Symmetry invariance for adapting biological systems
| Autor: | Eduardo D. Sontag, Uri Alon, Oren Shoval |
|---|---|
| Rok vydání: | 2010 |
| Předmět: |
0209 industrial biotechnology
Property (philosophy) Dynamical systems theory media_common.quotation_subject Gene regulatory network FOS: Physical sciences Context (language use) 02 engineering and technology Systems and Control (eess.SY) Quantitative Biology - Quantitative Methods Adaptability 03 medical and health sciences 020901 industrial engineering & automation FOS: Electrical engineering electronic engineering information engineering FOS: Mathematics Physics - Biological Physics Mathematics - Optimization and Control Sensory cue Quantitative Methods (q-bio.QM) 030304 developmental biology media_common 0303 health sciences Complement (complexity) Optimization and Control (math.OC) Biological Physics (physics.bio-ph) Modeling and Simulation FOS: Biological sciences Computer Science - Systems and Control Biological system Constant (mathematics) Analysis |
| DOI: | 10.48550/arxiv.1012.2782 |
| Popis: | For a general class of dynamical systems, this paper presents a necessary and sufficient charac- terization of invariance of transient responses to symmetries in inputs. A particular example of this property, scale-invariance or "fold-change detection" (FCD), has been shown to be exhibited in biological sensory systems ranging from bacterial chemotaxis pathways to signal transduction mechanisms in eukaryotes. The characterization is in terms of a notion of equivariance and amounts to the solvability of an associated partial differential equation. For several simple system motifs that are recurrent in biology, the solvability criterion may be checked explicitly. 1. Introduction. We study in this paper certain properties of the responses of dynamical systems to external inputs. Our results are purely mathematical and thus of wide applicability, but our motivation arises from molecular systems biology. Indeed, the behavior, adaptability, and survival of organisms depend critically upon their capability to formulate appropriate responses to chemical and physical environmental cues. In particular, signal transduction and gene regulatory networks in individual cells mediate the processing of measured chemical concentrations and physical conditions, such as ligand concentrations or stresses, eventually leading to regulatory changes in metabolism and gene expression. Often, the ultimate goal of these changes is to maintain a narrow range of concentration levels of vital quantities (homeostasis, adaptation) while at the same time appropriately reacting to changes in the environment (signal detection). Much theoretical, modeling, and analysis effort has been devoted to the understanding of these questions, traditionally in the context of steady-state responses to constant or step-changing stimuli. In this work, we are concerned with questions that complement the analysis of simple temporal inputs and steady-state responses, focusing on certain properties of transient be- haviors, both for simple stimuli like step changes and for more complex time-varying input profiles. The study of transient responses is of central concern in cell biology, since behavior at the time-scale of signaling may have important consequences for cell survival. Moreover, typical signals encountered by cells in their natural environments may well exhibit interest- ing temporal information, and thus characterizing responses to fluctuating temporal patterns |
| Databáze: | OpenAIRE |
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