An Overview of Network-Based and -Free Approaches for Stochastic Simulation of Biochemical Systems.
Ontology highlight
ABSTRACT:
SUBMITTER: Gupta A
PROVIDER: S-EPMC6013266 | biostudies-literature | 2018 Mar
REPOSITORIES: biostudies-literature
Publications
An Overview of Network-Based and -Free Approaches for Stochastic Simulation of Biochemical Systems.
Gupta Abhishekh A Mendes Pedro P
Computation (Basel, Switzerland) 20180131 1
Stochastic simulation has been widely used to model the dynamics of biochemical reaction networks. Several algorithms have been proposed that are exact solutions of the chemical master equation, following the work of Gillespie. These stochastic simulation approaches can be broadly classified into two categories: network-based and -free simulation. The network-based approach requires that the full network of reactions be established at the start, while the network-free approach is based on reacti ...[more]
Similar Datasets
Project description:Rule-based models, which are typically formulated to represent cell signaling systems, can now be simulated via various network-free simulation methods. In a network-free method, reaction rates are calculated for rules that characterize molecular interactions, and these rule rates, which each correspond to the cumulative rate of all reactions implied by a rule, are used to perform a stochastic simulation of reaction kinetics. Network-free methods, which can be viewed as generalizations of Gillespie's method, are so named because these methods do not require that a list of individual reactions implied by a set of rules be explicitly generated, which is a requirement of other methods for simulating rule-based models. This requirement is impractical for rule sets that imply large reaction networks (i.e. long lists of individual reactions), as reaction network generation is expensive. Here, we compare the network-free simulation methods implemented in RuleMonkey and NFsim, general-purpose software tools for simulating rule-based models encoded in the BioNetGen language. The method implemented in NFsim uses rejection sampling to correct overestimates of rule rates, which introduces null events (i.e. time steps that do not change the state of the system being simulated). The method implemented in RuleMonkey uses iterative updates to track rule rates exactly, which avoids null events. To ensure a fair comparison of the two methods, we developed implementations of the rejection and rejection-free methods specific to a particular class of kinetic models for multivalent ligand-receptor interactions. These implementations were written with the intention of making them as much alike as possible, minimizing the contribution of irrelevant coding differences to efficiency differences. Simulation results show that performance of the rejection method is equal to or better than that of the rejection-free method over wide parameter ranges. However, when parameter values are such that ligand-induced aggregation of receptors yields a large connected receptor cluster, the rejection-free method is more efficient.
| S-EPMC3168694 | biostudies-literature
Project description:Typical multiscale biochemical models contain fast-scale and slow-scale reactions, where "fast" reactions fire much more frequently than "slow" ones. This feature often causes stiffness in discrete stochastic simulation methods such as Gillespie's algorithm and the Tau-Leaping method leading to inefficient simulation. This paper proposes a new strategy to automatically detect stiffness and identify species that cause stiffness for the Tau-Leaping method, as well as two stiffness reduction methods. Numerical results on a stiff decaying dimerization model and a heat shock protein regulation model demonstrate the efficiency and accuracy of the proposed methods for multiscale biochemical systems.
| S-EPMC3045418 | biostudies-other
Project description:We propose a new framework for rigorous robustness analysis of stochastic biochemical systems that is based on probabilistic model checking techniques. We adapt the general definition of robustness introduced by Kitano to the class of stochastic systems modelled as continuous time Markov Chains in order to extensively analyse and compare robustness of biological models with uncertain parameters. The framework utilises novel computational methods that enable to effectively evaluate the robustness of models with respect to quantitative temporal properties and parameters such as reaction rate constants and initial conditions. We have applied the framework to gene regulation as an example of a central biological mechanism where intrinsic and extrinsic stochasticity plays crucial role due to low numbers of DNA and RNA molecules. Using our methods we have obtained a comprehensive and precise analysis of stochastic dynamics under parameter uncertainty. Furthermore, we apply our framework to compare several variants of two-component signalling networks from the perspective of robustness with respect to intrinsic noise caused by low populations of signalling components. We have successfully extended previous studies performed on deterministic models (ODE) and showed that stochasticity may significantly affect obtained predictions. Our case studies demonstrate that the framework can provide deeper insight into the role of key parameters in maintaining the system functionality and thus it significantly contributes to formal methods in computational systems biology.
| S-EPMC3994026 | biostudies-literature
Project description:Interacting Particle Systems (IPSs) are used to model spatio-temporal stochastic systems in many disparate areas of science. We design an algorithmic framework that reduces IPS simulation to simulation of well-mixed Chemical Reaction Networks (CRNs). This framework minimizes the number of associated reaction channels and decouples the computational cost of the simulations from the size of the lattice. Decoupling allows our software to make use of a wide class of techniques typically reserved for well-mixed CRNs. We implement the direct stochastic simulation algorithm in the open source programming language Julia. We also apply our algorithms to several complex spatial stochastic phenomena. including a rock-paper-scissors game, cancer growth in response to immunotherapy, and lipid oxidation dynamics. Our approach aids in standardizing mathematical models and in generating hypotheses based on concrete mechanistic behavior across a wide range of observed spatial phenomena.
| S-EPMC7924777 | biostudies-literature
Project description:BackgroundThe importance of stochasticity in cellular processes having low number of molecules has resulted in the development of stochastic models such as chemical master equation. As in other modelling frameworks, the accompanying rate constants are important for the end-applications like analyzing system properties (e.g. robustness) or predicting the effects of genetic perturbations. Prior knowledge of kinetic constants is usually limited and the model identification routine typically includes parameter estimation from experimental data. Although the subject of parameter estimation is well-established for deterministic models, it is not yet routine for the chemical master equation. In addition, recent advances in measurement technology have made the quantification of genetic substrates possible to single molecular levels. Thus, the purpose of this work is to develop practical and effective methods for estimating kinetic model parameters in the chemical master equation and other stochastic models from single cell and cell population experimental data.ResultsThree parameter estimation methods are proposed based on the maximum likelihood and density function distance, including probability and cumulative density functions. Since stochastic models such as chemical master equations are typically solved using a Monte Carlo approach in which only a finite number of Monte Carlo realizations are computationally practical, specific considerations are given to account for the effect of finite sampling in the histogram binning of the state density functions. Applications to three practical case studies showed that while maximum likelihood method can effectively handle low replicate measurements, the density function distance methods, particularly the cumulative density function distance estimation, are more robust in estimating the parameters with consistently higher accuracy, even for systems showing multimodality.ConclusionsThe parameter estimation methodologies described in this work have provided an effective and practical approach in the estimation of kinetic parameters of stochastic systems from either sparse or dense cell population data. Nevertheless, similar to kinetic parameter estimation in other modelling frameworks, not all parameters can be estimated accurately, which is a common problem arising from the lack of complete parameter identifiability from the available data.
| S-EPMC2928803 | biostudies-literature
Project description:Adaptation is a crucial biological function possessed by many sensory systems. Early work has shown that some influential equilibrium models can achieve accurate adaptation. However, recent studies indicate that there are close relationships between adaptation and nonequilibrium. In this paper, we provide an explanation of these two seemingly contradictory results based on Markov models with relatively simple networks. We show that as the nonequilibrium driving becomes stronger, the system under consideration will undergo a phase transition along a fixed direction: from non-adaptation to simple adaptation then to oscillatory adaptation, while the transition in the opposite direction is forbidden. This indicates that although adaptation may be observed in equilibrium systems, it tends to occur in systems far away from equilibrium. In addition, we find that nonequilibrium will improve the performance of adaptation by enhancing the adaptation efficiency. All these results provide a deeper insight into the connection between adaptation and nonequilibrium. Finally, we use a more complicated network model of bacterial chemotaxis to validate the main results of this paper.
| S-EPMC4873145 | biostudies-literature
Project description:In the mathematical modeling of biochemical reactions, a convenient standard approach is to use ordinary differential equations (ODEs) that follow the law of mass action. However, this deterministic ansatz is based on simplifications; in particular, it neglects noise, which is inherent to biological processes. In contrast, the stochasticity of reactions is captured in detail by the discrete chemical master equation (CME). Therefore, the CME is frequently applied to mesoscopic systems, where copy numbers of involved components are small and random fluctuations are thus significant. Here, we compare those two common modeling approaches, aiming at identifying parallels and discrepancies between deterministic variables and possible stochastic counterparts like the mean or modes of the state space probability distribution. To that end, a mathematically flexible reaction scheme of autoregulatory gene expression is translated into the corresponding ODE and CME formulations. We show that in the thermodynamic limit, deterministic stable fixed points usually correspond well to the modes in the stationary probability distribution. However, this connection might be disrupted in small systems. The discrepancies are characterized and systematically traced back to the magnitude of the stoichiometric coefficients and to the presence of nonlinear reactions. These factors are found to synergistically promote large and highly asymmetric fluctuations. As a consequence, bistable but unimodal, and monostable but bimodal systems can emerge. This clearly challenges the role of ODE modeling in the description of cellular signaling and regulation, where some of the involved components usually occur in low copy numbers. Nevertheless, systems whose bimodality originates from deterministic bistability are found to sustain a more robust separation of the two states compared to bimodal, but monostable systems. In regulatory circuits that require precise coordination, ODE modeling is thus still expected to provide relevant indications on the underlying dynamics.
| S-EPMC5005346 | biostudies-literature
Project description:MotivationMathematical modelling is central to systems and synthetic biology. Using simulations to calculate statistics or to explore parameter space is a common means for analysing these models and can be computationally intensive. However, in many cases, the simulations are easily parallelizable. Graphics processing units (GPUs) are capable of efficiently running highly parallel programs and outperform CPUs in terms of raw computing power. Despite their computational advantages, their adoption by the systems biology community is relatively slow, since differences in hardware architecture between GPUs and CPUs complicate the porting of existing code.ResultsWe present a Python package, cuda-sim, that provides highly parallelized algorithms for the repeated simulation of biochemical network models on NVIDIA CUDA GPUs. Algorithms are implemented for the three popular types of model formalisms: the LSODA algorithm for ODE integration, the Euler-Maruyama algorithm for SDE simulation and the Gillespie algorithm for MJP simulation. No knowledge of GPU computing is required from the user. Models can be specified in SBML format or provided as CUDA code. For running a large number of simulations in parallel, up to 360-fold decrease in simulation runtime is attained when compared to single CPU implementations.Availabilityhttp://cuda-sim.sourceforge.net/
| S-EPMC3051321 | biostudies-literature
Project description:Network medicine relies on different types of networks: from the molecular level of protein?protein interactions to gene regulatory network and correlation studies of gene expression. Among network approaches based on the analysis of the topological properties of protein?protein interaction (PPI) networks, we discuss the widespread DIAMOnD (disease module detection) algorithm. Starting from the assumption that PPI networks can be viewed as maps where diseases can be identified with localized perturbation within a specific neighborhood (i.e., disease modules), DIAMOnD performs a systematic analysis of the human PPI network to uncover new disease-associated genes by exploiting the connectivity significance instead of connection density. The past few years have witnessed the increasing interest in understanding the molecular mechanism of post-transcriptional regulation with a special emphasis on non-coding RNAs since they are emerging as key regulators of many cellular processes in both physiological and pathological states. Recent findings show that coding genes are not the only targets that microRNAs interact with. In fact, there is a pool of different RNAs-including long non-coding RNAs (lncRNAs) -competing with each other to attract microRNAs for interactions, thus acting as competing endogenous RNAs (ceRNAs). The framework of regulatory networks provides a powerful tool to gather new insights into ceRNA regulatory mechanisms. Here, we describe a data-driven model recently developed to explore the lncRNA-associated ceRNA activity in breast invasive carcinoma. On the other hand, a very promising example of the co-expression network is the one implemented by the software SWIM (switch miner), which combines topological properties of correlation networks with gene expression data in order to identify a small pool of genes-called switch genes-critically associated with drastic changes in cell phenotype. Here, we describe SWIM tool along with its applications to cancer research and compare its predictions with DIAMOnD disease genes.
| S-EPMC6162385 | biostudies-literature
Project description:Detailed modeling and simulation of biochemical systems is complicated by the problem of combinatorial complexity, an explosion in the number of species and reactions due to myriad protein-protein interactions and post-translational modifications. Rule-based modeling overcomes this problem by representing molecules as structured objects and encoding their interactions as pattern-based rules. This greatly simplifies the process of model specification, avoiding the tedious and error prone task of manually enumerating all species and reactions that can potentially exist in a system. From a simulation perspective, rule-based models can be expanded algorithmically into fully-enumerated reaction networks and simulated using a variety of network-based simulation methods, such as ordinary differential equations or Gillespie's algorithm, provided that the network is not exceedingly large. Alternatively, rule-based models can be simulated directly using particle-based kinetic Monte Carlo methods. This "network-free" approach produces exact stochastic trajectories with a computational cost that is independent of network size. However, memory and run time costs increase with the number of particles, limiting the size of system that can be feasibly simulated. Here, we present a hybrid particle/population simulation method that combines the best attributes of both the network-based and network-free approaches. The method takes as input a rule-based model and a user-specified subset of species to treat as population variables rather than as particles. The model is then transformed by a process of "partial network expansion" into a dynamically equivalent form that can be simulated using a population-adapted network-free simulator. The transformation method has been implemented within the open-source rule-based modeling platform BioNetGen, and resulting hybrid models can be simulated using the particle-based simulator NFsim. Performance tests show that significant memory savings can be achieved using the new approach and a monetary cost analysis provides a practical measure of its utility.
| S-EPMC3974646 | biostudies-literature