Abstract GABAergic interneurons can be subdivided into three subclasses: parvalbumin positive (PV), somatostatin positive (SOM) and serotonin positive neurons. With principal cells (PCs) they form complex networks. We examine PCs and PV responses in mouse anterior lateral motor cortex (ALM) and barrel cortex (S1) upon PV photostimulation in vivo . In layer 5, the PV response is paradoxical: photoexcitation reduces their activity. This is not the case in ALM layer 2/3. We combine analytical calculations and numerical simulations to investigate how these results constrain the architecture. Two-population models cannot account for the results. Networks with three inhibitory populations and V1-like architecture account for the data in ALM layer 2/3. Our data in layer 5 can be accounted for if SOM neurons receive inputs only from PCs and PV neurons. In both four-population models, the paradoxical effect implies not too strong recurrent excitation. It is not evidence for stabilization by inhibition.
A hierarchical model of ten cortical areas is examinated to explain representation of stimulus contrast. In each area, the activity is integrated and then non-linearly transmitted feedforwardly to the next area. This arrangement of interactions creates a gradient from simple to complex visual patterns as one move from lower to higher cortical levels. In the model, each unit describes the neural activity represented by a fring-rate model where the gain controls the steepness of the input-output relation. A Gaussian random input is applied to level one as the distribution was modified in width, similar to variation in contrast in visual stimuli. The output activity ratio between a lower and higher contrast is analysed for the last level to observe sensitivity to a contrast and contrast invariant tuning. For a purely feedforward system, in a small gain range, the output of the last area presents aproximate contrast invariance, whereas the sensitivity to contrast was poor. To analyse other cortico-cortical interactions, positive and negative feedback connections from higher to lower cortical areas are then incorporated. In this case, neither the sentivity to contrast nor the contrast invariance of the tuning were improved. To account for an alternative visual processing pathway, non-reciprocal connections from and to a paralel pulvinar like-structure of nine areas are coupled to the system. Compared to the pure feedforward model, cortico-pulvino-cortical output presents more sensitivity to contrast and keep similar values of the tuning contrast invariance.
The width of the orientation tuning curves of the spike response of neurons in V1 is invariant to contrast. This property constrains the possible mechanisms underlying orientation selectivity. It has been suggested that noise circumvents the iceberg effect that would prevent contrast invariance in the purely feedforward mechanism. Here we investigate systematically how noise contributes to the contrast invariance of orientation tuning curves in V1. We study three models of increasing complexity: a simple threshold-linear firing rate model, a leaky integrate-and-fire model, and a conductance-based model. We show that the noise transmutes the threshold nonlinearity of the input–output relationships into an approximate power law without a threshold within some firing rate range. This implies that, under certain conditions which are derived here, the tuning of the neuron output is approximately contrast invariant. In particular we show that this mechanism for contrast invariance requires that the neuron firing rate must not be too large and that increasing or lowering the contrast too much destroys this invariance. We also show that if this mechanism operates in V1, the spike response, R, and average voltage response V of the neurons in V1 should vary with the contrast, C, according to R(C) ∝ V(C)γ. The exponent γ can be estimated from the amount by which the spike tuning curve is sharpened with respect to the voltage tuning curves of the neurons. This prediction does not depend on the specifics of the model and can be tested experimentally.
This study examines the ability of neurons to track temporally varying inputs, namely by investigating how the instantaneous firing rate of a neuron is modulated by a noisy input with a small sinusoidal component with frequency (f). Using numerical simulations of conductance-based neurons and analytical calculations of one-variable nonlinear integrate-and-fire neurons, we characterized the dependence of this modulation on f. For sufficiently high noise, the neuron acts as a low-pass filter. The modulation amplitude is approximately constant for frequencies up to a cutoff frequency, fc, after which it decays. The cutoff frequency increases almost linearly with the firing rate. For higher frequencies, the modulation amplitude decays as C/falpha, where the power alpha depends on the spike initiation mechanism. For conductance-based models, alpha = 1, and the prefactor C depends solely on the average firing rate and a spike "slope factor," which determines the sharpness of the spike initiation. These results are attributable to the fact that near threshold, the sodium activation variable can be approximated by an exponential function. Using this feature, we propose a simplified one-variable model, the "exponential integrate-and-fire neuron," as an approximation of a conductance-based model. We show that this model reproduces the dynamics of a simple conductance-based model extremely well. Our study shows how an intrinsic neuronal property (the characteristics of fast sodium channels) determines the speed with which neurons can track changes in input.
We study the emergence of synchronized burst activity in networks of neurons with spike adaptation. We show that networks of tonically firing adapting excitatory neurons can evolve to a state where the neurons burst in a synchronized manner. The mechanism leading to this burst activity is analyzed in a network of integrate-and-fire neurons with spike adaptation. The dependence of this state on the different network parameters is investigated, and it is shown that this mechanism is robust against inhomogeneities, sparseness of the connectivity, and noise. In networks of two populations, one excitatory and one inhibitory, we show that decreasing the inhibitory feedback can cause the network to switch from a tonically active, asynchronous state to the synchronized bursting state. Finally, we show that the same mechanism also causes synchronized burst activity in networks of more realistic conductance-based model neurons.
The firing rate gain of neurons, defined as the slope of the relation between input to a neuron and its firing rate, has received considerable attention in the past few years. This has been largely motivated by the many experimental demonstrations of behavior related gain changes in a variety of neural circuits of the CNS. A surprising result was that a prime candidate, shunting inhibition, apparently does not change the firing rate gain of neurons. However, in this paper, we show a physiologically plausible mechanism by which shunting inhibition in the dendritic tree does, in a simple and direct manner, modulate the firing gain of neurons. The effect is due to a strong attenuation of the dendritic current arriving at the soma by shunting dendritic inhibition. Increasing the dendritic inhibitory conductance enhances the attenuation of current flowing from the dendritic to the somatic compartment and thus reduces firing gain. This mechanism relies on known physiological and anatomical properties of CNS neurons and does not require special features such as tunable neural noise inputs. Gain control by the proposed mechanism may prove to be a ubiquitous feature of neural circuit operations and it is readily verifiable experimentally.
