The scripts following below reproduce the simulation results presented in the manuscript:
Victor Matveev (2016)
Padé Approximation of a Stationary SingleChannel Ca2+ Nanodomain.
Biophysical Journal, 111(9): 20622074
Full Text
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It is best to download and place all scripts in the same directory:
PadeApproximation.m
MATLAB function
[Buff, Cal] = PadeApproximation(N, lambda, mu)
computes Pade approximation of order
N for nondimensionalized Buffer
and Ca
^{2+} concentrations for given parameter values
(lambda, mu), and
returns symbolic functions of distance
r=rho from the channel,
Buff(r)
and
Cal(r). Note that doubleprecision roundoff errors are possible
in coefficients.
PadeApproximationPlots.m
MATLAB script
PadeApproximationPlots produces data in Figure 3 of the
manuscript, using Pade Approximations generated by the MATLAB function
PadeApproximation(N, lambda, mu)
Finally, below is a simpler (and more stable with respect to future MATLAB version changes) code
computing the 2
^{nd}order Pade approximant, given by a closedform solution of a
quartic polynomial equation system in Eqs. (27) of the manuscript:
PadeApproximationQuadraticExplicit.m
MATLAB function
[Buff, Cal] = PadeApproximationQuadraticExplicit(lambda, mu, rr, plotFlag)
computes 2
^{nd}order Pade approximation for nondimensionalized Buffer
and Ca
^{2+} concentrations for given parameter values
(lambda, mu), and
returns symbolic functions of distance from the channel,
Buff(r)
and
Cal(r). The array of distances
rr will be populated automatically
if an empty array is passed. Set
plotFlag to a nonzero value to see
a plot of buffer concentration.
Supported in part by the
National Science Foundation grant
DMS 1517085 to Victor Matveev
Victor Matveev
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Last modified: Apr 2, 2019