required to establish arterial and HSC identity. Furthermore, we explore how Delta-Notch coupling, which generates salt-and-pepper patterns, may drive the average gene expression levels higher than their homogeneous levels. The models considered here can qualitatively reproduce experimental observations. Using laboratory experiments, I was able to isolate DA cells from transgenic zebrafish embryos and generate temporal gene expression data using qPCR. We show that it is possible to fit ODE models to such data but more reliable data and a greater number of replicates at each time point is required to make further progress. The same VEGF-Delta-Notch signalling pathway is involved in tip cell selection in angiogenic sprouting. Using an ODE model, we rigourously study the dynamics of a VEGF-Delta-Notch feedback loop which is capable of amplifying differences betwen cells to form period-2 spatial patterns of alternating tip and stalk cells. The analysis predicts that the feeback strengths of Delta ligand and VEGFR-2 production dictate the onset of patterning in the same way, irrespective of the parameter values used. This model is extended to incorporate feedback from filopodia, growing in a gradient of extracellular VEGF, which are capable of facilitating tip cell selection by amplifying the resulting patterns. Lastly, we develop a PDE model which is able to properly account for VEGF receptor distributions in the cell membrane and filopodia. Receptors can diffuse and be advected due to domain growth, defined by a constitutive law, in this model. Our analysis and simulations predict that when receptor diffusivity is large, the ODE model for filopodia growth is an excellent approximation to the PDE model, but that for smaller diffusivity, the PDE model provides valuable insight into the pattern forming potential of the system.

APA, Harvard, Vancouver, ISO, and other styles

6

Durney, Clinton H. "A Two-Component Model For Bacterial Chemotaxis." The Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1366312981.

Full text

APA, Harvard, Vancouver, ISO, and other styles

7

Moi, Adriano. "Mathematical modelling of integrin-like receptors systems." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2016. http://amslaurea.unibo.it/11255/.

Full text

Abstract:

Nel presente lavoro, ho studiato e trovato le soluzioni esatte di un modello matematico applicato ai recettori cellulari della famiglia delle integrine. Nel modello le integrine sono considerate come un sistema a due livelli, attivo e non attivo. Quando le integrine si trovano nello stato inattivo possono diffondere nella membrana, mentre quando si trovano nello stato attivo risultano cristallizzate nella membrana, incapaci di diffondere. La variazione di concentrazione nella superficie cellulare di una sostanza chiamata attivatore dà luogo all’attivazione delle integrine. Inoltre, questi eterodimeri possono legare una molecola inibitrice con funzioni di controllo e regolazione, che chiameremo v, la quale, legandosi al recettore, fa aumentare la produzione della sostanza attizzatrice, che chiameremo u. In questo modo si innesca un meccanismo di retroazione positiva. L’inibitore v regola il meccanismo di produzione di u, ed assume, pertanto, il ruolo di modulatore. Infatti, grazie a questo sistema di fine regolazione il meccanismo di feedback positivo è in grado di autolimitarsi. Si costruisce poi un modello di equazioni differenziali partendo dalle semplici reazioni chimiche coinvolte. Una volta che il sistema di equazioni è impostato, si possono desumere le soluzioni per le concentrazioni dell’inibitore e dell’attivatore per un caso particolare dei parametri. Infine, si può eseguire un test per vedere cosa predice il modello in termini di integrine. Per farlo, ho utilizzato un’attivazione del tipo funzione gradino e l’ho inserita nel sistema, valutando la dinamica dei recettori. Si ottiene in questo modo un risultato in accordo con le previsioni: le integrine legate si trovano soprattutto ai limiti della zona attivata, mentre le integrine libere vengono a mancare nella zona attivata.

APA, Harvard, Vancouver, ISO, and other styles

8

Bakshi, Suruchi D. "Mathematical modelling of Centrosomin incorporation in Drosophila centrosomes." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:baefde65-bc38-4a11-bd92-e2e4cccad784.

Full text

Abstract:

Centrosomin (Cnn) is an integral centrosomal protein in Drosophila with orthologues in several species, including humans. The human orthologue of Cnn is required for brain development with Cnn hypothesised to play a similar role in Drosophila. Control of Cnn incorporation into centrosomes is crucial for controlling asymmetric division in certain types of Drosophila stem cells. FRAP experiments on Cnn show that Cnn recovers in a pe- culiar fashion, which suggest that Cnn may be incorporated closest to the centrioles and then spread radially outward, either diffusively or ad- vectively. The aim of this thesis is to understand the mechanism of Cnn incorporation into the Drosophila centrosomes, to determine the mode of transport of the incorporated Cnn, and to obtain parameter estimates for transport and biochemical reactions. A crucial unknown in the modelling process is the distribution of Cnn receptors. We begin by constructing coupled partial differential equation models with either diffusion or advection as the mechanism for incorpo- rated Cnn transport. The simplest receptor distribution we begin with involves a spherical, infinitesimally thick, impermeable shell. We refine the diffusion models using the insights gained from comparing the model out- put with data (gathered during mitosis) and through careful assessment of the behaviour of the data. We show that a Gaussian receptor distribution is necessary to explain the Cnn FRAP data and that the data cannot be explained by other simpler receptor distributions. We predict the exact form of the receptor distribution through data fitting and present pre- liminary experimental results from our collaborators that suggest that a protein called DSpd2 may show a matching distribution. Not only does this provide strong experimental support for a key prediction from our model, but it also suggests that DSpd2 acts as a Cnn receptor. We also show using the mitosis FRAP data that Cnn does not exhibit appreciable radial movement during mitosis, which precludes the use of these data to distinguish between diffusive and advective transport of Cnn. We use long time Cnn FRAP data gathered during S-phase for this purpose. We fit the S-phase FRAP data using the DSpd2 profiles gath- ered for time points corresponding to the Cnn FRAP experiments. We also use data from FRAP experiments where colchicine is injected into the embryos to destroy microtubules (since microtubules are suspected to play a role in advective transport of Cnn). From the analysis of all these data we show that Cnn is transported in part by advection and in part by diffusion. Thus, we are able to provide the first mechanistic description of the Cnn incorporation process. Further, we estimate parameters from the model fitting and predict how some of the parameters may be altered as nuclei progress from S-phase to mitosis. We also generate testable predic- tions regarding the control of the Cnn incorporation process. We believe that this work will be useful to understand the role of Cnn incorporation in centrosome function, particularly in asymmetrically dividing stem cells.

APA, Harvard, Vancouver, ISO, and other styles

9

Chapman, Lloyd A. C. "Mathematical modelling of cell growth in tissue engineering bioreactors." Thesis, University of Oxford, 2015. https://ora.ox.ac.uk/objects/uuid:7c9ee131-7d9b-4e5d-8534-04a059fbd039.

Full text

Abstract:

Expanding cell populations extracted from patients or animals is essential to the process of tissue engineering and is commonly performed in laboratory incubation devices known as bioreactors. Bioreactors provide a means of controlling the chemical and mechanical environment experienced by cells to ensure growth of a functional population. However, maximising this growth requires detailed knowledge of how cell proliferation is affected by bioreactor operating conditions, such as the flow rate of culture medium into the bioreactor, and by the initial cell seeding distribution in the bioreactor. Mathematical modelling can provide insight into the effects of these factors on cell expansion by describing the chemical and physical processes that affect growth and how they interact over different length- and time-scales. In this thesis we develop models to investigate how cell expansion in bioreactors is affected by fluid flow, solute transport and cell seeding. For this purpose, a perfused single-fibre hollow fibre bioreactor is used as a model system. We start by developing a model of the growth of a homogeneous cell layer on the outer surface of the hollow fibre in response to local nutrient and waste product concentrations and fluid shear stress. We use the model to simulate the cell layer growth with different flow configurations and operating conditions for cell types with different nutrient demands and responses to fluid shear stress. We then develop a 2D continuum model to investigate the influence of oxygen delivery, fluid shear stress and cell seeding on cell aggregate growth along the outer surface of the fibre. Using the model we predict operating conditions and initial aggregate distributions that maximise the rate of growth to confluence over the fibre surface for different cell types. A potential limitation of these models is that they do not explicitly consider individual cell interaction, movement and growth. To address this, we conclude the thesis by assessing the suitability of a hybrid framework for modelling bioreactor cell aggregate growth, with a discrete cell model coupled to a continuum nutrient transport model. We consider a simple set-up with a 1D cell aggregate growing along the base of a 2D nutrient bath. Motivated by trying to reduce the high computational cost of simulating large numbers of cells with a cell-based model, and to assess the validity of our previous continuum description of cell aggregate growth, we derive a continuum approximation of the discrete model in the large cell number limit and determine whether it agrees with the discrete model via numerical simulations.

APA, Harvard, Vancouver, ISO, and other styles

10

Osman, Mohamad Hussein. "Mathematical modelling and simulation of biofuel cells." Thesis, University of Southampton, 2013. https://eprints.soton.ac.uk/363762/.

Full text

Abstract:

Bio-fuel cells are driven by diverse and abundant bio-fuels and biological catalysts. The production/consumption cycle of bio-fuels is considered to be carbon neutral and, in principle, more sustainable than that of conventional fuel cells. The cost benefits over traditional precious-metal catalysts, and the mild operating conditions represent further advantages. It is important that mathematical models are developed to reduce the burden on laboratory based testing and accelerate the development of practical systems. In this study, recent key developments in bio-fuel cell technology are reviewed and two different approaches to modelling biofuel cells are presented, a detailed physics-based approach, and a data-driven regression model. The current scientific and engineering challenges involved in developing practical bio-fuel cell systems are described, particularly in relation to a fundamental understanding of the reaction environment, the performance and stability requirements, modularity and scalability. New materials and methods for the immobilization of enzymes and mediators on electrodes are examined, in relation to performance characteristics and stability. Fuels, mediators and enzymes used (anode and cathode), as well as the cell configurations employed are discussed. New developments in microbial fuel cell technologies are reviewed in the context of fuel sources, electron transfer mechanisms, anode materials and enhanced O2 reduction. Multi-dimensional steady-state and dynamic models of two enzymatic glucose/air fuel cells are presented. Detailed mass and charge balances are combined with a model for the reaction mechanism in the electrodes. The models are validated against experimental results. The dynamic performance under different cell voltages is simulated and the evolution of the system is described. Parametric studies are performed to investigate the effect of various operating conditions. A data-driven model, based on a reduced-basis form of Gaussian process regression, is also presented and tested. The improved computational efficiency of data-driven models makes them better candidates for modelling large complex systems.

APA, Harvard, Vancouver, ISO, and other styles

11

Shabala, Alexander. "Mathematical modelling of oncolytic virotherapy." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:cca2c9bc-cbd4-4651-9b59-8a4dea7245d1.

Full text

Abstract:

This thesis is concerned with mathematical modelling of oncolytic virotherapy: the use of genetically modified viruses to selectively spread, replicate and destroy cancerous cells in solid tumours. Traditional spatially-dependent modelling approaches have previously assumed that virus spread is due to viral diffusion in solid tumours, and also neglect the time delay introduced by the lytic cycle for viral replication within host cells. A deterministic, age-structured reaction-diffusion model is developed for the spatially-dependent interactions of uninfected cells, infected cells and virus particles, with the spread of virus particles facilitated by infected cell motility and delay. Evidence of travelling wave behaviour is shown, and an asymptotic approximation for the wave speed is derived as a function of key parameters. Next, the same physical assumptions as in the continuum model are used to develop an equivalent discrete, probabilistic model for that is valid in the limit of low particle concentrations. This mesoscopic, compartment-based model is then validated against known test cases, and it is shown that the localised nature of infected cell bursts leads to inconsistencies between the discrete and continuum models. The qualitative behaviour of this stochastic model is then analysed for a range of key experimentally-controllable parameters. Two-dimensional simulations of in vivo and in vitro therapies are then analysed to determine the effects of virus burst size, length of lytic cycle, infected cell motility, and initial viral distribution on the wave speed, consistency of results and overall success of therapy. Finally, the experimental difficulty of measuring the effective motility of cells is addressed by considering effective medium approximations of diffusion through heterogeneous tumours. Considering an idealised tumour consisting of periodic obstacles in free space, a two-scale homogenisation technique is used to show the effects of obstacle shape on the effective diffusivity. A novel method for calculating the effective continuum behaviour of random walks on lattices is then developed for the limiting case where microscopic interactions are discrete.

APA, Harvard, Vancouver, ISO, and other styles

12

Wearing, Helen Jane. "Mathematical modelling of cell-cell signalling in developmental biology and wound healing." Thesis, Heriot-Watt University, 2001. http://hdl.handle.net/10399/1184.

Full text

APA, Harvard, Vancouver, ISO, and other styles

13

Cobbold, Christina Anne. "Mathematical modelling of problems in human biology : dermal wound healing and atherosclerosis." Thesis, Heriot-Watt University, 2001. http://hdl.handle.net/10399/471.

Full text

APA, Harvard, Vancouver, ISO, and other styles

14

Schofield, James W. "Aspects of modelling solid tumours." Thesis, University of Oxford, 2010. http://ora.ox.ac.uk/objects/uuid:b7c50880-ed03-451e-9841-209f2de6a982.

Full text

Abstract:

This thesis considers aspects of modelling solid tumours. We begin by considering the common assumption that nutrient or drug concentrations in avascular tumour spheroids are radially symmetric. We derive a simple Poisson equation for biomolecular diffusion into an avascular tumour, but with highly oscillatory boundary conditions due to the surrounding capillary network. We find that the assumption of radial symmetry is legitimate for biomolecules that are taken up in sufficient quantities by proliferating cancer cells; however radially symmetric profiles need not be observed otherwise. We then investigate how the gap between an avascular tumour and the neighbouring vasculature varies as the tumour grows. This is explored by (i) using scaling arguments based on ordinary differential equations, (ii) coupling the rate of oxygen flux from the vasculature to oxygen evolution within the tumour, and (iii) deriving a system of six coupled non-linear partial differential equations modelling the tumour evolution. It is found that as the tumour grows any initial gap between the tumour and neighbouring vasculature closes since there is no mechanism which would sufficiently up-regulate non-cancerous cell proliferation. This is in contrast to the intra-cornea implantation observations, upon which several mathematical models are based. Finally, we study the growth and treatment of a vascular tumour subjected to chemotherapies, particularly when the therapies can exhibit an anti-angiogenic effect and resistance to the therapy is incorporated. A multi-compartment model is derived for the evolution of a tumour undergoing treatment and parameters are estimated, with extensions to incorporate numerous different therapy protocols in the literature. We find that anti-angiogens can be effective, though the appropriate scheduling is counter-intuative and contradicts many standard therapy rules. We conclude that chemotherapy protocol design is very sensitive to the mode of action of the drug and simple general strategies will, in many cases, not be the most effective.

APA, Harvard, Vancouver, ISO, and other styles

15

Gadelha, Hermes. "Mathematical modelling of human sperm motility." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:34a11669-5d14-470b-b10b-361cf3688a30.

Full text

Abstract:

The propulsion mechanics driving the movement of living cells constitutes one of the most incredible engineering works of nature. Active cell motility via the controlled movement of a flagellum beating is among the phylogentically oldest forms of motility, and has been retained in higher level organisms for spermatozoa transport. Despite this ubiquity and importance, the details of how each structural component within the flagellum is orchestrated to generate bending waves, or even the elastic material response from the sperm flagellum, is far from fully understood. By using microbiomechanical modelling and simulation, we develop bio-inspired mathematical models to allow the exploration of sperm motility and the material response of the sperm flagellum. We successfully construct a simple biomathematical model for the human sperm movement by taking into account the sperm cell and its interaction with surrounding fluid, through resistive-force theory, in addition to the geometrically non-linear response of the flagellum elastic structure. When the surrounding fluid is viscous enough, the model predicts that the sperm flagellum may buckle, leading to profound changes in both the waveforms and the swimming cell trajectories. Furthermore, we show that the tapering of the ultrastructural components found in mammalian spermatozoa is essential for sperm migration in high viscosity medium. By reinforcing the flagellum in regions where high tension is expected this flagellar accessory complex is able to prevent tension-driven elastic instabilities that compromise the spermatozoa progressive motility. We equally construct a mathematical model to describe the structural effect of passive link proteins found in flagellar axonemes, providing, for the first time, an explicit mathematical demonstration of the counterbend phenomenon as a generic property of the axoneme, or any cross-linked filament bundle. Furthermore, we analyse the differences between the elastic cross-link shear and pure material shear resistance. We show that pure material shearing effects from Cosserat rod theory or, equivalently, Timoshenko beam theory or are fundamentally different from elastic cross-link induced shear found in filament bundles, such as the axoneme. Finally, we demonstrate that mechanics and modelling can be utilised to evaluate bulk material properties, such as bending stiffness, shear modulus and interfilament sliding resistance from flagellar axonemes its constituent elements, such as microtubules.

APA, Harvard, Vancouver, ISO, and other styles

16

McGillen, Jessica Buono. "Mathematical modelling of metabolism and acidity in cancer." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:552f9ea8-ac6c-4413-9535-0318e855d85c.

Full text

Abstract:

Human cancers exhibit the common phenotype of elevated glycolytic metabolism, which causes acidification of the tissue microenvironment and may facilitate tumour invasion. In this thesis, we use mathematical models to address a series of open problems underlying the glycolytic tumour phenotype and its attendant acidity. We first explore tissue-scale consequences of metabolically-derived acid. Incorporating more biological detail into a canonical model of acidity at the tumour-host interface, we extend the range of tumour behaviours captured by the modelling framework. We then carry out an asymptotic travelling wave analysis to express invasive tumour properties in terms of fundamental parameters, and find that interstitial gaps between an advancing tumour and retreating healthy tissue, characteristic of aggressive invasion and comprising a controversial feature of the original model, are less significant under our generalised formulation. Subsequently, we evaluate a potential role of lactate---historically assumed to be a passive byproduct of glycolytic metabolism---in a perfusion-dependent metabolic symbiosis that was recently proposed as a beneficial tumour behaviour. Upon developing a minimal model of dual glucose-lactate consumption in vivo and employing a multidimensional sensitivity analysis, we find that symbiosis may not be straightforwardly beneficial for our model tumour. Moreover, new in vitro experiments, carried out by an experimental collaborator, place U87 glioblastoma tumours in a weakly symbiotic parameter regime despite their clinical malignancy. These results suggest that intratumoural metabolic cooperation is unlikely to be an important role for lactate. Finally, we examine the complex pH regulation system that governs expulsion of metabolically derived acid loads across tumour cell membranes. This system differs from the healthy system by expression of only a few key proteins, yet its dynamics are non-intuitive in the crowded and poorly perfused in vivo environment. We systematically develop a model of tumour pH regulation, beginning with a single-cell scenario and progressing to a spheroid, within a Bayesian framework that incorporates information from in vitro data contributed by a second experimental collaborator. We predict that a net effect of pH regulation is a straightforward transmembrane pH gradient, but also that existing treatments are unable to disrupt the system strongly enough to cause tumour cell death. Taken together, our models help to elucidate previously unresolved features of glycolytic tumour metabolism, and illustrate the utility of a combined mathematical, statistical, and experimental approach for testing biological hypotheses. Opportunities for further investigation are discussed.

APA, Harvard, Vancouver, ISO, and other styles

17

Podéus, Henrik. "Neural response of a Neuron population : A mathematical modelling approach." Thesis, Linköpings universitet, Avdelningen för medicinsk teknik, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-177797.

Full text

Abstract:

The brain – the organ that allows us to be aware of our surroundings – consists of a complex network of neurons, which seemingly allows the human brain to be able of abstract thinking, emotions, and cognitive function. To learn how the brain is capable of this, the two main branches of neuroscience study either neurons in detail, or how they communicate within neuronal networks. Both these branches often tackle the complexity using a combination of experiments and mathematical modelling. A third and less studied aspect of neuroscience concerns the neurovascular coupling (NVC), for which my research group has previously developed mathematical models. However, these NVC models have still not integrated valuable data from rodents and primates, and the NVC models are also not connected to existing neuronal network models. In this project, I address both of these two shortcomings. First, an existing model for the NVC was connected with a simple model for neuronal networks, establishing a connection between the NVC models and the software NEURON. Second, we established a way to preserved information from NVC data from rodents and mice into NVC models humans. This work thus connects the previously developed NVC model both with data from other species and with other types of models. This brings us one step closer to a more holistic and interconnected understanding of the brain and its many intriguing cognitive and physiological functions.

APA, Harvard, Vancouver, ISO, and other styles

18

Szekely, Tamas. "Stochastic modelling and simulation in cell biology." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:f9b8dbe6-d96d-414c-ac06-909cff639f8c.

Full text

Abstract:

Modelling and simulation are essential to modern research in cell biology. This thesis follows a journey starting from the construction of new stochastic methods for discrete biochemical systems to using them to simulate a population of interacting haematopoietic stem cell lineages. The first part of this thesis is on discrete stochastic methods. We develop two new methods, the stochastic extrapolation framework and the Stochastic Bulirsch-Stoer methods. These are based on the Richardson extrapolation technique, which is widely used in ordinary differential equation solvers. We believed that it would also be useful in the stochastic regime, and this turned out to be true. The stochastic extrapolation framework is a scheme that admits any stochastic method with a fixed stepsize and known global error expansion. It can improve the weak order of the moments of these methods by cancelling the leading terms in the global error. Using numerical simulations, we demonstrate that this is the case up to second order, and postulate that this also follows for higher order. Our simulations show that extrapolation can greatly improve the accuracy of a numerical method. The Stochastic Bulirsch-Stoer method is another highly accurate stochastic solver. Furthermore, using numerical simulations we find that it is able to better retain its high accuracy for larger timesteps than competing methods, meaning it remains accurate even when simulation time is speeded up. This is a useful property for simulating the complex systems that researchers are often interested in today. The second part of the thesis is concerned with modelling a haematopoietic stem cell system, which consists of many interacting niche lineages. We use a vectorised tau-leap method to examine the differences between a deterministic and a stochastic model of the system, and investigate how coupling niche lineages affects the dynamics of the system at the homeostatic state as well as after a perturbation. We find that larger coupling allows the system to find the optimal steady state blood cell levels. In addition, when the perturbation is applied randomly to the entire system, larger coupling also results in smaller post-perturbation cell fluctuations compared to non-coupled cells. In brief, this thesis contains four main sets of contributions: two new high-accuracy discrete stochastic methods that have been numerically tested, an improvement that can be used with any leaping method that introduces vectorisation as well as how to use a common stepsize adapting scheme, and an investigation of the effects of coupling lineages in a heterogeneous population of haematopoietic stem cell niche lineages.

APA, Harvard, Vancouver, ISO, and other styles

19

Pearson, Natalie Clare. "Mathematical modelling of flow and transport phenomena in tissue engineering." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:43688cc7-b523-4676-8c41-72db7fc07814.

Full text

Abstract:

Tissue engineering has great potential as a method for replacing or repairing lost or damaged tissue. However, progress in the field to date has been limited, with only a few clinical successes despite active research covering a wide range of cell types and experimental approaches. Mathematical modelling can complement experiments and help improve understanding of the inherently complex tissue engineering systems, providing an alternative perspective in a more cost- and time-efficient manner. This thesis focusses on one particular experimental setup, a hollow fibre membrane bioreactor (HFMB). We develop a suite of mathematical models which consider the fluid flow, solute transport, and cell yield and distribution within a HFMB, each relevant to a different setup which could be implemented experimentally. In each case, the governing equations are obtained by taking the appropriate limit of a generalised multiphase model, based on porous flow mixture theory. These equations are then reduced as far as possible, through exploitation of the small aspect ratio of the bioreactor and by considering suitable parameter limits in the subsequent asymptotic analysis. The reduced systems are then either solved numerically or, if possible, analytically. In this way we not only aim to illustrate typical behaviours of each system in turn, but also highlight the dependence of results on key experimentally controllable parameter values in an analytically tractable and transparent manner. Due to the flexibility of the modelling approach, the models we present can readily be adapted to specific experimental conditions given appropriate data and, once validated, be used to inform and direct future experiments.

APA, Harvard, Vancouver, ISO, and other styles

20

Shipley, Rebecca Julia. "Multiscale modelling of fluid and drug transport in vascular tumours." Thesis, University of Oxford, 2009. http://ora.ox.ac.uk/objects/uuid:8f663f70-8d23-49ad-8348-1763359d8f62.

Full text

Abstract:

Understanding the perfusion of blood and drugs in tumours is fundamental to foreseeing the eﬃcacy of treatment regimes and predicting tumour growth. In particular, the dependence of these processes on the tumour vascular structure is poorly established. The objective of this thesis is to derive eﬀective equations describing blood, and drug perfusion in vascular tumours, and speciﬁcally to determine the dependence of these on the tumour vascular structure. This dependence occurs through the interaction between two diﬀerent length scales - that which characterizes the structure of the vascular network, and that which characterizes the tumour as a whole. Our method throughout is to use homogenization as a tool to evaluate this interaction. In Chapter 1 we introduce the problem. In Chapter 2 we develop a theoretical model to describe ﬂuid ﬂow in solid tumours through both the vasculature and the interstitium, at a number of length scales. Ultimately we homogenize over a network of capillaries to form a coupled porous medium model in terms of a vascular density. Whereas in Chapter 2 it is necessary to specify the vascular structure to derive the eﬀective equations, in Chapter 3 we employ asymptotic homogenization through multiple scales to derive the coupled equations for an arbitrary periodic vascular network. In Chapter 4, we extend this analysis to account for advective and diﬀusive transport of anticancer drugs delivered intravenously; we consider a range of reaction properties in the interstitium and boundary conditions on the vascular wall. The models derived in Chapters 2–4 could be applied to any drug type and treatment regime; to demonstrate their potential, we simulate the delivery of vinblastine in dorsal skinfold chambers in Chapter 5 and make quantitative predictions regarding the optimal treatment regime. In the ﬁnal Chapter we summarize the main results and indicate directions for further work.

APA, Harvard, Vancouver, ISO, and other styles

21

Duchesne, Ronan. "Erythroid differentiation in vitro under the lens of mathematical modelling." Thesis, Lyon, 2019. http://www.theses.fr/2019LYSEN082.

Full text

Abstract:

Depuis quelques années, de plus en plus d’études démontrent que la différenciation cellulaire est accompagnée d’une augmentation de la variabilité de l’expression des gènes. L’hypothèse de notre équipe est que cette variabilité influence en retour la différenciation. Pour tester cette hypothèse, nous avons identifié trois drogues chimiques (l’artémisinine,l’indométhacine et MB3) qui influencent à la fois cette variabilité, et le nombre de cellules différenciées dans une culture de progéniteurs érythocytaires aviaires. Cette thèse, divisée en deux parties, s’inscrit dans la continuité de ces observations. Dans un premier temps, nous définissons un modèle mathématique de la différenciation éythroïde aviaire in vitro, et nous le calibrons à l’aide de nos données expérimentales. Cette approche nous permet de quantifier l’effet des drogues sur la prolifération et la différenciation cellulaires. Puisque la comparaison de valeurs de paramètres entre les conditions traitées et non-traitées doit s’appuyer sur des estimations précises, une partie importante de notre travail porte sur l’identifiabilité de notre modèle. Nous démontrons dans cette partie que les drogues qui diminuent la variabilité de l’expression des gènes (l’artémisinine et l’indométhacine) diminuent aussi le taux de différenciation des cellules, et que la drogue qui augmente la variabilité (MB3) augmente aussi ce taux.Dans une second partie, nous observons que le résultat de l’expérience de différenciation in vitro qui nous sert à calibrer notre modèle est très variable. Nous essayons alors d’adapter notre modèle sous la forme d’un modèle à effets mixtes, dans lequel chaque réplicat de l’expérience est caractérisé par ses propres valeurs de paramètres. Les modèles à effets mixtes forment une classe de modèles statistiques dans laquelle les valeurs fixées des paramètres sont remplacées par des distributions de variables aléatoires, pour décrire la répétition d’une même mesure sur différents individus d’une population. Chaque individu est alors décrit par ses propres valeurs de paramètres, et la population est décrite par la distribution des valeurs de paramètres entre les individus. Nous démontrons que notre modèle à effets mixtes est non-identifiable et nous explorons ensuite différentes façon de le rendre identifiable, à travers une approche de design expérimental et une approche de réduction de modèle
During the past several years, several independent studies have shown that cell differentiation is accompanied by anincrease of the level of variability of gene expression. Hypothesizing that gene expression variability is a driver of celldifferentiation, our group has identified three chemical drugs (called artemisinin, indomethacin and MB3) whichinfluence both the extent of this variability and the number of differentiated cells in a culture of avian erythroidprogenitors.This thesis follows these observations, and is divided in two parts. First, we define a mathematical model ofavian in vitro erythroid differentiation and confront it to our experimental data, in order to disentangle the effect of thedrugs on cell proliferation, differentiation and death. Since the comparison of parameter values between the treated anduntreated conditions requires precise parameter estimates, an important part of the design of our model is theidentifiability of its parameters. We prove that the drugs which decrease gene expression variability (artemisinin andinndomethacin) also decrease the differentiation rate of the cells, and that the drug which increase variability (MB3)also increases the differentiation rate.Then, observing significant variability in the outcome of our in vitro differentiation experiment, we motivate thedesign of a mixed effect model of erythropoiesis, in which each replicate of the experiment is an individual characterizedby its own parameter values. Mixed effect models are a type of statistical models in which the fixed parameters arereplaced by distributions of random variables, in order to describe the repeated measurement of the same process ondifferent individuals from the same population. Each individual is then described by its own parameter values, and thepopulation is described by the distribution of parameter values across all individuals. We demonstrate the unidentifiabilityof this mixed effect model, and we finish by exploring ways of rendering it identifiable, using experimental design andmodel reduction

APA, Harvard, Vancouver, ISO, and other styles

22

Norris, Eleanor S. "Modelling the growth of avascular tumours and their response to chemotherapy." Thesis, University of Nottingham, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.246319.

Full text

APA, Harvard, Vancouver, ISO, and other styles

23

Goodes, L. R. "Observation and prediction of biocide release with fluorescence techniques and mathematical modelling." Thesis, University of Southampton, 2013. https://eprints.soton.ac.uk/360332/.

Full text

Abstract:

Antifouling coatings are crucial for protection of vessels’ hulls against marine biofouling. A range of technologies is available, although biocidal coatings - containing toxic or deterrent compounds – still represent a majority of the market. A long-term goal is the development of less environmentally harmful and persistent compounds; one of many potential avenues is that of synthetic analogues of natural products from marine organisms. The development of coatings using natural products has been hampered by poor performance in the field without sufficient work on their leach rates and behaviour. Furthermore, little work has been carried out on the leach rate of traditional organic biocides as used in modern coatings. Prediction of biocide diffusion is crucial to estimation of antifouling efficacy. However, diffusion in glassy polymers is a complex and oft-neglected topic; the chemically and physically changeable environment of the ocean and swelling of the polymer in such a ternary system also increase the complexity of models. A test matrix of antifouling paint coatings was composed, including polymethylmethacrylate (pMMA), an erodible rosin-based commercial binder and a novel trityl methacrylate/butylacrylate copolymer (pTrMA/BA) as binders. Copper (I) oxide and usnic acid, a natural product biocide of interest, were incorporated into the binders and the coatings were subjected to 10 months of natural immersion and 6 months of accelerated rotor immersion tests (17 knots, 25 °C). A novel application of fluorescence microscopy was developed, allowing quantification of the usnic acid content within the test coatings from both immersion schemes. This fluorescence technique and optical microscopy techniques were applied to these coatings before and after immersion, allowing quantification of the organic biocide and pigment distribution. Existing literature models for diffusion in glassy systems were adapted with a novel method for taking into account the presence of seawater as a diluent, to obtain effective diffusion coefficients for usnic acid. These have been integrated into mathematical models of diffusion to predict biocide lifetime. These data were compared with experimental data for biocide leaching from the long term immersions. The biocide leached completely from the p(TrMA/BA) binder during rotor testing, compared to 35% from the pMMA binder. For pontoon immersions, 61% of the additive was lost from the pMMA coating, and 53% from the rosin-based binder. An accelerated loss of usnic acid occurred in the surface of the rosin-based binder, due to rosin depletion. In all samples, release of the biocide was inhibited beyond the cuprous oxide front, which was congruent with the leached layer in samples where cuprous oxide release occurred. The erodible binder was the only one which demonstrated synchronous depletion of both additives, and it demonstrated a good resistance to fouling in immersion trials. Results of the mathematical modelling of the biocide diffusion were in good agreement with the observed data in the case of pMMA, highlighting in particular the importance of water uptake with respect to biocide diffusion. However, there was poor agreement in the case of p(TrMA/BA), for which the model under-predicted the release rate by about three orders of magnitude.

APA, Harvard, Vancouver, ISO, and other styles

24

Martins, Bruno Miguel Cardoso. "Mathematical modelling of signal sensing and transduction : revisiting classical mechanisms." Thesis, University of Edinburgh, 2013. http://hdl.handle.net/1842/17969.

Full text

Abstract:

The ability of cells to react to changes in their environment is critical to their survival. Effective decision making strategies leading to the activation of specific intracellular pathways hinge on cells sensing and processing extracellular variation. We will only be able to understand and manipulate how cells make decisions if we understand the “design” of the mechanisms that enable them to make such decisions, in terms of how they function, and in terms of their limitations and architecture. In this thesis, using mathematical modelling, I revisited classical signal sensing and transduction mechanisms in light of recent developments in methodological approaches and data collection. I studied the sensing characteristics of one of the simplest of sensors, the allosteric sensor, to understand the limits and effectiveness of its “design”. Using the classical Monod-Wyman-Changeux model of allostery, I defined and evaluated six engineering-inspired characteristics as a function of the parameters and number of sensors. I found that specifying one characteristic strongly constrains others and I determined the trade-offs that follow from these constraints. I also calculated the probability distribution of the number of input molecules that maximizes information transfer and, as a consequence, the number of environmental states a given population of sensors can discriminate between. Next, I proposed a new general model of phosphorylation cycles that can account for experimental reports of ultrasensitivity occurring in regimes that are far away from Goldbeter and Koshland’s zero-order saturation, the classical ultrasensitivity-generating mechanism. The new model exhibits robust ultrasensitivity in “anti-zero-order” regimes. The degree of ultrasensitivity, its limits, and its dependence on the parameters of the system are analytically tractable. The model can, additionally, explain in an intuitive way some puzzling experimental observations. Finally, I addressed the problem of integrating different types of signals from multiple sources, and performed some preliminary exploration of how cells can “learn” to associate and dissociate correlated signals in non-evolutionary time-scales. This work provides insights into the function and robustness of signal sensing and transduction mechanisms and as such is applicable to both the study of endogenous systems and the design of synthetic ones.

APA, Harvard, Vancouver, ISO, and other styles

25

Bowden, Lucie Grace. "Mathematical approaches to modelling healing of full thickness circular skin wounds." Thesis, University of Oxford, 2015. http://ora.ox.ac.uk/objects/uuid:f28f39d3-923d-45ac-8faf-2750d8e8f96e.

Full text

Abstract:

Wound healing is a complex process, in which a sequence of interrelated events at both the cell and tissue levels interact and contribute to the reduction in wound size. For diabetic patients, many of these processes are compromised, so that wound healing slows down and in some cases halts. In this thesis we develop a series of increasingly detailed mathematical models to describe and investigate healing of full thickness skin wounds. We begin by developing a time-dependent ordinary differential equation model. This phenomenological model focusses on the main processes contributing to closure of a full thickness wound: proliferation in the epidermis and growth and contraction in the dermis. Model simulations suggest that the relative contributions of growth and contraction to healing of the dermis are altered in diabetic wounds. We investigate further the balance between growth and contraction by developing a more detailed, spatially-resolved model using continuum mechanics. Due to the initial large retraction of the wound edge upon injury, we adopt a non-linear elastic framework. Morphoelasticity theory is applied, with the total deformation of the material decomposed into an addition of mass and an elastic response. We use the model to investigate how interactions between growth and stress influence dermal wound healing. The model reveals that contraction alone generates unrealistically high tension in the dermal tissue and, hence, volumetric growth must contribute to healing. We show that, in the simplified case of homogeneous growth, the tissue must grow anisotropically in order to reduce the size of the wound and we postulate mechanosensitive growth laws consistent with this result. After closure the surrounding tissue remodels, returning to its residually stressed state. We identify the steady state growth profile associated with this remodelled state. The model is used to predict the outcome of rewounding experiments as a method of quantifying the amount of stress in the tissue and the application of pressure treatments to control tissue synthesis. The thesis concludes with an extension to the spatially-resolved mechanical model to account for the effects of the biochemical environment. Partial differential equations describing the dynamics of fibroblasts and a regulating growth factor are coupled to equations for the tissue mechanics, described in the morphoelastic framework. By accounting for biomechanical and biochemical stimuli the model allows us to formulate mechanistic laws for growth and contraction. We explore how disruption of mechanical and chemical feedback can lead to abnormal wound healing and use the model to identify specific treatments for normalising healing in these cases.

APA, Harvard, Vancouver, ISO, and other styles

26

Gilbert, Mark. "Modelling species invasions in heterogeneous landscapes." Thesis, University of Oxford, 2016. https://ora.ox.ac.uk/objects/uuid:944d15d3-257a-47e5-acb9-9bdfba26985b.

Full text

Abstract:

Biological invasions are devastating ecosystems and economies world-wide, while many native species' survival depends on their ability to track climate change. Characterising the spread of biological populations is therefore of utmost importance, and can be studied with spatially explicit, discrete-time integro-difference equations (IDEs), which reflect numerous species' processes of demography and dispersal. While spatial variation has often been ignored when implementing IDE models, real landscapes are rarely spatially uniform and environmental variation is crucial in determining biological spread. To address this, we use novel methods to characterise population spread in heterogeneous landscapes. Asymptotic analysis is used for highly fragmented landscapes, where habitat patches are isolated and smaller than the dispersal scale, and in landscapes with low environmental variation, where the ecological parameters vary by no more than a small factor from their mean values. We find that the choice of dispersal kernel determines the effect of landscape structure on spreading speed, indicating that accurately fitting a kernel to data is important in accurately predicting speed. For the low-variation case, the spreading speeds in the heterogeneous and homogeneous landscapes differ by ϵ², where ϵ governs the degree of variation, suggesting that in many cases, a simpler homogeneous model gives similar spread rates. For irregular landscapes, analytical methods become intractable and numerical simulation is needed to predict spread. Accurate simulation requires high spatial resolution, which, using existing techniques, requires prohibitive amounts of computational resources (RAM, CPU etc). We overcome this by developing and implementing a novel algorithm that uses adaptive mesh refinement. The approximations and simulation algorithm produce accurate results, with the adaptive algorithm providing large improvements in efficiency without significant losses of accuracy compared to non-adaptive simulations. Hence, the adaptive algorithm enables faster simulation at previously unfeasible scales and resolutions, permitting novel areas of scientific research in species spread modelling.

APA, Harvard, Vancouver, ISO, and other styles

27

Rosser, Gabriel A. "Mathematical modelling and analysis of aspects of bacterial motility." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:1af98367-aa2f-4af3-9344-8c361311b553.

Full text

Abstract:

The motile behaviour of bacteria underlies many important aspects of their actions, including pathogenicity, foraging efficiency, and ability to form biofilms. In this thesis, we apply mathematical modelling and analysis to various aspects of the planktonic motility of flagellated bacteria, guided by experimental observations. We use data obtained by tracking free-swimming Rhodobacter sphaeroides under a microscope, taking advantage of the availability of a large dataset acquired using a recently developed, high-throughput protocol. A novel analysis method using a hidden Markov model for the identification of reorientation phases in the tracks is described. This is assessed and compared with an established method using a computational simulation study, which shows that the new method has a reduced error rate and less systematic bias. We proceed to apply the novel analysis method to experimental tracks, demonstrating that we are able to successfully identify reorientations and record the angle changes of each reorientation phase. The analysis pipeline developed here is an important proof of concept, demonstrating a rapid and cost-effective protocol for the investigation of myriad aspects of the motility of microorganisms. In addition, we use mathematical modelling and computational simulations to investigate the effect that the microscope sampling rate has on the observed tracking data. This is an important, but often overlooked aspect of experimental design, which affects the observed data in a complex manner. Finally, we examine the role of rotational diffusion in bacterial motility, testing various models against the analysed data. This provides strong evidence that R. sphaeroides undergoes some form of active reorientation, in contrast to the mainstream belief that the process is passive.

APA, Harvard, Vancouver, ISO, and other styles

28

Bentil, Daniel Ekow. "Aspects of dynamic pattern generation in embryology and epidemiology." Thesis, University of Oxford, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.276528.

Full text

APA, Harvard, Vancouver, ISO, and other styles

29

Connor, Anthony J. "In silico modelling of tumour-induced angiogenesis." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:f6b6c496-3adb-43c4-a3b3-aaf4d1b866b4.

Full text

Abstract:

Angiogenesis, the process by which new vessels form from existing ones, is a key event in the development of a large and malignant vascularised tumour. A rapid expansion in in vivo and in vitro angiogenesis research in recent years has led to increased knowledge about the processes underlying angiogenesis and to promising steps forward in the development of anti-angiogenic therapies for the treatment of various cancers. However, substantial gaps in knowledge persist and the development of effective treatments remains a major challenge. In this thesis we study tumour-induced angiogenesis within the context of a highly controllable experimental environment: the cornea micropocket assay. Using a multidisciplinary approach that combines experiments, image processing and analysis, and mathematical and computational modelling, we aim to provide mechanistic insight into the action of two angiogenic factors which are known to play central roles during tumour-induced angiogenesis: vascular endothelial growth factor A (VEGF-A) and basic fibroblast growth factor (bFGF). Image analysis techniques are used to extract quantitative data, which are both spatially and temporally resolved, from experimental images. These data are then used to develop and parametrise mathematical models describing the evolution of the corneal vasculature in response to both VEGF-A and bFGF. The first models developed in this thesis are one-dimensional continuum models of angiogenesis in which VEGF-A and/or bFGF are released from a pellet implanted into a mouse cornea. We also use an object-oriented framework, designed to facilitate the re-use and extensibility of hybrid multiscale models of angiogenesis and vascular tumour growth, to develop a complementary three-dimensional hybrid model of the same system. The hybrid model incorporates a new non-local cell sensing model which facilitates the formation of well-perfused and functional vascular networks in three dimensions. The continuum models are used to assess the utility of the cornea micropocket assay as a quantitative assay for angiogenesis, to characterise proposed synergies between VEGF-A and bFGF, and to generate experimentally testable predictions regarding the effect of anti-VEGF-A therapies on bFGF-induced angiogenesis. Meanwhile, the hybrid model is used to provide context for the comparison that is drawn between the continuum models and the data, to study the relative distributions of perfused and unperfused vessels in the evolving neovasculature, and to investigate the impact of tip cell sensing dysregulation on the angiogenic response in the cornea. We have found that by exploiting a close link with quantitative data we have been able to extend the predictive and hypothesis-testing capabilities of our models. As such, this thesis demonstrates the potential for integrating mathematical modelling with image analysis techniques to increase insight into the mechanisms underlying angiogenesis.

APA, Harvard, Vancouver, ISO, and other styles

30

Li, Liren. "Modelling of calcium handling in genetically modified mice." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:fa351516-9b3c-43c0-8bdc-5b0317cd5967.

Full text

Abstract:

This thesis develops biophysically-based data-driven mathematical models of intracellular calciumdynamics in ventricularmyocytes for both normal and genetically modified mouse hearts, based on species- and temperature-consistent experimental data. The models were subsequently applied to quantitatively examine the changes in calcium dynamics in mice with cardiomyocyte-specific knockout (KO) of the cardiac sarco/endoplasmic reticulum ATPase (SERCA2) gene, to determine the contributing mechanisms which underlie the ultimate development of heart failure in these animals. In Chapter 1, with emphasis on calcium dynamics and calcium regulation in heart failure, an overview of cardiac electrophysiology, excitation-contraction coupling and mathematical models of cardiac electrophysiology is provided. In Chapter 2, models of calcium dynamics in the ventricular myocytes from the C57BL/6 mouse heart at a physiological temperature is developed and validated based on species- and temperature-consistent measurements. In Chapter 3, the C57BL/6 model framework is re-parameterised to experimental data from the control and SERCA2 KO mice at 4 weeks after gene deletion. The models are then used to quantitatively characterise changes in calcium dynamics in the KO animals and the role of the compensatory mechanisms. In Chapter 4, the model framework is extended to include differential distributions of ion channels in the sarcolemma and the calcium dynamics in the sub-sarcolemmal space, with parameters in these sub-components fitted to experimentally measured calcium dynamics from the control and KO cardiomyocytes at 7-week after gene deletion. Finally in Chapter 5, conclusions are drawn, the limitations of this study are discussed, and the future extensions to this study are described.

APA, Harvard, Vancouver, ISO, and other styles

31

Johnston, Matthew David. "Mathematical modelling of cell population dynamics in the colonic crypt with application to colorectal cancer." Thesis, University of Oxford, 2008. http://ora.ox.ac.uk/objects/uuid:eb1daf53-203c-4ed5-a8af-ab261a61a88c.

Full text

Abstract:

Colorectal cancer has the third highest mortality and incidence rates of all cancers worldwide, but the prognosis for long-term survival is good if diagnosed early. It is a well-characterised disease, and is initiated in colonic crypts which line the colon wall. The aim of this thesis is to use mathematical modelling to describe the heavily regulated cell renewal cycle in the crypt to determine the key features of the system kinetics, and help to explain the initiation of tumourigenesis. The dynamics of a single colorectal crypt is considered using a compartmental approach, which accounts for populations of stem, transit-amplifying and fullydifferentiated cells. A number of different model formulations are derived, and their validity and suitability are discussed. Two mechanisms are presented that could regulate the growth of cell numbers and maintain homeostasis (equilibrium), and it is illustrated how a model can describe both regulated and unregulated growth, with cancer-driving cells deriving from stem and/or transit cells. This model is used to explain the long lag phases observed in carcinogenesis, which occur between periods of rapid tumour expansion, before unlimited growth in cell numbers ensues. Significantly, it is found that, contrary to general belief, the proportion of cancer-driving cells in the exponential growth phase of a tumour may vary depending on tumour type. The process of cells accumulating mutations is also examined by considering both a stochastic individual cell-based model and an analytic approach. Finally, an ordinary differential equation model is shown to be valid by considering a simplified description of a one-dimensional spatial model, and the latter is used to consider the effect of changing the crypt shape. The suitability of this modelling approach to tracking stem cells in a niche, as well as mutant cell clones as they propagate in the crypt, is also discussed.

APA, Harvard, Vancouver, ISO, and other styles

32

Koivumäki, J. (Jussi). "Regulation of excitation-contraction coupling in cardiac myocytes:insights from mathematical modelling." Doctoral thesis, University of Oulu, 2009. http://urn.fi/urn:isbn:9789514293047.

Full text

Abstract:

Abstract Background – The heart cell is a prime example of a system, in which numerous interconnected regulatory mechanisms affect the dynamic balance of cellular function. The function of the system emerges from the interactions of its components rather than from their individual properties. Thus, it is a challenging task to understand the causal relations within such a system, based on the analysis of experimental results. Facing this complexity, the systems biological approach has gained interest during recent years, since with using it we can make an effort to observe, quantitatively and simultaneously, multiple components and their interdependencies in biological networks. Methods and aims – One of the most important tools in systems biology is mathematical modelling. In this thesis, novel model components have been developed and existing components integrated to describe mathematically the calcium dynamics in cardiac myocytes with improved physiological accuracy. Special attention was paid to both the activity-dependent and automatic regulation of the dynamics. This enabled the quantitative analysis of the regulation’s role in both physiological and pathophysiological conditions. Results – Validation of the novel model components that describe the calcium transport mechanisms indicates that the developed schemes are accurate and applicable also beyond the normal physiological state of the cardiac myocyte. Results also highlight the importance of autoregulation of calcium dynamics in the excitation-contraction coupling. Furthermore, the analysis indicates that the CaMK-dependent regulation of the calcium uptake to and release from the sarcoplasmic reticulum calcium stores could have substantial roles as downstream effectors in beta-adrenergic stimulation. Conclusions – Results emphasize mathematical modelling as a valuable complement to experiments in understanding causal relations within complex biological systems such as the cardiac myocytes. That is, rigorous data integration with mathematical models can provide significant insight to the quantitative role of both the individual model components and the interconnected regulatory loops. This is especially true for the analysis of genetically engineered animal models, in which the intended modification is always accompanied by compensatory changes that can mask to a varying degree the actual phenomenon of interest.

APA, Harvard, Vancouver, ISO, and other styles

33

Moxon, Thomas Edward. "Mathematical modelling of gastric emptying and nutrient absorption in the human digestive system." Thesis, University of Birmingham, 2017. http://etheses.bham.ac.uk//id/eprint/7857/.

Full text

Abstract:

Mathematical modelling of the digestive system can be achieved by assuming the digestive system is described as a series of ideal reactors. A well formulated model could give an understanding of how food products behave within the body, and offer some predictive possibility allowing the design of functional foods to have tailored nutritional responses. The models developed showed good estimates of the gastric emptying rates and glucose absorption rates for solutions with different viscosities and glucose concentrations, when a feedback mechanism is included. Implementing a population balance for solid breakdown in the stomach allowed for parameters to be linked to meal type. With parameter estimates from experimental gastric emptying of a solid meal being further validated against results for the same food type from different experimental results. The main outcomes of this work are (i) the inclusion of meals viscosity into models, and its effects on the gastric secretion and emptying rate as well as the mass transfer of nutrients in the intestinal lumen, (ii) the inclusion of a feedback mechanism on the rate of gastric emptying, and (iii) the development of a population balance to model solid breakdown within the stomach.

APA, Harvard, Vancouver, ISO, and other styles

34

Smith, Robert William. "Mathematical modelling of photoperiodic external coincidence mechanisms in the model plant, Arabidopsis thaliana." Thesis, University of Edinburgh, 2014. http://hdl.handle.net/1842/11734.

Full text

Abstract:

As plants are sessile organisms, processes controlling plant growth and development must react to fluctuations in the external environment to aid plant survival. However, as the climate of the Earth changes and becomes more extreme, plants become less able to develop to their optimal capacity and this can have an adverse effect on crop yield and biofuel feedstock production. Thus, it is becoming increasingly important to understand the molecular mechanisms used by plants to respond to external stimuli. One important system that plants utilise in their response to environmental fluctuations is the circadian clock. The circadian clock is a time-measuring device that buffers the timing of plant growth and development against fluctuations in the local environment, such as temperature, light quality and light intensity. Importantly, the circadian clock is also able to measure day-length (photoperiod). Thus, plant development and growth is co-ordinated with photoperiod that is closely linked to seasonal changes. A key example of this is the time taken for a plant to flower. Flowering of Arabidopsis thaliana occurs specifically in long-days (LDs) of spring/summer months. Thus, the circadian clock is a key regulator promoting flowering in LD conditions. In conjunction with experimental studies, mathematical modelling has proven to be a successful method of elucidating the mechanisms that underlie complex biological systems. One example of this 'systems biology' approach is in uncovering the components that make up the Arabidopsis circadian clock mechanism. Previous research in our group has also led to the development of a model describing photoperiodic flowering that is tentatively linked to the circadian clock mechanism. In this thesis I shall develop on these models to highlight five key results: 1. using rhythmic PHYTOCHROME INTERACTING FACTOR 4 (PIF4) and PIF5 mRNA as an example, I shall show that multiple circadian regulators are required to describe rhythmic transcription of target genes across multiple photoperiods; 2. the stabilisation of CONSTANS (CO) protein by the blue light-signalling component FLAVIN-BINDING, KELCH REPEAT, F-BOX 1 (FKF1) is required to for flowering in LDs and has a relatively larger impact on photoperiodic flowering than FKF1-dependent degradation of CYCLING DOF FACTOR 1 (CDF1), an inhibitor of flowering; 3. multiple components of the circadian clock play specific post-translational roles in photoperiodic flowering to promote the acceleration of flowering specifically in LDs; 4. temperature regulation of photoperiodic flowering can be explained through an interaction between CO and PIF proteins, limiting the effects of temperature to a specific time-window in a 24-hour day; 5. red light- and temperature-control of the circadian clock can be explained by altering the post-translational regulation of circadian clock components.

APA, Harvard, Vancouver, ISO, and other styles

35

Batenchuk, Cory. "Development of a Mathematical Model to Understand, Design & Improve Oncolytic Virus Therapies." Thesis, Université d'Ottawa / University of Ottawa, 2014. http://hdl.handle.net/10393/31182.

Full text

Abstract:

Oncolytic viruses (OVs) are emerging as a potent therapeutic platform for the treatment of malignant disease. The tumor cells inability to induce antiviral defences in response to a small cytokine known as interferon (IFN) is a common defect exploited by OVs. Heterogeneity in IFN signalling across tumors is therefore a pillar element of resistance to these therapies. I have generated a mathematical model and simulation platform to study the impact of IFN on OV dynamics in normal and cancerous tissues. In the first part of my thesis, I used this model to identify novel OV engineering strategies which could be implemented to overcome IFN based resistance in tumor tissues. From these simulations, it appears that a positive feedback loop, established by virus-mediated expression of an interferon-binding decoy receptor, could increase tumor cytotoxicity without compromising normal cells. The predictions set forth by this model have been validated both qualitatively and quantitatively in in-vitro and in-vivo models using two independent OV strains. This model has subsequently been used to investigate OV attenuation mechanisms, the impact of tumor cell heterogeneity, as well as drug-OV interactions. Following these results, it became apparent that selectivity should equally be observed when overwhelming the cell with a non replicating virus. While normal tissues will clear this pseudo-infection rapidly, owing to their high baseline in antiviral products at the onset of infection, tumor cells with defective anti-viral pathways should not have readily available biomachinery required to degrade this pro-apoptotic signal. Recapitulated by the mathematical model, non-replicating virus-derived particles generated by means of UV irradiation selectively kill tumor cells in cultured cell lines and patient samples, leading to long term cures in murine models. Taken together, this thesis uses a novel mathematical model and simulation platform to understand, design & improve oncolytic virus-based therapeutics.

APA, Harvard, Vancouver, ISO, and other styles

36

Leonard, Katherine H. L. "Mathematical and computational modelling of tissue engineered bone in a hydrostatic bioreactor." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:05845740-1a74-4e19-95ea-6b5229d1af27.

Full text

Abstract:

In vitro tissue engineering is a method for developing living and functional tissues external to the body, often within a device called a bioreactor to control the chemical and mechanical environment. However, the quality of bone tissue engineered products is currently inadequate for clinical use as the implant cannot bear weight. In an effort to improve the quality of the construct, hydrostatic pressure, the pressure in a fluid at equilibrium that is required to balance the force exerted by the weight of the fluid above, has been investigated as a mechanical stimulus for promoting extracellular matrix deposition and mineralisation within bone tissue. Thus far, little research has been performed into understanding the response of bone tissue cells to mechanical stimulation. In this thesis we investigate an in vitro bone tissue engineering experimental setup, whereby human mesenchymal stem cells are seeded within a collagen gel and cultured in a hydrostatic pressure bioreactor. In collaboration with experimentalists a suite of mathematical models of increasing complexity is developed and appropriate numerical methods are used to simulate these models. Each of the models investigates different aspects of the experimental setup, from focusing on global quantities of interest through to investigating their detailed local spatial distribution. The aim of this work is to increase understanding of the underlying physical processes which drive the growth and development of the construct, and identify which factors contribute to the highly heterogeneous spatial distribution of the mineralised extracellular matrix seen experimentally. The first model considered is a purely temporal model, where the evolution of cells, solid substrate, which accounts for the initial collagen scaffold and deposited extracellular matrix along with attendant mineralisation, and fluid in response to the applied pressure are examined. We demonstrate that including the history of the mechanical loading of cells is important in determining the quantity of deposited substrate. The second and third models extend this non-spatial model, and examine biochemically and biomechanically-induced spatial patterning separately. The first of these spatial models demonstrates that nutrient diffusion along with nutrient-dependent mass transfer terms qualitatively reproduces the heterogeneous spatial effects seen experimentally. The second multiphase model is used to investigate whether the magnitude of the shear stresses generated by fluid flow, can qualitatively explain the heterogeneous mineralisation seen in the experiments. Numerical simulations reveal that the spatial distribution of the fluid shear stress magnitude is highly heterogeneous, which could be related to the spatial heterogeneity in the mineralisation seen experimentally.

APA, Harvard, Vancouver, ISO, and other styles

37

Dyson, Louise. "Mathematical models of cranial neural crest cell migration." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:66955fb9-691f-4d27-ad26-39bb2b089c64.

Full text

Abstract:

From the developing embryo to the evacuation of football stadiums, the migration and movement of populations of individuals is a vital part of human life. Such movement often occurs in crowded conditions, where the space occupied by each individual impacts on the freedom of others. This thesis aims to analyse and understand the effects of occupied volume (volume exclusion) on the movement of the individual and the population. We consider, as a motivating system, the rearrangement of individuals required to turn a clump of cells into a functioning embryo. Specifically, we consider the migration of cranial neural crest cells in the developing chick embryo. Working closely with experimental collaborators we construct a hybrid model of the system, consisting of a continuum chemoattractant and individual-based cell description and find that multiple cell phenotypes are required for successful migration. In the crowded environment of the migratory system, volume exclusion is highly important and significantly enhances the speed of cell migration in our model, whilst reducing the numbers of individuals that can enter the domain. The developed model is used to make experimental predictions, that are tested in vivo, using cycles of modelling and experimental work to give greater insight into the biological system. Our formulated model is computational, and is thus difficult to analyse whilst considering different parameter regimes. The second part of the thesis is driven by the wish to systematically analyse our model. As such, it concentrates on developing new techniques to derive continuum equations from diffusive and chemotactic individual-based and hybrid models in one and two spatial dimensions with the incorporation of volume exclusion. We demonstrate the accuracy of our techniques under different parameter regimes and using different mechanisms of movement. In particular, we show that our derived continuum equations almost always compare better to data averaged over multiple simulations than the equivalent equations without volume exclusion. Thus we establish that volume exclusion has a substantial effect on the evolution of a migrating population.

APA, Harvard, Vancouver, ISO, and other styles

38

Maddison, Louise. "Experimental and theoretical modelling of the MAPK pathway." Thesis, University of Manchester, 2012. https://www.research.manchester.ac.uk/portal/en/theses/experimental-and-theoretical-modelling-of-the-mapk-pathway(46773da5-85dd-4a3f-8e6c-e3559ba04f46).html.

Full text

Abstract:

The MAPK pathway plays a crucial role in regulating cellular response to external stimuli. Binding of growth factors and other mitogenic signals to cell surface receptors initiates a phosphorylation-dependent relay of protein activation, resulting in altered transcription, ultimately regulating cell proliferation and differentiation. Signalling through this pathway is regulated by the coordinated function of specific protein kinases and protein phosphatases. As perturbation of this signalling system is often associated with diseases such as cancer, modelling is a useful means to help understand the outcomes that may result following changes in component levels or activity. The determination of absolute quantification data, in copies per cell, for proteins of the MAPK pathway will allow the expansion of and improved accuracy within predictive models. The strategy used within this thesis is based on the established technique of stable isotope dilution, generating isotopically labelled peptides using the QconCAT methodology. Recombinant DNA techniques were used to generate artificial concatamers of large numbers of tryptic peptides as quantification standards. A QconCAT, LM1, of 49 KDa (29 tryptic peptides), corresponding to the scaffold proteins was designed and built to encode two peptides per protein. A second QconCAT, LM2, of 58 KDa (34 tryptic peptides), encoded peptides from the dual-specificity phosphatases (DUSPs) and substrates. Quantification was performed using ultra performance liquid chromatography coupled to mass spectrometry. A selected reaction monitoring (SRM) approach was employed where the most intense y-ions per peptide were selected either from experimental data or predictions in silico. Using the ratio of the signal for the light:heavy isotopologues, the amount of light isotopologue can be inferred, allowing copies per cell quantifications to be established. Native peptides were present below the lower limit of quantification, and therefore the upper bounds of copies per cell were obtained for the three cell lines; colon cancer cells HCT 116 (K-Ras mutant) and HT-29 (B-Raf mutant) and a control cell line of HEK-293. Finally, mathematical modelling was undertaken to explore the mass-action kinetics of a three component scaffold signalling molecule. It was found that the optimal scaffold concentration is between the lowest and second lowest concentration of signalling protein.

APA, Harvard, Vancouver, ISO, and other styles

39

González, Flo Eva 1993. "Engineering living biomedical devices : Mathematical and experimental tools for the rational design of cellular devices." Doctoral thesis, TDX (Tesis Doctorals en Xarxa), 2020. http://hdl.handle.net/10803/670358.

Full text

Abstract:

The engineering of biology strives on the creation of biological devices concerning society-impact applications. In this PhD thesis, we developed mathematical and experimental tools for the standard and rational design of living devices for biomedical purposes, offering robust and reliable responses. By breaking-up cellular device complexity into functional modules, we have analysed how extracellular information is detected, processed and transformed thanks to re-engineering intrinsic cellular components. We show how the desired range of action of a biosensor could be tuned by modifying the relative levels from two-component receptors’ biosensors. Regarding information processing, combining multicellularity and space permits to develop a 2D multi-branch approach inspired from printed electronics, allowing to perform logic computation by transferring device complexity into the geometrical arrangement. Sensing and processing capabilities have been applied as a proof-of-concept for the design of cellular devices for Diabetes Mellitus. Treating the cellular device closed-loop response as the fourth-functional module allowed to in silico decipher device characteristics on glycaemia regulation and design novel strategies based on dietary modulation, putting the manifest the need to combine both experimental and computational tools for living device application-based designs.
L’aplicació de principis d’enginyeria en biologia permet somniar en l’ús de dispositius biològics per abordar problemes de la societat. Concretament, en aquesta tesi doctoral, s’ha abordat el disseny de dispositius biològics per aplicacions biomèdiques mitjançant la combinació d’eines experimentals i computacionals. La creació d’aquests dispositius demana d’un disseny racional que ofereixi respostes robustes i fiables. L’estudi de la creació de dispositius biològics s’ha fet seguint una aproximació modular, on s’ha analitzat com es poden re-enginyeritzar components cel·lulars per obtenir una resposta que s’adeqüi a l’aplicació requerida. Hem demostrat com podem modular el rang de detecció de la capa sensora a través de la modulació de l’element receptor de sensors bastats en dos components. Hem analitzat com integrar informació de diferents fonts de manera sistemàtica i robusta introduint com a nou element de computació l’espai i la divisió de tasques; tot desenvolupant un marc teòric i validant experimentalment per un seguit de funcions lògiques. Finalment, hem desenvolupat dispositius biològics que responen a molècules fisiològiques. Concretament, hem abordat el disseny de dispositius biològics pel tractament de la Diabetes Mellitus. Una primera validació experimental ens ha permès establir l’ús d’aquests dispositius in vitro. Seguidament, hem aprofundit en l’estudi de la seva aplicació mitjançant l’ús d’un simulador de pacient diabètic que ens ha permès el seu tractament virtual i l’anàlisi de les característiques del dispositiu per la regulació de la glicèmia. Finalment, hem explorat com la combinació dels dispositius cel·lulars amb la regulació del patró d’ingestes introdueix millores en els nivells de glucosa en sang. Posant de manifest el potencial que ofereix la creació d’una plataforma hibrida pel disseny de dispositius cel·lulars per una determinada aplicació.

APA, Harvard, Vancouver, ISO, and other styles

40

Mohd, Jaffar Mai. "Mathematical models of hyphal tip growth." Thesis, University of Dundee, 2012. https://discovery.dundee.ac.uk/en/studentTheses/140f9a81-12ca-4337-a311-2f82441f1ea6.

Full text

Abstract:

Filamentous fungi are important in an enormous variety of ways to our life, with examples ranging from bioremediation, through the food and drinks industry to human health. These organisms can form huge networks stretching metres and even kilometres. However, their mode of growth is by the extension of individual hyphal tips only a few microns in diameter. Tip growth is mediated by the incorporation of new wall building materials at the soft apex. Just how this process is controlled (in fungi and in cell elongation in other organisms) has been the subject of intense study over many years and has attracted considerable attention from mathematical modellers. In this thesis, we consider mathematical models of fungal tip growth that can be classified as either geometrical or biomechanical. In every model we examine, a 2-D axisymmetric semihemisphere-like curve represents half the medial section of fungal tip geometry. A geometrical model for the role of the Spitzenkorper in the tip growth was proposed by Bartnicki-Garcia et al (1989), where a number of problems with the mathematical derivation were pointed out by Koch (2001). A suggestion is given as an attempt to revise the derivation by introducing a relationship between arc length of a growing tip, deposition of wall-building materials and tip curvature. We also consider two types of geometrical models as proposed by Goriely et al (2005). The first type considers a relationship between the longitudinal curvature and the function used to model deposition of wall-building materials. For these types of models, a generalized formulae for the tip shape is introduced, which allows localization of deposition of wall-building materials to be examined. The second type considers a relationship between longitudinal and latitudinal curvatures and the function used to model deposition of wall-building materials. For these types of models, a new formulation of the function used to model deposition of wall-building materials is introduced. Finally, a biomechanical model as proposed by Goriely et al (2010). Varying arc length of the stretchable region on the tip suggests differences in geometry of tip shape and the effective pressure profile. The hypothesis of orthogonal growth is done by focusing only on the apex of a "germ tube". Following that, it suggests that material points on the tip appear to move in a direction perpendicular to the tip either when surface friction is increased or decreased.

APA, Harvard, Vancouver, ISO, and other styles

41

Gill, Mandeep Singh. "Application of software engineering methodologies to the development of mathematical biological models." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:35178f3a-7951-4f1c-aeab-390cdd622b05.

Full text

Abstract:

Mathematical models have been used to capture the behaviour of biological systems, from low-level biochemical reactions to multi-scale whole-organ models. Models are typically based on experimentally-derived data, attempting to reproduce the observed behaviour through mathematical constructs, e.g. using Ordinary Differential Equations (ODEs) for spatially-homogeneous systems. These models are developed and published as mathematical equations, yet are of such complexity that they necessitate computational simulation. This computational model development is often performed in an ad hoc fashion by modellers who lack extensive software engineering experience, resulting in brittle, inefficient model code that is hard to extend and reuse. Several Domain Specific Languages (DSLs) exist to aid capturing such biological models, including CellML and SBML; however these DSLs are designed to facilitate model curation rather than simplify model development. We present research into the application of techniques from software engineering to this domain; starting with the design, development and implementation of a DSL, termed Ode, to aid the creation of ODE-based biological models. This introduces features beneficial to model development, such as model verification and reproducible results. We compare and contrast model development to large-scale software development, focussing on extensibility and reuse. This work results in a module system that enables the independent construction and combination of model components. We further investigate the use of software engineering processes and patterns to develop complex modular cardiac models. Model simulation is increasingly computationally demanding, thus models are often created in complex low-level languages such as C/C++. We introduce a highly-efficient, optimising native-code compiler for Ode that generates custom, model-specific simulation code and allows use of our structured modelling features without degrading performance. Finally, in certain contexts the stochastic nature of biological systems becomes relevant. We introduce stochastic constructs to the Ode DSL that enable models to use Stochastic Differential Equations (SDEs), the Stochastic Simulation Algorithm (SSA), and hybrid methods. These use our native-code implementation and demonstrate highly-efficient stochastic simulation, beneficial as stochastic simulation is highly computationally intensive. We introduce a further DSL to model ion channels declaratively, demonstrating the benefits of DSLs in the biological domain. This thesis demonstrates the application of software engineering methodologies, and in particular DSLs, to facilitate the development of both deterministic and stochastic biological models. We demonstrate their benefits with several features that enable the construction of large-scale, reusable and extensible models. This is accomplished whilst providing efficient simulation, creating new opportunities for biological model development, investigation and experimentation.

APA, Harvard, Vancouver, ISO, and other styles

42

Blount, Kathryn. "Cancer systems biology : is the devil in the glycolytic detail?" Thesis, University of Manchester, 2014. https://www.research.manchester.ac.uk/portal/en/theses/cancer-systems-biology-is-the-devil-in-the-glycolytic-detail(e0ad0c6b-76ec-4bba-8dd3-b583910f46f4).html.

Full text

Abstract:

An approach to investigating cancer that has recently seen resurgence of interest is the “Warburg effect”. Otto Warburg originally described the altered metabolism of cancer cells and identified that they exhibit an increase in glucose uptake and lactate production. This up-regulation of glycolytic flux and glucose transport is now associated with 90% of cancers. In order to improve the overall understanding of the “Warburg effect” two forms of systems biology have been implemented - comparative in vitro analysis of kinetic activities and dynamic modelling. In this analysis, human breast cancer cell lines MCF-7, MDA-MB-231 and T47D and a non transformed breast cell line MCF-10A were used to identify key similarities and differences in kinetic activities across the glycolytic pathway. Additionally, activities of key glycolytic enzymes hexokinase, pyruvate kinase and lactate dehydrogenase were compared under hypoxic conditions to further understand regulation of cancer cells. The most prominent feature that arose from comparing the kinetic activities of the three malignant and one non-malignant cell line is that each cell line has its own specific set of activities for glycolysis. This indicates that there are differences in regulation across the glycolytic pathway for each of these cell lines. This is of specific interest in the search for therapeutic targets. Further, we determined that despite the prominence of oncogenic HIF signalling activities of hexokinase, pyruvate kinase and lactate dehydrogenase were further modulated by growth under hypoxic conditions. Despite the lack of obvious distinct kinetic differences between the non-cancerous and cancerous cells lines some discernible differences are apparent when modelled in silico.

APA, Harvard, Vancouver, ISO, and other styles

43

Nguyen, Lan K. "Dynamical modelling of feedback gene regulatory networks." Diss., Lincoln University, 2009. http://hdl.handle.net/10182/1340.

Full text

Abstract:

Living cells are made up of networks of interacting genes, proteins and other bio-molecules. Simple interactions between network components in forms of feedback regulations can lead to complex collective dynamics. A key task in cell biology is to gain a thorough understanding of the dynamics of intracellular systems and processes. In this thesis, a combined approach of mathematical modelling, computational simulation and analytical techniques, has been used to obtain a deeper insight into the dynamical aspects of a variety of feedback systems commonly encountered in cells. These systems range from model system with detailed available molecular knowledge to general regulatory motifs with varying network structures. Deterministic as well as stochastic modelling techniques have been employed, depending primarily on the specific questions asked. The first part of the thesis focuses on dissecting the principles behind the regulatory design of the Tryptophan Operon system in Escherichia coli. It has evolved three negative feedback loops, namely repression, attenuation and enzyme inhibition, as core regulator mechanisms to control the intracellular level of tryptophan amino acid, which is taken up for protein synthesis. Despite extensive experimental knowledge, the roles of these seemingly redundant loops remain unclear from a dynamical point of view. We aim to understand why three loops, rather than one, have evolved. Using a large-scale perturbation/response analysis through modelling and simulations and novel metrics for transient dynamics quantification, it has been revealed that the multiple negative feedback loops employed by the tryptophan operon are not redundant. In fact, they have evolved to concertedly give rise to a much more efficient, adaptive and stable system, than any single mechanism would provide. Since even the full topology of feedback interactions within a network is insufficient to determine its behavioural dynamics, other factors underlying feedback loops must be characterised to better predict system dynamics. In the second part of the thesis, we aim to derive these factors and explore how they shape system dynamics. We develop an analytical approach for stability and bifurcation analysis and apply it to class of feedback systems commonly encountered in cells. Our analysis showed that the strength and the Hill coefficient of a feedback loop play key role in determining the dynamics of the system carrying the loop. Not only that, the position of the loop was also found to be crucial in this decision. The analytical method we developed also facilitates parameter sensitivity analysis in which we investigate how the production and degradation rates affect system dynamics. We find that these rates are quite different in the way they shape up system behaviour, with the degradation rates exhibiting a more intricate manner. We demonstrated that coupled-loop systems display greater complexity and a richer repertoire of behaviours in comparison with single-loop ones. Different combinations of the feedback strengths of individual loops give rise to different dynamical regimes. The final part of the thesis aims to understand the effects of molecular noise on dynamics of specific systems, in this case the Tryptophan Operon. We developed two stochastic models for the system and compared their predictions to those given by the deterministic model. By means of simulations, we have shown that noise can induce oscillatory behaviour. On the other hand, incorporating noise in an oscillatory system can alter the characteristics of oscillation by shifting the bifurcation point of certain parameters by a substantial amount. Measurement of fluctuations reveals that that noise at the transcript level is most significant while noise at the enzyme level is smallest. This study highlights that noise should not be neglected if we want to obtain a complete understanding of the dynamic behaviour of cells.

APA, Harvard, Vancouver, ISO, and other styles

44

Shum, Henry. "Simulations and modelling of bacterial flagellar propulsion." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:c9f002d8-2939-4744-987e-9a4e659d93ef.

Full text

Abstract:

Motility of flagellated bacteria has been a topic of increasing scientific interest over the past decades, attracting the attention of mathematicians, physicists, biologists and engineers alike. Bacteria and other micro-organisms cause substantial damage through biofilm growth on submerged interfaces in water cooling systems, ship hulls and medical implants. This gives social and economic motivations for learning about how micro-organisms swim and behave in different environments. Fluid flows on such small scales are dominated by viscosity and therefore behave differently from the inertia-dominated flows that we are more familiar with, making bacterial motility a physically intriguing phenomenon to study as well. We use the boundary element method (BEM) to simulate the motion of singly flagellated bacteria in a viscous, Newtonian fluid. One of our main objectives is to investigate the influence of external surfaces on swimming behaviour. We show that the precise shape of the cell body and flagellum can be important for determining boundary behaviour, in particular, whether bacteria are attracted or repelled from surfaces. Furthermore, we investigate the types of motion that may arise between two parallel plates and in rectangular channels of fluid and show how these relate to the plane boundary interactions. As an extension to original models of flagellar propulsion in bacteria that assume a rotation of the rigid helical flagellum about an axis fixed relative to the cell body, we consider flexibility of the bacterial hook connecting the aforementioned parts of the swimmer. This is motivated by evidence that the hook is much more flexible than the rest of the flagellum, which we therefore treat as a rigid structure. Elastic dynamics of the hook are modelled using the equations for a Kirchhoff rod. In some regimes, the dynamics are well described by a rigid hook model but we find the possibility of additional modes of behaviour.

APA, Harvard, Vancouver, ISO, and other styles

45

Franz, Benjamin. "Recent modelling frameworks for systems of interacting particles." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:ac76d159-4cdd-40c9-b378-6ea1faf48aed.

Full text

Abstract:

In this thesis we study three different modelling frameworks for biological systems of dispersal and combinations thereof. The three frameworks involved are individual-based models, group-level models in the form of partial differential equations (PDEs) and robot swarms. In the first two chapters of the thesis, we present ways of coupling individual based models with PDEs in so-called hybrid models, with the aim of achieving improved performance of simulations. Two classes of such hybrid models are discussed that allow an efficient simulation of multi-species systems of dispersal with reactions, but involve individual resolution for certain species and in certain parts of a computational domain if desired. We generally consider two types of example systems: bacterial chemotaxis and reaction-diffusion systems, and present results in the respective application area as well as general methods. The third chapter of this thesis introduces swarm robotic experiments as an additional tool to study systems of dispersal. In general, those experiments can be used to mimic animal behaviour and to study the impact of local interactions on the group-level dynamics. We concentrate on a target finding problem for groups of robots. We present how PDE descriptions can be adjusted to incorporate the finite turning times observed in the robotic system and that the adjusted models match well with experimental data. In the fourth and last chapter, we consider interactions between robots in the form of hard-sphere collisions and again derive adjusted PDE descriptions. We show that collisions have a significant impact on the speed with which the group spreads across a domain. Throughout these two chapters, we apply a combination of experiments, individual-based simulations and PDE descriptions to improve our understanding of interactions in systems of dispersal.

APA, Harvard, Vancouver, ISO, and other styles

46

Robison, Pamula J. "Mathematical Modelling of Biofilm Growth and Decay Through Various Deliveries of Antimicrobial." University of Akron / OhioLINK, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=akron1258769688.

Full text

APA, Harvard, Vancouver, ISO, and other styles

47

Smith, Amy. "Multi-scale modelling of blood flow in the coronary microcirculation." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:e6f576a2-75d9-4778-a640-a1e8551141a6.

Full text

Abstract:

The importance of coronary microcirculatory perfusion is highlighted by the severe impact of microvascular diseases such as diabetes and hypertension on heart function. Recently, highly-detailed three-dimensional (3D) data on ex vivo coronary microvascular structure have become available. However, hemodynamic information in individual myocardial capillaries cannot yet be obtained using current in vivo imaging techniques. In this thesis, a novel data-driven modelling framework is developed to predict tissue-scale flow properties from discrete anatomical data, which can in future be used to aid interpretation of coarse-scale perfusion imaging data in healthy and diseased states. Mathematical models are parametrised by the 3D anatomical data set of Lee (2009) from the rat myocardium, and tested using flow measurements in two-dimensional rat mesentery networks. Firstly, algorithmic and statistical tools are developed to separate branching arterioles and venules from mesh-like capillaries, and then to extract geometrical properties of the 3D capillary network. The multi-scale asymptotic homogenisation approach of Shipley and Chapman (2010) is adapted to derive a continuum model of coronary capillary fluid transport incorporating a non-Newtonian viscosity term. Tissue-scale flow is captured by Darcy's Law whose coefficient, the permeability tensor, transmits the volume-averaged capillary-scale flow variations to the tissue-scale equation. This anisotropic permeability tensor is explicitly calculated by solving the capillary-scale fluid mechanics problem on synthetic, stochastically-generated periodic networks parametrised by the geometrical data statistics, and a thorough sensitivity analysis is conducted. Permeability variations across the myocardium are computed by parametrising synthetic networks with transmurally-dependent data statistics, enabling the hypothesis that subendocardial permeability is much higher in diastole to compensate for severely-reduced systolic blood flow to be tested. The continuum Darcy flow model is parametrised by purely structural information to provide tissue-scale perfusion metrics, with the hypothesis that this model is less sensitive and more reliably parametrised than an alternative, estimated discrete network flow solution.

APA, Harvard, Vancouver, ISO, and other styles

48

Alshammari, Abdullah A. A. M. F. "Mathematical modelling of oxygen transport in skeletal and cardiac muscles." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:65a34cb0-ef00-44c9-a04d-4147844c76ac.

Full text

Abstract:

Understanding and characterising the diffusive transport of capillary oxygen and nutrients in striated muscles is key to assessing angiogenesis and investigating the efficacy of experimental and therapeutic interventions for numerous pathological conditions, such as chronic ischaemia. In articular, the influence of both muscle tissue and microvascular heterogeneities on capillary oxygen supply is poorly understood. The objective of this thesis is to develop mathematical and computational modelling frameworks for the purpose of extending and generalising the current use of histology in estimating the regions of tissue supplied by individual capillaries to facilitate the exploration of functional capillary oxygen supply in striated muscles. In particular, we aim to investigate the balance between local capillary supply of oxygen and oxygen demand in the presence of various anatomical and functional heterogeneities, by capturing tissue details from histological imaging and estimating or predicting regions of capillary supply. Our computational method throughout is based on a finite element framework that captures the anatomical details of tissue cross sections. In Chapter 1 we introduce the problem. In Chapter 2 we develop a theoretical model to describe oxygen transport from capillaries to uniform muscle tissues (e.g. cardiac muscle). Transport is then explored in terms of oxygen levels and capillary supply regions. In Chapter 3 we extend this modelling framework to explore the influence of the surrounding tissue by accounting for the spatial anisotropies of fibre oxygen demand and diffusivity and the heterogeneity in fibre size and shape, as exemplified by mixed muscle tissues (e.g. skeletal muscle). We additionally explore the effects of diffusion through the interstitium, facilitated--diffusion by myoglobin, and Michaelis--Menten kinetics of tissue oxygen consumption. In Chapter 4, a further extension is pursued to account for intracellular heterogeneities in mitochondrial distribution and diffusive parameters. As a demonstration of the potential of the models derived in Chapters 2--4, in Chapter 5 we simulate oxygen transport in myocardial tissue biopsies from rats with either impaired angiogenesis or impaired arteriolar perfusion. Quantitative predictions are made to help explain and support experimental measurements of cardiac performance and metabolism. In the final chapter we summarize the main results and indicate directions for further work.

APA, Harvard, Vancouver, ISO, and other styles

49

Al-Nuaimi, Yusur Mamoon. "A systems biology approach to the human hair cycle." Thesis, University of Manchester, 2011. https://www.research.manchester.ac.uk/portal/en/theses/a-systems-biology-approach-to-the-human-hair-cycle(a576aff0-5fbe-4db6-9e13-8211f07e2883).html.

Full text

Abstract:

The hair cycle represents a dynamic process during which a complex mini- organ, the hair follicle, rhythmically regresses and regenerates. The control mechanism that governs the hair cycle ('hair cycle clock') is thought to be an autonomous oscillator system, however, its exact nature is not known. This thesis aims to understand the human hair cycle as a systems biology problem using theoretical and experimental techniques in three distinct study approaches. Using mathematical modelling, a simple two-compartment model of the human hair cycle was developed. The model concentrates on the growth control of matrix keratinocytes, a key cell population responsible for hair growth, and bi-directional communication between these cells and the inductive fibroblasts of the dermal papilla. A bistable switch and feedback inhibition produces key characteristics of human hair cycle dynamics. This study represents the first mathematically formulated theory of the 'hair cycle clock'.A second chronobiological approach was adopted to explore the molecular control of the human hair follicle by a peripheral clock mechanism. The hypothesis was tested that selected circadian clock genes regulate the human hair cycle, namely the clinically crucial follicle transformation from organ growth (anagen) to organ regression (catagen). This revealed that intra- follicular expression of core clock and clock-controlled genes display a circadian rhythm and is hair cycle-dependent. Knock-down of Period1 and Clock promotes anagen maintenance, hair matrix keratinocyte proliferation and stimulates hair follicle pigmentation. This provides the first evidence that peripheral Period1 and Clock gene activity is a component of the human 'hair cycle clock' mechanism. Lastly, an unbiased gene expression profiling approach was adopted to establish important genes and signalling pathways that regulate the human hair cycle. This revealed that similar genes and pathways previously shown to control the murine hair cycle in vivo, such as Sgk3, Msx2 and the BMP pathway, are also differentially regulated during the anagen-catagen transformation of human hair follicles. In summary, by using a three-pronged systems biology approach, the thesis has shed new light on the control of human hair follicle cycling and has generated clinically relevant information: a) The hair cycle model may predict how hair cycle modulatory agents alter human hair growth. b) Period1 and Clock are new therapeutic targets for human hair growth manipulation. c) Gene expression profiling points to additional key players in human hair cycle control with potential for future therapeutic targets.

APA, Harvard, Vancouver, ISO, and other styles

50

Dunn, Sara-Jane Nicole. "Towards a computational model of the colonic crypt with a realistic, deformable geometry." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:c3c9440a-52ac-4a3d-8e1c-5dc276b8eb6c.

Full text

Abstract:

Colorectal cancer (CRC) is one of the most prevalent and deadly forms of cancer. Its high mortality rate is associated with difficulties in early detection, which is crucial to survival. The onset of CRC is marked by macroscopic changes in intestinal tissue, originating from a deviation in the healthy cell dynamics of glands known as the crypts of Lieberkuhn. It is believed that accumulated genetic alterations confer on mutated cells the ability to persist in the crypts, which can lead to the formation of a benign tumour through localised proliferation. Stress on the crypt walls can lead to buckling, or crypt fission, and the further spread of mutant cells. Elucidating the initial perturbations in crypt dynamics is not possible experimentally, but such investigations could be made using a predictive, computational model. This thesis proposes a new discrete crypt model, which focuses on the interaction between cell- and tissue-level behaviour, while incorporating key subcellular components. The model contains a novel description of the role of the surrounding tissue and musculature, which allows the shape of the crypt to evolve and deform. A two-dimensional (2D) cross-sectional geometry is considered. Simulation results reveal how the shape of the crypt base may contribute mechanically to the asymmetric division events typically associated with the stem cells in this region. The model predicts that epithelial cell migration may arise due to feedback between cell loss at the crypt collar and density-dependent cell division, an hypothesis which can be investigated in a wet lab. Further, in silico experiments illustrate how this framework can be used to investigate the spread of mutations, and conclude that a reduction in cell migration is key to confer persistence on mutant cell populations. A three-dimensional (3D) model is proposed to remove the spatial restrictions imposed on cell migration in 2D, and preliminary simulation results agree with the hypotheses generated in 2D. Computational limitations that currently restrict extension to a realistic 3D geometry are discussed. These models enable investigation of the role that mechanical forces play in regulating tissue homeostasis, and make a significant contribution to the theoretical study of the onset of crypt deformation under pre-cancerous conditions.

APA, Harvard, Vancouver, ISO, and other styles

Dissertations / Theses on the topic 'Mathematical modelling/biology'

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles