An Interneuron Circuit Reproducing Essential Spectral Features of Field Potentials

This document is the Accepted Manuscript version of the following article: Reinoud Maex, ‘An Interneuron Circuit Reproducing Essential Spectral Features of Field Potentials’, Neural Computation, March 2018. Under embargo until 22 June 2018. The final, definitive version of this paper is available online at doi: https://doi.org/10.1162/NECO_a_01068. © 2018 Massachusetts Institute of Technology. Content in the UH Research Archive is made available for personal research, educational, and non-commercial purposes only. Unless otherwise stated, all content is protected by copyright, and in the absence of an open license, permissions for further re-use should be sought from the publisher, the author, or other copyright holder.Recent advances in engineering and signal processing have renewed the interest in invasive and surface brain recordings, yet many features of cortical field potentials remain incompletely understood. In the present computational study, we show that a model circuit of interneurons, coupled via both GABA(A) receptor synapses and electrical synapses, reproduces many essential features of the power spectrum of local field potential (LFP) recordings, such as 1/f power scaling at low frequency (< 10 Hz) , power accumulation in the γ-frequency band (30–100 Hz), and a robust α rhythm in the absence of stimulation. The low-frequency 1/f power scaling depends on strong reciprocal inhibition, whereas the α rhythm is generated by electrical coupling of intrinsically active neurons. As in previous studies, the γ power arises through the amplifica- tion of single-neuron spectral properties, owing to the refractory period, by parameters that favour neuronal synchrony, such as delayed inhibition. The present study also confirms that both synaptic and voltage-gated membrane currents substantially contribute to the LFP, and that high-frequency signals such as action potentials quickly taper off with distance. Given the ubiquity of electrically coupled interneuron circuits in the mammalian brain, they may be major determinants of the recorded potentials.Peer reviewe

Lamina-specific AMPA receptor dynamics following visual deprivation in vivo.

Regulation of AMPA receptor (AMPAR) expression is central to synaptic plasticity and brain function, but how these changes occur in vivo remains elusive. Here, we developed a method to longitudinally monitor the expression of synaptic AMPARs across multiple cortical layers in awake mice using two-photon imaging. We observed that baseline AMPAR expression in individual spines is highly dynamic with more dynamics in primary visual cortex (V1) layer 2/3 (L2/3) neurons than V1 L5 neurons. Visual deprivation through binocular enucleation induces a synapse-specific and depth-dependent change of synaptic AMPARs in V1 L2/3 neurons, wherein deep synapses are potentiated more than superficial synapses. The increase is specific to L2/3 neurons and absent on apical dendrites of L5 neurons, and is dependent on expression of the AMPAR-binding protein GRIP1. Our study demonstrates that specific neuronal connections, across cortical layers and even within individual neurons, respond uniquely to changes in sensory experience

Active dendrites enhance neuronal dynamic range

Since the first experimental evidences of active conductances in dendrites, most neurons have been shown to exhibit dendritic excitability through the expression of a variety of voltage-gated ion channels. However, despite experimental and theoretical efforts undertaken in the last decades, the role of this excitability for some kind of dendritic computation has remained elusive. Here we show that, owing to very general properties of excitable media, the average output of a model of active dendritic trees is a highly non-linear function of their afferent rate, attaining extremely large dynamic ranges (above 50 dB). Moreover, the model yields double-sigmoid response functions as experimentally observed in retinal ganglion cells. We claim that enhancement of dynamic range is the primary functional role of active dendritic conductances. We predict that neurons with larger dendritic trees should have larger dynamic range and that blocking of active conductances should lead to a decrease of dynamic range.Comment: 20 pages, 6 figure

Low-rate firing limit for neurons with axon, soma and dendrites driven by spatially distributed stochastic synapses

Analytical forms for neuronal firing rates are important theoretical tools for the analysis of network states. Since the 1960s, the majority of approaches have treated neurons as being electrically compact and therefore isopotential. These approaches have yielded considerable insight into how single-cell properties affect network activity; however, many neuronal classes, such as cortical pyramidal cells, are electrically extended objects. Calculation of the complex flow of electrical activity driven by stochastic spatio-temporal synaptic input streams in these structures has presented a significant analytical challenge. Here we demonstrate that an extension of the level-crossing method of Rice, previously used for compact cells, provides a general framework for approximating the firing rate of neurons with spatial structure. Even for simple models, the analytical approximations derived demonstrate a surprising richness including: independence of the firing rate to the electrotonic length for certain models, but with a form distinct to the point-like leaky integrate-and-fire model; a non-monotonic dependence of the firing rate on the number of dendrites receiving synaptic drive; a significant effect of the axonal and somatic load on the firing rate; and the role that the trigger position on the axon for spike initiation has on firing properties. The approach necessitates only calculating the mean and variances of the non-thresholded voltage and its rate of change in neuronal structures subject to spatio-temporal synaptic fluctuations. The combination of simplicity and generality promises a framework that can be built upon to incorporate increasing levels of biophysical detail and extend beyond the low-rate firing limit treated in this paper

Simplest relationship between local field potential and intracellular signals in layered neural tissue.

The relationship between the extracellularly measured electric field potential resulting from synaptic activity in an ensemble of neurons and intracellular signals in these neurons is an important but still open question. Based on a model neuron with a cylindrical dendrite and lumped soma, we derive a formula that substantiates a proportionality between the local field potential and the total somatic transmembrane current that emerges from the difference between the somatic and dendritic membrane potentials. The formula is tested by intra- and extracellular recordings of evoked synaptic responses in hippocampal slices. Additionally, the contribution of different membrane currents to the field potential is demonstrated in a two-population mean-field model. Our formalism, which allows for a simple estimation of unknown dendritic currents directly from somatic measurements, provides an interpretation of the local field potential in terms of intracellularly measurable synaptic signals. It is also applicable to the study of cortical activity using two-compartment neuronal population models

Can my chip behave like my brain?

Many decades ago, Carver Mead established the foundations of neuromorphic systems. Neuromorphic systems are analog circuits that emulate biology. These circuits utilize subthreshold dynamics of CMOS transistors to mimic the behavior of neurons. The objective is to not only simulate the human brain, but also to build useful applications using these bio-inspired circuits for ultra low power speech processing, image processing, and robotics. This can be achieved using reconfigurable hardware, like field programmable analog arrays (FPAAs), which enable configuring different applications on a cross platform system. As digital systems saturate in terms of power efficiency, this alternate approach has the potential to improve computational efficiency by approximately eight orders of magnitude. These systems, which include analog, digital, and neuromorphic elements combine to result in a very powerful reconfigurable processing machine.Ph.D

Analytical Modeling of a Communication Channel Based on Subthreshold Stimulation of Neurobiological Networks

The emergence of wearable and implantable machines manufactured artificially or synthesized biologically opens up a new horizon for patient-centered health services such as medical treatment, health monitoring, and rehabilitation with minimized costs and maximized popularity when provided remotely via the Internet. In particular, a swarm of machines at the scale of a single cell down to the nanoscale can be deployed in the body by the non-invasive or minimally invasive operation (e.g., swallowing and injection respectively) to perform various tasks. However, an individual machine is only able to perform basic tasks so it needs to exchange data with the others and outside world through an efficient and reliable communication infrastructure to coordinate and aggregate their functionalities. We introduce in this thesis Neuronal Communication (NC) as a novel paradigm for utilizing the nervous system \emph{in vivo} as a communication medium to transmit artificial data across the body. NC features body-wide communication coverage while it demands zero investment cost on the infrastructure, does not rely on any external energy source, and exposes the body to zero electromagnetic radiation. n addition, unlike many conventional body area networking techniques, NC is able to provide communication among manufactured electronic machines and biologically engineered ones at the same time. We provide a detailed discussion of the theoretical and practical aspects of designing and implementing distinct paradigms of NC. We also discuss NC future perspectives and open challenges. Adviser: Massimiliano Pierobo

Modeling ionic flow between small targets: insights from diffusion and electro-diffusion theory

The flow of ions through permeable channels causes voltage drop in physiological nanodomains such as synapses, dendrites and dendritic spines, and other protrusions. How the voltage changes around channels in these nanodomains has remained poorly studied. We focus this book chapter on summarizing recent efforts in computing the steady-state current, voltage and ionic concentration distributions based on the Poisson-Nernst-Planck equations as a model of electro-diffusion. We first consider the spatial distribution of an uncharged particle density and derive asymptotic formulas for the concentration difference by solving the Laplace's equation with mixed boundary conditions. We study a constant particles injection rate modeled by a Neumann flux condition at a channel represented by a small boundary target, while the injected particles can exit at one or several narrow patches. We then discuss the case of two species (positive and negative charges) and take into account motions due to both concentration and electrochemical gradients. The voltage resulting from charge interactions is calculated by solving the Poisson's equation. We show how deep an influx diffusion propagates inside a nanodomain, for populations of both uncharged and charged particles. We estimate the concentration and voltage changes in relations with geometrical parameters and quantify the impact of membrane curvature.Comment: 17 pages, 8 figures, 1 tabl

Stochastic models of intracellular transport

The interior of a living cell is a crowded, heterogenuous, fluctuating environment. Hence, a major challenge in modeling intracellular transport is to analyze stochastic processes within complex environments. Broadly speaking, there are two basic mechanisms for intracellular transport: passive diffusion and motor-driven active transport. Diffusive transport can be formulated in terms of the motion of an over-damped Brownian particle. On the other hand, active transport requires chemical energy, usually in the form of ATP hydrolysis, and can be direction specific, allowing biomolecules to be transported long distances; this is particularly important in neurons due to their complex geometry. In this review we present a wide range of analytical methods and models of intracellular transport. In the case of diffusive transport, we consider narrow escape problems, diffusion to a small target, confined and single-file diffusion, homogenization theory, and fractional diffusion. In the case of active transport, we consider Brownian ratchets, random walk models, exclusion processes, random intermittent search processes, quasi-steady-state reduction methods, and mean field approximations. Applications include receptor trafficking, axonal transport, membrane diffusion, nuclear transport, protein-DNA interactions, virus trafficking, and the self–organization of subcellular structures