This article is part of the Physical Review Research collection titled Physics of Neuroscience.

Predictive remapping ($P_{RE}$)—the ability of cells in retinotopic brain structures to transiently exhibit spatiotemporal shifts beyond the spatial extent of their classical anatomical receptive fields—has been proposed as a primary mechanism that stabilizes an organism's percept of the visual world around the time of a saccadic eye movement. Despite the well-documented effects of $P_{RE}$, a biologically plausible mathematical framework that specifies a fundamental law and the functional neural architecture that actively mediates this ubiquitous phenomenon does not exist. We introduce the Newtonian model of $P_{RE}$, where each modular component of $P_{RE}$ manifests as three temporally overlapping forces: centripetal $\left(\stackrel{\rightharpoonup }{f_C}\right)$, convergent $\left(\stackrel{\rightharpoonup }{f_P}\right)$, and translational $\left(\stackrel{\rightharpoonup }{f_T}\right)$, that perturb retinotopic cells from their equilibrium extent. The resultant and transient influences of these forces $\stackrel{\rightharpoonup }{f_C}+\stackrel{\rightharpoonup }{f_P}+\stackrel{\rightharpoonup }{f_T}$ gives rise to a neuronal force field that governs the spatiotemporal dynamics of $P_{RE}$. This neuronal force field fundamentally obeys an inverse-distance law $P_{RE}\propto \frac{1}{r^{1.6}}$, akin to Newton's law of universal gravitation [I. Newton, Newton's Principia: The Mathematical Principles of Natural Philosophy (Geo. P. Putnam, New-York, 1850)] and activates retinotopic elastic fields $\mathrm{el}\phi$'s. We posit that $\mathrm{el}\phi$'s are transient functional neural structures that are self-generated by visual systems during active vision and approximate the sloppiness (or degrees of spatial freedom) within which receptive fields are allowed to shift, while ensuring that retinotopic organization does not collapse. The predictions of this general model are borne out by the spatiotemporal changes in visual sensitivity to probe stimuli in human subjects around the time of an eye movement and qualitatively match neural sensitivity signatures associated with predictive shifts in the receptive fields of cells in premotor and higher-order retinotopic brain structures. The introduction of this general model opens the search for possible biophysical implementations and provides experimentalists with a simple, elegant, yet powerful mathematical framework they can now use to generate experimentally testable predictions across a range of biological systems.

• Received 24 October 2022
• Accepted 13 March 2023

DOI:https://doi.org/10.1103/PhysRevResearch.5.013214

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Published by the American Physical Society

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Physics of Neuroscience

Physics of Neuroscience has emerged as an area of research at the edge of a breadth of multiple disciplines, ranging from statistical physics and computer science all the way to biomedical research. As a venue committed to multi- and interdisciplinary work with a connection to physics, Physical Review Research is delighted to start a Collection, organized by guest editors David Schwab and Carina Curto, to host the outstanding research that is being produced in this field and to invite this burgeoning community to partner with us in our mission to disseminate novel and significant content to the public.