A multiscale continuum model of the vertebrate outer retina: The temporal dynamics of background-induced flicker enhancement

Steven M. Baer, Shaojie Chang, Sharon M. Crook, Carl L. Gardner, Jeremiah R. Jones, Christian Ringhofer, Ralph F. Nelson

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


The retina is a part of the central nervous system that is accessible, well documented, and studied by researchers spanning the clinical, experimental, and theoretical sciences. Here, we mathematically model the subcircuits of the outer plexiform layer of the retina on two spatial scales: that of an individual synapse and that of the scale of the receptive field (hundreds to thousands of synapses). To this end we formulate a continuum spine model (a partial differential equation system) that incorporates the horizontal cell syncytium and its numerous processes (spines) within cone pedicles. With this multiscale modeling approach, detailed biophysical mechanisms at the synaptic level are retained while scaling up to the receptive field level. As an example of its utility, the model is applied to study background-induced flicker enhancement in which the onset of a dim background enhances the center flicker response of horizontal cells. Simulation results, in comparison with flicker enhancement data for square, slit, and disk test regions, suggest that feedback mechanisms that are voltage-axis modulators of cone calcium channels (for example, ephaptic and/or pH feedback) are robust in capturing the temporal dynamics of background-induced flicker enhancement. The value and potential of this continuum spine approach is that it provides a framework for mathematically modeling the input-output properties of the entire receptive field of the outer retina while implementing the latest models for transmission mechanisms at the synaptic level.

Original languageEnglish (US)
Article number110763
JournalJournal of Theoretical Biology
StatePublished - Sep 21 2021


  • Dendritic spines
  • Feedback
  • Retinal cone photoreceptors
  • Retinal horizontal cells
  • Synaptic transmission

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • General Biochemistry, Genetics and Molecular Biology
  • General Immunology and Microbiology
  • General Agricultural and Biological Sciences
  • Applied Mathematics


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