Non-cortical - precise spike timing may matter

Predicting Every Spike: A Model for the Responses of Visual Neurons

Abstract: In the early visual system, neuronal responses can be extremely precise. Under a wide range of stimuli, cells in the retina and thalamus fire spikes very reproducibly, often with millisecond precision on subsequent stimulus repeats. Here we develop a mathematical description of the firing process that, given the recent visual input, accurately predicts the timing of individual spikes. The formalism is successful in matching the spike trains from retinal ganglion cells in salamander, rabbit, and cat, as well as from lateral geniculate nucleus neurons in cat. It adapts to many different response types, from very precise to highly variable. The accuracy of the model allows a compact description of how these neurons encode the visual stimulus.

Cortical - precise spike timing matters much less

Sensitivity to perturbations in vivo implies high noise and suggests rate coding in cortex

Abstract: It is well known that neural activity exhibits variability, in the sense that identical sensory stimuli produce different responses1, 2, 3, but it has been difficult to determine what this variability means. Is it noise, or does it carry important information—about, for example, the internal state of the organism? Here we address this issue from the bottom up, by asking whether small perturbations to activity in cortical networks are amplified. Based on in vivo whole-cell patch-clamp recordings in rat barrel cortex, we find that a perturbation consisting of a single extra spike in one neuron produces approximately 28 additional spikes in its postsynaptic targets. We also show, using simultaneous intra- and extracellular recordings, that a single spike in a neuron produces a detectable increase in firing rate in the local network. Theoretical analysis indicates that this amplification leads to intrinsic, stimulus-independent variations in membrane potential of the order of ±2.2–4.5 mV—variations that are pure noise, and so carry no information at all. Therefore, for the brain to perform reliable computations, it must either use a rate code, or generate very large, fast depolarizing events, such as those proposed by the theory of synfire chains4, 5. However, in our in vivo recordings, we found that such events were very rare. Our findings are thus consistent with the idea that cortex is likely to use primarily a rate code.

Large-scale model of mammalian thalamocortical systems

Quote: Each Neuron Matters. Unlike the real brain, where there are many sources of sensory input and neuronal noise, the model exhibited self-sustained activity autonomously in a noiseless environment. To investigate whether the activity is chaotic, we tested for the major hallmark of chaos — the sensitivity of the system to a small perturbation of initial conditions, i.e., the ‘‘butterf ly effect’’: Can one spike make a difference? That is, can the state of the entire activity pattern be changed by a firing of a single neuron? In Fig. 5 we show two traces of total electrical activity (the sum of local-field potentials at every cortical location; see SI Appendix), starting from the same initial conditions with the only difference being an extra spike of one pyramidal neuron in layer 2/3 of the frontal cortex (manually introduced). Initially, the traces look similar, but after just a few hundred milliseconds, they diverge and result in completely different global activity patterns. In Fig. 5 Lower, we show the difference in the spike rastergrams. As one can see, the extra spike triggered an avalanche of extra spikes (blue dots) or missed spikes (red dots) that eventually spread over the entire network and changed the activity of every neuron.

Abstract: The understanding of the structural and dynamic complexity of mammalian brains is greatly facilitated by computer simulations. We present here a detailed large-scale thalamocortical model based on experimental measures in several mammalian species. The model spans three anatomical scales. (i) It is based on global (white-matter) thalamocortical anatomy obtained by means of diffusion tensor imaging (DTI) of a human brain. (ii) It includes multiple thalamic nuclei and six-layered cortical microcircuitry based on in vitro labeling and three-dimensional reconstruction of single neurons of cat visual cortex. (iii) It has 22 basic types of neurons with appropriate laminar distribution of their branching dendritic trees. The model simulates one million multicompartmental spiking neurons calibrated to reproduce known types of responses recorded in vitro in rats. It has almost half a billion synapses with appropriate receptor kinetics, short-term plasticity, and long-term dendritic spike-timing-dependent synaptic plasticity (dendritic STDP). The model exhibits behavioral regimes of normal brain activity that were not explicitly built-in but emerged spontaneously as the result of interactions among anatomical and dynamic processes. We describe spontaneous activity, sensitivity to changes in individual neurons, emergence of waves and rhythms, and functional connectivity on different scales.

Theoretical analysis of rate vs temporal code

Distortion of neural signals by spike coding

Quote: Despite the somewhat misleading title, this paper presents a theoretical analysis of the rate vs temporal code question using a channel model for spiking neurons. The models include properties of the encoder and decoder, the inclusion of the latter is the key idea here. The analysis suggests that there is no simple answer to the coding question but rather operating regimes that are dictated by task requirements and biophysical properties of neurons, such as bandwidth and jitter, as well as the fundamental noise due to the quantization process. It is all about tradeoffs!

Abstract: Analog neural signals must be converted into spike trains for transmission over electrically leaky axons. This spike encoding and subsequent decoding leads to distortion. We quantify this distortion by deriving approximate expressions for the mean square error between the inputs and outputs of a spiking link. We use integrate-and-fire and Poisson encoders to convert naturalistic stimuli into spike trains and spike count and inte-rspike interval decoders to generate reconstructions of the stimulus. The distortion expressions enable us to compare these spike coding schemes over a large parameter space. We verify that the integrate-and-fire encoder is more effective than the Poisson encoder. The disparity between the two encoders diminishes as the stimulus coefficient of variation (CV) increases, at which point, the variability attributed to the stimulus overwhelms the variability attributed to Poisson statistics. When the stimulus CV is small, the interspike interval decoder is superior, as the distortion resulting from spike count decoding is dominated by a term that is attributed to the discrete nature of the spike count. In this regime, additive noise has a greater impact on the interspike interval decoder than the spike count decoder. When the stimulus CV is large, the average signal excursion is much larger than the quantization step size, and spike count decoding is superior.