Time-delayed models of gene regulatory networks

We discuss different mathematical models of gene regulatory networks as relevant to the onset and development of cancer. After discussion of alternativemodelling approaches, we use a paradigmatic two-gene network to focus on the role played by time delays in the dynamics of gene regulatory networks. We contrast the dynamics of the reduced model arising in the limit of fast mRNA dynamics with that of the full model. The review concludes with the discussion of some open problems

Simultaneous learning of instantaneous and time-delayed genetic interactions using novel information theoretic scoring technique

BACKGROUND: Understanding gene interactions is a fundamental question in systems biology. Currently, modeling of gene regulations using the Bayesian Network (BN) formalism assumes that genes interact either instantaneously or with a certain amount of time delay. However in reality, biological regulations, both instantaneous and time-delayed, occur simultaneously. A framework that can detect and model both these two types of interactions simultaneously would represent gene regulatory networks more accurately. RESULTS: In this paper, we introduce a framework based on the Bayesian Network (BN) formalism that can represent both instantaneous and time-delayed interactions between genes simultaneously. A novel scoring metric having firm mathematical underpinnings is also proposed that, unlike other recent methods, can score both interactions concurrently and takes into account the reality that multiple regulators can regulate a gene jointly, rather than in an isolated pair-wise manner. Further, a gene regulatory network (GRN) inference method employing an evolutionary search that makes use of the framework and the scoring metric is also presented. CONCLUSION: By taking into consideration the biological fact that both instantaneous and time-delayed regulations can occur among genes, our approach models gene interactions with greater accuracy. The proposed framework is efficient and can be used to infer gene networks having multiple orders of instantaneous and time-delayed regulations simultaneously. Experiments are carried out using three different synthetic networks (with three different mechanisms for generating synthetic data) as well as real life networks of Saccharomyces cerevisiae, E. coli and cyanobacteria gene expression data. The results show the effectiveness of our approach

Simultaneous learning of instantaneous and time-delayed genetic interactions using novel information theoretic scoring technique

Background: Understanding gene interactions is a fundamental question in systems biology. Currently, modeling of gene regulations using the Bayesian Network (BN) formalism assumes that genes interact either instantaneously or with a certain amount of time delay. However in reality, biological regulations, both instantaneous and time-delayed, occur simultaneously. A framework that can detect and model both these two types of interactions simultaneously would represent gene regulatory networks more accurately. Results: In this paper, we introduce a framework based on the Bayesian Network (BN) formalism that can represent both instantaneous and time-delayed interactions between genes simultaneously. A novel scoring metric having firm mathematical underpinnings is also proposed that, unlike other recent methods, can score both interactions concurrently and takes into account the reality that multiple regulators can regulate a gene jointly, rather than in an isolated pair-wise manner. Further, a gene regulatory network (GRN) inference method employing an evolutionary search that makes use of the framework and the scoring metric is also presented. Conclusion: By taking into consideration the biological fact that both instantaneous and time-delayed regulations can occur among genes, our approach models gene interactions with greater accuracy. The proposed framework is efficient and can be used to infer gene networks having multiple orders of instantaneous and time-delayed regulations simultaneously. Experiments are carried out using three different synthetic networks (with three different mechanisms for generating synthetic data) as well as real life networks of Saccharomyces cerevisiae, E. coli and cyanobacteria gene expression data. The results show the effectiveness of our approach

On delayed genetic regulatory networks with polytopic uncertainties: Robust stability analysis

Copyright [2008] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, we investigate the robust asymptotic stability problem of genetic regulatory networks with time-varying delays and polytopic parameter uncertainties. Both cases of differentiable and nondifferentiable time-delays are considered, and the convex polytopic description is utilized to characterize the genetic network model uncertainties. By using a Lyapunov functional approach and linear matrix inequality (LMI) techniques, the stability criteria for the uncertain delayed genetic networks are established in the form of LMIs, which can be readily verified by using standard numerical software. An important feature of the results reported here is that all the stability conditions are dependent on the upper and lower bounds of the delays, which is made possible by using up-to-date techniques for achieving delay dependence. Another feature of the results lies in that a novel Lyapunov functional dependent on the uncertain parameters is utilized, which renders the results to be potentially less conservative than those obtained via a fixed Lyapunov functional for the entire uncertainty domain. A genetic network example is employed to illustrate the applicability and usefulness of the developed theoretical results

Robust H∞ feedback control for uncertain stochastic delayed genetic regulatory networks with additive and multiplicative noise

The official published version can found at the link below.Noises are ubiquitous in genetic regulatory networks (GRNs). Gene regulation is inherently a stochastic process because of intrinsic and extrinsic noises that cause kinetic parameter variations and basal rate disturbance. Time delays are usually inevitable due to different biochemical reactions in such GRNs. In this paper, a delayed stochastic model with additive and multiplicative noises is utilized to describe stochastic GRNs. A feedback gene controller design scheme is proposed to guarantee that the GRN is mean-square asymptotically stable with noise attenuation, where the structure of the controllers can be specified according to engineering requirements. By applying control theory and mathematical tools, the analytical solution to the control design problem is given, which helps to provide some insight into synthetic biology and systems biology. The control scheme is employed in a three-gene network to illustrate the applicability and usefulness of the design.This work was funded by Royal Society of the U.K.; Foundation for the Author of National Excellent Doctoral Dissertation of China. Grant Number: 2007E4; Heilongjiang Outstanding Youth Science Fund of China. Grant Number: JC200809; Fok Ying Tung Education Foundation. Grant Number: 111064; International Science and Technology Cooperation Project of China. Grant Number: 2009DFA32050; University of Science and Technology of China Graduate Innovative Foundation

Reverse engineering of genetic networks with time delayed recurrent neural networks and clustering techniques

In the iterative process of experimentally probing biological networks and computationally inferring models for the networks, fast, accurate and flexible computational frameworks are needed for modeling and reverse engineering biological networks. In this dissertation, I propose a novel model to simulate gene regulatory networks using a specific type of time delayed recurrent neural networks. Also, I introduce a parameter clustering method to select groups of parameter sets from the simulations representing biologically reasonable networks. Additionally, a general purpose adaptive function is used here to decrease and study the connectivity of small gene regulatory networks modules. In this dissertation, the performance of this novel model is shown to simulate the dynamics and to infer the topology of gene regulatory networks derived from synthetic and experimental time series gene expression data. Here, I assess the quality of the inferred networks by the use of graph edit distance measurements in comparison to the synthetic and experimental benchmarks. Additionally, I compare between edition costs of the inferred networks obtained with the time delay recurrent networks and other previously described reverse engineering methods based on continuous time recurrent neural and dynamic Bayesian networks. Furthermore, I address questions of network connectivity and correlation between data fitting and inference power by simulating common experimental limitations of the reverse engineering process as incomplete and highly noisy data. The novel specific type of time delay recurrent neural networks model in combination with parameter clustering substantially improves the inference power of reverse engineered networks. Additionally, some suggestions for future improvements are discussed, particularly under the data driven perspective as the solution for modeling complex biological systems

Synchronization of stochastic genetic oscillator networks with time delays and Markovian jumping parameters

The official published version of the article can be found at the link below.Genetic oscillator networks (GONs) are inherently coupled complex systems where the nodes indicate the biochemicals and the couplings represent the biochemical interactions. This paper is concerned with the synchronization problem of a general class of stochastic GONs with time delays and Markovian jumping parameters, where the GONs are subject to both the stochastic disturbances and the Markovian parameter switching. The regulatory functions of the addressed GONs are described by the sector-like nonlinear functions. By applying up-to-date ‘delay-fractioning’ approach for achieving delay-dependent conditions, we construct novel matrix functional to derive the synchronization criteria for the GONs that are formulated in terms of linear matrix inequalities (LMIs). Note that LMIs are easily solvable by the Matlab toolbox. A simulation example is used to demonstrate the synchronization phenomena within biological organisms of a given GON and therefore shows the applicability of the obtained results.This work was supported in part by the Biotechnology and Biological Sciences Research Council (BBSRC) of the UK under Grants BB/C506264/1 and 100/EGM17735, the Royal Society of the UK, the National Natural Science Foundation of China under Grant 60804028, the Teaching and Research Fund for Excellent Young Teachers at Southeast University of China, the International Science and Technology Cooperation Project of China under Grant 2009DFA32050, and the Alexander von Humboldt Foundation of Germany

On robust stability of stochastic genetic regulatory networks with time delays: A delay fractioning approach

Copyright [2009] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.Robust stability serves as an important regulation mechanism in system biology and synthetic biology. In this paper, the robust stability analysis problem is investigated for a class of nonlinear delayed genetic regulatory networks with parameter uncertainties and stochastic perturbations. The nonlinear function describing the feedback regulation satisfies the sector condition, the time delays exist in both translation and feedback regulation processes, and the state-dependent Brownian motions are introduced to reflect the inherent intrinsic and extrinsic noise perturbations. The purpose of the addressed stability analysis problem is to establish some easy-to-verify conditions under which the dynamics of the true concentrations of the messenger ribonucleic acid (mRNA) and protein is asymptotically stable irrespective of the norm-bounded modeling errors. By utilizing a new Lyapunov functional based on the idea of “delay fractioning”, we employ the linear matrix inequality (LMI) technique to derive delay-dependent sufficient conditions ensuring the robust stability of the gene regulatory networks. Note that the obtained results are formulated in terms of LMIs that can easily be solved using standard software packages. Simulation examples are exploited to illustrate the effectiveness of the proposed design procedures