Relevant bibliographies by topics / Mathematical modelling/biology

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Mathematical modelling/biology'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Mathematical modelling/biology"

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Vasieva, Olga, Manan'Iarivo Rasolonjanahary, and Bakhtier Vasiev. "Mathematical modelling in developmental biology." REPRODUCTION 145, no. 6 (2013): R175—R184. http://dx.doi.org/10.1530/rep-12-0081.

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In recent decades, molecular and cellular biology has benefited from numerous fascinating developments in experimental technique, generating an overwhelming amount of data on various biological objects and processes. This, in turn, has led biologists to look for appropriate tools to facilitate systematic analysis of data. Thus, the need for mathematical techniques, which can be used to aid the classification and understanding of this ever-growing body of experimental data, is more profound now than ever before. Mathematical modelling is becoming increasingly integrated into biological studies in general and into developmental biology particularly. This review outlines some achievements of mathematics as applied to developmental biology and demonstrates the mathematical formulation of basic principles driving morphogenesis. We begin by describing a mathematical formalism used to analyse the formation and scaling of morphogen gradients. Then we address a problem of interplay between the dynamics of morphogen gradients and movement of cells, referring to mathematical models of gastrulation in the chick embryo. In the last section, we give an overview of various mathematical models used in the study of the developmental cycle of Dictyostelium discoideum, which is probably the best example of successful mathematical modelling in developmental biology.
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Tomlin, Claire J., and Jeffrey D. Axelrod. "Biology by numbers: mathematical modelling in developmental biology." Nature Reviews Genetics 8, no. 5 (2007): 331–40. http://dx.doi.org/10.1038/nrg2098.

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Jäger, Willi. "Mathematical Modelling in Chemistry and Biology." Interdisciplinary Science Reviews 11, no. 2 (1986): 181–88. http://dx.doi.org/10.1179/isr.1986.11.2.181.

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Chaplain, M. A. J. "Multiscale mathematical modelling in biology and medicine." IMA Journal of Applied Mathematics 76, no. 3 (2011): 371–88. http://dx.doi.org/10.1093/imamat/hxr025.

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Lei, Jinzhi. "Viewpoints on modelling: Comments on "Achilles and the tortoise: Some caveats to mathematical modelling in biology"." Mathematics in Applied Sciences and Engineering 1, no. 1 (2020): 85–90. http://dx.doi.org/10.5206/mase/10267.

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Mathematical modelling has been proven to be useful in understanding some problems from biological science, provided that it is used properly. However, it has also attracted some criticisms as partially presented in a recent opinion article \cite{Gilbert2018} from biological community. This note intends to clarify some confusion and misunderstanding in regard to mathematically modelling by commenting on those critiques raised in \cite{Gilbert2018}, with a hope of initiating some further discussion so that both applied mathematicians and biologist can better use mathematical modelling and better understand the results from modelling.
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Middleton, A., M. Owen, M. Bennett, and J. King. "Mathematical modelling of gibberellinsignalling." Comparative Biochemistry and Physiology Part A: Molecular & Integrative Physiology 150, no. 3 (2008): S46. http://dx.doi.org/10.1016/j.cbpa.2008.04.023.

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Butler, George, Jonathan Rudge, and Philip R. Dash. "Mathematical modelling of cell migration." Essays in Biochemistry 63, no. 5 (2019): 631–37. http://dx.doi.org/10.1042/ebc20190020.

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Abstract The complexity of biological systems creates challenges for fully understanding their behaviour. This is particularly true for cell migration which requires the co-ordinated activity of hundreds of individual components within cells. Mathematical modelling can help understand these complex systems by breaking the system into discrete steps which can then be interrogated in silico. In this review, we highlight scenarios in cell migration where mathematical modelling can be applied and discuss what types of modelling are most suited. Almost any aspect of cell migration is amenable to mathematical modelling from the modelling of intracellular processes such as chemokine receptor signalling and actin filament branching to larger scale processes such as the movement of individual cells or populations of cells through their environment. Two common ways of approaching this modelling are the use of models based on differential equations or agent-based modelling. The application of both these approaches to cell migration are discussed with specific examples along with common software tools to facilitate the process for non-mathematicians. We also highlight the challenges of modelling cell migration and the need for rigorous experimental work to effectively parameterise a model.
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Divya, B., and K. Kavitha. "A REVIEW ON MATHEMATICAL MODELLING IN BIOLOGY AND MEDICINE." Advances in Mathematics: Scientific Journal 9, no. 8 (2020): 5869–79. http://dx.doi.org/10.37418/amsj.9.8.54.

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MacArthur, B. D., C. P. Please, M. Taylor, and R. O. C. Oreffo. "Mathematical modelling of skeletal repair." Biochemical and Biophysical Research Communications 313, no. 4 (2004): 825–33. http://dx.doi.org/10.1016/j.bbrc.2003.11.171.

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Shone, John. "Working at the biology/mathematics interface: mathematical modelling and sixth form biology." International Journal of Mathematical Education in Science and Technology 19, no. 4 (1988): 501–9. http://dx.doi.org/10.1080/0020739880190402.

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

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

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

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

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

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

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

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

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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.
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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.

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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.
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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.

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

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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.
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Books on the topic "Mathematical modelling/biology"

1

Morris, Richard J., ed. Mathematical Modelling in Plant Biology. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-99070-5.

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Brebbia, C. A. Modelling in medicine and biology. WIT Press, 2011.

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Wilkinson, Darren James. Stochastic modelling for systems biology. 2nd ed. Taylor & Francis, 2012.

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R, Carson Ewart, ed. Mathematical modelling of dynamic biological systems. 2nd ed. Research Studies Press, 1985.

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Demin, Oleg. Kinetic modelling in systems biology. Chapman & Hall/CRC, 2009.

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Nisbet, R. M. Modelling fluctuating populations. Blackburn Press, 2003.

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Nisbet, R. M. Modelling fluctuating populations. University Microfilms International, 1992.

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Daley, Daryl J. Epidemic modelling: An introduction. Cambridge University Press, 1999.

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Wilkinson, Darren James. Stochastic modelling for systems biology. Chapman & Hall/CRC Press, 2007.

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Stochastic modelling for systems biology. Taylor & Francis, 2006.

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Book chapters on the topic "Mathematical modelling/biology"

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Pérez-Escobar, José Antonio. "Mathematical Modelling and Teleology in Biology." In Proceedings of the Canadian Society for History and Philosophy of Mathematics/ Société canadienne d’histoire et de philosophie des mathématiques. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-31298-5_4.

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Wedgwood, K. C. A., J. Tabak, and K. Tsaneva-Atanasova. "Modelling Ion Channels." In Mathematical Modelling in Plant Biology. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-99070-5_3.

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Ahmed, Danish A., Joseph D. Bailey, Sergei V. Petrovskii, and Michael B. Bonsall. "Mathematical Bases for 2D Insect Trap Counts Modelling." In Computational Biology. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-69951-2_6.

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Slavova, Angela. "CNN modelling in biology, physics and ecology." In Mathematical Modelling: Theory and Applications. Springer Netherlands, 2003. http://dx.doi.org/10.1007/978-94-017-0261-4_4.

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Greulich, Philip. "Mathematical Modelling of Clonal Stem Cell Dynamics." In Computational Stem Cell Biology. Springer New York, 2019. http://dx.doi.org/10.1007/978-1-4939-9224-9_5.

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Deinum, Eva E., and Bela M. Mulder. "Modelling the Plant Microtubule Cytoskeleton." In Mathematical Modelling in Plant Biology. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-99070-5_4.

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D’Agostino, Daniele, Andrea Clematis, Emanuele Danovaro, and Ivan Merelli. "Modelling of Protein Surface Using Parallel Heterogeneous Architectures." In Mathematical Models in Biology. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-23497-7_14.

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Dumond, Mathilde, and Arezki Boudaoud. "Physical Models of Plant Morphogenesis." In Mathematical Modelling in Plant Biology. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-99070-5_1.

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Živković, Daniel, and Aurélien Tellier. "All But Sleeping? Consequences of Soil Seed Banks on Neutral and Selective Diversity in Plant Species." In Mathematical Modelling in Plant Biology. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-99070-5_10.

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Blyth, M. G., and R. J. Morris. "Fluid Transport in Plants." In Mathematical Modelling in Plant Biology. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-99070-5_2.

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Conference papers on the topic "Mathematical modelling/biology"

1

Sabrekov, A. F., M. V. Glagolev, I. E. Terentieva, and S. Y. Mochenov. "Identification of soil methane oxidation activity by inverse modelling." In Mathematical Biology and Bioinformatics. IMPB RAS - Branch of KIAM RAS, 2018. http://dx.doi.org/10.17537/icmbb18.77.

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Iaparov, B. I., and V. V. Ivchenko. "Mathematical modelling of the ryanodine receptor’s activation time dependence on magnesium." In Mathematical Biology and Bioinformatics. IMPB RAS - Branch of KIAM RAS, 2018. http://dx.doi.org/10.17537/icmbb18.69.

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Sabrekov, A. F., M. V. Glagolev, and I. E. Terentieva. "Measuring methane flux from the soil by inverse modelling using adjoint equations." In Mathematical Biology and Bioinformatics. IMPB RAS - Branch of KIAM RAS, 2018. http://dx.doi.org/10.17537/icmbb18.85.

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Romanov, M. S., and V. B. Masterov. "Modelling of the Steller’s Sea Eagle Population: Stable Demographic Structure vs. Transient Dynamics." In Mathematical Biology and Bioinformatics. IMPB RAS - Branch of KIAM RAS, 2018. http://dx.doi.org/10.17537/icmbb18.99.

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Okenov, A. O., B. Ya Iaparov, and A. S. Moskvin. "Kramers rate theory as a starting point for modelling temperature effects in TRP channels." In Mathematical Biology and Bioinformatics. IMPB RAS - Branch of KIAM RAS, 2018. http://dx.doi.org/10.17537/icmbb18.38.

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Polyakov, M. V., and A. S. Astakhov. "Mathematical Processing and Computer Analysis of Data from Numerical Modelling of Radiothermometric Medical Examinations." In Mathematical Biology and Bioinformatics. IMPB RAS - Branch of KIAM RAS, 2020. http://dx.doi.org/10.17537/icmbb20.23.

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Nikolaev, G. I., N. A. Shuldov, I. P. Bosko, A. I. Anischenko, A. V. Tuzikov, and A. M. Andrianov. "Application of Deep Learning and Molecular Modelling Methods to Identify Potential HIV-1 Entry Inhibitors." In Mathematical Biology and Bioinformatics. IMPB RAS - Branch of KIAM RAS, 2020. http://dx.doi.org/10.17537/icmbb20.6.

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van Leeuwen, Ingeborg M. M., Helen M. Byrne, Matthew D. Johnston, et al. "Modelling multiscale aspects of colorectal cancer." In INTERNATIONAL CONFERENCE ON MATHEMATICAL BIOLOGY 2007: ICMB07. AIP, 2008. http://dx.doi.org/10.1063/1.2883865.

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BANERJEE, M., M. BENMIR, and V. VOLPERT. "MULTI-SCALE MODELLING IN CELL DYNAMICS." In International Symposium on Mathematical and Computational Biology. WORLD SCIENTIFIC, 2015. http://dx.doi.org/10.1142/9789814667944_0020.

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MONDAINI, RUBEM P., and ROBERTO A. C. PRATA. "GEODESIC CURVES FOR BIOMOLECULAR STRUCTURE MODELLING." In International Symposium on Mathematical and Computational Biology. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812812339_0018.

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