Interplay between Constraints,Objectives, and Optimality for Genome-Scale Stoichiometric Models

High-throughput data generation and genome-scale stoichiometric models have greatly facilitated the comprehensive study of metabolic networks. The computation of all feasible metabolic routes with these models, given stoichiometric, thermodynamic, and steady-state constraints, provides important insights into the metabolic capacities of a cell. How the feasible metabolic routes emerge from the interplay between flux constraints, optimality objectives, and the entire metabolic network of a cell is, however, only partially understood. We show how optimal metabolic routes, resulting from flux balance analysis computations, arise out of elementary flux modes, constraints, and optimization objectives. We illustrate our findings with a genome-scale stoichiometric model of Escherichia coli metabolism. In the case of one flux constraint, all feasible optimal flux routes can be derived from elementary flux modes alone. We found up to 120 million of such optimal elementary flux modes. We introduce a new computational method to compute the corner points of the optimal solution space fast and efficiently. Optimal flux routes no longer depend exclusively on elementary flux modes when we impose additional constraints; new optimal metabolic routes arise out of combinations of elementary flux modes. The solution space of feasible metabolic routes shrinks enormously when additional objectives---e.g. those related to pathway expression costs or pathway length---are introduced. In many cases, only a single metabolic route remains that is both feasible and optimal. This paper contributes to reaching a complete topological understanding of the metabolic capacity of organisms in terms of metabolic flux routes, one that is most natural to biochemists and biotechnologists studying and engineering metabolism.     

Network Reconstruction Using Nonparametric Additive ODE Models

Network representations of biological systems are widespread and reconstructing unknown networks from data is a focal problem for computational biologists. For example, the series of biochemical reactions in a metabolic pathway can be represented as a network, with nodes corresponding to metabolites and edges linking reactants to products. In a different context, regulatory relationships among genes are commonly represented as directed networks with edges pointing from influential genes to their targets. Reconstructing such networks from data is a challenging problem receiving much attention in the literature. There is a particular need for approaches tailored to time-series data and not reliant on direct intervention experiments, as the former are often more readily available. In this paper, we introduce an approach to reconstructing directed networks based on dynamic systems models. Our approach generalizes commonly used ODE models based on linear or nonlinear dynamics by extending the functional class for the functions involved from parametric to nonparametric models. Concomitantly we limit the complexity by imposing an additive structure on the estimated slope functions. Thus the submodel associated with each node is a sum of univariate functions. These univariate component functions form the basis for a novel coupling metric that we define in order to quantify the strength of proposed relationships and hence rank potential edges. We show the utility of the method by reconstructing networks using simulated data from computational models for the glycolytic pathway of Lactocaccus Lactis and a gene network regulating the pluripotency of mouse embryonic stem cells. For purposes of comparison, we also assess reconstruction performance using gene networks from the DREAM challenges. We compare our method to those that similarly rely on dynamic systems models and use the results to attempt to disentangle the distinct roles of linearity, sparsity, and derivative estimation.     

From Enzyme Kinetics to Metabolic Network Modeling – Visualization Tool for Enhanced Kinetic Analysis of Biochemical Network Models

Model‐based analysis of enzyme kinetics allows the determination of optimal conditions for their use in biocatalysis. For biotransformations or fermentative approaches the modeling of metabolic pathways or complex metabolic networks is necessary to obtain model‐based predictions of steps which limit product formation within the network. To set up adequate kinetic models, relevant mechanistic information about enzyme properties is required and can be taken from in vitro studies with isolated enzymes or from in vivo investigations using stimulus‐response experiments which provide a lot of kinetic information about the metabolic network. But with increasing number of reaction steps and regulatory interdependencies in the network structure the amount of simulation data dramatically increases and the simulation results from the dynamic models become difficult to analyze and interpret. Demonstrated for an Escherichia coli model of the central carbon metabolism, methods for visualization and animation of simulation data were applied and extended to facilitate model analysis and biological interpretation. The dynamic metabolite pool and metabolic flux changes were visualized simultaneously by a software tool. In addition, a new quantification method for enzyme activation/inhibition was proposed, and this information was implemented in the metabolic visualization.     

Extended Kalman Filter for Estimation of Parameters in Nonlinear State-Space Models of Biochemical Networks

It is system dynamics that determines the function of cells, tissues and organisms. To develop mathematical models and estimate their parameters are an essential issue for studying dynamic behaviors of biological systems which include metabolic networks, genetic regulatory networks and signal transduction pathways, under perturbation of external stimuli. In general, biological dynamic systems are partially observed. Therefore, a natural way to model dynamic biological systems is to employ nonlinear state-space equations. Although statistical methods for parameter estimation of linear models in biological dynamic systems have been developed intensively in the recent years, the estimation of both states and parameters of nonlinear dynamic systems remains a challenging task. In this report, we apply extended Kalman Filter (EKF) to the estimation of both states and parameters of nonlinear state-space models. To evaluate the performance of the EKF for parameter estimation, we apply the EKF to a simulation dataset and two real datasets: JAK-STAT signal transduction pathway and Ras/Raf/MEK/ERK signaling transduction pathways datasets. The preliminary results show that EKF can accurately estimate the parameters and predict states in nonlinear state-space equations for modeling dynamic biochemical networks.     

Multiomics metabolic and epigenetics regulatory network in cancer: A systems biology perspective

Genetic, epigenetic, and metabolic alterations are all hallmarks of cancer. However, the epigenome and metabolome are both highly complex and dynamic biological networks in vivo. The interplay between the epigenome and metabolome contributes to a biological system that is responsive to the tumor microenvironment and possesses a wealth of unknown biomarkers and targets of cancer therapy. From this perspective, we first review the state of high-throughput biological data acquisition(i.e. multiomics data)and analysis(i.e. computational tools) and then propose a conceptual in silico metabolic and epigenetic regulatory network(MER-Net) that is based on these current high-throughput methods. The conceptual MER-Net is aimed at linking metabolomic and epigenomic networks through observation of biological processes, omics data acquisition, analysis of network information, and integration with validated database knowledge. Thus, MER-Net could be used to reveal new potential biomarkers and therapeutic targets using deep learning models to integrate and analyze large multiomics networks. We propose that MER-Net can serve as a tool to guide integrated metabolomics and epigenomics research or can be modified to answer other complex biological and clinical questions using multiomics data.     

Antiidiotypic networks

Jerne envisions the immune system as a web of V domains that constitutes an idiotypic network. He thinks that regulatory processes governed by idiotypic interactions can explain the generation of the various immune states. We discuss a few models that furnish information about the possible configuration of this immune network: closed or open ended. It appears that closed configurations only can generate stable immune states. Moreover, we cite some experimental data in favor of the network hypothesis. We show how they can lead to propose the structure of functional regulatory circuits whose cellular and molecular interactions are mediated by idiotypic recognition processes.     

Stochastic Computations in Cortical Microcircuit Models

Experimental data from neuroscience suggest that a substantial amount of knowledge is stored in the brain in the form of probability distributions over network states and trajectories of network states. We provide a theoretical foundation for this hypothesis by showing that even very detailed models for cortical microcircuits, with data-based diverse nonlinear neurons and synapses, have a stationary distribution of network states and trajectories of network states to which they converge exponentially fast from any initial state. We demonstrate that this convergence holds in spite of the non-reversibility of the stochastic dynamics of cortical microcircuits. We further show that, in the presence of background network oscillations, separate stationary distributions emerge for different phases of the oscillation, in accordance with experimentally reported phase-specific codes. We complement these theoretical results by computer simulations that investigate resulting computation times for typical probabilistic inference tasks on these internally stored distributions, such as marginalization or marginal maximum-a-posteriori estimation. Furthermore, we show that the inherent stochastic dynamics of generic cortical microcircuits enables them to quickly generate approximate solutions to difficult constraint satisfaction problems, where stored knowledge and current inputs jointly constrain possible solutions. This provides a powerful new computing paradigm for networks of spiking neurons, that also throws new light on how networks of neurons in the brain could carry out complex computational tasks such as prediction, imagination, memory recall and problem solving.     

Stoichiometric network analysis

Stoichiometric network analysis is a systematic, general approach to the qualitative, nonlinear dynamics of chemical reaction mechanisms and other systems with stoichiometry. The advantage of a qualitative approach is that no rate constants are needed to determine qualitative features of the dynamics. If one is interested in stability, the approach yields inequalities among the steady-state concentrations and the rate of flow through sequences of important reactions. These parameters are often the ones most easily measured experimentally. By comparing such experiments with the inequalities derived from stoichiometric network analysis, one can often prove that certain mechanisms cannot account for oscillations or other types of observed dynamics. The approach covers far more than stability. The existence of steady states of zero concentration has an interesting mathematics and applies to chemical evolution. The folding of the manifold of steady states can be found by direct calculation and plays a role in switching enzymes on and off. The approach leads to theorems showing that some steady states are globally attracting or, possibly, that a region containing chaos or an oscillation is globally attracting. The subject of sensitivity analysis has been reformulated in this context. Algorithms that apply many of the theoretical results to chemical networks have been developed and combined into a computer program package.     

Modeling DNA sequence-based cis-regulatory gene networks

Gene network analysis requires computationally based models which represent the functional architecture of regulatory interactions, and which provide directly testable predictions. The type of model that is useful is constrained by the particular features of developmentally active cis-regulatory systems. These systems function by processing diverse regulatory inputs, generating novel regulatory outputs. A computational model which explicitly accommodates this basic concept was developed earlier for the cis-regulatory system of the endo16 gene of the sea urchin. This model represents the genetically mandated logic functions that the system executes, but also shows how time-varying kinetic inputs are processed in different circumstances into particular kinetic outputs. The same basic design features can be utilized to construct models that connect the large number of cis-regulatory elements constituting developmental gene networks. The ultimate aim of the network models discussed here is to represent the regulatory relationships among the genomic control systems of the genes in the network, and to state their functional meaning. The target site sequences of the cis-regulatory elements of these genes constitute the physical basis of the network architecture. Useful models for developmental regulatory networks must represent the genetic logic by which the system operates, but must also be capable of explaining the real time dynamics of cis-regulatory response as kinetic input and output data become available. Most importantly, however, such models must display in a direct and transparent manner fundamental network design features such as intra- and intercellular feedback circuitry; the sources of parallel inputs into each cis-regulatory element; gene battery organization; and use of repressive spatial inputs in specification and boundary formation. Successful network models lead to direct tests of key architectural features by targeted cis-regulatory analysis.     

Allele-Specific Behavior of Molecular Networks: Understanding Small-Molecule Drug Response in Yeast

The study of systems genetics is changing the way the genetic and molecular basis of phenotypic variation, such as disease susceptibility and drug response, is being analyzed. Moreover, systems genetics aids in the translation of insights from systems biology into genetics. The use of systems genetics enables greater attention to be focused on the potential impact of genetic perturbations on the molecular states of networks that in turn affects complex traits. In this study, we developed models to detect allele-specific perturbations on interactions, in which a genetic locus with alternative alleles exerted a differing influence on an interaction. We utilized the models to investigate the dynamic behavior of an integrated molecular network undergoing genetic perturbations in yeast. Our results revealed the complexity of regulatory relationships between genetic loci and networks, in which different genetic loci perturb specific network modules. In addition, significant within-module functional coherence was found. We then used the network perturbation model to elucidate the underlying molecular mechanisms of individual differences in response to 100 diverse small molecule drugs. As a result, we identified sub-networks in the integrated network that responded to variations in DNA associated with response to diverse compounds and were significantly enriched for known drug targets. Literature mining results provided strong independent evidence for the effectiveness of these genetic perturbing networks in the elucidation of small-molecule responses in yeast.     

Food web models: a plea for groups

The concept of a group is ubiquitous in biology. It underlies classifications in evolution and ecology, including those used to describe phylogenetic levels, the habitat and functional roles of organisms in ecosystems. Surprisingly, this concept is not explicitly included in simple models for the structure of food webs, the ecological networks formed by consumer–resource interactions. We present here the simplest possible model based on groups, and show that it performs substantially better than current models at predicting the structure of large food webs. Our group-based model can be applied to different types of biological and non-biological networks, and for the first time merges in the same framework two important notions in network theory: that of compartments (sets of highly interacting nodes) and that of roles (sets of nodes that have similar interaction patterns). This model provides a basis to examine the significance of groups in biological networks and to develop more accurate models for ecological network structure. It is especially relevant at a time when a new generation of empirical data is providing increasingly large food webs.     

Multivariate analysis of noise in genetic regulatory networks

Stochasticity is an intrinsic property of genetic regulatory networks due to the low copy numbers of the major molecular species, such as, DNA, mRNA, and regulatory proteins. Therefore, investigation of the mechanisms that reduce the stochastic noise is essential in understanding the reproducible behaviors of real organisms and is also a key to design synthetic genetic regulatory networks that can reliably work. We use an analytical and systematic method, the linear noise approximation of the chemical master equation along with the decoupling of a stoichiometric matrix. In the analysis of fluctuations of multiple molecular species, the covariance is an important measure of noise. However, usually the representation of a covariance matrix in the natural coordinate system, i.e. the copy numbers of the molecular species, is intractably complicated because reactions change copy numbers of more than one molecular species simultaneously. Decoupling of a stoichiometric matrix, which is a transformation of variables, significantly simplifies the representation of a covariance matrix and elucidates the mechanisms behind the observed fluctuations in the copy numbers. We apply our method to three types of fundamental genetic regulatory networks, that is, a single-gene autoregulatory network, a two-gene autoregulatory network, and a mutually repressive network. We have found that there are multiple noise components differently originating. Each noise component produces fluctuation in the characteristic direction. The resulting fluctuations in the copy numbers of the molecular species are the sum of these fluctuations. In the examples, the limitation of the negative feedback in noise reduction and the trade-off of fluctuations in multiple molecular species are clearly explained. The analytical representations show the full parameter dependence. Additionally, the validity of our method is tested by stochastic simulations.     

A Tutorial on Analysis and Simulation of Boolean Gene Regulatory Network Models

Driven by the desire to understand genomic functions through the interactions among genes and gene products, the research in gene regulatory networks has become a heated area in genomic signal processing. Among the most studied mathematical models are Boolean networks and probabilistic Boolean networks, which are rule-based dynamic systems. This tutorial provides an introduction to the essential concepts of these two Boolean models, and presents the up-to-date analysis and simulation methods developed for them. In the Analysis section, we will show that Boolean models are Markov chains, based on which we present a Markovian steady-state analysis on attractors, and also reveal the relationship between probabilistic Boolean networks and dynamic Bayesian networks (another popular genetic network model), again via Markov analysis; we dedicate the last subsection to structural analysis, which opens a door to other topics such as network control. The Simulation section will start from the basic tasks of creating state transition diagrams and finding attractors, proceed to the simulation of network dynamics and obtaining the steady-state distributions, and finally come to an algorithm of generating artificial Boolean networks with prescribed attractors. The contents are arranged in a roughly logical order, such that the Markov chain analysis lays the basis for the most part of Analysis section, and also prepares the readers to the topics in Simulation section.     

Mechanistic pathway modeling for industrial biotechnology: challenging but worthwhile

Mechanistic (also called kinetic) models quantitatively describe dynamic and steady states of biochemical pathways. They are based on network structure (stoichiometry), regulatory information (enzyme inhibitors and activators) and the corresponding reaction kinetics. Although this approach to understand and predict the behavior of biochemical networks has now been in use for almost half a century, its experimental foundation has dramatically changed in the data-rich age of systems biology. Large mechanistic models, ranging up to the genome scale, are now being built and lots of data are available to validate and test them. From the broad scope of possible modeling applications, this survey focuses on the recent developments and central problems of metabolic network modeling in the field of bioprocess development for industrial biotechnology.     

Gene and epigene networks: Two levels in organizing the hereditary system

Intracellular governing gene networks consisting of genes and regulatory bonds among them are considered as the first level in organizing the hereditary system. We give examples of both prokaryotic gene network that controls the development of the λ-phage and eukaryotic gene network that controls the early Drosophila ontogenesis. Using the method of generalized threshold models kinetic curves are shown for some gene products of these networks. Gene networks that govern ontogenetic processes can be envisioned as epigene networks, the networks of the subsequent level in organizing the hereditary systems. Based on the mathematical model our computer experiments show that even the simplest hypothetical two-epigene network is capable of ensuring divergent determination, conservation of determinate states and reproduction of the initial “zygotic” functional state. In addition, the experimental results are given on construction an artificial epigene.