|
8 | 8 | importos |
9 | 9 |
|
10 | 10 | importnumpyasnp |
11 | | -importmatplotlib.pyplotasmpl |
| 11 | +importmatplotlib.pyplotasplt |
12 | 12 | fromscipy.integrateimportodeint |
13 | 13 | fromcontrolimportphase_plot,box_grid |
14 | 14 |
|
15 | 15 | # Simple model of a genetic switch |
16 | | -# |
| 16 | + |
17 | 17 | # This function implements the basic model of the genetic switch |
18 | 18 | # Parameters taken from Gardner, Cantor and Collins, Nature, 2000 |
19 | 19 | defgenswitch(y,t,mu=4,n=2): |
20 | | -return(mu/(1+y[1]**n)-y[0],mu/(1+y[0]**n)-y[1]) |
| 20 | +returnmu/(1+y[1]**n)-y[0],mu/(1+y[0]**n)-y[1] |
21 | 21 |
|
22 | 22 | # Run a simulation from an initial condition |
23 | 23 | tim1=np.linspace(0,10,100) |
24 | 24 | sol1=odeint(genswitch, [1,5],tim1) |
25 | 25 |
|
26 | | -# Extract theequlibirum points |
27 | | -mu=4;n=2;# switch parameters |
28 | | -eqpt=np.empty(3); |
29 | | -eqpt[0]=sol1[0,-1] |
30 | | -eqpt[1]=sol1[1,-1] |
31 | | -eqpt[2]=0;# fzero(@(x) mu/(1+x^2) - x, 2); |
| 26 | +# Extract theequilibrium points |
| 27 | +mu=4;n=2# switch parameters |
| 28 | +eqpt=np.empty(3) |
| 29 | +eqpt[0]=sol1[0,-1] |
| 30 | +eqpt[1]=sol1[1,-1] |
| 31 | +eqpt[2]=0# fzero(@(x) mu/(1+x^2) - x, 2) |
32 | 32 |
|
33 | 33 | # Run another simulation showing switching behavior |
34 | | -tim2=np.linspace(11,25,100); |
35 | | -sol2=odeint(genswitch,sol1[-1,:]+ [2,-2],tim2) |
| 34 | +tim2=np.linspace(11,25,100) |
| 35 | +sol2=odeint(genswitch,sol1[-1,:]+ [2,-2],tim2) |
36 | 36 |
|
37 | 37 | # First plot out the curves that define the equilibria |
38 | 38 | u=np.linspace(0,4.5,46) |
39 | | -f=np.divide(mu, (1+u**n))# mu /(1 + u^n),elementwise |
| 39 | +f=np.divide(mu, (1+u**n))# mu/(1 + u^n),element-wise |
40 | 40 |
|
41 | | -mpl.figure(1);mpl.clf(); |
42 | | -mpl.axis([0,5,0,5]);# box on; |
43 | | -mpl.plot(u,f,'-',f,u,'--')# 'LineWidth', AM_data_linewidth); |
44 | | -mpl.legend(('z1, f(z1)','z2, f(z2)'))# legend(lgh, 'boxoff'); |
45 | | -mpl.plot([0,3], [0,3],'k-')# 'LineWidth', AM_ref_linewidth); |
46 | | -mpl.plot(eqpt[0],eqpt[1],'k.',eqpt[1],eqpt[0],'k.', |
47 | | -eqpt[2],eqpt[2],'k.')# 'MarkerSize', AM_data_markersize*3); |
48 | | -mpl.xlabel('z1, f(z2)'); |
49 | | -mpl.ylabel('z2, f(z1)'); |
| 41 | +plt.figure(1);plt.clf() |
| 42 | +plt.axis([0,5,0,5])# box on; |
| 43 | +plt.plot(u,f,'-',f,u,'--')# 'LineWidth', AM_data_linewidth) |
| 44 | +plt.legend(('z1, f(z1)','z2, f(z2)'))# legend(lgh, 'boxoff') |
| 45 | +plt.plot([0,3], [0,3],'k-')# 'LineWidth', AM_ref_linewidth) |
| 46 | +plt.plot(eqpt[0],eqpt[1],'k.',eqpt[1],eqpt[0],'k.', |
| 47 | +eqpt[2],eqpt[2],'k.')# 'MarkerSize', AM_data_markersize*3) |
| 48 | +plt.xlabel('z1, f(z2)') |
| 49 | +plt.ylabel('z2, f(z1)') |
50 | 50 |
|
51 | 51 | # Time traces |
52 | | -mpl.figure(3);mpl.clf();# subplot(221); |
53 | | -mpl.plot(tim1,sol1[:,0],'b-',tim1,sol1[:,1],'g--'); |
54 | | -# set(pl, 'LineWidth', AM_data_linewidth); |
55 | | -mpl.plot([tim1[-1],tim1[-1]+1], |
56 | | - [sol1[-1,0],sol2[0,1]],'ko:', |
57 | | - [tim1[-1],tim1[-1]+1], [sol1[-1,1],sol2[0,0]],'ko:'); |
58 | | -# set(pl, 'LineWidth', AM_data_linewidth, 'MarkerSize', AM_data_markersize); |
59 | | -mpl.plot(tim2,sol2[:,0],'b-',tim2,sol2[:,1],'g--'); |
60 | | -# set(pl, 'LineWidth', AM_data_linewidth); |
61 | | -mpl.axis([0,25,0,5]); |
| 52 | +plt.figure(3);plt.clf()# subplot(221) |
| 53 | +plt.plot(tim1,sol1[:,0],'b-',tim1,sol1[:,1],'g--') |
| 54 | +# set(pl, 'LineWidth', AM_data_linewidth) |
| 55 | +plt.plot([tim1[-1],tim1[-1]+1], |
| 56 | + [sol1[-1,0],sol2[0,1]],'ko:', |
| 57 | + [tim1[-1],tim1[-1]+1], [sol1[-1,1],sol2[0,0]],'ko:') |
| 58 | +# set(pl, 'LineWidth', AM_data_linewidth, 'MarkerSize', AM_data_markersize) |
| 59 | +plt.plot(tim2,sol2[:,0],'b-',tim2,sol2[:,1],'g--') |
| 60 | +# set(pl, 'LineWidth', AM_data_linewidth) |
| 61 | +plt.axis([0,25,0,5]) |
62 | 62 |
|
63 | | -mpl.xlabel('Time {\itt} [scaled]'); |
64 | | -mpl.ylabel('Protein concentrations [scaled]'); |
65 | | -mpl.legend(('z1 (A)','z2 (B)'))# 'Orientation', 'horizontal'); |
66 | | -# legend(legh, 'boxoff'); |
| 63 | +plt.xlabel('Time {\itt} [scaled]') |
| 64 | +plt.ylabel('Protein concentrations [scaled]') |
| 65 | +plt.legend(('z1 (A)','z2 (B)'))# 'Orientation', 'horizontal') |
| 66 | +# legend(legh, 'boxoff') |
67 | 67 |
|
68 | 68 | # Phase portrait |
69 | | -mpl.figure(2);mpl.clf();# subplot(221); |
70 | | -mpl.axis([0,5,0,5]);# set(gca, 'DataAspectRatio', [1, 1, 1]); |
71 | | -phase_plot(genswitch,X0=box_grid([0,5,6], [0,5,6]),T=10, |
72 | | -timepts= [0.2,0.6,1.2]) |
| 69 | +plt.figure(2) |
| 70 | +plt.clf()# subplot(221) |
| 71 | +plt.axis([0,5,0,5])# set(gca, 'DataAspectRatio', [1, 1, 1]) |
| 72 | +phase_plot(genswitch,X0=box_grid([0,5,6], [0,5,6]),T=10, |
| 73 | +timepts=[0.2,0.6,1.2]) |
73 | 74 |
|
74 | 75 | # Add the stable equilibrium points |
75 | | -mpl.plot(eqpt[0],eqpt[1],'k.',eqpt[1],eqpt[0],'k.', |
76 | | -eqpt[2],eqpt[2],'k.')# 'MarkerSize', AM_data_markersize*3); |
| 76 | +plt.plot(eqpt[0],eqpt[1],'k.',eqpt[1],eqpt[0],'k.', |
| 77 | +eqpt[2],eqpt[2],'k.')# 'MarkerSize', AM_data_markersize*3) |
77 | 78 |
|
78 | | -mpl.xlabel('Protein A [scaled]'); |
79 | | -mpl.ylabel('Protein B [scaled]');# 'Rotation', 90); |
| 79 | +plt.xlabel('Protein A [scaled]') |
| 80 | +plt.ylabel('Protein B [scaled]')# 'Rotation', 90) |
80 | 81 |
|
81 | 82 | if'PYCONTROL_TEST_EXAMPLES'notinos.environ: |
82 | | -mpl.show() |
| 83 | +plt.show() |