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

Frequency-domain analysis of membrane polarization in two-compartment model neurons with weak alternating electric fields

Transcranial alternating current stimulation (tACS) is widely used in studying brain functions and the treatment of neuropsychiatric diseases in a frequency-specific manner. However, how tACS works on neuronal activity has been poorly understood. In this paper, we use linear system analysis to investigate how weak alternating electric fields (EFs) affect the membrane polarization of neurons in the frequency domain. Two biophysically realistic conductance-based two-compartment models of cortical pyramidal neurons are developed to simulate subthreshold membrane polarization with weak alternating EFs. We linearize the original nonlinear models at the stable equilibrium points and further simplify them to the two- or three-dimensional linear systems. Thus, we calculate the transfer functions of the low-dimensional linear models to model neuronal polarization patterns. Based on the transfer functions, we compute the amplitude- and phase-frequency characteristics to describe the relationship between weak EFs and membrane polarization. We also computed the parameters (gain, zeros, and poles) and structures (the number of zeros and poles) of transfer functions to reveal how neuronal intrinsic properties affect the parameters and structure of transfer functions and thus the frequency-dependent membrane polarization with alternating EFs. We find that the amplitude and phase of membrane polarization both strongly depended on EF frequency, and these frequency responses are modulated by the intrinsic properties of neurons. The compartment geometry, internal coupling conductance, and ionic currents (except Ih) affect the frequency-dependent polarization by mainly changing the gain and pole of transfer functions. Larger gain contributes to larger amplitude-frequency characteristics. The closer the pole is to the imaginary axis, the lower phase-frequency characteristics. However, Ih changes the structure of transfer function in the dendrite by introducing a new pair of zero-pole points, which decrease the amplitude at low frequencies and thus lead to a visible resonance. These results highlight the effects of passive properties and active ion currents on subthreshold membrane polarization with alternating EFs in the frequency domain, which provide an explainable connection of how intrinsic properties of neurons modulate the neuronal input-output functions with weak EF stimulation.

The cytoplasmic localization of ADNP through 14-3-3 promotes sex-dependent neuronal morphogenesis, cortical connectivity, and calcium signaling

Defective neuritogenesis is a contributing pathogenic mechanism underlying a variety of neurodevelopmental disorders. Single gene mutations in activity-dependent neuroprotective protein (ADNP) are the most frequent among autism spectrum disorders (ASDs) leading to the ADNP syndrome. Previous studies showed that during neuritogenesis, Adnp localizes to the cytoplasm/neurites, and Adnp knockdown inhibits neuritogenesis in culture. Here, we hypothesized that Adnp is localized in the cytoplasm during neurite formation and that this process is mediated by 14-3-3. Indeed, applying the 14-3-3 inhibitor, difopein, blocked Adnp cytoplasmic localization. Furthermore, co-immunoprecipitations showed that Adnp bound 14-3-3 proteins and proteomic analysis identified several potential phosphorylation-dependent Adnp/14-3-3 binding sites. We further discovered that knockdown of Adnp using in utero electroporation of mouse layer 2/3 pyramidal neurons in the somatosensory cortex led to previously unreported changes in neurite formation beginning at P0. Defects were sustained throughout development, the most notable included increased basal dendrite number and axon length. Paralleling the observed morphological aberrations, ex vivo calcium imaging revealed that Adnp deficient neurons had greater and more frequent spontaneous calcium influx in female mice. GRAPHIC, a novel synaptic tracing technology substantiated this finding, revealing increased interhemispheric connectivity between female Adnp deficient layer 2/3 pyramidal neurons. We conclude that Adnp is localized to the cytoplasm by 14-3-3 proteins, where it regulates neurite formation, maturation, and functional cortical connectivity significantly building on our current understanding of Adnp function and the etiology of ADNP syndrome.

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.

High-throughput kinase inhibitor screening reveals roles for Aurora and Nuak kinases in neurite initiation and dendritic branching

Kinases are essential regulators of a variety of cellular signaling processes, including neurite formation—a foundational step in neurodevelopment. Aberrant axonal sprouting and failed regeneration of injured axons are associated with conditions like traumatic injury, neurodegenerative disease, and seizures. Investigating the mechanisms underlying neurite formation will allow for identification of potential therapeutics. We used a kinase inhibitor library to screen 493 kinase inhibitors and observed that 45% impacted neuritogenesis in Neuro2a (N-2a) cells. Based on the screening, we further investigated the roles of Aurora kinases A, B, and C and Nuak kinases 1 and 2. The roles of Aurora and Nuak kinases have not been thoroughly studied in the nervous system. Inhibition or overexpression of Aurora and Nuak kinases in primary cortical neurons resulted in various neuromorphological defects, with Aurora A regulating neurite initiation, Aurora B and C regulating neurite initiation and elongation, all Aurora kinases regulating arborization, and all Nuak kinases regulating neurite initiation and elongation and arborization. Our high-throughput screening and analysis of Aurora and Nuak kinases revealed their functions and may contribute to the identification of therapeutics.

Protein kinases: master regulators of neuritogenesis and therapeutic targets for axon regeneration

Proper neurite formation is essential for appropriate neuronal morphology to develop and defects at this early foundational stage have serious implications for overall neuronal function. Neuritogenesis is tightly regulated by various signaling mechanisms that control the timing and placement of neurite initiation, as well as the various processes necessary for neurite elongation to occur. Kinases are integral components of these regulatory pathways that control the activation and inactivation of their targets. This review provides a comprehensive summary of the kinases that are notably involved in regulating neurite formation, which is a complex process that involves cytoskeletal rearrangements, addition of plasma membrane to increase neuronal surface area, coupling of cytoskeleton/plasma membrane, metabolic regulation, and regulation of neuronal differentiation. Since kinases are key regulators of these functions during neuromorphogenesis, they have high potential for use as therapeutic targets for axon regeneration after injury or disease where neurite formation is disrupted.

Metabolic Cost of Dendritic Ca2+ Action Potentials in Layer 5 Pyramidal Neurons

Pyramidal neurons consume most signaling-related energy to generate action potentials (APs) and perform synaptic integration. Dendritic Ca²⁺ spike is an important integration mechanism for coupling inputs from different cortical layers. Our objective was to quantify the metabolic energy associated with the generation of Ca²⁺ APs in the dendrites. We used morphology-based computational models to simulate the dendritic Ca²⁺ spikes in layer 5 pyramidal neurons. We calculated the energy cost by converting Ca²⁺ influx into the number of ATP required to restore and maintain the homeostasis of intracellular Ca²⁺ concentrations. We quantified the effects of synaptic inputs, dendritic voltage, back-propagating Na⁺ spikes, and Ca²⁺ inactivation on Ca²⁺ spike cost. We showed that much more ATP molecules were required for reversing Ca²⁺ influx in the dendrites than for Na⁺ ion pumping in the soma during a Ca²⁺ AP. Increasing synaptic input increased the rate of dendritic depolarization and underlying Ca²⁺ influx, resulting in higher ATP consumption. Depolarizing dendritic voltage resulted in the inactivation of Ca²⁺ channels and reduced the ATP cost, while dendritic hyperpolarization increased the spike cost by de-inactivating Ca²⁺ channels. A back-propagating Na⁺ AP initiated in the soma increased Ca²⁺ spike cost in the apical dendrite when it coincided with a synaptic input within a time window of several milliseconds. Increasing Ca²⁺ inactivation rate reduced Ca²⁺ spike cost, while slowing Ca²⁺ inactivation increased the spike cost. The results revealed that the energy demand of a Ca²⁺ AP was dynamically dependent on the state of dendritic activity. These findings were important for predicting the energy budget for signaling in pyramidal cells, interpreting functional imaging data, and designing energy-efficient neuromorphic devices.

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.

Inhibitory effects of cannabidiol on voltage-dependent sodium currents

Cannabis sativa contains many related compounds known as phytocannabinoids. The main psychoactive and nonpsychoactive compounds are Δ9-tetrahydrocannabinol (THC) and cannabidiol (CBD), respectively. Much of the evidence for clinical efficacy of CBD-mediated antiepileptic effects has been from case reports or smaller surveys. The mechanisms for CBD's anticonvulsant effects are unclear and likely involve noncannabinoid receptor pathways. CBD is reported to modulate several ion channels, including sodium channels (Nav). Evaluating the therapeutic mechanisms and safety of CBD demands a richer understanding of its interactions with central nervous system targets. Here, we used voltage-clamp electrophysiology of HEK-293 cells and iPSC neurons to characterize the effects of CBD on Nav channels. Our results show that CBD inhibits hNav1.1-1.7 currents, with an IC50 of 1.9-3.8 μm, suggesting that this inhibition could occur at therapeutically relevant concentrations. A steep Hill slope of ∼3 suggested multiple interactions of CBD with Nav channels. CBD exhibited resting-state blockade, became more potent at depolarized potentials, and also slowed recovery from inactivation, supporting the idea that CBD binding preferentially stabilizes inactivated Nav channel states. We also found that CBD inhibits other voltage-dependent currents from diverse channels, including bacterial homomeric Nav channel (NaChBac) and voltage-gated potassium channel subunit Kv2.1. Lastly, the CBD block of Nav was temperature-dependent, with potency increasing at lower temperatures. We conclude that CBD's mode of action likely involves 1) compound partitioning in lipid membranes, which alters membrane fluidity affecting gating, and 2) undetermined direct interactions with sodium and potassium channels, whose combined effects are loss of channel excitability.

Effects of Metabolic Energy on Synaptic Transmission and Dendritic Integration in Pyramidal Neurons

As a sophisticated computing unit, the pyramidal neuron requires sufficient metabolic energy to fuel its powerful computational capabilities. However, the majority of previous works focus on nonlinear integration and energy consumption in individual pyramidal neurons but seldom on the effects of metabolic energy on synaptic transmission and dendritic integration. Here, we developed biologically plausible models to simulate the synaptic transmission and dendritic integration of pyramidal neurons, exploring the relations between synaptic transmission and metabolic energy and between dendritic integration and metabolic energy. We find that synaptic energy not only drives synaptic vesicle cycle, but also participates in the regulation of this cycle. Release probability of synapses adapts to synaptic energy levels by regulating the speed of synaptic vesicle cycle. Besides, we also find that to match neural energy levels, only a part of the synapses receive presynaptic signals during a given period so that neurons have a low action potential frequency. That is, the number of simultaneously active synapses over a period of time should be adapted to neural energy levels.

Effects of acidosis on neuronal voltage-gated sodium channels: Nav1.1 and Nav1.3

Voltage-gated sodium channels are key contributors to membrane excitability. These channels are expressed in a tissue-specific manner. Mutations and modulation of these channels underlie various physiological and pathophysiological manifestations. The effects of changes in extracellular pH on channel gating have been studied on several sodium channel subtypes. Among these, Nav1.5 is the most pH-sensitive channel, with Nav1.2 and Nav1.4 being mostly pH-resistant channels. However, pH effects have not been characterized on other sodium channel subtypes. In this study, we sought to determine whether Nav1.1 and Nav1.3 display resistance or sensitivity to changes in extracellular pH. These two sodium channel subtypes are predominantly found in inhibitory neurons. The expression of these channels highly depends on age and the developmental stage of neurons, with Nav1.3 being found mostly in neonatal neurons, and Nav1.1 being found in adult neurons. Our present results indicate that, during extracellular acidosis, both channels show a depolarization in the voltage-dependence of activation and moderate reduction in current density. Voltage-dependence of steady-state fast inactivation and recovery from fast inactivation were unchanged. We conclude that Nav1.1 and Nav1.3 have similar pH-sensitivities.