Dataset Information

Balancing robustness against the dangers of multiple attractors in a Hopfield-type model of biological attractors.

ABSTRACT:

Background

Many chronic human diseases are of unclear origin, and persist long beyond any known insult or instigating factor. These diseases may represent a structurally normal biologic network that has become trapped within the basin of an abnormal attractor.

Methodology/principal findings

We used the Hopfield net as the archetypical example of a dynamic biological network. By progressively removing the links of fully connected Hopfield nets, we found that a designated attractor of the nets could still be supported until only slightly more than 1 link per node remained. As the number of links approached this minimum value, the rate of convergence to this attractor from an arbitrary starting state increased dramatically. Furthermore, with more than about twice the minimum of links, the net became increasingly able to support a second attractor.

Conclusions/significance

We speculate that homeostatic biological networks may have evolved to assume a degree of connectivity that balances robustness and agility against the dangers of becoming trapped in an abnormal attractor.

SUBMITTER: Anafi RC

PROVIDER: S-EPMC3008716 | biostudies-literature | 2010 Dec

REPOSITORIES: biostudies-literature

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Publications

Balancing robustness against the dangers of multiple attractors in a Hopfield-type model of biological attractors.

Anafi Ron C RC Bates Jason H T JH

PloS one 20101222 12

<h4>Background</h4>Many chronic human diseases are of unclear origin, and persist long beyond any known insult or instigating factor. These diseases may represent a structurally normal biologic network that has become trapped within the basin of an abnormal attractor.<h4>Methodology/principal findings</h4>We used the Hopfield net as the archetypical example of a dynamic biological network. By progressively removing the links of fully connected Hopfield nets, we found that a designated attractor ...[more]

PMID: 21203505

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Project description:The analysis of gene network robustness to noise and mutation is important for fundamental and practical reasons. Robustness refers to the stability of the equilibrium expression state of a gene network to variations of the initial expression state and network topology. Numerical simulation of these variations is commonly used for the assessment of robustness. Since there exists a great number of possible gene network topologies and initial states, even millions of simulations may be still too small to give reliable results. When the initial and equilibrium expression states are restricted to being saturated (i.e., their elements can only take values 1 or -1 corresponding to maximum activation and maximum repression of genes), an analytical gene network robustness assessment is possible. We present this analytical treatment based on determination of the saturated fixed point attractors for sigmoidal function models. The analysis can determine (a) for a given network, which and how many saturated equilibrium states exist and which and how many saturated initial states converge to each of these saturated equilibrium states and (b) for a given saturated equilibrium state or a given pair of saturated equilibrium and initial states, which and how many gene networks, referred to as viable, share this saturated equilibrium state or the pair of saturated equilibrium and initial states. We also show that the viable networks sharing a given saturated equilibrium state must follow certain patterns. These capabilities of the analytical treatment make it possible to properly define and accurately determine robustness to noise and mutation for gene networks. Previous network research conclusions drawn from performing millions of simulations follow directly from the results of our analytical treatment. Furthermore, the analytical results provide criteria for the identification of model validity and suggest modified models of gene network dynamics. The yeast cell-cycle network is used as an illustration of the practical application of this analytical treatment.

Dataset Information

Balancing robustness against the dangers of multiple attractors in a Hopfield-type model of biological attractors.

Background

Methodology/principal findings

Conclusions/significance

Publications

Balancing robustness against the dangers of multiple attractors in a Hopfield-type model of biological attractors.

Similar Datasets

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