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Computer Mathematical Simulation of the Dynamic Interactions

Computer Mathematical Simulation of the Dynamic Interactions Between Synapsin I, Synaptic Vesicles, and the Cytoskeleton in vitro studies of indepdendent components of this system have been studied and characterized. Kinetic constants obtained through previous studies were used in this work to construct a novel theoretical model for the pre_synaptic neurotransmitter release.

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Abstract

The regulation of neurotransmitter release has long been an important area in neurochemistry, affecting such facets of brain and nerve function as cognition, emotion, memory, and metacognitive processing. To this end, in vitro studies of indepdendent components of this system have been studied and characterized. Kinetic constants obtained through previous studies were used in this work to construct a novel theoretical model for the pre_synaptic neurotransmitter release.

Synapsins constitute a group of three types of phosphoproteins that interact with synaptic vesicles and are a vital component in the regulation of neurotransmitter release. By acting as a cytoskeletal "tether," they are able to mediate the translocation of synaptic vesicles containing neurotransmitter within a cell. Their affinity for actin filaments and synaptic vesicles is modulated by their phosphorylation thereby allowing the dynamic modelling of the interaction of these components.

A computer mathematical model was proposed to illustrate the interactions between Synapsin (phosphorylated and dephosphorylated forms), actin filaments of the cytoskeleton, and synaptic vesicles. Literature constants were used to approximate the in vivo interactions between the four components. Attempts were made to formulate a related system to integrate calcium/calmodulin_dependent Kinase (CaM Kinase II) and its interactions with Synapsin Ia.

Introduction

Synapsins represent a family of abundant synaptic vesicle-associated phosphoproteins which are involved in synaptic vesicle dynamics in nerve terminals (Hosaka and Sudhof, 1998; Geppert et al ., 1994; Sudhof, 1995). They account for approximately 9% of the membrane proteins associated with synaptic vesicles (Esser et al ., 1998). Synapsin were originally discovered in 1977 by Ueda and Greengard and were originally called “Protein 1.” Until recently, two synapsin genes were known: Synapsin I and Synapsin II (Sudhof, 1995). The products of these two genes are alternatively spliced to produce the four synapsin proteins: synapsins Ia, Ib, IIa, and IIb (Sudhof, 1995). Hosaka and Sudhof (1998) recently, however, proposed the existence of a novel Synapsin–Synapsin III.

Thus far, synapsin interactions with brain spectrin, actin filaments, neurofilaments, and microtubules have been reported (Bennett et al ., 1991). Virtually all neurons, regardless of the neurotransmitter released, contain synapsins (Greengard et al ., 1994). In nerve terminals, Synapsin I is specifically located on the cytoplasmic surface of small synaptic vesicles (Benfenati et al ., 1989). There is strong evidence that synapsin I is a regulator of neurotransmitter release through the immobilization of these small synaptic vesicles to the cyotoskeleton, thereby allowing the accumulation of a releasable pool of neurotransmitter (Bahler et al ., 1989). The maintenance of this releasable pool of neurotransmitter allows the rapid recovery and firing of neurons. Further, Bahler et al . (1989) proposed that this regulation is strongly dependent upon the phosphorylation of the synapsin I molecule itself.

In the rat, Synapsins Ia and Ib are 704- and 668-amino acid proteins and Synapsins IIa and IIb are 586- and 479-amino acid proteins, respectively (Greengard et al ., 1994). Between rat, bovine, and human forms, Synapsin maintains a high degree of identity (Esser et al ., 1998). In each case, it comprises five domains: A, B, C, D, and E/F. Each domain is distinguished by its composition and conservation. Of these, Esser et al . (1998) point out that the C-domain is the most highly conserved. It is 39% hydrophobic and 27% charged, and is located in the amino terminal, globular region of the protein.

Synapsin I has a collagenase-insensitive head domain and a collagenase-sensitive tail region (Benfenati et alI., 1989). It has three recognized sites at which it may be phosphorylated by cAMP-dependent protein kinase or Ca 2+ /calmodulin-dependent protein kinase (CaMKII). Benfenati et al . (1989) discovered one serine residue in the head domain (“Site 1"), which is phosphorylated by cAMP-dependent protein kinase, and two serine residues in the tail domain, phosphorylated by CaMKII. It has been shown that phosphorylation at these residues influences the affinity of synapsin for synaptic vesicles (Benfenati et al ., 1989; Esser et al ., 1998; Benfenati et al ., 1989).

Neurotransmitters are stored in synaptic vesicles and released by exocytosis. The only known function of these small synaptic vesicles is the storage and release of neurotransmitters. This relative simplicity has led to the synaptic vesicle being one of the best-studied organelles in biology. Although synapsin I is a very well-characterized protein, and many equilibrium interactions have been demonstrated, as yet there have been no attempts at simulating the real-time interactions between synapsin I, synaptic vesicles, and the cytoskeleton. The purpose of this project is therefore to construct a real-time mathematical computer simulation that reflects possible interactions between phosphorylated and dephosphorylated synapsin I with synaptic vesicles and actin filaments using estimated kinetic constants and computer simulation software.

There is a general consensus that synapsins are necessary for regulation of synaptic vesicle exocytosis and therefore neurotransmitter release. In spite of this vital regulatory function, several experimenters have proven that the lack of synapsins is not lethal. Experiments on mice have led to more debate regarding the necessity of synapsins to normal neurological function. Certain experiments have revealed that mice lacking synapsins expressed no gross anatomical abnormalities, yet experienced grand mal seizures proportional to the number of mutant synapsin alleles (Rosahl et al ., 1995) and others revealed that mice lacking synapsin I exhibited no apparent changes in well-being or gross nervous system function. This evidence suggests that synapsin I normally functions to inhibit neurotransmitter release on a millisecond timescale immediately following a calcium signal, generally thought to occur through C-terminal phosphorylation of synapsin by CaM Kinase II (Sudhof, 1995).

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