To develop, optimize, and validate a generalized mass action, equilibrium solution that incorporates measured concentrations of albumin as well as cortisol binding globulin (CBG) to estimate free cortisol.
In previous works [ 24- 26], we have showed that in the absence of bifurcation in the mass action kinetics, the unique equilibrium remains stable, globally and asymptotically.
Kohn et al. [ 14] proposed a simple ordered ter ter mechanism based on two assumptions: first, the concentrations of substrates always exceed their respective Km values; second, the flux is primarily controlled by the deviation of the mass action ratio from the equilibrium constant.
The algebraic constraints come from the adjunction of mass action laws related to the equilibriums, whereas the bounds account for the positivity of the computed quantities.
Through decomposition of reaction network via Gauss-Jordan column reduction: (a) redundant fast reactions and irrelevant kinetic reactions are removed from the system; (b) fast reactions and slow reactions are decoupled; and (c) species reaction equations are transformed into two sets: equilibrium species mass action equations and kinetic-variable reaction equations.
Experimental distribution ratios obtained for water, nitric acid and ruthenium were described with a physicochemical model based on the application of the mass action law on each extraction equilibrium and by taking into account deviations from thermodynamic ideal behaviour both in aqueous and organic phase using Mikulin and Sergievskii-Dannus equations.
Isolated reaction networks endowed with mass action kinetics achieve the thermodynamic equilibrium which has been demonstrated to be globally asymptotically stable [ 15, 16] precluding any kind of complex nonlinear behavior such as bistability or limit cycles.
An equilibrium model that employs the mass action law was also developed to evaluate the optimum apparent equilibrium constants (KE), stoichiometric ratio (m) and physical constant (S).
An extraction model, based on the law of mass action, was formulated to predict the equilibrium distribution of the phenols.
In contrast, models based on the equilibrium concept of mass action (Eqs. 2-4 below) accomplish this, but to be used, methods that deal with multiple models and models that are over-parameterized [ 2] need to be developed.
