Stochasticity, spikes and decoding: sufficiency and utility of order statistics

Quantification and classification of neuronal responses in kernel-smoothed peristimulus time histograms

Peristimulus time histograms are a widespread form of visualizing neuronal responses. Kernel convolution methods transform these histograms into a smooth, continuous probability density function. This provides an improved estimate of a neuron's actual response envelope. We here develop a classifier, called the h-coefficient, to determine whether time-locked fluctuations in the firing rate of a neuron should be classified as a response or as random noise. Unlike previous approaches, the h-coefficient takes advantage of the more precise response envelope estimation provided by the kernel convolution method. The h-coefficient quantizes the smoothed response envelope and calculates the probability of a response of a given shape to occur by chance. We tested the efficacy of the h-coefficient in a large data set of Monte Carlo simulated smoothed peristimulus time histograms with varying response amplitudes, response durations, trial numbers, and baseline firing rates. Across all these conditions, the h-coefficient significantly outperformed more classical classifiers, with a mean false alarm rate of 0.004 and a mean hit rate of 0.494. We also tested the h-coefficient's performance in a set of neuronal responses recorded in humans. The algorithm behind the h-coefficient provides various opportunities for further adaptation and the flexibility to target specific parameters in a given data set. Our findings confirm that the h-coefficient can provide a conservative and powerful tool for the analysis of peristimulus time histograms with great potential for future development.

Spike generation estimated from stationary spike trains in a variety of neurons in vivo

To any model of brain function, the variability of neuronal spike firing is a problem that needs to be taken into account. Whereas the synaptic integration can be described in terms of the original Hodgkin-Huxley (H-H) formulations of conductance-based electrical signaling, the transformation of the resulting membrane potential into patterns of spike output is subjected to stochasticity that may not be captured with standard single neuron H-H models. The dynamics of the spike output is dependent on the normal background synaptic noise present in vivo, but the neuronal spike firing variability in vivo is not well studied. In the present study, we made long-term whole cell patch clamp recordings of stationary spike firing states across a range of membrane potentials from a variety of subcortical neurons in the non-anesthetized, decerebrated state in vivo. Based on the data, we formulated a simple, phenomenological model of the properties of the spike generation in each neuron that accurately captured the stationary spike firing statistics across all membrane potentials. The model consists of a parametric relationship between the mean and standard deviation of the inter-spike intervals, where the parameter is linearly related to the injected current over the membrane. This enabled it to generate accurate approximations of spike firing also under inhomogeneous conditions with input that varies over time. The parameters describing the spike firing statistics for different neuron types overlapped extensively, suggesting that the spike generation had similar properties across neurons.

Visual cortex combines a stimulus and an error-like signal with a proportion that is dependent on time, space, and stimulus contrast

Even though the visual cortex is one of the most studied brain areas, the neuronal code in this area is still not fully understood. In the literature, two codes are commonly hypothesized, namely stimulus and predictive (error) codes. Here, we examined whether and how these two codes can coexist in a neuron. To this end, we assumed that neurons could predict a constant stimulus across time or space, since this is the most fundamental type of prediction. Prediction was examined in time using electrophysiology and voltage-sensitive dye imaging in the supragranular layers in area 18 of the anesthetized cat, and in space using a computer model. The distinction into stimulus and error code was made by means of the orientation tuning of the recorded unit. The stimulus was constructed as such that a maximum response to the non-preferred orientation indicated an error signal, and the maximum response to the preferred orientation indicated a stimulus signal. We demonstrate that a single neuron combines stimulus and error-like coding. In addition, we observed that the duration of the error coding varies as a function of stimulus contrast. For low contrast the error-like coding was prolonged by around 60-100%. Finally, the combination of stimulus and error leads to a suboptimal free energy in a recent predictive coding model. We therefore suggest a straightforward modification that can be applied to the free energy model and other predictive coding models. Combining stimulus and error might be advantageous because the stimulus code enables a direct stimulus recognition that is free of assumptions whereas the error code enables an experience dependent inference of ambiguous and non-salient stimuli.

STDP allows fast rate-modulated coding with Poisson-like spike trains

Spike timing-dependent plasticity (STDP) has been shown to enable single neurons to detect repeatedly presented spatiotemporal spike patterns. This holds even when such patterns are embedded in equally dense random spiking activity, that is, in the absence of external reference times such as a stimulus onset. Here we demonstrate, both analytically and numerically, that STDP can also learn repeating rate-modulated patterns, which have received more experimental evidence, for example, through post-stimulus time histograms (PSTHs). Each input spike train is generated from a rate function using a stochastic sampling mechanism, chosen to be an inhomogeneous Poisson process here. Learning is feasible provided significant covarying rate modulations occur within the typical timescale of STDP (∼10–20 ms) for sufficiently many inputs (∼100 among 1000 in our simulations), a condition that is met by many experimental PSTHs. Repeated pattern presentations induce spike-time correlations that are captured by STDP. Despite imprecise input spike times and even variable spike counts, a single trained neuron robustly detects the pattern just a few milliseconds after its presentation. Therefore, temporal imprecision and Poisson-like firing variability are not an obstacle to fast temporal coding. STDP provides an appealing mechanism to learn such rate patterns, which, beyond sensory processing, may also be involved in many cognitive tasks.

In vivo neural responses to stimuli are known to have a lot of variability across trials. If the same number of spikes is emitted from trial to trial, the neuron is said to be reliable. If the timing of such spikes is roughly preserved across trials, the neuron is said to be precise. Here we demonstrate both analytically and numerically that the well-established Hebbian learning rule of spike-timing-dependent plasticity (STDP) can learn response patterns despite relatively low reliability (Poisson-like variability) and low temporal precision (10–20 ms). These features are in line with many experimental observations, in which a poststimulus time histogram (PSTH) is evaluated over multiple trials. In our model, however, information is extracted from the relative spike times between afferents without the need of an absolute reference time, such as a stimulus onset. Relevantly, recent experiments show that relative timing is often more informative than the absolute timing. Furthermore, the scope of application for our study is not restricted to sensory systems. Taken together, our results suggest a fine temporal resolution for the neural code, and that STDP is an appropriate candidate for encoding and decoding such activity.

Submillisecond firing synchrony between different subtypes of cortical interneurons connected chemically but not electrically

Synchronous firing is commonly observed in the brain, but its underlying mechanisms and neurobiological meaning remain debated. Most commonly, synchrony is attributed either to electrical coupling by gap junctions or to shared excitatory inputs. In the cerebral cortex and hippocampus, fast-spiking (FS) or somatostatin-containing (SOM) inhibitory interneurons are electrically coupled to same-type neighbors, and each subtype-specific network tends to fire in synchrony. Electrical coupling across subtypes is weak or absent, but SOM-FS and FS-FS pairs are often connected by inhibitory synapses. Theoretical studies suggest that purely inhibitory coupling can also promote synchrony; however, this has not been confirmed experimentally. We recorded from 74 pairs of electrically noncoupled layer 4 interneurons in mouse somatosensory cortex in vitro, and found that tonically depolarized FS-FS and SOM-FS pairs connected by unidirectional or bidirectional inhibitory synapses often fired within 1 ms of each other. Using a novel, jitter-based measure of synchrony, we found that synchrony correlated with inhibitory coupling strength. Importantly, synchrony was resistant to ionotropic glutamate receptors antagonists but was strongly reduced when GABA(A) receptors were blocked, confirming that in our experimental system IPSPs were both necessary and sufficient for synchrony. Submillisecond firing lags emerged in a computer simulation of pairs of spiking neurons, in which the only assumed interaction between neurons was by inhibitory synapses. We conclude that cortical interneurons are capable of synchronizing both within and across subtypes, and that submillisecond coordination of firing can arise by mutual synaptic inhibition alone, with neither shared inputs nor electrical coupling.