Metabolic Energy of Action Potentials Modulated by Spike Frequency Adaptation

Postsynaptic Potential Energy as Determinant of Synaptic Plasticity

Metabolic energy can be used as a unifying principle to control neuronal activity. However, whether and how metabolic energy alone can determine the outcome of synaptic plasticity remains unclear. This study proposes a computational model of synaptic plasticity that is completely determined by energy. A simple quantitative relationship between synaptic plasticity and postsynaptic potential energy is established. Synaptic weight is directly proportional to the difference between the baseline potential energy and the suprathreshold potential energy and is constrained by the maximum energy supply. Results show that the energy constraint improves the performance of synaptic plasticity and avoids setting the hard boundary of synaptic weights. With the same set of model parameters, our model can reproduce several classical experiments in homo- and heterosynaptic plasticity. The proposed model can explain the interaction mechanism of Hebbian and homeostatic plasticity at the cellular level. Homeostatic synaptic plasticity at different time scales coexists. Homeostatic plasticity operating on a long time scale is caused by heterosynaptic plasticity and, on the same time scale as Hebbian synaptic plasticity, is caused by the constraint of energy supply.

Neural optimization: Understanding trade-offs with Pareto theory

Nervous systems, like any organismal structure, have been shaped by evolutionary processes to increase fitness. The resulting neural 'bauplan' has to account for multiple objectives simultaneously, including computational function, as well as additional factors such as robustness to environmental changes and energetic limitations. Oftentimes these objectives compete, and quantification of the relative impact of individual optimization targets is non-trivial. Pareto optimality offers a theoretical framework to decipher objectives and trade-offs between them. We, therefore, highlight Pareto theory as a useful tool for the analysis of neurobiological systems from biophysically detailed cells to large-scale network structures and behavior. The Pareto approach can help to assess optimality, identify relevant objectives and their respective impact, and formulate testable hypotheses.

Frequency-Dependent Energy Demand of Dendritic Responses to Deep Brain Stimulation in Thalamic Neurons: A Model-Based Study

Thalamic deep brain stimulation (DBS) generates excitatory postsynaptic currents and action potentials (APs) by triggering large numbers of synaptic inputs to local cells, which also activates axonal spikes to antidromically invade the soma and dendrites. To maintain signaling, the evoked dendritic responses require metabolic energy to restore ion gradients in each dendrite. The objective of this study is to estimate the energy demand associated with dendritic responses to thalamic DBS. We use a morphologically realistic computational model to simulate dendritic activity in thalamocortical (TC) relay neurons with axonal intracellular stimulation or DBS-like extracellular stimulation. We determine the metabolic cost by calculating the number of adenosine triphosphate (ATP) expended to pump Na⁺ and Ca²⁺ ions out of each dendrite. The ATP demand of dendritic activity exhibits frequency dependence, which is determined by the number of spikes in the dendrites. Each backpropagating AP from the soma activates a spike in the dendrites, and the dendritic firing is dominated by antidromic activation of the soma. High stimulus frequencies decrease dendritic ATP cost by reducing the fidelity of antidromic activation. Synaptic inputs and stimulus-induced polarization govern the ATP cost of dendritic responses by facilitating/suppressing antidromic activation, which also influences the ATP cost by depolarizing/hyperpolarizing each dendrite. These findings are important for understanding the synaptic signaling energy in TC relay neurons and metabolism-dependent functional imaging data of thalamic DBS.

Average firing rate rather than temporal pattern determines metabolic cost of activity in thalamocortical relay neurons

Thalamocortical (TC) relay cells exhibit different temporal patterns of activity, including tonic mode and burst mode, to transmit sensory information to the cortex. Our aim was to quantify the metabolic cost of different temporal patterns of neural activity across a range of average firing rates. We used a biophysically-realistic model of a TC relay neuron to simulate tonic and burst patterns of firing. We calculated the metabolic cost by converting the calculated ion fluxes into the demand for ATP to maintain homeostasis of intracellular ion concentrations. Most energy was expended on reversing Na⁺ entry during action potentials and pumping Ca²⁺ out of the cell. Average firing rate determined the ATP cost across firing patterns by controlling the overall number of spikes. Varying intraburst frequency or spike number in each burst influenced the metabolic cost by altering the interactions of inward and outward currents on multiple timescales, but temporal pattern contributed substantially less to the metabolic demand of neural activity as compared to average firing rate. These predictions should be considered when interpreting findings of functional imaging studies that rely of estimates of neuronal metabolic demand, e.g., functional magnetic resonance imaging.

Energy Cost of Action Potential Generation and Propagation in Thalamocortical Relay Neurons During Deep Brain Stimulation

Thalamocortical (TC) relay neurons generate antidromic and orthodromic action potentials (APs) during thalamic deep brain stimulation (DBS). To maintain signaling, each AP requires Na⁺/K⁺ pump to expend adenosine triphosphate (ATP) to restore Na⁺ and K⁺ gradients. Our aim was to estimate the energy demand associated with AP generation and propagation within TC relay cells during DBS. We used a morphology-based computational model to simulate the APs at different locations. We determined AP energy cost by calculating the amount of ATP required to reverse Na⁺ influx during the spike and measured metabolic efficiency by using Na⁺/K⁺ charge overlap. The ATP cost for AP generation exhibited location dependence, which was determined by spike shape, spatial morphology, and heterogeneously distributed currents. The APs in the axonal initial segment (AIS) were energetically efficient, but backpropagation to the soma and forward propagation to the axon were inefficient. Due to large surface area, the soma and AIS dominated the overall ATP usage. The AP cost also depended on membrane potential, which controlled T-type Ca²⁺ conductance and degree of availability of Na⁺ and K⁺ channels. The excitatory/inhibitory synaptic inputs affected spike cost by increasing/reducing the excitability of local cells. There was a tradeoff between AP cost and firing rate at high firing frequencies. We explained a fundamental link between biophysics of ionic currents, spatial morphology of neural segments, and ATP cost per AP. The predictions should be considered when understanding the functional magnetic resonance imaging data of thalamic DBS.

Low-intensity pulsed ultrasound modulates multi-frequency band phase synchronization between LFPs and EMG in mice

OBJECTIVE

Low-intensity pulsed ultrasound stimulation (LIPUS) targeted to the mouse motor cortex can simultaneously induce local field potentials (LFPs) and electromyogram (EMG) responses. However, the functional coupling relationship between LFP and EMG signals has not been elucidated to date. This study aimed to investigate the phase synchronization between LFP and EMG signals induced by LIPUS over the mouse motor cortex.

APPROACH

LIPUS at 500 kHz with varied sonication intensities and duty cycles (DCs), was delivered to the mouse motor cortex. LFPs of the motor cortex and EMG responses of the tail were simultaneously recorded during LIPUS. We then evaluated two control groups using the same experimental parameters, but changed the position of EMG recording to the hind leg and the ultrasound stimulus target to the primary visual cortex. The phase synchronization between LFPs and EMG signals was evaluated by performing a phase locking value (PLV) analysis in the time-frequency domain and was compared across specific frequency bands.

MAIN RESULTS

The results showed that LIPUS increased the phase synchronization in a broad frequency band (5-150 Hz), and the maximum duration of the increased PLV was stable at approximately 200 ms. It is worth noting that the sonication parameters directly affected the time-frequency domain distribution of cortico-muscular synchronization. Specifically, significant alpha and beta synchronization appeared at 0.2 and 0.4 W cm^-2 I _sppa stimulation, while gamma synchronization occurred at 0.8 and 1.1 W cm^-2 I _sppa stimulation. The synchronization in all frequency bands apparently increased at 30% DC. Beta synchronization weakened when the DC was less than 30%. Furthermore, no significant phase synchronization was observed in the two control groups.

SIGNIFICANCE

Considering the close association between specific motor function and cortical-muscular synchronization in different frequency bands, we suggest that LIPUS over the motor cortex could selectively modulate motor function via different sonication parameters. Additionally, the phase synchronization between LFPs and EMG might be an invaluable index for assessing the ultrasonic effect on the motor system, which could be used in future clinical research to optimize ultrasound parameters. Thus, this study provides new insight into evaluating the neuromodulatory effects of ultrasound on motor function, thereby supporting the therapeutic application of ultrasound in neurological disorders characterized by motor deficits.

Dendritic Properties Control Energy Efficiency of Action Potentials in Cortical Pyramidal Cells

Neural computation is performed by transforming input signals into sequences of action potentials (APs), which is metabolically expensive and limited by the energy available to the brain. The metabolic efficiency of single AP has important consequences for the computational power of the cell, which is determined by its biophysical properties and morphologies. Here we adopt biophysically-based two-compartment models to investigate how dendrites affect energy efficiency of APs in cortical pyramidal neurons. We measure the Na⁺ entry during the spike and examine how it is efficiently used for generating AP depolarization. We show that increasing the proportion of dendritic area or coupling conductance between two chambers decreases Na⁺ entry efficiency of somatic AP. Activating inward Ca²⁺ current in dendrites results in dendritic spike, which increases AP efficiency. Activating Ca²⁺-activated outward K⁺ current in dendrites, however, decreases Na⁺ entry efficiency. We demonstrate that the active and passive dendrites take effects by altering the overlap between Na⁺ influx and internal current flowing from soma to dendrite. We explain a fundamental link between dendritic properties and AP efficiency, which is essential to interpret how neural computation consumes metabolic energy and how biophysics and morphologies contribute to such consumption.