Biomedical subjects

Liam Paninski

Publications and source records attributed to Liam Paninski.

14 recordsLinked to original sources

PubMed2006

Linear encoding of muscle activity in primary motor cortex and cerebellum.

The activity of neurons in primary motor cortex (M1) and cerebellum is known to correlate with extrinsic movement parameters, including hand position and velocity. Relatively few studies have addressed the encoding of intrinsic parameters, such as muscle activity. Here we applied a generalized regression analysis to describe the relationship of neurons in M1 and cerebellar dentate nucleus to electromyographic (EMG) activity from hand and forearm muscles, during performance of precision grip by macaque monkeys. We showed that cells in both M1 and dentate encode muscle activity in a linear fashion, and that EMG signals provide predictions of neural discharge that are equally accurate to those from kinematic information under these task conditions. Neural activity in M1 was significantly more correlated with both EMG and kinematic signals than was activity in dentate nucleus. Furthermore, the analysis enabled us to look at the temporal properties of muscle encoding. Cells were broadly tuned to muscle activity as a function of the lag between spiking and EMG and there was considerable heterogeneity in the optimal delay among individual neurons. However, a single lag (40 ms) was generally sufficient to provide good fits. Finally, incorporating spike history effects in our model offered no advantage in predicting novel spike trains, reinforcing the simple nature of the muscle encoding that we observed here.

Algorithms↗

PubMed2006

The most likely voltage path and large deviations approximations for integrate-and-fire neurons.

We develop theory and numerical methods for computing the most likely subthreshold voltage path of a noisy integrate-and-fire (IF) neuron, given observations of the neuron's superthreshold spiking activity. This optimal voltage path satisfies a second-order ordinary differential (Euler-Lagrange) equation which may be solved analytically in a number of special cases, and which may be solved numerically in general via a simple "shooting" algorithm. Our results are applicable for both linear and nonlinear subthreshold dynamics, and in certain cases may be extended to correlated subthreshold noise sources. We also show how this optimal voltage may be used to obtain approximations to (1) the likelihood that an IF cell with a given set of parameters was responsible for the observed spike train; and (2) the instantaneous firing rate and interspike interval distribution of a given noisy IF cell. The latter probability approximations are based on the classical Freidlin-Wentzell theory of large deviations principles for stochastic differential equations. We close by comparing this most likely voltage path to the true observed subthreshold voltage trace in a case when intracellular voltage recordings are available in vitro.

Action Potentials↗

PubMed2006

Efficient estimation of detailed single-neuron models.

Biophysically accurate multicompartmental models of individual neurons have significantly advanced our understanding of the input-output function of single cells. These models depend on a large number of parameters that are difficult to estimate. In practice, they are often hand-tuned to match measured physiological behaviors, thus raising questions of identifiability and interpretability. We propose a statistical approach to the automatic estimation of various biologically relevant parameters, including 1) the distribution of channel densities, 2) the spatiotemporal pattern of synaptic input, and 3) axial resistances across extended dendrites. Recent experimental advances, notably in voltage-sensitive imaging, motivate us to assume access to: i) the spatiotemporal voltage signal in the dendrite and ii) an approximate description of the channel kinetics of interest. We show here that, given i and ii, parameters 1-3 can be inferred simultaneously by nonnegative linear regression; that this optimization problem possesses a unique solution and is guaranteed to converge despite the large number of parameters and their complex nonlinear interaction; and that standard optimization algorithms efficiently reach this optimum with modest computational and data requirements. We demonstrate that the method leads to accurate estimations on a wide variety of challenging model data sets that include up to about 10(4) parameters (roughly two orders of magnitude more than previously feasible) and describe how the method gives insights into the functional interaction of groups of channels.

Algorithms↗

PubMed2006

The spike-triggered average of the integrate-and-fire cell driven by gaussian white noise.

We compute the exact spike-triggered average (STA) of the voltage for the nonleaky integrate-and-fire (IF) cell in continuous time, driven by gaussian white noise. The computation is based on techniques from the theory of renewal processes and continuous-time hidden Markov processes (e.g., the backward and forward Fokker-Planck partial differential equations associated with first-passage time densities). From the STA voltage, it is straightforward to derive the STA input current. The theory also gives an explicit asymptotic approximation for the STA of the leaky IF cell, valid in the low-noise regime sigma --> 0. We consider both the STA and the conditional average voltage given an observed spike "doublet" event, that is, two spikes separated by some fixed period of silence. In each case, we find that the STA as a function of time-preceding-spike, tau, has a square root singularity as tau approaches zero from below and scales linearly with the scale of injected noise current. We close by briefly examining the discrete-time case, where similar phenomena are observed.

Action Potentials↗

PubMed2005

Prediction and decoding of retinal ganglion cell responses with a probabilistic spiking model.

Sensory encoding in spiking neurons depends on both the integration of sensory inputs and the intrinsic dynamics and variability of spike generation. We show that the stimulus selectivity, reliability, and timing precision of primate retinal ganglion cell (RGC) light responses can be reproduced accurately with a simple model consisting of a leaky integrate-and-fire spike generator driven by a linearly filtered stimulus, a postspike current, and a Gaussian noise current. We fit model parameters for individual RGCs by maximizing the likelihood of observed spike responses to a stochastic visual stimulus. Although compact, the fitted model predicts the detailed time structure of responses to novel stimuli, accurately capturing the interaction between the spiking history and sensory stimulus selectivity. The model also accounts for the variability in responses to repeated stimuli, even when fit to data from a single (nonrepeating) stimulus sequence. Finally, the model can be used to derive an explicit, maximum-likelihood decoding rule for neural spike trains, thus providing a tool for assessing the limitations that spiking variability imposes on sensory performance.

Action Potentials↗

PubMed2005

Asymptotic theory of information-theoretic experimental design.

We discuss an idea for collecting data in a relatively efficient manner. Our point of view is Bayesian and information-theoretic: on any given trial, we want to adaptively choose the input in such a way that the mutual information between the (unknown) state of the system and the (stochastic) output is maximal, given any prior information (including data collected on any previous trials). We prove a theorem that quantifies the effectiveness of this strategy and give a few illustrative examples comparing the performance of this adaptive technique to that of the more usual nonadaptive experimental design. In particular, we calculate the asymptotic efficiency of the information-maximization strategy and demonstrate that this method is in a well-defined sense never less efficient--and is generically more efficient--than the nonadaptive strategy. For example, we are able to explicitly calculate the asymptotic relative efficiency of the staircase method widely employed in psychophysics research and to demonstrate the dependence of this efficiency on the form of the psychometric function underlying the output responses.

Journal Article↗

PubMed2004

Superlinear population encoding of dynamic hand trajectory in primary motor cortex.

Neural activity in primary motor cortex (MI) is known to correlate with hand position and velocity. Previous descriptions of this tuning have (1) been linear in position or velocity, (2) depended only instantaneously on these signals, and/or (3) not incorporated the effects of interneuronal dependencies on firing rate. We show here that many MI cells encode a superlinear function of the full time-varying hand trajectory. Approximately 20% of MI cells carry information in the hand trajectory beyond just the position, velocity, and acceleration at a single time lag. Moreover, approximately one-third of MI cells encode the trajectory in a significantly superlinear manner; as one consequence, even small position changes can dramatically modulate the gain of the velocity tuning of MI cells, in agreement with recent psychophysical evidence. We introduce a compact nonlinear "preferred trajectory" model that predicts the complex structure of the spatiotemporal tuning functions described in previous work. Finally, observing the activity of neighboring cells in the MI network significantly increases the predictability of the firing rate of a single MI cell; however, we find interneuronal dependencies in MI to be much more locked to external kinematic parameters than those described recently in the hippocampus. Nevertheless, this neighbor activity is approximately as informative as the hand velocity, supporting the view that neural encoding in MI is best understood at a population level.

Action Potentials↗

PubMed2004

Maximum likelihood estimation of a stochastic integrate-and-fire neural encoding model.

We examine a cascade encoding model for neural response in which a linear filtering stage is followed by a noisy, leaky, integrate-and-fire spike generation mechanism. This model provides a biophysically more realistic alternative to models based on Poisson (memoryless) spike generation, and can effectively reproduce a variety of spiking behaviors seen in vivo. We describe the maximum likelihood estimator for the model parameters, given only extracellular spike train responses (not intracellular voltage data). Specifically, we prove that the log-likelihood function is concave and thus has an essentially unique global maximum that can be found using gradient ascent techniques. We develop an efficient algorithm for computing the maximum likelihood solution, demonstrate the effectiveness of the resulting estimator with numerical simulations, and discuss a method of testing the model's validity using time-rescaling and density evolution techniques.

Algorithms↗

PubMed2004

Maximum likelihood estimation of cascade point-process neural encoding models.

Recent work has examined the estimation of models of stimulus-driven neural activity in which some linear filtering process is followed by a nonlinear, probabilistic spiking stage. We analyze the estimation of one such model for which this nonlinear step is implemented by a known parametric function; the assumption that this function is known speeds the estimation process considerably. We investigate the shape of the likelihood function for this type of model, give a simple condition on the nonlinearity ensuring that no non-global local maxima exist in the likelihood-leading, in turn, to efficient algorithms for the computation of the maximum likelihood estimator-and discuss the implications for the form of the allowed nonlinearities. Finally, we note some interesting connections between the likelihood-based estimators and the classical spike-triggered average estimator, discuss some useful extensions of the basic model structure, and provide two novel applications to physiological data.

Algorithms↗

PubMed2003

Spatiotemporal tuning of motor cortical neurons for hand position and velocity.

A pursuit-tracking task (PTT) and multielectrode recordings were used to investigate the spatiotemporal encoding of hand position and velocity in primate primary motor cortex (MI). Continuous tracking of a randomly moving visual stimulus provided a broad sample of velocity and position space, reduced statistical dependencies between kinematic variables, and minimized the nonstationarities that are found in typical "step-tracking" tasks. These statistical features permitted the application of signal-processing and information-theoretic tools for the analysis of neural encoding. The multielectrode method allowed for the comparison of tuning functions among simultaneously recorded cells. During tracking, MI neurons showed heterogeneity of position and velocity coding, with markedly different temporal dynamics for each. Velocity-tuned neurons were approximately sinusoidally tuned for direction, with linear speed scaling; other cells showed sinusoidal tuning for position, with linear scaling by distance. Velocity encoding led behavior by about 100 ms for most cells, whereas position tuning was more broadly distributed, with leads and lags suggestive of both feedforward and feedback coding. Individual cells encoded velocity and position weakly, with comparable amounts of information about each. Linear regression methods confirmed that random, 2-D hand trajectories can be reconstructed from the firing of small ensembles of randomly selected neurons (3-19 cells) within the MI arm area. These findings demonstrate that MI carries information about evolving hand trajectory during visually guided pursuit tracking, including information about arm position both during and after its specification. However, the reconstruction methods used here capture only the low-frequency components of movement during the PTT. Hand motion signals appear to be represented as a distributed code in which diverse information about position and velocity is available within small regions of MI.

Action Potentials↗

PubMed2003

Sequential movement representations based on correlated neuronal activity.

We tested the hypothesis that sequential movements are represented in the correlated activity of motor cortical neurons. We simultaneously recorded multiple single neurons in the motor cortex while monkeys performed a two-segment movement sequence. Before any movement began the correlated spike firing between pairs of neurons differed when these sequences were planned as whole (planned) as compared to when they were planned one segment at a time (unplanned) even when the firing rates of these neurons did not distinguish between the two conditions. Moreover, the correlation strength was significantly larger when the directional preferences of the neurons matched the direction of the final segment of the sequence. Our results suggest that spatially distributed groups of MI neurons form dynamic correlation structures that distinguish different forms of sequential action.

Animals↗

PubMed2003

Robustness of neuroprosthetic decoding algorithms.

We assessed the ability of two algorithms to predict hand kinematics from neural activity as a function of the amount of data used to determine the algorithm parameters. Using chronically implanted intracortical arrays, single- and multineuron discharge was recorded during trained step tracking and slow continuous tracking tasks in macaque monkeys. The effect of increasing the amount of data used to build a neural decoding model on the ability of that model to predict hand kinematics accurately was examined. We evaluated how well a maximum-likelihood model classified discrete reaching directions and how well a linear filter model reconstructed continuous hand positions over time within and across days. For each of these two models we asked two questions: (1) How does classification performance change as the amount of data the model is built upon increases? (2) How does varying the time interval between the data used to build the model and the data used to test the model affect reconstruction? Less than 1 min of data for the discrete task (8 to 13 neurons) and less than 3 min (8 to 18 neurons) for the continuous task were required to build optimal models. Optimal performance was defined by a cost function we derived that reflects both the ability of the model to predict kinematics accurately and the cost of taking more time to build such models. For both the maximum-likelihood classifier and the linear filter model, increasing the duration between the time of building and testing the model within a day did not cause any significant trend of degradation or improvement in performance. Linear filters built on one day and tested on neural data on a subsequent day generated error-measure distributions that were not significantly different from those generated when the linear filters were tested on neural data from the initial day (p<0.05, Kolmogorov-Smirnov test). These data show that only a small amount of data from a limited number of cortical neurons appears to be necessary to construct robust models to predict kinematic parameters for the subsequent hours. Motor-control signals derived from neurons in motor cortex can be reliably acquired for use in neural prosthetic devices. Adequate decoding models can be built rapidly from small numbers of cells and maintained with daily calibration sessions.

Action Potentials↗

PubMed2003

Convergence properties of three spike-triggered analysis techniques.

We analyse the convergence properties of three spike-triggered data analysis techniques. Our results are obtained in the setting of a probabilistic linear-nonlinear (LN) cascade neural encoding model; this model has recently become popular in the study of the neural coding of natural signals. We start by giving exact rate-of-convergence results for the common spike-triggered average technique. Next, we analyse a spike-triggered covariance method, variants of which have been recently exploited successfully by Bialek, Simoncelli and colleagues. Unfortunately, the conditions that guarantee that these two estimators will converge to the correct parameters are typically not satisfied by natural signal data. Therefore, we introduce an estimator for the LN model parameters which is designed to converge under general conditions to the correct model. We derive the rate of convergence of this estimator, provide an algorithm for its computation and demonstrate its application to simulated data as well as physiological data from the primary motor cortex of awake behaving monkeys. We also give lower bounds on the convergence rate of any possible LN estimator. Our results should prove useful in the study of the neural coding of high-dimensional natural signals.

Action Potentials↗

PubMed2002

Instant neural control of a movement signal.

The activity of motor cortex (MI) neurons conveys movement intent sufficiently well to be used as a control signal to operate artificial devices, but until now this has called for extensive training or has been confined to a limited movement repertoire. Here we show how activity from a few (7-30) MI neurons can be decoded into a signal that a monkey is able to use immediately to move a computer cursor to any new position in its workspace (14 degrees x 14 degrees visual angle). Our results, which are based on recordings made by an electrode array that is suitable for human use, indicate that neurally based control of movement may eventually be feasible in paralysed humans.

Algorithms↗