A hybrid multiscale Monte Carlo algorithm (HyMSMC) to cope with disparity in time scales and species populations in intracellular networks

Background  

The fundamental role that intrinsic stochasticity plays in cellular functions has been shown via numerous computational and experimental studies. In the face of such evidence, it is important that intracellular networks are simulated with stochastic algorithms that can capture molecular fluctuations. However, separation of time scales and disparity in species population, two common features of intracellular networks, make stochastic simulation of such networks computationally prohibitive. While recent work has addressed each of these challenges separately, a generic algorithm that can simultaneously tackle disparity in time scales and population scales in stochastic systems is currently lacking. In this paper, we propose the hybrid, multiscale Monte Carlo (HyMSMC) method that fills in this void.     

Quantifying robustness of biochemical network models

Background  

Robustness of mathematical models of biochemical networks is important for validation purposes and can be used as a means of selecting between different competing models. Tools for quantifying parametric robustness are needed.     

A method for the generation of standardized qualitative dynamical systems of regulatory networks

Background  

Modeling of molecular networks is necessary to understand their dynamical properties. While a wealth of information on molecular connectivity is available, there are still relatively few data regarding the precise stoichiometry and kinetics of the biochemical reactions underlying most molecular networks. This imbalance has limited the development of dynamical models of biological networks to a small number of well-characterized systems. To overcome this problem, we wanted to develop a methodology that would systematically create dynamical models of regulatory networks where the flow of information is known but the biochemical reactions are not. There are already diverse methodologies for modeling regulatory networks, but we aimed to create a method that could be completely standardized, i.e. independent of the network under study, so as to use it systematically.     

A new computational method to split large biochemical networks into coherent subnets

Background  

Compared to more general networks, biochemical networks have some special features: while generally sparse, there are a small number of highly connected metabolite nodes; and metabolite nodes can also be divided into two classes: internal nodes with associated mass balance constraints and external ones without. Based on these features, reclassifying selected internal nodes (separators) to external ones can be used to divide a large complex metabolic network into simpler subnetworks. Selection of separators based on node connectivity is commonly used but affords little detailed control and tends to produce excessive fragmentation.     

Propagation of kinetic uncertainties through a canonical topology of the TLR4 signaling network in different regions of biochemical reaction space

Background  

Signal transduction networks represent the information processing systems that dictate which dynamical regimes of biochemical activity can be accessible to a cell under certain circumstances. One of the major concerns in molecular systems biology is centered on the elucidation of the robustness properties and information processing capabilities of signal transduction networks. Achieving this goal requires the establishment of causal relations between the design principle of biochemical reaction systems and their emergent dynamical behaviors.     

Parameter inference for discretely observed stochastic kinetic models using stochastic gradient descent

Background  

Stochastic effects can be important for the behavior of processes involving small population numbers, so the study of stochastic models has become an important topic in the burgeoning field of computational systems biology. However analysis techniques for stochastic models have tended to lag behind their deterministic cousins due to the heavier computational demands of the statistical approaches for fitting the models to experimental data. There is a continuing need for more effective and efficient algorithms. In this article we focus on the parameter inference problem for stochastic kinetic models of biochemical reactions given discrete time-course observations of either some or all of the molecular species.     

A method for determining the robustness of bio-molecular oscillator models

Background  

Quantifying the robustness of biochemical models is important both for determining the validity of a natural system model and for designing reliable and robust synthetic biochemical networks. Several tools have been proposed in the literature. Unfortunately, multiparameter robustness analysis suffers from computational limitations.     

Cluster analysis of networks generated through homology: automatic identification of important protein communities involved in cancer metastasis

Background  

Protein-protein interactions have traditionally been studied on a small scale, using classical biochemical methods to investigate the proteins of interest. More recently large-scale methods, such as two-hybrid screens, have been utilised to survey extensive portions of genomes. Current high-throughput approaches have a relatively high rate of errors, whereas in-depth biochemical studies are too expensive and time-consuming to be practical for extensive studies. As a result, there are gaps in our knowledge of many key biological networks, for which computational approaches are particularly suitable.     

Modeling cardiac β-adrenergic signaling with normalized-Hill differential equations: comparison with a biochemical model

Background  

New approaches are needed for large-scale predictive modeling of cellular signaling networks. While mass action and enzyme kinetic approaches require extensive biochemical data, current logic-based approaches are used primarily for qualitative predictions and have lacked direct quantitative comparison with biochemical models.     

Stochastic simulations of the tetracycline operon

Background  

The tetracycline operon is a self-regulated system. It is found naturally in bacteria where it confers resistance to antibiotic tetracycline. Because of the performance of the molecular elements of the tetracycline operon, these elements are widely used as parts of synthetic gene networks where the protein production can be efficiently turned on and off in response to the presence or the absence of tetracycline. In this paper, we investigate the dynamics of the tetracycline operon. To this end, we develop a mathematical model guided by experimental findings. Our model consists of biochemical reactions that capture the biomolecular interactions of this intriguing system. Having in mind that small biological systems are subjects to stochasticity, we use a stochastic algorithm to simulate the tetracycline operon behavior. A sensitivity analysis of two critical parameters embodied this system is also performed providing a useful understanding of the function of this system.     

Intervention in gene regulatory networks via greedy control policies based on long-run behavior

Background  

A salient purpose for studying gene regulatory networks is to derive intervention strategies, the goals being to identify potential drug targets and design gene-based therapeutic intervention. Optimal stochastic control based on the transition probability matrix of the underlying Markov chain has been studied extensively for probabilistic Boolean networks. Optimization is based on minimization of a cost function and a key goal of control is to reduce the steady-state probability mass of undesirable network states. Owing to computational complexity, it is difficult to apply optimal control for large networks.     

Probability distributed time delays: integrating spatial effects into temporal models

Background  

In order to provide insights into the complex biochemical processes inside a cell, modelling approaches must find a balance between achieving an adequate representation of the physical phenomena and keeping the associated computational cost within reasonable limits. This issue is particularly stressed when spatial inhomogeneities have a significant effect on system's behaviour. In such cases, a spatially-resolved stochastic method can better portray the biological reality, but the corresponding computer simulations can in turn be prohibitively expensive.     

Facile: a command-line network compiler for systems biology

Background  

A goal of systems biology is the quantitative modelling of biochemical networks. Yet for many biochemical systems, parameter values and even the existence of interactions between some chemical species are unknown. It is therefore important to be able to easily investigate the effects of adding or removing reactions and to easily perform a bifurcation analysis, which shows the qualitative dynamics of a model for a range of parameter values.     

Bayesian inference of biochemical kinetic parameters using the linear noise approximation

Background  

Fluorescent and luminescent gene reporters allow us to dynamically quantify changes in molecular species concentration over time on the single cell level. The mathematical modeling of their interaction through multivariate dynamical models requires the deveopment of effective statistical methods to calibrate such models against available data. Given the prevalence of stochasticity and noise in biochemical systems inference for stochastic models is of special interest. In this paper we present a simple and computationally efficient algorithm for the estimation of biochemical kinetic parameters from gene reporter data.     

Generalized method of moments for estimating parameters of stochastic reaction networks

Background

Discrete-state stochastic models have become a well-established approach to describe biochemical reaction networks that are influenced by the inherent randomness of cellular events. In the last years several methods for accurately approximating the statistical moments of such models have become very popular since they allow an efficient analysis of complex networks.

Results

We propose a generalized method of moments approach for inferring the parameters of reaction networks based on a sophisticated matching of the statistical moments of the corresponding stochastic model and the sample moments of population snapshot data. The proposed parameter estimation method exploits recently developed moment-based approximations and provides estimators with desirable statistical properties when a large number of samples is available. We demonstrate the usefulness and efficiency of the inference method on two case studies.

Conclusions

The generalized method of moments provides accurate and fast estimations of unknown parameters of reaction networks. The accuracy increases when also moments of order higher than two are considered. In addition, the variance of the estimator decreases, when more samples are given or when higher order moments are included.

     

Modelling biochemical networks with intrinsic time delays: a hybrid semi-parametric approach

Background  

This paper presents a method for modelling dynamical biochemical networks with intrinsic time delays. Since the fundamental mechanisms leading to such delays are many times unknown, non conventional modelling approaches become necessary. Herein, a hybrid semi-parametric identification methodology is proposed in which discrete time series are incorporated into fundamental material balance models. This integration results in hybrid delay differential equations which can be applied to identify unknown cellular dynamics.     

Toward the automated generation of genome-scale metabolic networks in the SEED

Background  

Current methods for the automated generation of genome-scale metabolic networks focus on genome annotation and preliminary biochemical reaction network assembly, but do not adequately address the process of identifying and filling gaps in the reaction network, and verifying that the network is suitable for systems level analysis. Thus, current methods are only sufficient for generating draft-quality networks, and refinement of the reaction network is still largely a manual, labor-intensive process.