Modeling spiking behavior of neurons with time-dependent Poisson processes.

Three kinds of interval statistics, as represented by the coefficient of variation, the skewness coefficient, and the correlation coefficient of consecutive intervals, are evaluated for three kinds of time-dependent Poisson processes: pulse regulated, sinusoidally regulated, and doubly stochastic. Among these three processes, the sinusoidally regulated and doubly stochastic Poisson processes, in the case when the spike rate varies slowly compared with the mean interval between spikes, are found to be consistent with the three statistical coefficients exhibited by data recorded from neurons in the prefrontal cortex of monkeys.

A cognitive and associative memory.

By introducing a physiological constraint in the auto-correlation matrix memory, the system is found to acquire an ability in cognition i.e. the ability to identify an input pattern by its proximity to any one of the stored memories. The physiological constraint here is that the attribute of a given synapse (i.e. excitatory or inhibitory) is uniquely determined by the neuron it belongs. Thus the synaptic coupling is generally not symmetric. Analytical and numerical analyses revealed that the present model retrieves a memory if an input pattern is close to the pattern of the stored memories; if not, it gives a clear response by going into a special mode where almost all neurons are in the same state in each time step. This uniform mode may be stationary or periodic, depending on whether or not the number of the excitatory neurons exceeds the number of inhibitory neurons.

The Ornstein-Uhlenbeck process does not reproduce spiking statistics of neurons in prefrontal cortex.

Cortical neurons of behaving animals generate irregular spike sequences. Recently, there has been a heated discussion about the origin of this irregularity. Softky and Koch (1993) pointed out the inability of standard single-neuron models to reproduce the irregularity of the observed spike sequences when the model parameters are chosen within a certain range that they consider to be plausible. Shadlen and Newsome (1994), on the other hand, demonstrated that a standard leaky integrate-and-fire model can reproduce the irregularity if the inhibition is balanced with the excitation. Motivated by this discussion, we attempted to determine whether the Ornstein-Uhlenbeck process, which is naturally derived from the leaky integration assumption, can in fact reproduce higher-order statistics of biological data. For this purpose, we consider actual neuronal spike sequences recorded from the monkey prefrontal cortex to calculate the higher-order statistics of the interspike intervals. Consistency of the data with the model is examined on the basis of the coefficient of variation and the skewness coefficient, which are, respectively, a measure of the spiking irregularity and a measure of the asymmetry of the interval distribution. It is found that the biological data are not consistent with the model if the model time constant assumes a value within a certain range believed to cover all reasonable values. This fact suggests that the leaky integrate-and-fire model with the assumption of uncorrelated inputs is not adequate to account for the spiking in at least some cortical neurons.

Temporally correlated inputs to leaky integrate-and-fire models can reproduce spiking statistics of cortical neurons.

There has been controversy over whether the standard neuro-spiking models are consistent with the irregular spiking of cortical neurons. In a previous study, we proposed examining this consistency on the basis of the high-order statistics of the inter-spike intervals (ISIs), as represented by the coefficient of variation and the skewness coefficient. In that study we found that a leaky integrate-and-fire model incorporating the assumption of temporally uncorrelated inputs is not able to account for the spiking data recorded from a monkey prefrontal cortex. In the present paper, we attempt to revise the neuro-spiking model so as to make it consistent with the biological data. Here we consider the correlation coefficient of consecutive ISIs, which was ignored in previous studies. Considering three statistical coefficients, we conclude that the leaky integrate-and-fire model with temporally correlated inputs does account for the biological data. The correlation time scale of the inputs needed to explain the biological statistics is found to be on the order of 100ms. We discuss possible origins of this input correlation.

Stimulus-dependent induction of long-term potentiation in CA1 area of the hippocampus: experiment and model.

In the CA1 area of the hippocampus, the magnitude of long-term potentiation (LTP) depends not only on the frequency of applied stimuli, but also on their number. With a slice preparation using extracellular recording in the hippocampus CA1 of a guinea pig, we investigate the magnitude of LTP induced by electrical stimuli with a range of frequencies and the number of applied stimuli. We find that the magnitude of the saturated potentiation obtained with periodic stimuli largely depends on the frequency and is insensitive to the number of stimuli, once the saturation level has been obtained. Furthermore, we investigated nonperiodic stimuli and found that the magnitude of the saturated potentiation is also sensitive to the statistical correlation between successive interstimulus intervals, even when their average frequency is held constant. In order to explain the LTP dependence on these various experimental parameters, we propose a simple mathematical model for the induction of LTP. In the model, an exponentially decaying element released as a result of previous stimuli is coupled with a new stimulus to act as the potentiation force, and the magnitude of potentiation is determined by this potentiation force. We can determine the decaying time constant of this hypothetical element as a model parameter by fitting the model to the experimental data. The time scale is found to be of the order of 200 msc. A molecular or cellular factor with this decaying time constant is likely to be induced in LTP induction.