A fundamental problem in neuroscience is understanding how sequences of action potentials ("spikes") encode information about sensory signals and motor outputs. Although traditional theories assume that this information is conveyed by the total number of spikes fired within a specified time interval (spike rate), recent studies have shown that additional information is carried by the millisecond-scale timing patterns of action potentials (spike timing). However, it is unknown whether or how subtle differences in spike timing drive differences in perception or behavior, leaving it unclear whether the information in spike timing actually plays a role in brain function. By examining the activity of individual motor units (the muscle fibers innervated by a single motor neuron) and manipulating patterns of activation of these neurons, we provide both correlative and causal evidence that the nervous system uses millisecond-scale variations in the timing of spikes within multispike patterns to control a vertebrate behavior-namely, respiration in the Bengalese finch, a songbird. These findings suggest that a fundamental assumption of current theories of motor coding requires revision.motor systems | neurophysiology | computational neuroscience | information theory | songbird T he brain uses sequences of spikes to encode sensory and motor signals. In principle, neurons can encode this information via their firing rates, the precise timing of their spikes, or both (1, 2). Although many studies have shown that spike timing contains information beyond that in the rate in sensory codes (3-5), these studies could not verify whether precise timing affects perception or behavior. In motor systems, rate coding approaches dominate (6, 7), but we recently showed that precise spike timing in motor cortex can predict upcoming behavior better than spike rates (8), showing that spike timing carries information in motor as well as sensory cortex. However, as in sensory systems, it remains unknown whether spike timing in motor systems actually controls variations in behavior (9, 10). Resolving this question, therefore, requires examining the spike code used by the neurons that innervate the muscles, because discovering an apparent spike timing code in any brain area upstream of motor neurons is subject to the same ambiguity about whether spike timing patterns actually affect behavior.A spike timing-based theory of motor production predicts that millisecond-scale fluctuations in spike timing, holding other spike train features constant, will causally influence behavior. We tested this prediction by analyzing the activity of single motor units (that is, the muscle fibers innervated by a single motor neuron), focusing largely on the minimal patterns that have variable spike timing but fixed firing rate, burst onset, and burst duration: sequences of three spikes ("triplets"), where the third spike is a fixed latency after the first, but the timing of the middle spike varies. We examined timing codes in songbirds by focusing on respiration, ...
Estimation of mutual information between (multidimensional) real-valued variables is used in analysis of complex systems, biological systems, and recently also quantum systems. This estimation is a hard problem, and universally good estimators provably do not exist. Kraskov et al. (PRE, 2004) introduced a successful mutual information estimation approach based on the statistics of distances between neighboring data points, which empirically works for a wide class of underlying probability distributions. Here we improve this estimator by (i) expanding its range of applicability, and by providing (ii) a self-consistent way of verifying the absence of bias, (iii) a method for estimation of its variance, and (iv) a criterion for choosing the values of the free parameter of the estimator. We demonstrate the performance of our estimator on synthetic data sets, as well as on neurophysiological and systems biology data sets.
We re-examined data from the classic Luria-Delbrück fluctuation experiment, which is often credited with establishing a Darwinian basis for evolution. We argue that, for the Lamarckian model of evolution to be ruled out by the experiment, the experiment must favor pure Darwinian evolution over both the Lamarckian model and a model that allows both Darwinian and Lamarckian mechanisms (as would happen for bacteria with CRISPR-Cas immunity). Analysis of the combined model was not performed in the original 1943 paper. The Luria-Delbrück paper also did not consider the possibility of neither model fitting the experiment. Using Bayesian model selection, we find that the Luria-Delbrück experiment, indeed, favors the Darwinian evolution over purely Lamarckian. However, our analysis does not rule out the combined model, and hence cannot rule out Lamarckian contributions to the evolutionary dynamics.
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