Impact of Correlated Synaptic Input on Output Firing Rate and Variability in Simple Neuronal Models
Open accessAbstract
Cortical neurons are typically driven by thousands of synaptic inputs. The arrival of a spike from one input may or may not be correlated with the arrival of other spikes from different inputs. How does this interdependence alter the probability that the postsynaptic neuron will fire? We constructed a simple random walk model in which the membrane potential of a target neuron fluctuates stochastically, driven by excitatory and inhibitory spikes arriving at random times. An analytic expression was derived for the mean output firing rate as a function of the firing rates and pairwise correlations of the inputs. This stochastic model made three quantitative predictions. (1) Correlations between pairs of excitatory or inhibitory inputs increase the fluctuations in synaptic drive, whereas correlations between excitatory-inhibitory pairs decrease them. (2) When excitation and inhibition are fully balanced (the mean net synaptic drive is zero), firing is caused by the fluctuations only. (3) In the balanced case, firing is irregular. These theoretical predictions were in excellent agreement with simulations of an integrate-and-fire neuron that included multiple conductances and received hundreds of synaptic inputs. The results show that, in the balanced regime, weak correlations caused by signals shared among inputs may have a multiplicative effect on the input-output rate curve of a postsynaptic neuron, i.e. they may regulate its gain; in the unbalanced regime, correlations may increase firing probability mainly around threshold, when output rate is low; and in all cases correlations are expected to increase the variability of the output spike train.
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Gain-modulated cells are suited to perform multimodal computations, such as conversions from sensory-centred into motor-centred reference frames, and for the generation of invariant responses to input features despite contextual variability.
“Gain-modulated cells are ideally suited to perform multimodal computations, such as conversions from sensory-centred into motor-centred reference frames, and for the generation of invariant responses to input features despite contextual variability6–9.”
From Mechanisms underlying gain modulation in the cortex (2020) · cites this paper as [9]
Correlations between pairs of excitatory inputs or pairs of inhibitory inputs increase fluctuations in synaptic drive, whereas excitatory-inhibitory correlations decrease fluctuations.
“Correlations between pairs of excitatory inputs or pairs of inhibitory inputs increase fluctuations in synaptic drive, whereas excitatory–inhibitory correlations decrease fluctuations9.”
From Mechanisms underlying gain modulation in the cortex (2020) · cites this paper as [9]
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- Authors
- Salinas, E., & Sejnowski, T. J.
- Affiliations
- Salk Institute for Biological Studies (US)
- ORCID
- Salinas, Emilio
- Venue
- The Journal of Neuroscience
- Publisher
- Society for Neuroscience
- Published
- 2000-08-15
- Volume
- 20
- Issue
- 16
- Pages
- 6193-6209
- ISSN
- 0270-6474 (ISSN-L)
- 1529-2401
- PMC
- PMC6772574
- OpenAlex
- W2146766016
- Cited by
- 472
- References
- 76
- Citations by year
- 2026: 7 · 2025: 14 · 2024: 8 · 2023: 23 · 2022: 10 · 2021: 12 · 2020: 17 · 2019: 13 · 2018: 13 · 2017: 12 · 2016: 11 · 2015: 23 · 2014: 17 · 2013: 29 · 2012: 20
- FWCI
- 11.18
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Journal of Neuroscience (publishedVersion)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- Funders
- Howard Hughes Medical Institute
- Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › stochastic dynamics and bifurcation
- Life Sciences › Neuroscience › Cellular and Molecular Neuroscience › Neuroscience and Neuropharmacology Research
- Keywords
- firing rate variability, integrate-and-fire neurons, random walks, membrane potential fluctuations, excitation-inhibition balance, cortical neurons, synaptic drive
- MeSH terms
- Action Potentials, Afferent Pathways, Models, Neurological, Neurons, Synapses
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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