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1.
We describe an algorithm which enables us to search the conformational space of the side chains of a protein to identify the global minimum energy combination of side chain conformations as well as all other conformations within a specified energy cutoff of the global energy minimum. The program is used to explore the side chain conformational energy surface of a number of proteins, to investigate how this surface varies with the energy model used to describe the interactions within the system and the rotamer library. Enumeration of the rotamer combinations enables us to directly evaluate the partition function, and thus calculate the side chain contribution to the conformational entropy of the folded protein. An investigation of these conformations and the relationships between them shows that most of the conformations near to the global energy minimum arise from changes in side chain conformations that are essentially independent; very few result from a concerted change in conformation of two or more residues. Some of the limitations of the approach are discussed. Proteins 33:227–239, 1998. © 1998 Wiley-Liss, Inc. 相似文献
2.
Recent advances in modeling protein structures at the atomic level have made it possible to tackle \"de novo\" computational protein design. Most procedures are based on combinatorial optimization using a scoring function that estimates the folding free energy of a protein sequence on a given main-chain structure. However, the computation of the conformational entropy in the folded state is generally an intractable problem, and its contribution to the free energy is not properly evaluated. In this article, we propose a new automated protein design methodology that incorporates such conformational entropy based on statistical mechanics principles. We define the free energy of a protein sequence by the corresponding partition function over rotamer states. The free energy is written in variational form in a pairwise approximation and minimized using the Belief Propagation algorithm. In this way, a free energy is associated to each amino acid sequence: we use this insight to rescore the results obtained with a standard minimization method, with the energy as the cost function. Then, we set up a design method that directly uses the free energy as a cost function in combination with a stochastic search in the sequence space. We validate the methods on the design of three superficial sites of a small SH3 domain, and then apply them to the complete redesign of 27 proteins. Our results indicate that accounting for entropic contribution in the score function affects the outcome in a highly nontrivial way, and might improve current computational design techniques based on protein stability. 相似文献
3.
Loss of side-chain conformational entropy is an important force opposing protein folding and the relative preferences of the amino acids for being buried or solvent exposed may be partially determined by which amino acids lose more side-chain entropy when placed in the core of a protein. To investigate these preferences, we have incorporated explicit modeling of side-chain entropy into the protein design algorithm, RosettaDesign. In the standard version of the program, the energy of a particular sequence for a fixed backbone depends only on the lowest energy side-chain conformations that can be identified for that sequence. In the new model, the free energy of a single amino acid sequence is calculated by evaluating the average energy and entropy of an ensemble of structures generated by Monte Carlo sampling of amino acid side-chain conformations. To evaluate the impact of including explicit side-chain entropy, sequences were designed for 110 native protein backbones with and without the entropy model. In general, the differences between the two sets of sequences are modest, with the largest changes being observed for the longer amino acids: methionine and arginine. Overall, the identity between the designed sequences and the native sequences does not increase with the addition of entropy, unlike what is observed when other key terms are added to the model (hydrogen bonding, Lennard-Jones energies, and solvation energies). These results suggest that side-chain conformational entropy has a relatively small role in determining the preferred amino acid at each residue position in a protein. 相似文献
4.
The conformational stability of the histidine-containing phosphocarrier protein (HPr) from Bacillus subtilis has been determined using a combination of thermal unfolding and solvent denaturation experiments. The urea-induced denaturation of HPr was monitored spectroscopically at fixed temperatures and thermal unfolding was performed in the presence of fixed concentrations of urea. These data were analyzed in several different ways to afford a measure of the cardinal parameters (delta Hg, Tg, delta Sg, and delta Cp) that describe the thermodynamics of folding for HPr. The method of Pace and Laurents (Pace CN, Laurents DV, 1989, Biochemistry 28:2520-2525) was used to estimate delta Cp as was a global analysis of the thermal- and urea-induced unfolding data. Each method used to analyze the data gives a similar value for delta Cp (1,170 +/- 50 cal mol-1K-1). Despite the high melting temperature for HPr (Tg = 73.5 degrees C), the maximum stability of the protein, which occurs at 26 degrees C, is quite modest (delta Gs = 4.2 kcal mol-1). In the presence of moderate concentrations of urea, HPr exhibits cold denaturation, and thus a complete stability curve for HPr, including a measure of delta Cp, can be achieved using the method of Chen and Schellman (Chen B, Schellman JA, 1989, Biochemistry 28:685-691). A comparison of the different methods for the analysis of solvent denaturation curves is provided and the effects of urea on the thermal stability of this small globular protein are discussed. The methods presented will be of general utility in the characterization of the stability curve for many small proteins. 相似文献
5.
Much effort has been invested in seeking to understand the thermodynamic basis of helix stability in both peptides and proteins. Recently, several groups have measured the helix-forming propensities of individual residues (Lyu, P. C., Liff, M. I., Marky, L. A., Kallenbach, N. R. Science 250:669–673, 1990; O'Neil, K. T., DeGrado, W. F. Science 250:646–651, 1990; Padmanabhan, S., Marqusee, S., Ridgeway, T., Laue, T. M., Baldwin, R. L. Nature (London) 344:268–270, 1990). Using Monte Carlo computer simulations, we tested the hypothesis that these differences in measured helix-forming propensity are due primarily to loss of side chain conformational entropy upon helix formation (Creamer, T. P., Rose, G. D. Proc. Natl. Acad. Sci. U.S.A. 89:5937–5941, 1992). Our previous study employed a rigid helix backbone, which is here generalized to a completely flexible helix model in order to ensure that earlier results were not a methodological artifact. Using this flexible model, side chain rotamer distributions and entropy losses are calculated and shown to agree with those obtained earlier. We note that the side chain conformational entropy calculated for Trp in our previous study was in error; a corrected value is presented. Extending earlier work, calculated entropy losses are found to correlate strongly with recent helix propensity scales derived from substitutions made within protein helices (Horovitz, A., Matthews, J. M., Fersht, A. R. J. Mol. Biol. 227:560–568, 1992; Blaber, M., Zhang, X.-J., Matthews, B. M. Science 260:1637–1640, 1993). In contrast, little correlation is found between these helix propensity scales and the accessible surface area buried upon formation of a model polyalanyl α-helix. Taken in sum, our results indicate that loss of side chain entropy is a major determinant of the helix-forming tendency of residues in both peptide and protein helices. © 1994 Wiley-Liss, Inc. 相似文献
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7.
C. Zhang J. L. Cornette C. Delisi 《Protein science : a publication of the Protein Society》1997,6(5):1057-1064
We report a new free energy decomposition that includes structure-derived atomic contact energies for the desolvation component, and show that it applies equally well to the analysis of single-domain protein folding and to the binding of flexible peptides to proteins. Specifically, we selected the 17 single-domain proteins for which the three-dimensional structures and thermodynamic unfolding free energies are available. By calculating all terms except the backbone conformational entropy change and comparing the result to the experimentally measured free energy, we estimated that the mean entropy gain by the backbone chain upon unfolding (delta Sbb) is 5.3 cal/K per mole of residue, and that the average backbone entropy for glycine is 6.7 cal/K. Both numbers are in close agreement with recent estimates made by entirely different methods, suggesting a promising degree of consistency between data obtained from disparate sources. In addition, a quantitative analysis of the folding free energy indicates that the unfavorable backbone entropy for each of the proteins is balanced predominantly by favorable backbone interactions. Finally, because the binding of flexible peptides to receptors is physically similar to folding, the free energy function should, in principle, be equally applicable to flexible docking. By combining atomic contact energies, electrostatics, and sequence-dependent backbone entropy, we calculated a priori the free energy changes associated with the binding of four different peptides to HLA-A2, 1 MHC molecule and found agreement with experiment to within 10% without parameter adjustment. 相似文献
8.
A. T. Alexandrescu K. Rathgeb-Szabo K. Rumpel W. Jahnke T. Schulthess R. A. Kammerer 《Protein science : a publication of the Protein Society》1998,7(2):389-402
Backbone 15N relaxation parameters (R1, R2, 1H-15N NOE) have been measured for a 22-residue recombinant variant of the S-peptide in its free and S-protein bound forms. NMR relaxation data were analyzed using the \"model-free\" approach (Lipari & Szabo, 1982). Order parameters obtained from \"model-free\" simulations were used to calculate 1H-15N bond vector entropies using a recently described method (Yang & Kay, 1996), in which the form of the probability density function for bond vector fluctuations is derived from a diffusion-in-a-cone motional model. The average change in 1H-15N bond vector entropies for residues T3-S15, which become ordered upon binding of the S-peptide to the S-protein, is -12.6+/-1.4 J/mol.residue.K. 15N relaxation data suggest a gradient of decreasing entropy values moving from the termini toward the center of the free peptide. The difference between the entropies of the terminal and central residues is about -12 J/mol residue K, a value comparable to that of the average entropy change per residue upon complex formation. Similar entropy gradients are evident in NMR relaxation studies of other denatured proteins. Taken together, these observations suggest denatured proteins may contain entropic contributions from non-local interactions. Consequently, calculations that model the entropy of a residue in a denatured protein as that of a residue in a di- or tri-peptide, might over-estimate the magnitude of entropy changes upon folding. 相似文献
9.
van den Bremer ET Keeble AH Jiskoot W Spelbrink RE Maier CS van Hoek A Visser AJ James R Moore GR Kleanthous C Heck AJ 《Protein science : a publication of the Protein Society》2004,13(5):1391-1401
The family of conserved colicin DNases E2, E7, E8, and E9 are microbial toxins that kill bacteria through random degradation of the chromosomal DNA. In the present work, we compare side by side the conformational stabilities of these four highly homologous colicin DNases. Our results indicate that the apo-forms of these colicins are at room temperature and neutral pH in a dynamic conformational equilibrium between at least two quite distinct conformers. We show that the thermal stabilities of the apo-proteins differ by up to 20 degrees C. The observed differences correlate with the observed conformational behavior, that is, the tendency of the protein to form either an open, less stable or closed, more stable conformation in solution, as deduced by both tryptophan accessibility studies and electrospray ionization mass spectrometry. Given these surprising structural differences, we next probed the catalytic activity of the four DNases and also observed a significant variation in relative activities. However, no unequivocal link between the activity of the protein and its thermal and structural stability could easily be made. The observed differences in conformational and functional properties of the four colicin DNases are surprising given that they are a closely related (> or =65% identity) family of enzymes containing a highly conserved (betabetaalpha-Me) active site motif. The different behavior of the apo-enzymes must therefore most likely depend on more subtle changes in amino acid sequences, most likely in the exosite region (residues 72-98) that is required for specific high-affinity binding of the cognate immunity protein. 相似文献
10.
Search and study of the general principles that govern kinetics and thermodynamics of protein folding generate a new insight into the factors controlling this process. Here, based on the known experimental data and using theoretical modeling of protein folding, we demonstrate that there exists an optimal relationship between the average conformational entropy and the average energy of contacts per residue-that is, an entropy capacity-for fast protein folding. Statistical analysis of conformational entropy and number of contacts per residue for 5829 protein structures from four general structural classes (all-alpha, all-beta, alpha/beta, alpha+beta) demonstrates that each class of proteins has its own class-specific average number of contacts (class alpha/beta has the largest number of contacts) and average conformational entropy per residue (class all-alpha has the largest number of rotatable angles phi, psi, and chi per residue). These class-specific features determine the folding rates: alpha proteins are the fastest folding proteins, then follow beta and alpha+beta proteins, and finally alpha/beta proteins are the slowest ones. Our result is in agreement with the experimental folding rates for 60 proteins. This suggests that structural and sequence properties are important determinants of protein folding rates. 相似文献