grow | Cellzilla2D Home |
Description
Needs["Cellzilla2D`"];
Return Value
Options
Simulation Control
"walls"→False | Set to True to include separate compartments for cell walls in growth simulations. |
"Upwards"→False | If set to True the dynamics are modified so that y' is always non-negative. |
"MaxRadius"→Infinity | In a typical simulation the modeller may want to allow cells to "drop over the side" of the simulation when they get further away from some central area. This parameter sets the distance, measured from the "Origin" beyond which cells are removed from the simulation to save computation time and memory. |
"Origin"→{0,0} | Referred to by other parameters. |
Reactions
"Reactions"→{} |
List of Cellerator reactions to be indexed and repeated in each
cell, for example, "Reactions"->{{A->B,k1},{B->A,k2}} expands to {{A[1][t]->B[1][t],k1},{A[2]->B[2][t],k1} ..., {B[1][t]->A[1][t],k2},{B[2][t]->A[2][t],k2},k2},...} The indices and the time-dependence should NOT be specified in the list of reactions. However, if any rate constants depend on variables, the time dependence (in the rate constants only) MUST be specified, e.g., "Reactions"->{...,{A->B,k*Q[t]]},...} expands to include {A[i][t]->B[i][t],k*Q[i][t]} for each cell. |
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"WallReactions"→{} | List of Cellerator reactions to include in wall compartments. | |||||||||
"Diffusion"→{} | List of diffusing species and permeabilities. For
unwalled tissues the format is "Diffusion"->{{X,β1}, {X,β1}, ...} where each β is either a permeability constant or a pure function of three variables (cell number, cell number, edge number.) For Walled tissue, permeabilities into and out of the cell wall, as well as between wall components, are allowed to be different, and may be specified as "Diffusion"->{{X,βout, βin, βwall}, ...} |
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"Intercellular"→{} | List of Cellerator GRN reactions that specify the affect of constituent X[i] (e.g., in cell i) directly on constituent Y[j] (in cell j) without any particular mechanism specified. The cells must be neighbors. Only implemented in unwalled tissue. | |||||||||
"Pumps"→{} |
List of transport reactions (across cell boundary). Format is
"Pumps"->{{V1, f1out, f1in},{V2, f2out,f2in},...} where each f is a function of three variables (cell number, cell number, wall number); the fout is the rate of transport out of the cell (with the first index) and the fin is the rate of transport into the cell. The rates of transport are as follows:
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"BoundaryConditions"→{} | Value of constituents in compartment zero (a single compartment, cell 0, encloses the entire outer boundary), e.g., "BoundaryConditions"->{A->0,B->1}. Used, e.g., for for diffusion. | |||||||||
"IC"→{} | List of intial values for simulation in the form of Matheamtica rules, "IC"->{A[1]->val, A[2]->val,...} |
Cell Division
"DivisionMode" | "Errera" or "Potential" |
"DivisionThreshold" | Mean value of division thresholds. |
"DivisionVariable"→area | Cell division is triggered when the division variable reaches a threshold. Typically, the division variable is area. At cell birth, each cell is assigned a threshold which is distributed normally with mean DivisionThreshold and standard deviation "DivisionSigma" |
"DivisionSigma" | Standard deviation of division thresholds. |
"L1Anticlinal"→True | Force anticlinal division in L1. Ignored unless "upwards"→True |
"L2Anticlinal"→False | Force anticlinal division in L2. Ignored unless "upwards"→True |
"MinAngleSpread"→135 | In the potential model, the end points of the new cell wall are required to be separated by a central angle δθ as measured from the cell center. |
"Weights" | Ignored unless "DivisionModel"→"Potential" |
"IgnoreDivisionRadius" -> Infinity | In a typical simulation the modeller may want to allow cells to "drop over the side" of the simulation when they get further away from some central area. This parameter sets the distance, measured from the "Origin" beyond which cell division is no longer performed, in order to save computational time and memory. |
"MaxDivisions" -> Infinity | Alternate stopping criterion - the simulation will terminate when the requested number of divisions have been reached, even if the stopping time has not yet been reached. |
Growth Model
"Growing"→False; | Flag to turn growth model on/off. |
"mu"→μ | Variable name for a non-indexed spring constant. If this version is used the value of the parameter μ should be set in "parameters"→{μ→value, ...} |
"mu"->{μ, f[i,j,k]} | Definition of indexed growth rate. First argument is variable
name; second argument is a pure function of three arguments. The
first two arguments are the two adjacent cell numbers, and the
third argument is the edge number. The value of μ should NOT be set in parameters. Example: "mu"->{μ,(A[#1][t]+B[#2][t])&} |
"mumax"→1, "mumin"→0, "muMaxDegrees"→0 |
Parameter values for anisotropic growth rate model. Values are
ignored unless "IsotropicGrowth"->False. Formula is: ((μmax-μmin)Cos(θ-θmax)+μmin) where θmax is the value of muMaxdegrees, and the total is modulated (multiplied) by the formula for the indexed variable if mu is indexed. |
"IsotropicGrowth" → True | By default all springs grow at a fixed rate proportional to their extension beyond the resting length. The constant of proportionality is the value of the parameter "mu". This constant can also be indexed, and/or it can be allowed to be angle dependent (but only of IsotropicGrowth→True). If μ is also an indexed variable, the indexed formula will be modulated by the angle-dependent formula determined by mumax,mumin,muMaxDegrees. |
"muOuter"->False | Special value of growth rate to use on outer boundary, unless set equal to False. |
"muL1"->False | Special value of growth rate to use on anticlinal walls of L1 Cells, unless set equal to False. |
"muL1L2"->False | Special value of growth rate to use on walls between L1 and L2 Cells, unless set equal to False. |
"P"-> P | Variable name for constant (fixed) pressure in all cells. A value must be set in parameters. |
"P"->{P, f[i]} | Pressure specification for indexed pressure. The first argument is the variable name, and the second argument is a pure function of one integer argument which is the cell index. If this option is used the value of pressure should not be set in parameters. |
Spring Model
"Restlength"→resting | Variable name to be used for dynamic resting length of springs. Each resting[i][t] is calcuated dynamically by the spring model. |
"EdgeVariable"→ell | Variable name to be used for dynamic length of cell wall. Each ell[i][t] is calcuated dynamically by the growth model and is the actual distance between the two vertices at a given time. |
"k"→k | Variable name for a non-indexed spring constant. If this version is used the value of the spring constant should be set in "parameters"→{k→value, ...} |
"k"->{k, f[i,j,k]} | Definition of indexed spring constant function. First argument
is variable name; second argument is a pure function of three
arguments. The first two arguments are the two adjacent cell
numbers, and the third argument is the edge number. The value of
k should NOT be set in parameters. Example: "k"->{k,(A[#1][t]+B[#2][t])&} |
"kmax"→1, "kmin"→0, "kMaxDegrees"→0 |
Parameter values for anisotropic spring constant model. Values
are ignored unless "IsotropicSprings"->False. Formula is: ((kmax-kmin)Cos(θ-θmax)+kmin) where θmax is the value of kMaxdegrees, and the total is modulated (multiplied) by the function for the indexed variable (if k is indexed). |
"IsotropicSprings" → True | By default all springs have a fixed (constant) spring constant; this can be modified either by setting the spring constant to be an indexed variable; or by using an angle-dependent variable. The angle dependent variable requires "IsotropicSprings"→False (The default is True) and then utilizes the values of the parameters kmax, kmin, kMaxDegrees. If k is also an indexed variable, the indexed formula will be modulated by the angle-dependent formula. |
System Variables
"CellVariable" | Name of variable used to area of cell i. It will always be indexed and time dependent. |
"EdgeVariable" | Name of variable used to describe length of edge i. It will always be indexed and time dependent. |
"k" | Spring constant variable. See description under spring model. |
"mu" | Growth rate variable. See description under growth model. |
"P" | Pressure variable. See description under growth model. |
"RestLength" | Spring resting length variable. See description under spring model. |
"x","y" | Coordinate variables. The coordinates of vertex i are {x[i][t],y[i][t]]} |
"center"->center | center[j,1] and center[j,2] gives the x and y coordinates of the center of cell j. |
"perimeter"->perimeter | perim[j] gives the perimeter of cell j. |
"tip"->tip | tip[1],tip[2] give the x and y coordinates of the "tip", the vertex with the maximal y value. Intended for meristem-shaped simulations. |
"tipdistance"->tipdistance | tipdistance[j,1],tipdistance[j,2] give the distance from the tip to the center of cell j. |
Output Control
Example
Implementation Notes
See Also