# This worksheet generates Figure 10.4 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=

nullX3:=Y(t)=solve(rhs(deqX)=0,Y(t));

NiM+SSdudWxsWDNHNiIvLUkiWUdGJTYjSSJ0R0YlKigsJkkjazFHRiUiIiIqJi1JIlhHRiVGKUYuSSRrMnBHRiVGLiEiIkYuRjBGM0klazJwcEdGJUYz

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

NiM+SSZudWxsWUc2IiwkKiwsMiomSSRrM3BHRiUiIiJJI0o0R0YlRishIiIqJkYqRistSSJZR0YlNiNJInRHRiVGK0YtKihGKkYrRi9GK0YsRitGKyomRipGK0YvIiIjRisqKEklazNwcEdGJUYrLUkiQUdGJUYxRitGLEYrRi0qKEY3RitGOEYrRi9GK0YtKipGN0YrRjhGK0YvRitGLEYrRisqKEY3RitGOEYrRi9GNUYrRitJI2s0R0YlRi0tSSJtR0YlRjFGLUYvRi0sKEkjSjNHRiVGK0YrRitGL0YtRi1GLQ==

nullY3:=factor(simplify(subs({A(t)=0,k3p=p*k4*m(t)},nullY)));

NiM+SSdudWxsWTNHNiIsJCosSSJwR0YlIiIiLCYhIiJGKS1JIllHRiU2I0kidEdGJUYpRiksJkkjSjRHRiVGKUYsRilGKUYsRissKEkjSjNHRiVGKUYpRilGLEYrRitGKw==

steadysol:=X(t)=subs(nullX3,nullY3);

NiM+SSpzdGVhZHlzb2xHNiIvLUkiWEdGJTYjSSJ0R0YlLCQqMEkicEdGJSIiIiwmISIiRi4qKCwmSSNrMUdGJUYuKiZGJ0YuSSRrMnBHRiVGLkYwRi5GJ0YwSSVrMnBwR0YlRjBGLkYuLCZJI0o0R0YlRi5GMUYuRi5GMkYwRidGLkY2Ri4sKEkjSjNHRiVGLkYuRi5GMUYwRjBGMA==

ssol:=subs(consts,steadysol);

NiM+SSVzc29sRzYiLy1JIlhHRiU2I0kidEdGJSwkKi5JInBHRiUiIiIsJiEiIkYuKiYsJiQiIiUhIiNGLkYnJCEiJUY1Ri5GJ0YwRi5GLiwmRjNGLkYxRi5GLkYyRjBGJ0YuLCYkIiQvIkY1Ri5GMUYwRjBGMA==

psol:=solve(ssol,X(t)):plot([psol[1],psol[2],psol[3]],p=0..0.3,0..1,color=BLACK,thickness=5);

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

psol2:=subs({X(t)=X},solve(ssol,p));

NiM+SSZwc29sMkc2IiwkKihJIlhHRiUiIiIsKEYoJCEjRyIiISRGKUYtRikqJEYoIiIjJCIjRkYtRiksJkYoJCIjRUYtJCEiIkYtRilGN0Y2

plot(psol2,X=0..1,0..0.3,thickness=5);

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