Titration curves protein structure

Theoretical titration curves for enzymes can be calculated from known crystal structures and first principles of electrostatics. Key amino acids at the active site have significantly perturbed pK values and unusual regions in which they are partially protonated over a wide pH region.3 In principle, such titration calculations can identify the active site of a protein whose structure is known, but whose function is not. 

The relation between structure and acidity of organic compounds has been the subject of much study. Those aspects which are of interest in connection with protein titration curves have been reviewed in definitive manner by Edsall and Wyman (1958) and by Edsall (1943), and the reader is referred to these reviews for a discussion of the theoretical and empirical principles which are involved. For the present purpose it is sufficient to extract the data which will lead to the expected pK values of the titratable groups of proteins, and this has been done in Table I. 

The preceding equations have not yet been used as basis for the analysis of any actual titration curve of a protein. It should be feasible soon to apply the theory to the titration curve of myoglobin, the complete three-dimensional structure of which should be available soon (Kendrew et al., 1961). This will permit exact localization of all titratable groups on the protein molecule and, hence, the theoretical evaluation of the from assumed intrinsic pK s. It is not to be expected that these values will accurately reproduce the titration curve, but it is to be expected that the cause of observed deviations will be relatively easy to determine. Essentially three possibilities would be looked for in such a first application of the theory. 

That the structure determined by X-ray diffraction of protein crystals is not exactly the same as the structure in solution. To test this possibility one would have to make a guess as to the probable location of possible structural changes (e.g., at points of contact between neighboring molecules in the crystal), and would then determine whether they improve the agreement between calculated and experimental titration curves. 

Hydrogen ion titration curves of proteins provide a powerful tool to reveal many aspects of the structures of individual proteins. The characteristic ionization constants of the acidic and basic groups in the amino acids and peptides may be profoundly modified when these groups are incorporated in a protein molecule. An increasing number of proteins have been found in which potentially reactive groups are inaccessible for titration in the native molecule, and become available only after denaturation. Such findings can, in the years ahead, be correlated with detailed knowledge of the three dimensional structure of proteins, as obtained by X-ray diffraction and other methods. The present state of the field is reviewed by Tanford, who has done so much to advance it over the last decade. 

Horner (1954) constructed a theoretical curve for the titration of wool with alkali using amino acid analyses and the pKa values obtained for the side-chain groups of lysine, tyrosine, and arginine in the form of the free acids. He obtained a better fit using the Donnan expression of Peters and Speakman (1949) than he did with the Gilbert-Rideal (1944) expression. Obviously, much depends on the pKa values used hydrogen bonding in a protein structure can shift these values by more than one pH unit. Also, the assumption was made that the affinity of sodium ions for the... 

Recently Tanford and his collaborators have made use of the electrostatic term w to analyze the titration curves of a number of proteins. By combining graphical methods and trial-and-error selection they obtained values of p(Kint) and w from experimental titration curves. In each case the value for the apparent average net charge was corrected for the binding of anions and cations as determined by independent experimental methods. Differences between their experimental values of w and those calculated from theory were interpreted by these workers in terms of alterations in molecular parameters or structure. For example, observed values which were low, especially when they became low only at pH s far removed from neutrality, were attributed to alteration in the size or shape of the molecule brought about by electrostatic repulsion. Thus, with human serum albumin Tanford (1950) found that although the basic branch of the titration curve could be computed from theory, the acid branch was much too steep... 

In some cases the quantities p(/ Ci t), and m yielded by analysis of titration curves may furnish special clues to the structure of particular proteins. For example, if ordinarily dissociable groups participate in formation of intramolecular bonds abnormal values for their intrinsic dissociation constants may result, or their number may even appear to be smaller than that found by amino acid assay. Examples will be furnished in the later sections on stoichiometry and on unreactive prototropic groups. 

Rather than resort to purely empirical selection of suitable values of ni and p(/Cint)< for equation 1 it is more usual to begin by fitting experimental data with values of m chosen to conform with the numbers of prototropic groups determined by several more direct and specific methods of examination of titration data. Even where the theoretical analysis of a titration curve is not attempted and exact values of p(Ki t), for each type of group are therefore lacking, the numbers of groups so determined may furnish valuable clues to the internal structure of the protein, especially when they are compared with the results of amino acid analyses. 

This is further bolstered by the fact that pK calculations on large enzymes routinely produce non-HH titration curves. Indeed the THEMATICS algorithm [63] for identifying active sites in protein structures has been designed around this principle, and it has been shown that strong unfavorable electrostatic interaction energies often are present in enzyme active sites [64]. It is therefore likely fhaf a... 

Since pairwise electrostatic interaction energies can be calculated from protein structures using Poisson-Boltzmann Equation (PBE) solvers [71,72], we can attempt to forge a unique link between protein structure and protein titration curves... 

The NMR chemical shift does not model the titrational event If it is clear that an altered protein dielectric constant cannot reconcile the protein structure with the titration curves, then it is time to examine the NMR titration curves themselves. Since the NMR chemical shift is very sensitive to small changes in the chemical... 

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