In many areas of the brain, neural spiking activity covaries with features of the external world, such as sensory stimuli or an animal's movement. Experimental findings suggest that the variability of neural activity changes over time and may provide information about the external world beyond the information provided by the average neural activity. To flexibly track time-varying neural response properties, we developed a dynamic model with Conway-Maxwell Poisson (CMP) observations. The CMP distribution can flexibly describe firing patterns that are both under- and overdispersed relative to the Poisson distribution. Here we track parameters of the CMP distribution as they vary over time. Using simulations, we show that a normal approximation can accurately track dynamics in state vectors for both the centering and shape parameters (λ and ν). We then fit our model to neural data from neurons in primary visual cortex, "place cells" in the hippocampus, and a speed-tuned neuron in the anterior pretectal nucleus. We find that this method outperforms previous dynamic models based on the Poisson distribution. The dynamic CMP model provides a flexible framework for tracking time-varying non-Poisson count data and may also have applications beyond neuroscience.

Theories of efficient coding propose that the auditory system is optimized for the statistical structure of natural sounds, yet the transformations underlying optimal acoustic representations are not well understood. Using a database of natural sounds including human speech and a physiologically-inspired auditory model, we explore the consequences of peripheral (cochlear) and mid-level (auditory midbrain) filter tuning transformations on the representation of natural sound spectra and modulation statistics. Whereas Fourier-based sound decompositions have constant time-frequency resolution at all frequencies, cochlear and auditory midbrain filters bandwidths increase proportional to the filter center frequency. This form of bandwidth scaling produces a systematic decrease in spectral resolution and increase in temporal resolution with increasing frequency. Here we demonstrate that cochlear bandwidth scaling produces a frequency-dependent gain that counteracts the tendency of natural sound power to decrease with frequency, resulting in a whitened output representation. Similarly, bandwidth scaling in mid-level auditory filters further enhances the representation of natural sounds by producing a whitened modulation power spectrum (MPS) with higher modulation entropy than both the cochlear outputs and the conventional Fourier MPS. These findings suggest that the tuning characteristics of the peripheral and mid-level auditory system together produce a whitened output representation in three dimensions (frequency, temporal and spectral modulation) that reduces redundancies and allows for a more efficient use of neural resources. This hierarchical multi-stage tuning strategy is thus likely optimized to extract available information and may underlies perceptual sensitivity to natural sounds.

Modern neural recording techniques allow neuroscientists to observe the spiking activity of many neurons simultaneously. Although previous work has illustrated how activity within and between known populations of neurons can be summarized by low-dimensional latent vectors, in many cases what determines a unique population may be unclear. Neurons differ in their anatomical location, but also, in their cell types and response properties. Moreover, multiple distinct populations may not be well described by a single low-dimensional, linear representation.To tackle these challenges, we develop a clustering method based on a mixture of dynamic Poisson factor analyzers (DPFA) model, with the number of clusters treated as an unknown parameter. To do the analysis of DPFA model, we propose a novel Markov chain Monte Carlo (MCMC) algorithm to efficiently sample its posterior distribution. Validating our proposed MCMC algorithm with simulations, we find that it can accurately recover the true clustering and latent states and is insensitive to the initial cluster assignments. We then apply the proposed mixture of DPFA model to multi-region experimental recordings, where we find that the proposed method can identify novel, reliable clusters of neurons based on their activity, and may, thus, be a useful tool for neural data analysis.

Synapses change on multiple timescales, ranging from milliseconds to minutes, due to a combination of both short- and long-term plasticity. Here we develop an extension of the common generalized linear model to infer both short- and long-term changes in the coupling between a pre- and postsynaptic neuron based on observed spiking activity. We model short-term synaptic plasticity using additive effects that depend on the presynaptic spike timing, and we model long-term changes in both synaptic weight and baseline firing rate using point process adaptive smoothing. Using simulations, we first show that this model can accurately recover time-varying synaptic weights (1) for both depressing and facilitating synapses, (2) with a variety of long-term changes (including realistic changes, such as due to STDP), (3) with a range of pre and postsynaptic firing rates, and (4) for both excitatory and inhibitory synapses. We then apply our model to two experimentally recorded putative synaptic connections. We find that simultaneously tracking fast changes in synaptic weights, slow changes in synaptic weights, and unexplained variations in baseline firing is essential. Omitting any one of these factors can lead to spurious inferences for the others. Altogether, this model provides a flexible framework for tracking short- and long-term variation in spike transmission.

Generalized linear models (GLMs) have a wide range of applications in systems neuroscience describing the encoding of stimulus and behavioral variables, as well as the dynamics of single neurons. However, in any given experiment, many variables that have an impact on neural activity are not observed or not modeled. Here we demonstrate, in both theory and practice, how these omitted variables can result in biased parameter estimates for the effects that are included. In three case studies, we estimate tuning functions for common experiments in motor cortex, hippocampus, and visual cortex. We find that including traditionally omitted variables changes estimates of the original parameters and that modulation originally attributed to one variable is reduced after new variables are included. In GLMs describing single-neuron dynamics, we then demonstrate how postspike history effects can also be biased by omitted variables. Here we find that omitted variable bias can lead to mistaken conclusions about the stability of single-neuron firing. Omitted variable bias can appear in any model with confounders-where omitted variables modulate neural activity and the effects of the omitted variables covary with the included effects. Understanding how and to what extent omitted variable bias affects parameter estimates is likely to be important for interpreting the parameters and predictions of many neural encoding models.

Short-term synaptic plasticity (STP) critically affects the processing of information in neuronal circuits by reversibly changing the effective strength of connections between neurons on time scales from milliseconds to a few seconds. STP is traditionally studied using intracellular recordings of postsynaptic potentials or currents evoked by presynaptic spikes. However, STP also affects the statistics of postsynaptic spikes. Here we present two model-based approaches for estimating synaptic weights and short-term plasticity from pre- and postsynaptic spike observations alone. We extend a generalized linear model (GLM) that predicts postsynaptic spiking as a function of the observed pre- and postsynaptic spikes and allow the connection strength (coupling term in the GLM) to vary as a function of time based on the history of presynaptic spikes. Our first model assumes that STP follows a Tsodyks-Markram description of vesicle depletion and recovery. In a second model, we introduce a functional description of STP where we estimate the coupling term as a biophysically unrestrained function of the presynaptic inter-spike intervals. To validate the models, we test the accuracy of STP estimation using the spiking of pre- and postsynaptic neurons with known synaptic dynamics. We first test our models using the responses of layer 2/3 pyramidal neurons to simulated presynaptic input with different types of STP, and then use simulated spike trains to examine the effects of spike-frequency adaptation, stochastic vesicle release, spike sorting errors, and common input. We find that, using only spike observations, both model-based methods can accurately reconstruct the time-varying synaptic weights of presynaptic inputs for different types of STP. Our models also capture the differences in postsynaptic spike responses to presynaptic spikes following short vs long inter-spike intervals, similar to results reported for thalamocortical connections. These models may thus be useful tools for characterizing short-term plasticity from multi-electrode spike recordings in vivo.

Accurately describing synaptic interactions between neurons and how interactions change over time are key challenges for systems neuroscience. Although intracellular electrophysiology is a powerful tool for studying synaptic integration and plasticity, it is limited by the small number of neurons that can be recorded simultaneously in vitro and by the technical difficulty of intracellular recording in vivo. One way around these difficulties may be to use large-scale extracellular recording of spike trains and apply statistical methods to model and infer functional connections between neurons. These techniques have the potential to reveal large-scale connectivity structure based on the spike timing alone. However, the interpretation of functional connectivity is often approximate, since only a small fraction of presynaptic inputs are typically observed. Here we use in vitro current injection in layer 2/3 pyramidal neurons to validate methods for inferring functional connectivity in a setting where input to the neuron is controlled. In experiments with partially-defined input, we inject a single simulated input with known amplitude on a background of fluctuating noise. In a fully-defined input paradigm, we then control the synaptic weights and timing of many simulated presynaptic neurons. By analyzing the firing of neurons in response to these artificial inputs, we ask 1) How does functional connectivity inferred from spikes relate to simulated synaptic input? and 2) What are the limitations of connectivity inference? We find that individual current-based synaptic inputs are detectable over a broad range of amplitudes and conditions. Detectability depends on input amplitude and output firing rate, and excitatory inputs are detected more readily than inhibitory. Moreover, as we model increasing numbers of presynaptic inputs, we are able to estimate connection strengths more accurately and detect the presence of connections more quickly. These results illustrate the possibilities and outline the limits of inferring synaptic input from spikes.

How interactions between neurons relate to tuned neural responses is a longstanding question in systems neuroscience. Here we use statistical modeling and simultaneous multi-electrode recordings to explore the relationship between these interactions and tuning curves in six different brain areas. We find that, in most cases, functional interactions between neurons provide an explanation of spiking that complements and, in some cases, surpasses the influence of canonical tuning curves. Modeling functional interactions improves both encoding and decoding accuracy by accounting for noise correlations and features of the external world that tuning curves fail to capture. In cortex, modeling coupling alone allows spikes to be predicted more accurately than tuning curve models based on external variables. These results suggest that statistical models of functional interactions between even relatively small numbers of neurons may provide a useful framework for examining neural coding.

Synaptic plasticity underlies learning and is thus central for development, memory, and recovery from injury. However, it is often difficult to detect changes in synaptic strength in vivo, since intracellular recordings are experimentally challenging. Here we present two methods aimed at inferring changes in the coupling between pairs of neurons from extracellularly recorded spike trains. First, using a generalized bilinear model with Poisson output we estimate time-varying coupling assuming that all changes are spike-timing-dependent. This approach allows model-based estimation of STDP modification functions from pairs of spike trains. Then, using recursive point-process adaptive filtering methods we estimate more general variation in coupling strength over time. Using simulations of neurons undergoing spike-timing dependent modification, we show that the true modification function can be recovered. Using multi-electrode data from motor cortex we then illustrate the use of this technique on in vivo data.

In many domains, humans appear to combine perceptual cues in a near-optimal, probabilistic fashion: two noisy pieces of information tend to be combined linearly with weights proportional to the precision of each cue. Here we present a case where structural information plays an important role. The presence of a background cue gives rise to the possibility of occlusion, and places a soft constraint on the location of a target – in effect propelling it forward. We present an ideal observer model of depth estimation for this situation where structural or ordinal information is important and then fit the model to human data from a stereo-matching task. To test whether subjects are truly using ordinal cues in a probabilistic manner we then vary the uncertainty of the task. We find that the model accurately predicts shifts in subject’s behavior. Our results indicate that the nervous system estimates depth ordering in a probabilistic fashion and estimates the structure of the visual scene during depth perception.

A large number of experiments have asked to what degree human reaching movements can be understood as being close to optimal in a statistical sense. However, little is known about whether these principles are relevant for other classes of movements. Here we analyzed movement in a task that is similar to surfing or snowboarding. Human subjects stand on a force plate that measures their center of pressure. This center of pressure affects the acceleration of a cursor that is displayed in a noisy fashion (as a cloud of dots) on a projection screen while the subject is incentivized to keep the cursor close to a fixed position. We find that salient aspects of observed behavior are well-described by optimal control models where a Bayesian estimation model (Kalman filter) is combined with an optimal controller (either a Linear-Quadratic-Regulator or Bang-bang controller). We find evidence that subjects integrate information over time taking into account uncertainty. However, behavior in this continuous steering task appears to be a highly non-linear function of the visual feedback. While the nervous system appears to implement Bayes-like mechanisms for a full-body, dynamic task, it may additionally take into account the specific costs and constraints of the task.