Energy aspects of the synchronization of model neurons

Torrealdea, Francisco; D’Anjou, Alicia; Graña, Manuel; Sarasola, C.

doi:10.1103/physreve.74.011905

Cited by 63 publications

(27 citation statements)

References 36 publications

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“…The time derivative of this energy gives the balance of energy consumption and provision during its signaling behavior. To our knowledge, apart from some previous attempts to find energy functions for neuron models with chaotic dynamics [30][31][32], this approach has not been used in the literature. The Hodgkin-Huxley model is both of wide interest and very appropriate for investigating energy aspects since it is based on sound biophysical principles.…”

Section: A the Energy Approachmentioning

confidence: 99%

Energy and information in Hodgkin-Huxley neurons

2011

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The generation of spikes by neurons is energetically a costly process and the evaluation of the metabolic energy required to maintain the signaling activity of neurons a challenge of practical interest. Neuron models are frequently used to represent the dynamics of real neurons but hardly ever to evaluate the electrochemical energy required to maintain that dynamics. This paper discusses the interpretation of a Hodgkin-Huxley circuit as an energy model for real biological neurons and uses it to evaluate the consumption of metabolic energy in the transmission of information between neurons coupled by electrical synapses, i.e., gap junctions. We show that for a single postsynaptic neuron maximum energy efficiency, measured in bits of mutual information per molecule of adenosine triphosphate (ATP) consumed, requires maximum energy consumption. For groups of parallel postsynaptic neurons we determine values of the synaptic conductance at which the energy efficiency of the transmission presents clear maxima at relatively very low values of metabolic energy consumption. Contrary to what could be expected, the best performance occurs at a low energy cost.

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Section: A the Energy Approachmentioning

confidence: 99%

Energy and information in Hodgkin-Huxley neurons

2011

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“…which is the expression for the energy of a three dimensional model that we reported in Ref. (Torrealdea et al 2006).…”

Section: Energy Consumption When Signalling In Isolationmentioning

confidence: 88%

“…8. This is due to the fact that in that region of values of the coupling strength both neurons synchronize in anti-phase producing large synchronization errors and maximum correlation values (Torrealdea et al 2006). Moreover, anti-phase synchronization occur at the least possible values of energy consumption, Fig.…”

Section: Mutual Information To Average Energy Consumption Ratiomentioning

confidence: 97%

“…In Ref. (Torrealdea et al 2006) we used this procedure to find an energy function for the well-known three variable Hinmarsh-Rose thalamic model of a neuron. In the last part of this section we apply the same procedure to find and energy function for the four dimensional version of the model that was introduced by Pinto et al in Ref.…”

Section: Energy Function Associated To a Model Neuronmentioning

confidence: 99%

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Energy efficiency of information transmission by electrically coupled neurons

Torrealdea¹,

Sarasola²,

D’Anjou³

et al. 2009

Biosystems

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The generation of spikes by neurons is energetically a costly process. This paper studies the consumption of energy and the information entropy in the signalling activity of a model neuron both when it is supposed isolated and when it is coupled to another neuron by an electrical synapse. The neuron has been modelled by a four-dimensional Hindmarsh-Rose type kinetic model for which an energy function has been deduced. For the isolated neuron values of energy consumption and information entropy at different signalling regimes have been computed. For two neurons coupled by a gap junction we have analyzed the roles of the membrane and synapse in the contribution of the energy that is required for their organized signalling. Computational results are provided for cases of identical and nonidentical neurons coupled by unidirectional and bidirectional gap junctions. One relevant result is that there are values of the coupling strength at which the organized signalling of two neurons induced by the gap junction takes place at relatively low values of energy consumption and the ratio of mutual information to energy consumption is relatively high. Therefore, communicating at these coupling values could be energetically the most efficient option.

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“…There has been a wealth of research recently focusing on understanding fundamental design principles that govern neuronal excitation, for instance in elucidating how sensory percepts are encoded (Koelling & Nykamp 2012; Machens, Gollisch, Kolesnikova, & Herz 2005; Watson, Barlow, & Robson 1983), as well as to populations of neurons within functioning networks to better understand how information is transmitted from neuron to neuron (Alle, Roth, & Geiger 2009; Attwell & Laughlin 2001; Sengupta, Stemmler, Laughlin, & Niven 2010; Torrealdea, D’Anjou, Grana, Sarasola, & D’Anjou 2006). If one hypothesized that metabolic energy, or ATP consumption, was what the endogenous stimulation optimized, one could construct an equation relating the number of ATPs consumed to the generation of the action potential itself, incorporate that into the optimization metric in the algorithm, and then determine a theoretical result that could be verified or refuted through experimental techniques.…”

Section: Discussionmentioning

confidence: 99%

Switching neuronal state: optimal stimuli revealed using a stochastically-seeded gradient algorithm

Chang

Paydarfar

2014

J Comput Neurosci

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Inducing a switch in neuronal state using energy optimal stimuli is relevant to a variety of problems in neuroscience. Analytical techniques from optimal control theory can identify such stimuli; however, solutions to the optimization problem using indirect variational approaches can be elusive in models that describe neuronal behavior. Here we develop and apply a direct gradient-based optimization algorithm to find stimulus waveforms that elicit a change in neuronal state while minimizing energy usage. We analyze standard models of neuronal behavior, the Hodgkin-Huxley and FitzHugh-Nagumo models, to show that the gradient-based algorithm: 1) enables automated exploration of a wide solution space, using stochastically generated initial waveforms that converge to multiple locally optimal solutions; and 2) finds optimal stimulus waveforms that achieve a physiological outcome condition, without a priori knowledge of the optimal terminal condition of all state variables. Analysis of biological systems using stochastically-seeded gradient methods can reveal salient dynamical mechanisms underlying the optimal control of system behavior. The gradient algorithm may also have practical applications in future work, for example, finding energy optimal waveforms for therapeutic neural stimulation that minimizes power usage and diminishes off-target effects and damage to neighboring tissue.

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Energy aspects of the synchronization of model neurons

Cited by 63 publications

References 36 publications

Energy and information in Hodgkin-Huxley neurons

Energy and information in Hodgkin-Huxley neurons

Energy efficiency of information transmission by electrically coupled neurons

Switching neuronal state: optimal stimuli revealed using a stochastically-seeded gradient algorithm

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