Real Gene Regulatory Networks Research Articles

Reverse network diffusion to remove indirect noise for better inference of gene regulatory networks.

Gene regulatory networks (GRNs) are vital tools for delineating regulatory relationships between transcription factors and their target genes. The boom in computational biology and various biotechnologies has made inferring GRNs from multi-omics data a hot topic. However, when networks are constructed from gene expression data, they often suffer from false-positive problem due to the transitive effects of correlation. The presence of spurious noise edges obscures the real gene interactions, which makes downstream analyses, such as detecting gene function modules and predicting disease-related genes, difficult and inefficient. Therefore, there is an urgent and compelling need to develop network denoising methods to improve the accuracy of GRN inference. In this study, we proposed a novel network denoising method named REverse Network Diffusion On Random walks (RENDOR). RENDOR is designed to enhance the accuracy of GRNs afflicted by indirect effects. RENDOR takes noisy networks as input, models higher-order indirect interactions between genes by transitive closure, eliminates false-positive effects using the inverse network diffusion method, and produces refined networks as output. We conducted a comparative assessment of GRN inference accuracy before and after denoising on simulated networks and real GRNs. Our results emphasized that the network derived from RENDOR more accurately and effectively captures gene interactions. This study demonstrates the significance of removing network indirect noise and highlights the effectiveness of the proposed method in enhancing the signal-to-noise ratio of noisy networks. The R package RENDOR is provided at https://github.com/Wu-Lab/RENDOR and other source code and data are available at https://github.com/Wu-Lab/RENDOR-reproduce.

Generation of Realistic Gene Regulatory Networks by Enriching for Feed-Forward Loops.

The regulatory relationships between genes and proteins in a cell form a gene regulatory network (GRN) that controls the cellular response to changes in the environment. A number of inference methods to reverse engineer the original GRN from large-scale expression data have recently been developed. However, the absence of ground-truth GRNs when evaluating the performance makes realistic simulations of GRNs necessary. One aspect of this is that local network motif analysis of real GRNs indicates that the feed-forward loop (FFL) is significantly enriched. To simulate this properly, we developed a novel motif-based preferential attachment algorithm, FFLatt, which outperformed the popular GeneNetWeaver network generation tool in reproducing the FFL motif occurrence observed in literature-based biological GRNs. It also preserves important topological properties such as scale-free topology, sparsity, and average in/out-degree per node. We conclude that FFLatt is well-suited as a network generation module for a benchmarking framework with the aim to provide fair and robust performance evaluation of GRN inference methods.

Network Classification Based on Reducibility With Respect to the Stability of Canalizing Power of Genes in a Gene Regulatory Network - A Boolean Network Modeling Perspective.

A key objective of studying biological systems is to design therapeutic intervention strategies for beneficially altering cell dynamics. Derivation of control policies is hindered by the high-dimensional state spaces associated with gene regulatory networks. Hence, it is critical to reduce the network complexity and the paper aims to address this issue by focusing on the distribution of the canalizing power (CP) of the genes in the model. Canalizing genes enforce broad corrective actions on cellular processes and play a crucial role in producing optimal reactions to external stimuli. Therefore, it is critical to reduce the network while preserving the canalizing power of genes. We reduce Boolean networks with perturbation by removing genes with the smallest canalizing power consecutively, and evaluate the stability of canalizing power. A systematic empirical study demonstrates that there are two classes of networks, reducible and irreducible with respect to the preservation of canalizing power of the genes. Based on these observations, we introduce the definition of reducible networks and proceed with the problem of selecting the relevant network features that allow for discriminating networks from the two different classes. We demonstrate the efficacy of the selected features on synthetic and real gene regulatory networks.

Reconstructing gene regulatory networks via memetic algorithm and LASSO based on recurrent neural networks

Reconstructing gene regulatory networks (GRNs) from gene expression data is an important and challenging problem in system biology. In general, the problem of reconstructing GRNs can be modeled as an optimization problem. Recurrent neural network (RNN) has been widely used for GRNs. However, in a real GRN, the number of genes is very large and the relationships between genes are usually very sparse. In this paper, we design a memetic algorithm to learn partial parameters of RNN, and develop a framework based on the least absolute shrinkage and selection operator (LASSO) to reconstruct GRNs based on RNN, which is termed as MALASSORNN-GRN. In the LASSO, the task of reconstructing GRNs is decomposed into a sparse signal reconstructing problem. In the experiments, MALASSORNN-GRN is applied on synthetic data and well-known benchmark datasets DREAM3 and DREAM4. The effect of parameters on MALASSORNN-GRN is discussed, and MALASSORNN-GRN is compared with three other algorithms which are all state-of-the-art RNN learning algorithms. The results show that MALASSORNN-GRN performs best and is capable of reconstructing large-scale GRNs.

Quantitative Analysis of a Transient Dynamics of a Genetic Regulatory Network

We make a quantitative analysis of a simple genetic regulatory network with positive feedback, and show that the proteins become extinct with certainty in the stationary distribution when the stochastic noise is present, contrary to the solution of the deterministic rate equation where the protein number is predicted to converge to a non-zero value. We show that as the stochastic noise approaches zero, the extinction time diverges exponentially. We also show that the leaky expression from the inactive gene ameliorates the effect of the stochastic noise. The order of magnitude estimates using biological parameters suggest that for a real gene regulatory network, the stochastic noise is sufficiently small so that not only is the extinction time much larger than biologically relevant time-scales, but also the effect of the leaky expression dominates over that of the stochastic noise, leading to the protection from the catastrophic rare event of protein extinction.

Quantitative analysis of a transient dynamics of a gene regulatory network

In a stochastic process, noise often modifies the picture offered by the mean-field dynamics. In particular, when there is an absorbing state, the noise erases a stable fixed point of the mean field equation from the stationary distribution and turns it into a transient peak. We make a quantitative analysis of this effect for a simple genetic regulatory network with positive feedback where the proteins become extinct in the presence of stochastic noise, contrary to the prediction of the deterministic rate equation that the protein number converges to a nonzero value. We show that the transient peak appears near the stable fixed point of the rate equation, and the extinction time diverges exponentially as the stochastic noise approaches zero. We also show how the baseline production from the inactive gene ameliorates the effect of the stochastic noise and interpret the opposite effects of the noise and the baseline production in terms of the position shift of the unstable fixed point. The order of magnitude estimates using biological parameters suggest that for a real gene regulatory network, the stochastic noise is sufficiently small so that not only is the extinction time much larger than biologically relevant timescales, but also the effect of the baseline production dominates over that of the stochastic noise, leading to protection from the catastrophic rare event of protein extinction.

Shortest path counting in probabilistic biological networks

BackgroundBiological regulatory networks, representing the interactions between genes and their products, control almost every biological activity in the cell. Shortest path search is critical to apprehend the structure of these networks, and to detect their key components. Counting the number of shortest paths between pairs of genes in biological networks is a polynomial time problem. The fact that biological interactions are uncertain events however drastically complicates the problem, as it makes the topology of a given network uncertain.ResultsIn this paper, we develop a novel method to count the number of shortest paths between two nodes in probabilistic networks. Unlike earlier approaches, which uses the shortest path counting methods that are specifically designed for deterministic networks, our method builds a new mathematical model to express and compute the number of shortest paths. We prove the correctness of this model.ConclusionsWe compare our novel method to three existing shortest path counting methods on synthetic and real gene regulatory networks. Our experiments demonstrate that our method is scalable, and it outperforms the existing methods in accuracy. Application of our shortest path counting method to detect communities in probabilistic networks shows that our method successfully finds communities in probabilistic networks. Moreover, our experiments on cell cycle pathway among different cancer types exhibit that our method helps in uncovering key functional characteristics of biological networks.

An experimental design framework for Markovian gene regulatory networks under stationary control policy

BackgroundA fundamental problem for translational genomics is to find optimal therapies based on gene regulatory intervention. Dynamic intervention involves a control policy that optimally reduces a cost function based on phenotype by externally altering the state of the network over time. When a gene regulatory network (GRN) model is fully known, the problem is addressed using classical dynamic programming based on the Markov chain associated with the network. When the network is uncertain, a Bayesian framework can be applied, where policy optimality is with respect to both the dynamical objective and the uncertainty, as characterized by a prior distribution. In the presence of uncertainty, it is of great practical interest to develop an experimental design strategy and thereby select experiments that optimally reduce a measure of uncertainty.ResultsIn this paper, we employ mean objective cost of uncertainty (MOCU), which quantifies uncertainty based on the degree to which uncertainty degrades the operational objective, that being the cost owing to undesirable phenotypes. We assume that a number of conditional probabilities characterizing regulatory relationships among genes are unknown in the Markovian GRN. In sum, there is a prior distribution which can be updated to a posterior distribution by observing a regulatory trajectory, and an optimal control policy, known as an “intrinsically Bayesian robust” (IBR) policy. To obtain a better IBR policy, we select an experiment that minimizes the MOCU remaining after applying its output to the network. At this point, we can either stop and find the resulting IBR policy or proceed to determine more unknown conditional probabilities via regulatory observation and find the IBR policy from the resulting posterior distribution. For sequential experimental design this entire process is iterated. Owing to the computational complexity of experimental design, which requires computation of many potential IBR policies, we implement an approximate method utilizing mean first passage times (MFPTs) – but only in experimental design, the final policy being an IBR policy.ConclusionsComprehensive performance analysis based on extensive simulations on synthetic and real GRNs demonstrate the efficacy of the proposed method, including the accuracy and computational advantage of the approximate MFPT-based design.

RGBM: regularized gradient boosting machines for identification of the transcriptional regulators of discrete glioma subtypes.

We propose a generic framework for gene regulatory network (GRN) inference approached as a feature selection problem. GRNs obtained using Machine Learning techniques are often dense, whereas real GRNs are rather sparse. We use a Tikonov regularization inspired optimal L-curve criterion that utilizes the edge weight distribution for a given target gene to determine the optimal set of TFs associated with it. Our proposed framework allows to incorporate a mechanistic active biding network based on cis-regulatory motif analysis. We evaluate our regularization framework in conjunction with two non-linear ML techniques, namely gradient boosting machines (GBM) and random-forests (GENIE), resulting in a regularized feature selection based method specifically called RGBM and RGENIE respectively. RGBM has been used to identify the main transcription factors that are causally involved as master regulators of the gene expression signature activated in the FGFR3-TACC3-positive glioblastoma. Here, we illustrate that RGBM identifies the main regulators of the molecular subtypes of brain tumors. Our analysis reveals the identity and corresponding biological activities of the master regulators characterizing the difference between G-CIMP-high and G-CIMP-low subtypes and between PA-like and LGm6-GBM, thus providing a clue to the yet undetermined nature of the transcriptional events among these subtypes.

Employing decomposable partially observable Markov decision processes to control gene regulatory networks.

Formulate the induction and control of gene regulatory networks (GRNs) from gene expression data using Partially Observable Markov Decision Processes (POMDPs). Different approaches exist to model GRNs; they are mostly simulated as mathematical models that represent relationships between genes. Actually, it has been realized that biological functions at the cellular level are controlled by genes; thus, by controlling the behavior of genes, it is possible to regulate these biological functions. The GRN control problem has been studied mostly with the aid of probabilistic Boolean networks, and corresponding control policies have been devised. Though turns into a more challenging problem, we argue that partial observability would be a more natural and realistic method for handling the control of GRNs. Partial observability is a fundamental aspect of the problem; it is mostly ignored and substituted by assumption that states of GRN are known precisely, prescribed as full observability. We propose a method for the construction of POMDP model of GRN from only raw gene expression data which is original and novel. Then, we introduce a novel approach to decompose/factor the POMDP model into sub-POMDP's in order to solve it efficiently with the help of divide-and-conquer strategy. In order to demonstrate the effectiveness of the proposed solution we experimented with two synthetic network and one real network data from the literature. We also conducted two sets of separate experiments used to explore the impact of network connectivity and data order to our approach CONCLUSIONS: The reported test results using both synthetic and real GRNs are promising in demonstrating the applicability, effectiveness and efficiency of the proposed approach. This is due to the fact that partial observability fits well to the problem of noisy acquisition of gene expression data as there are technological limitations to measure precisely exact expression levels of genes.

Reverse engineering highlights potential principles of large gene regulatory network design and learning

Inferring transcriptional gene regulatory networks from transcriptomic datasets is a key challenge of systems biology, with potential impacts ranging from medicine to agronomy. There are several techniques used presently to experimentally assay transcription factors to target relationships, defining important information about real gene regulatory networks connections. These techniques include classical ChIP-seq, yeast one-hybrid, or more recently, DAP-seq or target technologies. These techniques are usually used to validate algorithm predictions. Here, we developed a reverse engineering approach based on mathematical and computer simulation to evaluate the impact that this prior knowledge on gene regulatory networks may have on training machine learning algorithms. First, we developed a gene regulatory networks-simulating engine called FRANK (Fast Randomizing Algorithm for Network Knowledge) that is able to simulate large gene regulatory networks (containing 104 genes) with characteristics of gene regulatory networks observed in vivo. FRANK also generates stable or oscillatory gene expression directly produced by the simulated gene regulatory networks. The development of FRANK leads to important general conclusions concerning the design of large and stable gene regulatory networks harboring scale free properties (built ex nihilo). In combination with supervised (accepting prior knowledge) support vector machine algorithm we (i) address biologically oriented questions concerning our capacity to accurately reconstruct gene regulatory networks and in particular we demonstrate that prior-knowledge structure is crucial for accurate learning, and (ii) draw conclusions to inform experimental design to performed learning able to solve gene regulatory networks in the future. By demonstrating that our predictions concerning the influence of the prior-knowledge structure on support vector machine learning capacity holds true on real data (Escherichia coli K14 network reconstruction using network and transcriptomic data), we show that the formalism used to build FRANK can to some extent be a reasonable model for gene regulatory networks in real cells.

Evaluation of artificial time series microarray data for dynamic gene regulatory network inference

High-throughput technology like microarrays is widely used in the inference of gene regulatory networks (GRNs). We focused on time series data since we are interested in the dynamics of GRNs and the identification of dynamic networks. We evaluated the amount of information that exists in artificial time series microarray data and the ability of an inference process to produce accurate models based on them. We used dynamic artificial gene regulatory networks in order to create artificial microarray data. Key features that characterize microarray data such as the time separation of directly triggered genes, the percentage of directly triggered genes and the triggering function type were altered in order to reveal the limits that are imposed by the nature of microarray data on the inference process. We examined the effect of various factors on the inference performance such as the network size, the presence of noise in microarray data, and the network sparseness. We used a system theory approach and examined the relationship between the pole placement of the inferred system and the inference performance. We examined the relationship between the inference performance in the time domain and the true system parameter identification. Simulation results indicated that time separation and the percentage of directly triggered genes are crucial factors. Also, network sparseness, the triggering function type and noise in input data affect the inference performance. When two factors were simultaneously varied, it was found that variation of one parameter significantly affects the dynamic response of the other. Crucial factors were also examined using a real GRN and acquired results confirmed simulation findings with artificial data. Different initial conditions were also used as an alternative triggering approach. Relevant results confirmed that the number of datasets constitutes the most significant parameter with regard to the inference performance.

CABeRNET: a Cytoscape app for augmented Boolean models of gene regulatory NETworks

BackgroundDynamical models of gene regulatory networks (GRNs) are highly effective in describing complex biological phenomena and processes, such as cell differentiation and cancer development. Yet, the topological and functional characterization of real GRNs is often still partial and an exhaustive picture of their functioning is missing.ResultsWe here introduce CABeRNET, a Cytoscape app for the generation, simulation and analysis of Boolean models of GRNs, specifically focused on their augmentation when a only partial topological and functional characterization of the network is available. By generating large ensembles of networks in which user-defined entities and relations are added to the original core, CABeRNET allows to formulate hypotheses on the missing portions of real networks, as well to investigate their generic properties, in the spirit of complexity science.ConclusionsCABeRNET offers a series of innovative simulation and modeling functions and tools, including (but not being limited to) the dynamical characterization of the gene activation patterns ruling cell types and differentiation fates, and sophisticated robustness assessments, as in the case of gene knockouts. The integration within the widely used Cytoscape framework for the visualization and analysis of biological networks, makes CABeRNET a new essential instrument for both the bioinformatician and the computational biologist, as well as a computational support for the experimentalist. An example application concerning the analysis of an augmented T-helper cell GRN is provided.

Efficient experimental design for uncertainty reduction in gene regulatory networks.

BackgroundAn accurate understanding of interactions among genes plays a major role in developing therapeutic intervention methods. Gene regulatory networks often contain a significant amount of uncertainty. The process of prioritizing biological experiments to reduce the uncertainty of gene regulatory networks is called experimental design. Under such a strategy, the experiments with high priority are suggested to be conducted first.ResultsThe authors have already proposed an optimal experimental design method based upon the objective for modeling gene regulatory networks, such as deriving therapeutic interventions. The experimental design method utilizes the concept of mean objective cost of uncertainty (MOCU). MOCU quantifies the expected increase of cost resulting from uncertainty. The optimal experiment to be conducted first is the one which leads to the minimum expected remaining MOCU subsequent to the experiment. In the process, one must find the optimal intervention for every gene regulatory network compatible with the prior knowledge, which can be prohibitively expensive when the size of the network is large. In this paper, we propose a computationally efficient experimental design method. This method incorporates a network reduction scheme by introducing a novel cost function that takes into account the disruption in the ranking of potential experiments. We then estimate the approximate expected remaining MOCU at a lower computational cost using the reduced networks.ConclusionsSimulation results based on synthetic and real gene regulatory networks show that the proposed approximate method has close performance to that of the optimal method but at lower computational cost. The proposed approximate method also outperforms the random selection policy significantly. A MATLAB software implementing the proposed experimental design method is available at http://gsp.tamu.edu/Publications/supplementary/roozbeh15a/.

Optimal Experimental Design for Gene Regulatory Networks in the Presence of Uncertainty.

Of major interest to translational genomics is the intervention in gene regulatory networks (GRNs) to affect cell behavior; in particular, to alter pathological phenotypes. Owing to the complexity of GRNs, accurate network inference is practically challenging and GRN models often contain considerable amounts of uncertainty. Considering the cost and time required for conducting biological experiments, it is desirable to have a systematic method for prioritizing potential experiments so that an experiment can be chosen to optimally reduce network uncertainty. Moreover, from a translational perspective it is crucial that GRN uncertainty be quantified and reduced in a manner that pertains to the operational cost that it induces, such as the cost of network intervention. In this work, we utilize the concept of mean objective cost of uncertainty (MOCU) to propose a novel framework for optimal experimental design. In the proposed framework, potential experiments are prioritized based on the MOCU expected to remain after conducting the experiment. Based on this prioritization, one can select an optimal experiment with the largest potential to reduce the pertinent uncertainty present in the current network model. We demonstrate the effectiveness of the proposed method via extensive simulations based on synthetic and real gene regulatory networks.

Hierarchical decomposition of dynamically evolving regulatory networks.

BackgroundGene regulatory networks describe the interplay between genes and their products. These networks control almost every biological activity in the cell through interactions. The hierarchy of genes in these networks as defined by their interactions gives important insights into how these functions are governed. Accurately determining the hierarchy of genes is however a computationally difficult problem. This problem is further complicated by the fact that an intrinsic characteristic of regulatory networks is that the wiring of interactions can change over time. Determining how the hierarchy in the gene regulatory networks changes with dynamically evolving network topology remains to be an unsolved challenge.ResultsIn this study, we develop a new method, named D-HIDEN (Dynamic-HIerarchical DEcomposition of Networks) to find the hierarchy of the genes in dynamically evolving gene regulatory network topologies. Unlike earlier methods, which recompute the hierarchy from scratch when the network topology changes, our method adapts the hierarchy based on the wiring of the interactions only for the nodes which have the potential to move in the hierarchy.ConclusionsWe compare D-HIDEN to five currently available hierarchical decomposition methods on synthetic and real gene regulatory networks. Our experiments demonstrate that D-HIDEN significantly outperforms existing methods in running time, accuracy, or both. Furthermore, our method is robust against dynamic changes in hierarchy. Our experiments on human gene regulatory networks suggest that our method may be used to reconstruct hierarchy in gene regulatory networks.

Evaluating a common semi-mechanistic mathematical model of gene-regulatory networks.

Modeling and simulation of gene-regulatory networks (GRNs) has become an important aspect of modern systems biology investigations into mechanisms underlying gene regulation. A key challenge in this area is the automated inference (reverse-engineering) of dynamic, mechanistic GRN models from gene expression time-course data. Common mathematical formalisms for representing such models capture two aspects simultaneously within a single parameter: (1) Whether or not a gene is regulated, and if so, the type of regulator (activator or repressor), and (2) the strength of influence of the regulator (if any) on the target or effector gene. To accommodate both roles, "generous" boundaries or limits for possible values of this parameter are commonly allowed in the reverse-engineering process. This approach has several important drawbacks. First, in the absence of good guidelines, there is no consensus on what limits are reasonable. Second, because the limits may vary greatly among different reverse-engineering experiments, the concrete values obtained for the models may differ considerably, and thus it is difficult to compare models. Third, if high values are chosen as limits, the search space of the model inference process becomes very large, adding unnecessary computational load to the already complex reverse-engineering process. In this study, we demonstrate that restricting the limits to the [−1, +1] interval is sufficient to represent the essential features of GRN systems and offers a reduction of the search space without loss of quality in the resulting models. To show this, we have carried out reverse-engineering studies on data generated from artificial and experimentally determined from real GRN systems.

Criticality Is an Emergent Property of Genetic Networks that Exhibit Evolvability

Accumulating experimental evidence suggests that the gene regulatory networks of living organisms operate in the critical phase, namely, at the transition between ordered and chaotic dynamics. Such critical dynamics of the network permits the coexistence of robustness and flexibility which are necessary to ensure homeostatic stability (of a given phenotype) while allowing for switching between multiple phenotypes (network states) as occurs in development and in response to environmental change. However, the mechanisms through which genetic networks evolve such critical behavior have remained elusive. Here we present an evolutionary model in which criticality naturally emerges from the need to balance between the two essential components of evolvability: phenotype conservation and phenotype innovation under mutations. We simulated the Darwinian evolution of random Boolean networks that mutate gene regulatory interactions and grow by gene duplication. The mutating networks were subjected to selection for networks that both (i) preserve all the already acquired phenotypes (dynamical attractor states) and (ii) generate new ones. Our results show that this interplay between extending the phenotypic landscape (innovation) while conserving the existing phenotypes (conservation) suffices to cause the evolution of all the networks in a population towards criticality. Furthermore, the networks produced by this evolutionary process exhibit structures with hubs (global regulators) similar to the observed topology of real gene regulatory networks. Thus, dynamical criticality and certain elementary topological properties of gene regulatory networks can emerge as a byproduct of the evolvability of the phenotypic landscape.

Constructing gene regulatory networks for long term photosynthetic light acclimation in Arabidopsis thaliana

BackgroundPhotosynthetic light acclimation is an important process that allows plants to optimize the efficiency of photosynthesis, which is the core technology for green energy. However, currently little is known about the molecular mechanisms behind the regulation of the photosynthetic light acclimation response. In this study, a systematic method is proposed to investigate this mechanism by constructing gene regulatory networks from microarray data of Arabidopsis thaliana.MethodsThe potential TF-gene regulatory pairs of photosynthetic light acclimation have been obtained by data mining of literature and databases. Following the identification of these potential TF-gene pairs, they have been refined using Pearson's correlation, allowing the construction of a rough gene regulatory network. This rough gene regulatory network is then pruned using time series microarray data of Arabidopsis thaliana via the maximum likelihood system identification method and Akaike's system order detection method to approach the real gene regulatory network of photosynthetic light acclimation.ResultsBy comparing the gene regulatory networks under the PSI-to-PSII light shift and the PSII-to-PSI light shift, it is possible to identify important transcription factors for the different light shift conditions. Furthermore, the robustness of the gene network, in particular the hubs and weak linkage points, are also discussed under the different light conditions to gain further insight into the mechanisms of photosynthesis.ConclusionsThis study investigates the molecular mechanisms of photosynthetic light acclimation for Arabidopsis thaliana from the physiological level. This has been achieved through the construction of gene regulatory networks from the limited data sources and literature via an efficient computation method. If more experimental data for whole-genome ChIP-chip data and microarray data with multiple sampling points becomes available in the future, the proposed method will be improved on by constructing the whole-genome gene regulatory network. These advances will greatly improve our understanding of the mechanisms of the photosynthetic system.

Construction of gene regulatory networks with colored noise

Given recent investigations of gene regulatory networks, an increasing amount of attention is focused on the nonlinearity and randomness in these networks. It has always been assumed that gene regulation is a random process with Gaussian white noise. However, in practice, there is no ideal white noise; therefore results obtained from a model with white noise are not always exactly correct. We constructed a dynamic model of gene regulatory networks based on a first-order stochastic differential equation, which is often used for quantitative analysis of gene regulatory networks. For biological realism, we added a colored noise item, based on a sliding autoregressive model. The abilities of regulatory genes and the intensities of the colored noise item were estimated using an extended recursive least-square algorithm. We applied the model to budding yeast data and reconstructed regulatory networks. Our experimental results showed that the proposed model is suitable for the description of real gene regulatory networks.