Relevant bibliographies by topics / Cell Division - Stochastic Simulation

Academic literature on the topic 'Cell Division - Stochastic Simulation'

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Published: 7 September 2023

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Journal articles on the topic "Cell Division - Stochastic Simulation"

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Van Segbroeck, Sven, Ann Nowé, and Tom Lenaerts. "Stochastic Simulation of the Chemoton." Artificial Life 15, no. 2 (April 2009): 213–26. http://dx.doi.org/10.1162/artl.2009.15.2.15203.

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Gánti's chemoton model is an illustrious example of a minimal cell model. It is composed of three stoichiometrically coupled autocatalytic subsystems: a metabolism, a template replication process, and a membrane enclosing the other two. Earlier studies on chemoton dynamics yield inconsistent results. Furthermore, they all appealed to deterministic simulations, which do not take into account the stochastic effects induced by small population sizes. We present, for the first time, results of a chemoton simulation in which these stochastic effects have been taken into account. We investigate the dynamics of the system and analyze in depth the mechanisms responsible for the observed behavior. Our results suggest that, in contrast to the most recent study by Munteanu and Solé, the stochastic chemoton reaches a unique stable division time after a short transient phase. We confirm the existence of an optimal template length and show that this is a consequence of the monomer concentration, which depends on the template length and the initiation threshold. Since longer templates imply shorter division times, these results motivate the selective pressure toward longer templates observed in nature.
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Charlebois, Daniel A., Jukka Intosalmi, Dawn Fraser, and Mads Kærn. "An Algorithm for the Stochastic Simulation of Gene Expression and Heterogeneous Population Dynamics." Communications in Computational Physics 9, no. 1 (January 2011): 89–112. http://dx.doi.org/10.4208/cicp.280110.070510a.

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AbstractWe present an algorithm for the stochastic simulation of gene expression and heterogeneous population dynamics. The algorithm combines an exact method to simulate molecular-level fluctuations in single cells and a constant-number Monte Carlo method to simulate time-dependent statistical characteristics of growing cell populations. To benchmark performance, we compare simulation results with steady-state and time-dependent analytical solutions for several scenarios, including steady-state and time-dependent gene expression, and the effects on population heterogeneity of cell growth, division, and DNA replication. This comparison demonstrates that the algorithm provides an efficient and accurate approach to simulate how complex biological features influence gene expression. We also use the algorithm to model gene expression dynamics within “bet-hedging” cell populations during their adaption to environmental stress. These simulations indicate that the algorithm provides a framework suitable for simulating and analyzing realistic models of heterogeneous population dynamics combining molecular-level stochastic reaction kinetics, relevant physiological details and phenotypic variability.
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Thomas, Philipp, and Vahid Shahrezaei. "Coordination of gene expression noise with cell size: analytical results for agent-based models of growing cell populations." Journal of The Royal Society Interface 18, no. 178 (May 2021): 20210274. http://dx.doi.org/10.1098/rsif.2021.0274.

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The chemical master equation and the Gillespie algorithm are widely used to model the reaction kinetics inside living cells. It is thereby assumed that cell growth and division can be modelled through effective dilution reactions and extrinsic noise sources. We here re-examine these paradigms through developing an analytical agent-based framework of growing and dividing cells accompanied by an exact simulation algorithm, which allows us to quantify the dynamics of virtually any intracellular reaction network affected by stochastic cell size control and division noise. We find that the solution of the chemical master equation—including static extrinsic noise—exactly agrees with the agent-based formulation when the network under study exhibits stochastic concentration homeostasis , a novel condition that generalizes concentration homeostasis in deterministic systems to higher order moments and distributions. We illustrate stochastic concentration homeostasis for a range of common gene expression networks. When this condition is not met, we demonstrate by extending the linear noise approximation to agent-based models that the dependence of gene expression noise on cell size can qualitatively deviate from the chemical master equation. Surprisingly, the total noise of the agent-based approach can still be well approximated by extrinsic noise models.
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Wen, Kunwen, Lifang Huang, Qi Wang, and Jianshe Yu. "Modulation of first-passage time for gene expression via asymmetric cell division." International Journal of Biomathematics 12, no. 05 (July 2019): 1950052. http://dx.doi.org/10.1142/s1793524519500529.

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How to balance the size of exponentially growing cells has always been a focus of biologists. Recent experiments have uncovered that the cell is divided into two daughter cells only when the level of time-keeper protein reaches a fixed threshold and cell division in prokaryote is not completely symmetric. The timing of cell division is essentially random because gene expression is stochastic, but cells seen to manage to have precise timing of cell division events. Although the inter-cellular variability of gene expression has attracted much attention, the randomness of event timing has been rarely studied. In our analysis, the timing of cell division is formulated as the first-passage time (denoted by FPT) for time-keeper protein’s level to cross a critical threshold firstly, we derive exact analytical formulae for the mean and noise of FPT based on stochastic gene expression model with asymmetric cell division. The results of numerical simulation show that the regulatory factors (division rate, newborn cell size, exponential growth rate and threshold) have significant influence on the mean and noise of FPT. We also show that both the increase of division rate and newborn cell size could reduce the mean of FPT and increase the noise of FPT, the larger the exponential growth rate is, the smaller the mean and noise of FPT will be; and the larger the threshold value is, the higher the mean of FPT is and the lower the noise is. In addition, compared with symmetric division, asymmetric division can reduce the mean of FPT and improve the noise of FPT. In summary, our results provide insight into the relationship between regulatory factors and FPT and reveal that asymmetric division is an effective mechanism to shorten the mean of FPT.
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Genthon, Arthur, Reinaldo García-García, and David Lacoste. "Branching processes with resetting as a model for cell division." Journal of Physics A: Mathematical and Theoretical 55, no. 7 (January 26, 2022): 074001. http://dx.doi.org/10.1088/1751-8121/ac491a.

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Abstract We study the stochastic thermodynamics of cell growth and division using a theoretical framework based on branching processes with resetting. Cell division may be split into two sub-processes: branching, by which a given cell gives birth to an identical copy of itself, and resetting, by which some properties of the daughter cells (such as their size or age) are reset to new values following division. We derive the first and second laws of stochastic thermodynamics for this process, and identify separate contributions due to branching and resetting. We apply our framework to well-known models of cell size control, such as the sizer, the timer, and the adder. We show that the entropy production of resetting is negative and that of branching is positive for these models in the regime of exponential growth of the colony. This property suggests an analogy between our model for cell growth and division and heat engines, and the introduction of a thermodynamic efficiency, which quantifies the conversion of one form of entropy production to another.
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Wang, Qi, Lifang Huang, Kunwen Wen, and Jianshe Yu. "The mean and noise of stochastic gene transcription with cell division." Mathematical Biosciences & Engineering 15, no. 5 (2018): 1255–70. http://dx.doi.org/10.3934/mbe.2018058.

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Ji, Xiangrui, and Jie Lin. "Implications of differential size-scaling of cell-cycle regulators on cell size homeostasis." PLOS Computational Biology 19, no. 7 (July 28, 2023): e1011336. http://dx.doi.org/10.1371/journal.pcbi.1011336.

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Accurate timing of division and size homeostasis is crucial for cells. A potential mechanism for cells to decide the timing of division is the differential scaling of regulatory protein copy numbers with cell size. However, it remains unclear whether such a mechanism can lead to robust growth and division, and how the scaling behaviors of regulatory proteins influence the cell size distribution. Here we study a mathematical model combining gene expression and cell growth, in which the cell-cycle activators scale superlinearly with cell size while the inhibitors scale sublinearly. The cell divides once the ratio of their concentrations reaches a threshold value. We find that the cell can robustly grow and divide within a finite range of the threshold value with the cell size proportional to the ploidy. In a stochastic version of the model, the cell size at division is uncorrelated with that at birth. Also, the more differential the cell-size scaling of the cell-cycle regulators is, the narrower the cell-size distribution is. Intriguingly, our model with multiple regulators rationalizes the observation that after the deletion of a single regulator, the coefficient of variation of cell size remains roughly the same though the average cell size changes significantly. Our work reveals that the differential scaling of cell-cycle regulators provides a robust mechanism of cell size control.
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Pham, Huy, Emile R. Shehada, Shawna Stahlheber, Kushagra Pandey, and Wayne B. Hayes. "No Cell Left behind: Automated, Stochastic, Physics-Based Tracking of Every Cell in a Dense, Growing Colony." Algorithms 15, no. 2 (January 30, 2022): 51. http://dx.doi.org/10.3390/a15020051.

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Motivation: Precise tracking of individual cells—especially tracking the family lineage, for example in a developing embryo—has widespread applications in biology and medicine. Due to significant noise in microscope images, existing methods have difficulty precisely tracking cell activities. These difficulties often require human intervention to resolve. Humans are helpful because our brain naturally and automatically builds a simulation “model” of any scene that we observe. Because we understand simple truths about the world—for example cells can move and divide, but they cannot instantaneously move vast distances—this model “in our heads” helps us to severely constrain the possible interpretations of what we see, allowing us to easily distinguish signal from noise, and track the motion of cells even in the presence of extreme levels of noise that would completely confound existing automated methods. Results: Here, we mimic the ability of the human brain by building an explicit computer simulation model of the scene. Our simulated cells are programmed to allow movement and cell division consistent with reality. At each video frame, we stochastically generate millions of nearby “Universes” and evolve them stochastically to the next frame. We then find and fit the best universes to reality by minimizing the residual between the real image frame and a synthetic image of the simulation. The rule-based simulation puts extremely stringent constraints on possible interpretations of the data, allowing our system to perform far better than existing methods even in the presense of extreme levels of image noise. We demonstrate the viability of this method by accurately tracking every cell in a colony that grows from 4 to over 300 individuals, doing about as well as a human can in the difficult task of tracking cell lineages.
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Barizien, A., M. S. Suryateja Jammalamadaka, G. Amselem, and Charles N. Baroud. "Growing from a few cells: combined effects of initial stochasticity and cell-to-cell variability." Journal of The Royal Society Interface 16, no. 153 (April 24, 2019): 20180935. http://dx.doi.org/10.1098/rsif.2018.0935.

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The growth of a cell population from a large inoculum appears deterministic, although the division process is stochastic at the single-cell level. Microfluidic observations, however, display wide variations in the growth of small populations. Here we combine theory, simulations and experiments to explore the link between single-cell stochasticity and the growth of a population starting from a small number of individuals. The study yields descriptors of the probability distribution function (PDF) of the population size under three sources of stochasticity: cell-to-cell variability, uncertainty in the number of initial cells and generation-dependent division times. The PDF, rescaled to account for the exponential growth of the population, is found to converge to a stationary distribution. All moments of the PDF grow exponentially with the same growth rate, which depends solely on cell-to-cell variability. The shape of the PDF, however, contains the signature of all sources of stochasticity, and is dominated by the early stages of growth, and not by the cell-to-cell variability. Thus, probabilistic predictions of the growth of bacterial populations can be obtained with implications for both naturally occurring conditions and technological applications of single-cell microfluidics.
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Baptista, Ines S. C., and Andre S. Ribeiro. "Stochastic models coupling gene expression and partitioning in cell division in Escherichia coli." Biosystems 193-194 (June 2020): 104154. http://dx.doi.org/10.1016/j.biosystems.2020.104154.

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Dissertations / Theses on the topic "Cell Division - Stochastic Simulation"

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Morton-Firth, Carl Jason. "Stochastic simulation of cell signalling pathways." Thesis, University of Cambridge, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.625063.

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

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Modelling and simulation are essential to modern research in cell biology. This thesis follows a journey starting from the construction of new stochastic methods for discrete biochemical systems to using them to simulate a population of interacting haematopoietic stem cell lineages. The first part of this thesis is on discrete stochastic methods. We develop two new methods, the stochastic extrapolation framework and the Stochastic Bulirsch-Stoer methods. These are based on the Richardson extrapolation technique, which is widely used in ordinary differential equation solvers. We believed that it would also be useful in the stochastic regime, and this turned out to be true. The stochastic extrapolation framework is a scheme that admits any stochastic method with a fixed stepsize and known global error expansion. It can improve the weak order of the moments of these methods by cancelling the leading terms in the global error. Using numerical simulations, we demonstrate that this is the case up to second order, and postulate that this also follows for higher order. Our simulations show that extrapolation can greatly improve the accuracy of a numerical method. The Stochastic Bulirsch-Stoer method is another highly accurate stochastic solver. Furthermore, using numerical simulations we find that it is able to better retain its high accuracy for larger timesteps than competing methods, meaning it remains accurate even when simulation time is speeded up. This is a useful property for simulating the complex systems that researchers are often interested in today. The second part of the thesis is concerned with modelling a haematopoietic stem cell system, which consists of many interacting niche lineages. We use a vectorised tau-leap method to examine the differences between a deterministic and a stochastic model of the system, and investigate how coupling niche lineages affects the dynamics of the system at the homeostatic state as well as after a perturbation. We find that larger coupling allows the system to find the optimal steady state blood cell levels. In addition, when the perturbation is applied randomly to the entire system, larger coupling also results in smaller post-perturbation cell fluctuations compared to non-coupled cells. In brief, this thesis contains four main sets of contributions: two new high-accuracy discrete stochastic methods that have been numerically tested, an improvement that can be used with any leaping method that introduces vectorisation as well as how to use a common stepsize adapting scheme, and an investigation of the effects of coupling lineages in a heterogeneous population of haematopoietic stem cell niche lineages.
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Chen, Minghan. "Stochastic Modeling and Simulation of Multiscale Biochemical Systems." Diss., Virginia Tech, 2019. http://hdl.handle.net/10919/90898.

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Numerous challenges arise in modeling and simulation as biochemical networks are discovered with increasing complexities and unknown mechanisms. With the improvement in experimental techniques, biologists are able to quantify genes and proteins and their dynamics in a single cell, which calls for quantitative stochastic models for gene and protein networks at cellular levels that match well with the data and account for cellular noise. This dissertation studies a stochastic spatiotemporal model of the Caulobacter crescentus cell cycle. A two-dimensional model based on a Turing mechanism is investigated to illustrate the bipolar localization of the protein PopZ. However, stochastic simulations are often impeded by expensive computational cost for large and complex biochemical networks. The hybrid stochastic simulation algorithm is a combination of differential equations for traditional deterministic models and Gillespie's algorithm (SSA) for stochastic models. The hybrid method can significantly improve the efficiency of stochastic simulations for biochemical networks with multiscale features, which contain both species populations and reaction rates with widely varying magnitude. The populations of some reactant species might be driven negative if they are involved in both deterministic and stochastic systems. This dissertation investigates the negativity problem of the hybrid method, proposes several remedies, and tests them with several models including a realistic biological system. As a key factor that affects the quality of biological models, parameter estimation in stochastic models is challenging because the amount of empirical data must be large enough to obtain statistically valid parameter estimates. To optimize system parameters, a quasi-Newton algorithm for stochastic optimization (QNSTOP) was studied and applied to a stochastic budding yeast cell cycle model by matching multivariate probability distributions between simulated results and empirical data. Furthermore, to reduce model complexity, this dissertation simplifies the fundamental cooperative binding mechanism by a stochastic Hill equation model with optimized system parameters. Considering that many parameter vectors generate similar system dynamics and results, this dissertation proposes a general α-β-γ rule to return an acceptable parameter region of the stochastic Hill equation based on QNSTOP. Different objective functions are explored targeting different features of the empirical data.
Doctor of Philosophy
Modeling and simulation of biochemical networks faces numerous challenges as biochemical networks are discovered with increased complexity and unknown mechanisms. With improvement in experimental techniques, biologists are able to quantify genes and proteins and their dynamics in a single cell, which calls for quantitative stochastic models, or numerical models based on probability distributions, for gene and protein networks at cellular levels that match well with the data and account for randomness. This dissertation studies a stochastic model in space and time of a bacterium’s life cycle— Caulobacter. A two-dimensional model based on a natural pattern mechanism is investigated to illustrate the changes in space and time of a key protein population. However, stochastic simulations are often complicated by the expensive computational cost for large and sophisticated biochemical networks. The hybrid stochastic simulation algorithm is a combination of traditional deterministic models, or analytical models with a single output for a given input, and stochastic models. The hybrid method can significantly improve the efficiency of stochastic simulations for biochemical networks that contain both species populations and reaction rates with widely varying magnitude. The populations of some species may become negative in the simulation under some circumstances. This dissertation investigates negative population estimates from the hybrid method, proposes several remedies, and tests them with several cases including a realistic biological system. As a key factor that affects the quality of biological models, parameter estimation in stochastic models is challenging because the amount of observed data must be large enough to obtain valid results. To optimize system parameters, the quasi-Newton algorithm for stochastic optimization (QNSTOP) was studied and applied to a stochastic (budding) yeast life cycle model by matching different distributions between simulated results and observed data. Furthermore, to reduce model complexity, this dissertation simplifies the fundamental molecular binding mechanism by the stochastic Hill equation model with optimized system parameters. Considering that many parameter vectors generate similar system dynamics and results, this dissertation proposes a general α-β-γ rule to return an acceptable parameter region of the stochastic Hill equation based on QNSTOP. Different optimization strategies are explored targeting different features of the observed data.
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Biehler, Eike [Verfasser], Werner [Akademischer Betreuer] Nagel, and Richard [Akademischer Betreuer] Cowan. "Cell division processes in tessellations : a stochastic geometry approach / Eike Biehler. Gutachter: Werner Nagel ; Richard Cowan." Jena : Thüringer Universitäts- und Landesbibliothek Jena, 2012. http://d-nb.info/1029294216/34.

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Ahmadian, Mansooreh. "Hybrid Modeling and Simulation of Stochastic Effects on Biochemical Regulatory Networks." Diss., Virginia Tech, 2020. http://hdl.handle.net/10919/99481.

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A complex network of genes and proteins governs the robust progression through cell cycles in the presence of inevitable noise. Stochastic modeling is viewed as a key paradigm to study the effects of intrinsic and extrinsic noise on the dynamics of biochemical networks. A detailed quantitative description of such complex and multiscale networks via stochastic modeling poses several challenges. First, stochastic models generally require extensive computations, particularly when applied to large networks. Second, the accuracy of stochastic models is highly dependent on the quality of the parameter estimation based on experimental observations. The goal of this dissertation is to address these problems by developing new efficient methods for modeling and simulation of stochastic effects in biochemical systems. Particularly, a hybrid stochastic model is developed to represent a detailed molecular mechanism of cell cycle control in budding yeast cells. In a single multiscale model, the proposed hybrid approach combines the advantages of two regimes: 1) the computational efficiency of a deterministic approach, and 2) the accuracy of stochastic simulations. The results show that this hybrid stochastic model achieves high computational efficiency while generating simulation results that match very well with published experimental measurements. Furthermore, a new hierarchical deep classification (HDC) algorithm is developed to address the parameter estimation problem in a monomolecular system. The HDC algorithm adopts a neural network that, via multiple hierarchical search steps, finds reasonably accurate ranges for the model parameters. To train the neural network in the presence of experimental data scarcity, the proposed method leverages the domain knowledge from stochastic simulations to generate labeled training data. The results show that the proposed HDC algorithm yields accurate ranges for the model parameters and highlight the potentials of model-free learning for parameter estimation in stochastic modeling of complex biochemical networks.
Doctor of Philosophy
Cell cycle is a process in which a growing cell replicates its DNA and divides into two cells. Progression through the cell cycle is regulated by complex interactions between networks of genes, transcripts, and proteins. These interactions inside the confined volume of a cell are subject to inherent noise. To provide a quantitative description of the cell cycle, several deterministic and stochastic models have been developed. However, deterministic models cannot capture the intrinsic noise. In addition, stochastic modeling poses the following challenges. First, stochastic models generally require extensive computations, particularly when applied to large networks. Second, the accuracy of stochastic models is highly dependent on the accuracy of the estimated model parameters. The goal of this dissertation is to address these challenges by developing new efficient methods for modeling and simulation of stochastic effects in biochemical networks. The results show that the proposed hybrid model that combines stochastic and deterministic modeling approaches can achieve high computational efficiency while generating accurate simulation results. Moreover, a new machine learning-based method is developed to address the parameter estimation problem in biochemical systems. The results show that the proposed method yields accurate ranges for the model parameters and highlight the potentials of model-free learning for parameter estimation in stochastic modeling of complex biochemical networks.
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Charlebois, Daniel A. "An algorithm for the stochastic simulation of gene expression and cell population dynamics." Thesis, University of Ottawa (Canada), 2010. http://hdl.handle.net/10393/28755.

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Over the past few years, it has been increasingly recognized that stochastic mechanisms play a key role in the dynamics of biological systems. Genetic networks are one example where molecular-level fluctuations are of particular importance. Here stochasticity in the expression of gene products can result in genetically identical cells in the same environment displaying significant variation in biochemical or physical attributes. This variation can influence individual and population-level fitness. In this thesis we first explore the background required to obtain analytical solutions and perform simulations of stochastic models of gene expression. Then we develop an algorithm for the stochastic simulation of gene expression and heterogeneous cell population dynamics. The algorithm combines an exact method to simulate molecular-level fluctuations in single cells and a constant-number Monte Carlo approach to simulate the statistical characteristics of growing cell populations. This approach permits biologically realistic and computationally feasible simulations of environment and time-dependent cell population dynamics. The algorithm is benchmarked against steady-state and time-dependent analytical solutions of gene expression models, including scenarios when cell growth, division, and DNA replication are incorporated into the modelling framework. Furthermore, using the algorithm we obtain the steady-state cell size distribution of a large cell population, grown from a small initial cell population undergoing stochastic and asymmetric division, to the size distribution of a small representative sample of this population simulated to steady-state. These comparisons demonstrate that the algorithm provides an accurate and efficient approach to modelling the effects of complex biological features on gene expression dynamics. The algorithm is also employed to simulate expression dynamics within 'bet-hedging' cell populations during their adaption to environmental stress. These simulations indicate that the cell population dynamics algorithm provides a framework suitable for simulating and analyzing realistic models of heterogeneous population dynamics combining molecular-level stochastic reaction kinetics, relevant physiological details, and phenotypic variability and fitness.
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Wang, Shuo. "Analysis and Application of Haseltine and Rawlings's Hybrid Stochastic Simulation Algorithm." Diss., Virginia Tech, 2016. http://hdl.handle.net/10919/82717.

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Stochastic effects in cellular systems are usually modeled and simulated with Gillespie's stochastic simulation algorithm (SSA), which follows the same theoretical derivation as the chemical master equation (CME), but the low efficiency of SSA limits its application to large chemical networks. To improve efficiency of stochastic simulations, Haseltine and Rawlings proposed a hybrid of ODE and SSA algorithm, which combines ordinary differential equations (ODEs) for traditional deterministic models and SSA for stochastic models. In this dissertation, accuracy analysis, efficient implementation strategies, and application of of Haseltine and Rawlings's hybrid method (HR) to a budding yeast cell cycle model are discussed. Accuracy of the hybrid method HR is studied based on a linear chain reaction system, motivated from the modeling practice used for the budding yeast cell cycle control mechanism. Mathematical analysis and numerical results both show that the hybrid method HR is accurate if either numbers of molecules of reactants in fast reactions are above certain thresholds, or rate constants of fast reactions are much larger than rate constants of slow reactions. Our analysis also shows that the hybrid method HR allows for a much greater region in system parameter space than those for the slow scale SSA (ssSSA) and the stochastic quasi steady state assumption (SQSSA) method. Implementation of the hybrid method HR requires a stiff ODE solver for numerical integration and an efficient event-handling strategy for slow reaction firings. In this dissertation, an event-handling strategy is developed based on inverse interpolation. Performances of five wildly used stiff ODE solvers are measured in three numerical experiments. Furthermore, inspired by the strategy of the hybrid method HR, a hybrid of ODE and SSA stochastic models for the budding yeast cell cycle is developed, based on a deterministic model in the literature. Simulation results of this hybrid model match very well with biological experimental data, and this model is the first to do so with these recently available experimental data. This study demonstrates that the hybrid method HR has great potential for stochastic modeling and simulation of large biochemical networks.
Ph. D.
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Joubaud, Maud. "Processus de Markov déterministes par morceaux branchants et problème d’arrêt optimal, application à la division cellulaire." Thesis, Montpellier, 2019. http://www.theses.fr/2019MONTS031/document.

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Les processus markoviens déterministes par morceaux (PDMP) forment une vaste classe de processus stochastiques caractérisés par une évolution déterministe entre des sauts à mécanisme aléatoire. Ce sont des processus de type hybride, avec une composante discrète de mode et une composante d’état qui évolue dans un espace continu. Entre les sauts du processus, la composante continue évolue de façon déterministe, puis au moment du saut un noyau markovien sélectionne la nouvelle valeur des composantes discrète et continue. Dans cette thèse, nous construisons des PDMP évoluant dans des espaces de mesures (de dimension infinie), pour modéliser des population de cellules en tenant compte des caractéristiques individuelles de chaque cellule. Nous exposons notre construction des PDMP sur des espaces de mesure, et nous établissons leur caractère markovien. Sur ces processus à valeur mesure, nous étudions un problème d'arrêt optimal. Un problème d'arrêt optimal revient à choisir le meilleur temps d'arrêt pour optimiser l'espérance d'une certaine fonctionnelle de notre processus, ce qu'on appelle fonction valeur. On montre que cette fonction valeur est solution des équations de programmation dynamique et on construit une famille de temps d'arrêt $epsilon$-optimaux. Dans un second temps, nous nous intéressons à un PDMP en dimension finie, le TCP, pour lequel on construit un schéma d'Euler afin de l'approcher. Ce choix de modèle simple permet d'estimer différents types d'erreurs. Nous présentons des simulations numériques illustrant les résultats obtenus
Piecewise deterministic Markov processes (PDMP) form a large class of stochastic processes characterized by a deterministic evolution between random jumps. They fall into the class of hybrid processes with a discrete mode and an Euclidean component (called the state variable). Between the jumps, the continuous component evolves deterministically, then a jump occurs and a Markov kernel selects the new value of the discrete and continuous components. In this thesis, we extend the construction of PDMPs to state variables taking values in some measure spaces with infinite dimension. The aim is to model cells populations keeping track of the information about each cell. We study our measured-valued PDMP and we show their Markov property. With thoses processes, we study a optimal stopping problem. The goal of an optimal stopping problem is to find the best admissible stopping time in order to optimize some function of our process. We show that the value fonction can be recursively constructed using dynamic programming equations. We construct some $epsilon$-optimal stopping times for our optimal stopping problem. Then, we study a simple finite-dimension real-valued PDMP, the TCP process. We use Euler scheme to approximate it, and we estimate some types of errors. We illustrate the results with numerical simulations
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Dao, Duc Khanh. "Modeling and analysis of neuronal networks, stochastic chemical reactions in cellular micro-domains and telomere dynamics." Paris 6, 2013. http://www.theses.fr/2013PA066513.

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Nous modélisons différents évènements aléatoires intervenant en biologie. Dans une première partie, on étudie certaines propriétés de populations de neurones. En utilisant un modèle de facilitation dépression synaptique, on étudie le phénomène de bursts synchrones observés à différentes échelles de populations. On étudie ensuite la transition entre état haut et bas de neurones induite par le bruit. Afin de comprendre le phénomène d’oscillations du temps de séjour dans l’état haut, onétudie le problème de premier temps de passage pour une classe de processus stochastiquesdans un domaine avec un attracteur situé près d’un cycle limite. On construit une classede systèmes conjugués à celui de Hopf que l’on étudie via les méthodes d’approximations WKB et couche limite. On s’intéresse enfin aux interactions entre neurones et astrocytes, et plus spécifiquement à l’intégration du potassium. En introduisant un modèle à trois compartiments, on simule les dynamiques du potassium pour différents protocoles de stimulations pour déterminer comment les canaux astrocytaires influencent la neurotransmission. Dans une deuxième partie, on s’intéresse au temps d’atteinte d’un seuil pour des réactions. Les méthodes introduites sont ensuite utilisées pour étudier le contrôle du fuseau mitotique et la régulation posttranscriptionnellede l’expression génétique dans le noyau et le cytoplasme. Dans la troisième partie, on modélise la dynamique stochastique des longueurs de télomères après chaque division cellulaire. En étudiant le processus de drift et saut associé, on prédit la distribution stationnaire ainsi que la longueur du télomère le plus court d’une cellule
In this PhD, we model specific stochastic events occurring in different biological contexts. In the first part, we study three different properties of neural networks. Using a mean field facilitation-depression synaptic model, we unravel the synchronous long lasting bursting observed at various scales of neural populations. Next, we study the neuronal noise induced transition between Up& Down states. To study the oscillatory peaks of the time spent in Up state, we consider the exit problem for a class of stochastic processes in a domain with an attractor located close to a limit cycle. We construct a class of systems conjugate to the Hopf bifurcation system that we study using WKB approximation and boundary layer analysis. We finally focus on neuroglial interactions and more specifically on astrocytic potassium. Using a tri-compartment model, we simulate the potassium dynamics for different stimulation protocols and we determine how astrocytic channels can influence neurotransmission. In the second part, we focus on the threshold activation for stochastic chemical reactions in cellular micro-domains. We compute the probability and the mean first time to reach a threshold for different reactions. The methods are applied to study the mitotic spindle checkpoint and the problem of gene expression and post-transcriptional regulation. The third part is finally dedicated to the stochastic dynamics of telomere length across cell divisions. We model the dynamics of telomere length as a drift and jump process, which allows predicting the distribution of telomere length and the length of the shortest telomere
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Wollrab, Viktoria. "Active gels in vivo : patterns and dynamics in cytokinetic rings and their functions in cell division." Thesis, Strasbourg, 2014. http://www.theses.fr/2014STRAF027/document.

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Les structures d'acto-myosine sont impliquées dans de nombreuses fonctions cellulaires. Comprendre leur organisation et leur comportement collectif est toujours difficile. Nous avons étudié l'anneau cytokinétique dans les cellules de mammifères et dans les levures de fission, en orientant les cellules dans les microcavités, ce qui permet de voir l'anneau dans un seul plan focal. Avec cette configuration, nous révélons de nouvelles structures et des dynamiques distinctes pour les deux systèmes cellulaires. Dans les cellules de mammifères, nous trouvons des motifs réguliers de la myosine et la formine. Les caractéristiques de ces motifs sont stables tout au long de sa fermeture et leur apparition coïncide avec la constriction. Nous proposons que ce phénomène est une propriété inhérente du réseau d'acto-myosine et que la formation de ces motifs entraîne une augmentation du stress. Ces hypothèses sont confirmées par notre modèle en champ moyen. Par contraste, l'anneau de levure de fission montre des inhomogénéités tournantes de l'actine, de la myosine, des protéines de la construction de la paroi (Bgs) et d'autres protéines. La dynamique des inhomogénéités de myosine est inchangée, si la croissance de la paroi est inhibée. Cependant, l'inhibition du mouvement des inhomogénéités conduit à l'arrêt de la fermeture. Nous proposons que la fermeture de l'anneau est entraînée par la rotation de l'actine et de la myosine qui tirent des protéines Bgs, lesquelles construisent ainsi le septum. Cette hypothèse est confirmée par nos calculs et par des simulations numériques. Nous suggérons que la transition entre les états de différents ordres et dynamiques pourrait être une façon de réguler in vivo les systèmes d'acto-myosine
Actomyosin structures are involved in many cell functions. Understanding their organization and collective behavior is still challenging. We study the cytokinetic ring in mammalian cells and in fission yeasts, by orienting cells in microcavities. This allows seeing the ring in a single plane of focus. With this setup, we reveal new structures and distinct dynamics for both cellular systems. In mammalian cells we find a pattern of regular clusters of myosin and formin. The characteristics of this pattern are stable throughout closure and its formation coincides with the onset of constriction. We propose that its characteristic is an inherent property of the actomyosin network and that its formation leads to an increase in stress generation. These hypotheses are supported by our theoretical mean field model. In contrast, fission yeast rings show rotating inhomogeneities (speckles), i.e. rotations of actin, myosin, cell wall building proteins (Bgs) and other proteins. Myosin speckles dynamic is unchanged, if wall growth is inhibited. However, the inhibition of speckle motion leads to stalled closure. We propose that the ring closure is driven by the rotation of actin and myosin, which pull Bgs thereby building the septum. This model is supported by our calculations and by numerical simulations. We suggest that the transition between states of different orders and dynamics might be a way to regulate actomyosin systems in vivo
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Book chapters on the topic "Cell Division - Stochastic Simulation"

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Bansaye, Vincent, and Sylvie Méléard. "Splitting Feller Diffusion for Cell Division with Parasite Infection." In Stochastic Models for Structured Populations, 79–87. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-21711-6_8.

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Vitvitsky, Anton. "Cellular Automata Simulation of Bacterial Cell Growth and Division." In Designing Beauty: The Art of Cellular Automata, 121–23. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-27270-2_19.

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Tranquillo, Robert T., Oana Brosteanu, and Wolfgang Alt. "Dynamic Morphology of Leukocytes: Statistical Analysis and a Stochastic Model for Receptor-Mediated Cell Motion and Orientation." In Biomechanics of Active Movement and Division of Cells, 437–43. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-642-78975-5_15.

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Karni, Y., M. Goldstein, and E. Bar-Ziv. "Simulation of Diffusion and Chemical Reactions with a Cell-Mixing Stochastic Model." In Springer Series in Chemical Physics, 346–54. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-642-83224-6_28.

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Burrage, Kevin, Pamela M. Burrage, André Leier, Tatiana Marquez-Lago, and Dan V. Nicolau. "Stochastic Simulation for Spatial Modelling of Dynamic Processes in a Living Cell." In Design and Analysis of Biomolecular Circuits, 43–62. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4419-6766-4_2.

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Burrage, Kevin, Pamela Burrage, Andre Leier, and Tatiana Marquez-Lago. "A Review of Stochastic and Delay Simulation Approaches in Both Time and Space in Computational Cell Biology." In Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology, 241–61. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-62627-7_11.

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Braccini, Michele, Andrea Roli, Marco Villani, and Roberto Serra. "A Comparison Between Threshold Ergodic Sets and Stochastic Simulation of Boolean Networks for Modelling Cell Differentiation." In Communications in Computer and Information Science, 116–28. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-78658-2_9.

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"Stochastic Simulation of Cell Signaling Pathways." In Computational Modeling of Genetic and Biochemical Networks. The MIT Press, 2001. http://dx.doi.org/10.7551/mitpress/2018.003.0014.

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Zhang, Xingyi, Yunyun Niu, Linqiang Pan, and Mario J. Pérez-Jiménez. "Linear Time Solution to Prime Factorization by Tissue P Systems with Cell Division." In Natural Computing for Simulation and Knowledge Discovery, 207–20. IGI Global, 2014. http://dx.doi.org/10.4018/978-1-4666-4253-9.ch014.

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Prime factorization is useful and crucial for public-key cryptography, and its application in public-key cryptography is possible only because prime factorization has been presumed to be difficult. A polynomial-time algorithm for prime factorization on a quantum computer was given by P. W. Shor in 1997. In this work, it is considered as a function problem, and in the framework of tissue P systems with cell division, a linear-time solution to prime factorization problem is given on biochemical computational devices – tissue P systems with cell division, instead of computational devices based on the laws of quantum physical.
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Doumic, Marie, and Marc Hoffmann. "Individual and Population Approaches for Calibrating Division Rates in Population Dynamics: Application to the Bacterial Cell Cycle." In Modeling and Simulation for Collective Dynamics, 1–81. WORLD SCIENTIFIC, 2023. http://dx.doi.org/10.1142/9789811266140_0001.

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Conference papers on the topic "Cell Division - Stochastic Simulation"

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Aguinaga, Sylvain, Olivier Simonin, Jacques Bore´e, and Vincent Herbert. "A Lagrangian Stochastic Model for Droplet Deposition Simulations in Connection With Wall Function Approaches." In ASME 2009 Fluids Engineering Division Summer Meeting. ASMEDC, 2009. http://dx.doi.org/10.1115/fedsm2009-78126.

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The deposition rate of droplets is strongly linked to their interaction with the boundary layer turbulence. In “industrial simulations”, droplets dispersion is usually modeled using Lagrangian stochastic simulations based on Reynold Average Navier Stokes (RANS) fluid calculations. Wall functions are also used to bound the number of mesh cells in the near wall region. But they also reduce the description of the boundary layer and lead to bad predictions of the droplets deposition rate. This study presents channel flow simulations using wall functions and run with the CFD code Fluent. In such configurations, the stochastic model of Fluent failed to represent the so-called “diffusion-impaction” regime of deposition. The “Concentration Wall Boundary Layer” model presented in this paper has been developed to predict deposition in simulations using industrial meshes with refinement such as y* > 20. This model calculates the deposition rate using only the intrinsic properties of the particles and the turbulent kinetic energy of the fluid expressed at the top of the boundary layer. The data provided by wall functions are then sufficient to calculate the deposition rate. This model is turned into a “Lagrangian stochastic wall boundary condition model” for the commercial CFD code Fluent. Various simulations have shown that this model improves remarkably the deposition predictions in channel flow. The dependence on the boundary cell size and the channel flow mean velocity has been tested. This model draws interesting perspectives to model deposition in complex configurations without requiring prohibiting mesh sizes.
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Pappu, Vijay, and Prosenjit Bagchi. "3D Computational Modeling and Simulation of Cell Motion on Adhesive Surfaces in Shear Flow." In ASME 2008 Fluids Engineering Division Summer Meeting collocated with the Heat Transfer, Energy Sustainability, and 3rd Energy Nanotechnology Conferences. ASMEDC, 2008. http://dx.doi.org/10.1115/fedsm2008-55113.

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A three-dimensional computational fluid dynamic (CFD) model is presented to simulate transient rolling adhesion and deformation of leukocytes over a P-selectin coated surface in shear flow. The computational model is based on immersed boundary method for cell deformation, and stochastic Monte Carlo simulation for receptor/ligand interaction. The model is shown to predict the characteristic ‘stop-and-go’ motion of rolling leukocytes. The objective here is to understand the coupling between external shear flow, cell deformation, microvilli deformation and various biophysical parameters that govern the formation of selectin bonds. We observe that compliant cells roll more stably with lesser fluctuations. Adhesion is seen to occur via multiple tethers, but often one tether is sufficient to support rolling. The force loading on individual microvillus is not continuous, rather occurs in steps. Further, it is also shown that only the microvilli whose undeformed length is above a certain cut off length, participate in bond formation and the cutoff length reduces with increasing cell rigidity.
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Sikarwar, Vandna, Vijayshri Chaurasia, J. S. Yadav, and Yashwant Kurmi. "Stochastic model analysis for Hes1/MiR-9 brain cell division system." In 2017 International Conference on Recent Innovations in Signal processing and Embedded Systems (RISE). IEEE, 2017. http://dx.doi.org/10.1109/rise.2017.8378208.

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Yi, Wenlong, Yinglong Wang, Yingzhao Jiang, Hongyu Jiang, and Jun Yang. "Simulation of Plant Cell Division Based on Combinatorial Topology." In 2021 IEEE Conference of Russian Young Researchers in Electrical and Electronic Engineering (ElConRus). IEEE, 2021. http://dx.doi.org/10.1109/elconrus51938.2021.9396716.

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Schulz, Hans-Jörg, Adelinde M. Uhrmacher, and Heidrun Schumann. "Visual analytics for stochastic simulation in cell biology." In the 11th International Conference. New York, New York, USA: ACM Press, 2011. http://dx.doi.org/10.1145/2024288.2024345.

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Soyhan, Hakan Serhad, Terese Løvås, and Fabian Mauss. "A Stochastic Simulation of an HCCI Engine Using an Automatically Reduced Mechanism." In ASME 2001 Internal Combustion Engine Division Fall Technical Conference. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/2001-ice-416.

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Abstract Homogeneous Charge Compression Ignition (HCCI) Engines are a promising alternative to the existing Spark Ignition Engines and Compression Ignition Engines. In an HCCI engine, the premixed fuel/air mixture ignites when sufficiently high temperature and pressure is reached. The entire bulk will auto-ignite at almost the same time because the physical conditions are similar throughout the combustion chamber. Therefore it is a justified assumption to consider the chemical reactions to be the rate-determining step for the ignition process. This gives us the opportunity to formulate a simple zero-dimensional model with detailed chemical kinetics for the calculations of the ignition process. Ignition calculations using this model have predicted a high sensitivity to fluctuations in temperature and fuel compositions. These predictions have later been confirmed by experiments. Partially stirred plug flow reactor (PaSPFR) can be used to conquer the assumption of homogeneity. The assumption is replaced by that of statistical homogeneity and thus statistical fluctuations caused by inhomogeneities can be studied. However, the CPU-time needed for this approach is increased considerably and the usage of mechanism reduction becomes evident. In this paper, we demonstrate how a reduced mechanism for natural gas as fuel is derived automatically. The original mechanism by Warnatz (589 reactions, 53 species) is first reduced to a skeletal mechanism (481 reactions, 43 species). By introduction of the quasi steady state assumption, the skeletal mechanism is reduced further to 23 species and 20 global reactions. The accuracy of the final mechanism is demonstrated using the stochastic reactor tool for an HCCI engine.
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Manninen, Tiina, Eeva Makiraatikka, Antti Ylipaa, Antti Pettinen, Kalle Leinonen, and Marja-Leena Linne. "Discrete stochastic simulation of cell signaling: comparison of computational tools." In Conference Proceedings. Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE, 2006. http://dx.doi.org/10.1109/iembs.2006.260023.

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Manninen, Tiina, Eeva Makiraatikka, Antti Ylipaa, Antti Pettinen, Kalle Leinonen, and Marja-Leena Linne. "Discrete stochastic simulation of cell signaling: comparison of computational tools." In Conference Proceedings. Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE, 2006. http://dx.doi.org/10.1109/iembs.2006.4397829.

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Peng, Zhangli, Xuejin Li, George Karniadakis, and Ming Dao. "Poster: Multiscale simulation of red blood cell tethering in a capillary." In 67th Annual Meeting of the APS Division of Fluid Dynamics. American Physical Society, 2014. http://dx.doi.org/10.1103/aps.dfd.2014.gfm.p0039.

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Wilmer, Brady M., and William F. Northrop. "Simulation of Turbulent Combustion in Gasoline Direct Injection Spark-Ignited Engines Using a Stochastic Reactor Model." In ASME 2021 Internal Combustion Engine Division Fall Technical Conference. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/icef2021-66622.

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Abstract In this work, a stochastic reactor model (SRM) is presented that bridges the gap between multi-dimensional computational fluid dynamics (CFD) models and zero-dimensional models for simulating spark-ignited internal combustion engines. The quasi-dimensional approach calculates spatial temperature and composition of stochastic “particles” in the combustion chamber without defining their spatial position, thus allowing for mixture stratification while keeping computational costs low. The SRM simulates flame propagation using a three-zone combustion model consisting of burned gas, flame front, and unburned gas. This “flame brush” approach assumes a hemispherical flame front that propagates through the cylinder based on estimated turbulent flame speed. Cycle-averaged turbulence intensity (u’) is used in the model, calibrated using experimental data. Through the use of a kinetic mechanism, the model predicts key emissions such as CO, CO2, NO, NO2, and HC from both port fuel injection (PFI) and gasoline direct injection (GDI) engines, the latter through the implementation of a simplified spray model. Experimental data from three engines, two GDI and one PFI, were used to validate the model and calibrate cycle-averaged u’. Across all engines, the model was able to produce pressure curves that matched the experimental data. In terms of emissions, the simplified chemical kinetics mechanism matched trends of the experimental data, with the PFI results having higher accuracy. Pressure, burned fraction, and engine-out emissions predictions show that the SRM can reliably match experimental results in certain operating ranges, thus providing a viable alternative to complex CFD and single zone models.
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