Linear Noise Approximation

This notebook demonstrates how to use Metabolic Control Analysis using basico. We start as always, by importing basico:

[1]:

from IPython.display import display, HTML
from basico import *

now we load BioModel #11

[2]:


dm = load_biomodel(11)
display(HTML(get_notes()))

MAPK cascade in solution (no scaffold)

Description
This model describes a basic 3- stage Mitogen Activated Protein Kinase (MAPK) cascade in solution. This cascade is typically expressed as RAF= =>MEK==>MAPK (alternative forms are K3==>K2==> K1 and KKK==>KK==>K) . The input signal is RAFK (RAF Kinase) and the output signal is MAPKpp ( doubly phosphorylated form of MAPK) . RAFK phosphorylates RAF once to RAFp. RAFp, the phosphorylated form of RAF induces two phoshporylations of MEK, to MEKp and MEKpp. MEKpp, the doubly phosphorylated form of MEK, induces two phosphorylations of MAPK to MAPKp and MAPKpp.
Rate constant       Reaction
a10 = 5. MAPKPH + MAPKpp -> MAPKppMAPKPH
a1 = 1. RAF + RAFK -> RAFRAFK
a2 = 0.5 RAFp + RAFPH -> RAFpRAFPH
a3 = 3.3 MEK + RAFp -> MEKRAFp
a4 = 10. MEKp + MEKPH -> MEKpMEKPH
a5 = 3.3 MEKp + RAFp -> MEKpRAFp
a6 = 10. MEKPH + MEKpp -> MEKppMEKPH
a7 = 20. MAPK + MEKpp -> MAPKMEKpp
a8 = 5. MAPKp + MAPKPH -> MAPKpMAPKPH
a9 = 20. MAPKp + MEKpp -> MAPKpMEKpp
d10 = 0.4 MAPKppMAPKPH -> MAPKPH + MAPKpp
d1 = 0.4 RAFRAFK -> RAF + RAFK
d2 = 0.5 RAFpRAFPH -> RAFp + RAFPH
d3 = 0.42 MEKRAFp -> MEK + RAFp
d4 = 0.8 MEKpMEKPH -> MEKp + MEKPH
d5 = 0.4 MEKpRAFp -> MEKp + RAFp
d6 = 0.8 MEKppMEKPH -> MEKPH + MEKpp
d7 = 0.6 MAPKMEKpp -> MAPK + MEKpp
d8 = 0.4 MAPKpMAPKPH -> MAPKp + MAPKPH
d9 = 0.6 MAPKpMEKpp -> MAPKp + MEKpp
k10 = 0.1 MAPKppMAPKPH -> MAPKp + MAPKPH
k1 = 0.1 RAFRAFK -> RAFK + RAFp
k2 = 0.1 RAFpRAFPH -> RAF + RAFPH
k3 = 0.1 MEKRAFp -> MEKp + RAFp
k4 = 0.1 MEKpMEKPH -> MEK + MEKPH
k5 = 0.1 MEKpRAFp -> MEKpp + RAFp
k6 = 0.1 MEKppMEKPH -> MEKp + MEKPH
k7 = 0.1 MAPKMEKpp -> MAPKp + MEKpp
k8 = 0.1 MAPKpMAPKPH -> MAPK + MAPKPH
k9 = 0.1 MAPKpMEKpp -> MAPKpp + MEKpp
Variable IC   ODE
MAPK 0.3 MAPK'[t] == d7*MAPKMEKpp[t] + k8*MAPKpMAPKPH[t] -  a7*MAPK[t]*MEKpp[t]
MAPKMEKpp 0 MAPKMEKpp'[t] == -(d7*MAPKMEKpp[t]) - k7*MAPKMEKpp[t]  + a7*MAPK[t]*MEKpp[t]
MAPKp 0 MAPKp'[t] == k7*MAPKMEKpp[t] - a8*MAPKp[t]*MAPKPH[t]  + d8*MAPKpMAPKPH[t] + d9*MAPKpMEKpp[t] + k10* MAPKppMAPKPH[t] - a9*MAPKp[t]*MEKpp[t]
MAPKPH 0.3 MAPKPH'[t] == -(a8*MAPKp[t]*MAPKPH[t]) + d8*MAPKpMAPKPH[ t] + k8*MAPKpMAPKPH[t] - a10*MAPKPH[t]*MAPKpp[t] +  d10*MAPKppMAPKPH[t] + k10*MAPKppMAPKPH[t]
MAPKpMAPKPH 0 MAPKpMAPKPH'[t] == a8*MAPKp[t]*MAPKPH[t] - d8* MAPKpMAPKPH[t] - k8*MAPKpMAPKPH[t]
MAPKpMEKpp 0 MAPKpMEKpp'[t] == -(d9*MAPKpMEKpp[t]) - k9*MAPKpMEKpp[t]  + a9*MAPKp[t]*MEKpp[t]
MAPKpp 0 MAPKpp'[t] == k9*MAPKpMEKpp[t] - a10*MAPKPH[t]*MAPKpp[t]  + d10*MAPKppMAPKPH[t]
MAPKppMAPKPH 0 MAPKppMAPKPH'[t] == a10*MAPKPH[t]*MAPKpp[t] - d10* MAPKppMAPKPH[t] - k10*MAPKppMAPKPH[t]
MEK 0.2 MEK'[t] == k4*MEKpMEKPH[t] + d3*MEKRAFp[t] -  a3*MEK[t]*RAFp[t]
MEKp 0 MEKp'[t] == -(a4*MEKp[t]*MEKPH[t]) + d4*MEKpMEKPH[t]  + k6*MEKppMEKPH[t] + d5*MEKpRAFp[t] + k3*MEKRAFp[ t] - a5*MEKp[t]*RAFp[t]
MEKPH 0.2 MEKPH'[t] == -(a4*MEKp[t]*MEKPH[t]) + d4*MEKpMEKPH[t]  + k4*MEKpMEKPH[t] - a6*MEKPH[t]*MEKpp[t] + d6* MEKppMEKPH[t] + k6*MEKppMEKPH[t]
MEKpMEKPH 0 MEKpMEKPH'[t] == a4*MEKp[t]*MEKPH[t] - d4*MEKpMEKPH[t]  - k4*MEKpMEKPH[t]
MEKpp 0 MEKpp'[t] == d7*MAPKMEKpp[t] + k7*MAPKMEKpp[t] +  d9*MAPKpMEKpp[t] + k9*MAPKpMEKpp[t] - a7*MAPK[t]* MEKpp[t] - a9*MAPKp[t]*MEKpp[t] - a6*MEKPH[t]*MEKpp[t]  + d6*MEKppMEKPH[t] + k5*MEKpRAFp[t]
MEKppMEKPH 0 MEKppMEKPH'[t] == a6*MEKPH[t]*MEKpp[t] - d6*MEKppMEKPH[ t] - k6*MEKppMEKPH[t]
MEKpRAFp 0 MEKpRAFp'[t] == -(d5*MEKpRAFp[t]) - k5*MEKpRAFp[t]  + a5*MEKp[t]*RAFp[t]
MEKRAFp 0 MEKRAFp'[t] == -(d3*MEKRAFp[t]) - k3*MEKRAFp[t] +  a3*MEK[t]*RAFp[t]
RAF 0.4 RAF'[t] == -(a1*RAF[t]*RAFK[t]) + k2*RAFpRAFPH[t] +  d1*RAFRAFK[t]
RAFK 0.1 RAFK'[t] == -(a1*RAF[t]*RAFK[t]) + d1*RAFRAFK[t] +  k1*RAFRAFK[t]
RAFp 0 RAFp'[t] == d5*MEKpRAFp[t] + k5*MEKpRAFp[t] +  d3*MEKRAFp[t] + k3*MEKRAFp[t] - a3*MEK[t]*RAFp[t]  - a5*MEKp[t]*RAFp[t] - a2*RAFp[t]*RAFPH[t] + d2* RAFpRAFPH[t] + k1*RAFRAFK[t]
RAFPH 0.3 RAFPH'[t] == -(a2*RAFp[t]*RAFPH[t]) + d2*RAFpRAFPH[t]  + k2*RAFpRAFPH[t]
RAFpRAFPH 0 RAFpRAFPH'[t] == a2*RAFp[t]*RAFPH[t] - d2*RAFpRAFPH[t]  - k2*RAFpRAFPH[t]
RAFRAFK 0 RAFRAFK'[t] == a1*RAF[t]*RAFK[t] - d1*RAFRAFK[t] -  k1*RAFRAFK[t]

Generated by Cellerator Version 1.4.3 (6-March-2004) using Mathematica 5.0 for Mac OS X (November 19, 2003), March 6, 2004 12:18:07, using (PowerMac, PowerPC,Mac OS X,MacOSX,Darwin)

author=B.E.Shapiro

This model originates from BioModels Database: A Database of Annotated Published Models (http://www.ebi.ac.uk/biomodels/). It is copyright (c) 2005-2010 The BioModels.net Team.
For more information see the terms of use .
To cite BioModels Database, please use: Li C, Donizelli M, Rodriguez N, Dharuri H, Endler L, Chelliah V, Li L, He E, Henry A, Stefan MI, Snoep JL, Hucka M, Le Novère N, Laibe C (2010) BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models. BMC Syst Biol., 4:92.

The LNA is computed running run_lna the optional argument return_results (default False) indicates whether the full result is returned, or only the status of the computation. To retrieve the results after a computation of the LNA the following methods may be used:

  • get_lna_status returns the status of the last computation

  • get_lna_covariance_matrix returns the full covariance matrix

  • get_lna_reduced_covariance_matrix returns the reduced covariance matrix

  • get_lna_reduced_b_matrix returns the reduced b Matrix

  • get_lna_solution returns the tuple: (status, covariance matrix, reduced covariance matrix, reduced b matrix)

[3]:

run_lna()

[3]:

'Steady State found.'

[4]:

import matplotlib.pyplot as plt

# Get the covariance matrix
df_cov_matrix = get_lna_covariance_matrix()

# Generate heatmap
plt.figure(figsize=(10, 8))
plt.imshow(df_cov_matrix, cmap='viridis', aspect='auto')
plt.colorbar()
plt.title('LNA Covariance Matrix Heatmap')
plt.xticks(range(df_cov_matrix.shape[1]), df_cov_matrix.columns, rotation=90)
plt.yticks(range(df_cov_matrix.shape[0]), df_cov_matrix.index)
plt.show()
../_images/notebooks_LinearNoiseApproximation_6_0.png