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.     

Polynomial-Time Algorithm for Controllability Test of a Class of Boolean Biological Networks

In recent years, Boolean-network-model-based approaches to dynamical analysis of complex biological networks such as gene regulatory networks have been extensively studied. One of the fundamental problems in control theory of such networks is the problem of determining whether a given substance quantity can be arbitrarily controlled by operating the other substance quantities, which we call the controllability problem. This paper proposes a polynomial-time algorithm for solving this problem. Although the algorithm is based on a sufficient condition for controllability, it is easily computable for a wider class of large-scale biological networks compared with the existing approaches. A key to this success in our approach is to give up computing Boolean operations in a rigorous way and to exploit an adjacency matrix of a directed graph induced by a Boolean network. By applying the proposed approach to a neurotransmitter signaling pathway, it is shown that it is effective.     

Stochastic Sensitivity Analysis and Kernel Inference via Distributional Data

Cellular processes are noisy due to the stochastic nature of biochemical reactions. As such, it is impossible to predict the exact quantity of a molecule or other attributes at the single-cell level. However, the distribution of a molecule over a population is often deterministic and is governed by the underlying regulatory networks relevant to the cellular functionality of interest. Recent studies have started to exploit this property to infer network states. To facilitate the analysis of distributional data in a general experimental setting, we introduce a computational framework to efficiently characterize the sensitivity of distributional output to changes in external stimuli. Further, we establish a probability-divergence-based kernel regression model to accurately infer signal level based on distribution measurements. Our methodology is applicable to any biological system subject to stochastic dynamics and can be used to elucidate how population-based information processing may contribute to organism-level functionality. It also lays the foundation for engineering synthetic biological systems that exploit population decoding to more robustly perform various biocomputation tasks, such as disease diagnostics and environmental-pollutant sensing.     

Stochastic Sensitivity Analysis and Kernel Inference via Distributional Data

Cellular processes are noisy due to the stochastic nature of biochemical reactions. As such, it is impossible to predict the exact quantity of a molecule or other attributes at the single-cell level. However, the distribution of a molecule over a population is often deterministic and is governed by the underlying regulatory networks relevant to the cellular functionality of interest. Recent studies have started to exploit this property to infer network states. To facilitate the analysis of distributional data in a general experimental setting, we introduce a computational framework to efficiently characterize the sensitivity of distributional output to changes in external stimuli. Further, we establish a probability-divergence-based kernel regression model to accurately infer signal level based on distribution measurements. Our methodology is applicable to any biological system subject to stochastic dynamics and can be used to elucidate how population-based information processing may contribute to organism-level functionality. It also lays the foundation for engineering synthetic biological systems that exploit population decoding to more robustly perform various biocomputation tasks, such as disease diagnostics and environmental-pollutant sensing.     

Biologically Inspired Information Processing and Synchronization in Ensembles of Non-Identical Threshold-Potential Nanostructures

Nanotechnology produces basic structures that show a significant variability in their individual physical properties. This experimental fact may constitute a serious limitation for most applications requiring nominally identical building blocks. On the other hand, biological diversity is found in most natural systems. We show that reliable information processing can be achieved with heterogeneous groups of non-identical nanostructures by using some conceptual schemes characteristic of biological networks (diversity, frequency-based signal processing, rate and rank order coding, and synchronization). To this end, we simulate the integrated response of an ensemble of single-electron transistors (SET) whose individual threshold potentials show a high variability. A particular experimental realization of a SET is a metal nanoparticle-based transistor that mimics biological spiking synapses and can be modeled as an integrate-and-fire oscillator. The different shape and size distributions of nanoparticles inherent to the nanoscale fabrication procedures result in a significant variability in the threshold potentials of the SET. The statistical distributions of the nanoparticle physical parameters are characterized by experimental average and distribution width values. We consider simple but general information processing schemes to draw conclusions that should be of relevance for other threshold-based nanostructures. Monte Carlo simulations show that ensembles of non-identical SET may show some advantages over ensembles of identical nanostructures concerning the processing of weak signals. The results obtained are also relevant for understanding the role of diversity in biophysical networks.     

Interplay between gene expression noise and regulatory network architecture

Complex regulatory networks orchestrate most cellular processes in biological systems. Genes in such networks are subject to expression noise, resulting in isogenic cell populations exhibiting cell-to-cell variation in protein levels. Increasing evidence suggests that cells have evolved regulatory strategies to limit, tolerate or amplify expression noise. In this context, fundamental questions arise: how can the architecture of gene regulatory networks generate, make use of or be constrained by expression noise? Here, we discuss the interplay between expression noise and gene regulatory network at different levels of organization, ranging from a single regulatory interaction to entire regulatory networks. We then consider how this interplay impacts a variety of phenomena, such as pathogenicity, disease, adaptation to changing environments, differential cell-fate outcome and incomplete or partial penetrance effects. Finally, we highlight recent technological developments that permit measurements at the single-cell level, and discuss directions for future research.     

Failure tolerance of motif structure in biological networks

Complex networks serve as generic models for many biological systems that have been shown to share a number of common structural properties such as power-law degree distribution and small-worldness. Real-world networks are composed of building blocks called motifs that are indeed specific subgraphs of (usually) small number of nodes. Network motifs are important in the functionality of complex networks, and the role of some motifs such as feed-forward loop in many biological networks has been heavily studied. On the other hand, many biological networks have shown some degrees of robustness in terms of their efficiency and connectedness against failures in their components. In this paper we investigated how random and systematic failures in the edges of biological networks influenced their motif structure. We considered two biological networks, namely, protein structure network and human brain functional network. Furthermore, we considered random failures as well as systematic failures based on different strategies for choosing candidate edges for removal. Failure in the edges tipping to high degree nodes had the most destructive role in the motif structure of the networks by decreasing their significance level, while removing edges that were connected to nodes with high values of betweenness centrality had the least effect on the significance profiles. In some cases, the latter caused increase in the significance levels of the motifs.     

Estimating gene regulatory networks and protein-protein interactions of Saccharomyces cerevisiae from multiple genome-wide data

MOTIVATION: Biological processes in cells are properly performed by gene regulations, signal transductions and interactions between proteins. To understand such molecular networks, we propose a statistical method to estimate gene regulatory networks and protein-protein interaction networks simultaneously from DNA microarray data, protein-protein interaction data and other genome-wide data. RESULTS: We unify Bayesian networks and Markov networks for estimating gene regulatory networks and protein-protein interaction networks according to the reliability of each biological information source. Through the simultaneous construction of gene regulatory networks and protein-protein interaction networks of Saccharomyces cerevisiae cell cycle, we predict the role of several genes whose functions are currently unknown. By using our probabilistic model, we can detect false positives of high-throughput data, such as yeast two-hybrid data. In a genome-wide experiment, we find possible gene regulatory relationships and protein-protein interactions between large protein complexes that underlie complex regulatory mechanisms of biological processes.     

RNA synthetic biology

RNA molecules play important and diverse regulatory roles in the cell by virtue of their interaction with other nucleic acids, proteins and small molecules. Inspired by this natural versatility, researchers have engineered RNA molecules with new biological functions. In the last two years efforts in synthetic biology have produced novel, synthetic RNA components capable of regulating gene expression in vivo largely in bacteria and yeast, setting the stage for scalable and programmable cellular behavior. Immediate challenges for this emerging field include determining how computational and directed-evolution techniques can be implemented to increase the complexity of engineered RNA systems, as well as determining how such systems can be broadly extended to mammalian systems. Further challenges include designing RNA molecules to be sensors of intracellular and environmental stimuli, probes to explore the behavior of biological networks and components of engineered cellular control systems.     

An integer optimization algorithm for robust identification of non-linear gene regulatory networks

ABSTRACT: BACKGROUND: Reverse engineering gene networks and identifying regulatory interactions are integral to understanding cellular decision making processes. Advancement in high throughput experimental techniques has initiated innovative data driven analysis of gene regulatory networks. However, inherent noise associated with biological systems requires numerous experimental replicates for reliable conclusions. Furthermore, evidence of robust algorithms directly exploiting basic biological traits are few. Such algorithms are expected to be efficient in their performance and robust in their prediction. RESULTS: We have developed a network identification algorithm to accurately infer both the topology and strength of regulatory interactions from time series gene expression data in the presence of significant experimental noise and non-linear behavior. In this novel formulism, we have addressed data variability in biological systems by integrating network identification with the bootstrap resampling technique, hence predicting robust interactions from limited experimental replicates subjected to noise. Furthermore, we have incorporated non-linearity in gene dynamics using the S-system formulation. The basic network identification formulation exploits the trait of sparsity of biological interactions. Towards that, the identification algorithm is formulated as an integer-programming problem by introducing binary variables for each network component. The objective function is targeted to minimize the network connections subjected to the constraint of maximal agreement between the experimental and predicted gene dynamics. The developed algorithm is validated using both in-silico and experimental data-sets. These studies show that the algorithm can accurately predict the topology and connection strength of the in silico networks, as quantified by high precision and recall, and small discrepancy between the actual and predicted kinetic parameters. Furthermore, in both the in silico and experimental case studies, the predicted gene expression profiles are in very close agreement with the dynamics of the input data. CONCLUSIONS: Our integer programming algorithm effectively utilizes bootstrapping to identify robust gene regulatory networks from noisy, non-linear time-series gene expression data. With significant noise and non-linearities being inherent to biological systems, the present formulism, with the incorporation of network sparsity, is extremely relevant to gene regulatory networks, and while the formulation has been validated against in silico and E. Coli data, it can be applied to any biological system.     

Modeling stochasticity and variability in gene regulatory networks

Modeling stochasticity in gene regulatory networks is an important and complex problem in molecular systems biology. To elucidate intrinsic noise, several modeling strategies such as the Gillespie algorithm have been used successfully. This article contributes an approach as an alternative to these classical settings. Within the discrete paradigm, where genes, proteins, and other molecular components of gene regulatory networks are modeled as discrete variables and are assigned as logical rules describing their regulation through interactions with other components. Stochasticity is modeled at the biological function level under the assumption that even if the expression levels of the input nodes of an update rule guarantee activation or degradation there is a probability that the process will not occur due to stochastic effects. This approach allows a finer analysis of discrete models and provides a natural setup for cell population simulations to study cell-to-cell variability. We applied our methods to two of the most studied regulatory networks, the outcome of lambda phage infection of bacteria and the p53-mdm2 complex.     

Using process diagrams for the graphical representation of biological networks

With the increased interest in understanding biological networks, such as protein-protein interaction networks and gene regulatory networks, methods for representing and communicating such networks in both human- and machine-readable form have become increasingly important. Although there has been significant progress in machine-readable representation of networks, as exemplified by the Systems Biology Mark-up Language (SBML) (http://www.sbml.org) issues in human-readable representation have been largely ignored. This article discusses human-readable diagrammatic representations and proposes a set of notations that enhances the formality and richness of the information represented. The process diagram is a fully state transition-based diagram that can be translated into machine-readable forms such as SBML in a straightforward way. It is supported by CellDesigner, a diagrammatic network editing software (http://www.celldesigner.org/), and has been used to represent a variety of networks of various sizes (from only a few components to several hundred components).