; Rafael Bravo, VirtualCryptModel020413G
; Nov. 26 2012, Jan. 8, 2013,
; Jan. 31, 2013 (Comment out duration = 8x interval)
;
; This program is free software: you can redistribute it and/or modify
; it under the terms of the GNU General Public License as published by
; the Free Software Foundation, version 3 of the License.
;
; This program is distributed in the hope that it will be useful,
; but WITHOUT ANY WARRANTY; without even the implied warranty of
; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
; GNU General Public License for more details.
;
; You can receive a copy of the GNU General Public License
; at .
globals[ ;variables that are accessed by mutliple methods (globally) are named here
keepgoing ;set as false when either the crypt is reduced to a single layer of cells or the crypt grows over the top of the world.
colorprogeny ;toggles whether color displays probdivide or cell ancestry.
MonoclonalTime; used to display how many ticks it takes for monoclonal conversion to occur
ExtinctionTime; displays the tick at which the crypt collapses
UnboundedSizeTime; displays the tick at which the crypt produces polyps (overflow)
CellsInLumen; displays the number of cells specifically in the lumen, above the crypt.
FissionTime; time it takes the crypt to split into multiple crypts after random cell div. is turned on
;Protrusion; distance from the lumenal surface that cells protrude (usually zero)
highest; depth of the crypt
chemoct ; used to keep track of the chemotherapy interval.
colored ; binary, keeps track of whether progeny are colored or not.s
top; size of world, altered by setup
CellsPerRow ; number of cells per row in crypt, altered by setup
CutOffAboveQuiescentRegion ; the cutoff between what is called a quiescent and a differentiated cell, since they are both defined as having a probability of dividing lower than DiffCellProbabilityThreshold
; is done spacially, by drawing a line "CutOffAboveQuiescentRegion" cell rows above the quiescent gradient, and all cells above this line are counted as differentiated, while cells below are counted as quiescent
; this indicator may miscount cells if the proliferating region is too small, and may need to be modified for the counts and plots below to print the desired cell groups.
CountSCq ; globals display respective cell types, useful for easier reporting in behavior space.
CountProlif
CountDiff
CountMutant
MONOCLONALCOMPLETE; temporary variable
] ;called by the cells every cycle, generates a random float from 0 to 1 similar to a "dice roll" to determine whether cells in the crypt divide and/or die.
breed [cells cell]
cells-own [; variables that the cells themselves posess are named here
probdivide ;float from 0 to 1, a cell will divide if rand is less than this value. imposed by applygradientchancedivide and can be influenced if cell is mutated.
probdividegoal
probdie ;float from 0 to 1, a cell will die if rand is less than this value. imposed by applygradientchancedie and can be influenced if cell is mutated.
probdiegoal
changespeeddiv; these are used for delayed feedback, stores the feedback of the current gradient
changespeeddie
mutant ;Boolean value, if true cell is considdered mutant and colored blue, MutantDivideDiff, MutantDieDiff, and IgnoreQuiesce only apply to mutated cells.
]
to setup ; properly sizes the world, and populates it with the specified number of cells OBS ONLY
let qdtemp QuiesceDepth; temporary variables store QuiesceDepth and RowsAtStart, which are sliders that have top as their maximum, so that the settings of these variables are not lost when top is set to 0 by clearall
let rastemp RowsAtStart
let ddetemp DieDepthEnd
clear-all
set CutOffAboveQuiescentRegion 5
set top SetTop
set RowsAtStart rastemp
set QuiesceDepth qdtemp
set DieDepthEnd ddetemp
set-default-shape cells "circle"
set CellsPerRow SetCellsPerRow
resize-world -4 cellsPerRow + 3 0 top + 2 ; world is sized so that it fits around the crypt with four spaces of buffer to the left and right. two spaces of buffer are added to the top of the crypt.
; y coordinates move up from 0 at bottom of the world to top+2 at the top.
set-patch-size 400 / top ; resizes world so that it will fit in the window space alotted, (Does not work in all cases, if crypt is too wide, world will overlap buttons)
let x 0
let y top
while [y > top - RowsAtStart][
set x 0
while [x < cellsPerRow][;this section of code populates the crypt, placing a cell at every location in the crypt from the bottom to RowsAtStart, going row by row.
makecell(.5)(.5)(x)(y) ;makecell creates cells at target location with starting values set.
set x x + 1]
set y y - 1]
set keepgoing true
set chemoct -1
set colored false
;globals are set to their starting values.
ask cells [
set probdivide probdividegoal
set probdie probdiegoal]
; temporary: for behaviorspace!!!!
;set interval duration * 8
set MONOCLONALCOMPLETE false
end
to go ; iterates the simulation OBS ONLY
; these variables are set to help with counting cells
set CountSCq count cells with [ycor < top - quiescedepth + CutOffAboveQuiescentRegion and probdivide < DiffCellProbabilityThreshold and Mutant = false]; variables defined for use with behavior space
set CountProlif count cells with [probdivide >= DiffCellProbabilityThreshold and Mutant = false]
set CountDiff count cells with [probdivide < DiffCellProbabilityThreshold and ycor >= top - quiescedepth + CutOffAboveQuiescentRegion and Mutant = false]
set CountMutant count cells with [Mutant = true]
; two reasons why the simulation would need to stop, either the crypt overflows or the crypt dies, the rest of the simulation assumes neither of these occured.
if count cells = 0 and keepgoing = true[set keepgoing false set ExtinctionTime ticks print (word "the crypt died at tick " ExtinctionTime)]; if there is less than one full row of cells, cell death and division stops, and the crypt is considdered dead.
if count cells with [ycor = top + 2]> 0 and keepgoing = true [ set keepgoing false set UnboundedSizeTime ticks print (word "the crypt overflowed at tick" UnboundedSizeTime) ]
if keepgoing = true[; keepgoing is set to false if the crypt dies or overflows, prevents simulation from continuing at that point.
; sets up protrusion (how far crypt should stick out into the lumen) and highest (approx number of rows of cells)
set highest round(count cells / cellsperrow); determines the approximate top of the crypt, estimated by the average height of the cell columns.
;ifelse highest > maxcryptdepth [set protrusion highest - maxcryptdepth][set protrusion 0]; if the average height of the cell columns is above the maximum crypt depth, the crypt height is set at maxcryptdepth
ask patches[set pcolor black]; sets all patches as black so the crypt can be redrawn.
if showgradients = false [ask patches[
if pycor <= top [
set pcolor 132]; patches that are considered in the crypt are colored light brown
]]; patches that are considdered outside the crypt are left black
; Sets up and applies gradient functions
; exponential gradient functions take arguments start height, end height, start value, end value
; and power. this scales the function y = x^(power) from zero to 1 so that the
; range is applied from start height to end height and so that the y value is proprtionally
; gradient values scaled to range between startvalue and endvalue.
applygradientprobdivide(top)(top - highest)(cptdivmin)(cptdivmax)(cptdivpwr)(DivideFbk) ;feedbackdiv set to quiescefeed so that both could be modified in parallel in behavior space.
applygradientprobdie(top - DieDepthEnd)(top)(cptdiemin)(cptdiemax)(cptdiepwr)(DieFbk) ;applies gradient that sets probdie of cells at every iteration
;applygradientprobdivide(top - protrusion + 1 )(top - protrusion + LumDivSiz + 1)(lumdivmin)(lumdivmax)(lumdivpwr)(feedbackdiv) ; 2d pair of gradients apply to the lumen
;applygradientprobdie(top - protrusion + 1 )(top - protrusion + LumDieSiz + 1)(lumdiemin)(lumdiemax)(lumdiepwr)(feedbackdie)
applygradientprobdivide(0)(top - quiescedepth)(0)(0)(0)(QuiescentFbk) ;quiescent gradient applies to cell division.
ask cells[set probdivide probdivide + (probdividegoal - probdivide) * changespeeddiv
set probdie probdie + (probdiegoal - probdie) * changespeeddie ; gradients are applied to cells, cells are only affected by the last probdivide and probdie gradients, in order as in the code
; all cells are given a chance to divide and die at every iteration.
; cell division and death occurs here
let rand random-float 1 ; generates a random floating point number from 0 to 1 for every comparison called rand
if rand < probdivide [
hatch-cells 1
makespace(self) ; if rand is less than the probdivide, the cell reproduces
]]
ask cells [; after cell proliferation is taken care of, all cells have a probability of dying.
let rand random-float 1
if rand < probdie [ ; if rand is less than probdie, the cell dies
die
]]
; sets up and applies chemotherapy
if activechemo = true and chemoct = -1 [
set chemoct 0] ; initiates chemotherapy
if activechemo = false and chemoct > -1 [set chemoct -1] ; stops chemotherapy if activechemo is set to false
if chemoct >= 0 [
if chemoct < duration[
ask cells[
let rand random-float 1
if rand / lethality < probdivide[
die]
]
]
ifelse chemoct = interval[set chemoct 0]
[set chemoct chemoct + 1]
]
shiftdown; keeps cell columns without gaps by forcing cells to move up if there is a space above them.
; sets up cell coloring under normal conditions, if viewprogeny is true cells are not colored.
if viewprogeny = false ; colors cells the standard colors, differentiated and quiescent cells are colored based on the height at which they first transitioned from actively dividing to differentiated
; actively dividing cells are colored based on their probablility of dividing.
[set colored false
set MonoclonalTime 0
ask cells [if probdivide <= DiffCellProbabilityThreshold [set color probdie / CptDieMax * 5 + 94]
if probdivide > DiffCellProbabilityThreshold [set color probdivide / CptDivMax * 9 + 11]
]]
ask cells with [mutant = true][set color 45] ; changes color of mutant cells to yellow so that they are easily visible. yellow color is retained even if colorprogeny is true
; sets up FissionTime reporter
ifelse PolarDivision[
set FissionTime 0][
let emptycolumn false
let x 0
repeat CellsPerRow [
if count cells with [xcor = x] = 0[
set emptycolumn true]
set x x + 1] ; iterates through all cell columns, seeing if any of them are empty
if emptycolumn = false [
set FissionTime FissionTime + 1]; if no empty column exists, fission time will continue to be incremented
]
; if viewprogeny is set to true, this section will handle cell coloring, as well as check whether monoclonal conversion has yet occured.
if viewprogeny = true and colored = false[
ask cells [
set color random-float 140 ; when this function is called and colorprogeny is set to true, all cells are given a random color
]
set colored true]
if viewprogeny = true and colored = true[
let increment false
let checkcolor 0
ask one-of cells[
set checkcolor color]
ask cells [
if checkcolor != color[set increment true]]
ifelse increment = true[set MonoclonalTime MonoclonalTime + 1][
set MONOCLONALCOMPLETE true]]; if all cells have the same color, then monoclonal conversion has occured.
; misc.
;ifelse count cells - cellsperrow * Maxcryptdepth > 0 [
; set CellsInLumen cellsperrow * protrusion]
; [set CellsInLumen 0]; reports the number of cells that are protruding into the lumen
do-plot ; plots cell populations at the end of each iteration.
if AdjustTime > ticks and cryptsizeadjust = true [
adjustcptdiemax] ; applies cryptsizeadjust if it is being used.
]
tick; view is updated at every tick
end
to makecell[setprobdivide setprobdie x y];places a cell with specified parameters at the specified x y coordinates, called by setup, OBS ONLY
create-cells 1 [
setxy x y
set probdivide setprobdivide; setprobdivide and setprobdie are specified at the method call.
set probdie setprobdie ; if cell falls within gradient limits, these values will be overwritten by gradient
set mutant false
set color 9.9
]
end
to mutaterows;turns proportion cells between rows startH and endH mutant, startH and endH counting from bottom of crypt
if startD > endD [let temp startD
set startD endD
set endD temp]
ask cells with [top - ycor >= startD and top - ycor <= endD][
let rand random-float 1
if rand < proportion[
set mutant true]]
end
to makespace[celltomove]; forces cells out of the way to make room for a newly generated cell
let currx [xcor] of celltomove
let curry [ycor] of celltomove
let nextx 0
ifelse polardivision [
set nextx random 2 + 1 + currx]
[set nextx random 3 - 1 + currx]; depending on whether or not divdirrand is on, cells will either move preferentially to the right, or move down with no right-left preference.
let nexty curry - 1
if nextx < 0 [
set nextx CellsperRow + nextx]
if nextx >= CellsperRow [
set nextx nextx - CellsperRow]
let nextcell one-of cells with [xcor = nextx and ycor = nexty]
ask celltomove[
setxy nextx nexty
while [count turtles-at 0 1 = 0 and ycor != top][setxy xcor ycor + 1]]
if nextcell != nobody [
makespace(nextcell)]
end
to shiftdown ;forces all cells up in columns so there are no gaps in the crypt.
let y top - 1
while [y >= 0][; goes from the top of the world to the bottom.
ask cells with [ycor = y and count cells-at 0 1 = 0][; gets all cells with an empty space above them in a particular row,
let movedown 0
while[count cells-at 0 (movedown + 1) = 0 and y + movedown <= top - 1][
set movedown movedown + 1] ; finds the highest space above the cell that does not contain a cell.
setxy xcor ycor + movedown ] ; moves the cell to this location
set y y - 1]
end
to do-plot ; parameters used in conjunction with plots, called by Go function at the end of each iteration, does not affect simulation itself.
set-current-plot "Total Cells"
set-current-plot-pen "cellspen"
plot count cells ; total cells plot displays total number of cells.
set-current-plot "Quiescent Stem Cells"
set-current-plot-pen "CountQuiescentpen"
plot count cells with [ycor < top - quiescedepth + CutOffAboveQuiescentRegion and probdivide < DiffCellProbabilityThreshold] ; Quiescent Stem Cell plot diplays number of quiescent cells. (blue cells)
set-current-plot "Proliferating Cells"
set-current-plot-pen "CountProliferatingPen"
plot count cells with [probdivide >= DiffCellProbabilityThreshold];Displays number of cells that are not quiecent and have probdivide grater than DiffCellProbabilityThreshold. (red cells)
set-current-plot "Differentiated Cells"
set-current-plot-pen "CountDifPen"
plot count cells with [probdivide < DiffCellProbabilityThreshold and ycor >= top - quiescedepth + CutOffAboveQuiescentRegion] ; Displays number of cells that have probdivide less than DiffCellProbabilityThreshold. (blue cells)
set-current-plot "Proportion Mutant Cells"
set-current-plot-pen "PropMuts"
if count cells > 0 [plot count cells with [mutant = true]/ count cells] ; Proportion Mutant cells diplays number of mutant cells divided by total number of cells.
end
; The following code creates a gradient effect over the area, startval and endval must be between 0 and 1, startpoint and endpoint must be between the
; beginning and end of the model. note, the variable that the gradient affects cannot be stated as a parameter for the function, so the
; function had to be duplicated to affect probdivide and probdie.
to applygradientprobdivide [starty endy startval endval power feedback] ; gradient that applies to probdivide of all cells between startval and endval.
if starty != endy [
if power < 0[ ; the function used here is x^n, where x is from 0 to 1. the value of x ranges between 0 and 1 regardless of the value of n,
let temp endy
set endy starty
set starty temp
set temp endval
set endval startval
set startval temp] ; this bit of code reverses variables so that negative powers cause the graph's inflection to bow outward from 0 to 1.
let range starty - endy ; graph originally goes from 0 to 1, but is scaled by range and set to go from starty to endy.
let shift startval - endval ; similarly, in x^n from 0 to 1, the value of x goes from 0 to 1, but is scaled by shift and set to go from startval to endval
let y starty
let counter 0
while[counter <= abs(range)][
ask cells with[ycor = y][; all cells in row y are altered by the following function
ifelse shift > 0
[set probdividegoal (- abs((ycor - starty) / range)^ abs(power)) * abs(shift) + startval
if mutant = true[set probdividegoal probdividegoal + mutantdividediff]] ; to apply negative gradient, scaled graph x^n is inverted
[set probdividegoal abs((ycor - starty) / range)^ abs(power) * abs(shift) + startval; positive scaled graph x^n is applied here
if mutant = true[set probdividegoal probdividegoal + mutantdividediff]] ; to apply negative gradient, scaled graph x^n is inverted
set changespeeddiv feedback ; modifies cell feedback value
]
if showgradients = true [ask patches with [pycor = y and pxcor < cellsperrow / 2][; this function modifies the patch color along the gradients.
ifelse shift > 0
[set pcolor 61 + 7 * (- abs((pycor - starty) / range)^ abs(power)) * abs(shift) + startval] ; to apply negative gradient, scaled graph x^n is inverted
[set pcolor 61 + 7 * abs((pycor - starty) / range)^ abs(power) * abs(shift) + startval]]] ;pcolor is affected rather than probdivide and probdie.
ifelse range < 0[set y y + 1][set y y - 1]
set counter counter + 1
]]
end
to applygradientprobdie [starty endy startval endval power feedback] ; a duplicate of applygradientprobdivide, only it affects probdie.
if starty != endy [
if power < 0[
let temp endy
set endy starty
set starty temp
set temp endval
set endval startval
set startval temp]
let range starty - endy
let shift startval - endval
let y starty
let counter 0
while[counter <= abs(range)][
ask cells with[ycor = y][
ifelse shift > 0
[set probdiegoal (- abs((ycor - starty) / range)^ abs(power)) * abs(shift) + startval
if mutant = true[set probdiegoal probdiegoal + mutantdiediff]]
[set probdiegoal abs((ycor - starty) / range)^ abs(power) * abs(shift) + startval
if mutant = true[set probdiegoal probdiegoal + mutantdiediff]]
set changespeeddie feedback ; modifies cell feedback value
]
if showgradients = true [ask patches with [pycor = y and pxcor >= cellsperrow / 2][
ifelse shift > 0
[set pcolor 12 + 7 * (- abs((pycor - starty) / range)^ abs(power)) * abs(shift) + startval] ; to apply negative gradient, scaled graph x^n is inverted
[set pcolor 12 + 7 * abs((pycor - starty) / range)^ abs(power) * abs(shift) + startval]]]
ifelse range < 0[set y y + 1][set y y - 1]
set counter counter + 1
]]
end
to defaults ; sets defaults for all variables modifyable in main interface, see information for justifications for values.
set Settop 100
set RowsAtStart 61; gets crypt into a steady state position as quickly as possible.
set setcellsperrow 38; simulates approximate number of cells to produce proper crypt diameter if wrapped into a cylinder
set quiescedepth 60; produces the proper number of cell rows
set CptDivMin 0; cells will not divide towards the top of the crypt
set CptDivMax .5; gives cells a high probability of dividing near the bottom of the crypt, so that feedback has greater effect
set CptDivPwr 11.5; keeps cell division happening only near the bottom of the crypt.
set CptDieMin 0; cells near the bottom of the crypt have almost zero probability of dividing, with cell removal only happening near the top
set CptDieMax .2; this kills off cells at the proper rate to keep a steady crypt with the right proportions of cells.
set CptDiePwr 14; keeps cell death only happening towards the extremem top of the crypt.
set DieDepthEnd 100; die gradient speads over the entire area of the crypt.
set DiffCellProbabilityThreshold .02; this value only changes the classification of cells in the crypt, and was adjusted to get proper cell proportions.
set mutantdividediff .16; makes mutant cells divide more quickly, one of the hallmarks of mutation leading to cancer.
set mutantdiediff .1; makes mutant cells more likely to die, also typically occurs with early mutant cells (less stability than normal cells.)
set MutateDepth 59
set showgradients false; increases running speed.
set Lethality 2; adjusted to this value to be more effective at killing off cells, since the crypt is more robust.
set activechemo false
set interval 24
set duration 3
set startD 55; ensures mutant cells begin in the quiescent region
set PolarDivision true
set endD 60
set proportion .2
set cryptsizeadjust false; activate if modifying other variables to keep crypt at proper size
set AdjustTime 1000
set CellTarget 2428; approx. number of cells in actual crypt, as observed experimentally.
set AdjustStr .1
set DivideFbk .5; values set to produce cell proportions most similar to those observed.
set DieFbk .5
set QuiescentFbk .1
end
to mutateonecell ; randomly sets a cell in the given row to mutate.
ifelse count cells with [ycor = top - mutatedepth and mutant = false] > 0[
ask one-of cells with [ycor = top - mutatedepth and mutant = false] [set mutant true]][
print "no elligible cells in the chosen row"]
end
to adjustCptDieMax; method is called by CryptSizeAdjust to attempt to set the size of the crypt to the requested value
set CptDieMax CptDieMax + (count turtles - Celltarget)/ Celltarget * (AdjustTime - ticks) / (AdjustTime) * AdjustStr
if CptDieMax < 0 [set CptDieMax 0]
if CptDieMax > 1 [set CptDieMax 1]
end
to togglecolor ; gives all cells a distinct color that is inherited by progeny so monoclonal conversion can be observed
ifelse colorprogeny = false[
set colorprogeny true
][set colorprogeny false] ; if colorprogeny was true, colorprogeny is set to false, and cells will be colored based on probDivide.
end
@#$#@#$#@
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MUTATES CELL BY ADDING THESE VALUES TO NORMAL CELL PROBABILITES
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1
-1000
INPUTBOX
981
485
1055
545
DivideFbk
0.5
1
0
Number
INPUTBOX
1055
485
1130
545
DieFbk
0.5
1
0
Number
INPUTBOX
722
484
796
544
AdjustTime
1000
1
0
Number
INPUTBOX
798
484
867
544
CellTarget
2428
1
0
Number
INPUTBOX
871
484
940
544
AdjustStr
0.1
1
0
Number
SWITCH
749
448
905
481
CryptSizeAdjust
CryptSizeAdjust
1
1
-1000
INPUTBOX
1130
485
1211
545
QuiescentFbk
0.1
1
0
Number
SWITCH
755
390
893
423
PolarDivision
PolarDivision
0
1
-1000
MONITOR
524
453
647
498
NIL
FissionTime
17
1
11
TEXTBOX
997
464
1295
506
GRADIENT FEEDBACK STRENGTHS\n
11
0.0
1
TEXTBOX
1036
10
1186
28
CRYPT PRESENTATION
11
0.0
1
TEXTBOX
728
360
949
402
TOGGLES BETWEEN POLAR AND RANDOM CELL DIVISION ORIENTATION
11
0.0
1
TEXTBOX
743
433
949
461
RESIZES CRYPT USING CptDieMax
11
0.0
1
SLIDER
1012
409
1184
442
DieDepthEnd
DieDepthEnd
0
top
100
1
1
NIL
HORIZONTAL
TEXTBOX
423
33
648
61
PLOTS OF CELLS AS FUNCTION OF TIME
11
0.0
1
TEXTBOX
484
434
634
452
TIMES TO EVENTS
11
0.0
1
TEXTBOX
198
34
348
52
VIRTUAL CRYPT
11
0.0
1
TEXTBOX
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24
188
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TO INITIATE\n SIMULATION
11
0.0
1
@#$#@#$#@
AGENT-BASED COMPUTATIONAL MODEL OF THE COLON CRYPT: DEVELOPMENT OF A VIRTUAL CRYPT FOR IN-SILICO EXPERIMENTS
-----------
January 8, 2013
Coded by Rafael Bravo
Written by Rafael Bravo and David Axelrod
Department of Genetics, Rutgers University, Piscataway, NJ 08854-8082
INTRODUCTION:
------------
Colon crypts are invaginations in the large intestine. They are shaped like a test tube with cells arranged along the sides of the test tube. The function of the colon crypts is to produce mucus to lubricate the feces above the crypt in the lumen of the colon, and remove water from the feces. Several different kinds of cells can be recognized, quiescent stem cells at the bottom, proliferating cells (including active stem cells and transient amplifying cells) near the bottom third, and differentiated non-proliferating cells near the top two-thirds of the crypt. Cells produced near the bottom of the crypt move up and are removed at the top of the crypt.
This is an agent-based model in which the crypt has emergent properties resulting from the behavior of a population of individual cells. Cell types are not fixed, rather at each iteration a given cell has a probability of dividing or dying, or dividing and then dying. A cell's probability is determined by its position in a divide gradient and a die gradient. The divide gradient value is greatest at the bottom of the crypt, and the die gradient value is greatest at the top. A cell that divides produces a progeny cell in the same position as the progenitor and a progeny cell that is placed to the right and below the progenitor cell. A cell that dies allows cells below it to move up. These two process result in a flow of cells from the bottom to the top of the crypt, a stochastic variation in the total number of cells per crypt, and in the number of each type of cell.
The goals of this model are (1) to simulate numbers of cell types meaured in biopsies of human crypts, and (2) to facilitate in silico experiments. These experiments provide information about the effect of mutations that affect probability of cell proliferation, cell death, orientation of cell division, and response to cytotoxic therapy, among others. Parameter values of normal and mutant cells, and their microenvironment gradients, can be input at the Interface without changing the code. Outputs of stochastic cell dynamics are shown as plots and as digital values in the Interface, and can be exported in spreadsheet format for further analysis.
PROGRAM OVERVIEW:
-------------------
Three views are available. The ÒInterfaceÓ view has a visual representation of the simulated crypt, buttons and sliders for input, and simulation outputs as plots of cell numbers as a function of time. TheÒInformationÓ view has the description of the program. The ÒProceduresÓ view has the commented code.
The Interface view includes a picture of a crypt with three types of cells: quiescent stem cells at the bottom of the crypt in blue, proliferating cells (active stem cells and transient amplifying cells) in the bottom third of the crypt in red, and differentiated cells at the top two thirds of the crypt in blue; mutant cells, if they exist, are yellow. The lamina propria surrounding the crypt cells is brown. The lumen above the crypt is black.
The initial properties of each cell type and cell environment (gradients of extracellular ligands) are specified with buttons and sliders. Outputs of simulations include a picture of different cell types by color and location, and plots as a function of time of the three cell types.
If a cell divides one of the progeny cells move to the lower right, displacing cells previously in that position. When cells reach the right edge of the crypt then they wrap around to the left. If a cell dies, cells below it move up. If a cell reaches the top of the crypt it is removed.
INITIATION
----------------
ÒSetupÓ: initializes the world, the height of the world is determined by "Top", the width by "CellsPerRow", and the size of the initial crypt by "DepthCellsAtStart", these can only be modified before setup.
ÒGoÓ: button that initiates the simulation. When clicked, all of the functions are implemented for repeated runs. A series of runs can be stopped by pressing the ÒGoÓ button again, which pauses the simulation at the conclusion of the most recent run.
ÒDefaultsÓ: sets input parameters to their default values as specified in the code. default values and justifications for these values can be found in the Procedures
APPLIED BY SETUP
ÒSetTopÓ: height of the world in which the crypt exists.
ÒSetCellsPerRowÓ : number of cells across crypt. Width of world is number of cells per row plus 2 on each side.
ÒRowsAtStartÓ : at beginning of simulation, sets number of cells in each column.
INPUTS:
--------------
MUTATES CELL BY ADDING THESE VALUES TO NORMAL CELL PROBABILITIES
ÒMutantDivideDiffÓ: the probability of a mutant cell dividing at a given location in the crypt is changed by adding the value of "MutantDivideDiff" to the value of the cell's own pobdivide determined by its position in the divide gradient. This causes a mutant cell to divide with a different probability than normal cells in the same position.
ÒMutantDieDiffÓ: the probability of a mutant cell dying at a given location in the crypt is changed by adding the value of "MutantDieDiff" to the value of the cell's own pobdie determined by its position in the die gradient. This causes a mutant cell to die with a different probability than normal cells in the same position.
MUTATES ONE OR MORE CELLS
ÒMutateOneCellÓ: button turns one cell from the crypt into a mutant. It appears as a yellow cell, and all of its progeny inherit the mutant trait. Mutant cells are altered by "MutantDivideDiff" and "MutantDieDiff", but are otherwise identical to normal cells.
ÒMutateDepthÓ: the number of rows from the top that a single cell will be produced.
"MutateRows": button mutates a "Proportion" of cells in rows between "StartD" and "EndD", where D (Depth) is the number of cell rows from the top of the crypt.
"StartD": start of mutation region for "MutateRows", see above.
"EndD": end of mutation region for "MutateRows", see above.
"Proportion": the proportion of cells between "StartD" and "EndD" that will be mutated when the "MutateRows" button is pressed.
APPLIES CHEMOTHERAPY
"ActiveChemo": toggle "On" begins a dose of cytotoxic therapy.
"Interval": the number of ticks from the beginning of one dose to the beginning of the next dose. The time between doses is "Interval" minus "Duration"
"Duration": the number of ticks during which a dose of chemotherapy is applied.
"Lethality": this constant is multiplied by each cell's own probddivide. The product is the probability that the cell will be killed in a given tick of therapy, and removed.
Example (dose = D, no dose = n):
Duration 1, Interval 3: DnnDnnDnnDnnDnnDnnDnnD
Duration 3, Interval 9: DDDnnnnnnDDDnnnnnnDDD
TOGGLES BETWEEN POLAR AND RANDOM CELL DIVISION ORIENTATION
"PolarDivision": when toggle is "On", after division one of the progeny cells moves to the right, either 1 or 2 cell positions, and down 1 cell position. This displaces the cell at that location, forcing it to in turn move with the same displacement as the progeny cell. This process continues until there is an empty space for the last displaced cell to occupy. When toggle is "Off", the progeny cell and the cells it displaces move down either diagonally to the left or right 1 cell position, or directly down one cell position.
RESIZES CRYPT USING CPTDIEMAX
"CryptSizeAdjust": toggle "On" allows the user to request a steady state size for the crypt, and the program will attempt to meet this size by correcting for the crypt being too large or too small. The program accomplishes this by modifying the "CptDieMax" variable to kill off more or fewer cells per tick, eventually resulting in a properly sized crypt. Toggle "Off" disables this feature.
"AdjustTime": the duration during which the crypt size will be adjusted, counting ticks from setup. The longer this period, the more time "CryptSizeAdjust" will have to reach the requested size, and the more likely a correct crypt size will result.
"CellTarget": target cell number per crypt.
"AdjustStr": determines how quickly the "CptDieMax" variable will be adjusted to compensate for the crypt growing too large or small. A higher value will make the crypt less likely to blow up or extinguish during the "AdjustTime", however it may cause the program to overcompensate for small fluctuations in crypt size.
CRYPT PRESENTATION
ÒViewProgenyÓ : toggle "Off" sets cell color based on type, proliferating cells are colored red, with a lighter shade indicating a higher probability of dividing. Differentiated cells, and quiescent stem cells, which have an extremely low probability of dividing, are colored blue, with a lighter shade cooresponding to a higher probability of dying. Toggle "On" assigns each cell a different random color, this color is inherited by the cell's progeny.
ÒShowGradientsÓ: toggle "On" displays colored gradients to the left and right of the crypt cells A green divide gradient is displayed on the left and a red die gradient on the right. The quiescent region which is coded as a gradient but whose power is set to 0, making a it a uniform region, is colored dark green, indicating a 0 probability of dividing in this region. Toggle "Off" doesn't display the gradients and allows the program to run faster.
ÒDiffCellProbabilityThresholdÓ : cells with a probability of dividing above the threshold value are considered proliferating cells in visuals and plots. Conversely, cells with a probability of dividing below this value are considered differentiated cells or quiescent cells depending on their location.
CRYPT GRADIENTS
Gradients: divide and die gradients are described by the following function: p = y^n, where 0<=p=<1, 0<=y=<1, p is the probability that a cell will divide or die, y is related to the range of the gradient, y is raised to the n power. y = 0 at top of the gradient, and y = 1 at the bottom of the gradient. Also, y is scaled so that at the bottom of the gradient y = ÒMinÓ and at the top it equals "Max".
The left three inputs affect the divide gradient, the the right three inputs affect the die gradient.
"CptDivMin", "CptDieMin": cooresponds to the gradient value at the minimum end of the gradient. The p = y^n function is scaled so that when y is at it's minimum for the gradient, p = Min.
"CptDivMax", "CptDieMax": cooresponds to the gradient value at the maximum end of the gradient. The p = y^n function is scaled so that when y is at it's maximum for the gradient, p = Max.
"CptDivPwr", "CptDiePwr": cooresponds to the n in the p=y^n function,i.e. the "power" to which y is rasied. This value determines how steeply the gradient approaches it's maximum value.
"QuiesceDepthÓ: slider that sets the distance from the top of the crypt to the top of the quiescent region. The quiescent region extends from the "QuiesceDepth" to the bottom of the world.
"DieDepthEnd": slider that sets the end of the die gradient. The die gradient extends from the top of the crypt to "DieDepthEnd".
GRADIENT FEEDBACK STRENGTHS
"DivideFbk": affects all cells in the crypt above the quiescent region. For a value of 1, at each tick a cell's "ProbDivide" is set to the value at it's height in the divide gradient. For values less than 1, a cell's "ProbDivide" is set to a value determined by both its value at the previous tick and the value of the gradient at the cell's new position in the gradient. This results in a delay in a cell responding to the new gradient value. For a value of 0, the cell is unaffected by the gradient, and retains its previous probdivide.
"DieFbk": affects all cells in the crypt above "DieDepthEnd". similarly to "DivideFbk", a value of 1 sets cell's "ProbDie" to the value of the gradient at the cell's height. For values less than 1, a cell's "ProbDie" is set to a value determined by both its value at the previous tick and the value of the gradient at the cell's new position in the gradient. This results in a delay in a cell responding to the new gradient value.For a value of 0, the cell is unaffected by the gradient, and retains its previous probdie.
"QuiescentFbk": affects all cells in the quiescent region. With a strength of 1, the cells immediately drop to probdivide = 0. With a strength of less than 1, the cell's probdivide will decriment over time, approaching 0. With a strength of 0, the Quiescent region has no effect.
OUTPUTS:
-----------------------
PLOTS OF CELLS AS A FUNCTION OF TIME
----------
Graphs as a function of time (ticks, iterations) of each of the following:
ÒTotal CellsÓ: number of all cells in crypt.
ÒDifferentiated CellsÓ: number of cells which have a probability of dividing greater than "DiffCellProbabilityThreshold" and are located above the quiescent region + "CutOffAboveQuiescentRegion" (this variable is set in the Procedures under setup).
ÒProliferating CellsÓ: number of cells which have a probability of dividing greater than ÒDiffCellProbabilityThresholdÓ, but not including quiescent stem cells. This can include cells which are traditionally referred to as active stem cells as well as transient amplifying cells.
ÒQuiescent Stem CellsÓ: number of cells which have a probability of dividing less than ÒDiffCellProbabilityThresholdÓ and are located below the quiescent region + "CutOffAboveQuiescentRegion".
ÒProportion of Mutant CellsÓ : number of mutant cells divided by total number of cells.
TIMES TO EVENTS
-----------
"UnboundedSizeTime": if the number of cell rows becomes greater than "SetTop", the crypt is considered unbounded. The "UnboundedSizeTime" reporter displays the number of ticks when this occurs.
"ExtinctionTime": if all of the cells die (removed), the crypt is considered extinct. The "ExtinctionTime" reporter displays the number of ticks when this occurs.
"MonoclonalTime": when the "Viewprogeny" toggle is "On" each cell is assigned a different random color, and this color is inherited by the cell's progeny. The "MonoclonalTime" reporter displays the time period between the time that "Viewprogeny" is toggled "On" and the time that all progeny cells in a crypt have the same color, i.e. that monoclonal conversion has occurred.
"FissionTime": the "FissionTime" reporter displays the period of time between when "PolarDivision" is toggled "On" and the time at which least one column occurs with no cells. A column with no cells that separtes two groups of columns with cells is considered to indicate crypt fission.
PARAMETER SWEEPING EXPERIMENTS:
ÒBehavior spaceÓ is accessed under "Tools". This produces numerical output of simulations. Output can be saved in an .csv format file, useful for export to Excel or statistical programs for descriptive statistics and graphs. It is possible to designate parameters to be changed, range of parameters, and intervals. For instance, with two parameters the program will run through the upper and lower limits of each the two parameters, each at designated intervals. The output will include a list of all of the parameter values for the simulation, not just those being swept. For more information see NetLogo User Manual, accessible under "Help".
CRITERIA FOR SELECTING DEFAULT VALUES:
-------------------------
The first three can only be changed before activating "Setup". Others can be changed after activating "Setup", but the mouse will need to be clicked outside of any input to activate a new value.
Top (100): convenient value for visualization. If larger, then can have larger number of crypt cells, if too large simulation is slower.
CellsPerRow,RowsAtStart (38): starts the simulation with approximately the number of cells per row and column measured in human crypts.
MutantDivideDiff(0.16): an example value that produces a mutant cell with a greater probability of dividing from others at the same location in the divide gradient.
MutantDieDiff (0.1): an example value that produces a mutant cell with a greater probability of dying from others at the same location in the die gradient.
StartD,EndD (55,60): cells mutated between these rows have a high probability of producing viable mutant progeny rather than dying out.
Proportion (0.2): set so that not all cells between start depth (StartD) and end depth (EndD) are mutated.
MutateHeight (59): Starting at this height, compared to other heights, a mutant cell is more likely to produce viable progeny rather than die out.
Interval, Duration, Lethality (24,3,2): given a lethality of 2, these interval and duration values give a minimum collateral damage with a short time to cure.
CellTarget (2428): average total number of cells measured in human crypts
AdjustTime,AdjustStr (1000,0.1): give "CryptSizeAdjust" a sufficient number of ticks and sufficient strength to achieve the target number of cells.
DiffCellProbabilityThreshold (0.02): gives the approximate numbers of differentiated, proliferating, and quiescent cells measured in human crypts.
CptDivMin,CptDivMax,CptDivPwr (0,0.5,11.5): this combination of values causes cell division behavior that simulates the numbers and proportion of each cell type as measured in human crypts.
CptDieMin,CptDieMax,CptDiePwr (0,0.2,14): this combination of values causes cell death behavior near the top of the crypt to simulate cell migration out of the crypt.
QuiesceDepth (60): simulates the measured total number of cells per crypt, also simulates the approximately measured number and proportion of quiescent cells.
DieDepthEnd (100): causes the die gradient to cover the entire crypt depth with SetTop as its default value.
DivdeFbk,DieFbk,QuiescentFbk (0.5,0.5,0.1): these give intermediate rates of delayed response of cells to their gradient position.
ACKNOWLEDGEMENTS:
-----------
This crypt model was produced with the NetLogo v.4.3.3 application. NetLogo is a multi-agent programmable modeling environment. It is authored by Uri Wilensky and developed at The Center for Connected Learning (CCL) and Computer-Based Modeling. It is an open-source application available at http://ccl.northwestern.edu/netlogo/.
@#$#@#$#@
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@#$#@#$#@
NetLogo 4.1.3
@#$#@#$#@
@#$#@#$#@
@#$#@#$#@
setup
go
ticks = 100
count cells
setup
go
count turtles
setup
go
count turtles
setup
go
mutateonecell
count turtles
setup
go
count cells with [ycor < top - protrusion - quiescedepth]
count cells with [probdivide >= DiffCellProbabilityThreshold and ycor >= top - protrusion - quiescedepth]
count cells with [probdivide < DiffCellProbabilityThreshold and ycor >= top - protrusion - quiescedepth]
count turtles
setup
go
count turtles
setup
go
count turtles
count cells with[ycor < top - protrusion - quiescedepth + 10 and probdivide < DiffCellProbabilityThreshold]
setup
go
count turtles
setup
go
count turtles
count cells with[ycor < top - protrusion - quiescedepth + 10 and probdivide < DiffCellProbabilityThreshold]
count cells with[ycor >= top - protrusion - quiescedepth + 10 and probdivide < DiffCellProbabilityThreshold]
count cells with[probdivide > DiffCellProbabilityThreshold]
setup
go
count turtles
setup
go
count turtles
setup
go
count turtles
CountSCq
CountProlif
CountDiff
CptDieMax
setup
go
if ticks = 500[
set DivDirRand true]
ticks = 1500
FissionTime
setup
go
if ticks = 500 [
set ViewProgeny true]
MonoclonalComplete = true
MonoclonalTime
setup
go
if ticks = 500 [
set ActiveChemo true]
CountSCq
CountDiff
CountProlif
Count cells
setup
go
if ticks > 200 and count cells with [Mutant true] = 0 and ActiveChemo = false[
MutateOneCell]
if count cells with [mutant = true] / count cells >= .5 and activechemo = false[
set activechemo true]
count cells = 0 or count cells with [mutant = true] = 0 and activechemo = true or if UnboundedSizeTime != 0
count turtles
count cells with [mutant = true] / count turtles
setup
go
count turtles
setup
go
if ticks = 200 [MutateRows]
ticks > 200 and CountMutant = 0 or CountMutant = count turtles
CountMutant / count turtles
@#$#@#$#@
@#$#@#$#@
default
0.0
-0.2 0 1.0 0.0
0.0 1 1.0 0.0
0.2 0 1.0 0.0
link direction
true
0
Line -7500403 true 150 150 90 180
Line -7500403 true 150 150 210 180
@#$#@#$#@
0
@#$#@#$#@