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

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.

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.<br>Doctor of Philosophy<br>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.

Le projet de thèse concerne la construction, la génération et l'identification de modèles continus stochastiques, pour des milieux hétérogènes exhibant des comportements non linéaires. Le domaine d'application principal visé est la biomécanique, notamment au travers du développement d'outils de modélisation multi-échelles et stochastiques, afin de quantifier les grandes incertitudes exhibées par les tissus mous. Deux aspects sont particulièrement mis en exergue. Le premier point a trait à la prise en compte des incertitudes en mécanique non linéaire, et leurs incidences sur les prédictions des quantités d'intérêt. Le second aspect concerne la construction, la génération (en grandes dimensions) et l'identification multi-échelle de représentations continues à partir de résultats expérimentaux limités<br>This work is concerned with the construction, generation and identification of stochastic continuum models, for heterogeneous materials exhibiting nonlinear behaviors. The main covered domains of applications are biomechanics, through the development of multiscale methods and stochastic models, in order to quantify the great variabilities exhibited by soft tissues. Two aspects are particularly highlighted. The first one is related to the uncertainty quantification in non linear mechanics, and its implications on the quantities of interest. The second aspect is concerned with the construction, the generation in high dimension and multiscale identification based on limited experimental data

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.<br>Doctor of Philosophy<br>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.

Fluid velocities and Brownian effects at nanoscales in the near-wall region of microchannels can be experimentally measured in an image plane parallel to the wall using, for example, evanescent wave illumination technique combined with particle image velocimetry [R. Sadr extit{et al.}, J. Fluid. Mech. 506, 357-367 (2004)]. The depth of field of this technique being difficult to modify, reconstruction of the out-of-plane dependence of the in-plane velocity profile remains extremely challenging. Tracer particles are not only carried by the flow, but they undergo random fluctuation imposed by the proximity of the wall. We study such a system under a particle based stochastic approach (Langevin) and a probabilistic approach (Fokker-Planck). The Langevin description leads to a coupled system of stochastic differential equations. Because the simulated data will be used to test a statistical hypothesis, we pay particular attention to the strong order of convergence of the scheme developing an appropriate Milstein scheme of strong order of convergence 1. Based on the probability density function of mean in-plane displacements, a statistical solution to the problem of the reconstruction of the out-of-plane dependence of the velocity profile is proposed. We developed a maximum likelihood algorithm which determines the most likely values for the velocity profile based on simulated perfect particle position, simulated perfect mean displacements and simulated observed mean displacements. Effects of Brownian motion on the approximation of the mean displacements are briefly discussed. A matched particle is a particle that starts and ends in the same image window after a measurement time. AS soon as the computation and observation domain are not the same, the distribution of the out-of-plane distances sampled by matched particles during the measurement time is not uniform. The combination of a forward and a backward solution of the one dimensional Fokker-Planck equation is used to determine this probability density function. The non-uniformity of the resulting distribution is believed to induce a bias in the determination of slip length and is quantified for relevant experimental parameters.

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.

Cell-extracellular matrix and cell-cell adhesion are essential for biological processes such as cell motility, signaling, proliferation, cytoskeletal organization and gene expression. For this reason, extensive effort has been devoted in the past few decades to measure cell adhesion as well as identify key molecules involved. This thesis focuses on two outstanding problems in this area, namely, how to quantitatively characterize the adhesion between neural cells and the substrate and how to model the turnover of adhesions in the intriguing phenomenon of stretch-induced cell realignment. First of all, using a combined atomic force (AFM) and total internal reflection fluorescence microscope (TIRFM) system a novel method was developed to systematically and quantitatively examine the adhesion between neurite branches and the extracellular matrix. Specifically, a tipless AFM cantilever was used to penetrate between a well-developed neurite and the functionalized substrate and then gradually peel the neurite from the surface. At the same time, a laser TIRFM was utilized to monitor the activities of different adhesion molecules during the detaching process. This approach provides a solution to the long-standing problem of how to quantitatively measure neuron-extracellular matrix interactions while, simultaneously, identify the roles of various adhesion proteins in the process. Besides heathy neurons, testes have also been conducted on cells affected by the Alzheimer's disease (AD) where the influence of such disease on the mechanical response of neural cells was demonstrated. Secondly, to better understand the observed peeling response of the neurite, as well as extract key information from it, finite element (FEM) simulation was carried out using ABAQUS. It was shown that a good fit between the simulation results and experimental data can be achieved by representing the adhesion between two surfaces with simple cohesive interactions. In particular, it was found that the apparent adhesion energy density, a quantity of central interest in cell adhesion studies, is in the range of 0.2-0.8 mj/m^2. Last but not the least, a mechanochemical modeling framework was developed to investigate the mechanism of cell reorientation induced by cyclic stretching on the substrate. It was shown that the final alignment of cells reflects the competition between stress fiber assembly or disassembly, focal adhesion growth or disruption, substrate stiffening and whole-cell rotation. Predictions from the model are consistent with a variety of experimental observations, suggesting that the main physics of this intriguing phenomenon may have been well captured.<br>published_or_final_version<br>Mechanical Engineering<br>Doctoral<br>Doctor of Philosophy

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.<br>Ph. D.

Les réseaux de fibre sont une structure omniprésente dans les tissus biologiques, aussi bien au niveau macroscopique, où ils sont l'ingrédient principal des tissus mous, qu'au niveau microscopique, en tant que constituants des structures collagèniques ou du cytosquelette. L'objectif de ce travail de thèse est de proposer un modèle basé sur la microstructure physique des réseaux de fibres afin d'obtenir une compréhension du comportement mécanique des réseaux de fibres biologiques. Le modèle est basé sur une description de fibres glissant les unes par rapport aux autres et interagissant via des ponts qui se comportent comme des ressorts. Ces ponts peuvent s'attacher et se détacher de manière stochastique avec un taux de détachement qui dépend de la force subie. Comparé aux modélisations existantes, notre travail met en jeu une configuration en glissement dynamique des fibres, ainsi que des sites d'attachement discrets ne permettant l'attachement qu'à des endroits localisés de la fibre. Le détachement des ponts est basé sur la diffusion thermique hors d'un puit de potentiel suivant la théorie de Kramers. Cette théorie donne un contexte physique à la dynamique du détachement ainsi qu'une dépendance naturelle du détachement au chargement via l'inclinaison du paysage énergétique par la force de chargement. Le modèle donne deux modes de contrôle du système : un contrôle à vitesse imposée, appelé système dur, et un contrôle à force imposée, appelé système mou. Notre travail permet également de visualiser le comportement du système à travers une simulation stochastique. Les simulations offrent deux algorithmes, chacun adapté à la méthode de contrôle du système, en système dur ou mou et respectant la causalité dans chacun des modes. Les résultats de la simulation sont explorés via la visualisation des données sortantes de la simulation, qui servent de support pour l'investigation paramétrique du comportement du modèle et ancrent l'interprétation physique des résultats. En particulier, l'influence de l'espacement des sites d'attachement du système, un point caractéristique du modèle, est examiné. De même, nous explorons l'effet de chargements complexes (transitoires, cycliques, etc.) qui représentent les chargements physiologiques des tissus fibreux<br>Fibre networks are ubiquitous structures in biological tissues, both at the macroscopic level being the main ingredient in soft tissues and at the microscopic level, as constituents of collagen structures or the cytoskeleton. The goal of this work is to propose a model based on the physical microstructure of fibre networks in order to provide an understanding of the mechanical behaviour of biological fibre networks. The current model starts from fibres sliding with respect to one another and interacting via spring-like cross-bridges. These cross-bridges can attach and detach stochastically with a load-dependent detachment rate. Compared to existing modelling approaches, this work features a dynamic sliding configuration for the interacting fibres and discrete binding sites which permit attachment on localised spaces of the fibre. The detachment of cross-bridges is based on thermal diffusion out of an energy well, following the Kramers rate theory. This theory provides a physical background to the detachment dynamics as well as a natural load dependency in the tilting of the energy landscape by the load force. The model provides two modes by which the depicted system may be driven: an imposed velocity driving, called a hard device and an imposed load driving, called a soft device. The work also provides a way of visualising the behaviour of the model by performing a stochastic simulation. The simulations provided present two algorithms, each tailored to represent the driving of the system, whether in hard or soft device, respecting the causality in each of the driving mode. Simulation results are explored via data visualisation of simulation output. These visualisation serve as an entry point into parametric investigation of the model behaviour and anchor the interpretation of the results into physical systems. In particular, the influence of binding site spacing, one of the key features of the model, is investigated. We also investigate the effects of complex loading paths (transitory, cyclic, etc.) which can be associated to the physiological loadings fibrous tissues