Possible dendritic contribution to unimodal numerosity tuning and Weber-Fechner law-dependent numerical cognition

Abstract

Humans and animals are known to share an ability to estimate or compare the numerosity of visual stimuli, and this ability is considered to be supported by the cortical neurons that have unimodal tuning for numerosity, referred to as the numerosity detector neurons. How such unimodal numerosity tuning is shaped through plasticity mechanisms is unknown. Here, I propose a testable hypothetical mechanism based on recently revealed features of the neuronal dendrite, namely, cooperative plasticity induction and nonlinear input integration at nearby dendritic sites, on the basis of the existing proposal that individual visual stimuli are represented as similar localized activities regardless of the size or the shape in a cortical region in the dorsal visual pathway. Intriguingly, the proposed mechanism naturally explains a prominent feature of the numerosity detector neurons, namely, the broadening of the tuning curve in proportion to the preferred numerosity, which is considered to underlie the known Weber–Fechner law-dependent accuracy of numerosity estimation and comparison. The simulated tuning curves are less sharp than reality, however, and together with the evidence from human imaging studies that numerical representation is a distributed phenomenon, it may not be likely that the proposed mechanism operates by itself. Rather, the proposed mechanism might facilitate the formation of hierarchical circuitry proposed in the previous studies, which includes neurons with monotonic numerosity tuning as well as those with sharp unimodal tuning, by serving as an efficient initial condition.

Response to change in the number of visual stimuli in zebrafish:A behavioural and molecular study

“…It could be that the gene expression modulation that we observed -e.g. in the telencephalon for number -could be due to the activation of single unimodal neurons that, by summating their inputs, activate the numerousness cluster corresponding to the presented numerosity 56 ; or alternatively that it could be due to the signal integration of the dendrites of specific number detector neurons 57 . Further analyses will be necessary to explore single unimodal or signal integration nature of, if existing, number neurons in the zebrafish brain.…”

Statistical physics approach to dendritic computation: The excitable-wave mean-field approximation

“…(17), and finally by backpropagating waves Eq. (18). This choice seems to be appropriate in the regime of weak external driving, insofar as the order coincides with that of the events observed in the experiments: forward dendritic spikes, a somatic spike, then backpropagating dendritic spikes [51].…”

“…Or, to put it in a renormalization group parlance, "realistic biophysical modeling" does not allow us to separate the relevant observables from the irrelevant ones that can be eliminated without significantly changing some robust property of the system. In fact, this has been recognized in the neuroscience literature, which has emphasized the need for theoretical support [12][13][14] and witnessed the increase of theoretical papers in the field of dendritic computation [15][16][17][18][19].…”

“…(19) through (21) are relatively straightforward, there is a degree of arbitrariness in the choice of Eqs. (16) through (18). As written, they prescribe an ad hoc priority order for the recruitment of the excitation components of the EW equations: first by synaptic stimuli Eq.…”

A Low-Order Model of Biological Neural Networks

“…Johnson (2001, 2002), found dendritic inhibition to enhance neural coding properties and unsupervised learning in neural networks. Computation by dendrites was also discussed in Goldman, Levine, Major, Tank, & Seung (2003), Morita, Okada, & Aihara (2007), Rhodes (2008), and Morita (2008Morita ( , 2009.…”