Biochemical Systems Theory#

Background#

One of the tenets of systems biology is the development of biochemical networks that can describe intricate mechanisms. Ordinary Differential Equations are widley used in this regard. However, linear models run the disadvantage of generalism, and a lack of accuracy & efficiency.

S-System Theory & Power Law Formalism was pioneered in the 1950s by Michael Savageau in an effort to represent organizationally complex (biological) systems & retain mathematical amenability. Moreover, the S-System theory is capable of aggregating a network of reactions, representating equations in matrix form, and transforming networks using a well-defined algorithm.

The core principle lies in the ability of non-linear rational functions to be appropriately represented & approximated by a straight-line in a log-log plot. This allows for the deduction of the rate of a process using the Taylor series in a logarithmic space. Logarithmic transformation has been shown to facilitate steady-state solutions & improve the efficiency of dynamic solutions.

BSTModelKit.jl#

The BSTModelKit.jl package is an implementation of the S-System & Power Law Formalism in the Julia programming language. Instructions for installation can be found here.

Additional Resources#

  • A detailed account on the recasting of nonlinear differential equations to S-System form can be found here