Binding neuron
The BN concept originated in 1996 and 1998 papers by A. K. Vidybida,[1][2] For a generic neuron the stimuli are excitatory impulses.
The high degree of temporal coherence between input impulses suggests that in external media all
"Although a neuron requires energy, its main function is to receive signals and to send them out that is, to handle information."
--- this words by Francis Crick point at the necessity to describe neuronal functioning in terms of processing of abstract signals [3] The two abstract concepts, namely, the "coincidence detector" and "temporal integrator" are offered in this course,[4][5] The first one expects that a neuron fires a spike if a number of input impulses are received at the same time.
In the temporal integrator concept a neuron fires a spike after receiving a number of input impulses distributed in time.
Each of the two takes into account some features of real neurons since it is known that a realistic neuron can display both coincidence detector and temporal integrator modes of activity depending on the stimulation applied, .
[6] At the same time, it is known that a neuron together with excitatory impulses receives also inhibitory stimulation.
For example, during visual perception, such features as form, color and stereopsis are represented in the brain by different neuronal assemblies.
[7] The experimentally approved opinion is that precise temporal coordination between neuronal impulses is required for the binding to occur,[8][9][10][11][12][13] This coordination mainly means that signals about different features must arrive to certain areas in the brain within a certain time window.
The BN concept reproduces at the level of single generic neuron the requirement, which is necessary for the feature binding to occur, and which was formulated earlier at the level of large-scale neuronal assemblies.
Its formulation is made possible by the analysis of response of the Hodgkin–Huxley model to stimuli similar to those the real neurons receive in the natural conditions, see "Mathematical implementations", below.
In the paper [14] the response of the H-H model was studied numerically to stimuli
composed of many excitatory impulses distributed randomly within a time window
The probability to generate action potential was calculated as a function of the window width
Different constant potassium conductances were added to the H-H equations in order to create certain levels of inhibitory potential.
, which is analogous to temporal coherence of impulses in the compound stimulus, have step-like form.
The location of the step is controlled by the level of inhibition potential, see Fig.
Due to this type of dependence, the H-H equations can be treated as mathematical model of the BN concept.
Therefore, the LIF neuron as well can be considered as mathematical model of the BN concept.
The binding neuron model implements the BN concept in the most refined form.
[15] In this model each input impulse is stored in the neuron during fixed time
This kind of memory serves as surrogate of the excitatory postsynaptic potential.
In the BN model, it is necessary to control the time to live of any stored impulse during calculation of the neuron's response to input stimulation.
This is in contrast to the LIF model, where traces of any impulse can be present infinitely long.
[18] The limiting case of BN with infinite memory, τ→∞, corresponds to the temporal integrator.
The limiting case of BN with infinitely short memory, τ→0, corresponds to the coincidence detector.
The above-mentioned and other neuronal models and nets made of them can be implemented in microchips.
Those features are used, e.g. in[19] and[20] As an abstract concept the BN model is subjected to necessary limitations.
Among those are such as ignoring neuronal morphology, identical magnitude of input impulses, replacement of a set of transients with different relaxation times, known for a real neuron, with a single time to live,
, of impulse in neuron, the absence of refractoriness and fast (chlorine) inhibition.
