Diffusion-Reaction Modeling, Non-Linear Dynamics, Feedback, Bifurcation and Chaotic Behaviour of the Acetylcholine Neurocycle and Their Relation to Alzheimer's and Parkinson's Diseases

The disturbances and abnormalities occurring in the components of the Acetylcholine (ACh) neurocycle are considered one of the main features of cholinergic sicknesses like Parkinson’s and Alzheimer’s diseases. A fundamental understanding of the ACh neurocycle is therefore very critical in order to design drugs that keep the ACh concentrations in the normal physiological range. In this dissertation, a novel two-enzyme-two-compartment model is proposed in order to explore the bifurcation, dynamics, and chaotic characteristics of the ACh neurocycle. The model takes into consideration the physiological events of the choline uptake into the presynaptic neuron and the ACh release in the postsynaptic neuron. In order to approach more realistic behavior, two complete kinetic mechanisms for enzymatic processes pH-dependent are built: the first mechanism is for the hydrolysis reaction catalyzed by the acetylcholinesterase (AChE) and the other is for the synthesis reaction catalyzed by the cholineacetyltransferase (ChAT). The effects of hydrogen ion feed concentrations, AChE activity, ChAT activity, feed ACh concentrations, feed choline concentrations, and feed acetate concentrations as bifurcation parameters, on the system performance are studied. It was found that hydrogen ions play an important role, where they create potential differences through the plasma membranes. The concentrations of ACh, choline and acetate in compartments 1 and 2 are affected by the activity of AChE through a certain range of their concentrations, where the activity of AChE is inhibited completely after reaching certain values. A detailed bifurcation analysis over a wide range of parameters is carried out in order to uncover some important features of the system, such as hysteresis, multiplicity, Hopf bifurcation, period doubling, chaotic characteristics, and other complex dynamics. The effects of the feed choline concentrations and the feed acetate concentrations as bifurcation parameters are studied in this dissertation. It is found that the feed choline concentrations play an important role and have a direct effect on the ACh neurocycle through a certain important range of the parameters. However, the feed acetate concentrations have less effect. It is concluded from the results that the feed choline is a more important factor than the feed acetate in ACh processes. The effects of ChAT activity and the choline recycle ratio as bifurcation parameters, on the system performance are investigated. It was found that as the ChAT activity increases, ACh concentrations in compartments 1 and 2 increase continuously. The effect of the choline recycle ratio shows that choline reuptake plays a very critical role in the synthesis of ACh in compartment 1, where it supplies the choline as a substrate for the synthesis reaction by ChAT. The concentrations of ACh, choline and acetate in compartments 1 and 2 are affected by the choline recycle ratio through a certain range of the choline recycle ratio; then, they become constant as the choline recycle ratio increases further. It is concluded from our results that choline uptake is the rate limiting step in the ACh processes in both compartments in comparison to ChAT activity. Based on partial dissociation of the acetic acid in compartments 1, and 2 of the ACh cholinergic system, the two-parameter continuation technique has been applied to investigate the pH range to be closer to physiological ranges of pH values. In addition, static/dynamic solutions of the ACh cholinergic neurocycle system based on feed choline concentration as the main bifurcation parameter in both compartments have been investigated. The findings of the above studies are related to the real phenomena occurring in the neurons, like periodic stimulation of neural cells and non-regular functioning of ACh receptors. It was found that ACh, choline, acetate, and pH exist inside the physiological range associated with taking into consideration the partial dissociation of the acetic acid. The disturbances and irregularities (chaotic attractors) occurring in the ACh cholinergic system may be good indications of cholinergic diseases such as Alzheimer’s and Parkinson’s diseases. The results have been compared to the results of physiological experiments and other published models. As there is strong evidence that cholinergic brain diseases like Alzheimer’s disease and Parkinson’s disease are related to the concentration of ACh, the present findings are useful for uncovering some of the characteristics of these diseases and encouraging more physiological research

Modeling the Interaction between β

The effect of β-amyloid aggregates on activity of choline acetyltransferase (ChAT) which is responsible for synthesizing acetylcholine (ACh) in human brain is investigated through the two-enzyme/two-compartment (2E2C) model where the presynaptic neuron is considered as compartment 1 while both the synaptic cleft and the postsynaptic neuron are considered as compartment 2 through suggesting three different kinetic mechanisms for the inhibition effect. It is found that the incorporation of ChAT inhibition by β-amyloid aggregates into the 2E2C model is able to yield dynamic solutions for concentrations of generated β-amyloid, ACh, choline, acetate, and pH in addition to the rates of ACh synthesis and ACh hydrolysis in compartments 1 and 2. It is observed that ChAT activity needs a high concentration of β-amyloid aggregates production rate. It is found that ChAT activity is reduced significantly when neurons are exposed to high levels of β-amyloid aggregates leading to reduction in levels of ACh which is one of the most significant physiological symptoms of AD. Furthermore, the system of ACh neurocycle is dominated by the oscillatory behavior when ChAT enzyme is completely inhibited by β-amyloid. It is observed that the direct inactivation of ChAT by β-amyloid aggregates may be a probable mechanism contributing to the development of AD

Pharmacokinetics/Pharmacodynamics and Analysis of the Effect of β-Amyloid Peptide on Acetylcholine Neurocycle and Alzheimer’s Disease Medications

The brain of Alzheimer’s disease (AD) is characterized by accumulations of β-amyloid peptide aggregates which promote neurodegentartive dysfunction. Comprehensive understanding of the interaction between β-amyloid aggregates and acetylcholine (ACh) neurocycle is required to uncover the physiological processes related to AD and might result in improving therapeutic approaches for AD. Pharmacokinetics (PK) and pharmacodynamics (PD) techniques were applied to allow predicting the extent of the interaction of certain doses of AD drugs and β-amyloid inhibitors and levels of ACh as well. Although many researchers focused on the β-amyloid interactions, the mechanisms by which β-amyloid affects cholinergic neurons and reduction of ACh are still unclear. The prediction of ACh and drug concentrations in the tissues and body needs an understanding of the physiology and mechanisms of β-amyloid aggregates processes and their compilation into a mechanistic model In this work, two hypotheses are proposed to investigate the dynamic behavior of the interaction between β-amyloid peptide aggregates and cholinergic neurocycle and the possible therapeutic approaches through proposing pharmacokinetic/pharmacodynamics (PK/PD) models to represent the impact of β-amyloid aggregates in AD. The effect of β-amyloid peptide aggregates is formulated through incorporating β- amyloid aggregates into non-linear model for the neurocycle of ACh where the presynaptic neuron is considered as compartment 1 and both synaptic cleft and postsynaptic neurons are considered as compartment 2. In the first hypothesis which is choline leakage hypothesis, β-amyloid peptide aggregates are considered to be located in the membrane of the presynaptic neuron and create pathways inside the membrane to allow for the intracellular choline to leak outside the cholinergic system. It is observed that β-amyloid aggregates via the choline leakage hypothesis could cause significant reductions of ACh and choline levels in both compartments. Furthermore, the process rates of ACh synthesis and hydrolysis have been affected negatively by a wide range of β-amyloid aggregate concentrations. It is found that as the input rate of β-amyloid aggregates to compartment 1 increases, the loss of choline from compartment 1 increases leading to an increase in the intracellular concentration of β-amyloid. In the second hypothesis, β-amyloid peptide aggregates are proposed to interact with the enzyme ChAT which is responsible for the synthesis of ACh in compartment 1; three different kinetic mechanisms are suggested to account for the interaction between β-amyloid aggregates and ChAT activity. In the first and second kinetic mechanisms, β-amyloid aggregate is supposed to attack different species in the enzyme. It is found that there is a significant decrease in the rate of ACh synthesis in compartment 1 and ACh concentrations in both compartments. However, it is observed that there is no effect on choline levels in both compartments, the rate of ACh hydrolysis in compartment 2, pH, and ACh levels in compartment 2. In the third kinetic mechanism, all species in ChAT are attacked by β-amyloid aggregates; it is observed that at very high input rates of β-amyloid aggregates, the oscillatory behavior dominates all components of the neurocycle of ACh. The disturbance observed in ACh levels in both compartments explains the harmful effect of the full attack of β-amyloid aggregates to all species of ChAT. It is found that to contribute significantly in ACh neurocycle, choline leakage hypothesis needs concentration of β-amyloid aggregates lower than that needed in ChAT activity hypothesis which is in agreement with experimental observations. The significant decrease in ACh levels observed in both choline leakage and loss of ChAT activity hypotheses leads to cognitive loss and memory impairment which were observed in individuals with AD. A one-compartment drug PK/PD model is proposed to investigate a therapeutic approach for inhibiting β-amyloid aggregation via choline leakage hypothesis where the maximum feed rate of β-amyloid (KL2 = 1) is considered. The drug is assumed to interact with the tissues of the presynaptic neurons where β-amyloid aggregates are located. The PK/PD model is built based on the effect of β-amyloid aggregates via choline leakage hypothesis where the maximum feed rate of β-amyloid aggregates is considered. The dynamic behavior of all concentrations of β-amyloid aggregates, choline, ACh, acetate, and pH in both compartments in addition to the rate of ACh synthesis in compartment 1 and ACh hydrolysis are investigated by monitoring the impacts of the drug on β-amyloid aggregates and cholinergic neurocycle over a wide range of the input drug dosage. The PK/PD model is able to predict the reduction in levels of β-amyloid aggregates and the increase in choline and ACh, in both compartments as well as both rates of ACh synthesis and hydrolysis catalyzed. The parameters of the PK/PD model such as maximum concentration (Cmax), maximum time (Tmax), area under the curve (AUC), and maximum effect (Emax) were investigated. It was found that it takes a longer time (Tmax) (3-5 h) to reach Emax as the drug dose increases. Furthermore, AUC was found to increase with increasing drug dosage. The results of the current work show that drugs / therapeutic agents inhibiting β- amyloid aggregation in the brain represent a likely successful therapeutic approach to give systematic highlights to develop future trials, new diagnostic techniques, and medications for AD. This study is helpful in designing PK and PD and developing experimental animal models to support AD drug development and therapy in the future