Abstract
Understanding how ensembles of neurons represent and transmit information in the patterns of their joint spiking activity is a fundamental question in computational neuroscience. At present, analyses of spiking activity from neuronal ensembles are limited because multivariate point process (MPP) models cannot represent simultaneous occurrences of spike events at an arbitrarily small time resolution. Solo recently reported a simultaneous-event multivariate point process (SEMPP) model to correct this key limitation. In this paper, we show how Solo's discrete-time formulation of the SEMPP model can be efficiently fit to ensemble neural spiking activity using a multinomial generalized linear model (mGLM). Unlike existing approximate procedures for fitting the discrete-time SEMPP model, the mGLM is an exact algorithm. The MPP time-rescaling theorem can be used to assess model goodness-of-fit. We also derive a new marked point-process (MkPP) representation of the SEMPP model that leads to new thinning and time-rescaling algorithms for simulating an SEMPP stochastic process. These algorithms are much simpler than multivariate extensions of algorithms for simulating a univariate point process, and could not be arrived at without the MkPP representation. We illustrate the versatility of the SEMPP model by analyzing neural spiking activity from pairs of simultaneously-recorded rat thalamic neurons stimulated by periodic whisker deflections, and by simulating SEMPP data. In the data analysis example, the SEMPP model demonstrates that whisker motion significantly modulates simultaneous spiking activity at the 1 ms time scale and that the stimulus effect is more than one order of magnitude greater for simultaneous activity compared with non-simultaneous activity. Together, the mGLM, the MPP time-rescaling theorem and the MkPP representation of the SEMPP model offer a theoretically sound, practical tool for measuring joint spiking propensity in a neuronal ensemble.
Highlights
The study of how neurons represent and transmit information in the patterns of their ensemble spiking activity has been greatly facilitated in the last 17 years by the technical capability to measure simultaneously multiple single neuron activity using multiple electrode recording techniques (Wilson and McNaughton, 1993; Maynard et al, 1997)
We propose a multinomial generalized linear model of a discrete-time formulation of the simultaneous-event multivariate point process (SEMPP), which can be efficiently fit to ensemble neural spiking activity, and derive a new marked point-process (MkPP) representation of the SEMPP model
MGLM: A VERSATILE PARADIGM FOR ENCODING ANALYSES OF ENSEMBLE NEURAL ACTIVITY We have presented a new algorithmic framework for the analysis of ensemble neural spiking activity based on the joint probability density of a multivariate point process (MPP) with simultaneous events
Summary
The study of how neurons represent and transmit information in the patterns of their ensemble spiking activity has been greatly facilitated in the last 17 years by the technical capability to measure simultaneously multiple single neuron activity using multiple electrode recording techniques (Wilson and McNaughton, 1993; Maynard et al, 1997) For this reason, the development of statistical methods to characterize ensemble spiking activity is an active field of neuroscience research (Brown et al, 2004; Grün, 2009). Several histogram-based methods have been used to analyze ensemble neural spiking activity These include the cross-correlogram (Brody, 1999), the cross-intensity function (Brillinger et al, 1976) and the joint peristimulus time histogram (Gerstein and Perkel, 1969). These methods only measure the association between pairs of neurons and the fundamental assumption of stationarity that underlies their construction can be hard to justify given that neural spiking activity is often highly plastic and adaptive
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