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We develop a theoretical approach that uses physiochemical kinetics modelling to describe cell population dynamics upon progression of viral infection in cell culture, which results in cell apoptosis (programmed cell death) and necrosis (direct cell death). Several model parameters necessary for computer simulation were determined by reviewing and analyzing available published experimental data. By comparing experimental data to computer modelling results, we identify the parameters that are the most sensitive to the measured system properties and allow for the best data fitting. Our model allows extraction of parameters from experimental data and also has predictive power. Using the model we describe interesting time-dependent quantities that were not directly measured in the experiment, and identify correlations among the fitted parameter values. Numerical simulation of viral infection progression is done by a rate-equation approach resulting in a system of stiff equations, which are solved by using a novel variant of the stochastic ensemble modelling approach. The latter was originally developed for coupled chemical reactions.
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We study the early stages of viral infection, and the distribution of times to obtain a persistent infection. The virus population proliferates by entering and reproducing inside a target cell until a sufficient number of new virus particles are released via a burst, with a given burst size distribution, which results in the death of the infected cell. Starting with a 2D model describing the joint dynamics of the virus and infected cell populations, we analyze the corresponding master equation using the probability generating function formalism. Exploiting time-scale separation between the virus and infected cell dynamics, the 2D model can be cast into an effective 1D model. To this end, we solve the 1D model analytically for a particular choice of burst size distribution. In the general case, we solve the model numerically by performing extensive Monte-Carlo simulations, and demonstrate the equivalence between the 2D and 1D models by measuring the Kullback-Leibler divergence between the corresponding distributions. Importantly, we find that the distribution of infection times is highly skewed with a fat exponential right tail. This indicates that there is non-negligible portion of individuals with an infection time, significantly longer than the mean, which may have implications on when HIV tests should be performed.
Apoptosis is essential for numerous processes, such as development, resistance to infections, and suppression of tumorigenesis. Here, we investigate the influence of the nutrient sensing and longevity-assuring enzyme SIRT6 on the dynamics of apoptosis triggered by serum starvation. Specifically, we characterize the progression of apoptosis in wild type and SIRT6 deficient mouse embryonic fibroblasts using time-lapse flow cytometry and computational modelling based on rate-equations and cell distribution analysis. We find that SIRT6 deficient cells resist apoptosis by delaying its initiation. Interestingly, once apoptosis is initiated, the rate of its progression is higher in SIRT6 null cells compared to identically cultured wild type cells. However, SIRT6 null cells succumb to apoptosis more slowly, not only in response to nutrient deprivation but also in response to other stresses. Our data suggest that SIRT6 plays a role in several distinct steps of apoptosis. Overall, we demonstrate the utility of our computational model to describe stages of apoptosis progression and the integrity of the cellular membrane. Such measurements will be useful in a broad range of biological applications. We describe a computational method to evaluate the progression of apoptosis through different stages. Using this method, we describe how cells devoid of SIRT6 longevity gene respond to apoptosis stimuli, specifically, how they respond to starvation. We find that SIRT6 cells resist apoptosis initiation; however, once initiated, they progress through the apoptosis at a faster rate. These data are first of the kind and suggest that SIRT6 activities might play different roles at different stages of apoptosis. The model that we propose can be used to quantitatively evaluate progression of apoptosis and will be useful in studies of cancer treatments and other areas where apoptosis is involved.
Many biological assays are employed in virology to quantify parameters of interest. Two such classes of assays, virus quantification assays (VQA) and infectivity assays (IA), aim to estimate the number of viruses present in a solution, and the ability of a viral strain to successfully infect a host cell, respectively. VQAs operate at extremely dilute concentrations and results can be subject to stochastic variability in virus-cell interactions. At the other extreme, high viral particle concentrations are used in IAs, resulting in large numbers of viruses infecting each cell, enough for measurable change in total transcription activity. Furthermore, host cells can be infected at any concentration regime by multiple particles, resulting in a statistical multiplicity of infection (SMOI) and yielding potentially significant variability in the assay signal and parameter estimates. We develop probabilistic models for SMOI at low and high viral particle concentration limits and apply them to the plaque (VQA), endpoint dilution (VQA), and luciferase reporter (IA) assays. A web-based tool implementing our models and analysis is also developed and presented. We test our proposed new methods for inferring experimental parameters from data using numerical simulations and show improvement on existing procedures in all limits.
Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose dynamics are governed by the Chemical Master Equation. Despite its simple structure, no analytic solutions to the Chemical Master Equation are known for most systems. Moreover, stochastic simulations are computationally expensive, making systematic analysis and statistical inference a challenging task. Consequently, significant effort has been spent in recent decades on the development of efficient approximation and inference methods. This article gives an introduction to basic modelling concepts as well as an overview of state of the art methods. First, we motivate and introduce deterministic and stochastic methods for modelling chemical networks, and give an overview of simulation and exact solution methods. Next, we discuss several approximation methods, including the chemical Langevin equation, the system size expansion, moment closure approximations, time-scale separation approximations and hybrid methods. We discuss their various properties and review recent advances and remaining challenges for these methods. We present a comparison of several of these methods by means of a numerical case study and highlight some of their respective advantages and disadvantages. Finally, we discuss the problem of inference from experimental data in the Bayesian framework and review recent methods developed the literature. In summary, this review gives a self-contained introduction to modelling, approximations and inference methods for stochastic chemical kinetics.
We investigate a model of cell division in which the length of telomeres within the cell regulate their proliferative potential. At each cell division the ends of linear chromosomes change and a cell becomes senescent when one or more of its telomeres become shorter than a critical length. In addition to this systematic shortening, exchange of telomere DNA between the two daughter cells can occur at each cell division. We map this telomere dynamics onto a biased branching diffusion process with an absorbing boundary condition whenever any telomere reaches the critical length. As the relative effects of telomere shortening and cell division are varied, there is a phase transition between finite lifetime and infinite proliferation of the cell population. Using simple first-passage ideas, we quantify the nature of this transition.
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