Abstract
AbstractThe neuron, when considered as a signal processing device, itsinputs are the frequency of pulses received at the synapses, and its output is the frequency of action potentials generated- in essence, a neuron is a pulse frequency signal processing device. In comparison, electrical devices use either digital or analog signals for communication or processing, and the mathematics behind these subjects is well understood. However, in regards to pulse frequency processing devices, there has not yet been a clear and persuasive mathematical model to describe the functions of neurons. It goes without saying that such a model is very important, not only for understanding neuron and neural system behavior, but also for undeveloped potential applications in industry. This paper proposes a method for obtaining the mathematical relationship between the input and output signals of a neuron based on physiological facts. The proposed method focuses on the currents across the postsynaptic membrane of each synapse, and the key is to recognize that the net charge across the whole membrane of a neuron over each action potential cycle must equal to zero. By analyzing the relationship between the input of a synapse and the currents across the postsynaptic membranes, a dynamic pulse frequency model of the neuron can be obtained. Here, we show that the transfer function of a neuron depends on the function of thepostsynaptic current of each synapse in resting state, which can be found by detecting the postsynaptic current when a pulse is received at the synapse. The transfer function of a typical neuron generally includes addition and subtraction of feedthrough terms and/or first order lag functions. To focus on the most basic characteristics of a neuron, accommodation, adaptation, learning, etc. are not discussed in this paper.
Highlights
The neuron, when considered as a signal processing device, its inputs are the frequency of pulses received at the synapses, and its output is the frequency of action potentials generated- in essence, a neuron is a pulse frequency signal processing device
By adjusting the types of neurotransmitters emitted, different signal processing functions can be composed. This characteristic highlights a very important principle; that is when structuring an equivalent circuit of a neuron, by adjusting the synapse circuit to vary the shape of the one pulse synaptic current, almost any transfer function can be realized
This paper analyzed the physiological mechanisms of a neuron using mathematical techniques and the salient points are as follows: (1) A neuron is a pulse frequency signal processing device
Summary
E1, E2, ..., EM represents the chemical potentials of each corresponding ions, ex. if Em is the chemical potential of Na+, Em=ENa. c. When an action potential from the presynaptic neuron arrives at a synapse, ion currents will flow into or out of the postsynaptic membrane. Since the shape of the membrane potential during the action period is almost always the same, and Tact is almost always constant, the frequency of action potentials can be considered to be dependent solely on the characteristics of ions flowing through the membrane during resting period Trest. Because the resting potential is close to the reverse chemical potential of chloride, considering the second and third cases, I speculate that there exists a type of chloride channel that opens during the refractory period, and/or the membrane is highly permeable to chloride ions flowing out, and relatively impermeable to chloride ions flowing in. Most Type I neurotransmitters are released from small vesicles (Fig.2)[7,9]
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