-
Notifications
You must be signed in to change notification settings - Fork 0
/
run_2D_dynamic_cell_model3.m
323 lines (268 loc) · 10.5 KB
/
run_2D_dynamic_cell_model3.m
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
clear; clc;
rng('shuffle');
numt = 5000000; %number of time steps
dt = 0.001; %time step
dx = 0.02; %spatial step
C_total_conc = 1;
I_total_conc = 3;
R_total_conc = 1;
S = [1000, 1000]; %size of the large canvas for cell simulation
cell_R = 80; %radius of the cell
Im_L = generate_regular_polyhedron(S, S/2, cell_R, 500);
Im_outline = outline_8p(~Im_L); %cell_outline
Cs_init = 0;
Is_init = 3;
Rs_init = 0;
Cs_L = Rs_init*ones(S).*Im_L;
C_L = (R_total_conc-Rs_init)*ones(S).*Im_L;
Is_L = Is_init*ones(S).*Im_L;
I_L = (I_total_conc-Is_init)*ones(S).*Im_L;
Rs_L = Cs_init*ones(S).*Im_L;
R_L = (C_total_conc-Cs_init)*ones(S).*Im_L;
k1 = 0.005;
gamma1 = 2;
K1_basal = 2.1;
K1_edge = 1.4;
K1_L = K1_basal*ones(size(Im_L));
K1_L(Im_outline==1) = K1_edge;
beta1 = 0.5;
n1 = 2;
k2 = 0.1;
k3 = 0.00001;
gamma3 = 0.2;
n3 = 2;
k4 = 0.01;
k5 = 0.005;
gamma5 = 0.3;
alpha5 = 0.8;
K5_basal = 2.1;
K5_edge = 1.4;
K5_L = K5_basal*ones(size(Im_L));
K5_L(Im_outline==1) = K5_edge;
n5 = 2;
k6 = 0.1;
DCs = 0.001;
DC = 0.1/3;
DIs = 0.003;
DI = 0.1/3;
DRs = 0.001;
DR = 0.1/3;
alpha_V = 0.001; %parameter for the volume factor in the model of moving cell (sharpnes of the sigmoid function, that describes deviation from the initial value of volume)
V0 = sum(Im_L(:))*1; %initial volume (area) of the cell
beta_V = 0.5; %parameter for the volume factor in the model of moving cell (scales pobability of protrusion and retraction from beta_V to 1-beta_V, introduced to make the volume factor weaker then the activ factor)
gamma_V = 0.5;
alpha_A = 50; %parameter for the actin factor in the model of moving cell (sharpnes of the sigmoid function, that describes deviation from the "default" value of A)
A_act = 1; %parameter for the actin factor in the model of moving cell ("default" value of A starting from which cell begins to protrude)
%parameters for the actin factor in the model of moving cell (increase/decrease of protrusion/retraction probability with the respect of basal level when A increases)
%see figure for explanation
beta_A = 0;
gamma_A = 0.1;
g = 2; %g parameter for the geometric factor in the model of moving cell (sensitivity to the curvature)
k = 3; %k parameter for the geometric factor in the model of moving cell (smoothnes of boundary)
sub_iter_N = 1; %number of iterations for sepparate reaction and diffusion steps (due to operator splitting)
mov_T = 50; %period of cell outline update
save_T = 1000; %period of saving cell state
crop_d = 2; %width of the outline while cropping the frame adound cell
n_alf = 5; %noise value
[Im, i_start, i_end, j_start, j_end] = crop_frame(Im_L, crop_d);
Cs = Cs_L(i_start:i_end, j_start:j_end);
C = C_L(i_start:i_end, j_start:j_end);
Is = Is_L(i_start:i_end, j_start:j_end);
I = I_L(i_start:i_end, j_start:j_end);
Rs = Rs_L(i_start:i_end, j_start:j_end);
R = R_L(i_start:i_end, j_start:j_end);
K1 = K1_L(i_start:i_end, j_start:j_end);
K5 = K5_L(i_start:i_end, j_start:j_end);
U = U_matrix(Im); %supplementary matrix for laplacian computation
s = size(Rs);
save_fold = 'E:\Asef_Cdc42_Rac1_model\Cdc42_regulator_nonlin_act_Rac1\2D_model_dynamic_differentiator';
subfold = strcat('cell_R_', num2str(cell_R), '_k5_', num2str(k5), ...
'_alpha5_', num2str(alpha5), '_k6_', num2str(k6), ...
'_alpha_A_', num2str(alpha_A), '_A_act_', num2str(A_act), ...
'_gamma_A_', num2str(gamma_A));
save_fold = fullfile(save_fold, subfold);
mkdir(save_fold);
mkdir(fullfile(save_fold, 'Cs_L'));
mkdir(fullfile(save_fold, 'Rs_L'));
mkdir(fullfile(save_fold, 'mat'));
mkdir(fullfile(save_fold, 'colored'));
save(fullfile(save_fold, 'parameters.mat'), ...
'numt', 'dt', 'dx', 'R_total_conc', 'I_total_conc', 'S', 'cell_R', ...
'Im_L', 'Im_outline', 'Cs_L', 'C_L', 'Is_L', 'I_L', 'Rs_L', 'R_L', ...
'k1', 'gamma1', 'K1_basal', 'K1_edge', 'K1_L', 'beta1', 'n1', 'k2', ...
'k3', 'gamma3', 'n3', 'k4', 'k5', 'gamma5', 'alpha5', 'K5_basal', ...
'K5_edge', 'K5_L', 'n5', 'k6', 'DRs', 'DR', 'DIs', 'DI', 'DCs', 'DC', ...
'alpha_V', 'V0', 'beta_V', 'gamma_V', 'alpha_A', 'A_act', 'beta_A', 'gamma_A', ...
'g', 'k', 'sub_iter_N', 'mov_T', 'save_T', 'crop_d', 'n_alf', 'Im', ...
'i_start', 'i_end', 'j_start', 'j_end', ...
'Cs', 'C', 'Is', 'I', 'Rs', 'R', 'U', 's');
V_vals = linspace(0.5*V0, 2*V0, 1000);
R_vals = -0.01:0.001:2;
%protrusion
vol_p_prot = 0.5 + beta_V - (beta_V+gamma_V)*(1-1./(1+exp(alpha_V*(V_vals-V0))));
act_p_prot = 0.5 - beta_A + (beta_A+gamma_A)*(1-1./(1+exp(alpha_A*(R_vals-A_act))));
%retraction
vol_p_ret = 0.5 - beta_V + (beta_V+gamma_V)*(1-1./(1+exp(alpha_V*(V_vals-V0))));
act_p_ret = 0.5 + beta_A - (beta_A+gamma_A)*(1-1./(1+exp(alpha_A*(R_vals-A_act))));
fig = figure('Position', [50 50 1000 400]);
subplot(1,2,1);
hold on;
grid off;
box on;
ylim([0, 1]);
plot(R_vals, act_p_prot, 'Color', [1 0 0], 'LineWidth', 3);
plot(R_vals, act_p_ret, 'Color', [0 1 0], 'LineWidth', 3);
xlim([min(R_vals), max(R_vals)]);
legend({'protrusion','retraction'});
xlabel('R');
set(gca, 'LineWidth', 2);
title('actin factor');
subplot(1,2,2);
hold on;
grid off;
box on;
plot(V_vals, vol_p_prot, 'Color', [1 0 0], 'LineWidth', 3);
plot(V_vals, vol_p_ret, 'Color', [0 1 0], 'LineWidth', 3);
xlim([min(V_vals), max(V_vals)]);
ylim([0, 1]);
legend({'protrusion','retraction'});
xlabel('V');
set(gca, 'LineWidth', 2);
title('volume factor');
saveas(fig, fullfile(save_fold, 'weigthts_plot.png'));
% close(fig);
fig = figure('Position', [50 50 800 800]);
for j = 1:numt
%protrude-retract
if mod(j, mov_T) == 0
[Im, Cs, C, Is, I, Rs, R] = protrude_extrapolate_diff_model3(Im, Cs, C, Is, I, Rs, R, F3, g, k, V0, alpha_V, beta_V, gamma_V, A_act, alpha_A, beta_A, gamma_A);
[Im, Cs, C, Is, I, Rs, R] = retract_reduce_diff_model3(Im, Cs, C, Is, I, Rs, R, F3, g, k, V0, alpha_V, beta_V, gamma_V, A_act, alpha_A, beta_A, gamma_A);
Im_L = return_frame_to_canvas(Im, S, i_start, i_end, j_start, j_end);
Rs_L = return_frame_to_canvas(Rs, S, i_start, i_end, j_start, j_end);
R_L = return_frame_to_canvas(R, S, i_start, i_end, j_start, j_end);
Is_L = return_frame_to_canvas(Is, S, i_start, i_end, j_start, j_end);
I_L = return_frame_to_canvas(I, S, i_start, i_end, j_start, j_end);
Cs_L = return_frame_to_canvas(Cs, S, i_start, i_end, j_start, j_end);
C_L = return_frame_to_canvas(C, S, i_start, i_end, j_start, j_end);
[Im, i_start, i_end, j_start, j_end] = crop_frame(Im_L, crop_d);
Cs = Cs_L(i_start:i_end, j_start:j_end);
C = C_L(i_start:i_end, j_start:j_end);
Is = Is_L(i_start:i_end, j_start:j_end);
I = I_L(i_start:i_end, j_start:j_end);
Rs = Rs_L(i_start:i_end, j_start:j_end);
R = R_L(i_start:i_end, j_start:j_end);
U = U_matrix(Im);
Im_outline = outline_8p(~Im_L);
K1_L = K1_basal*ones(size(Im_L));
K1_L(Im_outline==1) = K1_edge;
K1 = K1_L(i_start:i_end, j_start:j_end);
K5_L = K5_basal*ones(size(Im_L));
K5_L(Im_outline==1) = K5_edge;
K5 = K5_L(i_start:i_end, j_start:j_end);
im1 = Rs;
im1(Im==1) = (im1(Im==1)-min(im1(Im==1)))/(max(im1(Im==1))-min(im1(Im==1)));
im2 = Cs;
im2(Im==1) = (im2(Im==1)-min(im2(Im==1)))/(max(im2(Im==1))-min(im2(Im==1)));
clf;
subplot(2,2,1);
hold on;
colormap hot;
axis ij;
axis off;
axis equal;
imagesc(Rs);
colorbar;
title('Rs');
subplot(2,2,2);
hold on;
colormap hot;
axis ij;
axis off;
axis equal;
imagesc(im1);
colorbar;
title('Rs scaled');
subplot(2,2,3);
hold on;
colormap hot;
axis ij;
axis off;
axis equal;
imagesc(Cs);
colorbar;
title('Cs');
subplot(2,2,4);
hold on;
colormap hot;
axis ij;
axis off;
axis equal;
imagesc(im2);
colorbar;
title('Cs scaled');
drawnow;
end
%diffuse with noise
for i = 1:sub_iter_N
noise_C = randn(size(Cs))*n_alf;
noise_I = randn(size(Is))*n_alf;
noise_R = randn(size(Rs))*n_alf;
Cs_new = Cs + (DCs*laplacian_DT(Cs,dx,U) + noise_C)*dt;
Cs_new(Im==0)=0;
Cs_neg = Cs_new;
Cs_neg(Cs_neg > 0) = 0;
Cs_new(Cs_new < 0) = 0;
C_new = C + (DC*laplacian_DT(C,dx,U) - noise_C)*dt;
C_new(Im==0)=0;
C_neg = C_new;
C_neg(C_neg > 0) = 0;
C_new(C_new < 0) = 0;
Cs = Cs_new + C_neg;
C = C_new + Cs_neg;
Is_new = Is + (DIs*laplacian_DT(Is,dx,U) + noise_I)*dt;
Is_new(Im==0)=0;
Is_neg = Is_new;
Is_neg(Is_neg > 0) = 0;
Is_new(Is_new < 0) = 0;
I_new = I + (DI*laplacian_DT(I,dx,U) - noise_I)*dt;
I_new(Im==0)=0;
I_neg = I_new;
I_neg(I_neg > 0) = 0;
I_new(I_new < 0) = 0;
Is = Is_new + I_neg;
I = I_new + Is_neg;
Rs_new = Rs + (DRs*laplacian_DT(Rs,dx,U) + noise_R)*dt;
Rs_new(Im==0)=0;
Rs_neg = Rs_new;
Rs_neg(Rs_neg > 0) = 0;
Rs_new(Rs_new < 0) = 0;
R_new = R + (DR*laplacian_DT(R,dx,U) - noise_R)*dt;
R_new(Im==0)=0;
R_neg = R_new;
R_neg(R_neg > 0) = 0;
R_new(R_new < 0) = 0;
Rs = Rs_new + R_neg;
R = R_new + Rs_neg;
end
%react
for i = 1:sub_iter_N
F1 = (k1 + gamma1*Cs.^n1./(K1.^n1+beta1*Is.^n1+Cs.^n1)).*C - k2.*Cs;
F2 = (k3 + gamma3*Cs.^n3).*I-k4.*Is;
F3 = (k5 + (gamma5+alpha5*Cs.^n5).*Rs.^n5./(K5.^n5+Rs.^n5)).*R-k6.*Rs;
Cs = Cs + F1*dt;
C = C - F1*dt;
Is = Is + F2*dt;
I = I - F2*dt;
Rs = Rs + F3*dt;
R = R - F3*dt;
end
%save
if mod(j, save_T) == 0
disp(j/save_T);
imwrite(Cs, fullfile(save_fold, 'Cs_L', strcat(num2str(j/save_T), '.tif')));
imwrite(Rs, fullfile(save_fold, 'Rs_L', strcat(num2str(j/save_T), '.tif')));
save(fullfile(save_fold, 'mat', strcat(num2str(j/save_T), '.mat')), ...
'Cs_L', 'C_L', 'Is_L', 'I_L', 'Rs_L', 'R_L', 'Im_L');
saveas(fig, fullfile(save_fold, 'colored', strcat(num2str(j/save_T), '.png')));
end
end