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      Spike-Threshold Adaptation Predicted by Membrane Potential Dynamics In Vivo

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          Abstract

          Neurons encode information in sequences of spikes, which are triggered when their membrane potential crosses a threshold. In vivo, the spiking threshold displays large variability suggesting that threshold dynamics have a profound influence on how the combined input of a neuron is encoded in the spiking. Threshold variability could be explained by adaptation to the membrane potential. However, it could also be the case that most threshold variability reflects noise and processes other than threshold adaptation. Here, we investigated threshold variation in auditory neurons responses recorded in vivo in barn owls. We found that spike threshold is quantitatively predicted by a model in which the threshold adapts, tracking the membrane potential at a short timescale. As a result, in these neurons, slow voltage fluctuations do not contribute to spiking because they are filtered by threshold adaptation. More importantly, these neurons can only respond to input spikes arriving together on a millisecond timescale. These results demonstrate that fast adaptation to the membrane potential captures spike threshold variability in vivo.

          Author Summary

          Neurons spike when their membrane potential exceeds a threshold value, but this value has been shown to be variable in the same neuron recorded in vivo. This variability could reflect noise, or deterministic processes that make the threshold vary with the membrane potential. The second alternative would have important functional consequences. Here, we show that threshold variability is a genuine feature of neurons, which reflects adaptation to the membrane potential at a short timescale, with little contribution from noise. This demonstrates that a deterministic model can predict spikes based only on the membrane potential.

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          Most cited references44

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          Action potential generation requires a high sodium channel density in the axon initial segment.

          The axon initial segment (AIS) is a specialized region in neurons where action potentials are initiated. It is commonly assumed that this process requires a high density of voltage-gated sodium (Na(+)) channels. Paradoxically, the results of patch-clamp studies suggest that the Na(+) channel density at the AIS is similar to that at the soma and proximal dendrites. Here we provide data obtained by antibody staining, whole-cell voltage-clamp and Na(+) imaging, together with modeling, which indicate that the Na(+) channel density at the AIS of cortical pyramidal neurons is approximately 50 times that in the proximal dendrites. Anchoring of Na(+) channels to the cytoskeleton can explain this discrepancy, as disruption of the actin cytoskeleton increased the Na(+) current measured in patches from the AIS. Computational models required a high Na(+) channel density (approximately 2,500 pS microm(-2)) at the AIS to account for observations on action potential generation and backpropagation. In conclusion, action potential generation requires a high Na(+) channel density at the AIS, which is maintained by tight anchoring to the actin cytoskeleton.
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            How spike generation mechanisms determine the neuronal response to fluctuating inputs.

            This study examines the ability of neurons to track temporally varying inputs, namely by investigating how the instantaneous firing rate of a neuron is modulated by a noisy input with a small sinusoidal component with frequency (f). Using numerical simulations of conductance-based neurons and analytical calculations of one-variable nonlinear integrate-and-fire neurons, we characterized the dependence of this modulation on f. For sufficiently high noise, the neuron acts as a low-pass filter. The modulation amplitude is approximately constant for frequencies up to a cutoff frequency, fc, after which it decays. The cutoff frequency increases almost linearly with the firing rate. For higher frequencies, the modulation amplitude decays as C/falpha, where the power alpha depends on the spike initiation mechanism. For conductance-based models, alpha = 1, and the prefactor C depends solely on the average firing rate and a spike "slope factor," which determines the sharpness of the spike initiation. These results are attributable to the fact that near threshold, the sodium activation variable can be approximated by an exponential function. Using this feature, we propose a simplified one-variable model, the "exponential integrate-and-fire neuron," as an approximation of a conductance-based model. We show that this model reproduces the dynamics of a simple conductance-based model extremely well. Our study shows how an intrinsic neuronal property (the characteristics of fast sodium channels) determines the speed with which neurons can track changes in input.
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              Axon physiology.

              Axons are generally considered as reliable transmission cables in which stable propagation occurs once an action potential is generated. Axon dysfunction occupies a central position in many inherited and acquired neurological disorders that affect both peripheral and central neurons. Recent findings suggest that the functional and computational repertoire of the axon is much richer than traditionally thought. Beyond classical axonal propagation, intrinsic voltage-gated ionic currents together with the geometrical properties of the axon determine several complex operations that not only control signal processing in brain circuits but also neuronal timing and synaptic efficacy. Recent evidence for the implication of these forms of axonal computation in the short-term dynamics of neuronal communication is discussed. Finally, we review how neuronal activity regulates both axon morphology and axonal function on a long-term time scale during development and adulthood.
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                Author and article information

                Contributors
                Role: Editor
                Journal
                PLoS Comput Biol
                PLoS Comput. Biol
                plos
                ploscomp
                PLoS Computational Biology
                Public Library of Science (San Francisco, USA )
                1553-734X
                1553-7358
                April 2014
                10 April 2014
                : 10
                : 4
                : e1003560
                Affiliations
                [1 ]Dominick P. Purpura Department of Neuroscience, Albert Einstein College of Medicine, Bronx, New York, United States of America
                [2 ]Laboratoire Psychologie de la Perception, CNRS and Université Paris Descartes, Paris, France
                [3 ]Département d'Etudes Cognitives, Ecole Normale Supérieure, Paris, France
                [4 ]Sorbonne Universités, UPMC Univ. Paris 06, UMR_S 968, Institut de la Vision, Paris, France
                [5 ]INSERM, U968, Paris, France
                [6 ]CNRS, UMR_7210, Paris, France
                Duke University, United States of America
                Author notes

                The authors have declared that no competing interests exist.

                Conceived and designed the experiments: BF RB. Performed the experiments: BF JLP. Analyzed the data: BF. Contributed reagents/materials/analysis tools: BF. Wrote the paper: BF JLP RB.

                Article
                PCOMPBIOL-D-13-01510
                10.1371/journal.pcbi.1003560
                3983065
                24722397
                c48e6cb7-cbf6-4b74-af68-97e7de4e57a7
                Copyright @ 2014

                This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

                History
                : 26 August 2013
                : 21 February 2014
                Page count
                Pages: 11
                Funding
                This work was supported by a European Marie Curie fellowship (PIOF-GA-2011-300753) to BF and grants from the European Research Council (ERC StG 240132) and Agence Nationale de la Recherche (ANR-11-0001-02 PSL* and ANR-10-LABX-0087) to RB and from the National Institute of Health (DC007690) to JLP. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
                Categories
                Research Article
                Biology and Life Sciences
                Computational Biology
                Computational Neuroscience
                Neuroscience

                Quantitative & Systems biology
                Quantitative & Systems biology

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