In the previous week while searching for papers for the literature review in PHYS3900, I came across an interesting article entitled " A solvable model for the diffusion and reaction of neurotransmitters in a synaptic junction" by Barreda et al.
The initial problem of the researchers had was the diffusion and reaction of transmitter acetylcholine in neuromuscular junctions and diffusion and binding of calcium in the synaptic clefts have only been modeled by finite-difference and finite-element solutions, thus the paper presented an analytical solution to a model of the interaction of acetylcholine with the neuromuscular junctions and calcium with the synaptic cleft.
In relevance to the course, the solution involves the use of the diffusion equation
where D is the diffusion constant and C(r,t) is the concentration of the ions with respect to distance and time. The paper goes by defining the boundary conditions and solving the equation using Laplace transform, thus leading to an expression of the total flux through the sink on the post synaptic face. (I didn't bother posting the equations used by the authors, since some of the expressions they used were not explained or they expected you to have a strong background in what they were implementing.) Using the parameters of the model to the flux equation, they acquired a diffusion constant ranging from 0.25 - 6 x 10^5 nm^2/s, in which according to them is comparable to the solutions obtained from the finite - difference or finite - element methods. By showing the capability of analytical solution, they hope that this method would provide a new avenue for modelling biochemical transport.
Thoughts?
Here's the bibliography just in case you guys want to look at the solution
Barreda, J. and H.-X. Zhou (2011). "A solvable model for the diffusion and reaction of neurotransmitters in a synaptic junction." BMC Biophysics 4(1): 5.
The initial problem of the researchers had was the diffusion and reaction of transmitter acetylcholine in neuromuscular junctions and diffusion and binding of calcium in the synaptic clefts have only been modeled by finite-difference and finite-element solutions, thus the paper presented an analytical solution to a model of the interaction of acetylcholine with the neuromuscular junctions and calcium with the synaptic cleft.
In relevance to the course, the solution involves the use of the diffusion equation
where D is the diffusion constant and C(r,t) is the concentration of the ions with respect to distance and time. The paper goes by defining the boundary conditions and solving the equation using Laplace transform, thus leading to an expression of the total flux through the sink on the post synaptic face. (I didn't bother posting the equations used by the authors, since some of the expressions they used were not explained or they expected you to have a strong background in what they were implementing.) Using the parameters of the model to the flux equation, they acquired a diffusion constant ranging from 0.25 - 6 x 10^5 nm^2/s, in which according to them is comparable to the solutions obtained from the finite - difference or finite - element methods. By showing the capability of analytical solution, they hope that this method would provide a new avenue for modelling biochemical transport.
Thoughts?
Here's the bibliography just in case you guys want to look at the solution
Barreda, J. and H.-X. Zhou (2011). "A solvable model for the diffusion and reaction of neurotransmitters in a synaptic junction." BMC Biophysics 4(1): 5.
This sort of work in simple, general analytical models is ever-more important in a world where direct numerical solution of very specific and detailed models for specific systems are the fashion. Ultimately the goal of science is to show people the best way to think about the physical world. Simple models that clearly exemplify a specific physics for a general system are the only real way to understand what's happening.
ReplyDeleteTo paraphrase:
"It is nice to know that the computer understands the problem. But I would like to understand it too." - Eugene Wigner
My question is why no-one ever thought to do it this way before?! I'm happy to do computation, but it has its limitations just the same as analytical expressions (just in different places).
ReplyDeleteOne of my favourites is this: you give a calculator a 99x99 matrix of zeros and ask it to calculate the 99th power of that matrix... it takes more than half an hour, whereas a human (even one who doesn't really know what a matrix is) can do it in about as long as it takes to read the question!