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Balance between noise and information flow maximizes set complexity of network dynamics.

ABSTRACT: Boolean networks have been used as a discrete model for several biological systems, including metabolic and genetic regulatory networks. Due to their simplicity they offer a firm foundation for generic studies of physical systems. In this work we show, using a measure of context-dependent information, set complexity, that prior to reaching an attractor, random Boolean networks pass through a transient state characterized by high complexity. We justify this finding with a use of another measure of complexity, namely, the statistical complexity. We show that the networks can be tuned to the regime of maximal complexity by adding a suitable amount of noise to the deterministic Boolean dynamics. In fact, we show that for networks with Poisson degree distributions, all networks ranging from subcritical to slightly supercritical can be tuned with noise to reach maximal set complexity in their dynamics. For networks with a fixed number of inputs this is true for near-to-critical networks. This increase in complexity is obtained at the expense of disruption in information flow. For a large ensemble of networks showing maximal complexity, there exists a balance between noise and contracting dynamics in the state space. In networks that are close to critical the intrinsic noise required for the tuning is smaller and thus also has the smallest effect in terms of the information processing in the system. Our results suggest that the maximization of complexity near to the state transition might be a more general phenomenon in physical systems, and that noise present in a system may in fact be useful in retaining the system in a state with high information content.

SUBMITTER: Maki-Marttunen T

PROVIDER: S-EPMC3596377 | biostudies-literature | 2013

REPOSITORIES: biostudies-literature

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Balance between noise and information flow maximizes set complexity of network dynamics.

Mäki-Marttunen Tuomo T Kesseli Juha J Nykter Matti M

PloS one 20130313 3

Boolean networks have been used as a discrete model for several biological systems, including metabolic and genetic regulatory networks. Due to their simplicity they offer a firm foundation for generic studies of physical systems. In this work we show, using a measure of context-dependent information, set complexity, that prior to reaching an attractor, random Boolean networks pass through a transient state characterized by high complexity. We justify this finding with a use of another measure o ...[more]

PMID: 23516395

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Project description:The tri-synaptic pathway in the mammalian hippocampus enables cognitive learning and memory. Despite decades of reports on anatomy and physiology, the functional architecture of the hippocampal network remains poorly understood in terms of the dynamics of axonal information transfer between subregions. Information inputs largely flow from the entorhinal cortex (EC) to the dentate gyrus (DG), and then are processed further in the CA3 and CA1 before returning to the EC. Here, we reconstructed elements of the rat hippocampus in a novel device over an electrode array that allowed for monitoring the directionality of individual axons between the subregions. The direction of spike propagation was determined by the transmission delay of the axons recorded between two electrodes in microfluidic tunnels. The majority of axons from the EC to the DG operated in the feed-forward direction, with other regions developing unexpectedly large proportions of feedback axons to balance excitation. Spike timing in axons between each region followed single exponential log-log distributions over two orders of magnitude from 0.01 to 1 s, indicating that conventional descriptors of mean firing rates are misleading assumptions. Most of the spiking occurred in bursts that required two exponentials to fit the distribution of inter-burst intervals. This suggested the presence of up-states and down-states in every region, with the least up-states in the DG to CA3 feed-forward axons and the CA3 subregion. The peaks of the log-normal distributions of intra-burst spike rates were similar in axons between regions with modes around 95 Hz distributed over an order of magnitude. Burst durations were also log-normally distributed around a peak of 88 ms over two orders of magnitude. Despite the diversity of these spike distributions, spike rates from individual axons were often linearly correlated to subregions. These linear relationships enabled the generation of structural connectivity graphs, not possible previously without the directional flow of axonal information. The rich axonal spike dynamics between subregions of the hippocampus reveal both constraints and broad emergent dynamics of hippocampal architecture. Knowledge of this network architecture may enable more efficient computational artificial intelligence (AI) networks, neuromorphic hardware, and stimulation and decoding from cognitive implants.

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Balance between noise and information flow maximizes set complexity of network dynamics.

Publications

Balance between noise and information flow maximizes set complexity of network dynamics.

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