Determinants of fast calcium dynamics in dendritic spines and dendrites (Cornelisse et al. 2007)

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Accession:97903
"... Calcium influx time course and calcium extrusion rate were both in the same range for spines and dendrites when fitted with a dynamic multi-compartment model that included calcium binding kinetics and diffusion. In a subsequent analysis we used this model to investigate which parameters are critical determinants in spine calcium dynamics. The model confirmed the experimental findings: a higher SVR (surface-to-volume ratio) is not sufficient by itself to explain the faster rise time kinetics in spines, but only when paired with a lower buffer capacity in spines. Simulations at zero calcium-dye conditions show that calmodulin is more efficiently activated in spines, which indicates that spine morphology and buffering conditions in neocortical spines favor synaptic plasticity. ..."
Reference:
1 . Cornelisse LN, van Elburg RA, 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:e1073 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Synapse; Dendrite;
Brain Region(s)/Organism:
Cell Type(s): Neocortex U1 L2/6 pyramidal intratelencephalic GLU cell;
Channel(s):
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: CalC Calcium Calculator;
Model Concept(s): Calcium dynamics;
Implementer(s): van Elburg, Ronald A.J. [R.van.Elburg at ai.rug.nl];
Search NeuronDB for information about:  Neocortex U1 L2/6 pyramidal intratelencephalic GLU cell;
%------------------------------------------------------------------------------------------
%
% 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








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