Biomaterial Database

Fundamental equation of thermodynamics for protein-ligand binding. 2003

Robert A Alberty

Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA 02139, USA. alberty@mit.edu

For the internal energy and every thermodynamic potential that can be defined by a Legendre transform, there is a fundamental equation that contains all the thermodynamic information about a system. For a system involving the binding of molecular oxygen and hydrogen ions by a protein, fundamental equations are given for the Gibbs energy G, the transformed Gibbs energy G' at specified pH, and the further transformed Gibbs energy G" at specified pH and specified concentration of molecular oxygen. The Maxwell equations for these various Gibbs energies are important because they provide the connection with experimentally determined properties and increase our understanding of these properties. Measurements of the average number of oxygen molecules bound as a function of T, pH and concentration of molecular oxygen make it possible to calculate Delta(f)G"(o) of the reactant. Maxwell equations make it possible to calculate the average number of hydrogen ions bound, Delta(f)S"(o), Delta(f)H"(o) and their partial derivatives. These relations are illustrated with numerical calculations on a simple reaction system.

UI	MeSH Term	Description	Entries
D008956	Models, Chemical	Theoretical representations that simulate the behavior or activity of chemical processes or phenomena; includes the use of mathematical equations, computers, and other electronic equipment.	Chemical Models,Chemical Model,Model, Chemical
D010100	Oxygen	An element with atomic symbol O, atomic number 8, and atomic weight [15.99903; 15.99977]. It is the most abundant element on earth and essential for respiration.	Dioxygen,Oxygen-16,Oxygen 16
D011485	Protein Binding	The process in which substances, either endogenous or exogenous, bind to proteins, peptides, enzymes, protein precursors, or allied compounds. Specific protein-binding measures are often used as assays in diagnostic assessments.	Plasma Protein Binding Capacity,Binding, Protein
D011506	Proteins	Linear POLYPEPTIDES that are synthesized on RIBOSOMES and may be further modified, crosslinked, cleaved, or assembled into complex proteins with several subunits. The specific sequence of AMINO ACIDS determines the shape the polypeptide will take, during PROTEIN FOLDING, and the function of the protein.	Gene Products, Protein,Gene Proteins,Protein,Protein Gene Products,Proteins, Gene
D006859	Hydrogen	The first chemical element in the periodic table with atomic symbol H, and atomic number 1. Protium (atomic weight 1) is by far the most common hydrogen isotope. Hydrogen also exists as the stable isotope DEUTERIUM (atomic weight 2) and the radioactive isotope TRITIUM (atomic weight 3). Hydrogen forms into a diatomic molecule at room temperature and appears as a highly flammable colorless and odorless gas.	Protium,Hydrogen-1
D006863	Hydrogen-Ion Concentration	The normality of a solution with respect to HYDROGEN ions; H+. It is related to acidity measurements in most cases by pH	pH,Concentration, Hydrogen-Ion,Concentrations, Hydrogen-Ion,Hydrogen Ion Concentration,Hydrogen-Ion Concentrations
D000465	Algorithms	A procedure consisting of a sequence of algebraic formulas and/or logical steps to calculate or determine a given task.	Algorithm
D013696	Temperature	The property of objects that determines the direction of heat flow when they are placed in direct thermal contact. The temperature is the energy of microscopic motions (vibrational and translational) of the particles of atoms.	Temperatures
D013816	Thermodynamics	A rigorously mathematical analysis of energy relationships (heat, work, temperature, and equilibrium). It describes systems whose states are determined by thermal parameters, such as temperature, in addition to mechanical and electromagnetic parameters. (From Hawley's Condensed Chemical Dictionary, 12th ed)	Thermodynamic