Computer Data Fitting in the Equilibrium Protein Folding Process Involving Multiple Intermediates

Hui-Chih Hung1, Guang-Yaw Liu2 and Gu-Gang Chang1




1Department of Biochemistry, National Defense Medical Center
161 Min-Chuan East Road,
Taipei 114, Taiwan
2Institute of Immunology, Chung-Shan Medical College
Taichung 408, Taiwan
REPUBLIC OF CHINA





Protein folding problem was identified as one of the major key questions drove biomedical research in the development of contemporary biochemistry and molecular biology [1]. For simple proteins consisting of single peptide chain, usually a highly cooperative unfolding curve is observed. However, for complex proteins containing multiple structural domains or for proteins consisting of multiple subunits, complicated unfolding curves are always observed that indicate multiple folding intermediates during folding process [2, 3, 4]. Due to the inherent instability of these folding intermediates [5], characterization of the folding pathway of large proteins can be a challenge to protein chemists. Analysis of complex folding process in a quantitative way is inherent complicated. For this reason, many complex folding data are treated qualitatively. For example, the experimental data of aldolase folding data has been fitted with third degree polynomial just for better visualization [6], which, however, loss considerable details of the folding process. More recently, a quantitative analysis of the equilibrium unfolding data for glycyl-tRNA synthetase had been evaluated by computer fitting algorithm, which involves up to four equilibrium state model [7]. With the precision of instrument improved, more and more folding intermediates will be characterized in the future. Mathematic models for folding process involving more intermediates are needed. We have reported a formal derivation of the mathematical model that describes a folding-unfolding process involving five intermediates. Herein we summary the application of the mathematical model to the real protein unfolding data.

Before performing protein folding-unfolding experiments, some physical probes (fluorescence or circular dichroism) are first evaluated for their suitability in monitoring the structural changes of the protein. The equations that describe the dependence of an observed structural signal upon unfolding for a seven-state unfolding model shown in the following scheme was derived

in which N and U are the native and unfolded states, respectively. I1-I5 are the various unfolding intermediates. K1-K6 are the dissociation constants of the corresponding steps. The overall equation that describes a folding-unfolding system like that shown in the above scheme is shown in the following equation.

where Gi is the free energy change of each step, m represents the dependence of the G on denaturant concentration [D]. R is gas constant and T is the absolute temperature in Kelvin.

A complex mathematical model like that shown in this equation looks formidable at the first glance. The actual fitting is, however, surprisingly easy. Global fitting of the original data to this equation estimates various thermodynamic parameters (G1o-G6o; m1-m6; YN, YD, YI1- YI5, etc.) involved in the unfolding process, where Yi is the yobs value of the folding intermediate at the corresponding plateau region.

Human placental alkaline phosphatase is a homodimer composed of multiple structural domains [8]. Unfolding of human placental alkaline phosphatase in urea resulted in multiple unfolding process as monitored by fluorescence and circular dichroism spectroscopy. The unfolding data monitored by fluorescence spectral change can be fitted well to a seven-state model described by the above equation. A generally applicable non-linear curve fitting program (SigmaPlot 5.0, Jandel) works fine. The fitting completes in a few minutes and not very sensitive to the initial guess values. The fitting residues are randomly distributed near the zero line.

The thermodynamic parameters calculated have large standard errors if limiting data points (less then 30) are used. From these parameters, the calculated urea concentrations (G/m = [D]0.5) that caused half unfolding of the corresponding transitions and thus an indication of the stability of that folding intermediate, however, are remarkably coincide with those judged visually. The [urea]0.5 levels corresponding to the N I1, I1 I2, I2 I3, I3 I4, I4 I5, and I5 U processes are 2.62 M, 4.07 M, 4.70 M, 5.51 M, 6.59 M, and 7.72 M, respectively, for human placental alkaline phosphatase. Among these, the [urea]0.5 value of 4.7 M for the I2 I3 step has large fitting errors because of the very small plateau region around 4.5 M urea concentration. This computer fitting method, even at limited data points, is thus useful in evaluating the stability of the various folding intermediates.

This work was supported by the National Science Council, Republic of China (Frontiers in Sciences Program, Grant NSC 89-2312-B016-001).

REFERENCES

  1. Kenneth, K. E. (1998) Enzyme catalytic power. J. Biol. Chem. 273, 25527-25528.
  2. Jaenicke, R. (1996) Protein folding and association: In vitro studies for self-organization and targeting in the cell. Curr. Top. Cellu. Regul. 34, 209-314.
  3. Bai, Y., and Englander, S. W. (1996) Future directions in folding: The multi-state nature of protein structure. Proteins 24, 145-151.
  4. Fink, A. L., Oberg, K. A., and Seshadri, S. (1998) Discrete intermediates versus molten globule models for protein folding: Characterization of partially folded intermediates of apomyoglobin. Fold. Des. 3, 19-25.
  5. Privalov, P. L. (1996) Intermediate states in protein folding. J. Mol. Biol. 258, 707-725.
  6. Dobryszycki, P., Rymarczuk, M., Bulaj, G., and Kochman, M. (1999) Effect of acrylamide on aldolase structure. I. Induction of intermediate states. Biochim. Biophys. Acta 1431, 338-350.
  7. Dignam, J. D., Qu, X., and Chairesm J. B. (2001) Equilibrium Unfolding of Bombyx mori Glycyl-tRNA Synthetase. J. Biol. Chem. 276, 4028-4037.
  8. Le Du, M. H., Stigbrand, T., Taussig, M. J., Ménez, A., and Stura, E. A. (2001) Crystal structure of alkaline p hosphatase from human placenta at 1.8 Ĺ resolution. Implication for a substrate specificity. J. Biol. Chem. 276, 9158-9165.