Sensitivity Analysis

Sensitivity analysis examines how perturbations to the processes in the model affect the output.

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Control coefficients for c-fos mRNA duration and integrated pc-Fos are shown by bars (blue, EGF; red, HRG). Numbers above bars indicate the reaction indices.

Description

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.

Requirements

• Python3+
  • numpy
  • scipy
  • matplotlib
  • jupyter

Usage

from sensitivity_analysis import analyze

analyze()

Installation

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

References

• 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

• 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

License

MIT