SUPPORTING MATERIAL 2

                   MATLAB code for the manuscript 

  "Closed-form approximations for stationary single-channel Ca2+ nanodomain
           in the presence of buffers with two binding sites"

                     Yinbo Chen and Victor Matveev

               Department of Mathematical Sciences, NJIT
			   
		 Corresponding Author: Victor Matveev (matveev@njit.edu)
			 

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 MATLAB functions in this folder implement all approximant expressions summarized
 in Tables 1 & 2, Appendix A, and in Supporting Material 1 file.

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  This folder contains the following files:
  
 1. Get_ApproximantByName_ZeroRestingCa.m
 2. Get_ApproximantByName_AnyRestingCa.m
 3. Get_RBA_AnyRestingCa.m
 4. Select_Best_Buffer_Approximant.m
 5. Select_Best_Ca_Approximant.m
 6. Figure1.m
 7. Figure1_Best_Approximant.m

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1. Get_ApproximantByName_ZeroRestingCa.m

 function [BufferCa0, BufferCa2, Calcium, R] = ...
   Get_ApproximantByName_ZeroRestingCa(Method, lambda2, nu2, eps, gamma, lineType)

 Compute an approximation for concentrations of
        Ca2+ and 2:1 buffer near a point channel / source
        Case of zero background / resting [Ca2+] at infinity

 Input variables: 
  (1)   Method string in the set {'RBA', 'ExpPadeA', 'ExpPadeB', 'ExpExp'}
  (2-5) Dimensional parameters: lambda2, nu2, eps, gamma
  (7)   lineType: MATLAB plot linetype string, e.g. 'b--'

 Return arrays: BufferCa0 = [Free buffer]        vs. distance from channel 
                BufferCa2 = [Fully bound buffer] vs. distance from channel 
                Calcium   = [Ca2+]               vs. distance from channel
                R         = Array of distances from channel see Eq. 28)

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 2. Get_ApproximantByName_AnyRestingCa.m
 
 function [BufferCa0, BufferCa2, Calcium] = ...
   Get_ApproximantByName_AnyRestingCa(Method, lambda2, nu2, eps, gamma, CaInfty, lineType)
 
 Compute an approximation for concentrations of
        Ca2+ and 2:1 buffer near a point channel / source
        Case of nonzero background / resting [Ca2+] at infinity, CaInfty

 Input variables: 
  (1)   Method string in the set {'RBA', 'ExpPade', 'ExpExp'}
  (2-6) Dimensional parameters: lambda2, nu2, eps, gamma, CaInfty
  (7)   lineType: MATLAB plot linetype string, e.g. 'b--'

 Return arrays: BufferCa0 = [Free buffer]        vs. distance from channel 
                BufferCa2 = [Fully bound buffer] vs. distance from channel 
                Calcium   = [Ca2+]               vs. distance from channel
                R         = Array of distances from channel see Eq. 28)

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 3. Get_RBA_AnyRestingCa.m
 
 [BufferCa0, BufferCa2, Calcium, r] = Get_RBA_AnyRestingCa(nu2, eps, gamma, CaInfty, lineType)
 
 Compute RBA approximation for concentrations of Ca2+ 
       and 2:1 buffer state concentrations near a point channel / source
       Case of nonzero background / resting [Ca2+] at infinity, CaInfty

 Input variables:
  (1-4) Dimensionless parameters: nu2, eps, gamma, CaInfty
  (7)   lineType: MATLAB plot linetype string, e.g. 'b--'

 Return arrays: BufferCa0 = [Free buffer]        vs. distance from channel 
                BufferCa2 = [Fully bound buffer] vs. distance from channel 
                Calcium   = [Ca2+]               vs. distanc(see Eq. 28)
                r         = Array of distances from channel see Eq. 28)
				
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4. Select_Best_Buffer_Approximant.m

  function Y = Select_Best_Buffer_Approximant(lambda2, nu2, epsilon, gamma)
  
  For the case of zero calcium concentration, selects the most accurate approximant 
  for estimating buffer state concentrations for given model parameters, 
  implementing parameter space segmentation shown in Fig. 3
  
  Output Y is an integer specifying the best approximant:
     Y=1: RBA; Y=2: ExpPadeA; Y=3: ExpPadeB; Y=4: ExpExp

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5. Select_Best_Ca_Approximant.m

  function Y = Select_Best_Ca_Approximant(lambda2, nu2, epsilon, gamma)
  
  For the case of zero calcium concentration, selects the most accurate 
  approximant for estimating calcium concentrations for given model parameters, 
  implementing parameter space segmentation shown in Fig. 5
  
  Output Y is an integer specifying the best approximant:
     Y=1: RBA; Y=2: ExpPadeA; Y=3: ExpPadeB; Y=4: ExpExp

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  6. Figure1.m
	
	function Figure1()
	
	This simple script uses MATLAB functions above to produce and plot the 
	approximants in Figure 1 of the manuscript
	
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  7. Figure1_Best_Approximant.m
	
	function Figure1_Best_Approximant()
	
	This script plots only the best approximant for each of the four parameter
	sets in Figure 1. The best approximant is determined using the algorithm
	provided by the function Select_Best_Buffer_Approximant.m
	
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