Characterizing multistationarity regimes in biochemical reaction networks

Switch like responses appear as common strategies in the regulation of cellular systems. Here we present a method to characterize bistable regimes in biochemical reaction networks that can be of use to both direct and reverse engineering of biological switches. In the design of a synthetic biological switch, it is important to study the capability for bistability of the underlying biochemical network structure. Chemical Reaction Network Theory (CRNT) may help at this level to decide whether a given network has the capacity for multiple positive equilibria, based on their structural properties. However, in order to build a working switch, we also need to ensure that the bistability property is robust, by studying the conditions leading to the existence of two different steady states. In the reverse engineering of biological switches, knowledge collected about the bistable regimes of the underlying potential model structures can contribute at the model identification stage to a drastic reduction of the feasible region in the parameter space of search. In this work, we make use and extend previous results of the CRNT, aiming not only to discriminate whether a biochemical reaction network can exhibit multiple steady states, but also to determine the regions within the whole space of parameters capable of producing multistationarity. To that purpose we present and justify a condition on the parameters of biochemical networks for the appearance of multistationarity, and propose an efficient and reliable computational method to check its satisfaction through the parameter space.     

From Boolean Network Model to Continuous Model Helps in Design of Functional Circuits

Computational circuit design with desired functions in a living cell is a challenging task in synthetic biology. To achieve this task, numerous methods that either focus on small scale networks or use evolutionary algorithms have been developed. Here, we propose a two-step approach to facilitate the design of functional circuits. In the first step, the search space of possible topologies for target functions is reduced by reverse engineering using a Boolean network model. In the second step, continuous simulation is applied to evaluate the performance of these topologies. We demonstrate the usefulness of this method by designing an example biological function: the SOS response of E. coli. Our numerical results show that the desired function can be faithfully reproduced by candidate networks with different parameters and initial conditions. Possible circuits are ranked according to their robustness against perturbations in parameter and gene expressions. The biological network is among the candidate networks, yet novel designs can be generated. Our method provides a scalable way to design robust circuits that can achieve complex functions, and makes it possible to uncover design principles of biological networks.     

Multisite phosphorylation and network dynamics of cyclin-dependent kinase signaling in the eukaryotic cell cycle

Multisite phosphorylation of regulatory proteins has been proposed to underlie ultrasensitive responses required to generate nontrivial dynamics in complex biological signaling networks. We used a random search strategy to analyze the role of multisite phosphorylation of key proteins regulating cyclin-dependent kinase (CDK) activity in a model of the eukaryotic cell cycle. We show that multisite phosphorylation of either CDK, CDC25, wee1, or CDK-activating kinase is sufficient to generate dynamical behaviors including bistability and limit cycles. Moreover, combining multiple feedback loops based on multisite phosphorylation do not destabilize the cell cycle network by inducing complex behavior, but rather increase the overall robustness of the network. In this model we find that bistability is the major dynamical behavior of the CDK signaling network, and that negative feedback converts bistability into limit cycle behavior. We also compare the dynamical behavior of several simplified models of CDK regulation to the fully detailed model. In summary, our findings suggest that multisite phosphorylation of proteins is a critical biological mechanism in generating the essential dynamics and ensuring robust behavior of the cell cycle.     

Gene regulatory network modeling via global optimization of high-order dynamic Bayesian network

ABSTRACT: BACKGROUND: Dynamic Bayesian network (DBN) is among the mainstream approaches for modeling various biological networks, including the gene regulatory network (GRN). Most current methods for learning DBN employ either local search such as hill-climbing, or a meta stochastic global optimization framework such as genetic algorithm or simulated annealing, which are only able to locate sub-optimal solutions. Further, current DBN applications have essentially been limited to small sized networks. RESULTS: To overcome the above difficulties, we introduce here a deterministic global optimization based DBN approach for reverse engineering genetic networks from time course gene expression data. For such DBN models that consist only of inter time slice arcs, we show that there exists a polynomial time algorithm for learning the globally optimal network structure. The proposed approach, named GlobalMIT+, employs the recently proposed information theoretic scoring metric named mutual information test (MIT). GlobalMIT+ is able to learn high-order time delayed genetic interactions, which are common to most biological systems. Evaluation of the approach using both synthetic and real data sets, including a 733 cyanobacterial gene expression data set, shows significantly improved performance over other techniques. CONCLUSIONS: Our studies demonstrate that deterministic global optimization approaches can infer large scale genetic networks.     

Memory switches in chemical reaction space

Just as complex electronic circuits are built from simple Boolean gates, diverse biological functions, including signal transduction, differentiation, and stress response, frequently use biochemical switches as a functional module. A relatively small number of such switches have been described in the literature, and these exhibit considerable diversity in chemical topology. We asked if biochemical switches are indeed rare and if there are common chemical motifs and family relationships among such switches. We performed a systematic exploration of chemical reaction space by generating all possible stoichiometrically valid chemical configurations up to 3 molecules and 6 reactions and up to 4 molecules and 3 reactions. We used Monte Carlo sampling of parameter space for each such configuration to generate specific models and checked each model for switching properties. We found nearly 4,500 reaction topologies, or about 10% of our tested configurations, that demonstrate switching behavior. Commonly accepted topological features such as feedback were poor predictors of bistability, and we identified new reaction motifs that were likely to be found in switches. Furthermore, the discovered switches were related in that most of the larger configurations were derived from smaller ones by addition of one or more reactions. To explore even larger configurations, we developed two tools: the “bistabilizer,” which converts almost-bistable systems into bistable ones, and frequent motif mining, which helps rank untested configurations. Both of these tools increased the coverage of our library of bistable systems. Thus, our systematic exploration of chemical reaction space has produced a valuable resource for investigating the key signaling motif of bistability.     

Reverse engineering of metabolic networks, a critical assessment

Inferring metabolic networks from metabolite concentration data is a central topic in systems biology. Mathematical techniques to extract information about the network from data have been proposed in the literature. This paper presents a critical assessment of the feasibility of reverse engineering of metabolic networks, illustrated with a selection of methods. Appropriate data are simulated to study the performance of four representative methods. An overview of sampling and measurement methods currently in use for generating time-resolved metabolomics data is given and contrasted with the needs of the discussed reverse engineering methods. The results of this assessment show that if full inference of a real-world metabolic network is the goal there is a large discrepancy between the requirements of reverse engineering of metabolic networks and contemporary measurement practice. Recommendations for improved time-resolved experimental designs are given.     

Hub-centered gene network reconstruction using automatic relevance determination

Network inference deals with the reconstruction of biological networks from experimental data. A variety of different reverse engineering techniques are available; they differ in the underlying assumptions and mathematical models used. One common problem for all approaches stems from the complexity of the task, due to the combinatorial explosion of different network topologies for increasing network size. To handle this problem, constraints are frequently used, for example on the node degree, number of edges, or constraints on regulation functions between network components. We propose to exploit topological considerations in the inference of gene regulatory networks. Such systems are often controlled by a small number of hub genes, while most other genes have only limited influence on the network's dynamic. We model gene regulation using a Bayesian network with discrete, Boolean nodes. A hierarchical prior is employed to identify hub genes. The first layer of the prior is used to regularize weights on edges emanating from one specific node. A second prior on hyperparameters controls the magnitude of the former regularization for different nodes. The net effect is that central nodes tend to form in reconstructed networks. Network reconstruction is then performed by maximization of or sampling from the posterior distribution. We evaluate our approach on simulated and real experimental data, indicating that we can reconstruct main regulatory interactions from the data. We furthermore compare our approach to other state-of-the art methods, showing superior performance in identifying hubs. Using a large publicly available dataset of over 800 cell cycle regulated genes, we are able to identify several main hub genes. Our method may thus provide a valuable tool to identify interesting candidate genes for further study. Furthermore, the approach presented may stimulate further developments in regularization methods for network reconstruction from data.     

MORE: Mixed Optimization for Reverse Engineering-An Application to Modeling Biological Networks Response via Sparse Systems of Nonlinear Differential Equations

Reverse engineering is the problem of inferring the structure of a network of interactions between biological variables from a set of observations. In this paper, we propose an optimization algorithm, called MORE, for the reverse engineering of biological networks from time series data. The model inferred by MORE is a sparse system of nonlinear differential equations, complex enough to realistically describe the dynamics of a biological system. MORE tackles separately the discrete component of the problem, the determination of the biological network topology, and the continuous component of the problem, the strength of the interactions. This approach allows us both to enforce system sparsity, by globally constraining the number of edges, and to integrate a priori information about the structure of the underlying interaction network. Experimental results on simulated and real-world networks show that the mixed discrete/continuous optimization approach of MORE significantly outperforms standard continuous optimization and that MORE is competitive with the state of the art in terms of accuracy of the inferred networks.     

Bifurcations of emergent bursting in a neuronal network

Complex neuronal networks are an important tool to help explain paradoxical phenomena observed in biological recordings. Here we present a general approach to mathematically tackle a complex neuronal network so that we can fully understand the underlying mechanisms. Using a previously developed network model of the milk-ejection reflex in oxytocin cells, we show how we can reduce a complex model with many variables and complex network topologies to a tractable model with two variables, while retaining all key qualitative features of the original model. The approach enables us to uncover how emergent synchronous bursting can arise from a neuronal network which embodies known biological features. Surprisingly, the bursting mechanisms are similar to those found in other systems reported in the literature, and illustrate a generic way to exhibit emergent and multiple time scale oscillations at the membrane potential level and the firing rate level.     

Evolving Robust Gene Regulatory Networks

Design and implementation of robust network modules is essential for construction of complex biological systems through hierarchical assembly of ‘parts’ and ‘devices’. The robustness of gene regulatory networks (GRNs) is ascribed chiefly to the underlying topology. The automatic designing capability of GRN topology that can exhibit robust behavior can dramatically change the current practice in synthetic biology. A recent study shows that Darwinian evolution can gradually develop higher topological robustness. Subsequently, this work presents an evolutionary algorithm that simulates natural evolution in silico, for identifying network topologies that are robust to perturbations. We present a Monte Carlo based method for quantifying topological robustness and designed a fitness approximation approach for efficient calculation of topological robustness which is computationally very intensive. The proposed framework was verified using two classic GRN behaviors: oscillation and bistability, although the framework is generalized for evolving other types of responses. The algorithm identified robust GRN architectures which were verified using different analysis and comparison. Analysis of the results also shed light on the relationship among robustness, cooperativity and complexity. This study also shows that nature has already evolved very robust architectures for its crucial systems; hence simulation of this natural process can be very valuable for designing robust biological systems.     

Trade-off between responsiveness and noise suppression in biomolecular system responses to environmental cues

When living systems detect changes in their external environment their response must be measured to balance the need to react appropriately with the need to remain stable, ignoring insignificant signals. Because this is a fundamental challenge of all biological systems that execute programs in response to stimuli, we developed a generalized time-frequency analysis (TFA) framework to systematically explore the dynamical properties of biomolecular networks. Using TFA, we focused on two well-characterized yeast gene regulatory networks responsive to carbon-source shifts and a mammalian innate immune regulatory network responsive to lipopolysaccharides (LPS). The networks are comprised of two different basic architectures. Dual positive and negative feedback loops make up the yeast galactose network; whereas overlapping positive and negative feed-forward loops are common to the yeast fatty-acid response network and the LPS-induced network of macrophages. TFA revealed remarkably distinct network behaviors in terms of trade-offs in responsiveness and noise suppression that are appropriately tuned to each biological response. The wild type galactose network was found to be highly responsive while the oleate network has greater noise suppression ability. The LPS network appeared more balanced, exhibiting less bias toward noise suppression or responsiveness. Exploration of the network parameter space exposed dramatic differences in system behaviors for each network. These studies highlight fundamental structural and dynamical principles that underlie each network, reveal constrained parameters of positive and negative feedback and feed-forward strengths that tune the networks appropriately for their respective biological roles, and demonstrate the general utility of the TFA approach for systems and synthetic biology.     

Gene regulatory network inference and validation using relative change ratio analysis and time-delayed dynamic Bayesian network

The Dialogue for Reverse Engineering Assessments and Methods (DREAM) project was initiated in 2006 as a community-wide effort for the development of network inference challenges for rigorous assessment of reverse engineering methods for biological networks. We participated in the in silico network inference challenge of DREAM3 in 2008. Here we report the details of our approach and its performance on the synthetic challenge datasets. In our methodology, we first developed a model called relative change ratio (RCR), which took advantage of the heterozygous knockdown data and null-mutant knockout data provided by the challenge, in order to identify the potential regulators for the genes. With this information, a time-delayed dynamic Bayesian network (TDBN) approach was then used to infer gene regulatory networks from time series trajectory datasets. Our approach considerably reduced the searching space of TDBN; hence, it gained a much higher efficiency and accuracy. The networks predicted using our approach were evaluated comparatively along with 29 other submissions by two metrics (area under the ROC curve and area under the precision-recall curve). The overall performance of our approach ranked the second among all participating teams.     

Thematic review series: systems biology approaches to metabolic and cardiovascular disorders. Multi-organ whole-genome measurements and reverse engineering to uncover gene networks underlying complex traits

Together with computational analysis and modeling, the development of whole-genome measurement technologies holds the potential to fundamentally change research on complex disorders such as coronary artery disease. With these tools, the stage has been set to reveal the full repertoire of biological components (genes, proteins, and metabolites) in complex diseases and their interplay in modules and networks. Here we review how network identification based on reverse engineering, as applied to whole-genome datasets from simpler organisms, is now being adapted to more complex settings such as datasets from human cell lines and organs in relation to physiological and pathological states. Our focus is on the use of a systems biological approach to identify gene networks in coronary atherosclerosis. We also address how gene networks will probably play a key role in the development of early diagnostics and treatments for complex disorders in the coming era of individualized medicine.     

Identification of a Topological Characteristic Responsible for the Biological Robustness of Regulatory Networks

Attribution of biological robustness to the specific structural properties of a regulatory network is an important yet unsolved problem in systems biology. It is widely believed that the topological characteristics of a biological control network largely determine its dynamic behavior, yet the actual mechanism is still poorly understood. Here, we define a novel structural feature of biological networks, termed ‘regulation entropy’, to quantitatively assess the influence of network topology on the robustness of the systems. Using the cell-cycle control networks of the budding yeast (Saccharomyces cerevisiae) and the fission yeast (Schizosaccharomyces pombe) as examples, we first demonstrate the correlation of this quantity with the dynamic stability of biological control networks, and then we establish a significant association between this quantity and the structural stability of the networks. And we further substantiate the generality of this approach with a broad spectrum of biological and random networks. We conclude that the regulation entropy is an effective order parameter in evaluating the robustness of biological control networks. Our work suggests a novel connection between the topological feature and the dynamic property of biological regulatory networks.     

Efficient reverse-engineering of a developmental gene regulatory network

Understanding the complex regulatory networks underlying development and evolution of multi-cellular organisms is a major problem in biology. Computational models can be used as tools to extract the regulatory structure and dynamics of such networks from gene expression data. This approach is called reverse engineering. It has been successfully applied to many gene networks in various biological systems. However, to reconstitute the structure and non-linear dynamics of a developmental gene network in its spatial context remains a considerable challenge. Here, we address this challenge using a case study: the gap gene network involved in segment determination during early development of Drosophila melanogaster. A major problem for reverse-engineering pattern-forming networks is the significant amount of time and effort required to acquire and quantify spatial gene expression data. We have developed a simplified data processing pipeline that considerably increases the throughput of the method, but results in data of reduced accuracy compared to those previously used for gap gene network inference. We demonstrate that we can infer the correct network structure using our reduced data set, and investigate minimal data requirements for successful reverse engineering. Our results show that timing and position of expression domain boundaries are the crucial features for determining regulatory network structure from data, while it is less important to precisely measure expression levels. Based on this, we define minimal data requirements for gap gene network inference. Our results demonstrate the feasibility of reverse-engineering with much reduced experimental effort. This enables more widespread use of the method in different developmental contexts and organisms. Such systematic application of data-driven models to real-world networks has enormous potential. Only the quantitative investigation of a large number of developmental gene regulatory networks will allow us to discover whether there are rules or regularities governing development and evolution of complex multi-cellular organisms.     

Gene network inference via structural equation modeling in genetical genomics experiments

Our goal is gene network inference in genetical genomics or systems genetics experiments. For species where sequence information is available, we first perform expression quantitative trait locus (eQTL) mapping by jointly utilizing cis-, cis-trans-, and trans-regulation. After using local structural models to identify regulator-target pairs for each eQTL, we construct an encompassing directed network (EDN) by assembling all retained regulator-target relationships. The EDN has nodes corresponding to expressed genes and eQTL and directed edges from eQTL to cis-regulated target genes, from cis-regulated genes to cis-trans-regulated target genes, from trans-regulator genes to target genes, and from trans-eQTL to target genes. For network inference within the strongly constrained search space defined by the EDN, we propose structural equation modeling (SEM), because it can model cyclic networks and the EDN indeed contains feedback relationships. On the basis of a factorization of the likelihood and the constrained search space, our SEM algorithm infers networks involving several hundred genes and eQTL. Structure inference is based on a penalized likelihood ratio and an adaptation of Occam's window model selection. The SEM algorithm was evaluated using data simulated with nonlinear ordinary differential equations and known cyclic network topologies and was applied to a real yeast data set.