Transmission across neocortical synapses depends on the frequency of presynaptic activity (Thomson & Deuchars, 1994). Interpyramidal synapses in layer V exhibit fast depression of synaptic transmission, while other types of synapses exhibit facilitation of transmission. To study the role of dynamic synapses in network computation, we propose a unified phenomenological model that allows computation of the postsynaptic current generated by both types of synapses when driven by an arbitrary pattern of action potential (AP) activity in a presynaptic population. Using this formalism, we analyze different regimes of synaptic transmission and demonstrate that dynamic synapses transmit different aspects of the presynaptic activity depending on the average presynaptic frequency. The model also allows for derivation of mean-field equations, which govern the activity of large, interconnected networks. We show that the dynamics of synaptic transmission results in complex sets of regular and irregular regimes of network activity.

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We analyze the dynamics of pulse coupled oscillators depending on strength and delay of the interaction. For two oscillators, we derive return maps for subsequent phase differences, and construct phase diagrams for a broad range of parameters. In-phase synchronization proves stable for inhibitory coupling and unstable for excitatory coupling if the delay is not zero. If the coupling strength is high, additional regimes with marginally stable synchronization are found. Simulations with Nӷ2 oscillators reveal a complex dynamics including spontaneous synchronization and desynchronization with excitatory coupling, and multistable phase clustering with inhibitory coupling. We simulate a continuous description of the system for N→ϱ oscillators and demonstrate that these phenomena are independent of the size of the system. Phase clustering is shown to relate to stability and basins of attraction of fixed points in the return map of two oscillators. Our findings are generic in the sense that they qualitatively are robust with respect to modeling details. We demonstrate this using also pulses of finite rise time and the more realistic model by Hodgkin and Huxley which exhibits multistable synchronization as predicted from our analysis as well.

Silberberg, G., M. Bethge, H. Markram, K. Pawelzik, and M. Tsodyks. Dynamics of population rate codes in ensembles of neocortical neurons. J Neurophysiol 91: 704 -709, 2004; 10.1152/jn.00415.2003. Information processing in neocortex can be very fast, indicating that neuronal ensembles faithfully transmit rapidly changing signals to each other. Apart from signal-to-noise issues, population codes are fundamentally constrained by the neuronal dynamics. In particular, the biophysical properties of individual neurons and collective phenomena may substantially limit the speed at which a graded signal can be represented by the activity of an ensemble. These implications of the neuronal dynamics are rarely studied experimentally. Here, we combine theoretical analysis and whole cell recordings to show that encoding signals in the variance of uncorrelated synaptic inputs to a neocortical ensemble enables faithful transmission of graded signals with high temporal resolution. In contrast, the encoding of signals in the mean current is subject to low-pass filtering.The firing rate of many neurons in the cortex is known to depend on various aspects of stimuli in a smooth way. While this finding suggests that the graded rate of an individual neuron is used to distinguish between different stimuli, it can be estimated only after a sufficiently large number of spikes have occurred. For this reason, reliable rate signals are necessarily slow if obtained from single neurons and hence cannot account for the rapid information processing observed in the cortex (Thorpe et al. 1996). In contrast, at the level of populations, this problem of signal-to-noise can be overcome such that the population rate of an ensemble of neurons (i.e., the average number of spikes in the population per time interval) can be estimated on a time scale that is even smaller than the interspike intervals of the individual neurons. If the neuronal responses are statistically independent from each other, the achievable time resolution will in fact depend only on the total number of neurons in the ensemble: the larger the ensemble, the higher the temporal precision with which the population rate can be estimated. Although it is possible to overcome the limitations of temporal precision due to noise by using an increasing number of neurons, there is another constraint on the speed of signal transmission caused by the neuronal dynamics: intrinsic properties of individual neurons like the membrane time constant and population effects like synchronization can severely limit the ability of neuronal ensembles to realize rapid rate codes (Knight 1972). Therefore we here investigate to what extent rapid transmission of graded rate signals between populations of cortical neurons rely on the encoding strategy due to the neuronal population dynamics.In contrast to the usual characterization of a signal by the temporally averaged mean and the variance components, we here consider the instantaneous distribution of input currents into the neurons of a functional ensemble at e...

It is shown that a topographic product P, first introduced in nonlinear dynamics, is an appropriate measure of the preservation or violation of neighborhood relations. It is sensitive to large-scale violations of the neighborhood ordering, but does not account for neighborhood ordering distortions caused by varying areal magnification factors. A vanishing value of the topographic product indicates a perfect neighborhood preservation; negative (positive) values indicate a too small (too large) output space dimensionality. In a simple example of maps from a 2D input space onto 1D, 2D, and 3D output spaces, it is demonstrated how the topographic product picks the correct output space dimensionality. In a second example, 19D speech data are mapped onto various output spaces and it is found that a 3D output space (instead of 2D) seems to be optimally suited to the data. This is an agreement with a recent speech recognition experiment on the same data set.