Continuum Simulations of Acetylcholine Consumption by Acetylcholinesterase:  A Poisson−Nernst−Planck Approach

Abstract

The Poisson-Nernst-Planck (PNP) equation provides a continuum description of electrostatic-driven diffusion and is used here to model the diffusion and reaction of acetylcholine (ACh) with acetylcholinesterase (AChE) enzymes. This study focuses on the effects of ion and substrate concentrations on the reaction rate and rate coefficient. To this end, the PNP equations are numerically solved with a hybrid finite element and boundary element method at a wide range of ion and substrate concentrations, and the results are compared with the partially coupled Smoluchowski-Poisson-Boltzmann model. The reaction rate is found to depend strongly on the concentrations of both the substrate and ions; this is explained by the competition between the intersubstrate repulsion and the ionic screening effects. The reaction rate coefficient is independent of the substrate concentration only at very high ion concentrations, whereas at low ion concentrations the behavior of the rate depends strongly on the substrate concentration. Moreover, at physiological ion concentrations, variations in substrate concentration significantly affect the transient behavior of the reaction. Our results offer a reliable estimate of reaction rates at various conditions and imply that the concentrations of charged substrates must be coupled with the electrostatic computation to provide a more realistic description of neurotransmission and other electrodiffusion and reaction processes. IntroductionAs one of the most important neurotransmitters, the cation acetylcholine (ACh) is responsible for the communication between neurons and muscle fibers. This communication occurs at a synapse called the neuromuscular junction (NMJ), where ACh is released from the presynaptic vesicles, diffuses across the synaptic cleft, and is hydrolyzed by acetylcholinesterase (AChE) clusters tethered to the postsynaptic membranes. The timely release of ACh and its consumption by AChE are essential for the communication, and the diffusion of ACh appears to be the rate-limiting step of this highly coordinated process. Various computational models have been developed to simulate this diffusion process, including continuum reactiondiffusion models 1-3 and discrete methods such as Monte Carlo, 37 Langevin dynamics, and the popular Brownian dynamics. 4,19 Most continuum models emphasize either the diffusion of ACh in the synaptic cleft or the diffusion and reaction of ACh with the AChE monomer or tetramer. In the former case, a rate coefficient is needed to provide the boundary condition for the diffusion equation at the surface of the enzymes, 2,3 whereas in the latter case a steady-state reaction rate coefficient is derived from the solution of the diffusion equations. [20][21][22][23][24]29 Therefore, an accurate estimate of this rate coefficient is of great importance in the study of neurotransmission.

Molecular surface-free continuum model for electrodiffusion processes

“…For high substrate concentration, the reaction rate coefficient can be even increased by the ionic screening effect in certain range of the strengths due to the competition between the favored substrate-receptor (electrostatic) attraction and the unfavored substrate-substrate (electrostatic) repulsion, both of which interactions are weakened by ionic screening. Similar phenomena was also observed in our recent surface-reaction model [1,7].…”

Self-consistent treatment of the local dielectric permittivity and electrostatic potential in solution for polarizable macromolecular force fields

“…In particular, the Nernst-Plank equation can be combined with PBE to calculate local ion currents, e.g., through trans-membrane channels, 65 or to estimate proteinligands association rates. 66 In all these problems interfacial electrostatic effects are important components of the underlying physics. The method may also be useful in situations where dielectric gradients are important or when transient, local liquid density variations affect electrostatics, e.g., in biological samples under the action of pressure shocks.…”

Computational Studies of Glycoside, Carboxylic Ester, and Thioester Hydrolase Mechanisms: A Review

“…In this case, the water molecule is found between Ser203 and Glu334, and it acts as a charge relayer as the inhibitor binds to the mutant, accepting a hydroxyl proton from Ser203 and donating a proton to the carboxyl group of Glu334. 85 88 The role of the oxyanion hole of AChE was explored using ab initio and hybrid DFT methods by Igarishi et al, 89 while MD was used by Olson to compare different solvent models while AChE loops were being reorganized. 90 Tachikawa et al applied ab initio molecular orbital and hybrid DFT calculations to the initial step of the acylation reaction.…”