Spiking History Research Articles

Method for analyzing spike patterns with Markov transition matrices and Kullback-Leibler divergence

We describe a novel method for analyzing neural data that uses a combination of Markov transition matrices and Kullback-Leibler divergence to characterize spike history and spike patterns. For this method, the interspike intervals (ISIs) are divided into bins by quantiles, and a Markov transition matrix is computed for the ISI sequence. This Markov transition matrix is then compared to another Markov transition matrix constructed under the assumption of independent spiking. We then compute the Kullback-Leibler divergence between the distributions of ISI transition probabilities for each bin. The purpose of this method is to quantify the effects of spike history on neuron output and to help better characterize the flaws associated with assuming independent spiking. We test this method on both simulated data and experimental data from primary visual cortex of cats, publicly available through CRCNS [1-3]. Interspike intervals are simulated based on exponential and gamma distributions fit to the corresponding experimental ISI distributions.

Non-linear dependency between spiking response and gamma-band power of local field potentials in the human auditory cortex

Recent advancement in recordings of extracellular potentials from multiple sites in the human brain [1] has allowed us to simultaneously record spiking activity and local field potentials (LFP) to examine the brain's response to experimental stimuli. Various mechanisms have been suggested for the generation of the LFP. A point of special interest is that LFP reflects not only the inputs to the tissue, but also local processing. For example, spike contribution to the high-frequency LFP through increased spike rate or increased synchrony has been suggested [2]. Subjects (n = 19 ) were epilepsy patients who needed intracranial electrode implantation and chronic monitoring of for diagnostic and treatment purposes. Protocols were approved by University of Iowa IRB. Recordings were made from micro contacts implanted in the Heschl's gyri during pure tone presentations. Single-trial gamma-band responses were extracted using band-pass filters (40-150 Hz). Spike trains at the same contacts were analyzed with Poisson generalized linear models (GLM) with coded stimulus convolved with finite impulse-response (FIR) function which was estimated from the data, as well as spiking history (up to 80 ms duration, determined by minimum BIC criterion) as covariates. We treated the system as a time-invariant black box and the relationship between spiking activity (rates) and gamma-band LFP power was analyzed with Volterra kernel expansion (memory length of 200 ms) up to the second-order to examine potentially non-linear dependencies [3] (Figure ​(Figure1A).1A). Estimated discharge rates were used as the inputs and gamma LFP power was used as the outputs of the system. Weighted least-squares support-vector machines were utilized for estimating the regression coefficients [4], and the kernels were expanded using Laguerre orthogonal basis. First order kernel (linear filter) typically decreased toward zero within 150 ms lag time (Figure ​(Figure1A1A and ​and1B),1B), and 2nd -order kernels typically contain negative components, indicating non-linear suppressive effect on the gamma. (Figure ​(Figure1B).1B). A separate correlation analysis between spike count and gamma-band power within post-stimulus 200 ms shows strong positive correlation (Figure ​(Figure1C1C). Figure 1

Dynamics and spike trains statistics in conductance-based integrate-and-fire neural networks with chemical and electric synapses

We investigate the effect of electric synapses (gap junctions) on collective neuronal dynamics and spike statistics in a conductance-based integrate-and-fire neural network, driven by Brownian noise, where conductances depend upon spike history. We compute explicitly the time evolution operator and show that, given the spike-history of the network and the membrane potentials at a given time, the further dynamical evolution can be written in a closed form. We show that spike train statistics is described by a Gibbs distribution whose potential can be approximated with an explicit formula, when the noise is weak. This potential form encompasses existing models for spike trains statistics analysis such as maximum entropy models or generalized linear models (GLM). We also discuss the different types of correlations: those induced by a shared stimulus and those induced by neurons interactions.

A Point Process Model-based Framework Reveals Reinforcement Mechanisms in Striatum during High Frequency STN DBS.

Striatum is a major stage of the motor loop but, despite a pivotal role in the execution of movements, it has been poorly studied thus far under Parkinsonian conditions and Deep Brain Stimulation (DBS). We propose a computational framework to analyze the spiking activity of striatal neurons under several conditions. This framework combines point process models and single unit recordings, and separately evaluates the effects of the spiking history, DBS frequency, and other cells on the neuronal discharge pattern, thus giving a full characterization of non-stationary neuronal dynamics and inter-neuronal dependencies. We applied this framework to 166 striatal neurons collected in a monkey both at rest and during DBS (30-130 Hz). Our analysis was conducted both before and after treatment of the animal with 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP), which evoked Parkinsonian-like motor disorders. We reported that high frequency (≥100 Hz) DBS reduces non-stationary dynamics and inter-neuronal dependencies by regularizing the discharge patterns both in MPTP and normal striatum, while the combination of MPTP and low frequency (30-80 Hz) DBS enhances these features, thus suggesting that pattern regularization in striatum might contribute to the therapeutic effect of high frequency DBS and presumably results from the overlap of feed-forward and feedback activation along the motor loop (reinforcement).

Coding and Decoding with Adapting Neurons: A Population Approach to the Peri-Stimulus Time Histogram

The response of a neuron to a time-dependent stimulus, as measured in a Peri-Stimulus-Time-Histogram (PSTH), exhibits an intricate temporal structure that reflects potential temporal coding principles. Here we analyze the encoding and decoding of PSTHs for spiking neurons with arbitrary refractoriness and adaptation. As a modeling framework, we use the spike response model, also known as the generalized linear neuron model. Because of refractoriness, the effect of the most recent spike on the spiking probability a few milliseconds later is very strong. The influence of the last spike needs therefore to be described with high precision, while the rest of the neuronal spiking history merely introduces an average self-inhibition or adaptation that depends on the expected number of past spikes but not on the exact spike timings. Based on these insights, we derive a ‘quasi-renewal equation’ which is shown to yield an excellent description of the firing rate of adapting neurons. We explore the domain of validity of the quasi-renewal equation and compare it with other rate equations for populations of spiking neurons. The problem of decoding the stimulus from the population response (or PSTH) is addressed analogously. We find that for small levels of activity and weak adaptation, a simple accumulator of the past activity is sufficient to decode the original input, but when refractory effects become large decoding becomes a non-linear function of the past activity. The results presented here can be applied to the mean-field analysis of coupled neuron networks, but also to arbitrary point processes with negative self-interaction.

Stress-Induced Impairment of a Working Memory Task: Role of Spiking Rate and Spiking History Predicted Discharge

Stress, pervasive in society, contributes to over half of all work place accidents a year and over time can contribute to a variety of psychiatric disorders including depression, schizophrenia, and post-traumatic stress disorder. Stress impairs higher cognitive processes, dependent on the prefrontal cortex (PFC) and that involve maintenance and integration of information over extended periods, including working memory and attention. Substantial evidence has demonstrated a relationship between patterns of PFC neuron spiking activity (action-potential discharge) and components of delayed-response tasks used to probe PFC-dependent cognitive function in rats and monkeys. During delay periods of these tasks, persistent spiking activity is posited to be essential for the maintenance of information for working memory and attention. However, the degree to which stress-induced impairment in PFC-dependent cognition involves changes in task-related spiking rates or the ability for PFC neurons to retain information over time remains unknown. In the current study, spiking activity was recorded from the medial PFC of rats performing a delayed-response task of working memory during acute noise stress (93 db). Spike history-predicted discharge (SHPD) for PFC neurons was quantified as a measure of the degree to which ongoing neuronal discharge can be predicted by past spiking activity and reflects the degree to which past information is retained by these neurons over time. We found that PFC neuron discharge is predicted by their past spiking patterns for nearly one second. Acute stress impaired SHPD, selectively during delay intervals of the task, and simultaneously impaired task performance. Despite the reduction in delay-related SHPD, stress increased delay-related spiking rates. These findings suggest that neural codes utilizing SHPD within PFC networks likely reflects an additional important neurophysiological mechanism for maintenance of past information over time. Stress-related impairment of this mechanism is posited to contribute to the cognition-impairing actions of stress.

Predicting Single-Neuron Activity in Locally Connected Networks

The characterization of coordinated activity in neuronal populations has received renewed interest in the light of advancing experimental techniques that allow recordings from multiple units simultaneously. Across both in vitro and in vivo preparations, nearby neurons show coordinated responses when spontaneously active and when subject to external stimuli. Recent work (Truccolo, Hochberg, & Donoghue, 2010 ) has connected these coordinated responses to behavior, showing that small ensembles of neurons in arm-related areas of sensorimotor cortex can reliably predict single-neuron spikes in behaving monkeys and humans. We investigate this phenomenon using an analogous point process model, showing that in the case of a computational model of cortex responding to random background inputs, one is similarly able to predict the future state of a single neuron by considering its own spiking history, together with the spiking histories of randomly sampled ensembles of nearby neurons. This model exhibits realistic cortical architecture and displays bursting episodes in the two distinct connectivity schemes studied. We conjecture that the baseline predictability we find in these instances is characteristic of locally connected networks more broadly considered.

Context Matters: The Illusive Simplicity of Macaque V1 Receptive Fields

Even in V1, where neurons have well characterized classical receptive fields (CRFs), it has been difficult to deduce which features of natural scenes stimuli they actually respond to. Forward models based upon CRF stimuli have had limited success in predicting the response of V1 neurons to natural scenes. As natural scenes exhibit complex spatial and temporal correlations, this could be due to surround effects that modulate the sensitivity of the CRF. Here, instead of attempting a forward model, we quantify the importance of the natural scenes surround for awake macaque monkeys by modeling it non-parametrically. We also quantify the influence of two forms of trial to trial variability. The first is related to the neuron’s own spike history. The second is related to ongoing mean field population activity reflected by the local field potential (LFP). We find that the surround produces strong temporal modulations in the firing rate that can be both suppressive and facilitative. Further, the LFP is found to induce a precise timing in spikes, which tend to be temporally localized on sharp LFP transients in the gamma frequency range. Using the pseudo R2 as a measure of model fit, we find that during natural scene viewing the CRF dominates, accounting for 60% of the fit, but that taken collectively the surround, spike history and LFP are almost as important, accounting for 40%. However, overall only a small proportion of V1 spiking statistics could be explained (R2∼5%), even when the full stimulus, spike history and LFP were taken into account. This suggests that under natural scene conditions, the dominant influence on V1 neurons is not the stimulus, nor the mean field dynamics of the LFP, but the complex, incoherent dynamics of the network in which neurons are embedded.

Bistable persistent spiking of layer II and layer V medial entorhinal cortical neurons during theta frequency oscillations in vitro

In the presence of muscarinic cholinergic modulation in vitro, persistent spiking neurons of medial entorhinal cortex (mEC) exhibit bistability in that they can be switched from quiescence to spiking by a brief depolarizing input. The spiking state is thought to be maintained by a positive feedback loop between a nonspecific, calcium-sensitive cationic current (ICAN) carried by canonical transient receptor potential (TRPC) channels and heightened intracellular calcium levels sustained during sufficiently fast spiking. Bistable persistent spiking (PSB) has been observed across layers and cell types in mEC and has been implicated in working memory and grid cell function, so cholinergic modulation of TRPC channels represents a potentially fundamental mechanism shaping the spiking output of mEC neurons. However, spiking of mEC neurons during navigation and goal directed behavior in vivo is strongly theta modulated (4-12 Hz), and it is not known how the PSB mechanism may interact with theta oscillations. In the present study we evaluated the effect of muscarinic modulation on input-output processing of mEC neurons to tonic, slowly varying, and oscillatory inputs. First, we investigated the frequency to injected current (FI) relationship using step and ramp current injection protocols in the presence of the muscarinic agonist carbachol (CCh). FI measures made following suprathreshold pre-pulse current injections exhibited higher spike frequencies than when measured following subthreshold pre-pulses, illustrating a spike-history dependence of the FI relationship. The instantaneous spike frequency measured during a range of current steps showed a positive slope for most PSB neurons, indicating that ICAN acts as a reverse spike frequency adaptation mechanism. In response to linearly increasing ramp current stimuli, mEC neurons showed a steep acceleration followed by a plateau of spike frequency. Spike frequency hysteresis during decreasing ramp stimuli demonstrated significant adaptation for higher input levels, but spiking was often maintained at lower levels of injected current. Next, using different combinations of theta frequency sinewave current injections and DC holding currents, we were able to generate a range of spiking patterns where spikes were elicited on different proportions of theta cycles and at different phases of the theta input. With muscarinic activation, spiking was elicited on a higher proportion of theta cycles and at earlier phases of the oscillatory input for lower levels of tonic current input. A subset of recorded neurons exhibitted repeated sequences of intrinsic phase precessing spiking behavior. Similar to the plateau in spike rate observed with ramp stimuli, in response to stimuli composed of sinewaves superimposed on ramps, spiking phase rapidly advanced and maintained an ‘early-phase plateau’ as DC current continued to increase. Taken together, we demonstrate that muscarinic modulation of TRPC channels determines the gain of the frequency to injected current relationship of mEC neurons, interacts with adaptation mechanisms to generate spike history dependencies of spike rate including hysteresis, and shapes the distribution of spiking phases relative to oscillatory input. We propose that increasing activation of ICAN by spike-triggered calcium influx as an animal enters a firing field may provide a cellular mechanism contributing to theta phase precession of mEC grid cells.

Heterogeneous short-term plasticity enables spectral separation of information in the neural spike train

In order to understand how information is processed in the brain, it is vital to investigate how a single neuron responds to inputs that encode multiple signals. As each neuron receives input from many other neurons, such a situation is no exception but the norm. Previous studies have investigated how the transmission of one signal is influenced by others that can be considered background noise [1]. However, when looking at signal gating and processing, we also need to ask how the information content of more than one input signal is reflected in a neuron's output. The interaction of signals is made complex not only by the nonlinearity of neuron dynamics, but also by short-term synaptic plasticity (STP) [2], which makes the amplitude of post-synaptic response dependent on the recent pre-synaptic spiking history. Synapses can exhibit qualitatively different kinds of STP. For instance, they can be predominantly facilitating or predominantly depressing. Previous studies have investigated the consequences of STP for information processing [3] and particularly pointed out that it can only lead to spectral filtering in the presence of noise or other signals [4,5]. In this study, we consider a scenario in which a neuron receives two stimuli through populations of purely facilitating and purely depressing synapses, respectively. Although such a setting is certainly an idealization, it resembles the difference in short-term plasticity of synaptic connections that parallel fibers and climbing fibers make to a Purkinje cell. Following the rate-coding paradigm, we model the input spike trains as inhomogeneous Poisson processes and use spectral measures such as the coherence to assess information throughput. We find that STP leads to a spectral separation of information into high and low frequency bands. This spectral separation is based on the respective other signal acting as a kind of noise in the disfavored frequency band. Further, we show that the total information transfer about one signal can still benefit from the presence of the other signal through a form of stochastic resonance.

Encoding of Coordinated Reach and Grasp Trajectories in Primary Motor Cortex

Though the joints of the arm and hand together comprise 27 degrees of freedom, an ethological movement like reaching and grasping coordinates many of these joints so as to operate in a reduced dimensional space. We used a generalized linear model to predict single neuron responses in primary motor cortex (MI) during a reach-to-grasp task based on 40 features that represent positions and velocities of the arm and hand in joint angle and Cartesian coordinates as well as the neurons' own spiking history. Two rhesus monkeys were trained to reach and grasp one of five objects, located at one of seven locations while we used an infrared camera motion-tracking system to track markers placed on their upper limb and recorded single-unit activity from a microelectrode array implanted in MI. The kinematic trajectories that described hand shaping and transport to the object depended on both the type of object and its location. Modeling the kinematics as temporally extensive trajectories consistently yielded significantly higher predictive power in most neurons. Furthermore, a model that included all feature trajectories yielded more predictive power than one that included any single feature trajectory in isolation, and neurons tended to encode feature velocities over positions. The predictive power of a majority of neurons reached a plateau for a model that included only the first five principal components of all the features' trajectories, suggesting that MI has evolved or adapted to encode the natural kinematic covariations associated with prehension described by a limited set of kinematic synergies.

Conditional intensity/point process model of task-related prefrontal spiking: effects of performance

The spiking activity of neurons in the prefrontal associational cortex (PFC) of animals engaged in cognitive tasks is posited to reflect diverse set of independent cognitive and behavioral processes required for the successful attainment of future goals. Additionally, a neural representation of past information (i.e. spike history) is likely critical for performance in these delayed-response tasks of working memory. In the current study, we used a conditional intensity - generalized linear model (CI-GLM) statistical framework to determine the degree to which spike history and components of a delayed-response task predict PFC neural spiking as opposed to traditional peri-event time histogram (PETH) analysis approaches. The final CI-GLM model takes the form,, such that the conditional intensity function λ(t|Ht) is predicted by a generalized linear model from a series covariates where (µ) is the intercept of the equation representing the background level of activity, represents an autoregressive process of order (K), and is the design matrix of each event-state (r) for each sample in time (t) of the behavioral task and βr are the estimated weighting parameters. The discretized time for increasing spiking history durations is represented as ΔNt–k with γk representing the autoregressive coefficients. We found that in rats performing a PFC-dependent delayed-alternation task of working memory, the vast majority of PFC neurons participate in the representation of more than one task-related event-state (multiplexer neurons). Additionally, the size of functional neural groups or cell assemblies was critically linked to the level of behavioral performance (Fig. ​(Fig.1).1). Poor behavioral performance was not solely associated with an attenuation of spiking activity, but instead the activation of inappropriate assemblies during error trials may actively direct the animal towards an incorrect choice. Furthermore, we demonstrate that spike history improves predictions of neural activity within the PFC. In particular, the event-state most strongly associated with spike history effects was when animals revealed the decision to enter a particular maze arm. Combined, these and other results suggest that PFC spiking activity may reflect an overarching action-plan or policy rather than multiple independent cognitive processes. Figure 1 Heterogeneous plPFC neurons participate in and multiplex multiple functional ensembles. Plotted are the percentages of neurons for which task event-states (see Supplemental Material, Fig. S4) associated with this task significantly predicts the spiking ...

Prediction of spatiotemporal patterns of neural activity using a higher-order Markov representation of instantaneous pairwise maximum entropy model

Maximum entropy (MaxEnt) models have been suggested to fit the spatiotemporal patterns of simultaneously observed neuronal spike trains. To build such models, the distribution, px(X), needs to be determined, where X is a sequence of neural patterns formed from the vector X1,…,Xn for n time samples, where Xi is a sample of the spike train of a population at time i . Each neural pattern itself is a binary sequence, for which one represents a spike, and zero otherwise. MaxEnt models are constructed by matching the moments between neuronal constituents with the analogous empirical estimates from the distribution px(X). MaxEnt models that incorporate the first and second order interactions among neurons, also referred to as the instantaneous pairwise MaxEnt model or the Ising model, are expressed as where the individual, hi, and coupling, Jij, terms are parameters associated with the first and second order interactions, respectively, and Z is a normalization factor to insure . This model was shown to be effective in representing almost 90 percent of the information in small populations (less than 20 neurons) [1,2]. The main disadvantage of this model, however, is that it ignores the temporal correlation that represents the effect of the history of spiking activity on the current population state. Extending the width of neural patterns has been proposed as a method to incorporate spiking history. It destroys, however, the information in precise spike timings [3]. To incorporate the history term without compromising information in spike times, a higher-order Markov model is constructed in which patterns from different time samples are added. An example first-order Markov representation is expressed as where and are the individual, and , and are the coupling terms among the neuronal elements. This spatiotemporal model is more general than the representation introduced in Marre et al [4] to account for history terms , but at the expense of increasing the number of parameters. We evaluated the performance of the extended MaxEnt model in predicting the activity pattern of cat V1 neurons in response to drifting grating stimuli. A population of 21 neurons was recorded with 5 tetrodes. We compared the prediction power of this model with the instantaneous pairwise MaxEnt model, as well as the independent model. We show that the iterative scaling algorithm makes the extended model converge faster compared to [4], and also reduces the Kullback-Leibler divergence between the estimated and true distributions by 20 percent. Taken together, these results suggest the importance of accounting for temporal correlations in predicting the spatiotemporal patterns.

EMG Prediction From Motor Cortical Recordings via a Nonnegative Point-Process Filter

A constrained point-process filtering mechanism for prediction of electromyogram (EMG) signals from multichannel neural spike recordings is proposed here. Filters from the Kalman family are inherently suboptimal in dealing with non-Gaussian observations, or a state evolution that deviates from the Gaussianity assumption. To address these limitations, we modeled the non-Gaussian neural spike train observations by using a generalized linear model that encapsulates covariates of neural activity, including the neurons' own spiking history, concurrent ensemble activity, and extrinsic covariates (EMG signals). In order to predict the envelopes of EMGs, we reformulated the Kalman filter in an optimization framework and utilized a nonnegativity constraint. This structure characterizes the nonlinear correspondence between neural activity and EMG signals reasonably. The EMGs were recorded from 12 forearm and hand muscles of a behaving monkey during a grip-force task. In the case of limited training data, the constrained point-process filter improved the prediction accuracy when compared to a conventional Wiener cascade filter (a linear causal filter followed by a static nonlinearity) for different bin sizes and delays between input spikes and EMG output. For longer training datasets, results of the proposed filter and that of the Wiener cascade filter were comparable.

A Granger causality measure for point process models of ensemble neural spiking activity.

The ability to identify directional interactions that occur among multiple neurons in the brain is crucial to an understanding of how groups of neurons cooperate in order to generate specific brain functions. However, an optimal method of assessing these interactions has not been established. Granger causality has proven to be an effective method for the analysis of the directional interactions between multiple sets of continuous-valued data, but cannot be applied to neural spike train recordings due to their discrete nature. This paper proposes a point process framework that enables Granger causality to be applied to point process data such as neural spike trains. The proposed framework uses the point process likelihood function to relate a neuron's spiking probability to possible covariates, such as its own spiking history and the concurrent activity of simultaneously recorded neurons. Granger causality is assessed based on the relative reduction of the point process likelihood of one neuron obtained excluding one of its covariates compared to the likelihood obtained using all of its covariates. The method was tested on simulated data, and then applied to neural activity recorded from the primary motor cortex (MI) of a Felis catus subject. The interactions present in the simulated data were predicted with a high degree of accuracy, and when applied to the real neural data, the proposed method identified causal relationships between many of the recorded neurons. This paper proposes a novel method that successfully applies Granger causality to point process data, and has the potential to provide unique physiological insights when applied to neural spike trains.

Hidden Markov Models for the Stimulus-Response Relationships of Multistate Neural Systems

Given recent experimental results suggesting that neural circuits may evolve through multiple firing states, we develop a framework for estimating state-dependent neural response properties from spike train data. We modify the traditional hidden Markov model (HMM) framework to incorporate stimulus-driven, non-Poisson point-process observations. For maximal flexibility, we allow external, time-varying stimuli and the neurons' own spike histories to drive both the spiking behavior in each state and the transitioning behavior between states. We employ an appropriately modified expectation-maximization algorithm to estimate the model parameters. The expectation step is solved by the standard forward-backward algorithm for HMMs. The maximization step reduces to a set of separable concave optimization problems if the model is restricted slightly. We first test our algorithm on simulated data and are able to fully recover the parameters used to generate the data and accurately recapitulate the sequence of hidden states. We then apply our algorithm to a recently published data set in which the observed neuronal ensembles displayed multistate behavior and show that inclusion of spike history information significantly improves the fit of the model. Additionally, we show that a simple reformulation of the state space of the underlying Markov chain allows us to implement a hybrid half-multistate, half-histogram model that may be more appropriate for capturing the complexity of certain data sets than either a simple HMM or a simple peristimulus time histogram model alone.

A generalized linear model for estimating spectrotemporal receptive fields from responses to natural sounds.

In the auditory system, the stimulus-response properties of single neurons are often described in terms of the spectrotemporal receptive field (STRF), a linear kernel relating the spectrogram of the sound stimulus to the instantaneous firing rate of the neuron. Several algorithms have been used to estimate STRFs from responses to natural stimuli; these algorithms differ in their functional models, cost functions, and regularization methods. Here, we characterize the stimulus-response function of auditory neurons using a generalized linear model (GLM). In this model, each cell's input is described by: 1) a stimulus filter (STRF); and 2) a post-spike filter, which captures dependencies on the neuron's spiking history. The output of the model is given by a series of spike trains rather than instantaneous firing rate, allowing the prediction of spike train responses to novel stimuli. We fit the model by maximum penalized likelihood to the spiking activity of zebra finch auditory midbrain neurons in response to conspecific vocalizations (songs) and modulation limited (ml) noise. We compare this model to normalized reverse correlation (NRC), the traditional method for STRF estimation, in terms of predictive power and the basic tuning properties of the estimated STRFs. We find that a GLM with a sparse prior predicts novel responses to both stimulus classes significantly better than NRC. Importantly, we find that STRFs from the two models derived from the same responses can differ substantially and that GLM STRFs are more consistent between stimulus classes than NRC STRFs. These results suggest that a GLM with a sparse prior provides a more accurate characterization of spectrotemporal tuning than does the NRC method when responses to complex sounds are studied in these neurons.

Encoding of Coordinated Grasp Trajectories in Primary Motor Cortex

Few studies have investigated how the cortex encodes the preshaping of the hand as an object is grasped, an ethological movement referred to as prehension. We developed an encoding model of hand kinematics to test whether primary motor cortex (MI) neurons encode temporally extensive combinations of joint motions that characterize a prehensile movement. Two female rhesus macaque monkeys were trained to grasp 4 different objects presented by a robot while their arm was held in place by a thermoplastic brace. We used multielectrode arrays to record MI neurons and an infrared camera motion tracking system to record the 3-D positions of 14 markers placed on the monkeys' wrist and digits. A generalized linear model framework was used to predict the firing rate of each neuron in a 4 ms time interval, based on its own spiking history and the spatiotemporal kinematics of the joint angles of the hand. Our results show that the variability of the firing rate of MI neurons is better described by temporally extensive combinations of finger and wrist joint angle kinematics rather than any individual joint motion or any combination of static kinematic parameters at their optimal lag. Moreover, a higher percentage of neurons encoded joint angular velocities than joint angular positions. These results suggest that neurons encode the covarying trajectories of the hand's joints during a prehensile movement.

Goodness-of-fit tests for neural population models: the multivariate time-rescaling theorem

Statistical models of neural activity are at the core of the field of modern computational neuroscience. The activity of single neurons has been modeled to successfully explain dependencies of neural dynamics to its own spiking history, to external stimuli or other covariates. Recently, there has been a growing interest in modeling spiking activity of a population of simultaneously recorded neurons to study the effects of correlations and functional connectivity on neural information processing (existing models include generalized linear models or maximum-entropy approaches). For point-process-based models of single neurons, the time-rescaling theorem has proven to be a useful toolbox to assess goodness-of-fit. In its univariate form, the time-rescaling theorem states that if the conditional intensity function of a point process is known, then its inter-spike intervals can be transformed or “rescaled” so that they are independent and exponentially distributed. However, the theorem in its original form lacks sensitivity to detect even strong dependencies between neurons. Here, we present how the theorem can be extended to be applied to neural population models and we provide a step-by-step procedure to perform the statistical tests. We then apply both the univariate and multivariate tests to simplified toy models, but also to more complicated many-neuron models and to neuronal populations recorded in V1 of awake monkey during natural scenes stimulation. We demonstrate that important features of the population activity can only be detected using the multivariate extension of the test. The time-rescaling theorem has been used extensively to assess goodness-of-fit and to compare different single-neuron models. Multivariate population models became popular only recently. Some of the approaches did not attempt any goodness-of-fit analysis at all or used the time-rescaling theorem separately for each modeled spike train. The proposed multivariate time-rescaling theorem fills the missing gap. Our studies using experimental data show that the use of the univariate theorem may erroneously indicate a good fit for independent encoding models. The lack of fit is detected by the multivariate extension and can be partly corrected for by including additional cross-interaction terms in the model. Overall, the proposed procedure is a simple-to-implement analysis tool for any population model that is based on the conditional intensity formalism.

Population decoding of motor cortical activity using a generalized linear model with hidden states

Generalized linear models (GLMs) have been developed for modeling and decoding population neuronal spiking activity in the motor cortex. These models provide reasonable characterizations between neural activity and motor behavior. However, they lack a description of movement-related terms which are not observed directly in these experiments, such as muscular activation, the subject’s level of attention, and other internal or external states. Here we propose to include a multi-dimensional hidden state to address these states in a GLM framework where the spike count at each time is described as a function of the hand state (position, velocity, and acceleration), truncated spike history, and the hidden state. The model can be identified by an Expectation–Maximization algorithm. We tested this new method in two datasets where spikes were simultaneously recorded using a multi-electrode array in the primary motor cortex of two monkeys. It was found that this method significantly improves the model-fitting over the classical GLM, for hidden dimensions varying from 1 to 4. This method also provides more accurate decoding of hand state (reducing the mean square error by up to 29% in some cases), while retaining real-time computational efficiency. These improvements on representation and decoding over the classical GLM model suggest that this new approach could contribute as a useful tool to motor cortical decoding and prosthetic applications.