4,858 research outputs found
A Characterization of Scale Invariant Responses in Enzymatic Networks
An ubiquitous property of biological sensory systems is adaptation: a step
increase in stimulus triggers an initial change in a biochemical or
physiological response, followed by a more gradual relaxation toward a basal,
pre-stimulus level. Adaptation helps maintain essential variables within
acceptable bounds and allows organisms to readjust themselves to an optimum and
non-saturating sensitivity range when faced with a prolonged change in their
environment. Recently, it was shown theoretically and experimentally that many
adapting systems, both at the organism and single-cell level, enjoy a
remarkable additional feature: scale invariance, meaning that the initial,
transient behavior remains (approximately) the same even when the background
signal level is scaled. In this work, we set out to investigate under what
conditions a broadly used model of biochemical enzymatic networks will exhibit
scale-invariant behavior. An exhaustive computational study led us to discover
a new property of surprising simplicity and generality, uniform linearizations
with fast output (ULFO), whose validity we show is both necessary and
sufficient for scale invariance of enzymatic networks. Based on this study, we
go on to develop a mathematical explanation of how ULFO results in scale
invariance. Our work provides a surprisingly consistent, simple, and general
framework for understanding this phenomenon, and results in concrete
experimental predictions
Exploring the concept of interaction computing through the discrete algebraic analysis of the Belousov–Zhabotinsky reaction
Interaction computing (IC) aims to map the properties of integrable low-dimensional non-linear dynamical systems to the discrete domain of finite-state automata in an attempt to reproduce in software the self-organizing and dynamically stable properties of sub-cellular biochemical systems. As the work reported in this paper is still at the early stages of theory development it focuses on the analysis of a particularly simple chemical oscillator, the Belousov-Zhabotinsky (BZ) reaction. After retracing the rationale for IC developed over the past several years from the physical, biological, mathematical, and computer science points of view, the paper presents an elementary discussion of the Krohn-Rhodes decomposition of finite-state automata, including the holonomy decomposition of a simple automaton, and of its interpretation as an abstract positional number system. The method is then applied to the analysis of the algebraic properties of discrete finite-state automata derived from a simplified Petri net model of the BZ reaction. In the simplest possible and symmetrical case the corresponding automaton is, not surprisingly, found to contain exclusively cyclic groups. In a second, asymmetrical case, the decomposition is much more complex and includes five different simple non-abelian groups whose potential relevance arises from their ability to encode functionally complete algebras. The possible computational relevance of these findings is discussed and possible conclusions are drawn
Correlation of Automorphism Group Size and Topological Properties with Program-size Complexity Evaluations of Graphs and Complex Networks
We show that numerical approximations of Kolmogorov complexity (K) applied to
graph adjacency matrices capture some group-theoretic and topological
properties of graphs and empirical networks ranging from metabolic to social
networks. That K and the size of the group of automorphisms of a graph are
correlated opens up interesting connections to problems in computational
geometry, and thus connects several measures and concepts from complexity
science. We show that approximations of K characterise synthetic and natural
networks by their generating mechanisms, assigning lower algorithmic randomness
to complex network models (Watts-Strogatz and Barabasi-Albert networks) and
high Kolmogorov complexity to (random) Erdos-Renyi graphs. We derive these
results via two different Kolmogorov complexity approximation methods applied
to the adjacency matrices of the graphs and networks. The methods used are the
traditional lossless compression approach to Kolmogorov complexity, and a
normalised version of a Block Decomposition Method (BDM) measure, based on
algorithmic probability theory.Comment: 15 2-column pages, 20 figures. Forthcoming in Physica A: Statistical
Mechanics and its Application
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