scholarly journals A hybrid stochastic-deterministic approach to explore multiple infection and evolution in HIV

2021 ◽  
Vol 17 (12) ◽  
pp. e1009713
Author(s):  
Jesse Kreger ◽  
Natalia L. Komarova ◽  
Dominik Wodarz
Keyword(s):  
Infected Cell ◽  
Population Size ◽  
Cell Population ◽  
Stochastic Dynamics ◽  
Heterogeneous Systems ◽  
Deterministic Algorithm ◽  
Stochastic Simulations ◽  
Computational Time ◽  
Multiple Infection ◽  
Deterministic Models

To study viral evolutionary processes within patients, mathematical models have been instrumental. Yet, the need for stochastic simulations of minority mutant dynamics can pose computational challenges, especially in heterogeneous systems where very large and very small sub-populations coexist. Here, we describe a hybrid stochastic-deterministic algorithm to simulate mutant evolution in large viral populations, such as acute HIV-1 infection, and further include the multiple infection of cells. We demonstrate that the hybrid method can approximate the fully stochastic dynamics with sufficient accuracy at a fraction of the computational time, and quantify evolutionary end points that cannot be expressed by deterministic models, such as the mutant distribution or the probability of mutant existence at a given infected cell population size. We apply this method to study the role of multiple infection and intracellular interactions among different virus strains (such as complementation and interference) for mutant evolution. Multiple infection is predicted to increase the number of mutants at a given infected cell population size, due to a larger number of infection events. We further find that viral complementation can significantly enhance the spread of disadvantageous mutants, but only in select circumstances: it requires the occurrence of direct cell-to-cell transmission through virological synapses, as well as a substantial fitness disadvantage of the mutant, most likely corresponding to defective virus particles. This, however, likely has strong biological consequences because defective viruses can carry genetic diversity that can be incorporated into functional virus genomes via recombination. Through this mechanism, synaptic transmission in HIV might promote virus evolvability.

scholarly journals A hybrid stochastic-deterministic approach to explore multiple infection and evolution in HIV

2020 ◽  
Author(s):  
Jesse Kreger ◽  
Natalia L. Komarova ◽  
Dominik Wodarz
Keyword(s):  
Synaptic Transmission ◽  
Hiv Infection ◽  
Single Cell ◽  
Virus Transmission ◽  
Cell Interaction ◽  
Deterministic Algorithm ◽  
Cell Subpopulation ◽  
Multiple Infection ◽  
Deterministic Models ◽  
Multiple Copies

AbstractMultiple infection (when a single cell can become super-infected with multiple copies of virus) can effect evolutionary processes in HIV infection, such as the generation and spread of different mutations. Synaptic transmission (where multiple copies of virus can be transferred during a single cell-to-cell interaction) leads to an increase in infection multiplicity. Here, we analyze the effect of multiple infection on the evolution of an HIV infection using a hybrid stochastic-deterministic algorithm. This algorithm allows us to stochastically simulate a large number of cells and large number of cell subpopulations in a computationally efficient way. Specifically, we classify each cell subpopulation as “large” or “small” based on some size threshold (for which we provide an analytical lower bound), and then simulate the small populations stochastically, while simultaneously using the deterministic equations for the large populations. We first demonstrate to what extent deterministic models are incomplete in predicting mutant dynamics, and then use the hybrid method to study aspects of mutant evolution. Focusing on the mutant populations at the time of peak infection, we find that overall, multiple infection promotes the existence of mutant strains of virus, both in terms of faster generation and overall number. It also increases the variance in mutant numbers and results in a larger probability to observe rare strains, such as triple mutants. In the context of multiple infection, synaptic transmission is superior at generating mutants, as it increases the number of transcription events that occur. This effect is observed for neutral and advantageous mutants, even in the presence of interference. For disadvantageous mutants, purely synaptic or purely free virus transmission pathways result in an increased number of mutants, but in the presence of complementation, purely synaptic transmission maximizes mutant production and spread.

scholarly journals Universally valid reduction of multiscale stochastic biochemical systems using simple non-elementary propensities

2021 ◽  
Author(s):  
Yun Min Song ◽  
Hyukpyo Hong ◽  
Jae Kyoung Kim
Keyword(s):  
Stochastic Dynamics ◽  
Stochastic Simulations ◽  
Mass Action ◽  
Elementary Functions ◽  
Deterministic Models ◽  
Bistable Switch ◽  
Elementary Reactions ◽  
Reversible Binding ◽  
Reaction Functions ◽  
Biochemical Systems

Biochemical systems consist of numerous elementary reactions governed by the law of mass action. However, experimentally characterizing all the elementary reactions is nearly impossible. Thus, over a century, their deterministic models that typically contain rapid reversible bindings have been simplified with non-elementary reaction functions (e.g., Michaelis-Menten and Morrison equations). Although the non-elementary functions are derived by applying the quasi-steady-state approximation(QSSA) to deterministic systems, they have also been widely used to derive propensities for stochastic simulations due to computational efficiency and simplicity. However, the validity condition for this heuristic approach has not been identified even for the reversible binding between molecules, such as protein-DNA, enzyme-substrate, and receptor-ligand, which is the basis for living cells. Here, we find that the non-elementary propensities based on the deterministic total QSSA can accurately capture the stochastic dynamics of the reversible binding in general. However, serious errors occur when reactant molecules with similar levels tightly bind, unlike deterministic systems.In that case, the non-elementary propensities distort the stochastic dynamics of a bistable switch in the cell cycle and an oscillator in the circadian clock. Accordingly, we derive alternative non-elementary propensities with the stochastic low-state QSSA,developed in this study. This provides a universally valid framework for simplifying multiscale stochastic biochemical systems with rapid reversible bindings, critical for efficient stochastic simulations of cell signaling and gene regulation.

scholarly journals Universally valid reduction of multiscale stochastic biochemical systems using simple non-elementary propensities

2021 ◽  
Vol 17 (10) ◽  
pp. e1008952
Author(s):  
Yun Min Song ◽  
Hyukpyo Hong ◽  
Jae Kyoung Kim
Keyword(s):  
Stochastic Dynamics ◽  
Elementary Reaction ◽  
Stochastic Simulations ◽  
Mass Action ◽  
Deterministic Models ◽  
Elementary Reactions ◽  
Reversible Binding ◽  
Deterministic Systems ◽  
Reaction Functions ◽  
Biochemical Systems

Biochemical systems consist of numerous elementary reactions governed by the law of mass action. However, experimentally characterizing all the elementary reactions is nearly impossible. Thus, over a century, their deterministic models that typically contain rapid reversible bindings have been simplified with non-elementary reaction functions (e.g., Michaelis-Menten and Morrison equations). Although the non-elementary reaction functions are derived by applying the quasi-steady-state approximation (QSSA) to deterministic systems, they have also been widely used to derive propensities for stochastic simulations due to computational efficiency and simplicity. However, the validity condition for this heuristic approach has not been identified even for the reversible binding between molecules, such as protein-DNA, enzyme-substrate, and receptor-ligand, which is the basis for living cells. Here, we find that the non-elementary propensities based on the deterministic total QSSA can accurately capture the stochastic dynamics of the reversible binding in general. However, serious errors occur when reactant molecules with similar levels tightly bind, unlike deterministic systems. In that case, the non-elementary propensities distort the stochastic dynamics of a bistable switch in the cell cycle and an oscillator in the circadian clock. Accordingly, we derive alternative non-elementary propensities with the stochastic low-state QSSA, developed in this study. This provides a universally valid framework for simplifying multiscale stochastic biochemical systems with rapid reversible bindings, critical for efficient stochastic simulations of cell signaling and gene regulation. To facilitate the framework, we provide a user-friendly open-source computational package, ASSISTER, that automatically performs the present framework.

scholarly journals Neural network aided approximation and parameter inference of non-Markovian models of gene expression

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Qingchao Jiang ◽  
Xiaoming Fu ◽  
Shifu Yan ◽  
Runlai Li ◽  
Wenli Du ◽  
...  
Keyword(s):  
Neural Network ◽  
Stochastic Dynamics ◽  
Stochastic Simulations ◽  
Parameter Inference ◽  
Biochemical Processes ◽  
Markovian Models ◽  
The Neural Network ◽  
Large Numbers ◽  
Small Set ◽  
Noisy Measurements

AbstractNon-Markovian models of stochastic biochemical kinetics often incorporate explicit time delays to effectively model large numbers of intermediate biochemical processes. Analysis and simulation of these models, as well as the inference of their parameters from data, are fraught with difficulties because the dynamics depends on the system’s history. Here we use an artificial neural network to approximate the time-dependent distributions of non-Markovian models by the solutions of much simpler time-inhomogeneous Markovian models; the approximation does not increase the dimensionality of the model and simultaneously leads to inference of the kinetic parameters. The training of the neural network uses a relatively small set of noisy measurements generated by experimental data or stochastic simulations of the non-Markovian model. We show using a variety of models, where the delays stem from transcriptional processes and feedback control, that the Markovian models learnt by the neural network accurately reflect the stochastic dynamics across parameter space.

Magnetic Markers Linked to Monoclonal Antibodies Allow in vitro Evaluation of Cell Population Size

Biomag 96 ◽  
2000 ◽  
pp. 643-646
Author(s):  
C. Del Gratta ◽  
S. Della Penna ◽  
P. Battista ◽  
L. Di Donato ◽  
P. Vitullo ◽  
...  
Keyword(s):  
Monoclonal Antibodies ◽  
Population Size ◽  
Cell Population ◽  
In Vitro Evaluation ◽  
Magnetic Markers

scholarly journals Noise-induced bistability in the quasineutral coexistence of viral RNA under different replication modes

2018 ◽  
Author(s):  
Josep Sardanyés ◽  
Andreu Arderiu ◽  
Santiago F. Elena ◽  
Tomás Alarcón
Keyword(s):  
Viral Replication ◽  
Evolutionary Dynamics ◽  
Rna Viruses ◽  
Initial Conditions ◽  
Rna Replication ◽  
Viral Rna ◽  
Stochastic Simulations ◽  
Strong Impact ◽  
Deterministic Models ◽  
The Impact

Evolutionary and dynamical investigations on real viral populations indicate that RNA replication can range between two extremes given by so-called stamping machine replication (SMR) and geometric replication (GR). The impact of asymmetries in replication for single-stranded, (+) sense RNA viruses has been up to now studied with deterministic models. However, viral replication should be better described by including stochasticity, since the cell infection process is typically initiated with a very small number of RNA macromolecules, and thus largely influenced by intrinsic noise. Under appropriate conditions, deterministic theoretical descriptions of viral RNA replication predict a quasineutral coexistence scenario, with a line of fixed points involving different strands’ equilibrium ratios depending on the initial conditions. Recent research on the quasineutral coexistence in two competing populations reveals that stochastic fluctuations fundamentally alters the mean-field scenario, and one of the two species outcompetes the other one. In this manuscript we study this phenomenon for RNA viral replication modes by means of stochastic simulations and a diffusion approximation. Our results reveal that noise has a strong impact on the amplification of viral RNA, also causing the emergence of noise-induced bistability. We provide analytical criteria for the dominance of (+) sense strands depending on the initial populations on the line of equilibria, which are in agreement with direct stochastic simulation results. The biological implications of this noise-driven mechanism are discussed within the framework of the evolutionary dynamics of RNA viruses with different modes of replication.

Regulation of interstitial cell differentiation in Hydra attenuata. I. Homeostatic control of interstitial cell population size

1976 ◽  
Vol 20 (1) ◽  
pp. 29-46 ◽  
Author(s):  
H.R. Bode ◽  
K.M. Flick ◽  
G.S. Smith
Keyword(s):  
Cell Differentiation ◽  
Epithelial Cells ◽  
Population Size ◽  
Cell Population ◽  
Interstitial Cell ◽  
Normal Population ◽  
Cell Types ◽  
Hydra Attenuata ◽  
I Cells ◽  
Continuous Labelling

Mechanisms regulating the population size of the multipotent interstitial cell (i-cell) in Hydra attenuata were investigated. Treatment of animals with 3 cycles of a regime of 24 h in 10-2 M hydroxyurea (HU) alternated with 12 h in culture medium selectively killed 95–99% of the i-cells, but had little effect on the epithelial cells. The i-cell population recovered to the normal i-cell:epithelial cell ratio of I:I within 35 days. Continuous labelling experiments with [3H]thymidine indicate that the recovery of the i-cell population is not due to a change in the length of the cell cycle of either the epithelial cells or the interstitial cells. In control animals 60% of the i-cell population undergo division daily while 40% undergo differentiation. Quantification of the cell types of HU-treated animals indicates that a greater fraction of the i-cells were dividing and fewer differentiating into nematocytes during the first 2 weeks of the recovery after HU treatment. Therefore, the mechanism for recovery involves a shift of the 60:40 division:differentiation ratio of i-cells towards a higher fraction in division until the normal population size of the i-cells is regained. This homeostatic mechanism represents one of the influences affecting i-cell differentiation.

scholarly journals Computation of Single-Cell Metabolite Distributions Using Mixture Models

2020 ◽  
Vol 8 ◽  
Author(s):  
Mona K. Tonn ◽  
Philipp Thomas ◽  
Mauricio Barahona ◽  
Diego A. Oyarzún
Keyword(s):  
Single Cell ◽  
Mixture Models ◽  
Single Cells ◽  
Gaussian Mixture Models ◽  
Gaussian Mixture ◽  
Stochastic Simulations ◽  
Deterministic Models ◽  
Metabolic Heterogeneity ◽  
Cell Expression ◽  
The Impact

Metabolic heterogeneity is widely recognized as the next challenge in our understanding of non-genetic variation. A growing body of evidence suggests that metabolic heterogeneity may result from the inherent stochasticity of intracellular events. However, metabolism has been traditionally viewed as a purely deterministic process, on the basis that highly abundant metabolites tend to filter out stochastic phenomena. Here we bridge this gap with a general method for prediction of metabolite distributions across single cells. By exploiting the separation of time scales between enzyme expression and enzyme kinetics, our method produces estimates for metabolite distributions without the lengthy stochastic simulations that would be typically required for large metabolic models. The metabolite distributions take the form of Gaussian mixture models that are directly computable from single-cell expression data and standard deterministic models for metabolic pathways. The proposed mixture models provide a systematic method to predict the impact of biochemical parameters on metabolite distributions. Our method lays the groundwork for identifying the molecular processes that shape metabolic heterogeneity and its functional implications in disease.

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