A numerical model for Hodgkin-Huxley neural stimulus reconstruction

The information about a neural activity is encoded in a neural response and usually the underlying stimulus that triggers the activity is unknown. This paper presents a numerical solution to reconstruct stimuli from Hodgkin-Huxley neural responses while retrieving the neural dynamics. The stimulus is reconstructed by first retrieving the maximal conductances of the ion channels and then solving the Hodgkin-Huxley equations for the stimulus. The results show that the reconstructed stimulus is a good approximation of the original stimulus, while the retrieved the neural dynamics, which represent the voltage-dependent changes in the ion channels, help to understand the changes in neural biochemistry. As high non-linearity of neural dynamics renders analytical inversion of a neuron an arduous task, a numerical approach provides a local solution to the problem of stimulus reconstruction and neural dynamics retrieval

The impact of spike timing variability on the signal-encoding performance of neural spiking models

It remains unclear whether the variability of neuronal spike trains in vivo arises due to biological noise sources or represents highly precise encoding of temporally varying synaptic input signals. Determining the variability of spike timing can provide fundamental insights into the nature of strategies used in the brain to represent and transmit information in the form of discrete spike trains. In this study, we employ a signal estimation paradigm to determine how variability in spike timing affects encoding of random time-varying signals. We assess this for two types of spiking models: an integrate-and-fire model with random threshold and a more biophysically realistic stochastic ion channel model. Using the coding fraction and mutual information as information-theoretic measures, we quantify the efficacy of optimal linear decoding of random inputs from the model outputs and study the relationship between efficacy and variability in the output spike train. Our findings suggest that variability does not necessarily hinder signal decoding for the biophysically plausible encoders examined and that the functional role of spiking variability depends intimately on the nature of the encoder and the signal processing task; variability can either enhance or impede decoding performance

Detecting and Estimating Signals in Noisy Cable Structures, I: Neuronal Noise Sources

In recent theoretical approaches addressing the problem of neural coding, tools from statistical estimation and information theory have been applied to quantify the ability of neurons to transmit information through their spike outputs. These techniques, though fairly general, ignore the specific nature of neuronal processing in terms of its known biophysical properties. However, a systematic study of processing at various stages in a biophysically faithful model of a single neuron can identify the role of each stage in information transfer. Toward this end, we carry out a theoretical analysis of the information loss of a synaptic signal propagating along a linear, one-dimensional, weakly active cable due to neuronal noise sources along the way, using both a signal reconstruction and a signal detection paradigm. Here we begin such an analysis by quantitatively characterizing three sources of membrane noise: (1) thermal noise due to the passive membrane resistance, (2) noise due to stochastic openings and closings of voltage-gated membrane channels (Na^+ and K^+), and (3) noise due to random, background synaptic activity. Using analytical expressions for the power spectral densities of these noise sources, we compare their magnitudes in the case of a patch of membrane from a cortical pyramidal cell and explore their dependence on different biophysical parameters

Inferring Synaptic Structure in presence of Neural Interaction Time Scales

Biological networks display a variety of activity patterns reflecting a web of interactions that is complex both in space and time. Yet inference methods have mainly focused on reconstructing, from the network's activity, the spatial structure, by assuming equilibrium conditions or, more recently, a probabilistic dynamics with a single arbitrary time-step. Here we show that, under this latter assumption, the inference procedure fails to reconstruct the synaptic matrix of a network of integrate-and-fire neurons when the chosen time scale of interaction does not closely match the synaptic delay or when no single time scale for the interaction can be identified; such failure, moreover, exposes a distinctive bias of the inference method that can lead to infer as inhibitory the excitatory synapses with interaction time scales longer than the model's time-step. We therefore introduce a new two-step method, that first infers through cross-correlation profiles the delay-structure of the network and then reconstructs the synaptic matrix, and successfully test it on networks with different topologies and in different activity regimes. Although step one is able to accurately recover the delay-structure of the network, thus getting rid of any \textit{a priori} guess about the time scales of the interaction, the inference method introduces nonetheless an arbitrary time scale, the time-bin $dt$ used to binarize the spike trains. We therefore analytically and numerically study how the choice of $dt$ affects the inference in our network model, finding that the relationship between the inferred couplings and the real synaptic efficacies, albeit being quadratic in both cases, depends critically on $dt$ for the excitatory synapses only, whilst being basically independent of it for the inhibitory ones

Two-photon imaging and analysis of neural network dynamics

The glow of a starry night sky, the smell of a freshly brewed cup of coffee or the sound of ocean waves breaking on the beach are representations of the physical world that have been created by the dynamic interactions of thousands of neurons in our brains. How the brain mediates perceptions, creates thoughts, stores memories and initiates actions remains one of the most profound puzzles in biology, if not all of science. A key to a mechanistic understanding of how the nervous system works is the ability to analyze the dynamics of neuronal networks in the living organism in the context of sensory stimulation and behaviour. Dynamic brain properties have been fairly well characterized on the microscopic level of individual neurons and on the macroscopic level of whole brain areas largely with the help of various electrophysiological techniques. However, our understanding of the mesoscopic level comprising local populations of hundreds to thousands of neurons (so called 'microcircuits') remains comparably poor. In large parts, this has been due to the technical difficulties involved in recording from large networks of neurons with single-cell spatial resolution and near- millisecond temporal resolution in the brain of living animals. In recent years, two-photon microscopy has emerged as a technique which meets many of these requirements and thus has become the method of choice for the interrogation of local neural circuits. Here, we review the state-of-research in the field of two-photon imaging of neuronal populations, covering the topics of microscope technology, suitable fluorescent indicator dyes, staining techniques, and in particular analysis techniques for extracting relevant information from the fluorescence data. We expect that functional analysis of neural networks using two-photon imaging will help to decipher fundamental operational principles of neural microcircuits.Comment: 36 pages, 4 figures, accepted for publication in Reports on Progress in Physic

Synaptic Transmission: An Information-Theoretic Perspective

Here we analyze synaptic transmission from an information-theoretic perspective. We derive closed-form expressions for the lower-bounds on the capacity of a simple model of a cortical synapse under two explicit coding paradigms. Under the ``signal estimation'' paradigm, we assume the signal to be encoded in the mean firing rate of a Poisson neuron. The performance of an optimal linear estimator of the signal then provides a lower bound on the capacity for signal estimation. Under the ``signal detection'' paradigm, the presence or absence of the signal has to be detected. Performance of the optimal spike detector allows us to compute a lower bound on the capacity for signal detection. We find that single synapses (for empirically measured parameter values) transmit information poorly but significant improvement can be achieved with a small amount of redundancy.Comment: 7 pages, 4 figures, NIPS97 proceedings: neuroscience. Originally submitted to the neuro-sys archive which was never publicly announced (was 9809002