Improved lower bound for the mutual information between signal and neural spike count

The steady state and response to a periodic stimulation of the firing rate for a theta neuron with correlated noise

The stochastic activity of neurons is caused by various sources of correlated fluctuations and can be described in terms of simplified, yet biophysically grounded, integrate-and-fire models. One paradigmatic model is the quadratic integrate-and-fire model and its equivalent phase description by the theta neuron. Here we study the theta neuron model driven by a correlated Ornstein-Uhlenbeck noise and by periodic stimuli. We apply the matrix-continued-fraction method to the associated Fokker-Planck equation to develop an efficient numerical scheme to determine the stationary firing rate as well as the stimulus-induced modulation of the instantaneous firing rate. For the stationary case, we identify the conditions under which the firing rate decreases or increases by the effect of the colored noise and compare our results to existing analytical approximations for limit cases. For an additional periodic signal we demonstrate how the linear and nonlinear response terms can be computed and report resonant behavior for some of them. We extend the method to the case of two periodic signals, generally with incommensurable frequencies, and present a particular case for which a strong mixed response to both signals is observed, i.e. where the response to the sum of signals differs significantly from the sum of responses to the single signals. We provide Python code for our computational method: https://github.com/jannikfranzen/theta_neuron .

Critical current for giant Fano factor in neural models with bistable firing dynamics and implications for signal transmission

Bistability in the firing rate is a prominent feature in different types of neurons as well as in neural networks. We show that for a constant input below a critical value, such bistability can lead to a giant spike-count diffusion. We study the transmission of a periodic signal and demonstrate that close to the critical bias current, the signal-to-noise ratio suffers a sharp increase, an effect that can be traced back to the giant diffusion and large Fano factor.

Information processing in tree networks of excitable elements

We study the collective response of small random tree networks of diffusively coupled excitable elements to stimuli applied to leaf nodes. Such networks model the morphology of certain sensory neurons that possess branched myelinated dendrites with excitable nodes of Ranvier at every branch point and at leaf nodes. Leaf nodes receive random inputs along with a stimulus and initiate action potentials that propagate through the tree. We quantify the collective response registered at the central node using mutual information. We show that in the strong-coupling limit, the statistics of the number of nodes and leaves determines the mutual information. At the same time, the collective response is insensitive to particular node connectivity and distribution of stimulus over leaf nodes. However, for intermediate coupling, the mutual information may strongly depend on the stimulus distribution among leaf nodes. We identify a mechanism behind the competition of leaf nodes that leads to nonmonotonous dependence of mutual information on coupling strength. We show that a localized stimulus given to a tree branch can be occluded by the background firing of unstimulated branches, thus suppressing mutual information. Nonetheless, the mutual information can be enhanced by a proper stimulus localization and tuning of coupling strength.

Information filtering by coincidence detection of synchronous population output: analytical approaches to the coherence function of a two-stage neural system

Information about time-dependent sensory stimuli is encoded in the activity of neural populations; distinct aspects of the stimulus are read out by different types of neurons: while overall information is perceived by integrator cells, so-called coincidence detector cells are driven mainly by the synchronous activity in the population that encodes predominantly high-frequency content of the input signal (high-pass information filtering). Previously, an analytically accessible statistic called the partial synchronous output was introduced as a proxy for the coincidence detector cell's output in order to approximate its information transmission. In the first part of the current paper, we compare the information filtering properties (specifically, the coherence function) of this proxy to those of a simple coincidence detector neuron. We show that the latter's coherence function can indeed be well-approximated by the partial synchronous output with a time scale and threshold criterion that are related approximately linearly to the membrane time constant and firing threshold of the coincidence detector cell. In the second part of the paper, we propose an alternative theory for the spectral measures (including the coherence) of the coincidence detector cell that combines linear-response theory for shot-noise driven integrate-and-fire neurons with a novel perturbation ansatz for the spectra of spike-trains driven by colored noise. We demonstrate how the variability of the synaptic weights for connections from the population to the coincidence detector can shape the information transmission of the entire two-stage system.

Information processing in the LGN: a comparison of neural codes and cell types

To understand how anatomy and physiology allow an organism to perform its function, it is important to know how information that is transmitted by spikes in the brain is received and encoded. A natural question is whether the spike rate alone encodes the information about a stimulus (rate code), or additional information is contained in the temporal pattern of the spikes (temporal code). Here we address this question using data from the cat Lateral Geniculate Nucleus (LGN), which is the visual portion of the thalamus, through which visual information from the retina is communicated to the visual cortex. We analyzed the responses of LGN neurons to spatially homogeneous spots of various sizes with temporally random luminance modulation. We compared the Firing Rate with the Shannon Information Transmission Rate , which quantifies the information contained in the temporal relationships between spikes. We found that the behavior of these two rates can differ quantitatively. This suggests that the energy used for spiking does not translate directly into the information to be transmitted. We also compared Firing Rates with Information Rates for X-ON and X-OFF cells. We found that, for X-ON cells the Firing Rate and Information Rate often behave in a completely different way, while for X-OFF cells these rates are much more highly correlated. Our results suggest that for X-ON cells a more efficient "temporal code" is employed, while for X-OFF cells a straightforward "rate code" is used, which is more reliable and is correlated with energy consumption.

Multiplicative noise is beneficial for the transmission of sensory signals in simple neuron models

We study simple integrate-and-fire type models with multiplicative noise and consider the transmission of a weak and slow signal, i.e. a signal that evokes a small modulation of the instantaneous firing rate on time scales that are much larger than the membrane time scale and the mean interspike interval. The specific question of interest is whether and how the state-dependence of the noise can be optimized with respect to information transmission. First, in a simple model in which the noise intensity varies linearly with the state variable, we show analytically that multiplicative fluctuations may benefit the signal transfer and we elucidate the mechanism for this improvement. In a conductance-based integrate-and-fire model with synaptically filtered shot-noise input, we show by means of extended numerical simulations that also in a biophysically more relevant situation, multiplicative noise can enhance the signal-to-noise ratio. Our results shed light on a so far unexplored aspect of stochastic signal transmission in neural systems.