Relating neural dynamics to neural coding

Switch of encoding characteristics in single neurons by subthreshold and suprathreshold stimuli

Spike-triggered analysis is a statistical method used to elucidate encoding properties in neural systems by estimating the statistical structure of input stimulus preceding spikes. A recent numerical study suggested that the profile of the spike-triggered average (STA) changes depending on whether the mean input stimuli are subthreshold or suprathreshold. Here we analytically verify the difference between subthreshold STA and suprathreshold STA by using the spike response model (SRM). We show by moment expansion that the suprathreshold STA is proportional to the first derivative of the response kernel, and that the subthreshold STA is expressed by a linear combination of the response kernel and its first derivative. We verify whether the analytical results obtained from the SRM can be applied to a multicompartment model with Hodgkin-Huxley type dynamics.

Coding of information in limit cycle oscillators

Starting from a general description of noisy limit cycle oscillators, we derive from the Fokker-Planck equations the linear response of the instantaneous oscillator frequency to a time-varying external force. We consider the time series of zero crossings of the oscillator's phase and compute the mutual information between it and the driving force. A direct link is established between the phase response curve summarizing the oscillator dynamics and the ability of a limit cycle oscillator, such as a heart cell or neuron, to encode information in the timing of peaks in the oscillation.

Weighted spike-triggered average of a fluctuating stimulus yielding the phase response curve

We demonstrate that the phase response curve (PRC) can be reconstructed using a weighted spike-triggered average of an injected fluctuating input. The key idea is to choose the weight to be proportional to the magnitude of the fluctuation of the oscillatory period. Particularly, when a neuron exhibits random switching behavior between two bursting modes, two corresponding PRCs can be simultaneously reconstructed, even from the data of a single trial. This method offers an efficient alternative to the experimental investigation of oscillatory systems, without the need for detailed modeling.

Type-II phase resetting curve is optimal for stochastic synchrony

The phase-resetting curve (PRC) describes the response of a neural oscillator to small perturbations in membrane potential. Its usefulness for predicting the dynamics of weakly coupled deterministic networks has been well characterized. However, the inputs to real neurons may often be more accurately described as barrages of synaptic noise. Effective connectivity between cells may thus arise in the form of correlations between the noisy input streams. We use constrained optimization and perturbation methods to prove that the PRC shape determines susceptibility to synchrony among otherwise uncoupled noise-driven neural oscillators. PRCs can be placed into two general categories: type-I PRCs are non-negative, while type-II PRCs have a large negative region. Here we show that oscillators with type-II PRCs receiving common noisy input synchronize more readily than those with type-I PRCs.

Stochastic phase reduction for a general class of noisy limit cycle oscillators

We formulate a phase-reduction method for a general class of noisy limit cycle oscillators and find that the phase equation is parametrized by the ratio between time scales of the noise correlation and amplitude relaxation of the limit cycle. The equation naturally includes previously proposed and mutually exclusive phase equations as special cases. The validity of the theory is numerically confirmed. Using the method, we reveal how noise and its correlation time affect limit cycle oscillations.

Temporal precision of spike response to fluctuating input in pulse-coupled networks of oscillating neurons

A single neuron is known to generate almost identical spike trains when the same fluctuating input is repeatedly applied. Here, we study the reliability of spike firing in a pulse-coupled network of oscillator neurons receiving fluctuating inputs. We can study the precise responses of the network as synchronization between uncoupled copies of the network by a common noisy input. To study the noise-induced synchronization between networks, we derive a self-consistent equation for the distribution of spike-time differences between the networks. Solving this equation, we elucidate how the spike precision changes as a function of the coupling strength.

Spike-triggered averages for passive and resonant neurons receiving filtered excitatory and inhibitory synaptic drive

A path-integral approach is developed for the analysis of spike-triggered average quantities in neurons with voltage-gated subthreshold currents. Using a linearization procedure to reduce the models to the generalized integrate-and-fire form, analytical expressions are obtained in an experimentally relevant limit of fluctuation-driven firing. The influences of voltage-gated channels as well as excitatory and inhibitory synaptic filtering are shown to affect significantly the neuronal dynamics prior to the spike. Analytical forms are given for all relevant physiological quantities, such as the mean voltage triggered to the spike, mean current flowing through voltage-gated channels, and the mean excitatory and inhibitory conductance waveforms prior to a spike. The mathematical results are shown to be in good agreement with numerical simulations of the underlying nonlinear conductance-based models. The method promises to provide a useful analytical tool for the prediction and interpretation of the temporal structure of spike-triggered averages measured experimentally.

The h channel mediates location dependence and plasticity of intrinsic phase response in rat hippocampal neurons

The presence of phenomenological inductances in neuronal membrane has been known for more than one-half a century. Despite this, the dramatic contributions of such inductive elements to the amplitude and, especially, phase of neuronal impedance, and their roles in modulating temporal dynamics of neuronal responses have surprisingly remained unexplored. In this study, we demonstrate that the h channel contributes a location-dependent and plastic phenomenological inductive component to the input impedance of CA1 pyramidal neurons. Specifically, we show that the h channels introduce an apparent negative delay in the local voltage response of these neurons with respect to the injected current within the theta frequency range. The frequency range and the extent of this lead expand with increases in h current either through hyperpolarization, or with increasing distance of dendritic location from the soma. We also demonstrate that a spatially widespread increase in this inductive phase component accompanies long-term potentiation. Finally, using impedance analysis, we show that both location and activity dependence of intrinsic phase response are attributable not to changes in a capacitive or a leak component, but to changes in h-channel properties. Our results suggest that certain voltage-gated ion channels can differentially regulate internal time delays within neurons, thus providing them with an independent control mechanism in temporal coding of neuronal information. Our analyses and results also establish impedance as a powerful measure of intrinsic dynamics and excitability, given that it quantifies temporal relationships among signals and excitability as functions of input frequency.