The initiation and propagation of action potentials (APs) places high demands on the energetic resources of neural tissue. Each AP forces ATP-driven ion pumps to work harder to restore the ionic concentration gradients, thus consuming more energy. Here, we ask whether the ionic currents underlying the AP can be predicted theoretically from the principle of minimum energy consumption. A long-held supposition that APs are energetically wasteful, based on theoretical analysis of the squid giant axon AP, has recently been overturned by studies that measured the currents contributing to the AP in several mammalian neurons. In the single compartment models studied here, AP energy consumption varies greatly among vertebrate and invertebrate neurons, with several mammalian neuron models using close to the capacitive minimum of energy needed. Strikingly, energy consumption can increase by more than ten-fold simply by changing the overlap of the Na⁺ and K⁺ currents during the AP without changing the APs shape. As a consequence, the height and width of the AP are poor predictors of energy consumption. In the Hodgkin–Huxley model of the squid axon, optimizing the kinetics or number of Na⁺ and K⁺ channels can whittle down the number of ATP molecules needed for each AP by a factor of four. In contrast to the squid AP, the temporal profile of the currents underlying APs of some mammalian neurons are nearly perfectly matched to the optimized properties of ionic conductances so as to minimize the ATP cost. Neurons produce a myriad of action potentials with different shapes and varying heights and widths; underlying these action potentials are highly nonlinear, voltage-dependent ionic conductances with varying biophysical properties. Each action potential comes at a cost: the brain uses a substantial portion of its total energy budget to generate and propagate action potentials. Recent results show that some mammalian action potentials have biophysical properties that make them energy efficient. Yet, how widespread are energy efficient action potentials? Using mathematical analysis and modeling, we show that there is no direct relationship between the height, width, and the energy consumption of a single action potential. Furthermore, we establish that many mammalian action potentials have biophysical properties that reduce the overlap between their inward and outward currents so as to minimize energy consumption. This reduction in overlap results from a combination of ion channel properties uniquely tailored for each particular neuron type and the functional purpose of the action potential in that neuron. By comparing the measured biophysical parameters to the parameters produced by numerical optimization for maximal energy-efficiency, we argue that natural selection for energy-efficiency could help explain both the shape of the action potential and the underlying biophysics of ionic currents.

In systems biology, questions concerning the molecular and cellular makeup of an organism are of utmost importance, especially when trying to understand how unreliable components—like genetic circuits, biochemical cascades, and ion channels, among others—enable reliable and adaptive behaviour. The repertoire and speed of biological computations are limited by thermodynamic or metabolic constraints: an example can be found in neurons, where fluctuations in biophysical states limit the information they can encode—with almost 20–60% of the total energy allocated for the brain used for signalling purposes, either via action potentials or by synaptic transmission. Here, we consider the imperatives for neurons to optimise computational and metabolic efficiency, wherein benefits and costs trade-off against each other in the context of self-organised and adaptive behaviour. In particular, we try to link information theoretic (variational) and thermodynamic (Helmholtz) free-energy formulations of neuronal processing and show how they are related in a fundamental way through a complexity minimisation lemma.

Given the amount of knowledge and data accruing in the neurosciences, is it time to formulate a general principle for neuronal dynamics that holds at evolutionary, developmental, and perceptual timescales? In this paper, we propose that the brain (and other self-organised biological systems) can be characterised via the mathematical apparatus of a gauge theory. The picture that emerges from this approach suggests that any biological system (from a neuron to an organism) can be cast as resolving uncertainty about its external milieu, either by changing its internal states or its relationship to the environment. Using formal arguments, we show that a gauge theory for neuronal dynamics—based on approximate Bayesian inference—has the potential to shed new light on phenomena that have thus far eluded a formal description, such as attention and the link between action and perception.

Identifying the determinants of neuronal energy consumption and their relationship to information coding is critical to understanding neuronal function and evolution. Three of the main determinants are cell size, ion channel density, and stimulus statistics. Here we investigate their impact on neuronal energy consumption and information coding by comparing single-compartment spiking neuron models of different sizes with different densities of stochastic voltage-gated Na⁺ and K⁺ channels and different statistics of synaptic inputs. The largest compartments have the highest information rates but the lowest energy efficiency for a given voltage-gated ion channel density, and the highest signaling efficiency (bits spike ⁻¹) for a given firing rate. For a given cell size, our models revealed that the ion channel density that maximizes energy efficiency is lower than that maximizing information rate. Low rates of small synaptic inputs improve energy efficiency but the highest information rates occur with higher rates and larger inputs. These relationships produce a Law of Diminishing Returns that penalizes costly excess information coding capacity, promoting the reduction of cell size, channel density, and input stimuli to the minimum possible, suggesting that the trade-off between energy and information has influenced all aspects of neuronal anatomy and physiology.

A balance between excitatory and inhibitory synaptic currents is thought to be important for several aspects of information processing in cortical neurons in vivo, including gain control, bandwidth and receptive field structure. These factors will affect the firing rate of cortical neurons and their reliability, with consequences for their information coding and energy consumption. Yet how balanced synaptic currents contribute to the coding efficiency and energy efficiency of cortical neurons remains unclear. We used single compartment computational models with stochastic voltage-gated ion channels to determine whether synaptic regimes that produce balanced excitatory and inhibitory currents have specific advantages over other input regimes. Specifically, we compared models with only excitatory synaptic inputs to those with equal excitatory and inhibitory conductances, and stronger inhibitory than excitatory conductances (i.e. approximately balanced synaptic currents). Using these models, we show that balanced synaptic currents evoke fewer spikes per second than excitatory inputs alone or equal excitatory and inhibitory conductances. However, spikes evoked by balanced synaptic inputs are more informative (bits/spike), so that spike trains evoked by all three regimes have similar information rates (bits/s). Consequently, because spikes dominate the energy consumption of our computational models, approximately balanced synaptic currents are also more energy efficient than other synaptic regimes. Thus, by producing fewer, more informative spikes approximately balanced synaptic currents in cortical neurons can promote both coding efficiency and energy efficiency. The adult human brain consumes more than 20% of the resting metabolism. With ∼19–23 billion neurons, the cerebral cortex consumes much of this energy, mainly to restore ion gradients across membranes for electrical signaling. Even small increases in the average spike rate of cortical neurons could cause the cortex to exceed the energy available for the whole brain. Consequently, the cortex is likely to be under considerable selective pressure to reduce spike rates but, given its important roles in behavior, to maintain information processing. Numerous experimental studies have shown that excitatory and inhibitory synaptic currents are balanced in cortical neurons. Could this feature of cortical neurons contribute to their efficiency? We tested this by making comparisons among computational models with different amounts of inhibition and excitation: excitation only, equal excitation and inhibition (balanced synaptic conductances), and more inhibition than excitation (balanced synaptic currents). Our simulations show that computational models with balanced synaptic currents have similar information rates to the other regimes but achieve this with fewer, more informative spikes that consume less energy. Therefore, in comparison to other synaptic regimes, balanced synaptic currents have the highest coding efficiency and the highest energy efficiency.

Maintaining the ability of the nervous system to perceive, remember, process, and react to the outside world requires a continuous energy supply. Yet the overall power consumption is remarkably low, which has inspired engineers to mimic nervous systems in designing artificial cochlea, retinal implants, and brain-computer interfaces (BCIs) to improve the quality of life in patients. Such neuromorphic devices are both energy efficient and increasingly able to emulate many functions of the human nervous system. We examine the energy constraints of neuronal signaling within biology, review the quantitative tradeoff between energy use and information processing, and ask whether the biophysics and design of nerve cells minimizes energy consumption.