Boolean modeling and fault diagnosis in oxidative stress response.

BACKGROUND: Oxidative stress is a consequence of normal and abnormal cellular metabolism and is linked to the development of human diseases. The effective functioning of the pathway responding to oxidative stress protects the cellular DNA against oxidative damage; conversely the failure of the oxidative stress response mechanism can induce aberrant cellular behavior leading to diseases such as neurodegenerative disorders and cancer. Thus, understanding the normal signaling present in oxidative stress response pathways and determining possible signaling alterations leading to disease could provide us with useful pointers for therapeutic purposes. Using knowledge of oxidative stress response pathways from the literature, we developed a Boolean network model whose simulated behavior is consistent with earlier experimental observations from the literature. Concatenating the oxidative stress response pathways with the PI3-Kinase-Akt pathway, the oxidative stress is linked to the phenotype of apoptosis, once again through a Boolean network model. Furthermore, we present an approach for pinpointing possible fault locations by using temporal variations in the oxidative stress input and observing the resulting deviations in the apoptotic signature from the normally predicted pathway. Such an approach could potentially form the basis for designing more effective combination therapies against complex diseases such as cancer. RESULTS: In this paper, we have developed a Boolean network model for the oxidative stress response. This model was developed based on pathway information from the current literature pertaining to oxidative stress. Where applicable, the behaviour predicted by the model is in agreement with experimental observations from the published literature. We have also linked the oxidative stress response to the phenomenon of apoptosis via the PI3k/Akt pathway. CONCLUSIONS: It is our hope that some of the additional predictions here, such as those pertaining to the oscillatory behaviour of certain genes in the presence of oxidative stress, will be experimentally validated in the near future. Of course, it should be pointed out that the theoretical procedure presented here for pinpointing fault locations in a biological network with feedback will need to be further simplified before it can be even considered for practical biological validation.

Cancer therapy design based on pathway logic.

MOTIVATION: Cancer encompasses various diseases associated with loss of cell cycle control, leading to uncontrolled cell proliferation and/or reduced apoptosis. Cancer is usually caused by malfunction(s) in the cellular signaling pathways. Malfunctions occur in different ways and at different locations in a pathway. Consequently, therapy design should first identify the location and type of malfunction to arrive at a suitable drug combination. RESULTS: We consider the growth factor (GF) signaling pathways, widely studied in the context of cancer. Interactions between different pathway components are modeled using Boolean logic gates. All possible single malfunctions in the resulting circuit are enumerated and responses of the different malfunctioning circuits to a 'test' input are used to group the malfunctions into classes. Effects of different drugs, targeting different parts of the Boolean circuit, are taken into account in deciding drug efficacy, thereby mapping each malfunction to an appropriate set of drugs.

Adaptive intervention in probabilistic boolean networks.

MOTIVATION: A basic problem of translational systems biology is to utilize gene regulatory networks as a vehicle to design therapeutic intervention strategies to beneficially alter network and, therefore, cellular dynamics. One strain of research has this problem from the perspective of control theory via the design of optimal Markov chain decision processes, mainly in the framework of probabilistic Boolean networks (PBNs). Full optimization assumes that the network is accurately modeled and, to the extent that model inference is inaccurate, which can be expected for gene regulatory networks owing to the combination of model complexity and a paucity of time-course data, the designed intervention strategy may perform poorly. We desire intervention strategies that do not assume accurate full-model inference. RESULTS: This article demonstrates the feasibility of applying on-line adaptive control to improve intervention performance in genetic regulatory networks modeled by PBNs. It shows via simulations that when the network is modeled by a member of a known family of PBNs, an adaptive design can yield improved performance in terms of the average cost. Two algorithms are presented, one better suited for instantaneously random PBNs and the other better suited for context-sensitive PBNs with low switching probability between the constituent BNs.

Multi-bit Boolean model for chemotactic drift of Escherichia coli.

Dynamic biological systems can be modelled to an equivalent modular structure using Boolean networks (BNs) due to their simple construction and relative ease of integration. The chemotaxis network of the bacterium Escherichia coli (E. coli) is one of the most investigated biological systems. In this study, the authors developed a multi-bit Boolean approach to model the drifting behaviour of the E. coli chemotaxis system. Their approach, which is slightly different than the conventional BNs, is designed to provide finer resolution to mimic high-level functional behaviour. Using this approach, they simulated the transient and steady-state responses of the chemoreceptor sensory module. Furthermore, they estimated the drift velocity under conditions of the exponential nutrient gradient. Their predictions on chemotactic drifting are in good agreement with the experimental measurements under similar input conditions. Taken together, by simulating chemotactic drifting, they propose that multi-bit Boolean methodology can be used for modelling complex biological networks. Application of the method towards designing bio-inspired systems such as nano-bots is discussed.

Fault detection and therapeutic intervention in gene regulatory networks using SAT solvers.

Random somatic mutations disrupt homeostasis of the cell resulting in various undesirable phenotypes including proliferation. One of the most important questions in systems medicine research is the therapeutic intervention design, which requires the knowledge of these mutations. A single or multiple mutations can occur in the diseases like cancer. These mutations have been successfully modeled as stuck-at faults in the Boolean network model of the underlying regulatory system. Identification of these fault types for multiple stuck-at faults is a non-trivial problem and requires some system theoretic introspection. This manuscript addresses the dual problem of the fault identification and the therapeutic intervention. Both the problems are mapped to the Boolean satisfiability (SAT) problem. The underlying problems are solved using a fast SAT solver. The synthetic and biological examples elucidate the effectiveness of the mapping.

Supercritical and subcritical Hopf-bifurcations in a two-delayed prey-predator system with density-dependent mortality of predator and strong Allee effect in prey.

One of the possible ways to visualize the effect of intra- and inter-species synergistic and antagonistic interactions in a natural ecosystem is the detailed analysis of the underlying prey-predator model, and the subsequent analytical findings may provide a definite justification towards the species coexistence, which often maintains biodiversity in nature. Here, our central motivation is to understand the combined effect of the Allee threshold and intra-species competition on the evolution of interacting species, which often experience delays in evolution due to its complex ecological and physiological processes. Therefore, in the present paper, we extensively analyze the stability of a two-delayed prey-predator system in the presence of strong Allee effects in prey and intra-species competition in predator. In addition, we capture the reality of time difference between the lifespan of the prey and predator through proper nondimensionalization. The two delays in the proposed retarded system correspond to the intra-specific competition-induced feedback time lag to the prey and predator gestation period. In the absence of intra-predator competition, the present dynamics unveils supercritical Hopf-bifurcation around the interior point of coexistence which is in-line with the existing literature. It is noteworthy to mention that the proposed Allee system exhibits subcritical Hopf-bifurcation in the presence of intra-species competition in predator. We confirm the occurrence of both supercritical and subcritical Hopf-bifurcations via calculating the direction and stability of Hopf-bifurcating periodic solutions using the normal form method and the center manifold theory. Moreover, the suggested delayed schema presents supercritical Hopf-bifurcation at the boundary steady-state, where the population density of prey exists at its maximum carrying capacity. We recognize the bistability between extinction and coexistence, and the proposed model also exhibits the 'chaotic concurrence between prey and predator,' which happens through the period-doubling bifurcation. The existence of chaos is validated using the estimated power spectrum and the spectrum of Lyapunov exponents. The primary finding of this paper is that Allee threshold induces the capability to the density-dependent death rate of predator towards changing the stability of 'oscillatory coexistence between prey and predator.'

Predicting Escherichia coli's chemotactic drift under exponential gradient.

Bacterial species are known to show chemotaxis, i.e., the directed motions in the presence of certain chemicals, whereas the motion is random in the absence of those chemicals. The bacteria modulate their run time to induce chemotactic drift towards the attractant chemicals and away from the repellent chemicals. However, the existing theoretical knowledge does not exhibit a proper match with experimental validation, and hence there is a need for developing alternate models and validating experimentally. In this paper a more robust theoretical model is proposed to investigate chemotactic drift of peritrichous Escherichia coli under an exponential nutrient gradient. An exponential gradient is used to understand the steady state behavior of drift because of the logarithmic functionality of the chemosensory receptors. Our theoretical estimations are validated through the experimentation and simulation results. Thus, the developed model successfully delineates the run time, run trajectory, and drift velocity as measured from the experiments.

Estimation of delays in generalized asynchronous Boolean networks.

A new generalized asynchronous Boolean network (GABN) model has been proposed in this paper. This continuous-time discrete-state model captures the biological reality of cellular dynamics without compromising the computational efficiency of the Boolean framework. The GABN synthesis procedure is based on the prior knowledge of the logical structure of the regulatory network, and the experimental transcriptional parameters. The novelty of the proposed methodology lies in considering different delays associated with the activation and deactivation of a particular protein (especially the transcription factors). A few illustrative examples of some well-studied network motifs have been provided to explore the scope of using the GABN model for larger networks. The GABN model of the p53-signaling pathway in response to γ-irradiation has also been simulated in the current paper to provide an indirect validation of the proposed schema.

Learning a Probabilistic Boolean Network model from biological pathways and time-series expression data.

The problem of inferring a stochastic model for gene regulatory networks is addressed here. The prior biological data includes biological pathways and time-series expression data. We propose a novel algorithm to use both of these data to construct a Probabilistic Boolean Network (PBN) which models the observed dynamics of genes with a high degree of precision. Our algorithm constructs a pathway tree and uses the time-series expression data to select an optimal level of tree, whose nodes are used to infer the PBN.

A Boolean approach to bacterial chemotaxis.

Bacterium such as Escherichia coli (E. coli) show biased Brownian motion in different chemical concentration gradients. This chemical sensitive motility or chemotaxis has gained considerable interest among scientists for some remarkable features such as chemo-sensory dynamic range, adaptation, diffusion and drift. A Boolean model of the whole chemotaxis process has been developed in this manuscript. The response of the circuit is in accordance with the experimental results available in the literature, providing indirect validation of the model. This simple Boolean network (BN) can be easily integrated into the paradigm of modular whole cell modelling. Another crucial application is in designing bio-inspired micro-robots to detect certain spatio-temporal chemical signatures.

Inference of asynchronous Boolean network from biological pathways.

Gene regulation is a complex process with multiple levels of interactions. In order to describe this complex dynamical system with tractable parameterization, the choice of the dynamical system model is of paramount importance. The right abstraction of the modeling scheme can reduce the complexity in the inference and intervention design, both computationally and experimentally. This article proposes an asynchronous Boolean network framework to capture the transcriptional regulation as well as the protein-protein interactions in a genetic regulatory system. The inference of asynchronous Boolean network from biological pathways information and experimental evidence are explained using an algorithm. The suitability of this paradigm for the variability of several reaction rates is also discussed. This methodology and model selection open up new research challenges in understanding gene-protein interactive system in a coherent way and can be beneficial for designing effective therapeutic intervention strategy.

Dynamics of cancer progression and suppression: A novel evolutionary game theory based approach.

In this paper, a novel mathematical approach is proposed for the dynamics of progression and suppression of cancer. We define mutant cell density, ρ(µ) (µ × ρ), as a primary factor in cancer dynamics, and use logistic growth model and replicator equation for defining the dynamics of total cell density (ρ) and mutant fraction (µ), respectively. Furthermore, in the proposed model, we introduce an analytical expression for a control parameter D (drug), to suppress the proliferation of mutants with extra fitness level σ. Lastly, we present a comparison of the proposed model with some existing models of tumour growth.

From biological pathways to regulatory networks.

This paper presents a general theoretical framework for generating Boolean networks whose state transitions realize a set of given biological pathways or minor variations thereof. This ill-posed inverse problem, which is of crucial importance across practically all areas of biology, is solved by using Karnaugh maps which are classical tools for digital system design. It is shown that the incorporation of prior knowledge, presented in the form of biological pathways, can bring about a dramatic reduction in the cardinality of the network search space. Constraining the connectivity of the network, the number and relative importance of the attractors, and concordance with observed time-course data are additional factors that can be used to further reduce the cardinality of the search space. The networks produced by the approaches developed here should facilitate the understanding of multivariate biological phenomena and the subsequent design of intervention approaches that are more likely to be successful in practice. As an example, the results of this paper are applied to the widely studied p53 pathway and it is shown that the resulting network exhibits dynamic behavior consistent with experimental observations from the published literature.