56 research outputs found
Dimension Reduction of Large AND-NOT Network Models
Boolean networks have been used successfully in modeling biological networks
and provide a good framework for theoretical analysis. However, the analysis of
large networks is not trivial. In order to simplify the analysis of such
networks, several model reduction algorithms have been proposed; however, it is
not clear if such algorithms scale well with respect to the number of nodes.
The goal of this paper is to propose and implement an algorithm for the
reduction of AND-NOT network models for the purpose of steady state
computation. Our method of network reduction is the use of "steady state
approximations" that do not change the number of steady states. Our algorithm
is designed to work at the wiring diagram level without the need to evaluate or
simplify Boolean functions. Also, our implementation of the algorithm takes
advantage of the sparsity typical of discrete models of biological systems. The
main features of our algorithm are that it works at the wiring diagram level,
it runs in polynomial time, and it preserves the number of steady states. We
used our results to study AND-NOT network models of gene networks and showed
that our algorithm greatly simplifies steady state analysis. Furthermore, our
algorithm can handle sparse AND-NOT networks with up to 1000000 nodes
Stochastic models of evidence accumulation in changing environments
Organisms and ecological groups accumulate evidence to make decisions.
Classic experiments and theoretical studies have explored this process when the
correct choice is fixed during each trial. However, we live in a constantly
changing world. What effect does such impermanence have on classical results
about decision making? To address this question we use sequential analysis to
derive a tractable model of evidence accumulation when the correct option
changes in time. Our analysis shows that ideal observers discount prior
evidence at a rate determined by the volatility of the environment, and the
dynamics of evidence accumulation is governed by the information gained over an
average environmental epoch. A plausible neural implementation of an optimal
observer in a changing environment shows that, in contrast to previous models,
neural populations representing alternate choices are coupled through
excitation. Our work builds a bridge between statistical decision making in
volatile environments and stochastic nonlinear dynamics.Comment: 26 pages, 7 figure
Identification of control targets in Boolean molecular network models via computational algebra
Motivation: Many problems in biomedicine and other areas of the life sciences
can be characterized as control problems, with the goal of finding strategies
to change a disease or otherwise undesirable state of a biological system into
another, more desirable, state through an intervention, such as a drug or other
therapeutic treatment. The identification of such strategies is typically based
on a mathematical model of the process to be altered through targeted control
inputs. This paper focuses on processes at the molecular level that determine
the state of an individual cell, involving signaling or gene regulation. The
mathematical model type considered is that of Boolean networks. The potential
control targets can be represented by a set of nodes and edges that can be
manipulated to produce a desired effect on the system. Experimentally, node
manipulation requires technology to completely repress or fully activate a
particular gene product while edge manipulations only require a drug that
inactivates the interaction between two gene products. Results: This paper
presents a method for the identification of potential intervention targets in
Boolean molecular network models using algebraic techniques. The approach
exploits an algebraic representation of Boolean networks to encode the control
candidates in the network wiring diagram as the solutions of a system of
polynomials equations, and then uses computational algebra techniques to find
such controllers. The control methods in this paper are validated through the
identification of combinatorial interventions in the signaling pathways of
previously reported control targets in two well studied systems, a p53-mdm2
network and a blood T cell lymphocyte granular leukemia survival signaling
network.Comment: 12 pages, 4 figures, 2 table
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