Rahul Simha

Publications (4)23.08 Total impact

• Article: Network class superposition analyses.

  Carl A B Pearson, Chen Zeng, Rahul Simha
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  ABSTRACT: Networks are often used to understand a whole system by modeling the interactions among its pieces. Examples include biomolecules in a cell interacting to provide some primary function, or species in an environment forming a stable community. However, these interactions are often unknown; instead, the pieces' dynamic states are known, and network structure must be inferred. Because observed function may be explained by many different networks (e.g., [Formula: see text] for the yeast cell cycle process [1]), considering dynamics beyond this primary function means picking a single network or suitable sample: measuring over all networks exhibiting the primary function is computationally infeasible. We circumvent that obstacle by calculating the network class ensemble. We represent the ensemble by a stochastic matrix [Formula: see text], which is a transition-by-transition superposition of the system dynamics for each member of the class. We present concrete results for [Formula: see text] derived from Boolean time series dynamics on networks obeying the Strong Inhibition rule, by applying [Formula: see text] to several traditional questions about network dynamics. We show that the distribution of the number of point attractors can be accurately estimated with [Formula: see text]. We show how to generate Derrida plots based on [Formula: see text]. We show that [Formula: see text]-based Shannon entropy outperforms other methods at selecting experiments to further narrow the network structure. We also outline an experimental test of predictions based on [Formula: see text]. We motivate all of these results in terms of a popular molecular biology Boolean network model for the yeast cell cycle, but the methods and analyses we introduce are general. We conclude with open questions for [Formula: see text], for example, application to other models, computational considerations when scaling up to larger systems, and other potential analyses.
  PLoS ONE 01/2013; 8(4):e59046. · 4.09 Impact Factor
• Source

  Available from: Chenghang Du

  Article: Process-driven inference of biological network structure: feasibility, minimality, and multiplicity.

  Guanyu Wang, Yongwu Rong, Hao Chen, Carl Pearson, Chenghang Du, Rahul Simha, Chen Zeng
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  ABSTRACT: A common problem in molecular biology is to use experimental data, such as microarray data, to infer knowledge about the structure of interactions between important molecules in subsystems of the cell. By approximating the state of each molecule as "on" or "off", it becomes possible to simplify the problem, and exploit the tools of boolean analysis for such inference. Amongst boolean techniques, the process-driven approach has shown promise in being able to identify putative network structures, as well as stability and modularity properties. This paper examines the process-driven approach more formally, and makes four contributions about the computational complexity of the inference problem, under the "dominant inhibition" assumption of molecular interactions. The first is a proof that the feasibility problem (does there exist a network that explains the data?) can be solved in polynomial-time. Second, the minimality problem (what is the smallest network that explains the data?) is shown to be NP-hard, and therefore unlikely to result in a polynomial-time algorithm. Third, a simple polynomial-time heuristic is shown to produce near-minimal solutions, as demonstrated by simulation. Fourth, the theoretical framework explains how multiplicity (the number of network solutions to realize a given biological process), which can take exponential-time to compute, can instead be accurately estimated by a fast, polynomial-time heuristic.
  PLoS ONE 01/2012; 7(7):e40330. · 4.09 Impact Factor
• Source

  Available from: Chenghang Du

  Article: Process-based network decomposition reveals backbone motif structure.

  Guanyu Wang, Chenghang Du, Hao Chen, Rahul Simha, Yongwu Rong, Yi Xiao, Chen Zeng
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  ABSTRACT: A central challenge in systems biology today is to understand the network of interactions among biomolecules and, especially, the organizing principles underlying such networks. Recent analysis of known networks has identified small motifs that occur ubiquitously, suggesting that larger networks might be constructed in the manner of electronic circuits by assembling groups of these smaller modules. Using a unique process-based approach to analyzing such networks, we show for two cell-cycle networks that each of these networks contains a giant backbone motif spanning all the network nodes that provides the main functional response. The backbone is in fact the smallest network capable of providing the desired functionality. Furthermore, the remaining edges in the network form smaller motifs whose role is to confer stability properties rather than provide function. The process-based approach used in the above analysis has additional benefits: It is scalable, analytic (resulting in a single analyzable expression that describes the behavior), and computationally efficient (all possible minimal networks for a biological process can be identified and enumerated).
  Proceedings of the National Academy of Sciences 06/2010; 107(23):10478-83. · 9.68 Impact Factor
• Source

  Available from: Weiqun Peng

  Article: Pathway switching explains the sharp response characteristic of hypoxia response network.

  Yihai Yu, Guanyu Wang, Rahul Simha, Weiqun Peng, Frank Turano, Chen Zeng
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  ABSTRACT: Hypoxia induces the expression of genes that alter metabolism through the hypoxia-inducible factor (HIF). A theoretical model based on differential equations of the hypoxia response network has been previously proposed in which a sharp response to changes in oxygen concentration was observed but not quantitatively explained. That model consisted of reactions involving 23 molecular species among which the concentrations of HIF and oxygen were linked through a complex set of reactions. In this paper, we analyze this previous model using a combination of mathematical tools to draw out the key components of the network and explain quantitatively how they contribute to the sharp oxygen response. We find that the switch-like behavior is due to pathway-switching wherein HIF degrades rapidly under normoxia in one pathway, while the other pathway accumulates HIF to trigger downstream genes under hypoxia. The analytic technique is potentially useful in studying larger biomedical networks.
  PLoS Computational Biology 09/2007; 3(8):e171. · 5.22 Impact Factor