%**********************************************************************************
%
% CalC version 5.4.0, script "FCT_main.par"
% Victor Matveev, January 4, 2005
%
% "Facilitation through Buffer Saturation:
% Constraints on Endogenous Buffering Properties"
% V. Matveev, A. Sherman and R. Zucker
% Biophys. J. (2004) 86:2691-2709
%
% This file contains the main definitions used by all simulations,
% except for the buffer's parameters which are defined in the parent script.
%__________________________________________________________________________________
%
% Units are: micrometers (um) for space, ms for time, microM (uM) for concentration.
% Note that definitions appearing in a CalC script may be included in arbitrary order.
%==================================================================================
%
% Geometry parameters are based on:
% Tang et al. (2000), p.2741: Ave. bouton diameter = 3 um
% (Biophys J 78: 2735-2751) Active zone diameter 160 nm
% AZ lies in the center of a 2.56 um^2 area = pi (0.9 um)^2
geometry = conical % Conical geometry: see Fig. 1.
% This instructs CalC to solve the equations in spherical
% coordinates (radius - polar theta angle).
AZ.R = 0.08 % radius of the AZ (80 nm)
S.R = 0.9 % radius of the cone's base (900 nm)
R = 3 / 2 % radius of the bouton (1.5 um)
Theta = S.R / R; % Angle corresponding to the conical volume edge (Fig. 1, bottom)
Alpha = AZ.R / R; % Angle corresponding to the the active zone edge (Fig. 1, top)
volume 0 R 0 Theta % Defines the conical volume in Fig. 1
Ca.source R 0 0 Alpha % Ca2+ source is centered at the vertex ( (R,0) in spherical
% coordinates), and has an angular span of Alpha
current.shape square % Specifies that the current is distributed uniformly over
% the area defined by the Alpha angle in the Ca.source statement
% above, and is zero outside of that area (i.e., as opposed
% to a smooth gaussian distribution).
grid 36 36 % Enough for an accuracy of a few percent
% The grid is non-uniform, and is denser near the active zone:
stretch.factor = 1.05 % Multiplication factor for each successive grid interval.
stretch r R R % In "stretch (r,theta) A B", [A,B] is the interval of minimal
stretch theta 0 Alpha % grid spacing; grid spacing is increased outside of [A,B]
%==================================================================================
buffer Buffer % This introduces the endogenous buffer, and gives it a name "Buffer" (duh!)
% Buffer parameters will be defined in the parent script
%==================================================================================
% Now define variables tracking [Ca2+] and [Buffer] at locations labeled "1"
% through "3" in Fig. 1 (top inset)
depth = R - 0.02
th1 = (AZ.R + 0.02) / R % Angle coordinate of location "1", 20 nm lateral to AZ edge
th2 = (AZ.R + 0.06) / R % Angle coordinate of location "2", 60 nm lateral to AZ edge
th3 = (AZ.R + 0.10) / R % Angle coordinate of location "3", 100 nm lateral to AZ edge
% Actually, in above we should have divided by "depth", not "R", but this has little
% effect on the results
Ca1 := Ca[depth,th1] ; Buffer1 := Buffer[depth,th1]
Ca2 := Ca[depth,th2] ; Buffer2 := Buffer[depth,th2]
Ca3 := Ca[depth,th3] ; Buffer3 := Buffer[depth,th3]
%==================================================================================
Ca.D = 0.22 % this defines the Ca diffusion coefficient (0.22 um^2/ms)
Ca.bgr = 0.0 % background Ca concentration = 0
M = 0.01 % Pump rate, in um / ms (Methods, p. 7)
K_PUMP = 0.2 % Pump affinity, uM (ibid)
A = - M / Ca.D / K_PUMP % Constant that appears in the pump boundary condition
% (see the CalC manual and Eq. 5 of the manuscript)
Ca.bc Noflux Pump Noflux Noflux % Only the top z-surface has a pump
bc.define Pump 1 A 0 K_INV % See CalC manual for b.c. definition syntax
K_INV = 1 / K_PUMP
%==================================================================================
% Current per active zone (Note: "ICa" is a reserved keyword, that's why we use "I.Ca")
I.Ca = 11.7 pA
% This value is the same as the one used in Tang et al. (2000), translated to
% the case of a 1 ms-long square pulse.
% Finally, the simulation statements: five 1 ms-long pulses at 100 Hz, which
% yields an interpulse interval of 9 ms.
fivePulse = 1 % Unless constant "fivePulse" is redefined in the
% parent script, simulate a five-pulse train:
if (fivePulse) then
Run adaptive 1.0; current I.Ca % 1 ms-long channel opening
Run adaptive 9.0; current 0 % Interpulse interval
Run adaptive 1.0; current I.Ca % Repeat five times
Run adaptive 9.0; current 0
Run adaptive 1.0; current I.Ca
Run adaptive 9.0; current 0
Run adaptive 1.0; current I.Ca
Run adaptive 9.0; current 0
Run adaptive 1.0; current I.Ca
Run adaptive 3.0; current 0
endif
%==================================================================================