Is counterion delocalization responsible for collapse in RNA folding?

Although energetic and phylogenetic methods have been very successful for prediction of nucleic acid secondary structures, arrangement of these secondary structure elements into tertiary structure has remained a difficult problem. Here we explore the packing arrangements of DNA, RNA, and DNA/RNA hybrid molecules in crystals. In the conventional view, the highly charged double helix will be pushed toward isolation by favorable solvation effects; interactions with other like-charged stacks would be strongly disfavored. Contrary to this expectation, we find that most of the cases analyzed ( approximately 80%) exhibit specific, preferential packing between elements of secondary structure, which falls into three categories: (i) interlocking of major grooves of two helices, (ii) side-by-side parallel packing of helices, and (iii) placement of the ribose-phosphate backbone ridge of one helix into the major groove of another. The preponderance of parallel packing motifs is especially surprising. This category is expected to be maximally disfavored by charge repulsion. Instead, it comprises in excess of 50% of all packing interactions in crystals of A-form RNA and has also been observed in crystal structures of large RNA molecules. To explain this puzzle, we introduce a novel model for RNA folding. A simple calculation suggests that the entropy gained by a cloud of condensed cations surrounding the helices more than offsets the Coulombic repulsion of parallel arrangements. We propose that these condensed counterions are responsible for entropy-driven RNA collapse, analogous to the role of the hydrophobic effect in protein folding.

The Flory isolated-pair hypothesis is not valid for polypeptide chains: implications for protein folding

Using an all-atom representation, we exhaustively enumerate all sterically allowed conformations for short polyalanyl chains. Only intrachain interactions are considered, including one adjustable parameter, a favorable backbone energy (e.g., a peptide hydrogen bond). The counting is used to reevaluate Flory's isolated-pair hypothesis, the simplifying assumption that each phi,psi pair is sterically independent. This hypothesis is a conceptual linchpin in helix-coil theories and protein folding. Contrary to the hypothesis, we find that systematic local steric effects can extend beyond nearest-chain neighbors and can restrict the size of accessible conformational space significantly. As a result, the entropy price that must be paid to adopt any specific conformation is far less than previously thought.

A physical basis for protein secondary structure

A physical theory of protein secondary structure is proposed and tested by performing exceedingly simple Monte Carlo simulations. In essence, secondary structure propensities are predominantly a consequence of two competing local effects, one favoring hydrogen bond formation in helices and turns, the other opposing the attendant reduction in sidechain conformational entropy on helix and turn formation. These sequence specific biases are densely dispersed throughout the unfolded polypeptide chain, where they serve to preorganize the folding process and largely, but imperfectly, anticipate the native secondary structure.

A complete conformational map for RNA

A simple stereochemical framework for understanding RNA structure has remained elusive to date. We present a comprehensive conformational map for two nucleoside-5',3'-diphosphates and for a truncated dinucleotide derived from a grid search of all potential conformers using hard sphere steric exclusion criteria to define allowed conformers. The eight-dimensional conformational space is presented as a series of two-dimensional projections. These projections reveal several well-defined allowed and disallowed regions which correlate well with data obtained from X-ray crystallography of both large and small RNA molecules. Furthermore, the two-dimensional projections show that consecutive and ribose ring-proximal torsion angles are interdependent, while more distant torsion angles are not. Remarkably, using steric criteria alone, it is possible to generate a predictive conformational map for RNA.

Identifying two ancient enzymes in Archaea using predicted secondary structure alignment

It is now possible to compare life forms at high levels of detail and completeness due to the increasing availability of whole genomes from all three domains. However, exploration of interesting hypotheses requires the ability to recognize a correspondence between proteins that may since have diverged beyond the threshold of detection by sequence-based methods. Since protein structure is far better conserved than protein sequence, structural information can enhance detection sensitivity, and this is the basis for the field of structural genomics. Demonstrating the effectiveness of this approach, we identify two important but previously elusive Archaeal enzymes: a homolog of dihydropteroate synthase and a thymidylate synthase. The former is especially noteworthy in that no Archaeal homolog of a bacterial folate biosynthetic enzyme has been found to date. Experimental confirmation of the deduced activity of both enzymes is described. Identification of two different proteins was attempted deliberately to help allay concern that predictive success is merely a lucky accident.

A protein taxonomy based on secondary structure

Does a protein's secondary structure determine its three-dimensional fold? This question is tested directly by analyzing proteins of known structure and constructing a taxonomy based solely on secondary structure. The taxonomy is generated automatically, and it takes the form of a tree in which proteins with similar secondary structure occupy neighboring leaves. Our tree is largely in agreement with results from the structural classification of proteins (SCOP), a multidimensional classification based on homologous sequences, full three-dimensional structure, information about chemistry and evolution, and human judgment. Our findings suggest a simple mechanism of protein evolution.

Is protein folding hierarchic? II. Folding intermediates and transition states

The folding reactions of some small proteins show clear evidence of a hierarchic process, whereas others, lacking detectable intermediates, do not. Evidence from folding intermediates and transition states suggests that folding begins locally, and that the formation of native secondary structure precedes the formation of tertiary interactions, not the reverse. Some notable examples in the literature have been interpreted to the contrary. For these examples, we have simulated the local structures that form when folding begins by using the LINUS program with nonlocal interactions turned off. Our results support a hierarchic model of protein folding.

Is protein folding hierarchic? I. Local structure and peptide folding

The folding reactions of some small proteins show clear evidence of a hierarchic process, whereas others, lacking detectable intermediates, do not. Nevertheless, we argue that both classes fold hierarchically and that folding begins locally. If this is the case, then the secondary structure of a protein is determined largely by local sequence information. Experimental data and theoretical considerations support this argument. Part I of this article reviews the relationship between secondary structures in proteins and their counterparts in peptides.

Seeking an ancient enzyme in Methanococcus jannaschii using ORF, a program based on predicted secondary structure comparisons

We have developed a simple procedure to identify protein homologs in genomic databases. The program, called ORF, is based on comparisons of predicted secondary structure. Protein structure is far better conserved than amino acid sequence, and structure-based methods have been effective in exploiting this fact to find homologs, even among proteins with scant sequence identity. ORF is a secondary structure-based method that operates solely on predictions from sequence and requires no experimentally determined information about the structure. The approach is illustrated by an example: Thymidylate synthase, a highly conserved enzyme essential to thymidine biosynthesis in both prokaryotes and eukaryotes, is thought to be used by Archaea, but a corresponding gene has yet to be identified. Here, a candidate thymidylate synthase is identified as a previously unassigned open reading frame from the genome of Methanococcus jannaschii, viz., MJ0757. Using primary structure information alone, the optimally aligned sequence identity between MJ0757 and Escherichia coli thymidylate synthase is 7%, well below the threshold of sensitivity for detection by sequence-based methods.

Helix capping

Helix-capping motifs are specific patterns of hydrogen bonding and hydrophobic interactions found at or near the ends of helices in both proteins and peptides. In an alpha-helix, the first four >N-H groups and last four >C=O groups necessarily lack intrahelical hydrogen bonds. Instead, such groups are often capped by alternative hydrogen bond partners. This review enlarges our earlier hypothesis (Presta LG, Rose GD. 1988. Helix signals in proteins. Science 240:1632-1641) to include hydrophobic capping. A hydrophobic interaction that straddles the helix terminus is always associated with hydrogen-bonded capping. From a global survey among proteins of known structure, seven distinct capping motifs are identified-three at the helix N-terminus and four at the C-terminus. The consensus sequence patterns of these seven motifs, together with results from simple molecular modeling, are used to formulate useful rules of thumb for helix termination. Finally, we examine the role of helix capping as a bridge linking the conformation of secondary structure to supersecondary structure.

Modeling unfolded states of proteins and peptides. II. Backbone solvent accessibility

Buried surface area is often used as a measure of the contribution to protein folding from the hydrophobic effect. Quantitatively, the surface buried upon folding is reckoned as the difference in area between the native and unfolded states. This calculation is well defined for a known structure but model-dependent for the unfolded state. In a previous paper [Creamer, T. P., Srinivasan, R., & Rose, G. D. (1995) Biochemistry 34, 16245-16250], we developed two models that bracket the surface area of the unfolded state between limiting extremes. Using these extrema, it was shown that earlier models, such as an extended tripeptide, overestimate the surface area of side chains in the unfolded state. In this sequel to our previous paper, we focus on backbone surface in the unfolded state, again adopting the strategy of trapping the area between limiting extrema. A principal conclusion of this present study is that most backbone surface in proteins is buried within local structure.

Modeling unfolded states of peptides and proteins

The hydrophobic effect is the major factor that drives a protein molecule toward collapse and folding. In this process, residues with apolar side chains associate to form a solvent-shielded hydrophobic core. Often, this hydrophobic contribution to folding is quantified by measuring buried apolar surface area, reckoned as the difference in area between hydrophobic groups in the folded protein and in a standard state. Typically, the standard state area of a residue is obtained from tripeptide models, with the results taken to implicitly represent values appropriate for the unfolded state. Here, we show that a tripeptide is a poor descriptor of the unfolded state, and its widespread use has prompted erroneous conclusions about folding. As an alternative, we explore two limiting models, chosen to bracket the expected behavior of the unfolded chain between reliable extremes. One extreme is represented by simulated hard-sphere peptides and shown to behave like a homopolymer with excluded volume in a good solvent. The other extreme is represented by fragments excised from folded proteins and conjectured to approximate the time-average behavior of a thermally denatured protein at Tm, the midpoint of the unfolding transition. Using these models, it is shown that the area buried by apolar side chains upon folding is considerably less than earlier estimates. For example, upon transfer from the unfolded state to the middle of an alpha-helix, an alanine side chain buries negligible area and, surprisingly, a valine side chain actually gains area. Among other applications, an improved model of the unfolded state can be used to better evaluate the driving force for helix formation in peptides and proteins.

Rigid domains in proteins: an algorithmic approach to their identification

A rigid domain, defined here as a tertiary structure common to two or more different protein conformations, can be identified numerically from atomic coordinates by finding sets of residues, one in each conformation, such that the distance between any two residues within the set belonging to one conformation is the same as the distance between the two structurally equivalent residues within the set belonging to any other conformation. The distance between two residues is taken to be the distance between their respective alpha carbon atoms. With the methods of this paper we have found in the deoxy and oxy conformations of the human hemoglobin alpha 1 beta 1 dimer a rigid domain closely related to that previously identified by Baldwin and Chothia (J. Mol. Biol. 129: 175-220, 1979). We provide two algorithms, both using the difference-distance matrix, with which to search for rigid domains directly from atomic coordinates. The first finds all rigid domains in a protein but has storage and processing demands that become prohibitively large with increasing protein size. The second, although not necessarily finding every rigid domain, is computationally tractable for proteins of any size. Because of its efficiency we are able to search protein conformations recursively for groups of non-intersecting domains. Different protein conformations, when aligned by superimposing their respective domain structures, can be examined for structural differences in regions complementing a rigid domain.

Interactions between hydrophobic side chains within alpha-helices

The thermodynamic basis of helix stability in peptides and proteins is a topic of considerable interest. Accordingly, we have computed the interactions between side chains of all hydrophobic residue pairs and selected triples in a model helix, using Boltzmann-weighted exhaustive modeling. Specifically, all possible pairs from the set Ala, Cys, His, Ile, Leu, Met, Phe, Trp, Tyr, and Val were modeled at spacings of (i, i + 2), (i, i + 3), and (i, i + 4) in the central turn of a model poly-alanyl alpha-helix. Significant interactions--both stabilizing and destabilizing-- were found to occur at spacings of (i, i + 3) and (i, i + 4), particularly in side chains with rings (i.e., Phe, Tyr, Trp, and His). In addition, modeling of leucine triples in a helix showed that the free energy can exceed the sum of pairwise interactions in certain cases. Our calculated interaction values both rationalize recent experimental data and provide previously unavailable estimates of the constituent energies and entropies of interaction.

LINUS: a hierarchic procedure to predict the fold of a protein

We describe LINUS, a hierarchic procedure to predict the fold of a protein from its amino acid sequence alone. The algorithm, which has been implemented in a computer program, was applied to large, overlapping fragments from a diverse test set of 7 X-ray-elucidated proteins, with encouraging results. For all proteins but one, the overall fragment topology is well predicted, including both secondary and supersecondary structure. The algorithm was also applied to a molecule of unknown conformation, groES, in which X-ray structure determination is presently ongoing. LINUS is an acronym for Local Independently Nucleated Units of Structure. The procedure ascends the folding hierarchy in discrete stages, with concomitant accretion of structure at each step. The chain is represented by simplified geometry and folds under the influence of a primitive energy function. The only accurately described energetic quantity in this work is hard sphere repulsion--the principal force involved in organizing protein conformation [Richards, F. M. Ann. Rev. Biophys. Bioeng. 6:151-176, 1977]. Among other applications, the method is a natural tool for use in the human genome initiative.

The T-to-R transformation in hemoglobin: a reevaluation

The relationship between the T, R, and R2 quaternary forms of hemoglobin is examined by computational experiments. Contrary to previous suggestions, we propose that the R quaternary form may lie on the pathway from T to R2. This proposal is consistent with four independent observations. (i) Difference distance maps are used to identify those parts of the molecule that undergo conformational change upon oxygenation. The simplest interpretation of these maps brackets R between T and R2. (ii) Linear interpolation from T to R2 passes through R. (iii) The well-known "switch" region (so called because, upon transition between the T and R quaternary forms, a residue from the beta 2 subunit toggles between two stable positions within the alpha 1 subunit) progresses from T through R to R2, successively. (iv) A hitherto-undocumented feature, diagnostic of the R structure, is noted within the alpha subunit: upon transformation from T to R, the beta-turns at the amino terminal of the E and F helices flip from one turn type to another. Upon transformation from R to R2, the latter turn--a strained conformation--flips back again.

Sequence determinants of the capping box, a stabilizing motif at the N-termini of alpha-helices

The capping box, a recurrent hydrogen bonded motif at the N-termini of alpha-helices, caps 2 of the initial 4 backbone amide hydrogen donors of the helix (Harper ET, Rose GD, 1993, Biochemistry 32:7605-7609). In detail, the side chain of the first helical residue forms a hydrogen bond with the backbone of the fourth helical residue and, reciprocally, the side chain of the fourth residue forms a hydrogen bond with the backbone of the first residue. We now enlarge the earlier definition of this motif to include an accompanying hydrophobic interaction between residues that bracket the capping box sequence on either side. The expanded box motif--in which 2 hydrogen bonds and a hydrophobic interaction are localized within 6 consecutive residues--resembles a glycine-based capping motif found at helix C-termini (Aurora R, Srinivasan R, Rose GD, 1994, Science 264:1126-1130).

Vigorous, aerobic exercise versus general motor training activities: effects on maladaptive and stereotypic behaviors of adults with both autism and mental retardation

Examined the effects of antecedent exercise conditions on maladaptive and stereotypic behaviors in 6 adults with both autism and moderate to profound mental retardation. The behaviors were observed in a controlled environment before and after 2 exercise and 1 non-exercise conditions. From the original group of 6 participants, 2 were selected subsequently to participate in aerobic exercise immediately before performing a community-integrated vocational task. Only antecedent aerobic exercise significantly reduced maladaptive and stereotypic behaviors in the controlled setting. Neither of the less vigorous antecedent conditions did. When aerobic exercise preceded the vocational task, similar reductions were observed. There were individual differences in response to antecedent exercise. Use of antecedent aerobic exercise to reduce maladaptive and stereotypic behaviors of adults with both autism and mental retardation is supported.

Molten globular characteristics of the native state of apomyoglobin

Apomyoglobin, myoglobin lacking the haem group, is a natural intermediate in biosynthesis of myoglobin, and has some structural features in common with the haem-containing native state. Unfolding or refolding studies of apomyoglobin have identified a molten globule intermediate at acid pH. We show here that both the native state of apomyoglobin and the molten globule intermediate have highly plastic structures. Substitution of single amino acids on the surface or in the interior of helices in the native protein produce dramatic changes in the helix content and tryptophan emission of apomyoglobin at neutral and acidic pH. The signals from the intermediate and native apomyoglobin correlate closely suggesting that apomyoglobin itself has a molten globule-like character, its structure representing a population of interconverting substates rather than a fixed conformation.

Alpha-helix-forming propensities in peptides and proteins

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 alpha-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.

Rules for alpha-helix termination by glycine

A predictive rule for protein folding is presented that involves two recurrent glycine-based motifs that cap the carboxyl termini of alpha helices. In proteins, helices that terminated in glycine residues were found predominantly in one of these two motifs. These glycine structures had a characteristic pattern of polar and apolar residues. Visual inspection of known helical sequences was sufficient to distinguish the two motifs from each other and from internal glycines that fail to terminate helices. These glycine motifs--in which the local sequence selects between available structures--represent an example of a stereochemical rule for protein folding.

Helix stop signals in proteins and peptides: the capping box

The alpha-helix [Pauling, L., Corey, R. B., & Branson, H. R. (1951) Proc. Natl. Acad. Sci. U.S.A. 37, 205-211] is a common motif in both proteins and peptides. Despite intense investigation, predictive understanding of helices is still lacking. A recent hypothesis [Presta, L. G., & Rose, G. D. (1988) Science 240, 1632-1641] proposed that the structural specificity of helices resides, in part, in those residues that flank helix termini. If so, then signals that arrest helix propagation--i.e., helix stop signals--should be found among these flanking residues. Evidence is presented for the existence of one such signal, a reciprocal backbone-side-chain hydrogen-bonding interaction, dubbed the capping box. In proteins, the capping box is found uniquely at helix N-termini. In peptides, the capping box can function as a helix stop signal, as shown in the work of Kallenbach and co-workers.

Effects of alanine substitutions in alpha-helices of sperm whale myoglobin on protein stability

The peptide backbones in folded native proteins contain distinctive secondary structures, alpha-helices, beta-sheets, and turns, with significant frequency. One question that arises in folding is how the stability of this secondary structure relates to that of the protein as a whole. To address this question, we substituted the alpha-helix-stabilizing alanine side chain at 16 selected sites in the sequence of sperm whale myoglobin, 12 at helical sites on the surface of the protein, and 4 at obviously internal sites. Substitution of alanine for bulky side chains at internal sites destabilizes the protein, as expected if packing interactions are disrupted. Alanine substitutions do not uniformly stabilize the protein, either in capping positions near the ends of helices or at mid-helical sites near the surface of myoglobin. When corrected for the extent of exposure of each side chain replaced by alanine at a mid-helix position, alanine replacement still has no clear effect in stabilizing the native structure. Thus linkage between the stabilization of secondary structure and tertiary structure in myoglobin cannot be demonstrated, probably because of the relatively small free energy differences between side chains in stabilizing isolated helix. By contrast, about 80% of the variance in free energy observed can be accounted for by the loss in buried surface area of the native residue substituted by alanine. The differential free energy of helix stabilization does not account for any additional variation.

Protein folding--what's the question?

The folding reactions of many small, globular proteins exhibit two-state kinetics, in which the folded and unfolded states interconvert readily without observable intermediates. Typically, the free energy difference, delta G, between the native and denatured states of such a protein is quite small, lying in the range of approximately -5 to -15 kcal/mol. We point out that, under these circumstances, a population of native-like molecules will persist, even in the presence of mutations sufficiently destabilizing to change the sign of delta G. Therefore, it is not energy per se that determines conformation. A corollary to this argument is that specificity--not stability--would be the more informative focus in future folding studies.

Hydrogen bonding in globular proteins

A global census of the hydrogen bonds in 42 X-ray-elucidated proteins was taken and the following demographic trends identified: (1) Most hydrogen bonds are local, i.e. between partners that are close in sequence, the primary exception being hydrogen-bonded ion pairs. (2) Most hydrogen bonds are between backbone atoms in the protein, an average of 68%. (3) All proteins studied have extensive hydrogen-bonded secondary structure, an average of 82%. (4) Almost all backbone hydrogen bonds are within single elements of secondary structure. An approximate rule of thirds applies: slightly more than one-third (37%) form i----i--3 hydrogen bonds, almost one-third (32%) form i----i--4 hydrogen bonds, and slightly less than one-third (26%) reside in paired strands of beta-sheet. The remaining 5% are not wholly within an individual helix, turn or sheet. (5) Side-chain to backbone hydrogen bonds are clustered at helix-capping positions. (6) An extensive network of hydrogen bonds is present in helices. (7) To a close approximation, the total number of hydrogen bonds is a simple function of a protein's helix and sheet content. (8) A unique quantity, termed the reduced number of hydrogen bonds, is defined as the maximum number of hydrogen bonds possible when every donor:acceptor pair is constrained to be 1:1. This quantity scales linearly with chain length, with 0.71 reduced hydrogen bond per residue. Implications of these results for pathways of protein folding are discussed.

Side-chain entropy opposes alpha-helix formation but rationalizes experimentally determined helix-forming propensities

In recent host-guest studies, the helix-forming tendencies of amino acid residues have been quantified by three groups, each obtaining similar results [Padmanabhan, S., Marqusee, S., Ridgeway, T., Laue, T. M. & Baldwin, R. L. (1990) Nature (London) 344, 268-270; O'Neil, K. T. & DeGrado, W. F. (1990) Science 250, 646-651; Lyu, P. C., Liff, M. I., Marky, L. A. & Kallenbach, N. R. (1990) Science 250, 669-673]. Here, we explore the hypothesis that these measured helix-forming propensities are due primarily to conformational restrictions imposed upon residue side chains by the helix itself. This proposition is tested by calculating the extent to which the bulky helix backbone "freezes out" available degrees of freedom in helix side chains. Specifically, for a series of apolar residues, the difference in configurational entropy, delta S, between each side chain in the unfolded state and in the alpha-helical state is obtained from a simple Monte Carlo calculation. These computed entropy differences are then compared with the experimentally determined values. Measured and calculated values are found to be in close agreement for naturally occurring amino acids and in total disagreement for non-natural amino acids. In the calculation, delta S(Ala) = 0. The rank order of entropy loss for the series of natural apolar side chains under consideration is Ala less than Leu less than Trp less than Met less than Phe less than Ile less than Tyr less than Val. Among these, none favor helix formation; Ala is neutral, and all remaining residues are unfavorable to varying degrees. Thus, applied to side chains, the term "helix preference" is a misnomer. While side chain-side chain interactions may modulate stability in some instances, our results indicate that the drive to form helices must originate in the backbone, consistent with Pauling's view of four decades ago [Pauling, L., Corey, R. B. & Branson, H. R. (1951) Proc. Natl. Acad. Sci. USA 37, 205-210].

The protein-folding problem: the native fold determines packing, but does packing determine the native fold?

A globular protein adopts its native three-dimensional structure spontaneously under physiological conditions. This structure is specified by a stereochemical code embedded within the amino acid sequence of that protein. Elucidation of this code is a major, unsolved challenge, known as the protein-folding problem. A critical aspect of the code is thought to involve molecular packing. Globular proteins have high packing densities, a consequence of the fact that residue side chains within the molecular interior fit together with an exquisite complementarity, like pieces of a three-dimensional jigsaw puzzle [Richards, F. M. (1977) Annu. Rev. Biophys. Bioeng. 6, 151]. Such packing interactions are widely viewed as the principal determinant of the native structure. To test this view, we analyzed proteins of known structure for the presence of preferred interactions, reasoning that if side-chain complementarity is an important source of structural specificity, then sets of residues that interact favorably should be apparent. Our analysis leads to the surprising conclusion that high packing densities--so characteristic of globular proteins--are readily attainable among clusters of the naturally occurring hydrophobic amino acid residues. It is anticipated that this realization will simplify approaches to the protein-folding problem.

Hydrophobicity of amino acid subgroups in proteins

Protein folding studies often utilize areas and volumes to assess the hydrophobic contribution to conformational free energy (Richards, F.M. Annu. Rev. Biophys. Bioeng. 6:151-176, 1977). We have calculated the mean area buried upon folding for every chemical group in each residue within a set of X-ray elucidated proteins. These measurements, together with a standard state cavity size for each group, are documented in a table. It is observed that, on average, each type of group buries a constant fraction of its standard state area. The mean area buried by most, though not all, groups can be closely approximated by summing contributions from three characteristic parameters corresponding to three atom types: (1) carbon or sulfur, which turn out to be 86% buried, on average; (2) neutral oxygen or nitrogen, which are 40% buried, on average; and (3) charged oxygen or nitrogen, which are 32% buried, on average.

Extra-anatomic bypass grafting: a rational approach

To determine predictors of long-term patency in extra-anatomic bypass grafting, the authors studied retrospectively the charts of 134 patients who underwent bypass grafting (axillofemoral in 17, axillobifemoral in 32 and femorofemoral in 85). Of the study group, 64% were men; the mean age was 65 +/- 12 years (+/- SEM). The indications for grafting were limb salvage (102), claudication (27) and replacement of septic grafts (5), and for using the extra-anatomic route included high risk (83), sepsis (8) and unilateral disease (34). Operative mortality was 6% and the early graft occlusion rate 7.4%. The late death rate was 44%. At 3 years, the life-table patency rates for the various procedures were axillofemoral 52.5%, axillobifemoral 67.7% and crossfemoral 86.9%. Smoking significantly (p less than 0.05) decreased the patency rate, but diabetes did not. However, amputation was more frequent in diabetics. Indications for operation did not alter patency rates, but did affect operative mortality. The authors conclude that extra-anatomic bypass grafting is highly successful, but not as successful as anatomic bypass. When appropriate, the axillobifemoral graft is preferred to the axillounifemoral graft because of its increased patency. Crossfemoral grafts must be carefully monitored to ensure that no donor limb stenosis occurs and this procedure should not be attempted unless the disease is truly unilateral.

Helix signals in proteins

The alpha helix, first proposed by Pauling and co-workers, is a hallmark of protein structure, and much effort has been directed toward understanding which sequences can form helices. The helix hypothesis, introduced here, provides a tentative answer to this question. The hypothesis states that a necessary condition for helix formation is the presence of residues flanking the helix termini whose side chains can form hydrogen bonds with the initial four-helix greater than N-H groups and final four-helix greater than C-O groups; these eight groups would otherwise lack intrahelical partners. This simple hypothesis implies the existence of a stereochemical code in which certain sequences have the hydrogen-bonding capacity to function as helix boundaries and thereby enable the helix to form autonomously. The three-dimensional structure of a protein is a consequence of the genetic code, but the rules relating sequence to structure are still unknown. The ensuing analysis supports the idea that a stereochemical code for the alpha helix resides in its boundary residues.

The behavioral treatment of Raynaud's disease: a review

Raynaud's disease is a peripheral vascular system disorder characterized by episodes of vasoconstriction in the hands and feet resulting in a lowering of skin temperature and pain. Recent studies are reviewed that focus on the behavioral treatment of Raynaud's disease--in particular, biofeedback and autogenic training. Methodological problems and other difficulties include the measurement of skin temperature, schedules of reinforcement/feedback, and characteristics of the experimenter and subject. Studies in this area indicate some promise for certain behavioral interventions, especially finger temperature biofeedback under cold stress conditions. On the other hand, further research is needed to clarify the mechanisms, especially that of vasodilation, and the applications of temperature biofeedback, as well as the role of attitudinal, interpersonal, and cognitive factors.

Loops in globular proteins: a novel category of secondary structure

The protein loop, a novel category of nonregular secondary structure, is a segment of contiguous polypeptide chain that traces a "loop-shaped" path in three-dimensional space; the main chain of an idealized loop resembles a Greek omega (omega). A systematic study was made of 67 proteins of known structure revealing 270 omega loops. Although such loops are typically regarded as "random coil," they are, in fact, highly compact substructures and may also be independent folding units. Loops are almost invariably situated at the protein surface where they are poised to assume important roles in molecular function and biological recognition. They are often observed to be modules of evolutionary exchange and are also natural candidates for bioengineering studies.

Compact units in proteins

An explicit measure of geometric compactness called the coefficient of compactness is introduced. This single value figure of merit identifies those continuous segments of the polypeptide chain having the smallest solvent-accessible surface area for their volume. These segments are the most compact units of the protein, and the larger ones correspond to conventional protein domains. To demonstrate the plausibility of this approach as a method of identifying protein domains, the measure is applied to lysozyme and ribonuclease to discover their constituent compact units. These units are then compared with domains, subdomains, and modules found by other methods. To show the sensitivity of the method, the measure is used to successfully differentiate between native and deliberately misfolded proteins [Novotný, J., Bruccoleri, R., & Karplus, M. (1984) J. Mol. Biol. 177, 787-818]. Methods that utilize only backbone atoms to define domains cannot distinguish between authentic and misfolded molecules because their backbone conformations are virtually superimposable. Compact units identified by this method exhibit a hierarchic organization. Such an organization suggests possible folding pathways that can be tested experimentally.

Hydrophobicity of amino acid residues in globular proteins

During biosynthesis, a globular protein folds into a tight particle with an interior core that is shielded from the surrounding solvent. The hydrophobic effect is thought to play a key role in mediating this process: nonpolar residues expelled from water engender a molecular interior where they can be buried. Paradoxically, results of earlier quantitative analyses have suggested that the tendency for nonpolar residues to be buried within proteins is weak. However, such analyses merely classify residues as either "exposed" or "buried." In the experiment reported in this article proteins of known structure were used to measure the average area that each residue buries upon folding. This characteristic quantity, the average area buried, is correlated with residue hydrophobicity.