Continuum simulations of acetylcholine diffusion with reaction-determined boundaries in neuromuscular junction models

Cheng, Yuhui; Suen, Jason K.; Radić, Zoran; Bond, Stephen D.; Holst, Michael; McCammon, J. Andrew

doi:10.1016/j.bpc.2007.01.003

Cited by 30 publications

(40 citation statements)

References 48 publications

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“…[21][22][23][24][25] Solvers were developed for the time-dependent SE, with no interaction fields, for studies of the NMJ. 21,22 Also, a software was developed to solve the PBE using a multigrid method, 26 and this was used with the steady-state SE to study the consumption of ACh by acetylcholinesterase ͑AChE͒.…”

Section: Introductionmentioning

confidence: 99%

Electrodiffusion: A continuum modeling framework for biomolecular systems with realistic spatiotemporal resolution

Zhou

Huber

et al. 2007

The Journal of Chemical Physics

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122

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A computational framework is presented for the continuum modeling of cellular biomolecular diffusion influenced by electrostatic driving forces. This framework is developed from a combination of state-of-the-art numerical methods, geometric meshing, and computer visualization tools. In particular, a hybrid of ͑adaptive͒ finite element and boundary element methods is adopted to solve the Smoluchowski equation ͑SE͒, the Poisson equation ͑PE͒, and the Poisson-Nernst-Planck equation ͑PNPE͒ in order to describe electrodiffusion processes. The finite element method is used because of its flexibility in modeling irregular geometries and complex boundary conditions. The boundary element method is used due to the convenience of treating the singularities in the source charge distribution and its accurate solution to electrostatic problems on molecular boundaries. Nonsteady-state diffusion can be studied using this framework, with the electric field computed using the densities of charged small molecules and mobile ions in the solvent. A solution for mesh generation for biomolecular systems is supplied, which is an essential component for the finite element and boundary element computations. The uncoupled Smoluchowski equation and Poisson-Boltzmann equation are considered as special cases of the PNPE in the numerical algorithm, and therefore can be solved in this framework as well. Two types of computations are reported in the results: stationary PNPE and time-dependent SE or Nernst-Planck equations solutions. A biological application of the first type is the ionic density distribution around a fragment of DNA determined by the equilibrium PNPE. The stationary PNPE with nonzero flux is also studied for a simple model system, and leads to an observation that the interference on electrostatic field of the substrate charges strongly affects the reaction rate coefficient. The second is a time-dependent diffusion process: the consumption of the neurotransmitter acetylcholine by acetylcholinesterase, determined by the SE and a single uncoupled solution of the Poisson-Boltzmann equation. The electrostatic effects, counterion compensation, spatiotemporal distribution, and diffusion-controlled reaction kinetics are analyzed and different methods are compared.

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Section: Introductionmentioning

confidence: 99%

Electrodiffusion: A continuum modeling framework for biomolecular systems with realistic spatiotemporal resolution

Zhou

Huber

et al. 2007

The Journal of Chemical Physics

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122

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“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Zhou

Huber

et al. 2007

J. Phys. Chem. B

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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.

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“…To demonstrate the generality of our mesh tool, we show here several other examples: the neuromuscular junction given as a triangulated surface mesh [15,45], a human head model given as a scalar volume (mimicked by the signed distance function) [54], and an actual CT medical image of human cardiovascular system. Fig.6(A) shows the surface mesh after the post-processing as discussed in Section 2.…”

Section: Mesh Generation For Other Applicationsmentioning

confidence: 99%

High-fidelity geometric modeling for biomedical applications

Holst

McCammon

2008

Finite Elements in Analysis and Design

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We describe a combination of algorithms for high fidelity geometric modeling and mesh generation. Although our methods and implementations are application-neutral, our primary target application is multiscale biomedical models that range in scales across the molecular, cellular, and organ levels. Our software toolchain implementing these algorithms is general in the sense that it can take as input a molecule in PDB/PQR forms, a 3D scalar volume, or a user-defined triangular surface mesh that may have very low quality. The main goal of our work presented is to generate high quality and smooth surface triangulations from the aforementioned inputs, and to reduce the mesh sizes by mesh coarsening. Tetrahedral meshes are also generated for finite element analysis in biomedical applications. Experiments on a number of bio-structures are demonstrated, showing that our approach possesses several desirable properties: feature-preservation, local adaptivity, high quality, and smoothness (for surface meshes). The availability of this software toolchain will give researchers in computational biomedicine and other modeling areas access to higher-fidelity geometric models.

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Continuum simulations of acetylcholine diffusion with reaction-determined boundaries in neuromuscular junction models

Cited by 30 publications

References 48 publications

Electrodiffusion: A continuum modeling framework for biomolecular systems with realistic spatiotemporal resolution

Electrodiffusion: A continuum modeling framework for biomolecular systems with realistic spatiotemporal resolution

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

High-fidelity geometric modeling for biomedical applications

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