What is ByoDyn?

Motivation

Recent systems biology approaches have given a second life to classical biochemical kinetics methods. It is becoming a routinely task to build models of increasing complexity on a given gene regulatory, signal transduction or metabolic network or pathway of interest. One of the main problems in building such models is the determination of the parameters underlying each modeled equation or process. ByoDyn has been designed to provide an easily extendable computational framework to deal with the estimation of parameters in highly uncharacterized models.

Availability

ByoDyn is an object oriented, Python based, program that makes use of several open source libraries freely available for non-commercial use: the PORT library from Netlib for Newtonian optimizations; the SciPy package version 0.6.0 for scientific libraries in Python, including the ODE solvers; and the libSBML (Gnu LGPL) library version 4.0.0 for handling SBML files. The program has been tested in Linux Fedora Core 2 and 4 and in Mac OS X platforms and its migration to any other platform is straightforward.

Aims

There are five main features of ByoDyn:

• run quantitative simulations of unicellular or multicellular biochemical networks both deterministically and stochastically.
• perform analysis of the sensitivity of the system with respect to the parameters of the model.
• estimate the numerical values of the biochemical parameters that match a given set of experimental data along time for any of the system's nodes.
• use the Fisher information matrix to help in designing optimal experiments for the calibration problem.
• determine the global shape of the parameter space thanks to Monte Carlo sampling coupled with cluster analysis and PCA.

Simulations

ByoDyn uses SBML format files to run unicellular systems or a homemade format for multicellular models. A parser based on libSBML has been developed to build the system of (nonlinear) ordinary differential equations (ODEs).

ByoDyn uses several routines from SciPy to solve the above problem. Also, package LSODA, is called because of its ability to switch automatically between both stiff and non-stiff integrators when necessary. As a secondary possibility ByoDyn can also make external calls to Octave, OpenModelica and XPPAUT, it is a powerful approach in order to solve other systems equations such as DAEs, events or delays (DDEs).

Finally, ByoDyn uses several functions to create nice PostScript or PNG plots like trajectories of the node concentration along time for unicellular systems and a cell matrices where the steady state node concentration is shown by color intensity. Sensitivity, identifiability, optimal experimental design and many other functions render too appropriate graphs.

Sensitivity analysis

The sensitivity analysis of the system along time with respect to a specific parameter is also performed. This step allows us to discriminate the parameters that are less affecting the dynamics of the system and that therefore might be excluded from the optimization routines. Global sensitivity can be explored thanks to the Monte Carlo sampling and principal component analysis of the resulting cluster of solutions.

Parameter estimation

If temporal quantitative data about the expression of the nodes is known along time, ByoDyn uses state of the art optimization algorithms to obtain the numerical values of the biochemical parameters that reproduce the given experimental behaviour. We have implemented different global and local optimization methods to obtain the best set of parameters in each particular case.

Optimal experimental design

Analysis of the covariance matrix for the change in the fitness function with respect to the parameters has lead to the implementation of optimal experimental design approaches. Fisher information matrix analyses are done to assess which point results more informative for the model calibration problem.