Computational approach to long-term potentiation in hippocampal CA1 area describes the efficacy of stimulation patterns

Background: Long-term potentiation (LTP) is the best characterized form of enhancement in synaptic plasticity, which is a widely accepted model of learning and memory. The modification of long-term plasticity is a complex process and varies throughout synaptic events.

Objective: To investigate efficacy of electrical stimulus patterns for LTP induction where characteristics of hippocampal LTP are described by least-squares curve fitting.

Methods: In vitro hippocampal brain slice techniques were used to investigate the effects of tetanic stimulation (consisting square pulse at 100 Hz in 1 second) and theta-burst stimulation (TBS; typically consisting of 3 trains of 10 brief 100 Hz burst, 4 impulses each, interval of 200 milliseconds between bursts and repeated in 10 seconds between trains). The experimental data were modeled as three mathematical equations, polynomial form, exponential form, and power form. Curve fitting with the least-squares procedure and parameter solving were computed using the Levenberg-Marquardt method, with OriginPro 8.5 software.

Results: The stimulation intensity was 0.37 ± 0.0677 V with tetanic stimulation and 0.31 ± 0.0862 V with TBS. There were no significant differences among groups (one-way ANOVA, p = 0.122). TBS effectively induces LTP more than tetanic stimulation with 144.42 ± 6.54% of baseline (n = 10) and 134.88 ± 6.92% of baseline (n = 10), respectively. Moreover, curve fitting with the power form produced the best adjusted R² value and initial posttetanic potentiation approximation. The polynomial model produced a small relative error with abundant residual. Therefore, the power form was a good model for LTP approximation.

Conclusion: Least-squares curve fitting could describe experimental results for investigating LTP induction under two patterns of stimuli: tetanic stimulation and TBS. We found that curve fitting with a power form is the most appropriate model for overall estimations when comparison is made with polynomial and exponential forms.