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Статті в журналах з теми "Cell cycle; mathematical models; differential equations"
1
TANG, BETTY. "MODELING THE CELL DIVISION CYCLE: A QUALITATIVE APPROACH." Journal of Biological Systems 03, no. 01 (March 1995): 55–61. http://dx.doi.org/10.1142/s021833909500006x.
Повний текст джерелаАнотація:
The underlying biochemical mechanisms that drive the cell division cycle involve the interactions and feedback controls between the cytoplasmic proteins cdc2 and cyclin, and the activities of the cdc2-cyclin complex MPF. Alternation between interphase and mitosis is associated with oscillatory MPF and cyclin levels. This paper describes an ordinary differential equations (ODE) model and a functional differential equations (FDE) model of the cell cycle based on experimental work with the newly fertilized frog egg. One major difference of these models from previous ones is the use of nonspecific reaction terms in describing the interactions between cdc2, cyclin and MPF. This qualitative approach makes possible the evaluation of the roles of the various reactions and feedback mechanisms in the control of the cell cycle.
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Tyson, John J. "From the Belousov–Zhabotinsky reaction to biochemical clocks, traveling waves and cell cycle regulation." Biochemical Journal 479, no. 2 (January 28, 2022): 185–206. http://dx.doi.org/10.1042/bcj20210370.
Повний текст джерелаАнотація:
In the last 20 years, a growing army of systems biologists has employed quantitative experimental methods and theoretical tools of data analysis and mathematical modeling to unravel the molecular details of biological control systems with novel studies of biochemical clocks, cellular decision-making, and signaling networks in time and space. Few people know that one of the roots of this new paradigm in cell biology can be traced to a serendipitous discovery by an obscure Russian biochemist, Boris Belousov, who was studying the oxidation of citric acid. The story is told here from an historical perspective, tracing its meandering path through glycolytic oscillations, cAMP signaling, and frog egg development. The connections among these diverse themes are drawn out by simple mathematical models (nonlinear differential equations) that share common structures and properties.
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Lo Presti, Elena, Laura D’Orsi, and Andrea De Gaetano. "A Mathematical Model of In Vitro Cellular Uptake of Zoledronic Acid and Isopentenyl Pyrophosphate Accumulation." Pharmaceutics 14, no. 6 (June 14, 2022): 1262. http://dx.doi.org/10.3390/pharmaceutics14061262.
Повний текст джерелаАнотація:
The mevalonate pathway is an attractive target for many areas of research, such as autoimmune disorders, atherosclerosis, Alzheimer’s disease and cancer. Indeed, manipulating this pathway results in the alteration of malignant cell growth with promising therapeutic potential. There are several pharmacological options to block the mevalonate pathway in cancer cells, one of which is zoledronic acid (ZA) (an N-bisphosphonate (N-BP)), which inhibits the farnesyl pyrophosphate (FPP) synthase enzyme, inducing cell cycle arrest, apoptosis, inhibition of protein prenylation, and cholesterol reduction, as well as leading to the accumulation of isopentenyl pyrophosphate (IPP). We extrapolated the data based on two independently published papers that provide numerical data on the uptake of zoledronic acid (ZA) and the accumulation of IPP (Ag) and its isomer over time by using in vitro human cell line models. Two different mathematical models for IPP kinetics are proposed. The first model (Model 1) is a simpler ordinary differential equation (ODE) compartmental system composed of 3 equations with 10 parameters; the second model (Model 2) is a differential algebraic equation (DAE) system with 4 differential equations, 1 algebraic equation and 13 parameters incorporating the formation of the ZA+enzyme+Ag complex. Each of the two models aims to describe two different experimental situations (continuous and pulse experiments) with the same ZA kinetics. Both models fit the collected data very well. With Model 1, we obtained a prevision accumulation of IPP after 24 h of 169.6 pmol/mgprot/h with an IPP decreasing rate per (pmol/mgprot) of ZA (kXGZ) equal to 13.24/h. With Model 2, we have comprehensive kinetics of IPP upon ZA treatment. We calculate that the IPP concentration was equal to 141.6 pmol/mgprot/h with a decreasing rate/percentage of 0.051 (kXGU). The present study is the first to quantify the influence of ZA on the pharmacodynamics of IPP. While still incorporating a small number of parameters, Model 2 better represents the complexity of the biological behaviour for calculating the IPP produced in different situations, such as studies on γδ T cell-based immunotherapy. In the future, additional clinical studies are warranted to further evaluate and fine-tune dosing approaches.
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Smieja, Jaroslaw, Andrzej Swierniak, and Zdzislaw Duda. "Gradient Method for Finding Optimal Scheduling in Infinite Dimensional Models of Chemotherapy." Journal of Theoretical Medicine 3, no. 1 (2000): 25–36. http://dx.doi.org/10.1080/10273660008833062.
Повний текст джерелаАнотація:
One of the major obstacles against succesful chemotherapy of cancer is the emergence of resistance of cancer cells to cytotoxic agents. Applying optimal control theory to mathematical models of cell cycle dynamics can be a very efficient method to understand and, eventually, overcome this problem. Results that have been hitherto obtained have already helped to explain some observed phenomena, concerning dynamical properties of cancer populations. Because of recent progress in understanding the way in which chemotherapy affects cancer cells, new insights and more precise mathematical formulation of control problem, in the meaning of finding optimal chemotherapy, became possible. This, together with a progress in mathematical tools, has renewed hopes for improving chemotherapy protocols. In this paper we consider a population of neoplastic cells stratified into subpopulations of cells of different types. Due to the mutational event a sensitive cell can acquire a copy of the gene that makes it resistant to the agent. Likewise, the division of resistant cells can result in the change of the number of gene copies. We convert the model in the form of an infinite dimensional system of ordinary differential state equations discussed in our previous publications (see e.g. Swierniak etal., 1996b; Polariski etal., 1997; Swierniak etaL, 1998c), into the integro-differential form. It enables application of the necessary conditions of optimality given by the appropriate version of Pontryagin's maximum principle, e.g. (Gabasov and Kirilowa, 1971). The performance index which should be minimized combines the negative cumulated cytotoxic effect of the drug and the terminal population of both sensitive and resistant neoplastic cells. The linear form of the cost function and the bilinear form of the state equation result in a bang-bang optimal control law. To find the switching times we propose to use a special gradient algorithm developed similarly to the one applied in our previous papers to finite dimensional problems (Duda 1994; 1997).
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Лузянина, Т., та T. Luzyanina. "Численный бифуркационный анализ математических моделей с запаздыванием по времени с использованием пакета программ DDE-BIFTOOL". Mathematical Biology and Bioinformatics 12, № 2 (13 грудня 2017): 496–520. http://dx.doi.org/10.17537/2017.12.496.
Повний текст джерелаАнотація:
Mathematical modeling with delay differential equations (DDEs) is widely used for analysis and making predictions in various areas of the life sciences, e.g., population dynamics, epidemiology, immunology, physiology, neural networks. The time delays in these models take into account a dependence of the present state of the modeled system on its past history. The delay can be related to the duration of certain hidden processes like the stages of the life cycle, the time between infection of a cell and the production of new viruses, the duration of the infectious period, the immune period and so on. Due to an infinite-dimensional nature of DDEs, analytical studies of the corresponding mathematical models can only give limited results. Therefore, a numerical analysis is the major way to achieve both a qualitative and quantitative understanding of the model dynamics. A bifurcation analysis of a dynamical system is used to understand how solutions and their stability change as the parameters in the system vary. The package DDE-BIFTOOL is the first general-purpose package for bifurcation analysis of DDEs. This package can be used to compute and analyze the local stability of steady-state (equilibria) and periodic solutions of a given system as well as to study the dependence of these solutions on system parameters via continuation. Further one can compute and continue several local and global bifurcations: fold and Hopf bifurcations of steady states; folds, period doublings and torus bifurcations of periodic orbits; and connecting orbits between equilibria. In this paper we describe the structure of DDE-BIFTOOL, numerical methods implemented in the package and we illustrate the use of the package using a certain DDE system.
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Oduola, Wasiu Opeyemi, and Xiangfang Li. "Multiscale Tumor Modeling With Drug Pharmacokinetic and Pharmacodynamic Profile Using Stochastic Hybrid System." Cancer Informatics 17 (January 1, 2018): 117693511879026. http://dx.doi.org/10.1177/1176935118790262.
Повний текст джерелаАнотація:
Effective cancer treatment strategy requires an understanding of cancer behavior and development across multiple temporal and spatial scales. This has resulted into a growing interest in developing multiscale mathematical models that can simulate cancer growth, development, and response to drug treatments. This study thus investigates multiscale tumor modeling that integrates drug pharmacokinetic and pharmacodynamic (PK/PD) information using stochastic hybrid system modeling framework. Specifically, (1) pathways modeled by differential equations are adopted for gene regulations at the molecular level; (2) cellular automata (CA) model is proposed for the cellular and multicellular scales. Markov chains are used to model the cell behaviors by taking into account the gene expression levels, cell cycle, and the microenvironment. The proposed model enables the prediction of tumor growth under given molecular properties, microenvironment conditions, and drug PK/PD profile. Simulation results demonstrate the effectiveness of the proposed approach and the results agree with observed tumor behaviors.
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Craig, Morgan, Antony Humphries, Fahima Nekka, Jun Li, Jacques Bélair, and Michael Mackey. "Physiologically-Based Mathematical Modelling of Neutrophil Dynamics during Concurrent Chemotherapy and Filgrastim Support." Blood 124, no. 21 (December 6, 2014): 5134. http://dx.doi.org/10.1182/blood.v124.21.5134.5134.
Повний текст джерелаАнотація:
Abstract A common and dose-limiting side effect of chemotherapy is the development of neutropenia (a reduction in neutrophil numbers). To avoid or mitigate drops in absolute neutrophil counts (ANCs), patients are typically given recombinant human granulocyte colony-stimulating factor (rhG-CSF/filgrastim) to minimise the myelosuppressive nature of anti-cancer treatments. Dosing recommendations for filgrastim after chemotherapy suggest treatment begin one day post-chemotherapy and continue for a given amount of time or until ANCs rise sufficiently. Indeed, filgrastim support in a given chemotherapy cycle can sometimes reach seven to ten days in a 14-day period. Due to the intricacy of neutrophil production from the hematopoeitic stem cells in addition to the complexity of the interactions of cytokines and their receptors, a complete understanding of the mechanisms underlying myelopoiesis remains elusive. Mathematical modelling of these processes is a method which provides a global view of the dynamics of blood cell production and helps to elucidate the implications of concurrent chemotherapy and rhG-CSF support upon the blood production system. Moreover, the mathematical treatment of myelopoiesis can suggest novel dosing regimens that may be more beneficial than current schedules by supporting currently-held hypotheses and/or revealing previously unstudied relationships and dynamics. In this study, we construct a physiologically-based model of myelopoiesis which incorporates an up-to-date understanding of the production of neutrophils with our group's previously published model of blood cell dynamics. This model is combined with pharmacokinetic and pharmcodynamic (PKPD) models of Zalypsis (PM00104), an anti-cancer drug currently in phase II clinical trials, and filgrastim, a myelostimulant. The physiological model of myelopoiesis directly relates observable delays in neutrophil production to temporal lags in the model through the use of delay differential equations. All parameters are comprehensively defined for an average patient by utilising previously published physiological and PKPD studies. The model is numerically implemented and simulated to compare its predictions to ANC time series of patients undergoing the CHOP14 protocol. Able to recreate previously published data, we then investigated the optimal timing of filgrastim administrations post-chemotherapy during 14-day periodic chemotherapy and examined the number of filgrastim administrations necessary to ward off neutropenia using this optimised timing. Our results indicate that delaying rhG-CSF administrations by six or seven days after the administration of chemotherapy lessens the myelosuppressive impact of anti-cancer treatment. In addition, we found that if filgrastim administration are started seven days post-chemotherapy, as few as three or four doses of rhG-CSF during a 14-day cycle would improve the ANC nadir experienced by an average patient during myelosuppressive chemotherapy. In all, our results suggest that it is possible to lessen the hematopoietic burden of chemotherapy on patients and that detailed physiological modelling of myelopoiesis is a useful tool to clinicians and researchers alike. Disclosures Off Label Use: We look at optimal dosing regimens of filgrastim during periodic chemotherapy in the context of physiological mathematical models. No clinical trials were undertaken and no patients underwent any regimen changes..
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Neyhouse, Bertrand J., Jonathan Lee, and Fikile R. Brushett. "Predicting Cell Cycling Performance in Redox Flow Batteries Using Reduced-Order Analytical Models." ECS Meeting Abstracts MA2022-01, no. 3 (July 7, 2022): 474. http://dx.doi.org/10.1149/ma2022-013474mtgabs.
Повний текст джерелаАнотація:
Achieving decarbonization across multiple sectors (e.g., electricity generation, transportation, manufacturing) requires widespread adoption of renewable energy technologies, which demand energy storage solutions to enable sustainable, reliable, and resilient power delivery.1 To this end, redox flow batteries (RFBs) are a promising grid-scale energy storage platform, owing to their improved scalability, simplified manufacturing, and long service life.2 However, state-of-the-art RFBs remain too expensive for broad adoption, motivating the development of novel electrolyte formulations and reactor designs to meet performance, cost, and scale targets for emerging applications.3 While many recently-reported next-generation materials offer short-term performance improvements and the potential for cost reductions when produced at-scale, they often complicate system operation over extended durations due to a multitude of interrelated parasitic processes (e.g., side reactions, crossover, species decomposition) which lead to capacity fade and efficiency losses.3,4 Such processes challenge the establishment of quantitative and unambiguous connections between individual component properties and overall cell behavior. Here, we aim to develop mathematical models that translate fundamental material properties to cell performance metrics, enabling more informed design criteria for system engineering. In this presentation, we introduce an analytically-derived, zero-dimensional modeling framework to predict cell cycling behavior in RFBs. While previously-developed zero- and one-dimensional models demonstrate accurate performance predictions when compared to experimental systems, they must solve coupled differential equations using numerical methods.5,6 As a result, these approaches become computationally expensive for multi-cycle simulations (i.e., 10s – 100s of cycles), frustrating their implementation in system design and optimization. By deriving analytical solutions to these models, we can markedly reduce computation times and enable analyses hitherto unachievable. To demonstrate the utility of this modeling framework, we explore several representative scenarios that examine the connection between RFB material properties, operating conditions, and performance (i.e., power output, accessible capacity, efficiency). Additionally, we investigate the impact of different parasitic processes on capacity fade, highlighting the effects of species decomposition and crossover in durational cell cycling. Finally, we discuss several modalities for expanding this framework to include additional sources of performance losses and for integrating these models into larger computational schemes (e.g., optimization, parameter estimation, techno-economic assessments). The mathematical models developed in this work have potential to advance foundational understanding in RFB design, leading to quantitatively informed selection criteria for emerging candidate materials. Acknowledgments This work was supported by the Joint Center for Energy Storage Research, an Energy Innovation Hub funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences. B.J.N gratefully acknowledges the NSF Graduate Research Fellowship Program under Grant Number 1122374. J.L gratefully acknowledges support from the MIT Materials Research Laboratory REU Program, as part of the MRSEC Program of the NSF under grant number DMR-14-19807. Any opinion, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the NSF. References S. Chu and A. Majumdar, Nature, 488, 294–303 (2012). M. L. Perry and A. Z. Weber, J. Electrochem. Soc., 163, A5064–A5067 (2016). F. R. Brushett, M. J. Aziz, and K. E. Rodby, ACS Energy Lett., 5, 879–884 (2020). M. L. Perry, J. D. Saraidaridis, and R. M. Darling, Current Opinion in Electrochemistry, 21, 311–318 (2020). M. Pugach, M. Kondratenko, S. Briola, and A. Bischi, Applied Energy, 226, 560–569 (2018). S. Modak and D. G. Kwabi, J. Electrochem. Soc., 168, 080528 (2021).
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Miranda, Raquel, Susana Vinga, and Duarte Valério. "Studying Bone Remodelling and Tumour Growth for Therapy Predictive Control." Mathematics 8, no. 5 (May 1, 2020): 679. http://dx.doi.org/10.3390/math8050679.
Повний текст джерелаАнотація:
Bone remodelling consists of cycles of bone resorption and formation executed mainly by osteoclasts and osteoblasts. Healthy bone remodelling is disrupted by diseases such as Multiple Myeloma and bone metastatic diseases. In this paper, a simple mathematical model with differential equations, which takes into account the evolution of osteoclasts, osteoblasts, bone mass and bone metastasis growth, is improved with a pharmacokinetic and pharmacodynamic (PK/PD) scheme of the drugs denosumab, bisphosphonates, proteasome inhibitors and paclitaxel. The major novelty is the inclusion of drug resistance phenomena, which resulted in two variations of the model, corresponding to different paradigms of the origin and development of the tumourous cell resistance condition. These models are then used as basis for an optimization of the drug dose applied, paving the way for personalized medicine. A Nonlinear Model Predictive Control scheme is used, which takes advantage of the convenient properties of a suggested adaptive and democratic variant of Particle Swarm Optimization. Drug prescriptions obtained in this way provide useful insights into dose administration strategies. They also show how results may change depending on which of the two very different paradigms of drug resistance is used to model the behaviour of the tumour.
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Quiroga-Campano, Ana Luz, Louise Enfield, Matthew Foster, Margaritis Kostoglou, Michael Georgiadis, Athanasios Mantalaris, and Nicki Panoskaltsis. "Personalized and Optimized Low-Dose and Intensive Chemotherapy Treatments for Patients with Acute Myeloid Leukemia (AML)." Blood 132, Supplement 1 (November 29, 2018): 3500. http://dx.doi.org/10.1182/blood-2018-99-119258.
Повний текст джерелаАнотація:
Abstract Patients with AML have heterogeneous features, including those specific to the patient as well as those specific to the disease, such as leukemic burden and dynamic sub-clonal populations. Outside of clinical trials, few of these components are used to determine treatment. In order to move towards precision medicine, we have developed πiChemo, a computational application based on a dynamic mathematical modelling framework, using patient-, leukemia- and treatment-specific data to predict outcomes and optimize chemotherapy regimens for patients with AML. The model consists of a pharmacokinetic and pharmacodynamic (PK/PD) module that calculates the concentration and effect of Cytarabine Arabinoside (Ara-C) and Daunorubicin (DNR) in bone marrow (BM); and a population balance models (PBMs) module that describes normal populations (stem cells, progenitors, precursors) and abnormal populations (leukemic sensitive blasts (LSB) and leukemic resistant blasts (LRB)) in BM. The PBMs module also determines mature cell numbers in three lineages found in BM and peripheral blood (PB): (1) red blood cells (RBC), (2) white blood cells (WBC) and (3) lymphocytes (L). Model structure was analysed by global sensitivity analysis, which identified the most significant parameters on outcome predictions, re-estimated for each patient. The final integrated PK/PD & PBMs model has 1,295 differential equations, 8,044 algebraic equations, 9,335 variables, 25 fixed parameters and 4 degrees of freedom or variables to be optimized (Ara-C dose, Ara-C injection duration, DNR dose and DNR injection duration). Model validation, predictions and optimizations were performed using anonymised retrospective data from 28 patients with AML. The model required: (i) patient features: height, weight, age and gender, (ii) patient status: initial BM differential and PB cell counts, (iii) leukemia data: cellularity, presence of dysplasia and initial blast percentage and, (iv) treatment data: type (low-dose (LD) or intensive (DA)), dose, administration route (SC vs IV), administration mode (bolus injection vs infusion), time between injections and between cycles. The model predicted the absolute numbers of stem cells, progenitors, precursors, WBC, RBC, L, LSB and LRB in BM, and WBC, RBC, L and neutrophil count in PB during treatment for all patients. Model simulations predicted outcomes for 18 patients who achieved complete remission (7 LD & 11 DA), 4 patients who entered partial remission (2 LD & 2 DA) and 6 patients who relapsed (2 LD & 4 DA). The most remarkable results are those of prediction for BM blast percentage after each chemotherapy cycle and the PB neutrophil count for all patients. The notable fit between model predictions and daily patient data demonstrate model robustness and accuracy in the capacity to track patient-specific restaging BM and daily PB count evolution before, during and after treatment. The same patient datasets were used to apply an optimization algorithm that could maximize normal cell number and reduce leukemia burden, to personalize chemotherapy dose and administration for best outcomes. The results show that doses and administration methods vary between patients and between chemotherapy cycles for the same patient, depending on the evolution of normal and abnormal populations in BM. Low-dose continuous Ara-C infusions were more effective than rapid bolus injections, due to reduced chemotherapy effects on normal cells and subsequent quicker recovery in the normal BM compartments. RBC progenitors and precursors recovered faster than WBC and L lineages, and the recovery of normal BM cells was faster than that of normal mature cells in PB. The πiChemo tool requires only patient- and leukemia-specific initial conditions at diagnosis, easily obtained in standard clinical practice, for outcome predictions and treatment optimizations. Real-time model-fit testing and comparison of model results against daily PB cell counts would enable the re-estimation of significant parameters, increasing model accuracy and treatment effectiveness whilst therapy is ongoing. The πiChemo precision therapy tool has the potential to personalize optimal standard and novel treatments for AML in real-time. Disclosures No relevant conflicts of interest to declare.
Дисертації з теми "Cell cycle; mathematical models; differential equations"
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Vittadello, Sean T. "Mathematical models for cell migration and proliferation informed by visualisation of the cell cycle." Thesis, Queensland University of Technology, 2020. https://eprints.qut.edu.au/204074/1/Sean_Vittadello_Thesis.pdf.
Повний текст джерелаАнотація:
Cell migration and proliferation are essential for normal physiological processes, however their misregulation contributes to pathologies including cancer. In this thesis we develop and analyse new mathematical models of cell migration and proliferation, based on new experimental studies that provide visualisation of cell cycle progression, to improve understanding of the migration and proliferation of cells. In particular, we investigate cell migration as a function of cell cycle dynamics, normally-hidden cell synchronisation in cellular assays, whether cell migration and proliferation are mutually exclusive processes, and cellular mechanisms that contribute to heterogeneous cell proliferation.
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Mente, Carsten. "Tracking of individual cell trajectories in LGCA models of migrating cell populations." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-166582.
Повний текст джерелаАнотація:
Cell migration, the active translocation of cells is involved in various biological processes, e.g. development of tissues and organs, tumor invasion and wound healing. Cell migration behavior can be divided into two distinct classes: single cell migration and collective cell migration. Single cell migration describes the migration of cells without interaction with other cells in their environment. Collective cell migration is the joint, active movement of multiple cells, e.g. in the form of strands, cohorts or sheets which emerge as the result of individual cell-cell interactions. Collective cell migration can be observed during branching morphogenesis, vascular sprouting and embryogenesis. Experimental studies of single cell migration have been extensive.
Collective cell migration is less well investigated due to more difficult experimental conditions than for single cell migration. Especially, experimentally identifying the impact of individual differences in cell phenotypes on individual cell migration behavior inside cell populations is challenging because the tracking of individual cell trajectories is required.
In this thesis, a novel mathematical modeling approach, individual-based lattice-gas cellular automata (IB-LGCA), that allows to investigate the migratory behavior of individual cells inside migrating cell populations by enabling the tracking of individual cells is introduced. Additionally, stochastic differential equation (SDE) approximations of individual cell trajectories for IB-LGCA models are constructed. Such SDE approximations allow the analytical description of the trajectories of individual cells during single cell migration. For a complete analytical description of the trajectories of individual cell during collective cell migration the aforementioned SDE approximations alone are not sufficient. Analytical approximations of the time development of selected observables for the cell population have to be added.
What observables have to be considered depends on the specific cell migration mechanisms that is to be modeled. Here, partial integro-differential equations (PIDE) that approximate the time evolution of the expected cell density distribution in IB-LGCA are constructed and coupled to SDE approximations of individual cell trajectories. Such coupled PIDE and SDE approximations provide an analytical description of the trajectories of individual cells in IB-LGCA with density-dependent cell-cell interactions.
Finally, an IB-LGCA model and corresponding analytical approximations were applied to investigate the impact of changes in cell-cell and cell-ECM forces on the migration behavior of an individual, labeled cell inside a population of epithelial cells. Specifically, individual cell migration during the epithelial-mesenchymal transition (EMT) was considered. EMT is a change from epithelial to mesenchymal cell phenotype which is characterized by cells breaking adhesive bonds with surrounding epithelial cells and initiating individual migration along the extracellular matrix (ECM).
During the EMT, a transition from collective to single cell migration occurs. EMT plays an important role during cancer progression, where it is believed to be linked to metastasis development. In the IB-LGCA model epithelial cells are characterized by balanced cell-cell and cell-ECM forces. The IB-LGCA model predicts that the balance between cell-cell and cell-ECM forces can be disturbed to some degree without being accompanied by a change in individual cell migration behavior. Only after the cell force balance has been strongly interrupted mesenchymal migration behavior is possible. The force threshold which separates epithelial and mesenchymal migration behavior in the IB-LGCA has been identified from the corresponding analytical approximation. The IB-LGCA model allows to obtain quantitative predictions about the role of cell forces during EMT which in the context of mathematical modeling of EMT is a novel approach.
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Yang, Jie. "Prediction of combination efficacy in cancer therapy." Thesis, University of Manchester, 2013. https://www.research.manchester.ac.uk/portal/en/theses/prediction-of-combination-efficacy-in-cancer-therapy(1b49824b-9d5f-4d21-89d7-6160a810d05e).html.
Повний текст джерелаАнотація:
The cell cycle is an essential process in all living organisms that must be carefully regulated to ensure successful cell growth and division. Disregulation of the cell cycle is a key contributing factor towards the formation of cancerous cells. Understanding events at a cellular level is the first step towards comprehending how cancer manifests at an organismal level. Mathematical modelling can be used as a means of formalising and predicting the behaviour of the biological systems involved in cancer. In response, cell cycle models have been constructed to simulate and predict what happens to the mammalian cell over a time course in response to variable parameters.Current cell cycle models rarely account for certain precursors of cell growth such as energy usage and the need for non-essential amino acids as fundamental building blocks of macromolecules. Normal and cancer cell metabolism differ in the way they derive energy from glucose. In addition, normal and cancer cells also demonstrate different levels of gene expression. Two versions of a mammalian cell cycle and metabolism model, based on ordinary differential equations (ODEs) that respond to fluctuations in glucose concentration levels, have been developed here for the normal and cancer cell scenarios. Sensitivity analysis is performed for both normal and cancer cells using these cell cycle and metabolism models to investigate which kinetic reaction steps have a greater effect over the cell cycle period. Detailed analysis of the models and quantitatively assessing metabolite levels at various stages of the cell cycle may offer novel insights into how the glycolytic rate varies during the cell cycle for both normal and cancer cells.The results of the sensitivity analysis are used to identify potential drug targets in cancer therapy. Combinations of these individual targets are also investigated to compare the different effects of single and multiple drug compounds on the time it takes to complete a cell division cycle.
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Yates, Christian. "Comparing stochastic discrete and deterministic continuum models of cell migration." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:6f9cb70e-937c-441f-83c3-50e37e1cb420.
Повний текст джерелаАнотація:
Multiscale mathematical modelling is one of the major driving forces behind the systems biology revolution. The inherently interdisciplinary nature of its study and the multiple spatial and temporal scales which characterise its dynamics make cell migration an ideal candidate for a systems biology approach. Due to its ease of analysis and its compatibility with the type of data available, phenomenological continuum modelling has long been the default framework adopted by the cell migration modelling community. However, in recent years, with increased computational power, complex, discrete, cell-level models, able to capture the detailed dynamics of experimental systems, have become more prevalent. These two modelling paradigms have complementary advantages and disadvantages. The challenge now is to combine these two seemingly disparate modelling regimes in order to exploit the benefits offered by each in a comprehensive, multiscale equivalence framework for modelling cell migration. The main aim of this thesis is to begin with an on-lattice, individual-based model and derive a continuum, population-based model which is equivalent to it in certain limits. For simple models this is relatively easy to achieve: beginning with a one-dimensional, discrete model of cell migration on a regular lattice we derive a partial differential equation for the evolution of cell density on the same domain. We are also able to simply incorporate various signal sensing dynamics into our fledgling equivalence framework. However, as we begin to incorporate more complex model attributes such as cell proliferation/death, signalling dynamics and domain growth we find that deriving an equivalent continuum model requires some innovative mathematics. The same is true when considering a non-uniform domain discretisation in the one-dimensional model and when determining appropriate domain discretisations in higher dimensions. Higher-dimensional simulations of individual-based models bring with them their own computational challenges. Increased lattice sites in order to maintain spatial resolution and increased cell numbers in order to maintain consistent densities lead to dramatic reductions in simulation speeds. We consider a variety of methods to increase the efficiency of our simulations and derive novel acceleration techniques which can be applied to general reaction systems but are especially useful for our spatially extended cell migration algorithms. The incorporation of domain growth in higher dimensions is the final hurdle we clear on our way to constructing a complex discrete-continuum modelling framework capable of representing signal-mediated cell migration on growing (possibly non-standard) domains in multiple dimensions.
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Smith, Aaron. "Vertex model approaches to epithelial tissues in developmental systems." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:4d19f232-764c-4e27-bca9-d2ede0ec2db9.
Повний текст джерелаАнотація:
The purpose of this thesis is to develop a vertex model framework that can be used to perform computational experiments related to the dynamics of epithelial tissues in developmental systems. We focus on three example systems: the Drosophila wing imaginal disc, the Drosophila epidermis and the visceral endoderm of the mouse embryo. Within these systems, key questions pertaining to size-control mechanisms and coordination of cell migration remain unanswered and are amenable to computational testing. The vertex model presented here builds upon existing frameworks in three key ways. Firstly, we include novel force terms, representing, for example, the reaction of a cell to being compressed and its shape becoming distorted during a highly dynamic process such as cell migration. Secondly, we incorporate a model of diffusing morphogenetic growth factors within the vertex framework, using an arbitrary Lagrangian-Eulerian formulation of the diffusion equation and solving with the finite-element method (FEM). Finally, we implement the vertex model on the surface of an ellipsoid, in order to simulate cell migration in the mouse embryo. Throughout this thesis, we validate our model by running simple simulations. We demonstrate convergence properties of the FEM scheme and discuss how the time taken to solve the system scales with tissue size. The model is applied to biological systems and its utility demonstrated in several contexts. We show that when growth is dependent on morphogen concentration in the Drosophila wing disc, proliferation occurs preferentially in regions of high concentration. In the Drosophila epidermis, we show that a recently proposed mechanism of compartment size-control, in which a growth-factor is released in limited amounts, is viable. Finally, we examine the phenomenon of rosettes in the mouse embryo, which occur when five or more cells meet at a common vertex. We show, by running simulations both with and without rosettes, that they are crucial facilitators of ordered migration, and are thus critical in the patterning of the early embryo.
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Simms, Kate T. "Mathematical models of cell cycle progression : applications to breast cancer cell lines." Thesis, 2012. http://hdl.handle.net/2440/78608.
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The aim of this thesis is to develop mathematical models of cell cycle progression which can be used in conjunction with biological experiments. The thesis focusses on modelling processes which have biological relevance, and uses mathematics to investigate biological hypotheses about mechanisms which drive experimental results. In this thesis, we introduce a mathematical model of cell cycle progression and apply it to the MCF-7 breast cancer cell line. The model considers the three typical cell cycle phases, which we further break up into model phases in order to capture certain features such as cells remaining in phases for a minimum amount of time. This results in a unique system of delay differential equations which are solved numerically using MATLAB. The model is also able to capture a uniquely important part of the cell cycle, during which time cells are responsive to their environment. The model parameters are carefully chosen using data from various sources in the biological literature. The model is then validated against a variety of experiments, and the excellent fit with experimental results allows for insight into the mechanisms that influence observed biological phenomena. In particular, the model is used to question the common assumption that a ‘slow cycling population’ is necessary to explain some results. A model analysis is also performed, and used to discuss misconceptions in the literature regarding the average length of the cell cycle. An extension is developed, where cell death is included in order to accurately model the effects of tamoxifen, a common first line anticancer drug in breast cancer patients. We conclude that the model has strong potential to be used as an aid in future experiments to gain further insight into cell cycle progression and cell death. The model is then applied to the T47D cell line, which has significantly different cell
cycle kinetics to the MCF-7 cell line. The aim of modelling this cell line, which is naturally receptive to the effects of progestins, is to model the effects of progestins on cell cycle
progression. It is important to understand the effects of this substance, as it has been used in hormone replacement therapies, and its effects on cell cycle progression are still not understood. In order to understand how progestins influence cell cycle progression, a more detailed protein model is developed to get a better understanding of how progestin influences protein concentrations within a cell. We find that progestin effects on cell cycle progression are complex, and that progestin can be considered to be both a proliferative hormone and an anti-proliferative hormone, depending on the cell’s previous history of progestin exposure, and on the length of time the cells have been exposed to progestin. The fact that the timing of progestin exposure can have different effects on cell behaviour has profound implications for treatments that contain progestins, such as combined hormone replacement therapies. In summary, this thesis develops mathematical models representing different aspects of the cell cycle, and uses a variety of sources in the literature to parameterise the models. The model results are used to give insight into mechanisms that play a role in cell cycle progression under different experimental conditions. The models have the potential to be used alongside experiments, giving further insight into the mechanisms that influence events, such as cell cycle progression in the presence of hormones, as well as cell death.Thesis (Ph.D.) -- University of Adelaide, School of Mathematical Sciences, 2012
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Mente, Carsten. "Tracking of individual cell trajectories in LGCA models of migrating cell populations." Doctoral thesis, 2014. https://tud.qucosa.de/id/qucosa%3A28683.
Повний текст джерелаАнотація:
Cell migration, the active translocation of cells is involved in various biological processes, e.g. development of tissues and organs, tumor invasion and wound healing. Cell migration behavior can be divided into two distinct classes: single cell migration and collective cell migration. Single cell migration describes the migration of cells without interaction with other cells in their environment. Collective cell migration is the joint, active movement of multiple cells, e.g. in the form of strands, cohorts or sheets which emerge as the result of individual cell-cell interactions. Collective cell migration can be observed during branching morphogenesis, vascular sprouting and embryogenesis. Experimental studies of single cell migration have been extensive.
Collective cell migration is less well investigated due to more difficult experimental conditions than for single cell migration. Especially, experimentally identifying the impact of individual differences in cell phenotypes on individual cell migration behavior inside cell populations is challenging because the tracking of individual cell trajectories is required.
In this thesis, a novel mathematical modeling approach, individual-based lattice-gas cellular automata (IB-LGCA), that allows to investigate the migratory behavior of individual cells inside migrating cell populations by enabling the tracking of individual cells is introduced. Additionally, stochastic differential equation (SDE) approximations of individual cell trajectories for IB-LGCA models are constructed. Such SDE approximations allow the analytical description of the trajectories of individual cells during single cell migration. For a complete analytical description of the trajectories of individual cell during collective cell migration the aforementioned SDE approximations alone are not sufficient. Analytical approximations of the time development of selected observables for the cell population have to be added.
What observables have to be considered depends on the specific cell migration mechanisms that is to be modeled. Here, partial integro-differential equations (PIDE) that approximate the time evolution of the expected cell density distribution in IB-LGCA are constructed and coupled to SDE approximations of individual cell trajectories. Such coupled PIDE and SDE approximations provide an analytical description of the trajectories of individual cells in IB-LGCA with density-dependent cell-cell interactions.
Finally, an IB-LGCA model and corresponding analytical approximations were applied to investigate the impact of changes in cell-cell and cell-ECM forces on the migration behavior of an individual, labeled cell inside a population of epithelial cells. Specifically, individual cell migration during the epithelial-mesenchymal transition (EMT) was considered. EMT is a change from epithelial to mesenchymal cell phenotype which is characterized by cells breaking adhesive bonds with surrounding epithelial cells and initiating individual migration along the extracellular matrix (ECM).
During the EMT, a transition from collective to single cell migration occurs. EMT plays an important role during cancer progression, where it is believed to be linked to metastasis development. In the IB-LGCA model epithelial cells are characterized by balanced cell-cell and cell-ECM forces. The IB-LGCA model predicts that the balance between cell-cell and cell-ECM forces can be disturbed to some degree without being accompanied by a change in individual cell migration behavior. Only after the cell force balance has been strongly interrupted mesenchymal migration behavior is possible. The force threshold which separates epithelial and mesenchymal migration behavior in the IB-LGCA has been identified from the corresponding analytical approximation. The IB-LGCA model allows to obtain quantitative predictions about the role of cell forces during EMT which in the context of mathematical modeling of EMT is a novel approach.
Книги з теми "Cell cycle; mathematical models; differential equations"
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Avner, Friedman, and Aguda B, eds. Tutorials in mathematical biosciences. Berlin: Springer, 2006.
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Avner, Friedman, and Aguda B, eds. Cell cycle, proliferation, and cancer. Berlin: Springer, 2006.
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(Contributor), B. Aguda, M. Chaplain (Contributor), A. Friedman (Contributor), M. Kimmel (Contributor), H. A. Levine (Contributor), G. Lolas (Contributor), A. Matzavinos (Contributor), M. Nilsen-Hamilton (Contributor), A. Swierniak (Contributor), and Avner Friedman (Editor), eds. Tutorials in Mathematical Biosciences III: Cell Cycle, Proliferation, and Cancer (Lecture Notes in Mathematics / Mathematical Biosciences Subseries). Springer, 2006.
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Thames, Howard D. "Mathematical Models of Dose and Cell Cycle Effects in Multifraction Radiotherapy." In Modeling and Differential Equations in Biology, 51–105. Routledge, 2017. http://dx.doi.org/10.1201/9780203746912-3.
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Benkahla, Alia, Lamia Guizani-Tabbane, Ines Abdeljaoued-Tej, Slimane Ben Miled, and Koussay Dellagi. "Systems Biology and Infectious Diseases." In Handbook of Research on Systems Biology Applications in Medicine, 377–402. IGI Global, 2009. http://dx.doi.org/10.4018/978-1-60566-076-9.ch023.
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This chapter reports a variety of molecular biology informatics and mathematical methods that model the cell response to pathogens. The authors first outline the main steps of the immune response, then list the high throughput biotechnologies, generating a wealth of information on the infected cell and some of the immune-related databases; and finally explain how to extract meaningful information from these sources. The modelling aspect is divided into modelling molecular interaction and regulatory networks, through dynamic Boolean and Bayesian models, and modelling biochemical networks and regulatory networks, through Differential/Difference Equations. The interdisciplinary approach explains how to construct a model that mimics the cell’s dynamics and can predict the evolution and the outcome of infection.
Тези доповідей конференцій з теми "Cell cycle; mathematical models; differential equations"
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Segalman, Daniel J., and Michael J. Starr. "Iwan Models and Their Provenance." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-71534.
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Iwan models have had some exposure recently in modeling the nonlinear response of individual joints. This popularity can be ascribed to their mathematical simplicity, their versatility, and their ability to capture the important responses of mechanical joints under unidirectional loads. There is a lot of history to this category of model. Masing explored kinematic hardening of metals with a model consisting of ten Jenkins elements in series. Soon after, Prandtl explored the behavior of a continuous distribution of such elements. Ishlinskii explored the mathematical structure of such continuous distributions. Much more recently, Iwan demonstrated practical application of such models in capturing various sorts of metal plasticity. Among the features that make such models interesting is a simple relationship between the asymptotic nature of the integral kernel at small values and the power-law relation between force amplitude and dissipation per cycle in harmonic loading. Iwan provided several differential equations for deducing the kernel from force-displacement relations. Segalman and Starr devised methods for deducing kernels from force-displacement curves of arbitrary Masing models. This is illustrated to generate a BPII model equivalent to the Ramberg-Osgood plasticity model. The Segalman-Starr relationship is used to find relationships among several other plasticity models.
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Ševček, Tomáš. "The Fractional-Order Goodwin Accelerator Model." In EDAMBA 2021 : 24th International Scientific Conference for Doctoral Students and Post-Doctoral Scholars. University of Economics in Bratislava, 2022. http://dx.doi.org/10.53465/edamba.2021.9788022549301.476-486.
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The accelerator model proposed by Goodwin in 1951 is one of the pioneering nonlinear mathematical models of the business cycle. It has been studied in three different mathematical formulations, namely as a first-order delay differential equation, as a second-order ordinary differential equation and as a dynamical system of two first-order ordinary differential equations. All these formulations exhibit chaotic behavior. In this article, we analyze a fractionalorder dynamical system of a specific form of the generalized dynamical system originating from the Goodwin accelerator model. We examine the steady-state stability of the commensurate as well as the incommensurate nonperturbed system. Subsequently, a numerical analysis of both the perturbed and the nonperturbed fractional-order system is conducted. Our main finding is that the incorporation of memory (or expectations) in the model can lead to local asymptotic stability of its equilibria and to less chaotic behavior. This can prove beneficial in modeling economic phenomena which are heavily dependent upon their past states.
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Sensoy, Tugba S., Sam Yang, and Juan C. Ordonez. "Volume Element Model for Modeling, Simulation, and Optimization of Parabolic Trough Solar Collectors." In ASME 2017 11th International Conference on Energy Sustainability collocated with the ASME 2017 Power Conference Joint With ICOPE-17, the ASME 2017 15th International Conference on Fuel Cell Science, Engineering and Technology, and the ASME 2017 Nuclear Forum. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/es2017-3597.
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In this paper we present a dynamic three-dimensional volume element model (VEM) of a parabolic trough solar collector (PTC) comprising an outer glass cover, annular space, absorber tube, and heat transfer fluid. The spatial domain in the VEM is discretized with lumped control volumes (i.e., volume elements) in cylindrical coordinates according to the predefined collector geometry; therefore, the spatial dependency of the model is taken into account without the need to solve partial differential equations. The proposed model combines principles of thermodynamics and heat transfer, along with empirical heat transfer correlations, to simplify the modeling and expedite the computations. The resulting system of ordinary differential equations is integrated in time, yielding temperature fields which can be visualized and assessed with scientific visualization tools. In addition to the mathematical formulation, we present the model validation using the experimental data provided in the literature, and conduct two simple case studies to investigate the collector performance as a function of annulus pressure for different gases as well as its dynamic behavior throughout a sunny day. The proposed model also exhibits computational advantages over conventional PTC models-the model has been written in Fortran with parallel computing capabilities. In summary, we elaborate the unique features of the proposed model coupled with enhanced computational characteristics, and demonstrate its suitability for future simulation and optimization of parabolic trough solar collectors.
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Listenbee, Ryan, Kwangkook Jeong, and Roy McCann. "Integrated Computational and Experimental Framework on Advanced Flow Battery for Renewable Power Plant Applications." In ASME 2014 8th International Conference on Energy Sustainability collocated with the ASME 2014 12th International Conference on Fuel Cell Science, Engineering and Technology. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/es2014-6501.
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A study has been conducted to develop advanced vanadium redox flow battery (VRFB) for renewable energy storage applications using integrated computational and experimental framework. Analytical modeling has been performed to predict electrical outputs based on combined approach including fluid mechanics, electrochemistry, and electric circuit. A lab-scale experimental setup has been designed and built to validate the modeling results. The VRFB project has been collaborated between Arkansas State University Jonesboro and University of Arkansas Fayetteville to focus on pin pointing the transient characteristics of the vanadium redox flow battery in terms of chemical reaction, fluid flow, and electric circuit by obtaining exact solutions from the associated governing differential equations using a numerical approach. To obtain comparable experimental data, a test bed made of two half cells is constructed and joined together by a permeable membrane designed to facilitate ion transfer between two separate vanadium electrolytes, and then the system will be scaled up to multiple cell stacks. This research aims to better understand the transient characteristics of the VRFB in order to refine the system in hopes of improving efficiency. In turn alternative energy such as multi megawatt wind and solar farms should gain more support as the ability to store energy becomes more reliable and economically feasible. This paper will focus on the steps taken to validate the supporting mathematical models, and the preliminary results of the tests conducted using the VRFB test bed. Future work will be addressed to develop a pilot-scale VRFB with enhanced efficiency and temperature limits.