Impact of network structure and cellular response on spike time correlations

Novel experimental techniques reveal the simultaneous activity of larger and larger numbers of neurons. As a result there is increasing interest in the structure of cooperative -- or correlated -- activity in neural populations, and in the possible impact of such correlations on the neural code. A fundamental theoretical challenge is to understand how the architecture of network connectivity along with the dynamical properties of single cells shape the magnitude and timescale of correlations. We provide a general approach to this problem by extending prior techniques based on linear response theory. We consider networks of general integrate-and-fire cells with arbitrary architecture, and provide explicit expressions for the approximate cross-correlation between constituent cells. These correlations depend strongly on the operating point (input mean and variance) of the neurons, even when connectivity is fixed. Moreover, the approximations admit an expansion in powers of the matrices that describe the network architecture. This expansion can be readily interpreted in terms of paths between different cells. We apply our results to large excitatory-inhibitory networks, and demonstrate first how precise balance --- or lack thereof --- between the strengths and timescales of excitatory and inhibitory synapses is reflected in the overall correlation structure of the network. We then derive explicit expressions for the average correlation structure in randomly connected networks. These expressions help to identify the important factors that shape coordinated neural activity in such networks

The Spatial Structure of Stimuli Shapes the Timescale of Correlations in Population Spiking Activity

Throughout the central nervous system, the timescale over which pairs of neural spike trains are correlated is shaped by stimulus structure and behavioral context. Such shaping is thought to underlie important changes in the neural code, but the neural circuitry responsible is largely unknown. In this study, we investigate a stimulus-induced shaping of pairwise spike train correlations in the electrosensory system of weakly electric fish. Simultaneous single unit recordings of principal electrosensory cells show that an increase in the spatial extent of stimuli increases correlations at short (~10 ms) timescales while simultaneously reducing correlations at long (~100 ms) timescales. A spiking network model of the first two stages of electrosensory processing replicates this correlation shaping, under the assumptions that spatially broad stimuli both saturate feedforward afferent input and recruit an open-loop inhibitory feedback pathway. Our model predictions are experimentally verified using both the natural heterogeneity of the electrosensory system and pharmacological blockade of descending feedback projections. For weak stimuli, linear response analysis of the spiking network shows that the reduction of long timescale correlation for spatially broad stimuli is similar to correlation cancellation mechanisms previously suggested to be operative in mammalian cortex. The mechanism for correlation shaping supports population-level filtering of irrelevant distractor stimuli, thereby enhancing the population response to relevant prey and conspecific communication inputs. © 2012 Litwin-Kumar et al

Motif Statistics and Spike Correlations in Neuronal Networks

Motifs are patterns of subgraphs of complex networks. We studied the impact of such patterns of connectivity on the level of correlated, or synchronized, spiking activity among pairs of cells in a recurrent network model of integrate and fire neurons. For a range of network architectures, we find that the pairwise correlation coefficients, averaged across the network, can be closely approximated using only three statistics of network connectivity. These are the overall network connection probability and the frequencies of two second-order motifs: diverging motifs, in which one cell provides input to two others, and chain motifs, in which two cells are connected via a third intermediary cell. Specifically, the prevalence of diverging and chain motifs tends to increase correlation. Our method is based on linear response theory, which enables us to express spiking statistics using linear algebra, and a resumming technique, which extrapolates from second order motifs to predict the overall effect of coupling on network correlation. Our motif-based results seek to isolate the effect of network architecture perturbatively from a known network state

Neural population coding: combining insights from microscopic and mass signals

Behavior relies on the distributed and coordinated activity of neural populations. Population activity can be measured using multi-neuron recordings and neuroimaging. Neural recordings reveal how the heterogeneity, sparseness, timing, and correlation of population activity shape information processing in local networks, whereas neuroimaging shows how long-range coupling and brain states impact on local activity and perception. To obtain an integrated perspective on neural information processing we need to combine knowledge from both levels of investigation. We review recent progress of how neural recordings, neuroimaging, and computational approaches begin to elucidate how interactions between local neural population activity and large-scale dynamics shape the structure and coding capacity of local information representations, make them state-dependent, and control distributed populations that collectively shape behavior

When do correlations increase with firing rates in recurrent networks?

A central question in neuroscience is to understand how noisy firing patterns are used to transmit information. Because neural spiking is noisy, spiking patterns are often quantified via pairwise correlations, or the probability that two cells will spike coincidentally, above and beyond their baseline firing rate. One observation frequently made in experiments, is that correlations can increase systematically with firing rate. Theoretical studies have determined that stimulus-dependent correlations that increase with firing rate can have beneficial effects on information coding; however, we still have an incomplete understanding of what circuit mechanisms do, or do not, produce this correlation-firing rate relationship. Here, we studied the relationship between pairwise correlations and firing rates in recurrently coupled excitatory-inhibitory spiking networks with conductance-based synapses. We found that with stronger excitatory coupling, a positive relationship emerged between pairwise correlations and firing rates. To explain these findings, we used linear response theory to predict the full correlation matrix and to decompose correlations in terms of graph motifs. We then used this decomposition to explain why covariation of correlations with firing rate—a relationship previously explained in feedforward networks driven by correlated input—emerges in some recurrent networks but not in others. Furthermore, when correlations covary with firing rate, this relationship is reflected in low-rank structure in the correlation matrix

The effect of neural adaptation of population coding accuracy

Most neurons in the primary visual cortex initially respond vigorously when a preferred stimulus is presented, but adapt as stimulation continues. The functional consequences of adaptation are unclear. Typically a reduction of firing rate would reduce single neuron accuracy as less spikes are available for decoding, but it has been suggested that on the population level, adaptation increases coding accuracy. This question requires careful analysis as adaptation not only changes the firing rates of neurons, but also the neural variability and correlations between neurons, which affect coding accuracy as well. We calculate the coding accuracy using a computational model that implements two forms of adaptation: spike frequency adaptation and synaptic adaptation in the form of short-term synaptic plasticity. We find that the net effect of adaptation is subtle and heterogeneous. Depending on adaptation mechanism and test stimulus, adaptation can either increase or decrease coding accuracy. We discuss the neurophysiological and psychophysical implications of the findings and relate it to published experimental data.Comment: 35 pages, 8 figure

Linear response for spiking neuronal networks with unbounded memory

We establish a general linear response relation for spiking neuronal networks, based on chains with unbounded memory. This relation allows us to predict the influence of a weak amplitude time-dependent external stimuli on spatio-temporal spike correlations, from the spontaneous statistics (without stimulus) in a general context where the memory in spike dynamics can extend arbitrarily far in the past. Using this approach, we show how linear response is explicitly related to neuronal dynamics with an example, the gIF model, introduced by M. Rudolph and A. Destexhe. This example illustrates the collective effect of the stimuli, intrinsic neuronal dynamics, and network connectivity on spike statistics. We illustrate our results with numerical simulations.Comment: 60 pages, 8 figure