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cell_migration_Ub1.m
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cell_migration_Ub1.m
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% Subfunction to handle cellular migration in the ABM model
% subfunction of ABM_EC_polarize_migrate_flow_H.m
% 09/14/2018
% --------------------
function [seg_cells, new_seg_cells] = cell_migration_Ub1(seg, seg_cells, new_seg_cells, migrate, Q, tau, branch_rule, alpha)
% branch_rule = 2;
cell_size = 10*1e-6; % Set the size of each cell (m)
% Calculate chance of migrating depending on flow
%mchance = (1 - abs(Q(seg))/Qmax); % Chance of a cell migrating depending on segment flow
mchance = 1;
if (mchance < 0)
mchance = 0;
end
if (seg_cells{seg,1} ~= 0)
for cell = 1:seg_cells{seg,1} % Iterate through each cell of each segment and use a random number to determine if it migrates against flow
mcell = rand();
if (mcell <= mchance) % If random number (0,1) is less than migration chacne...
polar_vect = seg_cells{seg,2}(:,cell);
migrate_vect = cell_size*polar_vect;
% For cells in the first or fourth vertical vessel...
if ((seg <= 5) || ((seg >= 21) && (seg <= 25)))
if (migrate_vect(2,1) >= cell_size/2) % If polarity vector is sufficiently aligned upwards, migrate upstream
seg_cells{seg,3}(1,cell) = 1;
migrate(seg) = migrate(seg) + 1;
else if (migrate_vect(2,1) <= -cell_size/2) % If polarity vector is sufficiently aligned downwards, migrate downstream
seg_cells{seg,3}(1,cell) = -1;
migrate(seg) = migrate(seg) + 1;
end
end
end
% For cells in the second or fifth horizontal vessel...
if (((seg >= 6) && (seg <= 15)) || ((seg >= 26) && (seg <= 35)))
if (migrate_vect(1,1) >= cell_size/2) % If polarity vector is sufficiently aligned to the right, migrate upstream
seg_cells{seg,3}(1,cell) = 1;
migrate(seg) = migrate(seg) + 1;
else if (migrate_vect(1,1) <= -cell_size/2) % If polarity vector is sufficiently aligned to the left, migrate downstream
seg_cells{seg,3}(1,cell) = -1;
migrate(seg) = migrate(seg) + 1;
end
end
end
% For cells in the third or sixth vertical vessel...
if (((seg >= 16) && (seg <= 20)) || (seg >= 36))
if (migrate_vect(2,1) >= cell_size/2) % If polarity vector is sufficiently aligned upwards, migrate downstream
seg_cells{seg,3}(1,cell) = -1;
migrate(seg) = migrate(seg) + 1;
else if (migrate_vect(2,1) <= -cell_size/2) % If polarity vector is sufficiently aligned downwards, migrate upstream
seg_cells{seg,3}(1,cell) = 1;
migrate(seg) = migrate(seg) + 1;
end
end
end
end
end
end
% Diffusion scheme to even out cell numbers in vertical vessel segments
down_seg = [];
if ((seg ~= 20) && (seg ~= 40))
down_seg = seg + 1;
end
if (seg == 20)
down_seg = 1;
end
if (seg == 40)
if ((seg_cells{15,1} < seg_cells{16,1}) && (seg_cells{15,1} ~= 0))
down_seg = 15;
else
down_seg = 16;
end
end
if (seg == 5)
if ((seg_cells{6,1} < seg_cells{21,1}) && (seg_cells{6,1} ~= 0))
down_seg = 6;
else
down_seg = 21;
end
end
if (isempty(down_seg) == 0)
if (seg_cells{seg,1} ~= 0)
if ((seg_cells{down_seg,1} < seg_cells{seg,1}) && (seg_cells{down_seg,1} ~= 0))
seg_cells{seg,3}(randi([1 seg_cells{seg,1}])) = 0;
migrate(seg) = migrate(seg) - 1;
end
end
end
% Move all cells that have been selected to migrate
if (migrate(seg) ~= 0)
for cell = 1:seg_cells{seg,1}
% If cell is migrating downstream (i.e., with flow if flow is positive)
if (seg_cells{seg,3}(1,cell) == 1)
new_seg_cells{seg,1} = new_seg_cells{seg,1} - 1; % Decrease the number of cells in the parent segment
cell_vect = seg_cells{seg,2}(:,cell); % Obtain the cell's polarity vector
new_seg_cells{seg,2}(:,cell) = [0; 0];
target = 0;
% Move the cell and it's polarity vector to the target segment (downstream segment)
if (seg ~= 20)
target = seg+1;
end
if (seg == 20)
target = 1;
end
if (seg == 40)
target = 16;
end
switch branch_rule
% Flow magnitude rule
case 1
if (seg == 5)
if (Q(6) > Q(21))
target = 6;
else
target = 21;
end
end
if (seg == 40)
if (Q(16) > Q(15))
target = 16;
else
target = 15;
end
end
% Polarity direction rule
case 2
if (seg == 5)
if (dot(cell_vect, [0; 1]) > dot(cell_vect, [1; 0]))
target = 21;
else
target = 6;
end
end
% Random rule
case 3
if (seg == 5)
if (sign(rand() - 0.5) < 0)
target = 21;
else
target = 6;
end
end
case 4
if (seg == 5)
if (sign(rand() - 0.3) < 0)
target = 21;
else
target = 6;
end
end
case 5
Q1 = Q(6);
Q2 = Q(21);
Qratio = Q2/(Q1 + Q2);
if (seg == 5)
if (sign(rand() - Qratio) < 0)
target = 21;
else
target = 6;
end
end
case 6
%alpha = 0.5;
Q1 = Q(6) + Q(7) + Q(8);
Q2 = Q(21) + Q(22) + Q(23);
Qratio = Q2/(Q1 + Q2);
% Nparent = (seg_cells{1,1} + seg_cells{2,1} + seg_cells{3,1} + seg_cells{4,1} + seg_cells{5,1});
% N2 = (seg_cells{21,1} + seg_cells{22,1} + seg_cells{23,1} + seg_cells{24,1} + seg_cells{25,1});
% N1 = (seg_cells{6,1} + seg_cells{7,1} + seg_cells{8,1} + seg_cells{9,1} + seg_cells{10,1});
% Nratio = N2/(N1 + N2);
Nparent = (seg_cells{3,1} + seg_cells{4,1} + seg_cells{5,1});
N2 = (seg_cells{21,1} + seg_cells{22,1} + seg_cells{23,1});
N1 = (seg_cells{6,1} + seg_cells{7,1} + seg_cells{8,1});
Nratio = N2/(N1 + N2);
P2 = alpha*Qratio + (1 - alpha)*Nratio;
if (seg == 5)
if (sign(rand() - P2) < 0)
target = 21;
else
target = 6;
end
end
case 7
tau1 = tau(6) + tau(7) + tau(8);
tau2 = tau(21) + tau(22) + tau(23);
tau_ratio = tau2/(tau1 + tau2);
% Nparent = (seg_cells{1,1} + seg_cells{2,1} + seg_cells{3,1} + seg_cells{4,1} + seg_cells{5,1});
% N2 = (seg_cells{21,1} + seg_cells{22,1} + seg_cells{23,1} + seg_cells{24,1} + seg_cells{25,1});
% N1 = (seg_cells{6,1} + seg_cells{7,1} + seg_cells{8,1} + seg_cells{9,1} + seg_cells{10,1});
% Nratio = N2/(N1 + N2);
Nparent = (seg_cells{3,1} + seg_cells{4,1} + seg_cells{5,1});
N2 = (seg_cells{21,1} + seg_cells{22,1} + seg_cells{23,1});
N1 = (seg_cells{6,1} + seg_cells{7,1} + seg_cells{8,1});
Nratio = N2/(N1 + N2);
P2 = alpha*tau_ratio + (1 - alpha)*Nratio;
if (seg == 5)
if (sign(rand() - P2) < 0)
target = 21;
else
target = 6;
end
end
end
% Rotate polarity vectors of cells crossing into a branch
if ((seg == 5) && (target == 6))
theta = -90;
cell_vect = [cosd(theta) -sind(theta); sind(theta) cosd(theta)]*cell_vect;
cell_vect = cell_vect/norm(cell_vect);
end
if ((seg == 25) && (target == 26))
theta = -90;
cell_vect = [cosd(theta) -sind(theta); sind(theta) cosd(theta)]*cell_vect;
cell_vect = cell_vect/norm(cell_vect);
end
if ((seg == 15) && ((target == 16) || (target == 40)))
theta = -90;
cell_vect = [cosd(theta) -sind(theta); sind(theta) cosd(theta)]*cell_vect;
cell_vect = cell_vect/norm(cell_vect);
end
if ((seg == 35) && (target == 36))
theta = -90;
cell_vect = [cosd(theta) -sind(theta); sind(theta) cosd(theta)]*cell_vect;
cell_vect = cell_vect/norm(cell_vect);
end
if ((seg == 20) && (target == 1))
theta = -180;
cell_vect = [cosd(theta) -sind(theta); sind(theta) cosd(theta)]*cell_vect;
cell_vect = cell_vect/norm(cell_vect);
end
new_seg_cells{target,1} = new_seg_cells{target,1} + 1;
new_seg_cells{target,2} = [new_seg_cells{target,2} cell_vect];
end
% If cell is migrating upstream (i.e., against flow if flow is positive)...
if (seg_cells{seg,3}(1,cell) == -1)
new_seg_cells{seg,1} = new_seg_cells{seg,1} - 1; % Decrease the number of cells in the parent segment
cell_vect = seg_cells{seg,2}(:,cell); % Obtain the cell's polarity vector
new_seg_cells{seg,2}(:,cell) = [0; 0];
target = 0;
% Move the cell and it's polarity vector to the target segment (upstream segment)
if (seg ~= 1)
target = seg-1;
end
if (seg == 1)
target = 20;
end
if (seg == 21)
target = 5;
end
switch branch_rule
% Flow magnitude rule
case 1
if (seg == 16)
if (Q(15) > Q(40))
target = 15;
else
target = 40;
end
end
if (seg == 6)
if (Q(5) > Q(21))
target = 5;
else
target = 21;
end
end
% Polarity direction rule
case 2
if (seg == 16)
if (dot(cell_vect, [0; 1]) > dot(cell_vect, [-1; 0]))
target = 40;
else
target = 15;
end
end
% Random rule
case 3
if (seg == 16)
if (sign(rand() - 0.5) < 0)
target = 40;
else
target = 15;
end
end
case 4
if (seg == 16)
if (sign(rand() - 0.3) < 0)
target = 40;
else
target = 15;
end
end
case 5
Qratio = Q(40)/(Q(40) + Q(15));
if (seg == 16)
if (sign(rand() - Qratio) < 0)
target = 40;
else
target = 15;
end
end
case 6
%alpha = 0.5;
Q1 = Q(15) + Q(14) + Q(13);
Q2 = Q(40) + Q(39) + Q(38);
Qratio = Q2/(Q1 + Q2);
% Nparent = (seg_cells{16,1} + seg_cells{17,1} + seg_cells{18,1} + seg_cells{19,1} + seg_cells{20,1});
% N2 = (seg_cells{40,1} + seg_cells{39,1} + seg_cells{38,1} + seg_cells{37,1} + seg_cells{36,1});
% N1 = (seg_cells{15,1} + seg_cells{14,1} + seg_cells{13,1} + seg_cells{12,1} + seg_cells{11,1});
% Nratio = N2/(N1 + N2);
Nparent = (seg_cells{16,1} + seg_cells{17,1} + seg_cells{18,1});
N2 = (seg_cells{40,1} + seg_cells{39,1} + seg_cells{38,1});
N1 = (seg_cells{15,1} + seg_cells{14,1} + seg_cells{13,1});
Nratio = N2/(N1 + N2);
P2 = alpha*Qratio + (1 - alpha)*Nratio;
if (seg == 16)
if (sign(rand() - P2) < 0)
target = 40;
else
target = 15;
end
end
case 7
tau1 = tau(15) + tau(14) + tau(13);
tau2 = tau(40) + tau(39) + tau(38);
tau_ratio = tau2/(tau1 + tau2);
% Nparent = (seg_cells{16,1} + seg_cells{17,1} + seg_cells{18,1} + seg_cells{19,1} + seg_cells{20,1});
% N2 = (seg_cells{40,1} + seg_cells{39,1} + seg_cells{38,1} + seg_cells{37,1} + seg_cells{36,1});
% N1 = (seg_cells{15,1} + seg_cells{14,1} + seg_cells{13,1} + seg_cells{12,1} + seg_cells{11,1});
% Nratio = N2/(N1 + N2);
Nparent = (seg_cells{16,1} + seg_cells{17,1} + seg_cells{18,1});
N2 = (seg_cells{40,1} + seg_cells{39,1} + seg_cells{38,1});
N1 = (seg_cells{15,1} + seg_cells{14,1} + seg_cells{13,1});
Nratio = N2/(N1 + N2);
P2 = alpha*tau_ratio + (1 - alpha)*Nratio;
if (seg == 16)
if (sign(rand() - P2) < 0)
target = 40;
else
target = 15;
end
end
end
% Rotate polarity vectors of cells crossing into a branch
if (((seg == 16) || (seg == 40)) && (target == 15))
theta = 90;
cell_vect = [cosd(theta) -sind(theta); sind(theta) cosd(theta)]*cell_vect;
cell_vect = cell_vect/norm(cell_vect);
end
if ((seg == 36) && (target == 35))
theta = 90;
cell_vect = [cosd(theta) -sind(theta); sind(theta) cosd(theta)]*cell_vect;
cell_vect = cell_vect/norm(cell_vect);
end
if ((seg == 26) && (target == 25))
theta = 90;
cell_vect = [cosd(theta) -sind(theta); sind(theta) cosd(theta)]*cell_vect;
cell_vect = cell_vect/norm(cell_vect);
end
if ((seg == 6) && ((target == 5) || (target == 21)))
theta = 90;
cell_vect = [cosd(theta) -sind(theta); sind(theta) cosd(theta)]*cell_vect;
cell_vect = cell_vect/norm(cell_vect);
end
if ((seg == 1) && (target == 20))
theta = 180;
cell_vect = [cosd(theta) -sind(theta); sind(theta) cosd(theta)]*cell_vect;
cell_vect = cell_vect/norm(cell_vect);
end
new_seg_cells{target,1} = new_seg_cells{target,1} + 1;
new_seg_cells{target,2} = [new_seg_cells{target,2} cell_vect];
end
end
end