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Estimates of the Loss of Main-Chain Conformational Entropy of Different Residues on Protein Folding

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Estimates of the Loss of Main-Chain Conformational Entropy of Different Residues on Protein Folding View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Publications of the IAS Fellows PROTEINS: Structure, Function, and Genetics 36:332–339 (1999) Estimates of the Loss of Main-Chain Conformational Entropy of Different Residues on Protein Folding Debnath Pal and Pinak Chakrabarti* Department of Biochemistry, Bose Institute, Calcutta, India ABSTRACT The average contribution of confor- cal/K.mol with respect to that of glycine. They further mational entropy for individual amino acid residues substantiated their result by computing the energy profile towards the free energy of protein folding is not well of the backbone conformations as a function of the main- understood. We have developed empirical scales for chain dihedral angles, ␾ and ␺. However, as discussed the loss of the main-chain (torsion angles, ␾ and ␺) below, the ␾,␺ angles can be influenced by the conforma- conformational entropy by taking its side-chain into tion of the side-chain of individual residues, and this needs account. The analysis shows that the main-chain to be taken into account while calculating the conforma- component of the total conformational entropy loss tional entropy of the main-chain. Here we report such a for a residue is significant and reflects intrinsic calculation to show that the main-chain of each residue characteristics associated with individual residues. makes a distinct contribution towards the loss of conforma- The values have direct correlation with the hydro- tional entropy on folding, and that the values are related to phobicity values and this has important bearing on hydrophobicity. the folding process. Proteins 1999;36:332–339. ௠ 1999 Wiley-Liss, Inc. Influence of the Side-Chain That each amino acid residue leaves its imprint on the Key words: conformation; conformational entropy; protein structure on the basis of the chemical nature of its hydrophobicity; protein folding; pro- side-chain, is undisputed. However, at a more subtle level tein engineering the side-chain can also influence the main-chain conforma- tion of the residue,21 and the assumption that the ␾,␺ INTRODUCTION space is independent of the residue type while calculating When a protein folds into a compact globule, the resi- the relative entropy values15 is not justified. Because of the dues lose degrees of freedom as lesser number of conforma- interdependence between the main-chain and the side- tions can be accessed by the main- and the side-chain— chain torsion angles,21–23 a residue is represented not by a this reduction in conformational entropy opposes the folding single ␾,␺ distribution, but by distributions at three 1,2 process. On the other hand, water molecules released discreet values of ␹1 (Ϫ60, 180 and 60°, which are desig- from contact with nonpolar side-chains (that get buried in nated as gϩ, t and gϪ conformational states, respectively), the folded state) gain in entropy. These are the source of or better yet, one should consider the distribution in the the hydrophobic effect, which is a major driving force for three-dimensional space (␾,␺,␹1). Additionally, instead of folding.3,4 However, as most globular proteins are only considering the influence of the side-chain up to the ␥ marginally stable (the free energy for a folding-unfolding position only (␹1-torsion), the effect of the whole side-chain reaction is around 5–20 kcal/mol)5 it appears that the can also be taken into account by calculating the ␾,␺ conformational entropy is the prime deterrent to folding.6 distribution for all the rotameric states of the side-chain. While the calculation/measurement of the free energy All these methods to incorporate the effect of the side- associated with hydrophobicity has received wide atten- chain while calculating the main-chain conformational tion, Cornette et al.7 reporting a comparison of 38 different entropy have been implemented by us. scales, the quantification of the conformational entropy changes has been rare and usually computation-inten- Folded and Unfolded States 1,8–13 sive. Some recent work in this area have determined If one attempts to calculate the change in conforma- scales for the conformational entropy change of side- tional entropy in bringing a particular residue to the 14–19 chains during protein folding. The backbone gets folded state, the unique conformation of the residue re- neglected in such studies, presumably with the assump- quires its entropy in the folded state to be set to zero.15 On tion that the restriction on the conformation of the main- the other hand, instead of dealing with a residue in specific chain on folding is the same for all residues, and hence its location in a protein structure, if we are interested in the inclusion will result in the addition of a constant term to all the entropy values such that the relative scale remains the same. D’Aquino et al.20 have recently shown experimen- tally that this assumption is not valid and that the *Correspondence to: Pinak Chakrabarti, Department of Biochemis- try, P-1/12 CIT Scheme VIIM, Bose Institute, Calcutta, 700 054, India. presence of the methyl group in alanine reduces the E-mail: [email protected] conformational entropy of the peptide backbone by 2.5 Received 17 December 1998; Accepted 8 April 1999 ௠ 1999 WILEY-LISS, INC. LOSS OF MAIN-CHAIN CONFORMATIONAL ENTROPY 333 average value for all residues of the same type then we have to consider the distribution of the conformational angles of the amino acid residue both in the folded and the unfolded states. For example, Creamer and Rose,14 while investigating the difference in conformational entropy between a series of apolar side-chains in the unfolded state and in the ␣-helical state, obtained these two distributions using Monte Carlo calculations. Although the rotational states that are being sampled by the main-chain in the folded state are directly available from the statistical analysis of known structures, the information on the unfolded state is not directly available. As a result, scales of main-chain entropy changes during folding have been proposed relative to the value for Gly (considering ␾,␺ distributions in native states only).8,24 Below we propose a procedure to fill in the lacuna on the unfolded state. We have recently shown21 that amino acid residues (barring Gly,Ala and Pro) can be classified into five classes depending on how the ␾,␺ distribution of individual resi- dues get affected by a change of the side-chain torsion angle ␹1. These are: Class I: Ser, Cys, Met, Glu, Gln, Lys and Arg; II: Leu; III: Asp and Asn; IV: His, Phe, Tyr and Trp; and V: Val, Ile and Thr. The classification is also Fig. 1. Distribution of points corresponding to all Ile residues in the chemically intuitive. Residues in a given class have similar three-dimensional space. For one cluster the standard deviations (magni- topological arrangements at least up to the ␥-position, fied four times) of the distribution of points are shown, which are the ellipsoidal axes used for the calculation of volume in Method 1. beyond which the side-chain atoms do not significantly interact with the main-chain atoms, and are non-invasive as regard to the ␾,␺ distribution.21 For example, Class I has linear side-chains (up to ␥-position), whereas Class V In one of the earliest studies Ne´methy et al.8 estimated the has aliphatic chains branched at C␤. As steric clash is the restrictions on folding of either the main-chain or the ␾ ␺ limiting factor that affects the , angles in the unfolded side-chain using: state, one can safely assume that the ranges of the ␾,␺ angles that all residues in a given class span in the ⌬S ϭ unfolded state are identical. Because of the additional short range interactions (like hydrogen bonding) that are accessible conformational space unfolded brought into play in the folded state (for example, due to ϪRln . (1) accessible conformational space folded the presence of different atoms, as in Val and Thr), the 1 2 distribution of angles within this allowed ␾,␺ space (in the unfolded state) becomes different for different residues in a Although they used the area spanned by the torsion angles ␾ ␺ class. Conversely then, the combined distribution of the , to determine the main-chain entropy changes during folding, we have used the equation by considering the ␾,␺ (and ␹1) values for all the members in a class can be ␾ ␺ ␹ taken as the representation of the distribution in the volume occupied by different residues in the ( , , 1) space. unfolded state for any member of the class. This translates Depending on the distribution of points, the 3-dimensional to the assumption that in the unfolded state a residue space is divided into a number of regions, such that each cannot assume a (␾,␺,␹1) value not accessible to any region encompasses a cluster of points (Fig. 1). For a given member of the class in the native state, and that the residue the mean and the standard deviation (␴)ofthe␾,␺ 21 distribution is random. Further justification for this as- and ␹1 values in a cluster are calculated. The product of sumption is provided by the energy calculations given in the three ␴ values gives the volume of an ellipsoid that the next section. provides an estimate of the dispersion of points in the cluster. The summation of these ellipsoidal volumes over all the regions give the conformational space available to Theory the residue in the folded state. The same procedure The change in the conformational entropy, ⌬S, for a repeated using the combined distribution of points for all main-chain taken from the unfolded state (U) to the folded the members in a class gives the value for the unfolded (F) state is given by: state of a member residue.
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