Electrostatic models for computing protonation and redox equilibria in proteins

Electrostatic interactions are the most relevant for understanding biochemical systems. Acid-base and redox reactions create or destroy unit charges in biomolecules and can thus be fundamental for their function. Besides association reactions and chemical modi®cations such as phosphorylations, they are the reason for changes in protein properties. Protonation or deprotonation of titratable groups can cause changes in binding anities, enzymatic activities, and structural properties. Very often, protonations or deprotonations are the key events in enzymatic reactions. The reduction or oxidation of redox-active groups has a similar importance. In particular, the reduction of disul®de bonds can cause unfolding or functionally important conformational transitions. Consequently, the function of most proteins depends crucially on the pH and on the redox potential of the solution. Acidic denaturation of proteins in the stomach is a prerequisite for protein degradation during digestion. Beside this rather unspeci®c e€ect, the environment can tune the physiological properties of proteins in a speci®c manner. Di€erent values of pH or redox potential in di€erent organs, tissues, cells, or cell compartments steer protein function. Physiological redox and pH bu€ers such as glutathione and phosphates control these environmental parameters in living systems strictly. A few examples emphasize the physiological importance of pH and redox potential. The pH gradient in mitochondria or chloroplasts drives ATP synthesis. This pH gradient is in both systems generated by several proton transfer steps that couple to a sequence of redox reactions. In hemoglobin, pH in uences O2 binding and thus regulates O2 release during blood circulation. This behavior is also known as the Bohr e€ect. Pepsinogen cleaves itself in an acidic environment to the highly active peptidase pepsin. Membrane fusion during in uenza virus infection involves large pH-induced structural changes of the protein hemagglutinin. Because of their outstanding signi®cance, electrostatic interactions in proteins have been investigated intensively in the last decades (for review see Warshel and Russel 1984; Harvey 1989; Sharp and Honig 1990; Bashford 1991; Warshel and AE qvist 1991; Moult 1992; Madura et al. 1994; Sharp 1994; Gilson 1995; Honig and Nicholls 1995; Beroza and Case 1998; Warshel and Papazyan 1998). Several di€erent approaches are used to describe the electrostatics of proteins. The most detailed descriptions can be made by quantum-chemical approaches (Szabo and Ostlund 1989; Ziegler 1991; Lowe 1993; Naray-Szabo and Ferenczy 1995; Baerends and Gritsenko 1997). Such computationally expensive methods, however, only work for relatively small molecules and peptides. A cruder approximation must be chosen for larger systems such as solvated proteins. Molecular mechanics force ®elds are widely used for that purpose (Karplus and Petsko 1990; van Gunsteren and Berendsen 1990; Brooks and Case 1993; Kollman 1993). In these force ®elds, electrostatic interactions are modeled by (screened) Coulomb potentials. Most often, the solvent is considered explicitly in these approaches, i.e., at a microscopic level. In these simulations, fractions of unit charges ± so-called atomic partial charges ± are assigned to each atom. The atomic partial charges are adjusted to ®t the electrostatic potential obtained from a quantum-chemical calculation of small molecules with equivalent chemical groups (Breneman and Wiberg 1990). Such atomic partial charges are also used in continuum electrostatic approaches that rely on the soEur Biophys J (1999) 28: 533±551 O Springer-Verlag 1999

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