Representation of Dynamical Stimuli in Populations of Threshold Neurons

Many sensory or cognitive events are associated with dynamic current modulations in cortical neurons. This raises an urgent demand for tractable model approaches addressing the merits and limits of potential encoding strategies. Yet, current theoretical approaches addressing the response to mean- and variance-encoded stimuli rarely provide complete response functions for both modes of encoding in the presence of correlated noise. Here, we investigate the neuronal population response to dynamical modifications of the mean or variance of the synaptic bombardment using an alternative threshold model framework. In the variance and mean channel, we provide explicit expressions for the linear and non-linear frequency response functions in the presence of correlated noise and use them to derive population rate response to step-like stimuli. For mean-encoded signals, we find that the complete response function depends only on the temporal width of the input correlation function, but not on other functional specifics. Furthermore, we show that both mean- and variance-encoded signals can relay high-frequency inputs, and in both schemes step-like changes can be detected instantaneously. Finally, we obtain the pairwise spike correlation function and the spike triggered average from the linear mean-evoked response function. These results provide a maximally tractable limiting case that complements and extends previous results obtained in the integrate and fire framework

Motoneuron membrane potentials follow a time inhomogeneous jump diffusion process

Stochastic leaky integrate-and-fire models are popular due to their simplicity and statistical tractability. They have been widely applied to gain understanding of the underlying mechanisms for spike timing in neurons, and have served as building blocks for more elaborate models. Especially the Ornstein–Uhlenbeck process is popular to describe the stochastic fluctuations in the membrane potential of a neuron, but also other models like the square-root model or models with a non-linear drift are sometimes applied. Data that can be described by such models have to be stationary and thus, the simple models can only be applied over short time windows. However, experimental data show varying time constants, state dependent noise, a graded firing threshold and time-inhomogeneous input. In the present study we build a jump diffusion model that incorporates these features, and introduce a firing mechanism with a state dependent intensity. In addition, we suggest statistical methods to estimate all unknown quantities and apply these to analyze turtle motoneuron membrane potentials. Finally, simulated and real data are compared and discussed. We find that a square-root diffusion describes the data much better than an Ornstein–Uhlenbeck process with constant diffusion coefficient. Further, the membrane time constant decreases with increasing depolarization, as expected from the increase in synaptic conductance. The network activity, which the neuron is exposed to, can be reasonably estimated to be a threshold version of the nerve output from the network. Moreover, the spiking characteristics are well described by a Poisson spike train with an intensity depending exponentially on the membrane potential

Spike-Timing-Based Computation in Sound Localization

Spike timing is precise in the auditory system and it has been argued that it conveys information about auditory stimuli, in particular about the location of a sound source. However, beyond simple time differences, the way in which neurons might extract this information is unclear and the potential computational advantages are unknown. The computational difficulty of this task for an animal is to locate the source of an unexpected sound from two monaural signals that are highly dependent on the unknown source signal. In neuron models consisting of spectro-temporal filtering and spiking nonlinearity, we found that the binaural structure induced by spatialized sounds is mapped to synchrony patterns that depend on source location rather than on source signal. Location-specific synchrony patterns would then result in the activation of location-specific assemblies of postsynaptic neurons. We designed a spiking neuron model which exploited this principle to locate a variety of sound sources in a virtual acoustic environment using measured human head-related transfer functions. The model was able to accurately estimate the location of previously unknown sounds in both azimuth and elevation (including front/back discrimination) in a known acoustic environment. We found that multiple representations of different acoustic environments could coexist as sets of overlapping neural assemblies which could be associated with spatial locations by Hebbian learning. The model demonstrates the computational relevance of relative spike timing to extract spatial information about sources independently of the source signal