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Electrophysiological Models of Neural Processing Mark E

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Electrophysiological Models of Neural Processing Mark E Focus Article Electrophysiological models of neural processing Mark E. Nelson∗ The brain is an amazing information processing system that allows organisms to adaptively monitor and control complex dynamic interactions with their environment across multiple spatial and temporal scales. Mathematical modeling and computer simulation techniques have become essential tools in understanding diverse aspects of neural processing ranging from sub-millisecond temporal coding in the sound localization circuity of barn owls to long-term memory storage and retrieval in humans that can span decades. The processing capabilities of individual neurons lie at the core of these models, with the emphasis shifting upward and downward across different levels of biological organization depending on the nature of the questions being addressed. This review provides an introduction to the techniques for constructing biophysically based models of individual neurons and local networks. Topics include Hodgkin-Huxley-type models of macroscopic membrane currents, Markov models of individual ion- channel currents, compartmental models of neuronal morphology, and network models involving synaptic interactions among multiple neurons. 2010 JohnWiley& Sons, Inc. WIREs Syst Biol Med 2011 3 74–92 DOI: 10.1002/wsbm.95 INTRODUCTION of emerging neuroinformatics approaches that can potentially link such models with a wealth of empirical nderstanding the electrophysiological basis of data currently being compiled and organized into Uneural coding, communication, and information large neuroscientific databases.3–5 In contrast, highly processing is central to modern neuroscience research. abstracted models lack sufficient biological detail Mathematical modeling and computer simulation to establish meaningful links to these databases, have become an integral part of the neuroscientist’s whereas large systems-level models involving multiple toolbox for exploring these phenomena at a variety brain regions are generally too diverse in structure of levels of organization, from the biophysical basis and function for neuroinformatics approaches to be of current flow through individual ion channels, to productive. In the intermediated term over the next the modeling of aspects of cognitive function arising several years, biophysically detailed models of single from the distributed activity of large populations of neurons and local networks will likely provide the neurons. Neural models can be constructed at many most fruitful level of analysis for uncovering new levels of abstraction. Some types of scientific questions functional relationships, dynamical principles, and can be addressed using highly reduced models that information-processing strategies. treat neurons as simple threshold devices, whereas How do electrophysiological models fit into an other questions require detailed models of membrane informatics approach to neuroscience? This question biophysics and intracellular signaling networks. is perhaps best answered in the context of a bottom- This article will focus on the tools and techniques up view of the problem. Starting at the molecular for constructing biophysically detailed compartmental level, sequence-based informatics approaches are models of individual neurons and local networks.1,2 being used to reveal information about structural and Such models are well positioned to take advantage evolutionary relationships among ion channels and ∗Correspondence to: [email protected] receptor proteins. Molecular dynamics simulations Department of Molecular and Integrative Physiology and The can help establish links from the structural level to Beckman Institute for Advanced Science and Technology, University the functional properties of individual ion channel of Illinois at Urbana-Champaign, Urbana, IL, USA and receptor complexes. Electrophysiological models DOI: 10.1002/wsbm.95 come into play at the next level of organization where 74 2010 John Wiley & Sons, Inc. Volume 3, January/February 2011 WIREs Systems Biology and Medicine Electrophysiological models information-processing properties emerge from the (e.g., Ref 15) and the biophysical properties of ion dynamic interactions of multiple channel and receptor channels (e.g., Ref 16). A brief glossary is provided types at the single-neuron level and interactions of here as a convenient reference for some of the key multiple neurons at the network level. terminology and functional concepts. Neurons typically contain numerous types of ion channels and membrane receptors. Different types of Glossary neurons express different combinations of these pro- teins, with varying densities and varying spatial dis- action potential A transient electrical impulse tributions. There are, for example, dozens of different + that propagates along an axon and serves as the types of voltage-gated K channels, but an individual most common form of electrical signaling between neuron may only express a few of these, and the neurons. The duration is typically on the order of expression might be restricted to the soma or to partic- 6,7 + a millisecond, and the amplitude is on the order ular regions of the dendrites. Different types of K of 100 mV. Action potentials are also called nerve channels vary in their electrophysiological properties, impulses or spikes. such as activation and inactivation voltages, time con- stants, and conductances. This heterogeneity suggests that K+ channels may be differentially expressed and axon An output branch of a neuron that conducts distributed in order to shape the electrophysiological action potentials away from the site of initiation response properties of individual neurons for carrying and conveys electrical signals to other neurons out particular types of information-processing tasks. or effectors. The axon usually starts off as a The contributions of different ion channels to the single long branch but may terminate in a complex information-processing capabilities of the system can- branched arbor that distributes outputs to large not be deduced from the properties of individual ion numbers of target neurons. channels alone. Rather, functional properties at the single-neuron level must be evaluated in the presence compartmental model A single-neuron model that of an appropriate mix of channel types, densities, and divides the cell into multiple spatial compartments. distributions and in the context of physiologically rel- Each compartment can have different properties evant spatiotemporal patterns of input. For example, + (length, diameter, membrane voltage, ion channel certain types of K channels from the Kv3 gene family densities, etc.). The model produces a coupled are known to be activated only at rather depolarized set of differential equations that are solved using membrane potentials and tend to have fast activation numerical integration techniques. and inactivation time constants.8 Using biophysically detailed compartmental models, neuroscientists have been able to achieve a detailed understanding of how conductance A measure of the ease with which Kv3 channel properties contribute to temporal signal electric current flows through a material; the processing in the electric sense of weakly electric reciprocal of resistance; conductance units are fish9–11 and in the mammalian auditory system.12 siemens; conductance (siemens) is a measure of If appropriate databases were available and suitable current (amperes) divided by voltage (volts). neuroinformatics tools existed, one could imagine undertaking a variety of interesting comparative dendrite An input branch of a neuron that typically investigations regarding the functional role of Kv3 receives synaptic contacts from other neurons and channels in other species, other sensory systems, and conveys graded electrical potentials to other parts other neural information-processing contexts. of the neuron. equilibrium potential The membrane potential BACKGROUND at which the effects of the electrical potential This article assumes a general familiarity with the difference and the concentration gradient across neurophysiological and biophysical mechanisms the membrane are balanced so as to produce associated with electrical signaling in neurons. Good no net ion flux. Also called the Nernst poten- introductory material in this area can be found in tial. Calculated from the Nernst equation: Eion = numerous undergraduate textbooks (e.g., Refs 13 (RT/zF) ln([ion]out/[ion]in), where R is the univer- and 14). Recent advanced texts are available that sal gas constant, T the temperature in Kelvin, z provide detailed, up-to-date coverage in areas such the ionic charge, F Faraday’s constant, and [ion]in as the cellular and molecular biology of nerve cells and [ion]out are ionic concentrations. Volume 3, January/February 2011 2010 John Wiley & Sons, Inc. 75 Focus Article www.wiley.com/wires/sysbio gating The process by which ion channels open and soma The cell body of the neuron; contains the close so as to regulate the flow of ions. Voltage- nucleus and much of the metabolic machinery of gated ion channels change their gating state the cell. based on the local electrical potential difference across the cell membrane. Ligand-gated channels reversal potential The membrane potential at change their gating state based on the binding which no net current flows through an open ion of signaling molecules (neurotransmitters). Gating channel or activated synapse. If the channel or usually involves a change in the conformation of synapse is permeable to a single ionic
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