Team:Harvard/Model Code
Curli Production Pathway¶
Import Libraries¶
In [1]:
from scipy.integrate import odeint
from scipy.integrate import ode
import numpy as np
import pandas as pd
import math
import plotly
#plotly.tools.set_credentials_file(username='hseo', api_key='itWYwnbNw3y7G8D3O65P')
import plotly.graph_objs as go
import plotly.figure_factory as ff
import plotly.plotly as py
import matplotlib.pyplot as plt
Define Parameters¶
In [2]:
### TIME INTERVAL
tmin = 0
tmax = 60
tint = 1
t = np.arange(tmin, tmax, tint)
### CONSTANTS
# Transcription
alpha1 = 0.0921 # csgA (seq/sec)
alpha2 = 0.0214 # csgBCEFG (seq/sec)
alpha = 0.0146 #csgBACEFG (seq/sec)
# mRNA Degradation
half_life = 408 # seconds
zeta = math.log(2)/half_life
# Translation
beta0 = 0.05 # (protein/sec)
brange = np.arange(0.0, 2.1, 0.4)
beta = beta0 * brange
# Periplasmic Export
gamma1 = 0.25 # uM^(-4)sec^(-1)
gamma1d = 0.025 # sec^(-1)
gamma2 = 0.0085 # uM^(-4)sec^(-1)
gamma3 = 1.00 # sec^(-1)
# Extracellular Secretion
delta1 = 0.76
delta1d = 28e-3 # s^-1
delta3 = 0.76
delta3d = 28e-3 # s^-1
delta4 = 0.0384 # uM^(-1)sec^(-1)
delta4d = 0.76 # also try 0.0385 ????? (homotetramer formation or dimerization?)
delta5 = 0.25 # uM^(-4)sec^(-1)
# Diffusion
N_A = 6.022e23
omega = 10e-9
D = 1e-10
SA = 4.42e-12
# Aggregation / Polymerization
epsilon1 = 1.038e-8 # s^(-1)uM^(-1)
epsilon1d = 2.805e-9 # s^(-1)uM^(-1)
epsilon2 = 0.764 # s^(-1)uM^(-1)
epsilon2d = 5.111e-4 # s^(-1)uM^(-1)
Define Initial Conditions¶
In [3]:
g_csgA_0 = 71.4e-8 # uM
g_csgBCEFG_0 = 71.4e-8 # uM
mRNA_csgA_0 = 0.0
mRNA_csgBCEFG_0 = 0.0
csgA_cyt_0 = 0.0
secBcsgA_0 = 0.0
secABYEGcsgA_0 = 0.0
F_cyt_0 = 0.0
csgB_cyt_0 = 0.0
secBcsgB_0 = 0.0
secABYEGcsgB_0 = 0.0
csgC_cyt_0 = 0.0
secBcsgC_0 = 0.0
secABYEGcsgC_0 = 0.0
csgE_cyt_0 = 0.0
secBcsgE_0 = 0.0
secABYEGcsgE_0 = 0.0
csgF_cyt_0 = 0.0
secBcsgF_0 = 0.0
secABYEGcsgF_0 = 0.0
csgG_cyt_0 = 0.0
secBcsgG_0 = 0.0
secABYEGcsgG_0 = 0.0
SecB_0 = 0.4 # uM
SecA_0 = 0.2
SecYEG_0 = 0.2
csgG_9_0 = 0.0
csgE_9_0 = 0.0
csgGEF_0 = 0.0
csgA_per_0 = 0.0
F_per_0 = 0.0
csgB_per_0 = 0.0
csgC_per_0 = 0.0
csgCcsgA_0 = 0.0
csgCcsgB_0 = 0.0
csgE_per_0 = 0.0
csgF_per_0 = 0.0
csgG_per_0 = 0.0
csgF_ECM_0 = 0.0
csgA_ECM_0 = 0.0
F_ECM_0 = 0.0
csgB_ECM_0 = 0.0
state_0 = [g_csgA_0, g_csgBCEFG_0, mRNA_csgA_0, mRNA_csgBCEFG_0, csgA_cyt_0, secBcsgA_0,
secABYEGcsgA_0, F_cyt_0, csgB_cyt_0, secBcsgB_0, secABYEGcsgB_0, csgC_cyt_0,
secBcsgC_0, secABYEGcsgC_0, csgE_cyt_0, secBcsgE_0, secABYEGcsgE_0, csgF_cyt_0,
secBcsgF_0, secABYEGcsgF_0, csgG_cyt_0, secBcsgG_0, secABYEGcsgG_0, SecB_0, SecA_0,
SecYEG_0, csgG_9_0, csgE_9_0, csgGEF_0, csgA_per_0, F_per_0, csgB_per_0, csgC_per_0,
csgCcsgA_0, csgCcsgB_0, csgE_per_0, csgF_per_0, csgG_per_0, csgF_ECM_0, csgA_ECM_0,
F_ECM_0, csgB_ECM_0]
ODE Solver¶
In [4]:
def CsgPathway(state, t, beta1, beta2, beta3, beta4, beta5, beta6):
# unpack state vector
g_csgA, g_csgBCEFG, mRNA_csgA, mRNA_csgBCEFG,csgA_cyt, secBcsgA, secABYEGcsgA, F_cyt, csgB_cyt, secBcsgB, secABYEGcsgB, csgC_cyt, secBcsgC, secABYEGcsgC, csgE_cyt, secBcsgE, secABYEGcsgE, csgF_cyt, secBcsgF, secABYEGcsgF, csgG_cyt, secBcsgG, secABYEGcsgG, secB, secA, secYEG, csgE_9, csgG_9, csgGEF, csgA_per, F_per, csgB_per, csgC_per, csgCcsgA, csgCcsgB, csgE_per, csgF_per, csgG_per, csgF_ECM, csgA_ECM, F_ECM, csgB_ECM = state
# compute derivatives
dmRNA_csgA = (alpha1 * g_csgA) - (zeta1 * mRNA_csgA)
dmRNA_csgBCEFG = (alpha2 * g_csgBCEFG) - (zeta2 * mRNA_csgBCEFG)
dcsgA_cyt = (beta1 * mRNA_csgA) - (gamma1 * csgA_cyt * (secB ** 4)) + (gamma1d * secBcsgA) - (epsilon1 * (csgA_cyt ** 2)) + (epsilon1d * F_cyt) - (epsilon2 * F_cyt * csgA_cyt) + (epsilon2d * F_cyt)
dsecBcsgA = (gamma1 * csgA_cyt * (secB **4)) - (gamma1d * secBcsgA) - (gamma2 * secBcsgA * (secA ** 2) * (secYEG ** 2))
dsecABYEGcsgA = (gamma2 * secBcsgA * (secA ** 2) * (secYEG ** 2)) - (gamma3 * secABYEGcsgA)
dF_cyt = (epsilon1 * (csgA_cyt ** 2)) - (epsilon1d * F_cyt)
dcsgB_cyt = (beta2 * mRNA_csgBCEFG) - (gamma1 * csgB_cyt * (secB ** 4)) + (gamma1d * secBcsgB)
dsecBcsgB = (gamma1 * csgB_cyt * (secB **4)) - (gamma1d * secBcsgB) - (gamma2 * secBcsgB * (secA ** 2) * (secYEG ** 2))
dsecABYEGcsgB = (gamma2 * secBcsgB * (secA ** 2) * (secYEG ** 2)) - (gamma3 * secABYEGcsgB)
dcsgC_cyt = (beta3 * mRNA_csgBCEFG) - (gamma1 * csgC_cyt * (secB ** 4)) + (gamma1d * secBcsgC)
dsecBcsgC = (gamma1 * csgC_cyt * (secB **4)) - (gamma1d * secBcsgB) - (gamma2 * secBcsgB * (secA ** 2) * (secYEG ** 2))
dsecABYEGcsgC = (gamma2 * secBcsgC * (secA ** 2) * (secYEG ** 2)) - (gamma3 * secABYEGcsgC)
dcsgE_cyt = (beta4 * mRNA_csgBCEFG) - (gamma1 * csgE_cyt * (secB ** 4)) + (gamma1d * secBcsgE)
dsecBcsgE = (gamma1 * csgE_cyt * (secB **4)) - (gamma1d * secBcsgE) - (gamma2 * secBcsgE * (secA ** 2) * (secYEG ** 2))
dsecABYEGcsgE = (gamma2 * secBcsgE * (secA ** 2) * (secYEG ** 2)) - (gamma3 * secABYEGcsgE)
dcsgF_cyt = (beta5 * mRNA_csgBCEFG) - (gamma1 * csgF_cyt * (secB ** 4)) + (gamma1d * secBcsgF)
dsecBcsgF = (gamma1 * csgF_cyt * (secB **4)) - (gamma1d * secBcsgF) - (gamma2 * secBcsgF * (secA ** 2) * (secYEG ** 2))
dsecABYEGcsgF = (gamma2 * secBcsgF * (secA ** 2) * (secYEG ** 2)) - (gamma3 * secABYEGcsgF)
dcsgG_cyt = (beta6 * mRNA_csgBCEFG) - (gamma1 * csgG_cyt * (secB ** 4)) + (gamma1d * secBcsgB)
dsecBcsgG = (gamma1 * csgG_cyt * (secB **4)) - (gamma1d * secBcsgG) - (gamma2 * secBcsgG * (secA ** 2) * (secYEG ** 2))
dsecABYEGcsgG = (gamma2 * secBcsgG * (secA ** 2) * (secYEG ** 2)) - (gamma3 * secABYEGcsgG)
dsecB = (gamma3 * (secABYEGcsgA + secABYEGcsgB + secABYEGcsgC + secABYEGcsgE + secABYEGcsgF + secABYEGcsgG)) - (gamma1 * (secB ** 4) * (csgA_cyt + csgB_cyt + csgC_cyt + csgE_cyt + csgF_cyt + csgG_cyt)) + (gamma1d * (secBcsgA + secBcsgB + secBcsgC + secBcsgE + secBcsgF + secBcsgG))
dsecA = (gamma3 * (secABYEGcsgA + secABYEGcsgB + secABYEGcsgC + secABYEGcsgE + secABYEGcsgF + secABYEGcsgG)) - (gamma2 * (secA ** 2) * (secYEG ** 2) * (secBcsgA + secBcsgB + secBcsgC + secBcsgE + secBcsgF + secBcsgG))
dsecYEG = (gamma3 * (secABYEGcsgA + secABYEGcsgB + secABYEGcsgC + secABYEGcsgE + secABYEGcsgF + secABYEGcsgG)) - (gamma2 * (secA ** 2) * (secYEG ** 2) * (secBcsgA + secBcsgB + secBcsgC + secBcsgE + secBcsgF + secBcsgG))
dcsgE_9 = (delta1 * (csgE_per ** 9)) - (delta1d * csgE_9)
dcsgG_9 = (delta3 * (csgG_per ** 9)) - (delta3d * csgG_9) - (delta4 * csgE_9 * (csgF_ECM ** 2) * csgG_9) + (delta4d * csgGEF)
dcsgGEF = (delta4 * csgE_9 * (csgF_ECM ** 2) * csgG_9) - (delta4d * csgGEF)
dcsgA_per = (gamma3 * secABYEGcsgA) - (delta5 * csgA_per * csgC_per) - (epsilon1 * (csgA_per ** 2)) + (epsilon1d * F_per) - (epsilon2 * F_per * csgA_per) + (epsilon2d * F_per)
dF_per = (epsilon1 * (csgA_per ** 2)) - (epsilon1d * F_per)
dcsgB_per = (gamma3 * secABYEGcsgB) - (delta5 * csgB_per * csgC_per)
dcsgC_per = (gamma3 * secABYEGcsgC) - (delta5 * csgA_per * csgC_per) - (delta5 * csgB_per * csgC_per) + (D * ((csgCcsgA - csgA_ECM) * 1e-3 / omega) * SA * N_A) + (D * ((csgCcsgB - csgB_ECM) * 1e-3 / omega) * SA * N_A)
dcsgCcsgA = (delta5 * csgA_per * csgC_per) - (D * ((csgCcsgA - csgA_ECM) * 1e-3 / omega))
dcsgCcsgB = (delta5 * csgB_per * csgC_per) - (D * ((csgCcsgB - csgB_ECM) * 1e-3 / omega))
dcsgE_per = (gamma3 * secABYEGcsgE)
dcsgF_per = (gamma3 * secABYEGcsgF) - D * ((csgF_per - csgF_ECM) * 1e-3 / omega) * SA * N_A
dcsgG_per = (gamma3 * secABYEGcsgF) - (delta3 * (csgG_per ** 9))
dcsgF_ECM = D * ((csgF_per - csgF_ECM) * 1e-3 / omega) * SA * N_A
dcsgA_ECM = (D * ((csgCcsgA - csgA_ECM) * 1e-3 / omega) * SA * N_A) - (epsilon1 * (csgA_cyt ** 2)) + (epsilon1d * F_cyt) - (epsilon2 * F_cyt * csgA_cyt) + (epsilon2d * F_cyt)
dF_ECM = (epsilon1 * (csgA_ECM ** 2)) - (epsilon1d * F_ECM)
dcsgB_ECM = D * ((csgCcsgB - csgB_ECM) * 1e-3 / omega) * SA * N_A
# return derivatives
derivatives = [g_csgA, g_csgBCEFG, dmRNA_csgA, dmRNA_csgBCEFG, dcsgA_cyt, dsecBcsgA, dsecABYEGcsgA, dF_cyt, dcsgB_cyt,
dsecBcsgB, dsecABYEGcsgB, dcsgC_cyt, dsecBcsgC, dsecABYEGcsgC, dcsgE_cyt,
dsecBcsgE, dsecABYEGcsgE, dcsgF_cyt, dsecBcsgF, dsecABYEGcsgF, dcsgG_cyt, dsecBcsgG,
dsecABYEGcsgG, dsecB, dsecA, dsecYEG, dcsgE_9, dcsgG_9, dcsgGEF, dcsgA_per, dF_per,
dcsgB_per, dcsgC_per, dcsgCcsgA, dcsgCcsgB, dcsgE_per, dcsgF_per, dcsgG_per,
dcsgF_ECM, dcsgA_ECM, dF_ECM, dcsgB_ECM]
derivatives_array = np.array(derivatives)
np.putmask(derivatives_array, derivatives_array < np.array([0]*42), 0)
return derivatives_array
Run Simulation¶
In [5]:
results = pd.DataFrame(np.zeros((np.size(brange), 40)))
for i in range(len(beta)):
tmp = odeint(CsgPathway, state_0, t, mxstep=1000000, args=(1, 1, 1, 1, 1, beta[i]))
tmp_df = pd.DataFrame(tmp)
results.iloc[i,:] = tmp_df.iloc[-1, :]
