%********************************************************************************** % % CalC version 5.4.5, script "actual.pde.par" % Victor Matveev, May 25, 2005 % % Supplemental material for the Letter to the Editor of the Biophys. J. % "New and Corrected Simulations of Synaptic Facilitation" % by V. Matveev, A. Sherman and R. Zucker % % This script defines the "actual" parameter set used to generate Fig. 7 (B and C) % of Tang et al., Biophys J (2000) 78:2735 (see Table 1 of the Letter). These % parameters were extracted from the original code ("20nmcont.cc") by T. Schlumpberger. % % This script is used by the main parent scripts "STF.growth.par", % "STF.decay.stage1.par" and "STF.decay.stage2.par" %__________________________________________________________________________________ % % Units are: micrometers for space, ms for time, microM for concentration, % and 1e-21 mole/ms for current (one can also use the conversion constant "pA" % which is predefined for convenience) % % Definitions appearing in a CalC script may be included in arbitrary order. %================================================================================== % 1. GEOMETRY PARAMETERS DEFINITIONS (cf p. 2741) %================================================================================== % The original program by T. Schlumpberger used grid intervals of 20 nm, but Ca2+ % channels were assigned to grid points (2,2), (2,5), (5,2) and (5,5), as in the 10 nm % resolution diagram of Figure 5: a = 0.03 ; b = 0.09 ; c = 0.01 % These are constant definitions Ca.source a a c Ca.source a b c Ca.source b a c Ca.source b b c % - Note that channels are "suspended" at a distance of c = 10 nm from the membrane. % This is the consequence of the way no flux (reflective, zero-derivative) boundary % conditions were implemented in the original code: the concentration values at two % sucessive grid points near the boundary were constrained to be equal, therefore the % boundary is located in the *middle* of the interval between these two grid points. % Thus, the concentration values correspond to the *centers* of elementary compartments, % exactly as shown in Fig. 5 of Tang et al. % % In the x- and y- directions, the model (quarter-)bouton size is 0.8 x 0.8 um. In the % z-direction, the original program assumed a non-uniform grid, with elementary % compartment size doubling at the 4th, 7th and 10th sheets (compare with description % on p. 2736). Here is the resulting schematic showing the z coordinates (in units of % nm) of the centers of elementary compartments: % % 10 50 120 220 300 380 500 660 820 980 1060 nm % |1|2|3|4 |5 |6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | % 0 30 80 160 nm % ^ ^ ^ ( pointers mark compartment doublings ) % % Therefore, the enclosure dimensions are: volume 0 0.8 0 0.8 0 1.06 % Next line defines the grid (discretization of space) for the numerical solver. % The number of points in the x- and y- directions is 34, and there are 40 points % in the z-direction (the channels lye in the x-y plane; cf. Fig. 5 of Tang et al.). % These grid dimensions guarantee a numerical accuracy of about 5 % grid 34 34 40 % To improve the spatial resolution, we use a non-uniform grid, with a higher % density of grid points close to the active zone (spatial gradients are the % largest in this region, so higher spatial resolution is required). The grid is % smoothly stretched in all directions away from the active zone; for a % given direction, each successive grid interval is given by a product of the % previous grid interval, and a factor slightly greater than one, defined by the % "stretch.factor" constant: stretch.factor = 1.07 % The following "stretch" commands describe the region of space where the grid % points are dense. The grid is stretched in all 3 directions away from this region. % In this case, the "dense" region is a 90 nm by 90 nm by 10 nm patch containing % the 4 Ca2+ channels (see "Ca.source" definitions above) stretch x 0 b % Stretch in the x-direction starts from x = b = 0.09 um = 90 nm stretch y 0 b % Same for the grid stretch in the y-direction stretch z 0 c % In the z-direction stretching starts from z = c = 10 nm %================================================================================== % 2. CALCIUM PARAMETERS DEFINITIONS (cf p. 2742) %================================================================================== Ca.D = 0.2 % The Ca2+ difussion coefficient (in units of um^2/ms; cf p. 2742). Ca.bgr = 0.1 % Background Ca2+ concentration = 0.1 uM = 100 nM % Now we define the boundary conditions (b.c.) for Ca2+, for each of the six % surfaces of the bouton volume: no flux boundaries in x- and y- directions, and % pump b.c. on the z-plane containing the active zone (channel array): Ca.bc Noflux Noflux Noflux Noflux Pump Noflux % While the no flux b.c. is defined internally, the "Pump" b.c. we have to define % ourselves. A b.c. is defined by 3 constants (a, b and c) in the boundary equation % "a dU/dn + b U = c", where U is the concentration field, and dU/dn is its % derivative in the direction normal to the boundary. For pump rate P, we have % % D dCa/dn - P (Ca - Ca.bgr) = 0 or dCa/dn - P/D Ca = - P/D Ca.bgr % % where D=0.2 um^2/ms is the diffusion coefficient and Ca.bgr=0.1 uM is the % steady-state Ca2+ concentration. Pump rate is P = 0.05 um/ms, so we define bc.define Pump 1 -0.25 0 % defines the pump b.c. d[Ca]/dn - 0.25 ([Ca] - Ca.bgr) = 0 %================================================================================== % 3. BUFFER PARAMETERS DEFINITIONS (cf p. 2742) %================================================================================== buffer Bf % This introduces the fixed buffer, and gives it a name "Bf" Bf.D = 0.0 % Diffusion coefficient is zero, since it is fixed Bf.total = 8000 % Total concentration is 8 mM ( cf quoted value of 5.76 nM ) Bf.kplus = 0.5 % Binding rate 0.5 / (uM ms) ( cf quoted value of 0.1 ) Bf.KD = 16 % Affinity is 16 uM Bf.bc all Noflux % Reflective boundary conditions on all surfaces (default; may % be omitted). buffer Bm % Let's call the mobile buffer "Bm" Bm.D = 0.01 % Diffusion coefficient is 0.05 um^2/ms Bm.total = 560 % Total concentration is 280 uM ( cf quoted value of 280 uM ) Bm.kplus = 0.5 % Binding rate 0.1 / (uM ms) ( cf quoted value of 0.1 ) Bm.KD = 4 % Affinity is 2 uM % Fura-2 indicator dye properties: % buffer F2 % Uncomment this line to include Fura-2 F2.D = 0.118 % Diffusion coefficient is 0.118 um^2/ms F2.total = 400 % Total concentration is 400 uM F2.kplus = 0.27 % Binding rate 0.1 / (uM ms) F2.kminus = 0.0967 % Unbinding rate 0.0967 / ms %================================================================================== % 4. AUXILIARY VARIABLE AND CONSTANT DEFINITIONS %================================================================================== % Here we define variables tracking Ca2+ concentration at the secretory and STF % sites. In the original code, the secretory site was placed in the elementary cell % {5,5,2}, which translates into coordinate {x = y = 90 nm, z = 30 nm}: CaX := Ca[b,b,0.03] % [Ca2+] at secretory sensor, 20 nm below corner channel % (recall that the channels are located 10 nm above the % surface - see above) % The facilitation site was placed in the first z-layer after the "doubled" compartment layer (see above), % at cell {3,3,4}, corresponding to coordinate {x = y = 100 nm, z = 80 nm}: CaY := Ca[0.1,0.1,0.08] % [Ca2+] at facilitation sensor, ca. 70 nm below channel % In the original code, Ca2+ currents are multiplied by a factor of 0.8 (cf p. 2741): I.AP = 0.8 * 1.35 % Ca2+ current during an AP = 1.35e-21 mol/ms = 1.35e-9 fmol/us I.tail = 0.8 * 4.60 % Ca2+ tail current = 4.6e-21 mol/ms = 4.6e-9 fmol/us %================================================================================== % T H E E N D %==================================================================================