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.

BioMASS is a biological modeling environment tailored to

1. Parameter Estimation of ODE Models
2. Sensitivity Analysis

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

• numpy
• scipy
• matplotlib
• seaborn

from biomass.models import Nakakuki_Cell_2010

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

from biomass import optimize

optimize(Nakakuki_Cell_2010, n)

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(Nakakuki_Cell_2010, n)

• If you want to search multiple parameter sets (from n1 to n2) simultaneously,

from biomass import optimize

optimize(Nakakuki_Cell_2010, n1, n2)

from biomass import run_simulation

run_simulation(Nakakuki_Cell_2010, 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

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(Nakakuki_Cell_2010, target='reaction', metric='integral', style='barplot')

target : str

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

metric : str

• 'maximum' : The maximum value.
• 'minimum' : The minimum value.
• 'duration' : The time it takes to decline below 10% of its maximum.
• 'integral' : The integral of concentration over the observation time.

style : str

• 'barplot'
• 'heatmap'

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.

$ git clone https://github.com/okadalabipr/biomass.git

• Nakakuki, T. et al. Ligand-specific c-Fos expression emerges from the spatiotemporal control of ErbB network dynamics. Cell 141, 884–896 (2010). https://doi.org/10.1016/j.cell.2010.03.054

• Kimura, S., Ono, I., Kita, H. & Kobayashi, S. An extension of UNDX based on guidelines for designing crossover operators: proposition and evaluation of ENDX. Trans. Soc. Instrum. Control Eng. 36, 1162–1171 (2000). https://doi.org/10.9746/sicetr1965.36.1162

• Kimura, S. & Konagaya, A. A Genetic Algorithm with Distance Independent Diversity Control for High Dimensional Function Optimization. J. Japanese Soc. Artif. Intell. 18, 193–202 (2003). https://doi.org/10.1527/tjsai.18.193

• Kimura, S., Nakakuki, T., Kirita, S. & Okada, M. AGLSDC: A Genetic Local Search Suitable for Parallel Computation. SICE J. Control. Meas. Syst. Integr. 4, 105–113 (2012). https://doi.org/10.9746/jcmsi.4.105

• Kholodenko, B. N., Demin, O. V. & Westerhoff, H. V. Control Analysis of Periodic Phenomena in Biological Systems. J. Phys. Chem. B 101, 2070–2081 (1997). https://doi.org/10.1021/jp962336u

• Kholodenko, B. N., Hoek, J. B., Westerhoff, H. V. & Brown, G. C. Quantification of information transfer via cellular signal transduction pathways. FEBS Lett. 414, 430–434 (1997). https://doi.org/10.1016/S0014-5793(97)01018-1

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