Cortical cells should fire regularly, but do not

When a typical nerve cell is injected with enough current, it fires a regular stream of action potentials. But cortical cells in vivo usually fire irregularly, reflecting synaptic input from presynaptic cells as well as intrinsic biophysical properties. We have applied the theory of stochastic processes to spike trains recorded from cortical neurons (Tuckwell 1989) and find a fundamental contradiction between the large interspike variability observed and the much lower values predicted by well-accepted biophysical models of single cells

The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs

How random is the discharge pattern of cortical neurons? We examined recordings from primary visual cortex (V1; Knierim and Van Essen, 1992) and extrastriate cortex (MT; Newsome et al., 1989a) of awake, behaving macaque monkey and compared them to analytical predictions. For nonbursting cells firing at sustained rates up to 300 Hz, we evaluated two indices of firing variability: the ratio of the variance to the mean for the number of action potentials evoked by a constant stimulus, and the rate-normalized coefficient of variation (Cv) of the interspike interval distribution. Firing in virtually all V1 and MT neurons was nearly consistent with a completely random process (e.g., Cv approximately 1). We tried to model this high variability by small, independent, and random EPSPs converging onto a leaky integrate-and- fire neuron (Knight, 1972). Both this and related models predicted very low firing variability (Cv << 1) for realistic EPSP depolarizations and membrane time constants. We also simulated a biophysically very detailed compartmental model of an anatomically reconstructed and physiologically characterized layer V cat pyramidal cell (Douglas et al., 1991) with passive dendrites and active soma. If independent, excitatory synaptic input fired the model cell at the high rates observed in monkey, the Cv and the variability in the number of spikes were both very low, in agreement with the integrate-and-fire models but in strong disagreement with the majority of our monkey data. The simulated cell only produced highly variable firing when Hodgkin-Huxley- like currents (INa and very strong IDR) were placed on distal dendrites. Now the simulated neuron acted more as a millisecond- resolution detector of dendritic spike coincidences than as a temporal integrator. We argue that neurons that act as temporal integrators over many synaptic inputs must fire very regularly. Only in the presence of either fast and strong dendritic nonlinearities or strong synchronization among individual synaptic events will the degree of predicted variability approach that of real cortical neurons

Auto and crosscorrelograms for the spike response of LIF neurons with slow synapses

An analytical description of the response properties of simple but realistic neuron models in the presence of noise is still lacking. We determine completely up to the second order the firing statistics of a single and a pair of leaky integrate-and-fire neurons (LIFs) receiving some common slowly filtered white noise. In particular, the auto- and cross-correlation functions of the output spike trains of pairs of cells are obtained from an improvement of the adiabatic approximation introduced in \cite{Mor+04}. These two functions define the firing variability and firing synchronization between neurons, and are of much importance for understanding neuron communication.Comment: 5 pages, 3 figure

Irregularity in the cortical spike code : noise or information?

How random is the discharge pattern of cortical neurons? We examined recordings from primary visual cortex (V1) and extrastriate cortex (MT) of awake, behaving macaque monkey, and compared them to analytical predictions. We measured two indices of firing variability: the ratio of the variance to the mean for the number of action potentials evoked by a constant stimulus, and the rate-normalized Coefficient of Variation (C_v) of the interspike interval distribution. Firing in virtually all V1 and MT neurons was nearly consistent with a completely random process (e.g., C_v ≈ 1). We tried to model this high variability by small, independent, and random EPSPs converging onto a leaky integrate-and-fire neuron (Knight, 1972). Both this and related models predicted very low firing variability ( C_v ≪ 1) for realistic EPSP depolarizations and membrane time constants. We also simulated a biophysically very detailed compartmental model of an anatomically reconstructed and physiologically characterized layer V cat pyramidal cell with passive dendrites and active soma. If independent, excitatory synaptic input fired the model cell at the high rates observed in monkey, the C_v and the variability in the number of spikes were both very low, in agreement with the integrate-and- fire models but in strong disagreement with the majority of our monkey data. The simulated cell only produced highly variable firing when Hodgkin-Huxley- like currents (I_(Na) and very strong I_(DR) were placed on the distal basal dendrites. Now the simulated neuron acted more as a millisecond-resolution detector of dendritic spike coincidences than as a temporal integrator, thereby increasing its bandwidth by an order of magnitude above traditional estimates. This hypothetical submillisecond coincidence detection mainly uses the cell's capacitive localization of very transient signals in thin dendrites. For millisecond-level events, different dendrites in the cell are electrically isolated from one another by dendritic capacitance, so that the cell can contain many independent computational units. This de-coupling occurs because charge takes time to equilibrate inside the cell, and can occur even in the presence of long membrane time constants. Simple approximations using cellular parameters (e.g., R_m, C_m, R_i, G_(Na) etc) can predict many effects of dendritic spiking, as confirmed by detailed compartmental simulations of the reconstructed pyramidal cell. Such expressions allow the extension of simulated results to untested parameter regimes. Coincidence-detection can occur by two methods: (1) Fast charge-equilization inside dendritic branches creates submillisecond EPSPs in those dendrites, so that individual branches can spike in response to coincidences among those fast EPSP's, (2) strong delayed-rectifier currents in dendrites allow the soma to fire only upon the submillisecond coincidence of two or more dendritic spikes. Such fast EPSPs and dendritic spikes produce somatic voltages consistent with intracellular observations. A simple measure of coincidence-detection "effectiveness" shows that cells containing these hypothetical dendritic spikes are far more sensitive to coincident EPSPs than to temporally separated ones, and suggest a conceptual mechanism for fast, parallel, nonlinear computations inside single cells. If a simplified model neuron acts as a coincidence-detector of single pulses, networks of such neurons can solve a simple but important perceptual problem-the "binding problem" -more easily and flexibly than traditional neurons can. In a simple toy model, different classes of coincidence-detecting neurons respond to different aspects of simple visual stimuli, for example shape and motion. The task of the population of neurons is to respond to multiple simultaneous stimuli while still identifying those neurons which respond to a particular stimulus. Because a coincidence-detecting neuron's output spike train retains some very precise information about the timing of its input spikes, all neurons which respond the same stimulus will produce output spikes with an above-random chance of coincidence, and hence will be easily distinguished from neurons responding to a different stimulus. This scheme uses the traditional average-rate code to represent each stimulus separately, while using precise single-spike times to multiplex information about the relation of different aspects of the stimuli to each other: In this manner the model's highly irregular spiking actually reflects information rather than noise.</p

Simple model for 1/f noise

We present a simple stochastic mechanism which generates pulse trains exhibiting a power law distribution of the pulse intervals and a $1/f^\alpha$ power spectrum over several decades at low frequencies with $\alpha$ close to one. The essential ingredient of our model is a fluctuating threshold which performs a Brownian motion. Whenever an increasing potential $V(t)$ hits the threshold, $V(t)$ is reset to the origin and a pulse is emitted. We show that if $V(t)$ increases linearly in time, the pulse intervals can be approximated by a random walk with multiplicative noise. Our model agrees with recent experiments in neurobiology and explains the high interpulse interval variability and the occurrence of $1/f^\alpha$ noise observed in cortical neurons and earthquake data.Comment: 4 pages, 4 figure

Response of Spiking Neurons to Correlated Inputs

The effect of a temporally correlated afferent current on the firing rate of a leaky integrate-and-fire (LIF) neuron is studied. This current is characterized in terms of rates, auto and cross-correlations, and correlation time scale $\tau_c$ of excitatory and inhibitory inputs. The output rate $\nu_{out}$ is calculated in the Fokker-Planck (FP) formalism in the limit of both small and large $\tau_c$ compared to the membrane time constant $\tau$ of the neuron. By simulations we check the analytical results, provide an interpolation valid for all $\tau_c$ and study the neuron's response to rapid changes in the correlation magnitude.Comment: 4 pages, 3 figure