Xiaoning Qian

Effect of Function Perturbation on the Steady-State Distribution of Genetic Regulatory Networks: Optimal Structural Intervention

The dynamics of a rule-based gene regulatory network are determined by the regulatory functions in conjunction with whatever probability distributions are involved in network transitions. In the case of Boolean networks (BNs) and, more generally, probabilistic Boolean networks (PBNs), there has been a significant amount of investigation into the effect of perturbing gene states, in particular, the design of intervention strategies based on finite- or infinite-horizon control polices. This paper considers the less investigated issue of function perturbations. A single function perturbation affects network dynamics and alters the long-run distribution, whereas any individual gene perturbation has only transient effects and does not change the long-run distribution. We derive analytic results for changes in the steady-state distributions of PBNs resulting from modifications to the underlying regulatory rules and apply the derived results to find optimal structural interventions to avoid undesirable states. The results are applied to a WNT5A network and a mammalian cell cycle related network, respectively, to achieve more favorable steady-state distributions and reduce the risk of getting into aberrant phenotypes.

Intervention in gene regulatory networks via greedy control policies based on long-run behavior.

BackgroundA salient purpose for studying gene regulatory networks is to derive intervention strategies, the goals being to identify potential drug targets and design gene-based therapeutic intervention. Optimal stochastic control based on the transition probability matrix of the underlying Markov chain has been studied extensively for probabilistic Boolean networks. Optimization is based on minimization of a cost function and a key goal of control is to reduce the steady-state probability mass of undesirable network states. Owing to computational complexity, it is difficult to apply optimal control for large networks.ResultsIn this paper, we propose three new greedy stationary control policies by directly investigating the effects on the network long-run behavior. Similar to the recently proposed mean-first-passage-time (MFPT) control policy, these policies do not depend on minimization of a cost function and avoid the computational burden of dynamic programming. They can be used to design stationary control policies that avoid the need for a user-defined cost function because they are based directly on long-run network behavior; they can be used as an alternative to dynamic programming algorithms when the latter are computationally prohibitive; and they can be used to predict the best control gene with reduced computational complexity, even when one is employing dynamic programming to derive the final control policy. We compare the performance of these three greedy control policies and the MFPT policy using randomly generated probabilistic Boolean networks and give a preliminary example for intervening in a mammalian cell cycle network.ConclusionThe newly proposed control policies have better performance in general than the MFPT policy and, as indicated by the results on the mammalian cell cycle network, they can potentially serve as future gene therapeutic intervention strategies.

Quantifying the Objective Cost of Uncertainty in Complex Dynamical Systems

Real-world problems often involve complex systems that cannot be perfectly modeled or identified, and many engineering applications aim to design operators that can perform reliably in the presence of such uncertainty. In this paper, we propose a novel Bayesian framework for objective-based uncertainty quantification (UQ), which quantifies the uncertainty in a given system based on the expected increase of the operational cost that it induces. This measure of uncertainty, called MOCU (mean objective cost of uncertainty), provides a practical way of quantifying the effect of various types of system uncertainties on the operation of interest. Furthermore, the proposed UQ framework provides a general mathematical basis for designing robust operators, and it can be applied to diverse applications, including robust filtering, classification, and control. We demonstrate the utility and effectiveness of the proposed framework by applying it to the problem of robust structural intervention of gene regulatory networks, an important application in translational genomics.

A CoD-based reduction algorithm for designing stationary control policies on Boolean networks

MOTIVATION Gene regulatory networks serve as models from which to derive therapeutic intervention strategies, in particular, stationary control policies over time that shift the probability mass of the steady state distribution (SSD) away from states associated with undesirable phenotypes. Derivation of control policies is hindered by the high-dimensional state spaces associated with gene regulatory networks. Hence, network reduction is a fundamental issue for intervention. RESULTS The network model that has been most used for the study of intervention in gene regulatory networks is the probabilistic Boolean network (PBN), which is a collection of constituent Boolean networks (BNs) with perturbation. In this article, we propose an algorithm that reduces a BN with perturbation, designs a control policy on the reduced network and then induces that policy to the original network. The coefficient of determination (CoD) is used to choose a gene for deletion, and a reduction mapping is used to rewire the remaining genes. This CoD-reduction procedure is used to construct a reduced network, then either the previously proposed mean first-passage time (MFPT) or SSD stationary control policy is designed on the reduced network, and these policies are induced to the original network. The efficacy of the overall algorithm is demonstrated on networks of 10 genes or less, where it is possible to compare the steady state shifts of the induced and original policies (because the latter can be derived), and by applying it to a 17-gene gastrointestinal network where it is shown that there is substantial beneficial steady state shift. AVAILABILITY The code for the algorithms is available at: http://gsp.tamu.edu/Publications/supplementary/ghaffari10a/ Please Contact Noushin Ghaffari at nghaffari@tamu.edu for further questions. SUPPLEMENTARY INFORMATION Supplementary data are available at Bioinformatics online.

Querying Pathways in Protein Interaction Networks Based on Hidden Markov Models

High-throughput techniques for measuring protein interactions have enabled the systematic study of complex protein networks. Comparing the networks of different organisms and identifying their common substructures can lead to a better understanding of the regulatory mechanisms underlying various cellular functions. To facilitate such comparisons, we present an efficient framework based on hidden Markov models (HMMs) that can be used for finding homologous pathways in a network of interest. Given a query path, our method identifies the top k matching paths in the network, which may contain any number of consecutive insertions and deletions. We demonstrate that our method is able to identify biologically significant pathways in protein interaction networks obtained from the DIP database, and the retrieved paths are closer to the curated pathways in the KEGG database when compared to the results from previous approaches. Unlike most existing algorithms that suffer from exponential time complexity, our algorithm has a polynomial complexity that grows linearly with the query size. This enables the search for very long paths with more than 10 proteins within a few minutes on a desktop computer. A software program implementing the algorithm is available upon request from the authors.

Stationary and structural control in gene regulatory networks: basic concepts

A major reason for constructing gene regulatory networks is to use them as models for determining therapeutic intervention strategies by deriving ways of altering their long-run dynamics in such a way as to reduce the likelihood of entering undesirable states. In general, two paradigms have been taken for gene network intervention: (1) stationary external control is based on optimally altering the status of a control gene (or genes) over time to drive network dynamics; and (2) structural intervention involves an optimal one-time change of the network structure (wiring) to beneficially alter the long-run behaviour of the network. These intervention approaches have mainly been developed within the context of the probabilistic Boolean network model for gene regulation. This article reviews both types of intervention and applies them to reducing the metastatic competence of cells via intervention in a melanoma-related network.

State reduction for network intervention in probabilistic Boolean networks

MOTIVATION A key goal of studying biological systems is to design therapeutic intervention strategies. Probabilistic Boolean networks (PBNs) constitute a mathematical model which enables modeling, predicting and intervening in their long-run behavior using Markov chain theory. The long-run dynamics of a PBN, as represented by its steady-state distribution (SSD), can guide the design of effective intervention strategies for the modeled systems. A major obstacle for its application is the large state space of the underlying Markov chain, which poses a serious computational challenge. Hence, it is critical to reduce the model complexity of PBNs for practical applications. RESULTS We propose a strategy to reduce the state space of the underlying Markov chain of a PBN based on a criterion that the reduction least distorts the proportional change of stationary masses for critical states, for instance, the network attractors. In comparison to previous reduction methods, we reduce the state space directly, without deleting genes. We then derive stationary control policies on the reduced network that can be naturally induced back to the original network. Computational experiments study the effects of the reduction on model complexity and the performance of designed control policies which is measured by the shift of stationary mass away from undesirable states, those associated with undesirable phenotypes. We consider randomly generated networks as well as a 17-gene gastrointestinal cancer network, which, if not reduced, has a 2(17) × 2(17) transition probability matrix. Such a dimension is too large for direct application of many previously proposed PBN intervention strategies.

Effective Identification of Conserved Pathways in Biological Networks Using Hidden Markov Models

Background The advent of various high-throughput experimental techniques for measuring molecular interactions has enabled the systematic study of biological interactions on a global scale. Since biological processes are carried out by elaborate collaborations of numerous molecules that give rise to a complex network of molecular interactions, comparative analysis of these biological networks can bring important insights into the functional organization and regulatory mechanisms of biological systems. Methodology/Principal Findings In this paper, we present an effective framework for identifying common interaction patterns in the biological networks of different organisms based on hidden Markov models (HMMs). Given two or more networks, our method efficiently finds the top matching paths in the respective networks, where the matching paths may contain a flexible number of consecutive insertions and deletions. Conclusions/Significance Based on several protein-protein interaction (PPI) networks obtained from the Database of Interacting Proteins (DIP) and other public databases, we demonstrate that our method is able to detect biologically significant pathways that are conserved across different organisms. Our algorithm has a polynomial complexity that grows linearly with the size of the aligned paths. This enables the search for very long paths with more than 10 nodes within a few minutes on a desktop computer. The software program that implements this algorithm is available upon request from the authors.

On the Long-run Sensitivity of Probabilistic Boolean Networks

Boolean networks and, more generally, probabilistic Boolean networks, as one class of gene regulatory networks, model biological processes with the network dynamics determined by the logic-rule regulatory functions in conjunction with probabilistic parameters involved in network transitions. While there has been significant research on applying different control policies to alter network dynamics as future gene therapeutic intervention, we have seen less work on understanding the sensitivity of network dynamics with respect to perturbations to networks, including regulatory rules and the involved parameters, which is particularly critical for the design of intervention strategies. This paper studies this less investigated issue of network sensitivity in the long run. As the underlying model of probabilistic Boolean networks is a finite Markov chain, we define the network sensitivity based on the steady-state distributions of probabilistic Boolean networks and call it long-run sensitivity. The steady-state distribution reflects the long-run behavior of the network and it can give insight into the dynamics or momentum existing in a system. The change of steady-state distribution caused by possible perturbations is the key measure for intervention. This newly defined long-run sensitivity can provide insight on both network inference and intervention. We show the results for probabilistic Boolean networks generated from random Boolean networks and the results from two real biological networks illustrate preliminary applications of sensitivity in intervention for practical problems.

Adaptive bi-level programming for optimal gene knockouts for targeted overproduction under phenotypic constraints

BackgroundOptimization procedures to identify gene knockouts for targeted biochemical overproduction have been widely in use in modern metabolic engineering. Flux balance analysis (FBA) framework has provided conceptual simplifications for genome-scale dynamic analysis at steady states. Based on FBA, many current optimization methods for targeted bio-productions have been developed under the maximum cell growth assumption. The optimization problem to derive gene knockout strategies recently has been formulated as a bi-level programming problem in OptKnock for maximum targeted bio-productions with maximum growth rates. However, it has been shown that knockout mutants in fact reach the steady states with the minimization of metabolic adjustment (MOMA) from the corresponding wild-type strains instead of having maximal growth rates after genetic or metabolic intervention. In this work, we propose a new bi-level computational framework--MOMAKnock--which can derive robust knockout strategies under the MOMA flux distribution approximation.MethodsIn this new bi-level optimization framework, we aim to maximize the production of targeted chemicals by identifying candidate knockout genes or reactions under phenotypic constraints approximated by the MOMA assumption. Hence, the targeted chemical production is the primary objective of MOMAKnock while the MOMA assumption is formulated as the inner problem of constraining the knockout metabolic flux to be as close as possible to the steady-state phenotypes of wide-type strains. As this new inner problem becomes a quadratic programming problem, a novel adaptive piecewise linearization algorithm is developed in this paper to obtain the exact optimal solution to this new bi-level integer quadratic programming problem for MOMAKnock.ResultsOur new MOMAKnock model and the adaptive piecewise linearization solution algorithm are tested with a small E. coli core metabolic network and a large-scale iAF1260 E. coli metabolic network. The derived knockout strategies are compared with those from OptKnock. Our preliminary experimental results show that MOMAKnock can provide improved targeted productions with more robust knockout strategies.