Commit 16142e59 authored by jeq008-uib's avatar jeq008-uib
Browse files

assignment 37 and 38 added

parent cc165350
%% Cell type:markdown id: tags:
# BIOINF 305. Assignment - week 37.
## Assem Maratova
%% Cell type:markdown id: tags:
**Simulate the dynamics of a feedforward loop (X->Y, Y->Z, X->Z).**
Make the following assumptions:
- The cell expresses numerous copies of protein X. Whenever signal Sx appears or disappears, step-like activation or deactivation of X is triggered (no delay between Sx switching on/off and X becoming activated/deactivated).
- The signal Sy for activation of Y is present throughout the simulation such that all copies of protein Y that are produced immediately become active, Y*=Y.
- The production rate of Y is modelled using an activating or repressing Hill function f(X).
- The production rate of Z is modelled using a product of activating or repressing Hill functions f(X)*g(Y) (AND logic).
%% Cell type:code id: tags:
``` python
import numpy as np
from scipy.integrate import odeint
import matplotlib.pyplot as plt
%matplotlib inline
```
%% Cell type:code id: tags:
``` python
# setting some parameters for plots
plt.style.use('seaborn')
SMALL_SIZE = 12
MEDIUM_SIZE = 16
BIGGER_SIZE = 20
plt.rc('font', size=SMALL_SIZE) # controls default text sizes
plt.rc('axes', titlesize=SMALL_SIZE) # fontsize of the axes title
plt.rc('axes', labelsize=MEDIUM_SIZE) # fontsize of the x and y labels
plt.rc('xtick', labelsize=SMALL_SIZE) # fontsize of the tick labels
plt.rc('ytick', labelsize=SMALL_SIZE) # fontsize of the tick labels
plt.rc('legend', fontsize=SMALL_SIZE) # legend fontsize
plt.rc('figure', titlesize=BIGGER_SIZE) # fontsize of the figure title
plt.rcParams['figure.figsize'] = 10 , 6 # default figure size
```
%% Cell type:code id: tags:
``` python
def Hill_activator(X,K,n):
Xn = np.power(X,n)
Kn = np.power(K,n)
f_X = Xn/((Kn)+Xn)
return f_X
def Hill_repressor(X,K,n):
f_X = 1.0 - Hill_activator(X,K,n)
return f_X
```
%% Cell type:code id: tags:
``` python
def Hill_y_regulator(Y,t,X,B,a,K,n):
return B*Hill_activator(X,K,n)-(a*Y)
def Hill_z_regulator(Z,t,X,Y,B,a,Kxy,Kyz,n):
return B*Hill_activator(X,Kxy,n)*Hill_activator(Y,Kyz,n)-(a*Z)
```
%% Cell type:code id: tags:
``` python
# data for simulation
Bx, ax = 1, 1
By, ay = 1, 1
Bz, az = 1, 1
Kxy, Kyz = 0.5, 0.75
n = 20
D = [5,15,25,28]
time = np.linspace(0,35,100)
signal = 1*((time>D[0])&(time<D[1])) | ((time>D[2])&(time<D[3]))
```
%% Cell type:code id: tags:
``` python
def rate_X_Y(u,t,ax,ay,az,Bx,By,Bz,Kxy,Kyz,n,D):
x,y,z = u
dxdt = step_x(x,t,Bx,ax,D)
if (t<D[0] and t>D[1]) or (t<D[2] and t>D[3]):
x = 0
dydt = Hill_y_regulator(y,t,x,By,ay,Kxy,n)
dzdt = Hill_z_regulator(z,t,x,y,Bz,az,Kxy,Kyz,n)
return [dxdt,dydt,dzdt]
def step_x(X,t,B,a,D):
if (t>D[0] and t<D[1]) or (t>D[2] and t<D[3]):
dxdt = B - (a*X)
else:
dxdt = -(a*X)
return dxdt
```
%% Cell type:code id: tags:
``` python
U1 = odeint(rate_X_Y,[0,0,0],time,
args=(ax,ay,az,Bx,By,Bz,Kxy,Kyz,n,D))
```
%% Cell type:code id: tags:
``` python
fig, (ax1, ax2) = plt.subplots(2, 1, sharex=True)
ax1.step(time,signal)
ax1.set_ylabel('Signal Sx')
ax2.plot(time,U1[:,0],label='X')
ax2.plot(time,U1[:,1],label='Y')
ax2.plot(time,U1[:,2],label='Z')
ax2.set_xlabel('Time')
ax2.set_ylabel('Production')
ax2.legend()
plt.show()
```
%%%% Output: display_data
![](data:image/png;base64,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)
%% Cell type:markdown id: tags:
**Coherent FFL where X and Y are both activators**
- Calculate the temporal profiles of Y and Z following an ON step of Sx (Sx=0 for t<=0 and Sx=1 for t>0).
- Calculate the temporal profiles of Y and Z following an OFF step of Sx (Sx=1 for t<=0 and Sx=0 for t>0).
- Calculate the temporal profiles of Y and Z for pulses of Sx (Sx=0 except for a pulse of duration D). Compare the profiles for pulses of various lengths.
**Incoherent FFL where X is an activator and Y a repressor**
- Calculate the temporal profiles of Y and Z following an ON step of Sx (Sx=0 for t<=0 and Sx=1 for t>0).
- Calculate the temporal profiles of Y and Z following an OFF step of Sx (Sx=1 for t<=0 and Sx=0 for t>0).
%% Cell type:code id: tags:
``` python
def d_x(X,t,b,a,D):
if t<D:
dxdt = b - (a*X)
else:
dxdt = -(a*X)
return dxdt
def d_y(Y,t,X,b,a,D):
if t<D:
dydt = b - (a*Y)
else:
dydt = -(a*Y)
return dydt
def d_z(Z,t,X,Y,b,b_,a,T_,D):
if t<T_:
dzdt = b - (a*Z)
elif (t>T_) and (t<D):
dzdt = b_ - (a*Z)
else:
dzdt = -(a*Z)
return dzdt
```
%% Cell type:code id: tags:
``` python
# additional data for simulation
Bz_ = 0.5
Xst, Yst = Bx/ax, By/ay
Zm, Zst= Bz/az, Bz_/az
T_ = (1/ay)*np.log(1/(1-(Kyz/Yst)))
D = 15
signal = 1*(time>0)&(time<D)
```
%% Cell type:code id: tags:
``` python
def rate_XY_2(u,t,ax,ay,az,Bx,By,Bz,Bz_,T_,D):
def rate_X_Y_2(u,t,ax,ay,az,Bx,By,Bz,Bz_,T_,D):
x,y,z = u
dxdt = d_x(x,t,Bx,ax,D)
dydt = d_y(y,t,x,By,ay,D)
dzdt = d_z(z,t,x,y,Bz,Bz_,az,T_,D)
return [dxdt,dydt,dzdt]
```
%% Cell type:code id: tags:
``` python
U2 = odeint(rate_XY_2,[0,0,0],time,args=(ax,ay,az,Bx,By,Bz,Bz_,T_,D))
U2 = odeint(rate_X_Y_2,[0,0,0],time,args=(ax,ay,az,Bx,By,Bz,Bz_,T_,D))
```
%% Cell type:code id: tags:
``` python
fig, (ax1, ax2) = plt.subplots(2, 1, sharex=False,figsize=(10, 6))
ax1.step(time,signal)
ax1.set_ylabel('Sx')
ax2.plot(time,U2[:,1],label='Y')
ax2.plot(time,U2[:,2],label='Z')
ax2.set_xlabel('Time')
ax2.set_ylabel('Production')
ax2.legend()
plt.show()
```
%%%% Output: display_data
![](data:image/png;base64,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)
%% Cell type:code id: tags:
``` python
```
......
%% Cell type:markdown id: tags:
# BIOINF 305. Assignment - week 38.
## Assem Maratova
%% Cell type:markdown id: tags:
Design and implement the network of interlocked feedforward loops shown in the figure such that the simulated profiles of the output genes in response to switching on X1 reproduce the profiles in the figure.
%% Cell type:markdown id: tags:
<img src="image.jpg" align="center"/>
%% Cell type:code id: tags:
``` python
import numpy as np
from scipy.integrate import odeint
import matplotlib.pyplot as plt
%matplotlib inline
```
%% Cell type:code id: tags:
``` python
# setting some parameters for plots
plt.style.use('seaborn')
SMALL_SIZE = 12
MEDIUM_SIZE = 16
BIGGER_SIZE = 20
plt.rc('font', size=SMALL_SIZE) # controls default text sizes
plt.rc('axes', titlesize=SMALL_SIZE) # fontsize of the axes title
plt.rc('axes', labelsize=MEDIUM_SIZE) # fontsize of the x and y labels
plt.rc('xtick', labelsize=SMALL_SIZE) # fontsize of the tick labels
plt.rc('ytick', labelsize=SMALL_SIZE) # fontsize of the tick labels
plt.rc('legend', fontsize=SMALL_SIZE) # legend fontsize
plt.rc('figure', titlesize=BIGGER_SIZE) # fontsize of the figure title
plt.rcParams['figure.figsize'] = 10 , 6 # default figure size
```
%% Cell type:code id: tags:
``` python
def Hill_activator(X,K,n):
Xn = np.power(X,n)
Kn = np.power(K,n)
f_X = Xn/((Kn)+Xn)
return f_X
def Hill_repressor(X,K,n):
f_X = 1.0 - Hill_activator(X,K,n)
return f_X
```
%% Cell type:code id: tags:
``` python
def Hill_y_regulator(Y,t,X,B,a,K,n):
return B*Hill_activator(X,K,n)-(a*Y)
def Hill_z_regulator(Z,t,X,Y,B,a,K1,K2,n,Y_act):
def Hill_z_regulator(Z,t,X,Y,B,a,Kxy,Kyz,n,Y_act):
if Y_act:
return B*Hill_activator(X,K1,n)*Hill_activator(Y,K2,n)-(a*Z)
return B*Hill_activator(X,Kxy,n)*Hill_activator(Y,Kyz,n)-(a*Z)
else:
return B*Hill_activator(X,K1,n)*Hill_repressor(Y,K2,n)-(a*Z)
return B*Hill_activator(X,Kxy,n)*Hill_repressor(Y,Kyz,n)-(a*Z)
```
%% Cell type:code id: tags:
``` python
def d_x(X,t,B,a):
return B - (a*X)
def rate_Z1_Z2_Z3(u,t,B,a,K,n):
x1, x2, y1, y2, z1, z2, z3 = u
dx1dt = d_x(x1,t,B,a)
dy1dt = Hill_y_regulator(y1,t,x1,B,a,K,n)
dx2dt = Hill_z_regulator(x2,t,x1,y1,B,a,K,K,n,Y_act=True)
dz1dt = Hill_z_regulator(z1,t,x1,y1,B,a,K,K,n,Y_act=False)
dy2dt = Hill_y_regulator(y2,t,x2,B,a,K,n)
dz2dt = Hill_z_regulator(z2,t,x2,y2,B,a,K,K,n,Y_act=False)
dz3dt = Hill_z_regulator(z3,t,x2,y2,B,a,K,K,n,Y_act=True)
return [dx1dt, dx2dt, dy1dt, dy2dt, dz1dt, dz2dt, dz3dt]
```
%% Cell type:code id: tags:
``` python
B, a = 1, 1
K = 0.7
n = 50
time = np.linspace(0,20,100)
U = odeint(rate_Z1_Z2_Z3,[0,0,0,0,0,0,0],time,args=(B,a,K,n))
```
%% Cell type:code id: tags:
``` python
plt.plot(time,U[:,4],label='Z1')
plt.plot(time,U[:,5],label='Z2')
plt.plot(time,U[:,6],label='Z3')
plt.xlabel('Time')
plt.ylabel('Z')
plt.legend()
plt.show()
```
%%%% Output: display_data
![](data:image/png;base64,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)
%% Cell type:code id: tags:
``` python
```
%% Cell type:code id: tags:
``` python
```
......
Markdown is supported
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment