Authored by Said Elnashaie*
Abstract
Enzymes-Reactions Model is used to study: dynamics, bifurcation, and chaos of the acetylcholine neurocycle (ACNC). The effects of feed choline concentrations, Acetylcholinesterase (AChE) activity as bifurcation parameters are studied. It was found that feed choline concentrations are important and have direct effect on ACNC through certain important range of parameters. Detailed bifurcation analysis is carried out in order to uncover important features of the system, such as static/dynamic bifurcation and chaos. These findings are related to the real phenomena occurring in the neurons, like periodic stimulation of neural cells and non-regular functioning of acetylcholine receptors. Results are compared to the results of physiological experiments and other published models. As there is strong evidence that cholinergic brain diseases like Alzheimer’s disease (AD) and Parkinson’s disease (PD) are related to the concentration of acetylcholine, the present findings are useful for uncovering some of the characteristics of these illnesses/remediation.
Keywords: Acetylcholinesterase; Acetylcholine; Choline; Acetate; Parkinson’s disease (PD); Alzheimer’s disease (AD); Dynamic behavior; Bifurcation; Chaos.
Introduction
A complete neurocycle of Acetylcholine (ACh) involves a coupled two-enzyme system with the following two simultaneous events [1]:
Synthesis event: ACh is synthesized from choline and acetyl- CoA bio catalyzed by the enzyme choline acetyltransferase (ChAT) and immediately stored in small vesicular compartments closely attached to the cytoplasmic side of the presynaptic membranes [1,2].
Degradation event: Once ACh has completed its activation duty, the synaptic cleft degradation begins removing the remaining ACh. This occurs when the ACh is consumed by the acetylcholinesterase (AChE) to form choline and acetic acid [3-5].
It has been found that the synthesis of ACh in the nerve endings is based on the preferential utilization of the choline which is supplied by the high affinity carrier from extra cellular fluid. Choline in the extra cellular fluid of the brain comes either directly from the free choline of the blood plasma, or from the brain cells, where it has been released from choline containing compounds [4,5] found that using the steam pulse sequence (one of the main techniques commonly used for the diagnosis of imaged brain abnormalities), concentrations of choline in human brain frontal lobe white matter are found to be 1.9±0.5 μmol/g wet wt. In the thalamus, the concentrations are 2.0±0.4 mol/g wet wt. Once in the extracellular space of the brain, choline can be taken up by all cells and used as a precursor of structural membrane phospholipids such as phosphatidylcholine and sphingomyelin and uniquely by cholinergic neurons for the conversion to ACh [6]. Phosphatidylcholine in these neurons also comprises a storage pool of choline, and the hydrolysis of phosphatidylcholine catalyzed by phospholipase Deliberates choline from this reservoir for the conversion to ACh by ChAT [7].
Several studies [8,9] indicate that neurotransmitter external choline (modified) availability is an important factor regulating the dynamics of ACh metabolism and it appears that choline may be the rate-limiting substrate for ACh synthesis in vivo. Although a controversy exists [10] concerning the form of choline that is transported from the periphery to the brain, it is generally agreed that brain choline available for ACh synthesis is derived from sources outside the cholinergic neuron and include: (I) choline in the form of phospholipids, (2) free choline in plasma, and (3) choline generated from the hydrolysis of ACh.(Kewitz et al.,1975 Ansell and Spanner ,1975) If a significant fraction of the choline used for ACh synthesis is derived from ACh hydrolysis, then under conditions of AChE inhibition, the size of this choline pool may be the limiting factor regulating the magnitude of the increase in ACh levels [2].
Several studies have suggested that acetate may affect the central nervous system (CNS) [Carmichael et al., (1991)]. The main entry point for acetate into metabolism in vertebrates is its conversion to acetyl-CoA by acetyl-CoA synthetase. The acetyl-CoA which is formed from acetate can be used for energy generation; on the other hand, acetyl-CoA is utilized in the brain’s cholinergic neurons for ACh synthesis. It has been shown that extracellular acetate is accumulated by cholinergic nerve terminals for ACh formation and release [11].
There are some factors other than choline availability to ChAT that regulates ACh synthesis such as choline uptake to the presynaptic neuron and acetate to prevent expansion of the tissue ACh store [12-14] showed that the effect of AChE inhibition experimentally, on ACh labeling from acetate offers little support to the idea [15] that reuptake of acetate derived from hydrolyzed transmitter plays a role in maintaining ACh synthesis. In this way, acetate differs from the other product of transmitter hydrolysis, choline, which has been shown to be recaptured and used for ACh synthesis [15].
[16] investigated the neurocycle of the ACh utilizing a twocompartment model with AChE as the only enzyme. The investigations unveiled complex static and dynamic behavior including bifurcation, instability, and chaos. [4] investigated a complete but simplified neurocycle for the ACh as a neurotransmitter in an AChE/ChAT system and found that complex dynamic bifurcations, hysteresis, multiplicity, period doubling and period halving, as well as period adding, and period subtracting dominated the dynamics of the system. [5] presented the formulation of a diffusion-reaction model utilizing available biokinetic information to simulate the in-vivo behavior of AChE and ChAT coupled enzymes system using a novel two-enzyme/two-compartment model to explore the bifurcation and chaotic behavior of this enzyme system simulating the ACh neurocycle in the brain. They carried out a detailed bifurcation analysis over a wide range of parameters in order to uncover some important information related to the phenomena occurring in the physiological experiments, like periodic stimulation of neural cells and non-regular functioning of ACh receptors. [5,16].
In this work we try to investigate the effect of choline, and AChE activity using two kinetic mechanisms one for the synthesis of ACh by the enzyme ChAT and the other for hydrolysis of ACh by the enzyme AChE. We attempt to analyze the synthesis of ACh at the level of single cells, rather than the whole nervous system and try to investigate the role of feed (external) choline and acetyl CoA on the ACh processes. The present work extends up on our earlier investigation [17-19]. Here we still employ a novel diffusionreaction model but improve upon our previous investigation by considering realistic kinetic schemes and data for ChAT synthesis reaction, and account for the recycle effects of choline.
Proposed New Diffusion Reaction Two-Enzyme / Two Compartment Model
The (AChE/ChAT) enzymes system inside the neural synaptic cleft can be schematically described in a simplified manner as shown in (Figure 1). The complete neurocycle of the ACh as a neurotransmitter is simulated as a simplified two-enzymes/twocompartment model. Each compartment is defined as a constant flow; constant volume, isothermal, continuous stirred tank reactor (CSTR) and the two compartments are separated by a permeable membrane. The behavior for a single synaptic vesicle is described by this simple two compartment model, assuming that all the events are homogeneous in all vesicles and using the proper dimensionless groups. From an enzyme kinetics point of view, the most general case is when the kinetics of both enzyme reactions has a double non-monotonic (dependence upon both state variables of substrate and hydrogen ions concentration). ACh is assumed to be synthesized in compartment 1 by ChAT due to the activation reaction as follows [5,12]:
Both reactions R(1) and R(2)are considered to be substrate inhibited and hydrogen ions affected. This leads to a non-monotonic dependence of the reaction rates on the substrates concentrations and pH. The rates can be formulated by employing certain assumptions and basic biokinetics knowledge as explained in the following section. The details of the derivation are given in our previous work (Mustafa et al., 2008). The final dimensionless forms of the ordinary differential equations of the eight state variables are summarized in (Table 1). The model equations are in terms of eight state variables S1(1) S1(2) S2(1) S2(2) S3(1) AND S3(2) and twentyfive parameters (Tables 2&3). All values of the parameters (with respective references) used in this investigation are given in (Table 1-3).
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