Proteins, folding

Proteins Generally Fold into Compact, Well-Defined, Three-Dimensional Structures 

The folding of a protein into a compact structure is accompanied by a large decrease in conformational entropy (disorder) of the protein, which is thermodynamically unfavorable. The native, folded conformation is maintained by a large number of weak, noncovalent interactions that act cooperatively to offset the unfavorable reduction in entropy. These noncovalent interactions include hydrogen bonds, and electrostatic, hydrophobic, and van der Waals interactions. These interactions ensure that the folded protein is (often just marginally) more stable than the unfolded form. 

Charged particles interact with one another according to Coulomb s law  

negatively charged moieties in proteins (such as the carboxylate side chains of Asp and Glu residues) frequently interact with positively charged side chains of Lys, Arg, or His residues. These electrostatic interactions often result in the formation of salt bridges, in which there is some degree of hydrogen bonding in addition to the electrostatic attraction, as illustrated in Fig. 4-3. 

Since water has a high dielectric constant of 80, the energy associated with an ion pair in a protein ranges from as low as 0.5-1.5 kJ mol-1 for a surface interaction up to 15 kJ mol-1 for an electrostatic interaction between residues buried in the interior of the protein, where the dielectric constant is expected to be lower. 

To search for folding intermediates, Khan et al. have examined the folding and unfolding kinetics of wild-type barnase and four mutants . These data combined with direct structural observations and simulation support a minimal reaction pathway for the folding of barnase that involves two detectable folding 

Many proteins are capable of populating partially folded states under specific solution conditions and, occasionally, coexistence of the folded and an unfolded state can be observed by NMR. Ding et al have reported amide residual dipolar couplings (RDCs), nitrogen transverse relaxation rates for varying pH values and different temperatures on the destabilized mutant of the B1 domain of protein G (GBl). The RDCs for the low pH, thermally unfolded state of GBl are very small and do not indicate the presence of any native-like structure. Their data provided clear evidence for intermediate conformations and multi-state equilibrium unfolding for this GBl variant  

Oxidative folding is the fusion of native disulfide bond formation with conformational folding. This complex process is guided by two types of interactions first, covalent interactions between cysteine residues, which transform into na- 

Atreya, H. S. Szyperski, T. Proceedings of the National Academy of Sciences of the United States of America 2004 101,9642-9647. 

Gronwald, W. Kalbitzer, H. R. Progress in Nuclear Magnetic Resonance Spectroscopy 2004 44, 33-96. 

The diffusion-collision model considers the protein molecule to be divided 

Clearly, these studies of protein folding dynamics are only the first steps in obtaining the solution to a very complex problem. Nevertheless, they provide insights that are relevant to experiments and suggest refinements needed in improved treatments of protein folding. 

One of the most intriguing problems in biochemistry is how and why nascent proteins fold into a precise three-dimensional (3-D) structure. It is known that some proteins, the best known being ribonuclease A, can fold spontaneously into its native folded form in a proper aqueous environment. 

The fact is that proteins do fold in a relatively short time, of the order of seconds or minutes. Therefore there must be some efficient route to the folding process. The fact that the protein does fold spontaneously has led to the conclusion that the information contained in the 1-D sequence of amino acids is sufficient to determine the ultimate 3-D structure of the protein. But how does the protein know how to translate this 1-D information into the 3-D structure This is often described as the 3-D code that is embedded in the sequence. Even if there is such a code, there must be some mechanism that deciphers it and translates it into executable orders. The situation may be likened to a book containing all the information required to construct a building. Such a building would never be constructed spontaneously unless some agent translates the information contained in the book into a series of executable orders. 

It is unlikely that there is a one-to-one 3-D code. The fact that there are many different sequences resulting in the formation of the same 3-D structure means that if such a code exists, it must be very redundant. Also, the structure of the native protein is not unique. Proteins always experience structural fluctuations therefore, a given sequence of amino acids does not determine a unique set of coordinates for the folded form of the protein. 

Yet the unfolded 1-D chain does fold into a functionally active unit, which maintains a reasonably well defined structure, within certain limits. It does so in a very short time, far shorter than any estimated time that would have been required by the random selection of a folding pathway. This means that there exists not only a thermodynamic force leading from the unfolded to the folded state, but there must be some dynamical forces, at least in part of the folding pathway, that direct the protein to move toward the final product. 

Having a given sequence of amino acids, one can in principle compute the force acting on each of its nuclei at any moment, and therefore in principle one can follow its folding trajectory under its own forces. This is a very complex problem. One needs to write the potential function for at least some 3M coordinates, where M is the number of residues, and compute the forces at any given configuration. Clearly, different sequences will have different trajectories. 

Other strategies for investigating protein folding have also emerged. Vug-meyster et al. interpret N Ri rho relaxation measurements and show that 

Gonzalez, G. M. Langdon, M. Bruix, A. Galvez, E. Valdivia, M. Maqueda, and M. Rico, Proc. Natl Acad. Sci. USA, 2000, 97,11221-11226. 

Hoffmann, A. Hafner, P. Schmieder, R. Volkmer-Engert, M. Hof, M. Wahl, J. Schneider-Mergener, U. Walter, H. Oschkinat, and 

Batchelor, S. Prasannan, S. Daniell, S. Reece, I. Connerton, G. Bloomberg, G. Dougan, G. Frankel, and S. Matthews, Embo J., 2000,19, 2452-2464. 

Gonnella, J. Koehn, N. Pathak, V. Ganu, R. Melton, 

Information about the biologically active (native) conformation of proteins is already encoded in their amino acid sequences. The native forms of many proteins arise spontaneously in the test tube and within a few minutes. Nevertheless, there are special auxiliary proteins (chaperonines) that support the folding of other proteins in the conditions present within the cell (see p. 232). An important goal of biochemistry is to understand the laws governing protein folding. This would make it possible to predict the conformation of a protein from the easily accessible DNA sequence (see p. 260). 

When the urea and thiol are removed by dialysis (see p. 78), secondary and tertiary structures develop again spontaneously. The cysteine residues thus return to a suf ciently close spatial vicinity that disulfide bonds can once again form under the oxidative effect of atmospheric oxygen. The active center also reestablishes itself In comparison with the denatured protein, the native form is astonishingly compact, at 4.5 2.5 nm. In this state, the apolar side chains (yellow) predominate in the interior of the protein, while the polar residues are mainly found on the surface. This distribution is due to the hydrophobic effect (see p. 28), and it makes a vital contribution to the stability of the native conformation (B). 

The folding of proteins to the native form is favored under physiological conditions. The native conformation is lost, as the result of denaturation, at extreme pH values, at high temperatures, and in the presence of organic solvents, detergents, and other denaturing substances, such as urea. 

The fact that a denatured protein can spontaneously return to its native conformation was demonstrated for the first time with ribonuclease, a digestive enzyme (see p. 266) consisting of 124 amino acids. In the native form (top right), there are extensive pleated sheet structures and three a helices. The eight cysteine residues of the protein are forming four disulfide bonds. Residues His-12, Lys-41 and His-119 (pink) are particularly important for catalysis. Together with additional amino acids, they form the enzyme s active center. 

The disulfide bonds can be reductively cleaved by thiols (e.g., mercaptoethanol, HO-CH2-CH2-SH). If urea at a high concentration is also added, the protein unfolds completely. In this form (left), it is up to 35 nm long. Polar (green) and apolar (yellow) side chains are distributed randomly. The denatured enzyme is completely inactive, because the catalytically important amino acids (pink) are too far away from each other to be able to interact with each other and with the substrate. 

and self are all constituted not by biochemistry, but by the higher-level patterns that biochemistry makes possible. 

The challenge in proteomics is to learn how final protein structures are formed, and the steps involved in their formations. With that knowledge, important proteins can be synthesized in the lab and in industry, improvements in protein enzyme activity can be attempted, and the proteins derived from genetic deficiencies may be able to be corrected. Protein study challenges are listed in Chen and Sivachenko (2005). 

Intricate three-dimensional shapes are crucial to protein functioning. These shapes come about by cross-linking between various biochemical functional groups (mostly amino acids) on the long-chain protein molecule (King et al., 2002). It is the cross-linking among these elanents that provides the motivation and the stability of protein structure. 

Protein folding is the result of interactions among very weak chemical attractions. Proteins have evolved to fold in conditions present in the cells. In some cases, chaperone proteins are required to help other proteins to fold properly. The structural proteins actin and tubulin cannot fold without their specific chaperonins present (King et al., 2002). 

If the protein fails to fold properly, its shape is incorrect and it cannot perform its intended function. Aberrations in protein folding appear to contribute to human diseases. Among these are Alzheimer s disease, prion diseases, emphysema and cirrhosis, amyelotrophic lateral sclerosis (Lou Gehrig s disease), cystic fibrosis, some tumors, and osteogenesis imperfecta (King et al., 2002). The prion that seems to cause ovine transmissible spongiform encephalopathy, for instance, appears as a pleated sheet rather than a smooth helix. 

Orientation-dependent PMF gives valuable insight into the nature of the orientation-dependent interaction between any two amino acid residues. The orientation-dependent PMF also reveals many unexpected pair interactions which defy the trend given by the hydropathy scale. An example is provided by the Arg-Arg pair interaction, which is found to be surprisingly attractive at short separahon, even though it is one of the most hydrophilic residues. 

The reason was found to be the presence of an HB that forms a bridge between the two arginine residues. Such specihc many-body effects cannot be captured in a hydropathy scale. 

Yet another interesting outcome of this recent study was the discovery of an anomalous strong effective attractive interaction between two histidine residues and between two tryptophan residues. This could be ascribed to the interaction mediated by metals, as these are residues that form coordination complexes with metals such as cobalt or iron. 

Barrett, R., Berry, M., Chan, T. E, Demmel,)., Donato, ]., Dongarra,)., Eijkhout, V., Pozo, R., Romine, C., and Van der Vorst, H. (1994). Templates for the Solution of Linear Systems Building Blocks for Iterative Methods, 2nd Edition (SIAM, Philadelphia, PA). 

Le Trong, I., Cerutti, D. S., Gulich, S., Stayton, P. S., Stenkamp, R. E., and Lybrand, T. P. (2010). A distal point mutation in the streptavidin/biotin complex preserves structure but diminishes binding affinity Experimental evidence of electronic polarization effects Biochemistry 49, pp. 4568-4570. 

Cieplak, P, Cornell, W., and Kollman, P. A. (1993). A well-behaved electrostatic potential based method using charge restraints for deriving atomic charges The RESP model. Journal of Physical Chemistry 97, pp. 10269-10280. 

Berente, I., Czinki, E., and Naray-szab6, G. (2007). A combined electronegativity equalization and electrostatic potential fit method for the determination of atomic point charges. Journal of Computational Chemistry 28,12, pp. 1936-1942. 

Cieplak, R, Cornell, W. D., Bayly, C., and Kollman, P. A. (1995]. Application of the multimolecule and multiconformational RESP methodology to biopolymers Charge derivation for DNA, RNA, and proteins, Journal of Computational Chemistry 16, pp. 1357-1377. 

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Both the structural and kinetic aspects of the protein-folding problem are complicated by the fact that folding takes place within a bath of water molecules. In fact, hydrophobic interactions are almost certainly crucial for both the relation of the sequence and the native structure, and the process by which a good sequence folds to its native structure. 

Asher S A and Chi Z H 1998 UV resonance Raman studies of protein folding in myoglobin and other proteins Biophys. 

Plenary 4. George J Thomas Jr et at, e-mail address thomasgj ,cctr.mnkc.edu (RS). Protein folding and assembly into superstructures. (Slow) time resolved RS probing of virus construction via protein assembly into an icosahedral (capsid) shell. 

C2.5 Introducing protein folding using simple models... 

Most reactions in cells are carried out by enzymes [1], In many instances the rates of enzyme-catalysed reactions are enhanced by a factor of a million. A significantly large fraction of all known enzymes are proteins which are made from twenty naturally occurring amino acids. The amino acids are linked by peptide bonds to fonn polypeptide chains. The primary sequence of a protein specifies the linear order in which the amino acids are linked. To carry out the catalytic activity the linear sequence has to fold to a well defined tliree-dimensional (3D) stmcture. In cells only a relatively small fraction of proteins require assistance from chaperones (helper proteins) [2]. Even in the complicated cellular environment most proteins fold spontaneously upon synthesis. The detennination of the 3D folded stmcture from the one-dimensional primary sequence is the most popular protein folding problem. 

From our perspective there are four major problems that comprise the protein folding enterjDrise. They are ... 

How to design sequences tliat adopt a specified fold [9] This is tire inverse protein folding problem tliat is vital to the biotechnology industry. There are some proteins tliat do not spontaneously reach tire native confomiation. In tire cells tliese proteins fold witli tire assistance of helper molecules referred to as chaperonins. The chaperonin-mediated folding problem involves an understanding of tire interactions between proteins. 

MES)==10 These results suggest tliat C(MES) grows (in all likelihood) only as In N with N. Thus tlie restriction of compactness and low energy of tlie native states may impose an upper bound on tlie number of distinct protein folds. 

C2.5.3.4 EXPLORING THE PROTEIN FOLDING MECHANISM USING THE LATTICE MODEL... 

The examples of modelling discussed in section C2.5.2 and section C2.5.3 are meant to illustrate tlie ideas behind tlie tlieoretical and computational approaches to protein folding. It should be borne in mind tliat we have discussed only a very limited aspect of tlie rich field of protein folding. The computations described in section C2.5.3 can be carried out easily on a desktop computer. Such an exercise is, perhaps, tlie best of way of appreciating tlie simple approach to get at tlie principles tliat govern tlie folding of proteins. 

Lorimer G H 1996 A quantitative assessment of the role of the ohaperonin proteins in protein folding in vivo FASEB J. 10 5-9... 

Lansbury P T 1999 Evolution of amyloids What normal protein folding oan tell us about fibrillogenesis and disease Proc. Nati Acad. Sci. (USA) 96 3342-4... 

Onuohio J N, Luthey-Sohulten Z A and Wolynes P G 1997 Theory of protein folding An energy landsoape perspeotive Ann. Rev. Phys. Chem. 48 545-600... 

Thirumalai D and Klimov D K 1999 Deoiphering the timesoales and meohanisms of protein folding using minimal off-lattioe models Curr. Opin. Stmct. Bid. 9 197-207... 

Garel T, Orland H and Thirumalai D 1996 Analytical theories of protein folding New Developments in Theoretical Studies of Protein Folding e6 R Elber (Singapore World Scientific) pp 197-268... 

Bryngelson J D and Wolynes P G 1987 Spin glasses and the statistical mechanics of protein folding Proc. Natl Acad. Sci. (USA) 84 7524-8... 

Dill K A, Bromberg S, Yue K, Fiebig K M, Yee D P, Thomas P D and Chan H S 1995 Principles of protein folding—a perspective from simple exact models Protein Sci. 561-602... 

Taketomi H, Ueda Y and Go N 1975 Studies on protein folding, unfolding, and fluctuations by computer simulation Int. J. Pept. Protein Res. 7 445-59... 

Li FI, Winfreen N and Tang C 1996 Emergence of preferred structures in a simple model of protein folding Science 273 666-9... 

Guo Z and Thirumalai D 1995 Kinetics of protein folding nucleation mechanism, time scales and pathways Biopolymers 36 83-103... 

Shakhnovich E I, Abkevich V and Ptitsyn O 1996 Conserved residues and the mechanism of protein folding Nature 379 96-8... 

Wang J and Wang W 1999 A computational approach to simplifying the protein folding alphabet Natur. Struct. Biol. 6 1033-8... 

Biological infonnation is also concerned witli tire analysis of biological messages and tlieir import. The fundamental premise of tire protein-folding problem section C2.14.2.2 is tliat tire full tliree-dimensional arrangement of tire protein molecule can be predicted, given only tire amino acid sequence, together witli tire solvent composition, temperature and pressure. One test of tire validity of tliis premise is to compare tire infonnation content of tire sequence witli tire infonnation contained in tire stmcture [169]. The fonner can be obtained from Shannon s fonnula ... 

Bryngelson J D, Onuchic J N, Socci N D and Wolynes P G 1995 Funnels, pathways, and the energy landscape of protein folding a synthesis Profe/ns 21 167-95... 

Fernandez A and Colubri A 1998 Microscopic dynamics from a coarsely defined solution to the protein folding problem J. Math. Phys. 39 3167-87... 

Williams S, Causgrove T P, Gilmanshin R, Fang KS, Callender R H, Woodruff WH and Dyer R B 1996 Fast events in protein folding helix melting and formation in a small peptide Biochemistry ZS 691-7... 

The method has severe limitations for systems where gradients on near-atomic scale are important (as in the protein folding process or in bilayer membranes that contain only two molecules in a separated phase), but is extremely powerful for (co)polymer mixtures and solutions [147, 148, 149]. As an example Fig. 6 gives a snapshot in the process of self-organisation of a polypropylene oxide-ethylene oxide copolymer PL64 in aqueous solution on its way from a completely homogeneous initial distribution to a hexagonal structure. 

Such globed master equations have recently gained attention in the study of protein folding. See for example C. De Dominicis, H. Orland and F. Lainee, J. Phys. Lett., 46 L463, 1985 E.I. Shakhnovich and A. M. Gutin, Eurphys. Lett., 9 569, 1989 J. G. Saven, J. Wang and P. G. Wolynes, J. Chem. Phys., 101 11037, 1994. 

New Techniques for the Construction of Residue Potentials for Protein Folding... 

Abstract. A smooth empirical potential is constructed for use in off-lattice protein folding studies. Our potential is a function of the amino acid labels and of the distances between the Ca atoms of a protein. The potential is a sum of smooth surface potential terms that model solvent interactions and of pair potentials that are functions of a distance, with a smooth cutoff at 12 Angstrom. Techniques include the use of a fully automatic and reliable estimator for smooth densities, of cluster analysis to group together amino acid pairs with similar distance distributions, and of quadratic progrmnming to find appropriate weights with which the various terms enter the total potential. For nine small test proteins, the new potential has local minima within 1.3-4.7A of the PDB geometry, with one exception that has an error of S.SA. 

Keywords, protein folding, tertiary structure, potential energy surface, global optimization, empirical potential, residue potential, surface potential, parameter estimation, density estimation, cluster analysis, quadratic programming... 

The protein folding problem is the task of understanding and predicting how the information coded in the amino acid sequence of proteins at the time of their formation translates into the 3-dimensional structure of the biologically active protein. A thorough recent survey of the problems involved from a mathematical point of view is given by Neumaier [22]. 

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