A solvable model for the diffusion and reaction of neurotransmitters in a synaptic junction

Background: The diffusion and reaction of the transmitter acetylcholine in neuromuscular junctions and the diffusion and binding of Ca(2+) in the dyadic clefts of ventricular myocytes have been extensively modeled by Monte Carlo simulations and by finite-difference and finite-element solutions. However, an analytical solution that can serve as a benchmark for testing these numerical methods has been lacking. Result: Here we present an analytical solution to a model for the diffusion and reaction of acetylcholine in a neuromuscular junction and for the diffusion and binding of Ca(2+) in a dyadic cleft. Our model is similar to those previously solved numerically and our results are also qualitatively similar. Conclusion: The analytical solution provides a unique benchmark for testing numerical methods and potentially provides a new avenue for modeling biochemical transport.