Kinetics of unfolding and refolding of proteins. I. Mathematical analysis.

Abstract A mathematical method for the phenomenological analysis of unimolecular reaction kinetics is presented. Starting from the solution to the differential equations of the system, equations have been developed to relate the unknown parameters inherent to any reaction mechanism, such as the microscopic rate constants for individual reaction steps, to the experimental quantities obtained from the rate of change of average physical properties of the system. Provided that kinetic measurements can be made in both forward and reverse directions, all unknown parameters can be evaluated for many simple mechanisms, and for some of them characteristic relations between observable quantities can be established, which can serve as criteria for immediate rejection. The results will be applied in the following papers to experimental studies of denaturation and renaturation of several proteins.

[1]  C. H. Chervenka.  Long-column meniscus depletion sedimentation equilibrium technique for the analytical ultracentrifuge. , 1970, Analytical biochemistry.

[2]  H. Tallan,et al.  Chromatographic studies on lysozyme. , 1953, The Journal of biological chemistry.

[3]  A. Ikai,et al.  Kinetic Evidence for Incorrectly Folded Intermediate States in the Refolding of Denatured Proteins , 1971, Nature.

[4]  Abu Nayeem Mohammad Salahuddin,et al.  Thermodynamics of the denaturation of ribonuclease by guanidine hydrochloride. , 1970, Biochemistry.

[5]  K. Mann,et al.  The estimation of polypeptide chain molecular weights by gel filtration in 6 M guanidine hydrochloride. , 1969, The Journal of biological chemistry.

[6]  E. Elson.  A sequential model of nucleation-dependent protein folding: kinetic studies of ribonuclease A. Analysis of the steady-state approximation for the sequential model. , 1972, Journal of molecular biology.

[7]  C. Tanford,et al.  Equilibrium and kinetics of the unfolding of lysozyme (muramidase) by guanidine hydrochloride. , 1966, Journal of molecular biology.

[8]  J. Bradbury,et al.  Denaturation of Proteins: Single or Multiple Step Process? , 1969, Nature.

[9]  C B Anfinsen,et al.  Kinetics of Folding of Staphylococcal Nuclease , 1970, Science.

[10]  D. Urry.  The heme chromophore in the ultraviolet. , 1967, The Journal of biological chemistry.

[11]  C. Tanford,et al.  Thermodynamics of the denaturation of lysozyme by guanidine hydrochloride. II. Dependence on denaturant concentration at 25 degrees. , 1969, Biochemistry.

[12]  Wetlaufer Db,et al.  Formation of three-dimensional structure in proteins. I. Rapid nonenzymic reactivation of reduced lysozyme. , 1970, Biochemistry.

[13]  C. Tanford,et al.  Hydrogen ion titration curve of lysozyme in 6 M guanidine hydrochloride. , 1971, Biochemistry.

[14]  P. George,et al.  THE 695-MMM. BAND OF FERRICYTOCHROME C AND ITS RELATIONSHIP TO PROTEIN CONFORMATION. , 1964, Biochemistry.

[15]  E. Stellwagen.  The reversible unfolding of horse heart ferricytochrome c. , 1968, Biochemistry.

[16]  R. L. Baldwin,et al.  A sequential model of nucleation-dependent protein folding: kinetic studies of ribonuclease A. , 1972, Journal of molecular biology.

[17]  C. Tanford.  Protein denaturation. , 1968, Advances in protein chemistry.

[18]  Abu Nayeem Mohammad Salahuddin,et al.  Proteins as random coils. 3. Optical rotatory dispersion in 6 M guanidine hydrochloride. , 1967, Journal of the American Chemical Society.

[19]  H. Neurath,et al.  The Chemistry of Protein Denaturation. , 1944 .

[20]  A Ikai,et al.  Kinetics of unfolding and refolding of proteins. II. Results for cytochrome c. , 1973, Journal of molecular biology.

[21]  D. Koshland,et al.  Kinetic aspects of conformational changes in proteins. I. Rate of regain of enzyme activity from denatured proteins. , 1971, Biochemistry.

[22]  Y. Myer.  Conformation of cytochromes. 3. Effect of urea, temperature, extrinsic ligands, and pH variation on the conformation of horse heart ferricytochrome c. , 1968, Biochemistry.

[23]  C. Tanford,et al.  Criteria of purity for guanidine hydrochloride. , 1971, Analytical biochemistry.

[24]  W. Kauzmann,et al.  The Kinetics of Protein Denaturation. I. The Behavior of the Optical Rotation of Ovalbumin in Urea Solutions1 , 1953 .

[25]  A Ikai,et al.  Kinetics of unfolding and refolding of proteins. 3. Results for lysozyme. , 1973, Journal of molecular biology.

[26]  A. Schechter,et al.  Folding of staphylococcal nuclease: kinetic studies of two processes in acid renaturation. , 1971, Journal of molecular biology.