biomass 0.4.0

A Python Framework for Modeling and Analysis of Signaling Systems

BioMASS

Mathematical modeling is a powerful method for the analysis of complex biological systems. Although there are many researches devoted on producing models to describe dynamical cellular signaling systems, most of these models are limited and do not cover multiple pathways. Therefore, there is a challenge to combine these models to enable understanding at a larger scale. Nevertheless, larger network means that it gets more difficult to estimate parameters to reproduce dynamic experimental data needed for deeper understanding of a system.

To overcome this problem, we developed BioMASS, a Python framework for Modeling and Analysis of Signaling Systems. The BioMASS framework allows efficient optimization of multiple parameter sets simultaneously and generates the multiple parameter candidates that explain the signaling dynamics of interest. These parameter candidates can be further evaluated by their distribution and sensitivity analysis as a part of alternative information about the hidden regulatory mechanism of the system.

Features

• Parameter estimation of ODE models
• Local sensitivity analysis
• Effective visualization of simulation results

Installation

The BioMASS library is available on PyPI.

$ pip install biomass

BioMASS supports Python 3.7 or newer.

Usage

• Circadian clock
• Immediate-early gene response
• Insulin signaling
• MAPK cascade
• NF-κB pathway
• TGF-β/SMAD pathway

We will use the model of immediate-early gene response (Nakakuki_Cell_2010) for parameter estimation, visualization of simulation results and sensitivity analysis.

Model Preparation

A brief description of each file/folder is below:

Name	Content
name2idx/	Names of model parameters and species
set_model.py	Differential equation, parameters and initial condition
observalbe.py	Observables, simulations and experimental data
viz.py	Plotting parameters for customizing figure properties
set_search_param.py	Model parameters to optimize and search region
fitness.py	An objective function to be minimized, i.e., the distance between model simulation and experimental data
reaction_network.py	Reaction indices grouped according to biological processes

from biomass import Model
from biomass.models import Nakakuki_Cell_2010

model = Model(Nakakuki_Cell_2010.__package__).create(show_info=True)

↓

Nakakuki_Cell_2010 information
------------------------------
36 species
115 parameters, of which 75 to be estimated

Parameter Estimation of ODE Models (n = 1, 2, 3, · · ·)

Parameters are adjusted to minimize the distance between model simulation and experimental data.

from biomass import optimize

optimize(
    model=model, start=1, options={
        "popsize": 3,
        "max_generation": 100,
        "allowable_error": 0.5,
        "local_search_method": "DE",
        "maxiter": 50,
    }
)

The temporary result will be saved in out/n/ after each iteration.

Progress list: out/n/optimization.log

Generation1: Best Fitness = 5.864228e+00
Generation2: Best Fitness = 5.864228e+00
Generation3: Best Fitness = 4.488934e+00
Generation4: Best Fitness = 3.793744e+00
Generation5: Best Fitness = 3.652047e+00
Generation6: Best Fitness = 3.652047e+00
Generation7: Best Fitness = 3.652047e+00
Generation8: Best Fitness = 3.452999e+00
Generation9: Best Fitness = 3.180878e+00
Generation10: Best Fitness = 1.392501e+00
Generation11: Best Fitness = 1.392501e+00
Generation12: Best Fitness = 1.392501e+00
Generation13: Best Fitness = 1.392501e+00
Generation14: Best Fitness = 7.018051e-01
Generation15: Best Fitness = 7.018051e-01
Generation16: Best Fitness = 7.018051e-01
Generation17: Best Fitness = 7.018051e-01
Generation18: Best Fitness = 7.018051e-01
Generation19: Best Fitness = 6.862063e-01
Generation20: Best Fitness = 6.862063e-01

• If you want to continue from where you stopped in the last parameter search,

from biomass import optimize_continue

optimize_continue(
    model=model, start=1, options={
        "popsize": 3,
        "max_generation": 200,
        "allowable_error": 0.5,
        "local_search_method": "DE",
        "maxiter": 50,
    }
)

• If you want to search multiple parameter sets (e.g., from 1 to 10) simultaneously,

from biomass import optimize

optimize(
    model=model, start=1, end=10, options={
        "popsize": 5,
        "max_generation": 100,
        "allowable_error": 0.5,
        "local_search_method": "DE",
        "maxiter": 50,
    }
)

• Data Export and Visualization

from biomass.result import OptimizationResults

res = OptimizationResults(model)
# Export optimized parameters in CSV format
res.to_csv()
# Visualize objective function traces for different optimization runs
res.trace_obj()

Visualization of Simulation Results

from biomass import run_simulation

run_simulation(model, viz_type='average', show_all=False, stdev=True)

Points (blue diamonds, EGF; red squares, HRG) denote experimental data, solid lines denote simulations

Sensitivity Analysis

The single parameter sensitivity of each reaction is defined by

s_i(q(v),v_i) = ∂ ln(q(v)) / ∂ ln(v_i) = ∂ q(v) / ∂ v_i · v_i / q(v)

where v_i is the i^th reaction rate, v is reaction vector v = (v₁, v₂, ...) and q(v) is a target function, e.g., time-integrated response, duration. Sensitivity coefficients were calculated using finite difference approximations with 1% changes in the reaction rates.

from biomass import run_analysis

run_analysis(model, target='reaction', metric='integral', style='barplot')

Control coefficients for integrated pc-Fos are shown by bars (blue, EGF; red, HRG). Numbers above bars indicate the reaction indices, and error bars correspond to simulation standard deviation.

Citation

When using BioMASS, please cite:

• Imoto, H., Zhang, S. & Okada, M. A Computational Framework for Prediction and Analysis of Cancer Signaling Dynamics from RNA Sequencing Data—Application to the ErbB Receptor Signaling Pathway. Cancers. 12, 2878 (2020). https://doi.org/10.3390/cancers12102878

  @article{imoto2020computational,
    title={A Computational Framework for Prediction and Analysis of Cancer Signaling Dynamics from RNA Sequencing Data—Application to the ErbB Receptor Signaling Pathway},
    author={Imoto, Hiroaki and Zhang, Suxiang and Okada, Mariko},
    journal={Cancers},
    volume={12},
    number={10},
    pages={2878},
    year={2020},
    publisher={Multidisciplinary Digital Publishing Institute}
  }
  

Author

Hiroaki Imoto