Analysis of the mechanism of synaptic integration focusing on the charge held in the spine

Abstract

Successful synaptic integration is said to require that multiple excitatory postsynaptic potentials (EPSPs) occur almost simultaneously over a short period of time, so that they overlap and increase. However, if brain function is based on a chain of successful synaptic integrations, then constraints on the spacing of multiple EPSP generation must be released to allow for a higher probability of successful synaptic integration. This paper demonstrates that Ca²⁺ ions retained in spines after EPSP generation polarize spine neck fluid and dendritic fluid as a dielectric medium, that polarization is transmitted through dendrites to the cell body (soma), that polarization is enhanced by the addition of polarization from each spine, and that I propose that synaptic integration is successful when the membrane potential, as determined by the enhanced polarization and membrane capacitance, reaches the threshold of voltage-gated Na⁺ channels. Furthermore, the approach taken in this study suggests that a single neuron can integrate synapses for many combinations of synaptic inputs, that successful synaptic integration depends on spine neck capacitance and spine head size, and that spines farther from the soma are able to contribute to successful synaptic integration, and led to the elucidation of a number of important issues, including the fact that inhibitory post-synapses on dendrites suppress s effectively synaptic integration.

Keywords: Ca2+ ion; action potential; dielectric constant; membrane potential; polarization.

Figure 1

Sum of potentials. (a); In case of success of addition of EPSPs. (b); In case of failure of addition of EPSPs. (c); Example of the success of synaptic integration by the membrane potential increased by the polarization of three spines holding Ca²⁺ ions. And action potentials are generated in tetanus stimulus manner.

Figure 2

State and name of inside the dendrite and soma. (a); Name of the dielectric fluid and non polarized state. (b); Name of the capacitance and non polarized state. (c); Polarized state by the spine holding Ca²⁺ ion, and location of potential V1, V2 andV3. The ellipse represents a state of dielectric fluid polarized by Ca²⁺ ions held in the spine.

Figure 3

Equivalent circuit of the neuron with one dendrite attached with m spines in which n spines holding Ca²⁺ ions. Since Csm is much smaller than Cs, Csm is ignored in the equation of electric charge. In this case, each potential is as follows, V1=n·Q/n·Cn, V2=n·Q/Cd and V3=n·Q/((m-n)Cns+Cdm+Csom).

Figure 4

Relationship between series capacitance Cs and distance from the soma. The spine is able to store amount of electric charge Q proportional to the Cs.

Figure 5

Relationship between distance from signal source and Attenuation ratio of the back propagation of action potential (BAP) and of the propagation of excitatory postsynaptic potential (EPSP).