Binding Neuron

Binding Neuron

Alexander Vidybida (Bogolyubov Institute for Theoretical Physics, Ukraine)
Copyright: © 2015 |Pages: 12
DOI: 10.4018/978-1-4666-5888-2.ch107
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Although a neuron requires energy, its main function is to receive signals and to send them out – that is, to handle information. - F. Crick, The Astonishing Hypothesis, 1994

The brain ability to perform meaningful signal processing tasks related to perception, pattern recognition, reasoning is normally attributed to large-scale neuronal networks. The main signals involved in the instantaneous neural processing are neural impulses, and the units, which process impulses in a network, are individual neurons. We now put a question: In the context of higher brain functions, like perception, what is a meaningful task a neuron performs with the signals it receives? Another question: Does the inhibition exist for taming neuronal activity only, or it can be endowed with a more intelligent signal processing role? In this article, we propose an abstract concept of signal processing in a generic neuron, which is relevant to the features/events binding well known for large-scale neural circuits. Within this concept, action of inhibition obtains its natural signal processing meaning.



Low-Level Concepts of Signal Processing in a Neuron

The main part of any biological neuron is the excitable membrane. The membrane is able to generate electrical (neural) impulses, if proper stimulated, and to propagate those impulses over long distances without attenuation. The low-level concepts are concerned with electro-chemical characteristics of initiating and propagating of the impulses. These concepts are expressed in the form of differential equations, which govern the time course of the transmembrane potential.

Hodgkin and Huxley Equations

If 978-1-4666-5888-2.ch107.m01 denotes the displacement of the transmembrane potential of the excitable membrane from its resting state, then its time course is defined by the transmembrane currents as follows:

(1) where 978-1-4666-5888-2.ch107.m03 is the number of different ionic currents considered, 978-1-4666-5888-2.ch107.m04 is the capacity of the membrane unit surface and 978-1-4666-5888-2.ch107.m05, 978-1-4666-5888-2.ch107.m06 denote ionic currents through that surface. In the Hodgkin and Huxley (H-H) model, (Hodgkin & Huxley, 1952), three currents were considered, namely, the potassium, sodium and leakage current. These currents depend on the 978-1-4666-5888-2.ch107.m07 by the following way:
(2) where 978-1-4666-5888-2.ch107.m09, 978-1-4666-5888-2.ch107.m10are time-independent. The so called gating parameters 978-1-4666-5888-2.ch107.m11 depend on 978-1-4666-5888-2.ch107.m12 in accordance to the following equations:


Here parameters978-1-4666-5888-2.ch107.m14, 978-1-4666-5888-2.ch107.m15,depend on 978-1-4666-5888-2.ch107.m16 in a nonlinear manner, see (Hodgkin & Huxley, 1952) for the exact expressions. The system (1)–(3) has resting state with 978-1-4666-5888-2.ch107.m17. The temporal dynamics is usually introduced into (1)–(3) through a choice of proper initial conditions with a nonzero 978-1-4666-5888-2.ch107.m18 value. This corresponds to experimental manipulation known as the voltage clamp method. After the voltage clamp is released, the temporal dynamics of 978-1-4666-5888-2.ch107.m19 can be observed either experimentally, or by solving (1)–(3) numerically.

The remarkable feature of the H-H set of equations is that if the initially clamped value of 978-1-4666-5888-2.ch107.m20 corresponds to depolarization and is high enough, then the dynamics itself builds up further depolarization up to a definite value, 978-1-4666-5888-2.ch107.m21, and then returns to its resting state. This transient process is known for real neurons as the action potential, or spike, and it constitutes the essence of the neural impulse, when propagates along the membrane of a neural fiber, (Hodgkin, 1971). Both for real neurons, and for the set of Equations (1)–(3) neither the time course of the action potential, nor its peak value does depend on the initially clamped value of 978-1-4666-5888-2.ch107.m22. Moreover, the time course of the action potential obtained by solving (1)–(3) is in perfect correspondence with that observed experimentally for the giant nerve fiber of squid (see Hodgkin & Huxley, 1952, Figs 13, 14).

The ideas of H-H equations received further development in several directions. First, additional ionic currents found in other neurons and the dynamical properties of corresponding ionic channels are added to the (2) and (3) (Huguenard & McCormick, 1992). Second, spatially distributed (compartmental) equations are considered in order to fit with morphology of real neurons (De Schutter & Bower, 1994). Third, for simplification of mathematical analysis, a reduced sets of equations were offered, which has lower dimension than (1)–(3), and still is suitable for generating spikes (FitzHugh, 1961).

Key Terms in this Chapter

Membrane Voltage: See “Transmembrane Potential.”

Synapse: Electrochemical construct at the end of neuronal fiber (axonal branch) of a neuron, attached to another neuron. The point, where interneuronal communication takes place.

Binding Problem: In neuroscience, the problem of how sensory elements in a scene organize into coherent perceived objects, or percepts. Has spatial aspect, when the elements to bind are scattered in space (mainly in visual perception) and temporal aspect, when the elements to bind are scattered in time (mainly in auditory and multimodal perception).

Synaptic Current: Transmembrane current, generated under synapse when neuronal impulse arrives to that synapse.

Axon: A long projection of a neuron through which spikes leave the neuron and course to other neurons or muscles. At the end, has branching structure through which a single action potential produced in the neuron can be delivered to many synapses at different neurons. The strength of any action potential delivered through a branch is identical to that of initially generated spike due to active properties of excitable membrane all axons are made of.

Transmembrane Potential: The electric potential difference between internal and external sides of membrane.

Action Potential: In the excitable membrane, an abrupt short-time change of the membrane voltage produced due to the membrane excitability. Can propagate along neuronal fibers. Serves as interneuronal communication unit (neuronal impulse).

Neural Impulse: See “Action Potential.”

Spike: See “Action Potential.”

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