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Cited by 20Gene Regulatory Network Analysisstochastic dynamics and bifurcationAdvanced Thermodynamics and Statistical Mechanics

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Signaling pathways have an inherent need for noise to acquire information

Open access
Azpeitia, Eugenio, Balanzario, Eugenio P., Wagner, Andreas·2020·BMC Bioinformatics
DOI 10.1186/s12859-020-03778-xPMC PMC7568421

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Abstract

Background: All living systems acquire information about their environment. At the cellular level, they do so through signaling pathways. Such pathways rely on reversible binding interactions between molecules that detect and transmit the presence of an extracellular cue or signal to the cell’s interior. These interactions are inherently stochastic and thus noisy. On the one hand, noise can cause a signaling pathway to produce the same response for different stimuli, which reduces the amount of information a pathway acquires. On the other hand, in processes such as stochastic resonance, noise can improve the detection of weak stimuli and thus the acquisition of information. It is not clear whether the kinetic parameters that determine a pathway’s operation cause noise to reduce or increase the acquisition of information. Results: We analyze how the kinetic properties of the reversible binding interactions used by signaling pathways affect the relationship between noise, the response to a signal, and information acquisition. Our results show that, under a wide range of biologically sensible parameter values, a noisy dynamic of reversible binding interactions is necessary to produce distinct responses to different stimuli. As a consequence, noise is indispensable for the acquisition of information in signaling pathways. Conclusions: Our observations go beyond previous work by showing that noise plays a positive role in signaling pathways, demonstrating that noise is essential when such pathways acquire information.

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Fig. 1 Relationship of acquired information with both noise and output range. Example of two hypothetical stimuli that produce different but overlapping response distributions (green and blue distributions). The amount of information acquired at different levels of noise (y axis) and with different output ranges (x axis) is indicated by the color bar. The black dashed line in a is a schematic representation of noise (i.e., the standard deviation of the response distributions, green and blue). The square bracket above the response distributions in a indicates the output range (i.e., the maximal difference of the mean values of the response distributions). Increasing the output range b and reducing noise c decrease the overlap (uncertainty) between response distributions observed in a. d Acquired information is largest (maximal) when noise is minimized and the output range is maximized
Fig. 1 Relationship of acquired information with both noise and output range. Example of two hypothetical stimuli that produce different but overlapping response distributions (green and blue distributions). The amount of information acquired at different levels of noise (y axis) and with different output ranges (x axis) is indicated by the color bar. The black dashed line in a is a schematic representation of noise (i.e., the standard deviation of the response distributions, green and blue). The square bracket above the response distributions in a indicates the output range (i.e., the maximal difference of the mean values of the response distributions). Increasing the output range b and reducing noise c decrease the overlap (uncertainty) between response distributions observed in a. d Acquired information is largest (maximal) when noise is minimized and the output range is maximizedCC BY · PubMed Central
Fig. 2 Noise, output range and information in the reversible binding of molecules. a Schematic representation of reversible binding involving a receptor and a signal as examples. ka and kd correspond to the association and dissociation rate, respectively. b Acquired information, output range, and noise for receptor-ligand binding at different affinity values (Keq). The black circle and the dotted line denote the affinity at which the mutual information between signal and output is maximized. Information, noise, and output range are normalized by their respective maximal values. Further panels show the system’s behavior at c, d weak affinity (Keq = 10–5), e, f strong affinity (Keq = 10–9), and g, h intermediate affinity (Keq = 10–7; g, h). c, e, g show the temporal dynamic of the receptor-signal complexes (NRS) at three different concentrations of the signal S. d, f, h show response distributions of the number of receptor-signal complexes at these signal concentrations (see color legend at the bottom of the figure)
Fig. 2 Noise, output range and information in the reversible binding of molecules. a Schematic representation of reversible binding involving a receptor and a signal as examples. ka and kd correspond to the association and dissociation rate, respectively. b Acquired information, output range, and noise for receptor-ligand binding at different affinity values (Keq). The black circle and the dotted line denote the affinity at which the mutual information between signal and output is maximized. Information, noise, and output range are normalized by their respective maximal values. Further panels show the system’s behavior at c, d weak affinity (Keq = 10–5), e, f strong affinity (Keq = 10–9), and g, h intermediate affinity (Keq = 10–7; g, h). c, e, g show the temporal dynamic of the receptor-signal complexes (NRS) at three different concentrations of the signal S. d, f, h show response distributions of the number of receptor-signal complexes at these signal concentrations (see color legend at the bottom of the figure)CC BY · PubMed Central
Fig. 3 Acquired information, output range and noise at different signal concentrations. Contour plots of a information, b output range, and c noise at different receptor signal ratios NRT/NSmax (x axis), and at different affinities (y axis). a–c The diagonal white-dashed lines circumscribe the region with maximal information acquisition. The large red-dashed rectangles circumscribe the region with biologically observed ranges of receptor-signal affinities ([10−6 M, 10−9 M]) and NRT/NSmax ratios (NRT = 10–8 and 10−7 M ≤ NSmax ≤ 10−5 M). The small red-dashed rectangles circumscribe the region where NSmax = NRT and where the system is noise-free, reaches the maximally possible output range, and where information acquisition is ‘perfect’. Acquired information, output range and noise are plotted from minimally to maximally observed values, color-coded as indicated by the color bar. d–f Noise, output range and information observed in numerical simulations of the receptor-signal system at different affinities (Keq) and with different concentrations of R and S. a R = 10−9 M and S = [10−9 M, 10−7 M]. b R = 10−8 M and S = [10−8 M, 10−6 M]. a R = 10−7 M and S = [10−7 M, 10−5 M]. Information, noise, and output range are normalized by their respective maximal values
Fig. 3 Acquired information, output range and noise at different signal concentrations. Contour plots of a information, b output range, and c noise at different receptor signal ratios NRT/NSmax (x axis), and at different affinities (y axis). a–c The diagonal white-dashed lines circumscribe the region with maximal information acquisition. The large red-dashed rectangles circumscribe the region with biologically observed ranges of receptor-signal affinities ([10−6 M, 10−9 M]) and NRT/NSmax ratios (NRT = 10–8 and 10−7 M ≤ NSmax ≤ 10−5 M). The small red-dashed rectangles circumscribe the region where NSmax = NRT and where the system is noise-free, reaches the maximally possible output range, and where information acquisition is ‘perfect’. Acquired information, output range and noise are plotted from minimally to maximally observed values, color-coded as indicated by the color bar. d–f Noise, output range and information observed in numerical simulations of the receptor-signal system at different affinities (Keq) and with different concentrations of R and S. a R = 10−9 M and S = [10−9 M, 10−7 M]. b R = 10−8 M and S = [10−8 M, 10−6 M]. a R = 10−7 M and S = [10−7 M, 10−5 M]. Information, noise, and output range are normalized by their respective maximal valuesCC BY · PubMed Central
Fig. 4 Information, output range and noise in a pair of reversible binding interactions. Contour plots of a noise, b output range, and c information acquisition in the receptor-signal-DNAbs complex (RSD) as a function of the affinities between both the receptor and the signal (KeqR,S), and the receptor-signal complex with the downstream molecule (KeqRS,D). Red-dashed rectangles circumscribe biologically sensible receptor-signal DNA affinities ([10−8 M, 10−13 M]) and receptor signal affinities ([10−6 M, 10−9 M]). White-dashed rectangles delineate the region of maximal information acquisition at the receptor-signal-DNAbs level. Acquired information, output range and noise are plotted from minimally to maximally observed values, color-coded as indicated by the color bar
Fig. 4 Information, output range and noise in a pair of reversible binding interactions. Contour plots of a noise, b output range, and c information acquisition in the receptor-signal-DNAbs complex (RSD) as a function of the affinities between both the receptor and the signal (KeqR,S), and the receptor-signal complex with the downstream molecule (KeqRS,D). Red-dashed rectangles circumscribe biologically sensible receptor-signal DNA affinities ([10−8 M, 10−13 M]) and receptor signal affinities ([10−6 M, 10−9 M]). White-dashed rectangles delineate the region of maximal information acquisition at the receptor-signal-DNAbs level. Acquired information, output range and noise are plotted from minimally to maximally observed values, color-coded as indicated by the color barCC BY · PubMed Central
Fig. 5 Noise, output range and information in gene regulation. a Schematic representation of our model of gene regulation. ka and kd correspond to the association and dissociation rate, respectively of a TF with its DNA binding site; k1 and k2 correspond to the mRNA and protein synthesis rate, respectively; d1 and d2 correspond to the mRNA and protein degradation rates, respectively. b Information, output range, and noise observed in numerical simulations of the system at different TF-DNA affinities (Keq). Information, noise, and output range are normalized by their respective maximal values. The black dotted line denote the affinity at which mutual information between signal and output is maximal. System behavior at weak (Keq = 10–9; c, d), intermediate (Keq = 10–11; e, f), and strong (Keq = 10–13; g, h) affinities. Temporal protein dynamics at three different TF concentrations are shown in c, e and g. Response distribution of the number of protein molecules for the same simulations are shown in d, f and h. The blue dashed line in c–h marks the expected mean protein value for constitutive (unregulated, always-on) expression
Fig. 5 Noise, output range and information in gene regulation. a Schematic representation of our model of gene regulation. ka and kd correspond to the association and dissociation rate, respectively of a TF with its DNA binding site; k1 and k2 correspond to the mRNA and protein synthesis rate, respectively; d1 and d2 correspond to the mRNA and protein degradation rates, respectively. b Information, output range, and noise observed in numerical simulations of the system at different TF-DNA affinities (Keq). Information, noise, and output range are normalized by their respective maximal values. The black dotted line denote the affinity at which mutual information between signal and output is maximal. System behavior at weak (Keq = 10–9; c, d), intermediate (Keq = 10–11; e, f), and strong (Keq = 10–13; g, h) affinities. Temporal protein dynamics at three different TF concentrations are shown in c, e and g. Response distribution of the number of protein molecules for the same simulations are shown in d, f and h. The blue dashed line in c–h marks the expected mean protein value for constitutive (unregulated, always-on) expressionCC BY · PubMed Central

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Metadata

Authors
Azpeitia, E., Balanzario, E. P., & Wagner, A.
Affiliations
  • SIB Swiss Institute of Bioinformatics (CH)
  • Centro de Ciencias Matemáticas (MX)
Corresponding author
Wagner, Andreas
ORCID
Venue
BMC Bioinformatics
Publisher
Springer Science and Business Media LLC
Published
2020-10-16
Volume
21
Issue
1
Pages
462-462
ISSN
1471-2105 (ISSN-L)
DOI
10.1186/s12859-020-03778-x
PMC
PMC7568421
OpenAlex
W3092838074
Cited by
20
References
6
Citations by year
2026: 2 · 2025: 4 · 2024: 5 · 2023: 2 · 2022: 3 · 2021: 2 · 2020: 2
FWCI
0.73
Type
journal article
Language
en
Open access
Licence
Locations
  • BMC Bioinformatics (publishedVersion, cc-by)
  • bioRxiv (Cold Spring Harbor Laboratory) (acceptedVersion, cc-by)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • Zurich Open Repository and Archive (University of Zurich) (acceptedVersion, cc-by)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • Zurich Open Repository and Archive (University of Zurich) (submittedVersion, cc-by)
  • Zurich Open Repository and Archive (University of Zurich)
Funders
  • National Science Foundation (31003A_172887)
  • Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (739874, 172887)
  • H2020 European Research Council (739874)
Topics
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Gene Regulatory Network Analysis
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › stochastic dynamics and bifurcation
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
Keywords
signaling pathways, noise, information acquisition, stochastic resonance, kinetic parameters, signal detection, stochastic dynamics
MeSH terms
Gene Expression Regulation, Kinetics, Ligands, Models, Biological, Signal Transduction

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