(190p) Combining Transformed and Constrained Gibbs Energies for Modelling Biochemical Systems

The application of thermodynamics in biology and biochemistry has recently gained increasing interest due to the general trend where substitutes for petrochemicals and entirely new, sustainable means of production are being sought. Biochemical pathways involved in biological production steps can be modified by metabolic engineering. The methodical improvement of these systems requires detailed analysis of the underlying reaction networks. While tedious and often costly experimental work is required to evaluate the molecular mechanisms of reactions and their kinetic parameters, advanced thermodynamic methods provide an alternative approach to look for the most promising pathways [1].

Transformed Gibbs energies are Gibbs energies for a standard state close to the real conditions of the system at interest. Solute concentrations within cells cannot currently be determined accurately enough for normal thermodynamic modeling. The regular method of dealing with these kinds of situations in chemistry is to assess the concentrations of the most influential compounds of the system and then evaluate all thermodynamic functions at those conditions. Transformed Gibbs energies for biological systems are primarily determined for specific pH and ionic strength but can be extended to include any number of components [2].

Computation of global chemical equilibria in multiphase systems by minimization of the Gibbs free energy is an established technique with many applications. Since equilibrium is defined in a limited timeframe with certain internal constraints that vary with time but not within the timeframe of inspection, some of these constraints can be included as a dynamic portion of a model to extend their frame of validity. Such dynamic constraints typically involve work terms of slow processes or kinetically limited chemical reactions. The potential corresponding to the added work term is then represented by a supplementary undetermined Lagrange multiplier. In addition, the maximum extents of selected catalyzed chemical reactions can be limited to any desired value and the related energy terms describe the thermodynamic affinities of the reactions. The method of Constrained Gibbs Energies thus adds kinetic reaction extent limitations to the internal constraints of the system [3].

The combination of reaction rates and multi-component Gibbs energy minimization enables direct calculation of the thermodynamic state properties during an irreversible chemical change. The obvious advantage of such modeling is the simultaneous and interdependent calculation of the chemical composition and thermodynamic quantities. For example, the co-dependent chemical composition changes and energetic/entropic changes are inherently followed, which can provide improved balance analysis of biochemical networks.

[1] C. S. Henry, L. J. Broadbelt, and V. Hatzimanikatis, Thermodynamics-Based Metabolic Flux Analysis, Biophysical Journal 92 (2007) 1792?1805.

[2] R. A. Alberty, Thermodynamics of biochemical reactions, John Wiley & Sons, Inc., Hoboken, New Jersey, 2003.

[3] P. Koukkari, and R. Pajarre, Calculation of constrained equilibria by Gibbs energy minimization, CALPHAD 30 (2006) 18-26.