A Canonical Model of Multistability and Scale-Invariance in Biological Systems

Multistability and scale-invariant fluctuations occur in a wide variety of biological organisms from bacteria to humans as well as financial, chemical and complex physical systems. Multistability refers to noise driven switches between multiple weakly stable states. Scale-invariant fluctuations aris...

Full description

Bibliographic Details
Main Authors:	Freyer, Frank, Roberts, James A., Ritter, Petra, Breakspear, Michael
Format:	Online
Language:	English
Published:	Public Library of Science 2012
Online Access:	https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3415415/

id	pubmed-3415415
recordtype	oai_dc
spelling	pubmed-34154152012-08-21 A Canonical Model of Multistability and Scale-Invariance in Biological Systems Freyer, Frank Roberts, James A. Ritter, Petra Breakspear, Michael Research Article Multistability and scale-invariant fluctuations occur in a wide variety of biological organisms from bacteria to humans as well as financial, chemical and complex physical systems. Multistability refers to noise driven switches between multiple weakly stable states. Scale-invariant fluctuations arise when there is an approximately constant ratio between the mean and standard deviation of a system's fluctuations. Both are an important property of human perception, movement, decision making and computation and they occur together in the human alpha rhythm, imparting it with complex dynamical behavior. Here, we elucidate their fundamental dynamical mechanisms in a canonical model of nonlinear bifurcations under stochastic fluctuations. We find that the co-occurrence of multistability and scale-invariant fluctuations mandates two important dynamical properties: Multistability arises in the presence of a subcritical Hopf bifurcation, which generates co-existing attractors, whilst the introduction of multiplicative (state-dependent) noise ensures that as the system jumps between these attractors, fluctuations remain in constant proportion to their mean and their temporal statistics become long-tailed. The simple algebraic construction of this model affords a systematic analysis of the contribution of stochastic and nonlinear processes to cortical rhythms, complementing a recently proposed biophysical model. Similar dynamics also occur in a kinetic model of gene regulation, suggesting universality across a broad class of biological phenomena. Public Library of Science 2012-08-09 /pmc/articles/PMC3415415/ /pubmed/22912567 http://dx.doi.org/10.1371/journal.pcbi.1002634 Text en © 2012 Freyer et al http://creativecommons.org/licenses/by/4.0/ This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited.
repository_type	Open Access Journal
institution_category	Foreign Institution
institution	US National Center for Biotechnology Information
building	NCBI PubMed
collection	Online Access
language	English
format	Online
author	Freyer, Frank Roberts, James A. Ritter, Petra Breakspear, Michael
spellingShingle	Freyer, Frank Roberts, James A. Ritter, Petra Breakspear, Michael A Canonical Model of Multistability and Scale-Invariance in Biological Systems
author_facet	Freyer, Frank Roberts, James A. Ritter, Petra Breakspear, Michael
author_sort	Freyer, Frank
title	A Canonical Model of Multistability and Scale-Invariance in Biological Systems
title_short	A Canonical Model of Multistability and Scale-Invariance in Biological Systems
title_full	A Canonical Model of Multistability and Scale-Invariance in Biological Systems
title_fullStr	A Canonical Model of Multistability and Scale-Invariance in Biological Systems
title_full_unstemmed	A Canonical Model of Multistability and Scale-Invariance in Biological Systems
title_sort	canonical model of multistability and scale-invariance in biological systems
description	Multistability and scale-invariant fluctuations occur in a wide variety of biological organisms from bacteria to humans as well as financial, chemical and complex physical systems. Multistability refers to noise driven switches between multiple weakly stable states. Scale-invariant fluctuations arise when there is an approximately constant ratio between the mean and standard deviation of a system's fluctuations. Both are an important property of human perception, movement, decision making and computation and they occur together in the human alpha rhythm, imparting it with complex dynamical behavior. Here, we elucidate their fundamental dynamical mechanisms in a canonical model of nonlinear bifurcations under stochastic fluctuations. We find that the co-occurrence of multistability and scale-invariant fluctuations mandates two important dynamical properties: Multistability arises in the presence of a subcritical Hopf bifurcation, which generates co-existing attractors, whilst the introduction of multiplicative (state-dependent) noise ensures that as the system jumps between these attractors, fluctuations remain in constant proportion to their mean and their temporal statistics become long-tailed. The simple algebraic construction of this model affords a systematic analysis of the contribution of stochastic and nonlinear processes to cortical rhythms, complementing a recently proposed biophysical model. Similar dynamics also occur in a kinetic model of gene regulation, suggesting universality across a broad class of biological phenomena.
publisher	Public Library of Science
publishDate	2012
url	https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3415415/
_version_	1611548825791496192

A Canonical Model of Multistability and Scale-Invariance in Biological Systems

Similar Items