Stefano Panzeri

Extracting information from neuronal populations: information theory and decoding approaches.

To a large extent, progress in neuroscience has been driven by the study of single-cell responses averaged over several repetitions of stimuli or behaviours. However,the brain typically makes decisions based on single events by evaluating the activity of large neuronal populations. Therefore, to further understand how the brain processes information, it is important to shift from a single-neuron, multiple-trial framework to multiple-neuron, single-trial methodologies. Two related approaches — decoding and information theory — can be used to extract single-trial information from the activity of neuronal populations. Such population analysis can give us more information about how neurons encode stimulus features than traditional single-cell studies.

The Role of Spike Timing in the Coding of Stimulus Location in Rat Somatosensory Cortex

Although the timing of single spikes is known to code for time-varying features of a sensory stimulus, it remains unclear whether time is also exploited in the neuronal coding of the spatial structure of the environment, where nontemporal stimulus features are fundamental. This report demonstrates that, in the whisker representation of rat cortex, precise spike timing of single neurons increases the information transmitted about stimulus location by 44%, compared to that transmitted only by the total number of spikes. Crucial to this code is the timing of the first spike after whisker movement. Complex, single neuron spike patterns play a smaller, synergistic role. Timing permits very few spikes to transmit high quantities of information about a behaviorally significant, spatial stimulus.

Spike-Phase Coding Boosts and Stabilizes Information Carried by Spatial and Temporal Spike Patterns

Several neural codes have been proposed in order to explain how neurons encode sensory information. Here we tested the hypothesis that different codes might be employed concurrently and provide complementary stimulus information. Quantifying the information encoded about natural sounds in the auditory cortex of alert animals, we found that temporal spike-train patterns and spatial populations were both highly informative. However, the relative phase of slow ongoing rhythms at which these (temporal or population) responses occurred provided much additional and complementary information. Such nested codes combining spike-train patterns with the phase of firing were not only most informative, but also most robust to sensory noise added to the stimulus. Our findings suggest that processing in sensory cortices could rely on the concurrent use of several codes that combine information across different spatiotemporal scales. In addition, they propose a role of slow cortical rhythms in stabilizing sensory representations by reducing effects of noise.

Sensory neural codes using multiplexed temporal scales

Determining how neuronal activity represents sensory information is central for understanding perception. Recent work shows that neural responses at different timescales can encode different stimulus attributes, resulting in a temporal multiplexing of sensory information. Multiplexing increases the encoding capacity of neural responses, enables disambiguation of stimuli that cannot be discriminated at a single response timescale, and makes sensory representations stable to the presence of variability in the sensory world. Thus, as we discuss here, temporal multiplexing could be a key strategy used by the brain to form an information-rich and stable representation of the environment.

Low-Frequency Local Field Potentials and Spikes in Primary Visual Cortex Convey Independent Visual Information

Local field potentials (LFPs) reflect subthreshold integrative processes that complement spike train measures. However, little is yet known about the differences between how LFPs and spikes encode rich naturalistic sensory stimuli. We addressed this question by recording LFPs and spikes from the primary visual cortex of anesthetized macaques while presenting a color movie. We then determined how the power of LFPs and spikes at different frequencies represents the visual features in the movie. We found that the most informative LFP frequency ranges were 1–8 and 60–100 Hz. LFPs in the range of 12–40 Hz carried little information about the stimulus, and may primarily reflect neuromodulatory inputs. Spike power was informative only at frequencies <12 Hz. We further quantified “signal correlations” (correlations in the trial-averaged power response to different stimuli) and “noise correlations” (trial-by-trial correlations in the fluctuations around the average) of LFPs and spikes recorded from the same electrode. We found positive signal correlation between high-gamma LFPs (60–100 Hz) and spikes, as well as strong positive signal correlation within high-gamma LFPs, suggesting that high-gamma LFPs and spikes are generated within the same network. LFPs <24 Hz shared strong positive noise correlations, indicating that they are influenced by a common source, such as a diffuse neuromodulatory input. LFPs <40 Hz showed very little signal and noise correlations with LFPs >40 Hz and with spikes, suggesting that low-frequency LFPs reflect neural processes that in natural conditions are fully decoupled from those giving rise to spikes and to high-gamma LFPs.

The upward bias in measures of information derived from limited data samples

Extracting information measures from limited experimental samples, such as those normally available when using data recorded in vivo from mammalian cortical neurons, is known to be plagued by a systematic error, which tends to bias the estimate upward. We calculate here the average of the bias, under certain conditions, as an asymptotic expansion in the inverse of the size of the data sample. The result agrees with numerical simulations, and is applicable, as an additive correction term, to measurements obtained under such conditions. Moreover, we discuss the implications for measurements obtained through other usual procedures.

Phase-of-Firing Coding of Natural Visual Stimuli in Primary Visual Cortex

We investigated the hypothesis that neurons encode rich naturalistic stimuli in terms of their spike times relative to the phase of ongoing network fluctuations rather than only in terms of their spike count. We recorded local field potentials (LFPs) and multiunit spikes from the primary visual cortex of anaesthetized macaques while binocularly presenting a color movie. We found that both the spike counts and the low-frequency LFP phase were reliably modulated by the movie and thus conveyed information about it. Moreover, movie periods eliciting higher firing rates also elicited a higher reliability of LFP phase across trials. To establish whether the LFP phase at which spikes were emitted conveyed visual information that could not be extracted by spike rates alone, we compared the Shannon information about the movie carried by spike counts to that carried by the phase of firing. We found that at low LFP frequencies, the phase of firing conveyed 54% additional information beyond that conveyed by spike counts. The extra information available in the phase of firing was crucial for the disambiguation between stimuli eliciting high spike rates of similar magnitude. Thus, phase coding may allow primary cortical neurons to represent several effective stimuli in an easily decodable format.

Modelling and analysis of local field potentials for studying the function of cortical circuits

The past decade has witnessed a renewed interest in cortical local field potentials (LFPs) — that is, extracellularly recorded potentials with frequencies of up to ∼500 Hz. This is due to both the advent of multielectrodes, which has enabled recording of LFPs at tens to hundreds of sites simultaneously, and the insight that LFPs offer a unique window into key integrative synaptic processes in cortical populations. However, owing to its numerous potential neural sources, the LFP is more difficult to interpret than are spikes. Careful mathematical modelling and analysis are needed to take full advantage of the opportunities that this signal offers in understanding signal processing in cortical circuits and, ultimately, the neural basis of perception and cognition.

Correlations and the encoding of information in the nervous system

Is the information transmitted by an ensemble of neurons determined solely by the number of spikes fired by each cell, or do correlations in the emission of action potentials also play a significant role? We derive a simple formula which enables this question to be answered rigorously for short time–scales. The formula quantifies the corrections to the instantaneous information rate which result from correlations in spike emission between pairs of neurons. The mutual information that the ensemble of neurons conveys about external stimuli can thus be broken down into firing rate and correlation components. This analysis provides fundamental constraints upon the nature of information coding, showing that over short time–scales, correlations cannot dominate information representation, that stimulus–independent correlations may lead to synergy (where the neurons together convey more information than they would if they were considered independently), but that only certain combinations of the different sources of correlation result in significant synergy rather than in redundancy or in negligible effects. This analysis leads to a new quantification procedure which is directly applicable to simultaneous multiple neuron recordings.

The Neurophysiology of Backward Visual Masking: Information Analysis

Backward masking can potentially provide evidence of the time needed for visual processing, a fundamental constraint that must be incorporated into computational models of vision. Although backward masking has been extensively used psychophysically, there is little direct evidence for the effects of visual masking on neuronal responses. To investigate the effects of a backward masking paradigm on the responses of neurons in the temporal visual cortex, we have shown that the response of the neurons is interrupted by the mask. Under conditions when humans can just identify the stimulus, with stimulus onset asynchronies (SOA) of 20 msec, neurons in macaques respond to their best stimulus for approximately 30 msec. We now quantify the information that is available from the responses of single neurons under backward masking conditions when two to six faces were shown. We show that the information available is greatly decreased as the mask is brought closer to the stimulus. The decrease is more marked than the decrease in firing rate because it is the selective part of the firing that is especially attenuated by the mask, not the spontaneous firing, and also because the neuronal response is more variable at short SOAs. However, even at the shortest SOA of 20 msec, the information available is on average 0.1 bits. This compares to 0.3 bits with only the 16-msec target stimulus shown and a typical value for such neurons of 0.4 to 0.5 bits with a 500-msec stimulus. The results thus show that considerable information is available from neuronal responses even under backward masking conditions that allow the neurons to have their main response in 30 msec. This provides evidence for how rapid the processing of visual information is in a cortical area and provides a fundamental constraint for understanding how cortical information processing operates.