# This worksheet generates Figure 10.3 of "Computational Cell Biology" by Fall et al.consts:={k1=0.04,k2p=0.04,k2pp=1,k2ppp=1,k3p=1,k3pp=10,k4p=2,k4=35,J3=0.04,J4=0.04,k5p=0.005,k5pp=0.2,k6=0.1,J5=0.3,n=4,mu=0.01,mstar=10};

NiM+SSdjb25zdHNHNiI8My9JJmsycHBwR0YlIiIiL0kjazFHRiUkIiIlISIjL0kkazJwR0YlRiwvSSVrMnBwR0YlRikvSSRrM3BHRiVGKS9JJWszcHBHRiUiIzUvSSRrNHBHRiUiIiMvSSNrNEdGJSIjTi9JI0ozR0YlRiwvSSNKNEdGJUYsL0kkazVwR0YlJCIiJiEiJC9JJWs1cHBHRiUkRjohIiIvSSNrNkdGJSRGKUZKL0kjSjVHRiUkIiIkRkovSSJuR0YlRi0vSSNtdUdGJSRGKUYuL0kmbXN0YXJHRiVGNw==

deqX:=diff(X(t),t)=k1-(k2p+k2pp*Y(t))*X(t);

NiM+SSVkZXFYRzYiLy1JJWRpZmZHSSpwcm90ZWN0ZWRHRik2JC1JIlhHRiU2I0kidEdGJUYuLCZJI2sxR0YlIiIiKiYsJkkkazJwR0YlRjEqJkklazJwcEdGJUYxLUkiWUdGJUYtRjFGMUYxRitGMSEiIg==

deqY:=diff(Y(t),t)=((k3p+k3pp*A(t))*(1-Y(t))/(J3+1-Y(t)))-(k4*m(t)*X(t)*Y(t))/(J4+Y(t));

NiM+SSVkZXFZRzYiLy1JJWRpZmZHSSpwcm90ZWN0ZWRHRik2JC1JIllHRiU2I0kidEdGJUYuLCYqKCwmSSRrM3BHRiUiIiIqJkklazNwcEdGJUYzLUkiQUdGJUYtRjNGM0YzLCZGM0YzRishIiJGMywoSSNKM0dGJUYzRjNGM0YrRjlGOUYzKixJI2s0R0YlRjMtSSJtR0YlRi1GMy1JIlhHRiVGLUYzRitGMywmSSNKNEdGJUYzRitGM0Y5Rjk=

nullX:=solve(rhs(deqX)=0,X(t));

NiM+SSZudWxsWEc2IiomSSNrMUdGJSIiIiwmSSRrMnBHRiVGKComSSVrMnBwR0YlRigtSSJZR0YlNiNJInRHRiVGKEYoISIi

simplify(subs({k1=beta*k2pp,k2p=J2*k2pp,A(t)=0},nullX));

NiMqJkklYmV0YUc2IiIiIiwmSSNKMkdGJUYmLUkiWUdGJTYjSSJ0R0YlRiYhIiI=

nullY:=solve(rhs(deqY)=0,X(t));

NiM+SSZudWxsWUc2IiwkKiwsMiomSSRrM3BHRiUiIiJJI0o0R0YlRishIiIqJkYqRistSSJZR0YlNiNJInRHRiVGK0YtKihGKkYrRi9GK0YsRitGKyomRipGK0YvIiIjRisqKEklazNwcEdGJUYrLUkiQUdGJUYxRitGLEYrRi0qKEY3RitGOEYrRi9GK0YtKipGN0YrRjhGK0YvRitGLEYrRisqKEY3RitGOEYrRi9GNUYrRitJI2s0R0YlRi0tSSJtR0YlRjFGLUYvRi0sKEkjSjNHRiVGK0YrRitGL0YtRi1GLQ==

factor(simplify(subs({A(t)=0,k3p=p*k4*m(t)},nullY)));

NiMsJCosSSJwRzYiIiIiLCYhIiJGJy1JIllHRiY2I0kidEdGJkYnRicsJkkjSjRHRiZGJ0YqRidGJ0YqRiksKEkjSjNHRiZGJ0YnRidGKkYpRilGKQ==

pnullX:=subs({A(t)=0} union consts,nullX);

NiM+SSdwbnVsbFhHNiIsJCokLCYkIiIlISIjIiIiLUkiWUdGJTYjSSJ0R0YlRiwhIiJGKQ==

pnullY:=subs({A(t)=0} union consts,nullY);

NiM+SSdwbnVsbFlHNiIsJCoqLCgkISIlISIjIiIiLUkiWUdGJTYjSSJ0R0YlJCEjJypGKyokRi0iIiNGLEYsLUkibUdGJUYvISIiRi1GNywmJCIkLyJGK0YsRi1GN0Y3I0Y3IiNO

pnullYm3:=subs(m(t)=0.3,pnullY);

NiM+SSlwbnVsbFltM0c2IiwkKigsKCQhIiUhIiMiIiItSSJZR0YlNiNJInRHRiUkISMnKkYrKiRGLSIiI0YsRixGLSEiIiwmJCIkLyJGK0YsRi1GNUY1JCErQiY0UV8qISM2

pnullYm6:=subs(m(t)=0.6,pnullY);

NiM+SSlwbnVsbFltNkc2IiwkKigsKCQhIiUhIiMiIiItSSJZR0YlNiNJInRHRiUkISMnKkYrKiRGLSIiI0YsRixGLSEiIiwmJCIkLyJGK0YsRi1GNUY1JCEralohPnclISM2

with(plots):plot([pnullYm6,pnullYm3,pnullX],Y=0..1,X=0.01..1,thickness=5);

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

#now solve for Y as a function of X so that we can do semilog plot like in Figure 10.3subsdeqX:=subs({A(t)=0} union consts,deqX):nullX2:=solve(rhs(subsdeqX)=0,Y(t)):subsdeqY:=subs({A(t)=0} union consts,deqY):nullY2:=solve(rhs(subsdeqY)=0,Y(t)):nullY2m3:=subs(m(t)=0.3,nullY2[2]):nullY2m6:=subs(m(t)=0.6,nullY2[2]):semilogplot([nullY2m6,nullY2m3,nullX2],X=0.01..10,Y=0..1,thickness=5);

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RltpbS8kISs0KyV6UiJGLEZbaW0vJCErJyoqSDVJIkYsRltpbS8kITItKysrdls9QSJGamhtRltpbS8kITItKysrJz4hXDoiRmpobUZbaW0vJCErOCsicDQiRixGW2ltLyQhKyJcZGQvIkYsRltpbS8kRi9GW2htUSMuMUZmaG0vJCErVitxKilwRi9GW2ltLyQhK151eUdfRi9GW2ltLyQhKygzKyV6UkYvRltpbS8kIStmKipINUlGL0ZbaW0vJCEyKysrcVwoWz1BISM8RltpbS8kISknPiFcOiEiKUZbaW0vJCExKysrIUgsNXAqRmNbbkZbaW0vJCEqMlxkZCVGL0ZbaW0vRlxobVEjMS5GZmhtLyQiK2QqKkg1SUYvRltpbS8kIitcREByWkYvRltpbS8kIis4KipmP2dGL0ZbaW0vJCIrVCtxKilwRi9GW2ltLyQiKy5EXiJ5KEYvRltpbS8kIikvKTRYKUZnW25GW2ltLyQiMSsrK3IpKiozLipGamhtRltpbS8kIiskNERDYSpGL0ZbaW0vRmlnbVElLjFlMkZmaG0vJCIrJyoqSDVJIkYsRltpbS8kIjItKytdREByWiJGamhtRltpbS8kIjItKys1KipmP2ciRmpobUZbaW0vJCIyLSsrUytxKilwIkZqaG1GW2ltLyQiKkReInk8RmdbbkZbaW0vJCIqLyk0WD1GZ1tuRltpbS8kIjIvKytxKSoqMy4+RmpobUZbaW0vJCIyKysrITREQ2E+RmpobUZbaW0iIiYtJSVGT05URzYjJShERUZBVUxURy0lK0FYRVNMQUJFTFNHNiRRIlhGZmhtUSJZRmZobS0lKlRISUNLTkVTU0c2I0ZiX24tJSVWSUVXRzYkO0ZjaG1GaWdtO0ZcaG1GaWdtLUZkX242JCUqSEVMVkVUSUNBR0ZqZ20=