BioMASS

Modeling and Analysis of Signaling Systems

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 modeling platform tailored to optimizing mathematical models of biological processes. By using BioMASS, users can efficiently optimize kinetic parameters to fit user-defined models to experimental data, while performing analysis on reaction networks to predict critical components affecting cellular output.

Features

BioMASS supports:

• Parameter Estimation of ODE Models
• Sensitivity Analysis
• Effective Visualization of Simulation Results

currently implimented for modeling immediate-early gene response (Nakakuki et al., Cell, 2010).

Installation

The BioMASS library is available on PyPI.

$ pip install biomass

BioMASS supports Python 3.7 or newer.

Create an executable model

from biomass.models import Nakakuki_Cell_2010

Nakakuki_Cell_2010.show_properties()

Model properties
----------------
36 species
115 parameters, of which 75 to be estimated

model = Nakakuki_Cell_2010.create()

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": 1000,
        "allowable_error": 0.5,
        "local_search_method": "DE",
    }
)

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

Progress list: out/n/optimization.log

Generation1: Best Fitness = 1.726069e+00
Generation2: Best Fitness = 1.726069e+00
Generation3: Best Fitness = 1.726069e+00
Generation4: Best Fitness = 1.645414e+00
Generation5: Best Fitness = 1.645414e+00
Generation6: Best Fitness = 1.645414e+00
Generation7: Best Fitness = 1.645414e+00
Generation8: Best Fitness = 1.645414e+00
Generation9: Best Fitness = 1.645414e+00
Generation10: Best Fitness = 1.645414e+00
Generation11: Best Fitness = 1.645414e+00
Generation12: Best Fitness = 1.645414e+00
Generation13: Best Fitness = 1.645414e+00
Generation14: Best Fitness = 1.645414e+00
Generation15: Best Fitness = 1.645414e+00
Generation16: Best Fitness = 1.249036e+00
Generation17: Best Fitness = 1.171606e+00
Generation18: Best Fitness = 1.171606e+00
Generation19: Best Fitness = 1.171606e+00
Generation20: Best Fitness = 1.171606e+00

• 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": 1000,
        "allowable_error": 0.5,
        "local_search_method": "DE",
    }
)

• 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": 2000,
        "allowable_error": 0.5,
        "local_search_method": "mutation",
        "n_children": 50
    }
)

• Exporting optimized parameters in CSV format

from biomass.result import OptimizationResults

res = OptimizationResults(model)
res.to_csv()

Visualization of Simulation Results

from biomass import run_simulation

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

viz_type : str

• 'average' : The average of simulation results with parameter sets in out/.

• 'best' : The best simulation result in out/, simulation with best_fit_param.

• 'original' : Simulation with the default parameters and initial values defined in set_model.py.

• 'n(=1,2,...)' : Use the parameter set in out/n/.

• 'experiment' : Draw the experimental data written in observable.py without simulation results.

show_all : bool

• Whether to show all simulation results.

stdev : bool

• If True, the standard deviation of simulated values will be shown (only when viz_type == 'average').

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')

target : str

• 'reaction'
• 'initial_condition'
• 'parameter'

metric : str

• 'maximum' : The maximum value.

• 'minimum' : The minimum value.

• 'argmax' : The time to reach the maximum value.

• 'argmin' : The time to reach the minimum value.

• 'timepoint' : The simulated value at the time point set via options['timepoint'].

• 'duration' : The time it takes to decline below the threshold set via options['duration'].

• 'integral' : The integral of concentration over the observation time.

style : str

• 'barplot'
• 'heatmap'

options : dict, optional

• timepoint : int

  • (metric == 'timepoint') Which timepoint to use.

• duration: float

  • (metric == 'duration') 0.1 for 10% of its maximum.

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