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 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 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 Noise control for molecular computing

2018 ◽  
Vol 15 (144) ◽  
pp. 20180199 ◽  
Author(s):  
Tomislav Plesa ◽  
Konstantinos C. Zygalakis ◽  
David F. Anderson ◽  
Radek Erban
Keyword(s):  
Stochastic Dynamics ◽  
Noise Control ◽  
Reaction System ◽  
Reaction Network ◽  
Intrinsic Noise ◽  
Biochemical Networks ◽  
Mass Action ◽  
Mass Action Kinetics ◽  
Interdisciplinary Field ◽  
Biochemical Systems

Synthetic biology is a growing interdisciplinary field, with far-reaching applications, which aims to design biochemical systems that behave in a desired manner. With the advancement in nucleic-acid-based technology in general, and strand-displacement DNA computing in particular, a large class of abstract biochemical networks may be physically realized using nucleic acids. Methods for systematic design of the abstract systems with prescribed behaviours have been predominantly developed at the (less-detailed) deterministic level. However, stochastic effects, neglected at the deterministic level, are increasingly found to play an important role in biochemistry. In such circumstances, methods for controlling the intrinsic noise in the system are necessary for a successful network design at the (more-detailed) stochastic level. To bridge the gap, the noise-control algorithm for designing biochemical networks is developed in this paper. The algorithm structurally modifies any given reaction network under mass-action kinetics, in such a way that (i) controllable state-dependent noise is introduced into the stochastic dynamics, while (ii) the deterministic dynamics are preserved. The capabilities of the algorithm are demonstrated on a production–decay reaction system, and on an exotic system displaying bistability. For the production–decay system, it is shown that the algorithm may be used to redesign the network to achieve noise-induced multistability. For the exotic system, the algorithm is used to redesign the network to control the stochastic switching, and achieve noise-induced oscillations.

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.

scholarly journals Training an asymmetric signal perceptron through reinforcement in an artificial chemistry

2014 ◽  
Vol 11 (93) ◽  
pp. 20131100 ◽  
Author(s):  
Peter Banda ◽  
Christof Teuscher ◽  
Darko Stefanovic
Keyword(s):  
State Of The Art ◽  
Chemical Species ◽  
Mass Action ◽  
Mass Action Kinetics ◽  
Dna Strand Displacement ◽  
Autonomous Adaptation ◽  
Biochemical Systems ◽  
Dna Strand ◽  
Logic Functions ◽  
Application Specific

State-of-the-art biochemical systems for medical applications and chemical computing are application-specific and cannot be reprogrammed or trained once fabricated. The implementation of adaptive biochemical systems that would offer flexibility through programmability and autonomous adaptation faces major challenges because of the large number of required chemical species as well as the timing-sensitive feedback loops required for learning. In this paper, we begin addressing these challenges with a novel chemical perceptron that can solve all 14 linearly separable logic functions. The system performs asymmetric chemical arithmetic, learns through reinforcement and supports both Michaelis–Menten as well as mass-action kinetics. To enable cascading of the chemical perceptrons, we introduce thresholds that amplify the outputs. The simplicity of our model makes an actual wet implementation, in particular by DNA-strand displacement, possible.

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.

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.

scholarly journals Noise-induced bistability in the quasi-neutral coexistence of viral RNAs under different replication modes

2018 ◽  
Vol 15 (142) ◽  
pp. 20180129 ◽  
Author(s):  
Josep Sardanyés ◽  
Andreu Arderiu ◽  
Santiago F. Elena ◽  
Tomás Alarcón
Keyword(s):  
Evolutionary Dynamics ◽  
Rna Viruses ◽  
Initial Conditions ◽  
Rna Replication ◽  
Viral Rna ◽  
Stochastic Simulations ◽  
Strong Impact ◽  
Deterministic Models ◽  
Viral Rnas ◽  
The Impact

Evolutionary and dynamical investigations into real viral populations indicate that RNA replication can range between the two extremes represented 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 mainly studied with deterministic models. However, viral replication should be better described by including stochasticity, as 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 quasi-neutral coexistence scenario, with a line of fixed points involving different strands' equilibrium ratios depending on the initial conditions. Recent research into the quasi-neutral coexistence in two competing populations reveals that stochastic fluctuations fundamentally alter the mean-field scenario, and one of the two species outcompetes the other. In this article, we study this phenomenon for viral RNA 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 RNAs, 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.

Simulation of the Denitrification Process of Waste Water with a Biochemical Systems Model: A Non-Conventional Approach

2014 ◽  
Vol 12 (2) ◽  
pp. 683-693
Author(s):  
Nouceiba Adouani ◽  
Lionel Limousy ◽  
Thomas Lendormi ◽  
Eberhard O. Voit ◽  
Olivier Sire
Keyword(s):  
Waste Water ◽  
Nitrate Reduction ◽  
International Association ◽  
Mass Action ◽  
Experimental Conditions ◽  
Systems Model ◽  
Theoretical Approaches ◽  
Biochemical Systems ◽  
Nitrate And Nitrite ◽  
Denitrification Process

Abstract Matching experimental and theoretical approaches have often been fruitful in the investigation of complex biological processes. Here we develop a novel non-conventional model for the denitrification of waste water. Earlier models of the denitrification process were compiled by the International Association on Water Quality group. The Activated Sludge Models 1–3, which are the most frequently used all over the world, are presently not adapted towards the integration of both nitrous and nitric oxide emissions during the denitrification process. In the present work, a Generalized Mass Action model, based on Biochemical Systems Theory, was designed to simulate the nitrate reduction observed in specific experimental conditions. The model was implemented and analysed with the software package PLAS. Data from a representative experiment were chosen (T=10°C, pH=7, C/N=3, with acetate as carbon source) to simulate greenhouse NO and N2O gas emissions, in order to test hypotheses about the corresponding bacterial metabolic pathways. The results show that the reduction of nitrate and nitrite is kinetically limiting and that nitrate reduction is limited by diffusion and support that distinct microbial subpopulations are involved in the denitrification pathway, which has consequences for NO emissions.

scholarly journals Irregular Oscillations in a Realistic Abstract Quadratic Mass Action System

1980 ◽  
Vol 35 (3) ◽  
pp. 317-318 ◽  
Author(s):  
K.-D. Willamowski ◽  
O. E. Rössler
Keyword(s):  
Numerical Simulation ◽  
Chaotic Behavior ◽  
Variable Mass ◽  
Second Order ◽  
Mass Action ◽  
Mass Action Kinetics ◽  
Elementary Reactions ◽  
Action System

Abstract An open three-variable mass action kinetics is presented which exhibits chaotic behavior under numerical simulation. The elementary reactions of this system are at most of second order and satisfy the requirements of thermodynamics as long as the system is closed.

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