%------------------------------------------------------------------------------------------
%
% Title: Calcium Signals in Small Structures
% Filename: CaSignal_main.par
% Author: Ronald van Elburg
%
% Associated Paper:
% Cornelisse LN, van Elburg RAJ, Meredith RM, Yuste R, Mansvelder HD (2007)
% High Speed Two-Photon Imaging of Calcium Dynamics in Dendritic Spines:
% Consequences for Spine Calcium Kinetics and Buffer Capacity.
% PLoS ONE 2(10): e1073 doi:10.1371/journal.pone.0001073
%
% Purpose:
% To show how the Calcium signal changes in time after an
% actionpotential and how these timecourses depend on the
% distance to the membrane and the membrane morphology which can be
% spherical (spine) or cylindrical (dendrite).
%
% History, Background, Related Papers:
% This file is developed for CalC 5.0.3
%
% Other Files Loaded: none
%
% Associated scripts:
% Calc:
% CaSignal_Exp<ExperimentName><GeometryName>.par
%
% Matlab postprocessing:
% CaSignal_Exp<ExperimentName>.m
%
% Output:
% None, this file contains a declarative definition off the model
% and its default parameters. The actual simulations are described in other
% par-files which include this file.
%
%
% Remark: Best viewed with tabsize=4
%
%
% Initial Creation Date: 2004-12-01
% ChangeNo Date ChangedBy Description of Changes
% PR001 2004-12-01 Ronald van Elburg Creation
% PR002 2007-04-23 Ronald van Elburg Parameters constrained experimentally
%-----------------------------------------------------------------------------------
% Meta Parameters:
% Because CalC language is almost purely declarative, it is possible
% to refer forward to the predefined constants when overruling the Structure
% setting from a script.
Structure = Disc_Structure
Sphere_Structure = 0
Cylinder_Structure = 1
Disc_Structure = 2
%Numerical accuracy adaptive timestep
accuracy = 0.01
% Default Parameter Values
%R_Structure = 0.57 % Radius of the simulated structure: Cylinder or Sphere (0.57 um)
CylinderLengthRadiusRatio = 2 % Length/Radius of the simulated structure
CylinderLength = CylinderLengthRadiusRatio * R_Structure % CylinderLength (um)
HalfCylinderLength = CylinderLength/2 % HalfCylinderLength (um) needed for positioning Current Source
D_Calcium = 0.22 % Ca diffusion coefficient (0.22 um^2/ms based on Allbritton et al. 1992)
Background_Ca = 0.11 % Uniform Initial Calcium Concentration 0.11 uM based on exp this paper
% (cf. 0.08 uM based on Sabatini et al. 2002)
D_EndogenousBuffer = 0 % Immobile endogenous buffer, diffusion coefficient =0
KPlus_EndogenousBuffer = 0.5 % Endogenous buffer calcium binding rate (0.5/(ms uM) based on Klingauf,Neher 1997)
KD_EndogenousBuffer = 10 % Endogenous buffer calcium affinity (10 uM based on Klingauf,Neher 1997, Neher Augustine,1992 )
D_Dye = 0.05 % Diffusion Constant Mobile Fluorescent Dye (0.05 um^2/ms based on Timmerman Ashley 1986, Wagner, Keizer, 1994)
Total_Dye = 100 % Total dye concentration (100 uM as in pipette)
KPlus_Dye = 0.45 % Fluorescent dye calcium binding rate (0.45/(ms uM) based on Naraghi 1997)
KD_Dye = 0.205 % Fluorescent dye calcium affinity (0.205 uM Sabatini 2002)
t_actionpotential = 10 % Centre position of calcium current pulse
% Dendrite and Spine specific parameters, these parameters were
% determined experimentally or derived from the first parameter scan.
if Structure==Disc_Structure
% Dendrite specific settings
Total_EndogenousBuffer = 660 % Total endogenous buffer concentration (660 uM, this paper)
n_ions = 4400 % Number of calcium ions entering with 1 actionpotential (this paper)
mingamma_0 = -0.465 % Extrusion rate (-0.24 uM/ms this paper)
pulselength = 1.75 % Width of the calcium current pulse
R_Structure = 0.61 % Radius of the simulated structure: Cylinder (0.61 um)
Sigma = 2/R_Structure % For backward compatabiltiy scripts relying on sigma
endif
if Structure==Cylinder_Structure
% Dendrite specific settings
Total_EndogenousBuffer = 660 % Total endogenous buffer concentration (660 uM, this paper)
n_ions = 4400 % Number of calcium ions entering with 1 actionpotential (this paper)
mingamma_0 = -0.465 % Extrusion rate (-0.49 uM/ms this paper)
pulselength = 1.75 % Width of the calcium current pulse
R_Structure = 0.61 % Radius of the simulated structure: Cylinder (0.61 um)
Sigma = 2/R_Structure % For backward compatabiltiy scripts relying on sigma
endif
if Structure==Sphere_Structure
% Spine specific settings
Total_EndogenousBuffer = 210 % Total endogenous buffer concentration (210 uM, this paper)
n_ions = 2000 % Number of calcium ions entering with 1 actionpotential (this paper)
mingamma_0 = -0.46 % Extrusion rate (-0.45 uM/ms this paper)
pulselength = 1.55 % Width of the calcium current pulse
R_Structure = 0.47 % Radius of the simulated structure: Cylinder (0.47 um)
Sigma = 3/R_Structure
endif
%Fundamental constants
pi = 3.14159265358979 % Pi
sqrt_of_pi = 1.77245385090552 % Square root of pi
elementaryCharge = 1.60217733e-19 % Electron charge (1.60217733e-19 C)
AvagradoConstant = 6.00221367e23 % Avagrado's Constant
E21OVERAvagrado = 1e21/AvagradoConstant % Transformation Factor Used to get Calcium Current in the right units
% Status Statements
verbose = 2 % Default level of simulation status statements, 0=silent
% Geometry
if Structure==Disc_Structure
geometry = disc % Cylinder Geometry (2 dimensional)
volume 0 R_Structure % Inner (0) and outer radius (R_Structure) of the Cylinder
Surface_Structure=2*pi*R_Structure % Size of the Surface
% Numerics
grid 25 % Use 25 shells for the computation
endif
if Structure==Cylinder_Structure
geometry = cylindrical % Cylinder Geometry (2 dimensional)
volume 0 R_Structure 0 CylinderLength % Inner (0) and outer radius (R_Structure) of the Cylinder
% and start (0) and end (CylinderLength) of the cylinder in the Z-direction
Surface_Structure=2*pi*R_Structure*CylinderLength % Size of the Surface
% Numerics
grid 25 25 % Use 25 shells and 25 disks for the computation
endif
if Structure==Sphere_Structure
geometry = spherical % Cylinder Geometry (2 dimensional)
volume 0 R_Structure % Inner (0) and outer radius (R_Structure) of the Sphere
Surface_Structure=4*pi*R_Structure*R_Structure % Size of the Surface
% Numerics
grid 25 % Use 25 shells for the computation
endif
% Calcium Diffusion and Sources
Ca.D = D_Calcium % this defines the Ca diffusion coefficient (um^2/ms)
Ca.bgr = Background_Ca % Initial and Background Ca concentration (uM)
% Boundary Conditions
bc.define CalciumPump Ca.D mingamma_0 0 0 % A linearized Calcium Pump: Ca.D d[Ca]/dr=mingamma_0([Ca]-[Ca]_background)
R_Source=0.99999999*R_Structure % Due to rounding errors in the C-code the source may end up outside the structure
% , shifting it in a small amount prevents this from happening.
if Structure==Disc_Structure
% Pump
Ca.bc Neumann CalciumPump
% Influx
Ca.source R_Source 0
endif
if Structure==Cylinder_Structure
% Pump
Ca.bc Neumann CalciumPump Neumann Neumann
% Influx
Ca.source R_Source HalfCylinderLength 0 HalfCylinderLength
current.shape square
endif
if Structure==Sphere_Structure
% Pump
Ca.bc Neumann CalciumPump
% Influx
Ca.source R_Source 0
endif
% Calcium Current:
CalciumCurrent:= n_ions*Surface_Structure*E21OVERAvagrado/(sqrt_of_pi*pulselength)*exp(-((t-t_actionpotential)/pulselength)^2)
% Endogenous Buffer
buffer EndogenousBuffer % Create Buffer EndogenousBuffer
EndogenousBuffer.D = D_EndogenousBuffer % Endogenous buffer diffusion coefficient (um^2/ms)
EndogenousBuffer.total = Total_EndogenousBuffer % Total endogenous buffer concentration (uM)
% Binding/Unbinding Rate Constants
EndogenousBuffer.kplus = KPlus_EndogenousBuffer % Endogenous buffer calcium binding rate (1/(ms uM))
EndogenousBuffer.KD = KD_EndogenousBuffer % Endogenous buffer calcium affinity (uM)
% Boundary Conditions
EndogenousBuffer.bc all Neumann % No flux of endogeous buffer through the boundary
% Fluorescent Dye
buffer Dye % Create buffer Dye: Oregon Green Bapta-1 fluorescent dye
Dye.D = D_Dye % Fluorescent dye diffusion coefficient (um^2/ms)
Dye.total = Total_Dye % Total dye concentration (uM)
% Binding/Unbinding Rate Constants
Dye.kplus = KPlus_Dye % Fluorescent dye calcium binding rate (1/(ms uM))
Dye.KD = KD_Dye % Fluorescent dye calcium affinity (uM)
% Boundary Conditions
Dye.bc all Neumann % No flux of dye through the boundary