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Logarithmic and Power Law Input-Output Relations in Sensory Systems with Fold-Change Detection

Two central biophysical laws describe sensory responses to input signals. One is a logarithmic relationship between input and output, and the other is a power law relationship. These laws are sometimes called the Weber-Fechner law and the Stevens power law, respectively. The two laws are found in a...

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Autores principales: Adler, Miri, Mayo, Avi, Alon, Uri
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Public Library of Science 2014
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4133048/
https://www.ncbi.nlm.nih.gov/pubmed/25121598
http://dx.doi.org/10.1371/journal.pcbi.1003781
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author Adler, Miri
Mayo, Avi
Alon, Uri
author_facet Adler, Miri
Mayo, Avi
Alon, Uri
author_sort Adler, Miri
collection PubMed
description Two central biophysical laws describe sensory responses to input signals. One is a logarithmic relationship between input and output, and the other is a power law relationship. These laws are sometimes called the Weber-Fechner law and the Stevens power law, respectively. The two laws are found in a wide variety of human sensory systems including hearing, vision, taste, and weight perception; they also occur in the responses of cells to stimuli. However the mechanistic origin of these laws is not fully understood. To address this, we consider a class of biological circuits exhibiting a property called fold-change detection (FCD). In these circuits the response dynamics depend only on the relative change in input signal and not its absolute level, a property which applies to many physiological and cellular sensory systems. We show analytically that by changing a single parameter in the FCD circuits, both logarithmic and power-law relationships emerge; these laws are modified versions of the Weber-Fechner and Stevens laws. The parameter that determines which law is found is the steepness (effective Hill coefficient) of the effect of the internal variable on the output. This finding applies to major circuit architectures found in biological systems, including the incoherent feed-forward loop and nonlinear integral feedback loops. Therefore, if one measures the response to different fold changes in input signal and observes a logarithmic or power law, the present theory can be used to rule out certain FCD mechanisms, and to predict their cooperativity parameter. We demonstrate this approach using data from eukaryotic chemotaxis signaling.
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spelling pubmed-41330482014-08-19 Logarithmic and Power Law Input-Output Relations in Sensory Systems with Fold-Change Detection Adler, Miri Mayo, Avi Alon, Uri PLoS Comput Biol Research Article Two central biophysical laws describe sensory responses to input signals. One is a logarithmic relationship between input and output, and the other is a power law relationship. These laws are sometimes called the Weber-Fechner law and the Stevens power law, respectively. The two laws are found in a wide variety of human sensory systems including hearing, vision, taste, and weight perception; they also occur in the responses of cells to stimuli. However the mechanistic origin of these laws is not fully understood. To address this, we consider a class of biological circuits exhibiting a property called fold-change detection (FCD). In these circuits the response dynamics depend only on the relative change in input signal and not its absolute level, a property which applies to many physiological and cellular sensory systems. We show analytically that by changing a single parameter in the FCD circuits, both logarithmic and power-law relationships emerge; these laws are modified versions of the Weber-Fechner and Stevens laws. The parameter that determines which law is found is the steepness (effective Hill coefficient) of the effect of the internal variable on the output. This finding applies to major circuit architectures found in biological systems, including the incoherent feed-forward loop and nonlinear integral feedback loops. Therefore, if one measures the response to different fold changes in input signal and observes a logarithmic or power law, the present theory can be used to rule out certain FCD mechanisms, and to predict their cooperativity parameter. We demonstrate this approach using data from eukaryotic chemotaxis signaling. Public Library of Science 2014-08-14 /pmc/articles/PMC4133048/ /pubmed/25121598 http://dx.doi.org/10.1371/journal.pcbi.1003781 Text en © 2014 Adler 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.
spellingShingle Research Article
Adler, Miri
Mayo, Avi
Alon, Uri
Logarithmic and Power Law Input-Output Relations in Sensory Systems with Fold-Change Detection
title Logarithmic and Power Law Input-Output Relations in Sensory Systems with Fold-Change Detection
title_full Logarithmic and Power Law Input-Output Relations in Sensory Systems with Fold-Change Detection
title_fullStr Logarithmic and Power Law Input-Output Relations in Sensory Systems with Fold-Change Detection
title_full_unstemmed Logarithmic and Power Law Input-Output Relations in Sensory Systems with Fold-Change Detection
title_short Logarithmic and Power Law Input-Output Relations in Sensory Systems with Fold-Change Detection
title_sort logarithmic and power law input-output relations in sensory systems with fold-change detection
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4133048/
https://www.ncbi.nlm.nih.gov/pubmed/25121598
http://dx.doi.org/10.1371/journal.pcbi.1003781
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