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Scaling theory for information networks.

ABSTRACT: Networks distribute energy, materials and information to the components of a variety of natural and human-engineered systems, including organisms, brains, the Internet and microprocessors. Distribution networks enable the integrated and coordinated functioning of these systems, and they also constrain their design. The similar hierarchical branching networks observed in organisms and microprocessors are striking, given that the structure of organisms has evolved via natural selection, while microprocessors are designed by engineers. Metabolic scaling theory (MST) shows that the rate at which networks deliver energy to an organism is proportional to its mass raised to the 3/4 power. We show that computational systems are also characterized by nonlinear network scaling and use MST principles to characterize how information networks scale, focusing on how MST predicts properties of clock distribution networks in microprocessors. The MST equations are modified to account for variation in the size and density of transistors and terminal wires in microprocessors. Based on the scaling of the clock distribution network, we predict a set of trade-offs and performance properties that scale with chip size and the number of transistors. However, there are systematic deviations between power requirements on microprocessors and predictions derived directly from MST. These deviations are addressed by augmenting the model to account for decentralized flow in some microprocessor networks (e.g. in logic networks). More generally, we hypothesize a set of constraints between the size, power and performance of networked information systems including transistors on chips, hosts on the Internet and neurons in the brain.

SUBMITTER: Moses ME

PROVIDER: S-EPMC2607348 | biostudies-literature | 2008 Dec

REPOSITORIES: biostudies-literature

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Scaling theory for information networks.

Moses Melanie E ME Forrest Stephanie S Davis Alan L AL Lodder Mike A MA Brown James H JH

Journal of the Royal Society, Interface 20081201 29

Networks distribute energy, materials and information to the components of a variety of natural and human-engineered systems, including organisms, brains, the Internet and microprocessors. Distribution networks enable the integrated and coordinated functioning of these systems, and they also constrain their design. The similar hierarchical branching networks observed in organisms and microprocessors are striking, given that the structure of organisms has evolved via natural selection, while micr ...[more]

PMID: 18468978

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Project description:BackgroundStochastic modeling and simulation provide powerful predictive methods for the intrinsic understanding of fundamental mechanisms in complex biochemical networks. Typically, such mathematical models involve networks of coupled jump stochastic processes with a large number of parameters that need to be suitably calibrated against experimental data. In this direction, the parameter sensitivity analysis of reaction networks is an essential mathematical and computational tool, yielding information regarding the robustness and the identifiability of model parameters. However, existing sensitivity analysis approaches such as variants of the finite difference method can have an overwhelming computational cost in models with a high-dimensional parameter space.ResultsWe develop a sensitivity analysis methodology suitable for complex stochastic reaction networks with a large number of parameters. The proposed approach is based on Information Theory methods and relies on the quantification of information loss due to parameter perturbations between time-series distributions. For this reason, we need to work on path-space, i.e., the set consisting of all stochastic trajectories, hence the proposed approach is referred to as "pathwise". The pathwise sensitivity analysis method is realized by employing the rigorously-derived Relative Entropy Rate, which is directly computable from the propensity functions. A key aspect of the method is that an associated pathwise Fisher Information Matrix (FIM) is defined, which in turn constitutes a gradient-free approach to quantifying parameter sensitivities. The structure of the FIM turns out to be block-diagonal, revealing hidden parameter dependencies and sensitivities in reaction networks.ConclusionsAs a gradient-free method, the proposed sensitivity analysis provides a significant advantage when dealing with complex stochastic systems with a large number of parameters. In addition, the knowledge of the structure of the FIM can allow to efficiently address questions on parameter identifiability, estimation and robustness. The proposed method is tested and validated on three biochemical systems, namely: (a) a protein production/degradation model where explicit solutions are available, permitting a careful assessment of the method, (b) the p53 reaction network where quasi-steady stochastic oscillations of the concentrations are observed, and for which continuum approximations (e.g. mean field, stochastic Langevin, etc.) break down due to persistent oscillations between high and low populations, and (c) an Epidermal Growth Factor Receptor model which is an example of a high-dimensional stochastic reaction network with more than 200 reactions and a corresponding number of parameters.

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Scaling theory for information networks.

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Scaling theory for information networks.

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