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ABRanProlif_UD.m
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% Implementing spatial Moran 2D algorithm: Normal cells=1's
% and PM cells = 0's.
% Input: 21 X 21 matrix with one 0 and rest all 1's
% Generate a randomproliferation matrix for A and B-
% <rB> = 1.5 and <rA> = 1.0
% rB: D = [1.4,1.6] and rA: D = [0.9,1.1]
%
clc; clear all;
RandStream.setDefaultStream(RandStream('mt19937ar','seed',sum(100*clock))); % Random seed
% create a grid
xmax = 21;
ymax = 21;
x = 0:1:xmax;
y = 0:1:ymax;
A_won = 0;
B_won = 0;
lowerlimitA = 0.9;
upperlimitA = 1.1;
rA = lowerlimitA + (upperlimitA-lowerlimitA).*rand(21,21);
lowerlimitB = 0.1;
upperlimitB = 2.9;
rB = lowerlimitB + (upperlimitB-lowerlimitB).*rand(21,21);
fid = fopen('RanProlifB-A[0.9,1.1]B[0.1,2.9]1.txt', 'wt');
%-------------Randomly choose (i,j) to place PM cell by 0--------------
sets_max = 1;
iter_max = 50000;
for sets=1:sets_max % Number of sets
sets;
for iterations = 1:iter_max
iterations;
fprintf(fid, 'Iterations: %g\n', iterations);
X = ones(xmax,ymax);
M = sum(X);
M1 = sum(M);
M2 = 0;
M1init = xmax*ymax-1;
%i1 = randint(1,1,[1,xmax]);
%j1 = randint(1,1,[1,ymax]);
i1 = randi(xmax,1,1);
j1 = randi(ymax,1,1);
X(i1,j1) = 0;
while ((M1 ~= sum(sum(X))) && (M2 ~= sum(sum(X))))
X;
%i2 = randint(1,1,[1,xmax]);
%j2 = randint(1,1,[1,ymax]);
i2 = randi(xmax,1,1);
j2 = randi(ymax,1,1);
X(i2,j2) = -1;
X_withcelldeath = X;
while (any(any(X==-1))==1) % two times any since it checks both rows and columns
X_minusonepresent = X;
[k l] = ind2sub(size(X),find(X==-1)); % check the position i,j for -1
i2 = k;
j2 = l;
% Interior part (2,2)...(2,4) and (4,2)...(4,4)
if ((i2>1) && (i2<xmax) && (j2>1) && (j2<ymax))
neighbours(1) = X(i2,j2-1); % left side
neighbours(2) = X(i2,j2+1); % right side
neighbours(3) = X(i2-1,j2); % Top
neighbours(4) = X(i2+1,j2) ;% Bottom
end
% Top part (1,2)...(1,4)
if (i2==1)
if ((j2>1) && (j2<ymax))
k = 1;
neighbours(1) = X(i2,j2-1);
neighbours(2) = X(i2,j2+1);
neighbours(3) = 10;
neighbours(4) = X(i2+1,j2);
end
end
% Bottom part (5,2)...(5,4)
if (i2==xmax)
if ((j2>1) && (j2<xmax))
k = 1;
neighbours(1) = X(i2,j2-1);
neighbours(2) = X(i2,j2+1);
neighbours(3) = X(i2-1,j2);
neighbours(4) = 10;
end
end
% Left Side part (2,1)...(4,1)
if (j2==1)
if ((i2>1) && (i2<xmax))
k = 1;
neighbours(1) = 10;
neighbours(2) = X(i2,j2+1);
neighbours(3) = X(i2-1,j2);
neighbours(4) = X(i2+1,j2);
end
end
% Right Side part (2,5)...(4,5)
if (j2==ymax)
if ((i2>1) && (i2<xmax))
k = 1;
neighbours(1) = X(i2,j2-1);
neighbours(2) = 10;
neighbours(3) = X(i2-1,j2);
neighbours(4) = X(i2+1,j2);
end
end
if ((i2==1) && (j2== 1))
k = 1;
neighbours(1) = 10;
neighbours(2) = X(i2,j2+1);
neighbours(3) = 10;
neighbours(4) = X(i2+1,j2);
end
if ((i2==1) && (j2== ymax))
k = 1;
neighbours(1) = X(i2,j2-1);
neighbours(2) = 10;
neighbours(3) = 10;
neighbours(4) = X(i2+1,j2);
end
if ((i2==xmax) && (j2== 1))
k = 1;
neighbours(1) = 10;
neighbours(2) = X(i2,j2+1);
neighbours(3) = X(i2-1,j2);
neighbours(4) = 10 ;
end
if ((i2==xmax) && (j2== ymax))
k = 1;
neighbours(1) = X(i2,j2-1);
neighbours(2) = 10;
neighbours(3) = X(i2-1,j2);
neighbours(4) = 10;
end
neighbours;
% Count the number of normal and pre-malignant cells surrounding
% the empty spot where cell death happened
a = sum(neighbours);
b = floor(a/10);
NCells = a - b*10;
PMCells = 4 - b - NCells;
%---------Calculate the probabilities----------
nA = NCells;
nB = PMCells;
[i2 j2];
%-----Calculate the average r------
if (length(find(neighbours==1) ~=0 ))
for r = 1:length(neighbours)
if (neighbours(1)==10)
rAtemp(1) = 0;
else
linearindex1 = sub2ind(size(X),i2,j2-1);
rAtemp(1) = rA(linearindex1);
end
if (neighbours(2)==10)
rAtemp(2) = 0;
else
linearindex2 = sub2ind(size(X),i2,j2+1);
rAtemp(2) = rA(linearindex2);
end
if (neighbours(3)==10)
rAtemp(3) = 0;
else
linearindex3 = sub2ind(size(X),i2-1,j2);
rAtemp(3) = rA(linearindex3);
end
if (neighbours(4)==10)
rAtemp(4) = 0;
else
linearindex4 = sub2ind(size(X),i2+1,j2);
rAtemp(4) = rA(linearindex4);
end
end
X;
rA;
rAtemp;
%pause
rAtemp1 = find(neighbours==1);
for t1 = 1:length(rAtemp1)
rAtemp2 = rAtemp(rAtemp1);
temp3 = rAtemp2;
end
temp3;
rAave = mean(temp3);
%pause
else
rAave = 0;
end
%------end of average rA code------
rAave;
%-----Calculate the average rB------
if (length(find(neighbours==0) ~=0 ))
for r = 1:length(neighbours)
if (neighbours(1)==10)
rBtemp(1) = 0;
else
linearindex1 = sub2ind(size(X),i2,j2-1);
rBtemp(1) = rB(linearindex1);
end
if (neighbours(2)==10)
rBtemp(2) = 0;
else
linearindex2 = sub2ind(size(X),i2,j2+1);
rBtemp(2) = rB(linearindex2);
end
if (neighbours(3)==10)
rBtemp(3) = 0;
else
linearindex3 = sub2ind(size(X),i2-1,j2);
rBtemp(3) = rB(linearindex3);
end
if (neighbours(4)==10)
rBtemp(4) = 0;
else
linearindex4 = sub2ind(size(X),i2+1,j2);
rBtemp(4) = rB(linearindex4);
end
end
X;
rB;
rBtemp;
%pause
rBtemp1 = find(neighbours==0);
for t1 = 1:length(rBtemp1)
rBtemp2 = rBtemp(rBtemp1);
temp3 = rBtemp2;
end
temp3;
rBave = mean(temp3);
%pause
else
rBave = 0;
end
%------end of average rB code------
rBave;
mA = 0;
mB = 0;
rBave;
Ktilde = nA*(rAave+mA) + nB*(rBave+mB);
ProbAdiv = (nA*rAave)/Ktilde;
ProbAmig = (nA*mA)/Ktilde;
ProbBdiv = (nB*rBave)/Ktilde;
ProbBmig = (nB*mB)/Ktilde;
Prob = [ProbAdiv ProbBdiv ProbAmig ProbBmig];
% Generate a random number to see which of the above events is
% likely to occur
r = rand;
if (r<=Prob(1))
%display('Event: A divides and places a cell in empty slot')
X(i2,j2) = 1 ;
M1updated = sum(sum(X));
M1init = M1updated;
X_Aafterbirth=X;
%pause
%return;
end
if ((Prob(1)< r) && (r<= Prob(1)+Prob(2)))
%display('Event: B divides and places a cell in empty slot')
[Q1 Q2] = ind2sub([xmax ymax],find(X==-1)); % check the position i,j for -1
Q = [Q1 Q2];
X(Q(1),Q(2)) = 0 ;
X;
Mupdated = sum(X);
M1updated = sum(Mupdated);
M1init = M1updated;
X_Bafterbirth = X;
%pause
%return;
end
if ((Prob(1)+Prob(2)< r) && (r<= Prob(1)+Prob(2)+Prob(3)))
%display('Event: A migrates into the empty spot')
%return;
end
if (Prob(1)+Prob(2)+Prob(3)< r)
%display('Event: B migrates into the empty spot')
Y = find(neighbours==0);
interval = Prob(4)/nB;
a1 = r - (Prob(1)+Prob(2)+Prob(3));
a2 = ceil(a1/interval);
if (Y(a2)==1)
X(i2,j2-1) = -1;
X(i2,j2) = 0;
end
if (Y(a2)==2)
X(i2,j2+1) = -1;
X(i2,j2) = 0;
end
if (Y(a2)==3)
X(i2-1,j2) = -1;
X(i2,j2) = 0;
end
if (Y(a2)==4)
X(i2+1,j2) = -1;
X(i2,j2) = 0;
end
X_aftermig = X;
%pause
end
Mupdated = sum(X);
M1updated = sum(Mupdated);
M1init = M1updated;
end
X;
end
if (sum(sum(X)) == xmax*ymax)
A_won = A_won + 1;
end
if (sum(sum(X)) == 0)
B_won = B_won + 1;
end
end
A(sets) = A_won;
B(sets) = B_won;
end
AverageA = A(sets_max)/(sets_max*iter_max);
AverageB = B(sets_max)/(sets_max*iter_max);
fprintf(fid, 'AverageA: %g\n', AverageA);
fprintf(fid, 'AverageB: %g ', AverageB);
fclose(fid);