Emergent tuning heterogeneity in cortical circuits is sensitive to cellular neuronal dynamics

TL;DR

The paper develops a tractable mean-field theory for feature-tuned balanced-state cortical networks using Gauss–Rice neurons to capture emergent tuning heterogeneity. It analyzes both random and ring-structured connectivity, deriving self-consistent equations for mean firing rates and their heterogeneity under exponential and von Mises synaptic kernels. A key finding is the universality of the population tuning profile under high-rank von Mises connectivity, contrasted with explicit self-consistency requirements in low-rank cosine networks to capture higher harmonics and quenched variability. The framework demonstrates how inhibitory stabilization sharpens tuning and can yield contrast-invariant selectivity, providing a rigorous basis for inferring circuit parameters from observed tuning heterogeneity.

Abstract

Cortical circuits exhibit high levels of response diversity, even across apparently uniform neuronal populations. While emerging data-driven approaches exploit this heterogeneity to infer effective models of cortical circuit computation (e.g. Genkin et al. Nature 2025), the power of response diversity to enable inference of mechanistic circuit models is largely unexplored. Within the landscape of cortical circuit models, spiking neuron networks in the balanced state naturally exhibit high levels of response and tuning diversity emerging from their internal dynamics. A statistical theory for this emergent tuning heterogeneity, however, has only been formulated for binary spin models (Vreeswijk & Sompolinsky, 2005). Here we present a formulation of feature-tuned balanced state networks that allows for arbitrary and diverse dynamics of postsynaptic currents and variable levels of heterogeneity in cellular excitability but nevertheless is analytically exactly tractable with respect to the emergent tuning curve heterogeneity. Using this framework, we present a case study demonstrating that, for a wide range of parameters even the population mean response is non-universal and sensitive to mechanistic circuit details. As our theory enables exactly and analytically obtaining the likelihood-function of tuning heterogeneity given circuit parameters, we argue that it forms a powerful and rigorous basis for neural circuit inference.

Figures (4)

• Figure 1: Schematic of ring model and input selectivity. (Left) Neurons are arranged on a ring according to their preferred angle $\phi_i$. Connection probability is determined by the angular distance, $p_{ij} = f(\phi_i - \phi_j)$ (blue), and external input by $I_i = g(\phi_0 - \phi_i)$ (orange), centered around stimulus angle $\phi_0$ (without loss of generality $\phi_0 = 0$ is fixed in the analysis). (Right) Example input and connectivity kernels. For orientation selectivity, only the zeroth and second Fourier modes are required, resulting in $\pi$-periodic tuning. For direction selectivity, one additionally needs the first Fourier mode, which breaks the $\pi$-symmetry and yields $2\pi$-periodic responses. A ring model operating in the balanced state will generate emergent response heterogeneity as illustrated by the angle-dependent firing rate distribution shown on the bottom left. The theory presented here enables obtaining it by direct analytical calculation.
• Figure 2: Shallow vs. sharp tuning in the cosine self-consistent network. For both cases, the same external input is applied (orange), $I_{\text{ext}}(\phi) = I_{0c} + I_{\mu c}(1 + \mu_c \cos(2\phi))$, with $I_{0c}=1.0$, $I_{\mu c}=4.0$, $\mu_c=0.05$, $J_0=1.0$, $\tau_I=5\,\mathrm{ms}$, $\tau_M=10\,\mathrm{ms}$. The network output firing rate profile $\nu(\phi)$ (black) and the self-consistent recurrent mean input $I_c(\phi)$ and variance $\alpha^2(\phi)$ (right column) are shown. (A) For narrower connection probability $p_c=0.4$ (more orientation-selective connectivity), the recurrent input weakly tunes the external drive, resulting in shallow tuning. (B) For broader connection probability $p_c=0.1$, the untuned components of the stimulus are strongly suppressed, resulting in a sharp tuning profile.
• Figure 3: Firing rate profile of von--Mises modulated networks. Both panels show the network firing rate profile $\nu(\phi)$ (black) compared to the external drive (orange) and its Gaussian approximation (blue, dashed), for $I_{0v} = 1.0, \; I_{\mu v} = 4.0$. The two cases correspond to different pairs of von--Mises concentration parameters: (Left)$(\kappa_\mu, \kappa_p) = (1.0, 1.3)$ and (Right)$(\kappa_\mu, \kappa_p) = (5.0, 10.0)$. In the left panel, the Gaussian approximation fails to capture the profile accurately because $\kappa_\mu$ is small, and the von--Mises distribution is far from Gaussian. Moreover, relative sharpening in the firing rate $\nu(\phi)$ is more pronounced when $\kappa_p$ is closer to $\kappa_\mu$, as seen in the left case.
• Figure 4: Comparison of network tunings. (Top) Within the universality regime, where the von--Mises kernel is well captured by its first Fourier (cosine) component and the resulting solution coincides with the self-consistent prediction. In this case, both input and connectivity are only weakly modulated, and sharpening is shallow, i.e. the orientation selectivity of the input is much broader than that of the connectivity. (Bottom) Outside the universality regime, where the orientation selectivity of the input approaches that of the connectivity. Here, higher Fourier components of the von--Mises kernel contribute significantly, and the cosine approximation no longer reproduces the self-consistent solution. Parameters: $I_{0v} = 1.0$, $I_{\mu v} = 4.0$, $\kappa_p = 0.2$, with $\kappa_\mu = 0.001$ (top) and $\kappa_\mu = 0.15$ (bottom).