Abstract
Information processing can leave distinct footprints on the statistics of neural spiking. For example, efficient coding minimizes the statistical dependencies on the spiking history, while temporal integration of information may require the maintenance of information over different timescales. To investigate these footprints, we developed a novel approach to quantify history dependence within the spiking of a single neuron, using the mutual information between the entire past and current spiking. This measure captures how much past information is necessary to predict current spiking. In contrast, classical time-lagged measures of temporal dependence like the autocorrelation capture how long-potentially redundant-past information can still be read out. Strikingly, we find for model neurons that our method disentangles the strength and timescale of history dependence, whereas the two are mixed in classical approaches. When applying the method to experimental data, which are necessarily of limited size, a reliable estimation of mutual information is only possible for a coarse temporal binning of past spiking, a so-called past embedding. To still account for the vastly different spiking statistics and potentially long history dependence of living neurons, we developed an embedding-optimization approach that does not only vary the number and size, but also an exponential stretching of past bins. For extra-cellular spike recordings, we found that the strength and timescale of history dependence indeed can vary independently across experimental preparations. While hippocampus indicated strong and long history dependence, in visual cortex it was weak and short, while in vitro the history dependence was strong but short. This work enables an information-theoretic characterization of history dependence in recorded spike trains, which captures a footprint of information processing that is beyond time-lagged measures of temporal dependence. To facilitate the application of the method, we provide practical guidelines and a toolbox.
Highlights
How is information processing organized in the brain, and what are the principles that govern neural coding? footprints of different information processing and neural coding strategies can be found in the firing statistics of individual neurons, and in particular in the history dependence, the statistical dependence of a single neuron’s spiking on its preceding activity
We demonstrate the differences between history dependence and time-lagged measures of temporal dependence for several models of neural spiking activity
To better understand how other well-established statistical measures relate to the total history dependence Rtot and the information timescale τR, we show Rtot and τR versus the median interspike interval (ISI), the coefficient of variation CV = σISI/μISI of the ISI distribution, and Together, total history dependence and the information timescale show clear differences between neural systems. (A) Embedding-optimized Shuffling estimates of the total history dependence Rtot are plotted against the information timescale τR for individual sorted units from four different neural systems
Summary
How is information processing organized in the brain, and what are the principles that govern neural coding? footprints of different information processing and neural coding strategies can be found in the firing statistics of individual neurons, and in particular in the history dependence, the statistical dependence of a single neuron’s spiking on its preceding activity.In classical, noise-less efficient coding, history dependence should be low to minimize redundancy and optimize efficiency of neural information transmission [1,2,3]. In addition to its magnitude, the timescale of history dependence provides an important footprint of processing at different processing stages in the brain [9,10,11]. This is because higher-level processing requires integrating information on longer timescales than lower-level processing [12]. History dependence in neural spiking should reach further into the past for neurons involved in higher-level processing [9, 13]. Quantifying history dependence and its timescale could probe these different footprints and yield valuable insights on how neural coding and information processing is organized in the brain
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