A Markovian approach to the control of genetic regulatory networks

This paper presents an approach for controlling gene networks based on a Markov chain model, where the state of a gene network is represented as a probability distribution, while state transitions are considered to be probabilistic. An algorithm is proposed to determine a sequence of control actions that drives (without state feedback) the state of a given network to within a desired state set with a prescribed minimum or maximum probability. A heuristic is proposed and shown to improve the efficiency of the algorithm for a class of genetic networks.     

A Bayesian regression approach to the inference of regulatory networks from gene expression data

MOTIVATION: There is currently much interest in reverse-engineering regulatory relationships between genes from microarray expression data. We propose a new algorithmic method for inferring such interactions between genes using data from gene knockout experiments. The algorithm we use is the Sparse Bayesian regression algorithm of Tipping and Faul. This method is highly suited to this problem as it does not require the data to be discretized, overcomes the need for an explicit topology search and, most importantly, requires no heuristic thresholding of the discovered connections. RESULTS: Using simulated expression data, we are able to show that this algorithm outperforms a recently published correlation-based approach. Crucially, it does this without the need to set any ad hoc threshold on possible connections.     

A biological approach to computational models of proteomic networks

Computational modeling is useful as a means to assemble and test what we know about proteins and networks. Models can help address key questions about the measurement, definition and function of proteomic networks. Here, we place these biological questions at the forefront in reviewing the computational strategies that are available to analyze proteomic networks. Recent examples illustrate how models can extract more information from proteomic data, test possible interactions between network proteins and link networks to cellular behavior. No single model can achieve all these goals, however, which is why it is critical to prioritize biological questions before specifying a particular modeling approach.     

Automated refinement and inference of analytical models for metabolic networks

The reverse engineering of metabolic networks from experimental data is traditionally a labor-intensive task requiring a priori systems knowledge. Using a proven model as a test system, we demonstrate an automated method to simplify this process by modifying an existing or related model--suggesting nonlinear terms and structural modifications--or even constructing a new model that agrees with the system's time series observations. In certain cases, this method can identify the full dynamical model from scratch without prior knowledge or structural assumptions. The algorithm selects between multiple candidate models by designing experiments to make their predictions disagree. We performed computational experiments to analyze a nonlinear seven-dimensional model of yeast glycolytic oscillations. This approach corrected mistakes reliably in both approximated and overspecified models. The method performed well to high levels of noise for most states, could identify the correct model de novo, and make better predictions than ordinary parametric regression and neural network models. We identified an invariant quantity in the model, which accurately derived kinetics and the numerical sensitivity coefficients of the system. Finally, we compared the system to dynamic flux estimation and discussed the scaling and application of this methodology to automated experiment design and control in biological systems in real time.     

Stopping-time resampling and population genetic inference under coalescent models

To extract full information from samples of DNA sequence data, it is necessary to use sophisticated model-based techniques such as importance sampling under the coalescent. However, these are limited in the size of datasets they can handle efficiently. Chen and Liu (2000) introduced the idea of stopping-time resampling and showed that it can dramatically improve the efficiency of importance sampling methods under a finite-alleles coalescent model. In this paper, a new framework is developed for designing stopping-time resampling schemes under more general models. It is implemented on data both from infinite sites and stepwise models of mutation, and extended to incorporate crossover recombination. A simulation study shows that this new framework offers a substantial improvement in the accuracy of likelihood estimation over a range of parameters, while a direct application of the scheme of Chen and Liu (2000) can actually diminish the estimate. The method imposes no additional computational burden and is robust to the choice of parameters.     

Applications of a formal approach to decipher discrete genetic networks

Background  

A growing demand for tools to assist the building and analysis of biological networks exists in systems biology. We argue that the use of a formal approach is relevant and applicable to address questions raised by biologists about such networks. The behaviour of these systems being complex, it is essential to exploit efficiently every bit of experimental information. In our approach, both the evolution rules and the partial knowledge about the structure and the behaviour of the network are formalized using a common constraint-based language.     

A proposal for using the ensemble approach to understand genetic regulatory networks

Understanding the genetic regulatory network comprising genes, RNA, proteins and the network connections and dynamical control rules among them, is a major task of contemporary systems biology. I focus here on the use of the ensemble approach to find one or more well-defined ensembles of model networks whose statistical features match those of real cells and organisms. Such ensembles should help explain and predict features of real cells and organisms. More precisely, an ensemble of model networks is defined by constraints on the "wiring diagram" of regulatory interactions, and the "rules" governing the dynamical behavior of regulated components of the network. The ensemble consists of all networks consistent with those constraints. Here I discuss ensembles of random Boolean networks, scale free Boolean networks, "medusa" Boolean networks, continuous variable networks, and others. For each ensemble, M statistical features, such as the size distribution of avalanches in gene activity changes unleashed by transiently altering the activity of a single gene, the distribution in distances between gene activities on different cell types, and others, are measured. This creates an M-dimensional space, where each ensemble corresponds to a cluster of points or distributions. Using current and future experimental techniques, such as gene arrays, these M properties are to be measured for real cells and organisms, again yielding a cluster of points or distributions in the M-dimensional space. The procedure then finds ensembles close to those of real cells and organisms, and hill climbs to attempt to match the observed M features. Thus obtains one or more ensembles that should predict and explain many features of the regulatory networks in cells and organisms.     

Gradient directed regularization for sparse Gaussian concentration graphs, with applications to inference of genetic networks

Large-scale microarray gene expression data provide the possibility of constructing genetic networks or biological pathways. Gaussian graphical models have been suggested to provide an effective method for constructing such genetic networks. However, most of the available methods for constructing Gaussian graphs do not account for the sparsity of the networks and are computationally more demanding or infeasible, especially in the settings of high dimension and low sample size. We introduce a threshold gradient descent (TGD) regularization procedure for estimating the sparse precision matrix in the setting of Gaussian graphical models and demonstrate its application to identifying genetic networks. Such a procedure is computationally feasible and can easily incorporate prior biological knowledge about the network structure. Simulation results indicate that the proposed method yields a better estimate of the precision matrix than the procedures that fail to account for the sparsity of the graphs. We also present the results on inference of a gene network for isoprenoid biosynthesis in Arabidopsis thaliana. These results demonstrate that the proposed procedure can indeed identify biologically meaningful genetic networks based on microarray gene expression data.     

Transient dynamics of reduced-order models of genetic regulatory networks

In systems biology, a number of detailed genetic regulatory networks models have been proposed that are capable of modeling the fine-scale dynamics of gene expression. However, limitations on the type and sampling frequency of experimental data often prevent the parameter estimation of the detailed models. Furthermore, the high computational complexity involved in the simulation of a detailed model restricts its use. In such a scenario, reduced-order models capturing the coarse-scale behavior of the network are frequently applied. In this paper, we analyze the dynamics of a reduced-order Markov Chain model approximating a detailed Stochastic Master Equation model. Utilizing a reduction mapping that maintains the aggregated steady-state probability distribution of stochastic master equation models, we provide bounds on the deviation of the Markov Chain transient distribution from the transient aggregated distributions of the stochastic master equation model.     

Discrete time piecewise affine models of genetic regulatory networks

We introduce simple models of genetic regulatory networks and we proceed to the mathematical analysis of their dynamics. The models are discrete time dynamical systems generated by piecewise affine contracting mappings whose variables represent gene expression levels. These models reduce to boolean networks in one limiting case of a parameter, and their asymptotic dynamics approaches that of a differential equation in another limiting case of this parameter. For intermediate values, the model present an original phenomenology which is argued to be due to delay effects. This phenomenology is not limited to piecewise affine model but extends to smooth nonlinear discrete time models of regulatory networks. In a first step, our analysis concerns general properties of networks on arbitrary graphs (characterisation of the attractor, symbolic dynamics, Lyapunov stability, structural stability, symmetries, etc). In a second step, focus is made on simple circuits for which the attractor and its changes with parameters are described. In the negative circuit of 2 genes, a thorough study is presented which concern stable (quasi-)periodic oscillations governed by rotations on the unit circle – with a rotation number depending continuously and monotonically on threshold parameters. These regular oscillations exist in negative circuits with arbitrary number of genes where they are most likely to be observed in genetic systems with non-negligible delay effects.     

Computational inference and analysis of genetic regulatory networks via a supervised combinatorial-optimization pattern

Background

Post-genome era brings about diverse categories of omics data. Inference and analysis of genetic regulatory networks act prominently in extracting inherent mechanisms, discovering and interpreting the related biological nature and living principles beneath mazy phenomena, and eventually promoting the well-beings of humankind.

Results

A supervised combinatorial-optimization pattern based on information and signal-processing theories is introduced into the inference and analysis of genetic regulatory networks. An associativity measure is proposed to define the regulatory strength/connectivity, and a phase-shift metric determines regulatory directions among components of the reconstructed networks. Thus, it solves the undirected regulatory problems arising from most of current linear/nonlinear relevance methods. In case of computational and topological redundancy, we constrain the classified group size of pair candidates within a multiobjective combinatorial optimization (MOCO) pattern.

Conclusions

We testify the proposed approach on two real-world microarray datasets of different statistical characteristics. Thus, we reveal the inherent design mechanisms for genetic networks by quantitative means, facilitating further theoretic analysis and experimental design with diverse research purposes. Qualitative comparisons with other methods and certain related focuses needing further work are illustrated within the discussion section.

     

Supervised inference of gene-regulatory networks

Background  

Inference of protein interaction networks from various sources of data has become an important topic of both systems and computational biology. Here we present a supervised approach to identification of gene expression regulatory networks.