Event Abstract Back to Event Bang-bang optimality of energy efficient spikes in single neuron models Biswa Sengupta1*, Martin Stemmler2, Jeremy Niven1, Andreas Herz2 and Simon Laughlin1 1 University of Cambridge, United Kingdom 2 LMU Munich , BCCN Munich, Germany About 50-80% of the total energy allocated to the mammalian brain is used for signaling, mainly to drive the $Na^+$/ $K^+$ pump (Attwell & Laughlin, 2001). Due to the substantial contribution of action potentials to the energy consumption, the biophysical properties generating an action potential can be matched to make them energy efficient (Alle et al., 2009). By combining different voltage-dependent ionic conductances with varying biophysical properties, different neurons express a myriad of action potential shapes characterized by varying heights and widths (Bean, 2007). How widespread are energy efficient action potentials and what are the major factors defining the energy efficiency of a single action potential ? The passive electric properties of a neuron, namely its capacitance and input resistance, set a lower bound for the cost of a given action potential. Inward ( $Na^+$) and outward ($K^+$) voltage-dependent currents act in a push-pull manner to change the voltage; these currents will invariably overlap, which can cause the energetic cost to rise to more than eleven-fold the baseline cost. We use seven single compartment models to assess the energy cost of vertebrate (cerebellar granule neurons, cortical interneurons, thalamo-cortical relay neurons and hippocampal interneurons) and invertebrate (squid axons, crab axons and bee kenyon cells) action potentials. We show that the energy consumption of a single action potential is directly dependent on the overlap between the $Na^+$ and $K^+$ currents that generate them. By optimizing the ionic conductance parameters that affect this overlap, we investigate how close each neuron type is to the minimal energy expenditure. Using sensitivity analysis and perturbation theory for periodic systems we show that an optimal model minimizes the overlap between $Na^+$ and $K^+$ currents. Just as in optimal control theory, the ionic conductance parameters allow for a bang-bang control of the underlying $Na^+$ and $K^+$ currents eliciting the action potential. Energy efficient action potentials are neuron-dependent but generally have narrower width, shorter height and exhibit an extremely rapid, explosive onset. Our modeling shows that in some neurons, such as the thalamo-cortical relay neurons, the hippocampal GABAergic interneurons or fast-spiking cortical interneurons, the properties of the currents that minimize the energy cost of the action potential are close to the experimentally measured currents, suggesting selection for reducing the energy costs. The experimentally observed properties of the squid giant axon model however, consumes substantial energy when compared to the optimal model that consumes far lower energy. We suggest that the deviation between the parameters generating the theoretical minimum cost of the action potential and those observed in neurons is dependent upon the function of the neuron. Conference: Computational and Systems Neuroscience 2010, Salt Lake City, UT, United States, 25 Feb - 2 Mar, 2010. Presentation Type: Poster Presentation Topic: Poster session II Citation: Sengupta B, Stemmler M, Niven J, Herz A and Laughlin S (2010). Bang-bang optimality of energy efficient spikes in single neuron models. Front. Neurosci. Conference Abstract: Computational and Systems Neuroscience 2010. doi: 10.3389/conf.fnins.2010.03.00085 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 20 Feb 2010; Published Online: 20 Feb 2010. * Correspondence: Biswa Sengupta, University of Cambridge, Paris, United Kingdom, bs393@cam.ac.uk Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Biswa Sengupta Martin Stemmler Jeremy Niven Andreas Herz Simon Laughlin Google Biswa Sengupta Martin Stemmler Jeremy Niven Andreas Herz Simon Laughlin Google Scholar Biswa Sengupta Martin Stemmler Jeremy Niven Andreas Herz Simon Laughlin PubMed Biswa Sengupta Martin Stemmler Jeremy Niven Andreas Herz Simon Laughlin Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.