Models Of Genetic Regulatory Networks Research Articles

Stochasticity, bistability and the wisdom of crowds: a model for associative learning in genetic regulatory networks.

It is generally believed that associative memory in the brain depends on multistable synaptic dynamics, which enable the synapses to maintain their value for extended periods of time. However, multistable dynamics are not restricted to synapses. In particular, the dynamics of some genetic regulatory networks are multistable, raising the possibility that even single cells, in the absence of a nervous system, are capable of learning associations. Here we study a standard genetic regulatory network model with bistable elements and stochastic dynamics. We demonstrate that such a genetic regulatory network model is capable of learning multiple, general, overlapping associations. The capacity of the network, defined as the number of associations that can be simultaneously stored and retrieved, is proportional to the square root of the number of bistable elements in the genetic regulatory network. Moreover, we compute the capacity of a clonal population of cells, such as in a colony of bacteria or a tissue, to store associations. We show that even if the cells do not interact, the capacity of the population to store associations substantially exceeds that of a single cell and is proportional to the number of bistable elements. Thus, we show that even single cells are endowed with the computational power to learn associations, a power that is substantially enhanced when these cells form a population.

Stability analysis for genetic regulatory networks with delays: The continuous-time case and the discrete-time case

Convergent dynamics are investigated in this paper for the genetic regulatory networks (GRNs) with delays in both the continuous-time case and the discrete-time form. First, by utilizing the Lyapunov functional method and some inequality techniques, sufficient criterion is derived to ensure the global exponential stability of the continuous-time GRNs. Second, by using the semi-discretization technique and the IMEX-θ method as sources of reference, two discrete-time analogues of the continuous-time GRN model are formulated respectively. Moreover, it is shown that under the same sufficient conditions derived earlier, these two discrete-time GRN systems are also globally exponentially stable, and the explicit exponential convergent rates are also given. Finally, a numerical example is illustrated to show the validity of the obtained theoretical results, and comparisons of the convergent rates for these two different discrete-time analogues are also demonstrated.

Consideration of mobile DNA: new forms of artificial genetic regulatory networks

This paper extends a recent abstract, tunable model of genomic structural change within the cell lifecycle and explores its use with simulated evolution. A Boolean model of genetic regulatory networks has been presented to include changes in structure based upon the current cell state, e.g., via transposable elements. In this paper the underlying behaviour of the resulting dynamical networks is investigated before their evolvability is explored using single and multi-celled models of fitness landscapes. Structural dynamism is found to be selected for under numerous conditions within the two models.

Model-based and model-free filtering of genomic data

Biological measurements are a rich source of information about the biological phenomena that are represented. For example, time-series dynamic genomic or metabolic microarray data can be used to construct dynamic genetic regulatory network models, which can be used to better understand the interactions among different genes within the biological system and to design intervention strategies to cure or manage major diseases. Unfortunately, biological measurements are usually highly contaminated with errors that mask the important features in the data and limit their applicability. Therefore, these noisy measurements need to be filtered to enhance their usefulness in practice. In this work, various model-based and model-free data filtering techniques are used to denoise (or filter) genomic data. In the availability of a dynamic model representing the biological system, state estimation techniques, such as extended Kalman filtering (EKF), unscented Kalman filtering (UKF), and particle filtering (PF) are used to filter the measured data. When a model is not available, on the other hand, low-pass as well as multiscale filtering techniques will be utilized. Low-pass filters include the mean and exponentially weighted moving average filters, while the multiscale filters include several online as well as batch wavelet-based thresholding techniques. In this paper, the performances of all filtering techniques will be demonstrated and compared through their application using simulated time-series metabolic data contaminated with white noise. The results show clear advantages for the model-based over the model-free filtering techniques, and that the PF outperforms other model-based methods. The results also show that in the absence of a model of the biological system, the model-free filtering techniques, especially multiscale filtering, can also provide acceptable performances. Online multiscale (OLMS) filtering is shown to outperform low-pass filtering, and the batch multiscale methods, i.e., translation invariant (TI) and boundary corrected TI (BCTI) provide enhanced smoothness, with improved ability of BCTI over TI at the edges. From a biological perspective, the model-based and online model-free filtering techniques can be used when filtering is needed online, such as within an intervention framework to cure diseases, while the batch model-free filtering techniques can be used within a modeling framework to enhance the quality of the estimated biological models.

Balance between noise and information flow maximizes set complexity of network dynamics.

Boolean networks have been used as a discrete model for several biological systems, including metabolic and genetic regulatory networks. Due to their simplicity they offer a firm foundation for generic studies of physical systems. In this work we show, using a measure of context-dependent information, set complexity, that prior to reaching an attractor, random Boolean networks pass through a transient state characterized by high complexity. We justify this finding with a use of another measure of complexity, namely, the statistical complexity. We show that the networks can be tuned to the regime of maximal complexity by adding a suitable amount of noise to the deterministic Boolean dynamics. In fact, we show that for networks with Poisson degree distributions, all networks ranging from subcritical to slightly supercritical can be tuned with noise to reach maximal set complexity in their dynamics. For networks with a fixed number of inputs this is true for near-to-critical networks. This increase in complexity is obtained at the expense of disruption in information flow. For a large ensemble of networks showing maximal complexity, there exists a balance between noise and contracting dynamics in the state space. In networks that are close to critical the intrinsic noise required for the tuning is smaller and thus also has the smallest effect in terms of the information processing in the system. Our results suggest that the maximization of complexity near to the state transition might be a more general phenomenon in physical systems, and that noise present in a system may in fact be useful in retaining the system in a state with high information content.

Modeling of genetic regulatory networks in the differentiation of neural crest stem cells to sensory neurons by means of boolean networks

In the present study we have generated a GRN comprising the process by which neural crest stem cells develop to two types of sensory neurons (Propioceptors and Nocioceptors). We have also been able to find patterns of regulation (motifs) that act cooperatively to control such process. Surprisingly, these motifs take place in similar stages during the development of erythrocytes from hematopoietic stem cells. Regarding the complexity of the GRN found, we then used Random Boolean Networks (RBN) for this purpose, which showed key components as well as the dynamics of the process through changes in initial conditions. Finally, the motifs were reflected in the model, suggesting insights for further studies.

Effects of community structure on the dynamics of random threshold networks

Random threshold networks (RTNs) have been widely used as models of neural or genetic regulatory networks. Network topology plays a central role in the dynamics of these networks. Recently it has been shown that many social and biological networks are scale-free and also exhibit community structure, in which autonomous modules are wired together to perform relatively independent functions. In this study we use both synchronous and asynchronous models of RTNs to systematically investigate how community structure affects the dynamics of RTNs with scale-free topology. Extensive simulation experiments show that RTNs with high modularity have more attractors than those RTNs with low modularity, and RTNs with smaller communities tend to have more attractors. Damage resulting from perturbation of initial conditions spreads less effectively in RTNs with higher modularity and RTNs with smaller communities. In addition, RTNs with high modularity can coordinate their internal dynamics better than RTNs with low modularity under the synchronous update scheme, and it is the other way around under the asynchronous update. This study shows that community structure has a strong effect on the dynamics of RTNs.

Robust stability analysis of Markov jump standard genetic regulatory networks with mixed time delays and uncertainties

This paper concerns the robust stability analysis problems for a class of nonlinear Markov jump standard genetic regulatory networks with mixed time-varying delays and parameter uncertainties. The standard genetic regulatory networks model is constructed via recurrent neural networks. The nonlinear regulatory function is assumed to satisfy the sector condition, and each regulatory function in the model has its own expression form. The mixed delays mean that the discrete delays and distributed delays are considered simultaneously. Based on linear matrix inequality techniques, sufficient conditions for robust stability of the underlying systems are first derived by using the conventional approach in the area of time-delay systems. Also, the “delay decomposition” approach is further utilized so as to improve the analytical results. Two numerical examples are exploited to verify the obtained theoretical findings.

Attractor Transformation by Impulsive Control in Boolean Control Network

Boolean control networks have recently been attracting considerable interests as computational models for genetic regulatory networks. In this paper, we present an approach of impulsive control for attractor transitions in Boolean control networks based on the recent developed matrix semitensor product theory. The reachability of attractors is estimated, and the controller is also obtained. The general derivation proposed here is exemplified with a kind of gene model, which is the protein-nucleic acid interactions network, on numerical simulations.

Linear Dynamic Controllers Evolved by Genetic Regulatory Network Based Artificial Cells

In this paper a linear representation of a synthetic genetic regulatory network (GRN) model is derived and it is used for evolving linear dynamic controllers for nonlinear systems. A case study is considered in which running the genetic algorithm on the elements of the system matrix of a linear controller is unable to evolve and reach the control ends, while running the genetic algorithm on the genes of an artificial cell with linear regulatory networks evolves and a linear controller is achieved. This justifies the computational burden imposed on computations due to GRN dynamics as GRN representation increases the evolvability of the controller.

A New Artificial Genetic Regulatory Network Model and its Application in Two Dimensional Robot Control

A New Artificial Genetic Regulatory Network Model and its Application in Two Dimensional Robot Control

State transition graph and stability of singular equilibria for piecewise linear biological models

Many biological networks such as gene regulatory networks and neural networks can be modeled by piecewise linear switching systems of differential equations. For these biological network models, it is very difficult to describe the dynamics of the governing system near singular equilibria as they belong to the discontinuity set of the system. In this paper, using the concept of Filippov solutions, with the help of the state transition graph, and employing a generalized Lyapunov method, we establish some stability results for singular equilibria of a class of piecewise linear biological models. Our results generalize many existing ones. In particular, we present an affirmative answer to Conjecture 5.4 proposed in [R. Casey, H. de Jong, J.-L. Gouzé, Piecewise-linear models of genetic regulatory networks: Equilibria and their stability, Journal of Mathematical Biology 52 (1) (2006) 27–56].

Robust stability analysis of delayed Takagi–Sugeno fuzzy genetic regulatory networks

In this paper, the nonlinear model of genetic regulatory networks is described by the Takagi–Sugeno fuzzy model representation with time-varying delays. Due to the highly complicated nonlinear stability and robust stability problems, a fuzzy approximation method is employed to interpolate several linear genetic regulatory networks at different operation points via fuzzy bases to approximate the nonlinear genetic regulatory network. In this context, the methods of the linear matrix inequality (LMI) technique could be employed to simplify the problems related to robust stability of genetic regulatory networks. Further, by involving triple integral terms in Lyapunov–Krasovskii functionals and LMI techniques, the stability criteria for the delayed fuzzy genetic regulatory networks are expressed as a convex combination of LMIs, which can be solved numerically by any LMI solvers. Several numerical examples are given to verify the effectiveness and applicability of the derived approach.

Multiscale Denoising of Biological Data: A Comparative Analysis

Measured microarray genomic and metabolic data are a rich source of information about the biological systems they represent. For example, time-series biological data can be used to construct dynamic genetic regulatory network models, which can be used to design intervention strategies to cure or manage major diseases. Also, copy number data can be used to determine the locations and extent of aberrations in chromosome sequences. Unfortunately, measured biological data are usually contaminated with errors that mask the important features in the data. Therefore, these noisy measurements need to be filtered to enhance their usefulness in practice. Wavelet-based multiscale filtering has been shown to be a powerful denoising tool. In this work, different batch as well as online multiscale filtering techniques are used to denoise biological data contaminated with white or colored noise. The performances of these techniques are demonstrated and compared to those of some conventional low-pass filters using two case studies. The first case study uses simulated dynamic metabolic data, while the second case study uses real copy number data. Simulation results show that significant improvement can be achieved using multiscale filtering over conventional filtering techniques.

Evolving Boolean Networks with Structural Dynamism

This short article presents an abstract, tunable model of genomic structural change within the cell life cycle and explores its use with simulated evolution. A well-known Boolean model of genetic regulatory networks is extended to include changes in node connectivity based upon the current cell state to begin to capture some of the effects of transposable elements. The evolvability of such networks is explored using a version of the NK model of fitness landscapes with both synchronous and asynchronous updating. Structural dynamism is found to be selected for in nonstationary environments with both update schemes and subsequently shown capable of providing a mechanism for evolutionary innovation when such reorganizations are inherited. This is also found to be the case in stationary environments with asynchronous updating.

Dynamical regimes and learning properties of evolved Boolean networks

Boolean networks (BNs) have been mainly considered as genetic regulatory network models and are the subject of notable works in complex systems biology literature. Nevertheless, in spite of their similarities with neural networks, their potential as learning systems has not yet been fully investigated and exploited. In this work, we show that by employing metaheuristic methods we can train BNs to deal with two notable tasks, namely, the problem of controlling the BN's trajectory to match a set of requirements and the density classification problem. These tasks represent two important categories of problems in machine learning. The former is an example of the problems in which a dynamical system has to be designed such that its dynamics satisfies given requirements. The latter one is a representative task in classification. We also analyse the performance of the optimisation techniques as a function of the characteristics of the networks and the objective function and we show that the learning process could influence and be influenced by the BNs' dynamical condition.

Exploring Discrete Dynamics.Andrew Wuensche. (2011, Luniver Press.) xxxvii + 498 pages, 290 figures, 31 tables.

<i>Exploring Discrete Dynamics.</i>Andrew Wuensche. (2011, Luniver Press.) xxxvii + 498 pages, 290 figures, 31 tables.

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.

Generating Stochastic Gene Regulatory Networks Consistent With Pathway Information and Steady-State Behavior

We present a procedure to generate a stochastic genetic regulatory network model consistent with pathway information. Using the stochastic dynamics of Markov chains, we produce a model constrained by the prior knowledge despite the sometimes incomplete, time independent, and often conflicting nature of these pathways. We apply the Markov theory to study the model's long run behavior and introduce a biologically important transformation to aid in comparison with real biological outcome prediction in the steady-state domain. Our technique produces biologically faithful models without the need for rate kinetics, detailed timing information, or complex inference procedures. To demonstrate the method, we produce a model using 28 pathways from the biological literature pertaining to the transcription factor family nuclear factor-κB. Predictions from this model in the steady-state domain are then validated against nine mice knockout experiments.

A Simple Computational Cell: Coupling Boolean Gene and Protein Networks

This article presents an abstract, tunable model containing two of the principal information-processing features of cells and explores its use with simulated evolution. The random Boolean model of genetic regulatory networks is extended to include a protein interaction network. The underlying behavior of the resulting two coupled dynamical networks is investigated before their evolvability is explored using a version of the NK model of fitness landscapes.