Unraveling Functional Diversity of Cortical Synaptic Architecture Through the Lens of Population Coding

Abstract

The synaptic inputs to single cortical neurons exhibit substantial diversity in their sensory-driven activity. What this diversity reflects is unclear, and appears counter-productive in generating selective somatic responses to specific stimuli. One possibility is that this diversity reflects the propagation of information from one neural population to another. To test this possibility, we bridge population coding theory with measurements of synaptic inputs recorded in vivo with two-photon calcium imaging. We construct a probabilistic decoder to estimate the stimulus orientation from the responses of a realistic, hypothetical input population of neurons to compare with synaptic inputs onto individual neurons of ferret primary visual cortex (V1) recorded with two-photon calcium imaging in vivo. We find that optimal decoding requires diverse input weights and provides a straightforward mapping from the decoder weights to excitatory synapses. Analytically derived weights for biologically realistic input populations closely matched the functional heterogeneity of dendritic spines imaged in vivo with two-photon calcium imaging. Our results indicate that synaptic diversity is a necessary component of information transmission and reframes studies of connectivity through the lens of probabilistic population codes. These results suggest that the mapping from synaptic inputs to somatic selectivity may not be directly interpretable without considering input covariance and highlights the importance of population codes in pursuit of the cortical connectome.

Keywords: input - output analysis; population coding; synapse; two-photon imaging; visual cortex.

Figure 1

A population decoding framework to study synaptic diversity. An upstream population of neurons is tuned for a single stimulus variable (orientation; top). This input population is readout by downstream decoder neurons (bottom). Downstream neurons decode stimulus identification by reading out spikes from the upstream input population. Each decoder neuron is defined by set weights (middle) over the upstream population, which are summed and rectified to produce an output.

Figure 2

Model simulations with homogenous and heterogeneous input populations. (A) Orientation tuning of a homogenous input population. Shown is a subset of the total population (n = 20/1,000). The ordinate is orientation preference, restricted between −90 ^o and 90^o. (B) Derived weights for a single decoder neuron (preferring 0^o) reading out the homogenous (blue) input population in (A). Weights for homogenous populations smoothly vary over orientation space. (C) Response output of the decoder neuron whose weights are shown in (B). (D–F) Same as in (A–C) for a heterogeneous input population with moderate correlation (c_o = 0.25). Note that decoder weights for heterogeneous input populations are not smooth.

Figure 3

Decoder performance of heterogeneous input populations depends on population size, correlations, and weight diversity. (A) Example weight distribution for a decoder neuron reading out a heterogeneous input population (top). Shown are the effects of progressively smoothing weights. Smooth parameters (see “Methods” Section) from top to bottom: (0, 0), (0.1, 1), (0.2, 2), (1, 10). The ordinate is orientation preference, restricted between −90^o and 90^o. (B) Decoder performance (inverse mean-squared-error) plotted for homogenous and heterogeneous input populations of increasing size. Simulations here include no correlations (c_o = 0). Shading indicates standard error. (C) Same as in (D) for input populations with moderate correlation (c_o = 0.25). (D) Same as in (B) for input populations with stronger correlation (c_o = 0.50).

Figure 4

Simulation of synaptic populations from decoder neuron weight distributions. (A) Example weight distribution for a single decoder neuron tuned to 0^o (left). Ordinates are orientation preference, restricted between −90^o and 90^o. The dashed line separates excitatory (positive) and inhibitory (negative) weights. Excitatory weight distribution over the input population is transformed into a frequency distribution, whereby greater amplitude equates to a greater frequency of occurrence (right). (B) Example simulated synaptic population (n = 100 spines) from the weight distribution in (A). Shown are the orientation tuning curves of each simulated synapse (normalized).

Figure 5

Orientation tuning diversity of dendritic spine populations in ferret V1 match simulations with correlated, heterogeneous input populations. (A) Two-photon standard deviation projection of example dendrite and spines recorded from a single cell (left). Inset: Two-photon standard-deviation projection of corresponding soma. The scale bar is 10 microns. Orientation tuning of soma (top) and all visually-responsive dendritic spines from this single cell (n = 159) are shown (right). Spine responses are normalized peak ΔF/F. Orientation preferences are shown relative to the somatic preference (aligned to 0^o). (B) Same as in (A) for another example cell (n = 162 visually-responsive spines). (C) Cumulative distributions of tuning correlation between individual dendritic spines or simulated synaptic inputs with corresponding somatic tuning or decoder output. Shown are correlations of simulations of homogenous (blue) or heterogeneous (red) input populations, compared to empirical data (gray). (D) Distributions of average tuning correlation between synaptic input and somatic output across measured cells (n = 45). Also shown are distributions of average tuning correlation for simulated cells. Triangles denote median values for each distribution. (E) Comparison of Kullback-Leibler divergence (D_KL) between data and each model type. Each data point represents an individual cell’s population of dendritic spines.