Computational Modeling of Therapy with the NMDA Antagonist in Neurodegenerative Disease: Information Theory in the Mechanism of Action of Memantine

Abstract

(1) Background: in patients with neurodegenerative diseases, noncompetitive N-methyl-D-aspartate (NMDA) receptor antagonists provide neuroprotective advantages. We performed memantine therapy and proved mathematical and computer modeling of neurodegenerative disease in this study. (2) Methods: a computer simulation environment of the N-methyl-D-aspartate receptor incorporating biological mechanisms of channel activation by high extracellular glutamic acid concentration. In comparison to controls, pathological models were essentially treated with doses of memantine 3−30 µM. (3) Results: the mean values and 95% CI for Shannon entropy in Alzheimer’s disease (AD) and memantine treatment models were 1.760 (95% CI, 1.704−1.818) vs. 2.385 (95% CI, 2.280−2.490). The Shannon entropy was significantly higher in the memantine treatment model relative to AD model (p = 0.0162). The mean values and 95% CI for the positive Lyapunov exponent in AD and memantine treatment models were 0.125 (95% CI, NE−NE) vs. 0.058 (95% CI, 0.044−0.073). The positive Lyapunov exponent was significantly higher in the AD model relative to the memantine treatment model (p = 0.0091). The mean values and 95% CI for transfer entropy in AD and memantine treatment models were 0.081 (95% CI, 0.048−0.114) vs. 0.040 (95% CI, 0.019−0.062). The transfer entropy was significantly higher in the AD model relative to the memantine treatment model (p = 0.0146). A correlation analysis showed positive and statistically significant correlations of the memantine concentrations and the positive Lyapunov exponent (correlation coefficient R = 0.87, p = 0.0023) and transfer entropy (TE) (correlation coefficient R = 0.99, p < 0.000001). (4) Conclusions: information theory results of simulation studies show that the NMDA antagonist, memantine, causes neuroprotective benefits in patients with AD. Our simulation study opens up remarkable new scenarios in which a medical product, drug, or device, can be developed and tested for efficacy based on parameters of information theory.

Keywords: Alzheimer’s disease; NMDA antagonists; computer simulation; memantine; neural networks; virtual therapy.

Figure 1

NMDA receptor activity in physiological (normal) synaptic transmission and pathological (neurodegenerative) dementia synaptic transmission situations, as well as treatment with memantine. (A) Normal synaptic transmission. The unblocking of the channel and the influx of Ca²⁺ ions into the cell are caused by the stimulus-induced activation of the receptor. After the arrival of an action potential, the input function InEx for excitatory synapses adds the values of the synaptic function to the relevant tables of shift registers: E(i)—is the tables of shift registers for excitatory inputs (glutamate receptors): AMPA and M(i)—is the tables of shift registers for excitatory inputs (glutamate receptors): NMDA. S(i)—is the actual value of summarized potential and, if S(i) > CaMT (CaMT = –68 mV—threshold for the removal of the Mg ion block for NMDA channels) then improvements will be made LTP. C(i)—LTP time, ReP = −80 mV (resting potential value), powerA, clog parameters. (B) Neurodegenerative synaptic transmission model. When neurotoxic substances activate the receptor, Mg²⁺ is released and an uncontrolled influx of Ca²⁺ into the cell occurs. Overactivation of glutamate (excitotoxicity) causes neuronal injury, and overactivation causes an increase in energy demand. The “powerB” (powerB > powerA) parameter is gradually increased to model the increase in extracellular glutamate concentration caused by over-stimulation of NMDA receptors and aggravation of excitotoxicity. The following values were used in the control model and the strength of the excitotoxicity phenomenon, respectively: 9, 56.7, 63, and 135. (C) The therapy with memantine. The depolarization induced by a strong stimulation is enough to break the blockage of the memantine channel and allow calcium ions to flow into the cell. NMDA receptor currents are inhibited by memantine in a concentration-dependent manner. Changes in the threshold for removing the Mg²⁺ ion block for NMDA channels were used to imitate virtual treatment (CaMem > CaMT). The following values were used in the control model and therapy with memantine, respectively: −68, −65, −63, and −55 mV.

Figure 2

Synaptic transmission “as a function” of transfer entropy (TE) and mutual information (MI) in control, AD, memantine treatment models. (A) Transfer entropy of control and AD models. (B) Mutual information of control and AD models. (C) Transfer entropy of control and memantine treatment models at three concentrations: 3, 10, and 30 µM. (D) Mutual information of control and memantine treatment models at three concentrations: 3, 10, and 30 µM.