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1
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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Lloyd-Price, Jason, Huy Tran, and Andre S. Ribeiro. "Dynamics of small genetic circuits subject to stochastic partitioning in cell division." Journal of Theoretical Biology 356 (September 2014): 11–19. http://dx.doi.org/10.1016/j.jtbi.2014.04.018.
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Beneteau, Thomas, Christian Selinger, Mircea T. Sofonea, and Samuel Alizon. "Episome partitioning and symmetric cell divisions: Quantifying the role of random events in the persistence of HPV infections." PLOS Computational Biology 17, no. 9 (September 7, 2021): e1009352. http://dx.doi.org/10.1371/journal.pcbi.1009352.
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Human Papillomaviruses (HPV) are one of the most prevalent sexually transmitted infections (STI) and the most oncogenic viruses known to humans. The vast majority of HPV infections clear in less than 3 years, but the underlying mechanisms, especially the involvement of the immune response, are still poorly known. Building on earlier work stressing the importance of randomness in the type of cell divisions in the clearance of HPV infection, we develop a stochastic mathematical model of HPV dynamics that combines the previous aspect with an explicit description of the intracellular level. We show that the random partitioning of virus episomes upon stem cell division and the occurrence of symmetric divisions dramatically affect viral persistence. These results call for more detailed within-host studies to better understand the relative importance of stochasticity and immunity in HPV infection clearance.
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Pin, Carmen, and József Baranyi. "Kinetics of Single Cells: Observation and Modeling of a Stochastic Process." Applied and Environmental Microbiology 72, no. 3 (March 2006): 2163–69. http://dx.doi.org/10.1128/aem.72.3.2163-2169.2006.
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ABSTRACT The successive generation times for single cells of Escherichia coli K-12 were measured as described by A. Elfwing, Y. LeMarc, J. Baranyi, and A. Ballagi (Appl. Environ. Microbiol. 70:675-678, 2004), and the histograms they generated were used as empirical distributions to simulate growth of the population as the result of the multiplication of its single cells. This way, a stochastic birth model in which the underlying distributions were measured experimentally was simulated. To validate the model, analogous bacterial growth curves were generated by the use of different inoculum levels. The agreement with the simulation was very good, proving that the growth of the population can be predicted accurately if the distribution of the first few division times for the single cells within that population is known. Two questions were investigated by the simulation. (i) To what extent can we say that the distribution of the detection time, i.e., the time by which a single-cell-generated subpopulation reaches a detectable level, can be identified with that of the lag time of the original single cell? (ii) For low inocula, how does the inoculum size affect the lag time of the population?
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Johnston, Iain G., and Nick S. Jones. "Closed-form stochastic solutions for non-equilibrium dynamics and inheritance of cellular components over many cell divisions." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, no. 2180 (August 2015): 20150050. http://dx.doi.org/10.1098/rspa.2015.0050.
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Stochastic dynamics govern many important processes in cellular biology, and an underlying theoretical approach describing these dynamics is desirable to address a wealth of questions in biology and medicine. Mathematical tools exist for treating several important examples of these stochastic processes, most notably gene expression and random partitioning at single-cell divisions or after a steady state has been reached. Comparatively little work exists exploring different and specific ways that repeated cell divisions can lead to stochastic inheritance of unequilibrated cellular populations. Here we introduce a mathematical formalism to describe cellular agents that are subject to random creation, replication and/or degradation, and are inherited according to a range of random dynamics at cell divisions. We obtain closed-form generating functions describing systems at any time after any number of cell divisions for binomial partitioning and divisions provoking a deterministic or random, subtractive or additive change in copy number, and show that these solutions agree exactly with stochastic simulation. We apply this general formalism to several example problems involving the dynamics of mitochondrial DNA during development and organismal lifetimes.
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Koutsoumanis, Konstantinos P., and Alexandra Lianou. "Stochasticity in Colonial Growth Dynamics of Individual Bacterial Cells." Applied and Environmental Microbiology 79, no. 7 (January 25, 2013): 2294–301. http://dx.doi.org/10.1128/aem.03629-12.
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ABSTRACTConventional bacterial growth studies rely on large bacterial populations without considering the individual cells. Individual cells, however, can exhibit marked behavioral heterogeneity. Here, we present experimental observations on the colonial growth of 220 individual cells ofSalmonella entericaserotype Typhimurium using time-lapse microscopy videos. We found a highly heterogeneous behavior. Some cells did not grow, showing filamentation or lysis before division. Cells that were able to grow and form microcolonies showed highly diverse growth dynamics. The quality of the videos allowed for counting the cells over time and estimating the kinetic parameters lag time (λ) and maximum specific growth rate (μmax) for each microcolony originating from a single cell. To interpret the observations, the variability of the kinetic parameters was characterized using appropriate probability distributions and introduced to a stochastic model that allows for taking into account heterogeneity using Monte Carlo simulation. The model provides stochastic growth curves demonstrating that growth of single cells or small microbial populations is a pool of events each one of which has its own probability to occur. Simulations of the model illustrated how the apparent variability in population growth gradually decreases with increasing initial population size (N0). For bacterial populations withN0of >100 cells, the variability is almost eliminated and the system seems to behave deterministically, even though the underlying law is stochastic. We also used the model to demonstrate the effect of the presence and extent of a nongrowing population fraction on the stochastic growth of bacterial populations.
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Wang, Yanli, Wing-Cheong Lo, and Ching-Shan Chou. "Modelling stem cell ageing: a multi-compartment continuum approach." Royal Society Open Science 7, no. 3 (March 2020): 191848. http://dx.doi.org/10.1098/rsos.191848.
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Stem cells are important to generate all specialized tissues at an early life stage, and in some systems, they also have repair functions to replenish the adult tissues. Repeated cell divisions lead to the accumulation of molecular damage in stem cells, which are commonly recognized as drivers of ageing. In this paper, a novel model is proposed to integrate stem cell proliferation and differentiation with damage accumulation in the stem cell ageing process. A system of two structured PDEs is used to model the population densities of stem cells (including all multiple progenitors) and terminally differentiated (TD) cells. In this system, cell cycle progression and damage accumulation are modelled by continuous dynamics, and damage segregation between daughter cells is considered at each division. Analysis and numerical simulations are conducted to study the steady-state populations and stem cell damage distributions under different damage segregation strategies. Our simulations suggest that equal distribution of the damaging substance between stem cells in a symmetric renewal and less damage retention in stem cells in the asymmetric division are favourable strategies, which reduce the death rate of the stem cells and increase the TD cell populations. Moreover, asymmetric damage segregation in stem cells leads to less concentrated damage distribution in the stem cell population, which may be more robust to the stochastic changes in the damage. The feedback regulation from stem cells can reduce oscillations and population overshoot in the process, and improve the fitness of stem cells by increasing the percentage of cells with less damage in the stem cell population.
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Cheeseman, Bevan L., Dongcheng Zhang, Benjamin J. Binder, Donald F. Newgreen, and Kerry A. Landman. "Cell lineage tracing in the developing enteric nervous system: superstars revealed by experiment and simulation." Journal of The Royal Society Interface 11, no. 93 (April 6, 2014): 20130815. http://dx.doi.org/10.1098/rsif.2013.0815.
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Cell lineage tracing is a powerful tool for understanding how proliferation and differentiation of individual cells contribute to population behaviour. In the developing enteric nervous system (ENS), enteric neural crest (ENC) cells move and undergo massive population expansion by cell division within self-growing mesenchymal tissue. We show that single ENC cells labelled to follow clonality in the intestine reveal extraordinary and unpredictable variation in number and position of descendant cells, even though ENS development is highly predictable at the population level. We use an agent-based model to simulate ENC colonization and obtain agent lineage tracing data, which we analyse using econometric data analysis tools. In all realizations, a small proportion of identical initial agents accounts for a substantial proportion of the total final agent population. We term these individuals superstars. Their existence is consistent across individual realizations and is robust to changes in model parameters. This inequality of outcome is amplified at elevated proliferation rate. The experiments and model suggest that stochastic competition for resources is an important concept when understanding biological processes which feature high levels of cell proliferation. The results have implications for cell-fate processes in the ENS.
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Lin, Jiaqi, Hui Sun, and JiaJia Dong. "Emergence of sector and spiral patterns from a two-species mutualistic cross-feeding model." PLOS ONE 17, no. 10 (October 19, 2022): e0276268. http://dx.doi.org/10.1371/journal.pone.0276268.
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The ubiquitous existence of microbial communities marks the importance of understanding how species interact within the community to coexist and their spatial organization. We study a two-species mutualistic cross-feeding model through a stochastic cellular automaton on a square lattice using kinetic Monte Carlo simulation. Our model encapsulates the essential dynamic processes such as cell growth, and nutrient excretion, diffusion and uptake. Focusing on the interplay among nutrient diffusion and individual cell division, we discover three general classes of colony morphology: co-existing sectors, co-existing spirals, and engulfment. When the cross-feeding nutrient is widely available, either through high excretion or fast diffusion, a stable circular colony with alternating species sector emerges. When the consumer cells rely on being spatially close to the producers, we observe a stable spiral. We also see one species being engulfed by the other when species interfaces merge due to stochastic fluctuation. By tuning the diffusion rate and the growth rate, we are able to gain quantitative insights into the structures of the sectors and the spirals.
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Canela-Xandri, Oriol, Samira Anbari, and Javier Buceta. "TiFoSi: an efficient tool for mechanobiology simulations of epithelia." Bioinformatics 36, no. 16 (June 26, 2020): 4525–26. http://dx.doi.org/10.1093/bioinformatics/btaa592.
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Abstract Motivation Emerging phenomena in developmental biology and tissue engineering are the result of feedbacks between gene expression and cell biomechanics. In that context, in silico experiments are a powerful tool to understand fundamental mechanisms and to formulate and test hypotheses. Results Here, we present TiFoSi, a computational tool to simulate the cellular dynamics of planar epithelia. TiFoSi allows to model feedbacks between cellular mechanics and gene expression (either in a deterministic or a stochastic way), the interaction between different cell populations, the custom design of the cell cycle and cleavage properties, the protein number partitioning upon cell division, and the modeling of cell communication (juxtacrine and paracrine signaling). Availability and implementation http://tifosi.thesimbiosys.com. Supplementary information Supplementary data are available at Bioinformatics online.
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Simonović, Julijana, and Thomas E. Woolley. "Generalised S-System-Type Equation: Sensitivity of the Deterministic and Stochastic Models for Bone Mechanotransduction." Mathematics 9, no. 19 (September 29, 2021): 2422. http://dx.doi.org/10.3390/math9192422.
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The formalism of a bone cell population model is generalised to be of the form of an S-System. This is a system of nonlinear coupled ordinary differential equations (ODEs), each with the same structure: the change in a variable is equal to a difference in the product of a power-law functions with a specific variable. The variables are the densities of a variety of biological populations involved in bone remodelling. They will be specified concretely in the cases of a specific periodically forced system to describe the osteocyte mechanotransduction activities. Previously, such models have only been deterministically simulated causing the populations to form a continuum. Thus, very little is known about how sensitive the model of mechanotransduction is to perturbations in parameters and noise. Here, we revisit this assumption using a Stochastic Simulation Algorithm (SSA), which allows us to directly simulate the discrete nature of the problem and encapsulate the noisy features of individual cell division and death. Critically, these stochastic features are able to cause unforeseen dynamics in the system, as well as completely change the viable parameter region, which produces biologically realistic results.
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Buijs, Jorn Op den, Mark Musters, Theo Verrips, Jan Andries Post, Branko Braam, and Natal van Riel. "Mathematical modeling of vascular endothelial layer maintenance: the role of endothelial cell division, progenitor cell homing, and telomere shortening." American Journal of Physiology-Heart and Circulatory Physiology 287, no. 6 (December 2004): H2651—H2658. http://dx.doi.org/10.1152/ajpheart.00332.2004.
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Maintenance of the endothelial cell (EC) layer of the vessel wall is essential for proper functioning of the vessel and prevention of vascular disorders. Replacement of damaged ECs could occur through division of surrounding ECs. Furthermore, EC progenitor cells (EPCs), derived from the bone marrow and circulating in the bloodstream, can differentiate into ECs. Therefore, these cells might also play a role in maintenance of the endothelial layer in the vascular system. The proliferative potential of both cell types is limited by shortening of telomeric DNA. Accelerated telomere shortening might lead to senescent vascular wall cells and eventually to the inability of the endothelium to maintain a continuous monolayer. The aim of this study was to describe the dynamics of EC damage and repair and telomere shortening by a mathematical model. In the model, ECs were integrated in a two-dimensional structure resembling the endothelium in a large artery. Telomere shortening was described as a stochastic process with oxidative damage as the main cause of attrition. Simulating the model illustrated that increased cellular turnover or elevated levels of oxidative stress could lead to critical telomere shortening and senescence at an age of 65 yr. The model predicted that under those conditions the EC layer could display defects, which could initiate severe vascular wall damage in reality. Furthermore, simulations showed that 5% progenitor cell homing/yr can significantly delay the EC layer defects. This stresses the potential importance of EPC number and function to the maintenance of vascular wall integrity during the human life span.
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Simonetto, Cristoforo, Ulrich Mansmann, and Jan Christian Kaiser. "Shape-specific characterization of colorectal adenoma growth and transition to cancer with stochastic cell-based models." PLOS Computational Biology 19, no. 1 (January 23, 2023): e1010831. http://dx.doi.org/10.1371/journal.pcbi.1010831.
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Colorectal adenoma are precursor lesions on the pathway to cancer. Their removal in screening colonoscopies has markedly reduced rates of cancer incidence and death. Generic models of adenoma growth and transition to cancer can guide the implementation of screening strategies. But adenoma shape has rarely featured as a relevant risk factor. Against this backdrop we aim to demonstrate that shape influences growth dynamics and cancer risk. Stochastic cell-based models are applied to a data set of 197,347 Bavarian outpatients who had colonoscopies from 2006-2009, 50,649 patients were reported with adenoma and 296 patients had cancer. For multi-stage clonal expansion (MSCE) models with up to three initiating stages parameters were estimated by fits to data sets of all shapes combined, and of sessile (70% of all adenoma), peduncular (17%) and flat (13%) adenoma separately for both sexes. Pertinent features of adenoma growth present themselves in contrast to previous assumptions. Stem cells with initial molecular changes residing in early adenoma predominantly multiply within two-dimensional structures such as crypts. For these cells mutation and division rates decrease with age. The absolute number of initiated cells in an adenoma of size 1 cm is small around 103, related to all bulk cells they constitute a share of about 10−5. The notion of very few proliferating stem cells with age-decreasing division rates is supported by cell marker experiments. The probability for adenoma transiting to cancer increases with squared linear size and shows a shape dependence. Compared to peduncular and flat adenoma, it is twice as high for sessile adenoma of the same size. We present a simple mathematical expression for the hazard ratio of interval cancers which provides a mechanistic understanding of this important quality indicator. We conclude that adenoma shape deserves closer consideration in screening strategies and as risk factor for transition to cancer.
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Jia, Chen, Abhyudai Singh, and Ramon Grima. "Concentration fluctuations in growing and dividing cells: Insights into the emergence of concentration homeostasis." PLOS Computational Biology 18, no. 10 (October 4, 2022): e1010574. http://dx.doi.org/10.1371/journal.pcbi.1010574.
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Intracellular reaction rates depend on concentrations and hence their levels are often regulated. However classical models of stochastic gene expression lack a cell size description and cannot be used to predict noise in concentrations. Here, we construct a model of gene product dynamics that includes a description of cell growth, cell division, size-dependent gene expression, gene dosage compensation, and size control mechanisms that can vary with the cell cycle phase. We obtain expressions for the approximate distributions and power spectra of concentration fluctuations which lead to insight into the emergence of concentration homeostasis. We find that (i) the conditions necessary to suppress cell division-induced concentration oscillations are difficult to achieve; (ii) mRNA concentration and number distributions can have different number of modes; (iii) two-layer size control strategies such as sizer-timer or adder-timer are ideal because they maintain constant mean concentrations whilst minimising concentration noise; (iv) accurate concentration homeostasis requires a fine tuning of dosage compensation, replication timing, and size-dependent gene expression; (v) deviations from perfect concentration homeostasis show up as deviations of the concentration distribution from a gamma distribution. Some of these predictions are confirmed using data for E. coli, fission yeast, and budding yeast.
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Wattis, Jonathan A. D., Qi Qi, and Helen M. Byrne. "Mathematical modelling of telomere length dynamics." Journal of Mathematical Biology 80, no. 4 (November 14, 2019): 1039–76. http://dx.doi.org/10.1007/s00285-019-01448-y.
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AbstractTelomeres are repetitive DNA sequences located at the ends of chromosomes. During cell division, an incomplete copy of each chromosome’s DNA is made, causing telomeres to shorten on successive generations. When a threshold length is reached replication ceases and the cell becomes ‘senescent’. In this paper, we consider populations of telomeres and, from discrete models, we derive partial differential equations which describe how the distribution of telomere lengths evolves over many generations. We initially consider a population of cells each containing just a single telomere. We use continuum models to compare the effects of various mechanisms of telomere shortening and rates of cell division during normal ageing. For example, the rate (or probability) of cell replication may be fixed or it may decrease as the telomeres shorten. Furthermore, the length of telomere lost on each replication may be constant, or may decrease as the telomeres shorten. Where possible, explicit solutions for the evolution of the distribution of telomere lengths are presented. In other cases, expressions for the mean of the distribution are derived. We extend the models to describe cell populations in which each cell contains a distinct subpopulation of chromosomes. As for the simpler models, constant telomere shortening leads to a linear reduction in telomere length over time, whereas length-dependent shortening results in initially rapid telomere length reduction, slowing at later times. Our analysis also reveals that constant telomere loss leads to a Gaussian (normal) distribution of telomere lengths, whereas length-dependent loss leads to a log-normal distribution. We show that stochastic models, which include a replication probability, also lead to telomere length distributions which are skewed.
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Billoud, Bernard, Aude Le Bail, and Bénédicte Charrier. "A stochastic 1D nearest-neighbour automaton models early development of the brown alga Ectocarpus siliculosus." Functional Plant Biology 35, no. 10 (2008): 1014. http://dx.doi.org/10.1071/fp08036.
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Early development of the filamentous brown alga Ectocarpus siliculosus (Dillwyn) Lyngbye involves two cell types that are arranged in a polymorphic, but constrained, pattern. The present study aimed to decipher the cellular processes responsible for the establishment of this pattern. Thorough observations characterised five different events of division and differentiation that occurred during the early development. The hypothesis that a local control is responsible for these processes was tested. To do so, Ectomat, a stochastic automaton in which each cell only interacts with its closest neighbour(s), was created. The probabilities for the five events were adjusted to fit to the observations. Simulations with Ectomat reconstructed most of the essential properties of the sporophyte development, in terms of cell-type proportion, relative position and growth dynamics. The whole organism properties emerged by applying local transition rules. In conclusion, no global position information system was required at this development stage. Randomly occurring cell events, driven by simple contact interactions, are sufficient to account for the early filament development and establishment of the cell-type pattern of E. siliculosus.
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Proctor, C. J., D. A. Lydall, R. J. Boys, C. S. Gillespie, D. P. Shanley, D. J. Wilkinson, and T. B. L. Kirkwood. "Modelling the checkpoint response to telomere uncapping in budding yeast." Journal of The Royal Society Interface 4, no. 12 (August 31, 2006): 73–90. http://dx.doi.org/10.1098/rsif.2006.0148.
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One of the DNA damage-response mechanisms in budding yeast is temporary cell-cycle arrest while DNA repair takes place. The DNA damage response requires the coordinated interaction between DNA repair and checkpoint pathways. Telomeres of budding yeast are capped by the Cdc13 complex. In the temperature-sensitive cdc13-1 strain, telomeres are unprotected over a specific temperature range leading to activation of the DNA damage response and subsequently cell-cycle arrest. Inactivation of cdc13-1 results in the generation of long regions of single-stranded DNA (ssDNA) and is affected by the activity of various checkpoint proteins and nucleases. This paper describes a mathematical model of how uncapped telomeres in budding yeast initiate the checkpoint pathway leading to cell-cycle arrest. The model was encoded in the Systems Biology Markup Language (SBML) and simulated using the stochastic simulation system Biology of Ageing e-Science Integration and Simulation (BASIS). Each simulation follows the time course of one mother cell keeping track of the number of cell divisions, the level of activity of each of the checkpoint proteins, the activity of nucleases and the amount of ssDNA generated. The model can be used to carry out a variety of in silico experiments in which different genes are knocked out and the results of simulation are compared to experimental data. Possible extensions to the model are also discussed.
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Winkle, James J., Bhargav R. Karamched, Matthew R. Bennett, William Ott, and Krešimir Josić. "Emergent spatiotemporal population dynamics with cell-length control of synthetic microbial consortia." PLOS Computational Biology 17, no. 9 (September 22, 2021): e1009381. http://dx.doi.org/10.1371/journal.pcbi.1009381.
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The increased complexity of synthetic microbial biocircuits highlights the need for distributed cell functionality due to concomitant increases in metabolic and regulatory burdens imposed on single-strain topologies. Distributed systems, however, introduce additional challenges since consortium composition and spatiotemporal dynamics of constituent strains must be robustly controlled to achieve desired circuit behaviors. Here, we address these challenges with a modeling-based investigation of emergent spatiotemporal population dynamics using cell-length control in monolayer, two-strain bacterial consortia. We demonstrate that with dynamic control of a strain’s division length, nematic cell alignment in close-packed monolayers can be destabilized. We find that this destabilization confers an emergent, competitive advantage to smaller-length strains—but by mechanisms that differ depending on the spatial patterns of the population. We used complementary modeling approaches to elucidate underlying mechanisms: an agent-based model to simulate detailed mechanical and signaling interactions between the competing strains, and a reductive, stochastic lattice model to represent cell-cell interactions with a single rotational parameter. Our modeling suggests that spatial strain-fraction oscillations can be generated when cell-length control is coupled to quorum-sensing signaling in negative feedback topologies. Our research employs novel methods of population control and points the way to programming strain fraction dynamics in consortial synthetic biology.
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Monzon, Gina A., Lara Scharrel, Ashwin DSouza, Verena Henrichs, Ludger Santen, and Stefan Diez. "Stable tug-of-war between kinesin-1 and cytoplasmic dynein upon different ATP and roadblock concentrations." Journal of Cell Science 133, no. 22 (November 15, 2020): jcs249938. http://dx.doi.org/10.1242/jcs.249938.
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ABSTRACTThe maintenance of intracellular processes, like organelle transport and cell division, depend on bidirectional movement along microtubules. These processes typically require kinesin and dynein motor proteins, which move with opposite directionality. Because both types of motors are often simultaneously bound to the cargo, regulatory mechanisms are required to ensure controlled directional transport. Recently, it has been shown that parameters like mechanical motor activation, ATP concentration and roadblocks on the microtubule surface differentially influence the activity of kinesin and dynein motors in distinct manners. However, how these parameters affect bidirectional transport systems has not been studied. Here, we investigate the regulatory influence of these three parameters using in vitro gliding motility assays and stochastic simulations. We find that the number of active kinesin and dynein motors determines the transport direction and velocity, but that variations in ATP concentration and roadblock density have no significant effect. Thus, factors influencing the force balance between opposite motors appear to be important, whereas the detailed stepping kinetics and bypassing capabilities of the motors only have a small effect.
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Almeida, Luis, Kevin Atsou, Marta Marulli, Diane Peurichard, and Rémi Tesson. "Phase transitions in a two-species model for cell segregation and logistic growth." ESAIM: Proceedings and Surveys 67 (2020): 1–15. http://dx.doi.org/10.1051/proc/202067001.
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We study a model of cell segregation in a population composed of two cell types. Starting from a model initially proposed in [3], we aim to understand the impact of a cell division process on the system’s segregation abilities. The original model describes a population of spherical cells interacting with their close neighbors by means of a repulsion potential and which centers are subject to Brownian motion. Here, we add a stochastic birth-death process in the agent-based model, that approaches a logistic growth term in the continuum limit. We address the linear stability of the spatially homogeneous steady states of the macroscopic model and obtain a precise criterion for the phase transition, which links the system segregation ability to the model parameters. By comparing the criterion with the one obtained without logistic growth, we show that the system’s segregation ability is the result of a complex interplay between logistic growth, diffusion and mechanical repulsive interactions. Numerical simulations are presented to illustrate the results obtained at the microscopic scale.
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Lou, Yuting, Ao Chen, Erika Yoshida, and Yu Chen. "Homeostasis and systematic ageing as non-equilibrium phase transitions in computational multicellular organizations." Royal Society Open Science 6, no. 7 (July 2019): 190012. http://dx.doi.org/10.1098/rsos.190012.
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Being a fatal threat to life, the breakdown of homeostasis in tissues is believed to involve multiscale factors ranging from the accumulation of genetic damages to the deregulation of metabolic processes. Here, we present a prototypical multicellular homeostasis model in the form of a two-dimensional stochastic cellular automaton with three cellular states, cell division, cell death and cell cycle arrest, of which the state-updating rules are based on fundamental cell biology. Despite the simplicity, this model illustrates how multicellular organizations can develop into diverse homeostatic patterns with distinct morphologies, turnover rates and lifespans without considering genetic, metabolic or other exogenous variations. Through mean-field analysis and Monte–Carlo simulations, those homeostatic states are found to be classified into extinctive, proliferative and degenerative phases, whereas healthy multicellular organizations evolve from proliferative to degenerative phases over a long time, undergoing a systematic ageing akin to a transition into an absorbing state in non-equilibrium physical systems. It is suggested that the collapse of homeostasis at the multicellular level may originate from the fundamental nature of cell biology regarding the physics of some non-equilibrium processes instead of subcellular details.
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Wu, Zhijie, Yuman Wang, Kun Wang, and Da Zhou. "Stochastic stem cell models with mutation: A comparison of asymmetric and symmetric divisions." Mathematical Biosciences 332 (February 2021): 108541. http://dx.doi.org/10.1016/j.mbs.2021.108541.
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Thurley, Kevin, and Martin Falcke. "Derivation of Ca2+ signals from puff properties reveals that pathway function is robust against cell variability but sensitive for control." Proceedings of the National Academy of Sciences 108, no. 1 (December 20, 2010): 427–32. http://dx.doi.org/10.1073/pnas.1008435108.
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Ca2+ is a universal second messenger in eukaryotic cells transmitting information through sequences of concentration spikes. A prominent mechanism to generate these spikes involves Ca2+ release from the endoplasmic reticulum Ca2+ store via inositol 1,4,5-trisphosphate (IP3)-sensitive channels. Puffs are elemental events of IP3-induced Ca2+ release through single clusters of channels. Intracellular Ca2+ dynamics are a stochastic system, but a complete stochastic theory has not been developed yet. We formulate the theory in terms of interpuff interval and puff duration distributions because, unlike the properties of individual channels, they can be measured in vivo. Our theory reproduces the typical spectrum of Ca2+ signals like puffs, spiking, and bursting in analytically treatable test cases as well as in more realistic simulations. We find conditions for spiking and calculate interspike interval (ISI) distributions. Signal form, average ISI and ISI distributions depend sensitively on the details of cluster properties and their spatial arrangement. In contrast to that, the relation between the average and the standard deviation of ISIs does not depend on cluster properties and cluster arrangement and is robust with respect to cell variability. It is controlled by the global feedback processes in the Ca2+ signaling pathway (e.g., via IP3-3-kinase or endoplasmic reticulum depletion). That relation is essential for pathway function because it ensures frequency encoding despite the randomness of ISIs and determines the maximal spike train information content. Hence, we find a division of tasks between global feedbacks and local cluster properties that guarantees robustness of function while maintaining sensitivity of control of the average ISI.
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Jia, Chen, Abhyudai Singh, and Ramon Grima. "Characterizing non-exponential growth and bimodal cell size distributions in fission yeast: An analytical approach." PLOS Computational Biology 18, no. 1 (January 18, 2022): e1009793. http://dx.doi.org/10.1371/journal.pcbi.1009793.
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Unlike many single-celled organisms, the growth of fission yeast cells within a cell cycle is not exponential. It is rather characterized by three distinct phases (elongation, septation, and reshaping), each with a different growth rate. Experiments also showed that the distribution of cell size in a lineage can be bimodal, unlike the unimodal distributions measured for the bacterium Escherichia coli. Here we construct a detailed stochastic model of cell size dynamics in fission yeast. The theory leads to analytic expressions for the cell size and the birth size distributions, and explains the origin of bimodality seen in experiments. In particular, our theory shows that the left peak in the bimodal distribution is associated with cells in the elongation phase, while the right peak is due to cells in the septation and reshaping phases. We show that the size control strategy, the variability in the added size during a cell cycle, and the fraction of time spent in each of the three cell growth phases have a strong bearing on the shape of the cell size distribution. Furthermore, we infer all the parameters of our model by matching the theoretical cell size and birth size distributions to those from experimental single-cell time-course data for seven different growth conditions. Our method provides a much more accurate means of determining the size control strategy (timer, adder or sizer) than the standard method based on the slope of the best linear fit between the birth and division sizes. We also show that the variability in added size and the strength of size control in fission yeast depend weakly on the temperature but strongly on the culture medium. More importantly, we find that stronger size homeostasis and larger added size variability are required for fission yeast to adapt to unfavorable environmental conditions.
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Unosson, Måns, Marco Brancaccio, Michael Hastings, Adam M. Johansen, and Bärbel Finkenstädt. "A spatio-temporal model to reveal oscillator phenotypes in molecular clocks: Parameter estimation elucidates circadian gene transcription dynamics in single-cells." PLOS Computational Biology 17, no. 12 (December 17, 2021): e1009698. http://dx.doi.org/10.1371/journal.pcbi.1009698.
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We propose a stochastic distributed delay model together with a Markov random field prior and a measurement model for bioluminescence-reporting to analyse spatio-temporal gene expression in intact networks of cells. The model describes the oscillating time evolution of molecular mRNA counts through a negative transcriptional-translational feedback loop encoded in a chemical Langevin equation with a probabilistic delay distribution. The model is extended spatially by means of a multiplicative random effects model with a first order Markov random field prior distribution. Our methodology effectively separates intrinsic molecular noise, measurement noise, and extrinsic noise and phenotypic variation driving cell heterogeneity, while being amenable to parameter identification and inference. Based on the single-cell model we propose a novel computational stability analysis that allows us to infer two key characteristics, namely the robustness of the oscillations, i.e. whether the reaction network exhibits sustained or damped oscillations, and the profile of the regulation, i.e. whether the inhibition occurs over time in a more distributed versus a more direct manner, which affects the cells’ ability to phase-shift to new schedules. We show how insight into the spatio-temporal characteristics of the circadian feedback loop in the suprachiasmatic nucleus (SCN) can be gained by applying the methodology to bioluminescence-reported expression of the circadian core clock gene Cry1 across mouse SCN tissue. We find that while (almost) all SCN neurons exhibit robust cell-autonomous oscillations, the parameters that are associated with the regulatory transcription profile give rise to a spatial division of the tissue between the central region whose oscillations are resilient to perturbation in the sense that they maintain a high degree of synchronicity, and the dorsal region which appears to phase shift in a more diversified way as a response to large perturbations and thus could be more amenable to entrainment.
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Pourhasanzade, F., and S. H. Sabzpoushan. "A New Mathematical Model for Controlling Tumor Growth Based on Microenvironment Acidity and Oxygen Concentration." BioMed Research International 2021 (January 25, 2021): 1–18. http://dx.doi.org/10.1155/2021/8886050.
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Hypoxia and the pH level of the tumor microenvironment have a great impact on the treatment of tumors. Here, the tumor growth is controlled by regulating the oxygen concentration and the acidity of the tumor microenvironment by introducing a two-dimensional multiscale cellular automata model of avascular tumor growth. The spatiotemporal evolution of tumor growth and metabolic variations is modeled based on biological assumptions, physical structure, states of cells, and transition rules. Each cell is allocated to one of the following states: proliferating cancer, nonproliferating cancer, necrotic, and normal cells. According to the response of the microenvironmental conditions, each cell consumes/produces metabolic factors and updates its state based on some stochastic rules. The input parameters are compatible with cancer biology using experimental data. The effect of neighborhoods during mitosis and simulating spatial heterogeneity is studied by considering multicellular layer structure of tumor. A simple Darwinist mutation is considered by introducing a critical parameter ( Nmm ) that affects division probability of the proliferative tumor cells based on the microenvironmental conditions and cancer hallmarks. The results show that Nmm regulation has a significant influence on the dynamics of tumor growth, the growth fraction, necrotic fraction, and the concentration levels of the metabolic factors. The model not only is able to simulate the in vivo tumor growth quantitatively and qualitatively but also can simulate the concentration of metabolic factors, oxygen, and acidity graphically. The results show the spatial heterogeneity effects on the proliferation of cancer cells and the rest of the system. By increasing Nmm , tumor shrinkage and significant increasing in the oxygen concentration and the pH value of the tumor microenvironment are observed. The results demonstrate the model’s ability, providing an essential tool for simulating different tumor evolution scenarios of a patient and reliable prediction of spatiotemporal progression of tumors for utilizing in personalized therapy.
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Stukalin, Evgeny B., and Sean X. Sun. "Simple Stochastic Models for Cell Division." Biophysical Journal 104, no. 2 (January 2013): 511a. http://dx.doi.org/10.1016/j.bpj.2012.11.2823.
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Luvsantseren, Purevdolgor, Enkhbayar Purevjav, and Khenmedeh Lochin. "Stochastic simulation of cell cycle." Advanced Studies in Biology 5 (2013): 1–9. http://dx.doi.org/10.12988/asb.2013.13001.
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Tyson, John J. "Effects of asymmetric division on a stochastic model of the cell division cycle." Mathematical Biosciences 96, no. 2 (October 1989): 165–84. http://dx.doi.org/10.1016/0025-5564(89)90057-6.
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Huh, Dann, and Johan Paulsson. "Non-genetic heterogeneity from stochastic partitioning at cell division." Nature Genetics 43, no. 2 (December 26, 2010): 95–100. http://dx.doi.org/10.1038/ng.729.
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Sei, Yoshitatsu, Jianying Feng, Carson C. Chow, and Stephen A. Wank. "Asymmetric cell division-dominant neutral drift model for normal intestinal stem cell homeostasis." American Journal of Physiology-Gastrointestinal and Liver Physiology 316, no. 1 (January 1, 2019): G64—G74. http://dx.doi.org/10.1152/ajpgi.00242.2018.
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The normal intestinal epithelium is continuously regenerated at a rapid rate from actively cycling Lgr5-expressing intestinal stem cells (ISCs) that reside at the crypt base. Recent mathematical modeling based on several lineage-tracing studies in mice shows that the symmetric cell division-dominant neutral drift model fits well with the observed in vivo growth of ISC clones and suggests that symmetric divisions are central to ISC homeostasis. However, other studies suggest a critical role for asymmetric cell division in the maintenance of ISC homeostasis in vivo. Here, we show that the stochastic branching and Moran process models with both a symmetric and asymmetric division mode not only simulate the stochastic growth of the ISC clone in silico but also closely fit the in vivo stem cell dynamics observed in lineage-tracing studies. In addition, the proposed model with highest probability for asymmetric division is more consistent with in vivo observations reported here and by others. Our in vivo studies of mitotic spindle orientations and lineage-traced progeny pairs indicate that asymmetric cell division is a dominant mode used by ISCs under normal homeostasis. Therefore, we propose the asymmetric cell division-dominant neutral drift model for normal ISC homeostasis. NEW & NOTEWORTHY The prevailing mathematical model suggests that intestinal stem cells (ISCs) divide symmetrically. The present study provides evidence that asymmetric cell division is the major contributor to ISC maintenance and thus proposes an asymmetric cell division-dominant neutral drift model. Consistent with this model, in vivo studies of mitotic spindle orientation and lineage-traced progeny pairs indicate that asymmetric cell division is the dominant mode used by ISCs under normal homeostasis.
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Wang, Haohua, Zhanjiang Yuan, Peijiang Liu, and Tianshou Zhou. "Division time-based amplifiers for stochastic gene expression." Molecular BioSystems 11, no. 9 (2015): 2417–28. http://dx.doi.org/10.1039/c5mb00391a.
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While cell-to-cell variability is a phenotypic consequence of gene expression noise, sources of this noise may be complex – apart from intrinsic sources such as the random birth/death of mRNA and stochastic switching between promoter states, there are also extrinsic sources of noise such as cell division where division times are either constant or random.
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Zaritsky, Arieh, Ping Wang, and Norbert O. E. Vischer. "Instructive simulation of the bacterial cell division cycle." Microbiology 157, no. 7 (July 1, 2011): 1876–85. http://dx.doi.org/10.1099/mic.0.049403-0.
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The coupling between chromosome replication and cell division includes temporal and spatial elements. In bacteria, these have globally been resolved during the last 40 years, but their full details and action mechanisms are still under intensive study. The physiology of growth and the cell cycle are reviewed in the light of an established dogma that has formed a framework for development of new ideas, as exemplified here, using the Cell Cycle Simulation (CCSim) program. CCSim, described here in detail for the first time, employs four parameters related to time (replication, division and inter-division) and size (cell mass at replication initiation) that together are sufficient to describe bacterial cells under various conditions and states, which can be manipulated environmentally and genetically. Testing the predictions of CCSim by analysis of time-lapse micrographs of Escherichia coli during designed manipulations of the rate of DNA replication identified aspects of both coupling elements. Enhanced frequencies of cell division were observed following an interval of reduced DNA replication rate, consistent with the prediction of a minimum possible distance between successive replisomes (an eclipse). As a corollary, the notion that cell poles are not always inert was confirmed by observed placement of division planes at perpendicular planes in monstrous and cuboidal cells containing multiple, segregating nucleoids.
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Alonso, Antonio A., Ignacio Molina, and Constantinos Theodoropoulos. "Modeling Bacterial Population Growth from Stochastic Single-Cell Dynamics." Applied and Environmental Microbiology 80, no. 17 (June 13, 2014): 5241–53. http://dx.doi.org/10.1128/aem.01423-14.
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ABSTRACTA few bacterial cells may be sufficient to produce a food-borne illness outbreak, provided that they are capable of adapting and proliferating on a food matrix. This is why any quantitative health risk assessment policy must incorporate methods to accurately predict the growth of bacterial populations from a small number of pathogens. In this aim, mathematical models have become a powerful tool. Unfortunately, at low cell concentrations, standard deterministic models fail to predict the fate of the population, essentially because the heterogeneity between individuals becomes relevant. In this work, a stochastic differential equation (SDE) model is proposed to describe variability within single-cell growth and division and to simulate population growth from a given initial number of individuals. We provide evidence of the model ability to explain the observed distributions of times to division, including the lag time produced by the adaptation to the environment, by comparing model predictions with experiments from the literature forEscherichia coli,Listeria innocua, andSalmonella enterica. The model is shown to accurately predict experimental growth population dynamics for both small and large microbial populations. The use of stochastic models for the estimation of parameters to successfully fit experimental data is a particularly challenging problem. For instance, if Monte Carlo methods are employed to model the required distributions of times to division, the parameter estimation problem can become numerically intractable. We overcame this limitation by converting the stochastic description to a partial differential equation (backward Kolmogorov) instead, which relates to the distribution of division times. Contrary to previous stochastic formulations based on random parameters, the present model is capable of explaining the variability observed in populations that result from the growth of a small number of initial cells as well as the lack of it compared to populations initiated by a larger number of individuals, where the random effects become negligible.
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Horowitz, Joseph, Mark D. Normand, Maria G. Corradini, and Micha Peleg. "Probabilistic Model of Microbial Cell Growth, Division, and Mortality." Applied and Environmental Microbiology 76, no. 1 (November 13, 2009): 230–42. http://dx.doi.org/10.1128/aem.01527-09.
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ABSTRACT After a short time interval of length δt during microbial growth, an individual cell can be found to be divided with probability Pd (t)δt, dead with probability Pm (t)δt, or alive but undivided with the probability 1 − [Pd (t) + Pm (t)]δt, where t is time, Pd (t) expresses the probability of division for an individual cell per unit of time, and Pm (t) expresses the probability of mortality per unit of time. These probabilities may change with the state of the population and the habitat's properties and are therefore functions of time. This scenario translates into a model that is presented in stochastic and deterministic versions. The first, a stochastic process model, monitors the fates of individual cells and determines cell numbers. It is particularly suitable for small populations such as those that may exist in the case of casual contamination of a food by a pathogen. The second, which can be regarded as a large-population limit of the stochastic model, is a continuous mathematical expression that describes the population's size as a function of time. It is suitable for large microbial populations such as those present in unprocessed foods. Exponential or logistic growth with or without lag, inactivation with or without a “shoulder,” and transitions between growth and inactivation are all manifestations of the underlying probability structure of the model. With temperature-dependent parameters, the model can be used to simulate nonisothermal growth and inactivation patterns. The same concept applies to other factors that promote or inhibit microorganisms, such as pH and the presence of antimicrobials, etc. With Pd (t) and Pm (t) in the form of logistic functions, the model can simulate all commonly observed growth/mortality patterns. Estimates of the changing probability parameters can be obtained with both the stochastic and deterministic versions of the model, as demonstrated with simulated data.
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Reynolds, Joseph, Mark Coles, Grant Lythe, and Carmen Molina-París. "Deterministic and stochastic naive T cell population dynamics: symmetric and asymmetric cell division." Dynamical Systems 27, no. 1 (March 2012): 75–103. http://dx.doi.org/10.1080/14689367.2011.645447.
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Doiron, Brent, André Longtin, Neil Berman, and Leonard Maler. "Subtractive and Divisive Inhibition: Effect of Voltage-Dependent Inhibitory Conductances and Noise." Neural Computation 13, no. 1 (January 1, 2001): 227–48. http://dx.doi.org/10.1162/089976601300014691.
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The influence of voltage-dependent inhibitory conductances on firing rate versus input current (f-I) curves is studied using simulations from a new compartmental model of a pyramidal cell of the weakly electric fish Apteronotus leptorhynchus. The voltage dependence of shunting-type inhibition enhances the subtractive effect of inhibition on f-I curves previously demonstrated in Holt and Koch (1997) for the voltage-independent case. This increased effectiveness is explained using the behavior of the average subthreshold voltage with input current and, in particular, the nonlinearity of Ohm's law in the subthreshold regime. Our simulations also reveal, for both voltage-dependent and -independent inhibitory conductances, a divisive inhibition regime at low frequencies (f < 40 Hz). This regime, dependent on stochastic inhibitory synaptic input and a coupling of inhibitory strength and variance, gives way to subtractive inhibition at higher-output frequencies (f > 40 Hz). A simple leaky integrate- and-fire type model that incorporates the voltage dependence supports the results from our full ionic simulations.
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Mange, Daniel, André Stauffer, Enrico Petraglio, and Gianluca Tempesti. "Artificial cell division." Biosystems 76, no. 1-3 (August 2004): 157–67. http://dx.doi.org/10.1016/j.biosystems.2004.05.010.
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Nakaoka, Shinji, and Kazuyuki Aihara. "Stochastic simulation of structured skin cell population dynamics." Journal of Mathematical Biology 66, no. 4-5 (December 20, 2012): 807–35. http://dx.doi.org/10.1007/s00285-012-0618-6.
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Stukalin, Evgeny B., Ivie Aifuwa, Jin Seob Kim, Denis Wirtz, and Sean X. Sun. "Age-dependent stochastic models for understanding population fluctuations in continuously cultured cells." Journal of The Royal Society Interface 10, no. 85 (August 6, 2013): 20130325. http://dx.doi.org/10.1098/rsif.2013.0325.
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For symmetrically dividing cells, large variations in the cell cycle time are typical, even among clonal cells. The consequence of this variation is important in stem cell differentiation, tissue and organ size control, and cancer development, where cell division rates ultimately determine the cell population. We explore the connection between cell cycle time variation and population-level fluctuations using simple stochastic models. We find that standard population models with constant division and death rates fail to predict the level of population fluctuation. Instead, variations in the cell division time contribute to population fluctuations. An age-dependent birth and death model allows us to compute the mean squared fluctuation or the population dispersion as a function of time. This dispersion grows exponentially with time, but scales with the population. We also find a relationship between the dispersion and the cell cycle time distribution for synchronized cell populations. The model can easily be generalized to study populations involving cell differentiation and competitive growth situations.
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Alt, Wolfgang, and John J. Tyson. "A stochastic model of cell division (with application to fission yeast)." Mathematical Biosciences 84, no. 2 (June 1987): 159–87. http://dx.doi.org/10.1016/0025-5564(87)90090-3.
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