Complex evolution of spike patterns during burst propagation through feed-forward networks

Exact solutions for signal propagation along an excitable transmission line

A simple transmission line composed of pulse-coupled units is presented. The model captures the basic properties of excitable media with, in particular, the robust transmission of information via traveling wave solutions. For rectified linear units with a cut-off threshold, the model is exactly solvable and analytical results on propagation are presented. The ability to convey a nontrivial message is studied in detail.

Bistability, non-ergodicity, and inhibition in pairwise maximum-entropy models

Pairwise maximum-entropy models have been used in neuroscience to predict the activity of neuronal populations, given only the time-averaged correlations of the neuron activities. This paper provides evidence that the pairwise model, applied to experimental recordings, would produce a bimodal distribution for the population-averaged activity, and for some population sizes the second mode would peak at high activities, that experimentally would be equivalent to 90% of the neuron population active within time-windows of few milliseconds. Several problems are connected with this bimodality: 1. The presence of the high-activity mode is unrealistic in view of observed neuronal activity and on neurobiological grounds. 2. Boltzmann learning becomes non-ergodic, hence the pairwise maximum-entropy distribution cannot be found: in fact, Boltzmann learning would produce an incorrect distribution; similarly, common variants of mean-field approximations also produce an incorrect distribution. 3. The Glauber dynamics associated with the model is unrealistically bistable and cannot be used to generate realistic surrogate data. This bimodality problem is first demonstrated for an experimental dataset from 159 neurons in the motor cortex of macaque monkey. Evidence is then provided that this problem affects typical neural recordings of population sizes of a couple of hundreds or more neurons. The cause of the bimodality problem is identified as the inability of standard maximum-entropy distributions with a uniform reference measure to model neuronal inhibition. To eliminate this problem a modified maximum-entropy model is presented, which reflects a basic effect of inhibition in the form of a simple but non-uniform reference measure. This model does not lead to unrealistic bimodalities, can be found with Boltzmann learning, and has an associated Glauber dynamics which incorporates a minimal asymmetric inhibition.

Networks of interacting units are ubiquitous in various fields of biology; e.g. gene regulatory networks, neuronal networks, social structures. If a limited set of observables is accessible, maximum-entropy models provide a way to construct a statistical model for such networks, under particular assumptions. The pairwise maximum-entropy model only uses the first two moments among those observables, and can be interpreted as a network with only pairwise interactions. If correlations are on average positive, we here show that the maximum entropy distribution tends to become bimodal. In the application to neuronal activity this is a problem, because the bimodality is an artefact of the statistical model and not observed in real data. This problem could also affect other fields in biology. We here explain under which conditions bimodality arises and present a solution to the problem by introducing a collective negative feedback, corresponding to a modified maximum-entropy model. This result may point to the existence of a homeostatic mechanism active in the system that is not part of our set of observable units.

A reafferent and feed-forward model of song syntax generation in the Bengalese finch

Adult Bengalese finches generate a variable song that obeys a distinct and individual syntax. The syntax is gradually lost over a period of days after deafening and is recovered when hearing is restored. We present a spiking neuronal network model of the song syntax generation and its loss, based on the assumption that the syntax is stored in reafferent connections from the auditory to the motor control area. Propagating synfire activity in the HVC codes for individual syllables of the song and priming signals from the auditory network reduce the competition between syllables to allow only those transitions that are permitted by the syntax. Both imprinting of song syntax within HVC and the interaction of the reafferent signal with an efference copy of the motor command are sufficient to explain the gradual loss of syntax in the absence of auditory feedback. The model also reproduces for the first time experimental findings on the influence of altered auditory feedback on the song syntax generation, and predicts song- and species-specific low frequency components in the LFP. This study illustrates how sequential compositionality following a defined syntax can be realized in networks of spiking neurons.

Flexible traffic control of the synfire-mode transmission by inhibitory modulation: nonlinear noise reduction

Intermingled neural connections apparent in the brain make us wonder what controls the traffic of propagating activity in the brain to secure signal transmission without harmful crosstalk. Here, we reveal that inhibitory input but not excitatory input works as a particularly useful traffic controller because it controls the degree of synchrony of population firing of neurons as well as controlling the size of the population firing bidirectionally. Our dynamical system analysis reveals that the synchrony enhancement depends crucially on the nonlinear membrane potential dynamics and a hidden slow dynamical variable. Our electrophysiological study with rodent slice preparations show that the phenomenon happens in real neurons. Furthermore, our analysis with the Fokker-Planck equations demonstrates the phenomenon in a semianalytical manner.

Relating neuronal firing patterns to functional differentiation of cerebral cortex

It has been empirically established that the cerebral cortical areas defined by Brodmann one hundred years ago solely on the basis of cellular organization are closely correlated to their function, such as sensation, association, and motion. Cytoarchitectonically distinct cortical areas have different densities and types of neurons. Thus, signaling patterns may also vary among cytoarchitectonically unique cortical areas. To examine how neuronal signaling patterns are related to innate cortical functions, we detected intrinsic features of cortical firing by devising a metric that efficiently isolates non-Poisson irregular characteristics, independent of spike rate fluctuations that are caused extrinsically by ever-changing behavioral conditions. Using the new metric, we analyzed spike trains from over 1,000 neurons in 15 cortical areas sampled by eight independent neurophysiological laboratories. Analysis of firing-pattern dissimilarities across cortical areas revealed a gradient of firing regularity that corresponded closely to the functional category of the cortical area; neuronal spiking patterns are regular in motor areas, random in the visual areas, and bursty in the prefrontal area. Thus, signaling patterns may play an important role in function-specific cerebral cortical computation.

Neurons, or nerve cells in the brain, communicate with each other using stereotyped electric pulses, called spikes. It is believed that neurons convey information mainly through the frequency of the transmitted spikes, called the firing rate. In addition, neurons may communicate some information through the finer temporal patterns of the spikes. Neuronal firing patterns may depend on cellular organization, which varies among the regions of the brain, according to the roles they play, such as sensation, association, and motion. In order to examine the relationship among signals, structure, and function, we devised a metric to detect firing irregularity intrinsic and specific to individual neurons and analyzed spike sequences from over 1,000 neurons in 15 different cortical areas. Here we report two results of this study. First, we found that neurons exhibit stable firing patterns that can be characterized as “regular”, “random”, and “bursty”. Second, we observed a strong correlation between the type of signaling pattern exhibited by neurons in a given area and the function of that area. This suggests that, in addition to reflecting the cellular organization of the brain, neuronal signaling patterns may also play a role in specific types of neuronal computations.