Glycine rich segments adopt polyproline II helices: Implications for biomolecular condensate formation.

Many intrinsically disordered proteins contain Gly-rich regions which are generally assumed to be disordered. Such regions often form biomolecular condensates which play essential roles in organizing cellular processes. However, the bases of their formation and stability are still not completely understood. Based on NMR studies of the Gly-rich H. harveyi "snow flea" antifreeze protein, we recently proposed that Gly-rich sequences, such as the third "RGG" region of Fused in Sarcoma (FUS) protein, may adopt polyproline II helices whose association might stabilize condensates. Here, this hypothesis is tested with a polypeptide corresponding to the third RGG region of FUS. NMR spectroscopy and molecular dynamics simulations suggest that significant populations of polyproline II helix are present. These findings are corroborated in a model peptide Ac-RGGYGGRGGWGGRGGY-NH2, where a peak characteristic of polyproline II helix is observed using CD spectroscopy. Its intensity suggests a polyproline II population of 40%. This result is supported by data from FTIR and NMR spectroscopies. In the latter, NOE correlations are observed between the Tyr and Arg, and Arg and Trp side chain hydrogens, confirming that side chains spaced three residues apart are close in space. Taken together, the data are consistent with a polyproline II helix, which is bent to optimize interactions between guanidinium and aromatic moieties, in equilibrium with a statistical coil ensemble. These results lend credence to the hypothesis that Gly-rich segments of disordered proteins may form polyproline II helices which help stabilize biomolecular condensates.

Studies of the aggregation of an amyloidogenic alpha-synuclein peptide fragment.

The deposition of alpha-syn (alpha-synuclein) fibrils in Lewy bodies is a characteristic feature of individuals with neurodegenerative disorders. A peptide comprising the central residues 71-82 of alpha-syn [alpha-syn(71-82)] is capable of forming beta-sheet-rich, amyloid-like fibrils with similar morphologies to fibrils of the full-length protein, providing a useful model of pathogenic alpha-syn fibrils that is suitable for detailed structural analysis. We have studied the morphology and gross structural features of alpha-syn(71-82) fibrils formed under different conditions in order to obtain reliable conditions for producing fibrils for further structural investigations. The results indicate that the rate of aggregation and the morphology of the fibrils formed are sensitive to pH and temperature.

The aggregation and membrane-binding properties of an alpha-synuclein peptide fragment.

alpha-Synuclein is a 140 amino acid protein, which is associated with presynaptic membranes in the brain, and is the major component of protein aggregates produced during the progression of many neurodegenerative diseases. It has been shown that a central hydrophobic region of alpha-synuclein comprising residues 71-82 is required for aggregation of the protein into the fibrillar form found in pathogenic aggregates [Giasson, Murray, Trojanowski and Lee (2001) J. Biol. Chem. 276, 2380-2386]. In the present study, we used (2)H NMR and electron microscopy to investigate the aggregation and membrane-binding properties of a synthetic peptide corresponding to this region. Results indicate that this region associates with phospholipid bilayers but also forms amyloid-like fibrils in the absence of lipid membranes.

Inhibition of toxicity and protofibril formation in the amyloid-beta peptide beta(25-35) using N-methylated derivatives.

Beta (25-35) is a fragment of beta-amyloid that retains its wild-type properties. N-methylated derivatives of beta(25-35) can block hydrogen bonding on the outer edge of the assembling amyloid, so preventing the aggregation and inhibiting the toxicity of the wild-type peptide. The effects are assayed by Congo Red and thioflavin T binding, electron microscopy and an MTT [3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide] toxicity assay. N-methyl-Gly-25 has similar properties to the wild- type, while five other methylation sites have varying effects on prefolded fibrils and fibril assembly. In particular, N-methyl-Gly-33 is able to completely prevent fibril assembly and reduces the toxicity of prefolded amyloid. With N-methyl-Leu-34 the fibril morphology is altered and toxicity reduced. A preliminary study of beta(25-35) structure in aqueous solution was made by small-angle neutron scattering (SANS). The protofibrillar aggregates are best described as a disc of radius 140 A and height 53 A (1 A = 0.1 nm), though the possibility of polydisperse aggregates cannot be ruled out. No aggregates form in the presence of N-methyl-Gly-33. We suggest that the use of N-methylated derivatives of amyloidogenic peptides and proteins could provide a general solution to the problem of amyloid deposition and toxicity and that SANS is an important technique for the direct observation of protofibril formation and destruction in solution.

Stabilizing nonpolar/polar side-chain interactions in the alpha-helix.

A simplistic, yet often used, view of protein stability is that amino acids attract other amino acids with similar polarity, whereas nonpolar and polar side chains repel. Here we show that nonpolar/polar interactions, namely Val or Ile bonding to Lys or Arg in alpha-helices, can in fact be stabilizing. Residues spaced i, i + 4 in alpha-helices are on the same face of the helix, with potential to favorably interact and stabilize the structure. We observe that the nonpolar/polar pairs Ile-Lys, Ile-Arg, and Val-Lys occur in protein helices more often than expected when spaced i, i + 4. Partially helical peptides containing pairs of nonpolar/polar residues were synthesized. Controls with i, i + 5 spacing have the residues on opposite faces of the helix and are less helical than the test peptides with the i, i + 4 interactions. Experimental circular dichroism results were analyzed with helix-coil theory to calculate the free energy for the interactions. All three stabilize the helix with DeltaG between -0.14 and -0.32 kcal x mol(-1). The interactions are hydrophobic with contacts between Val or Ile and the alkyl groups in Arg or Lys. Side chains such as Lys and Arg can thus interact favorably with both polar and nonpolar residues.

Structure, stability and folding of the alpha-helix.

Pauling first described the alpha-helix nearly 50 years ago, yet new features of its structure continue to be discovered, using peptide model systems, site-directed mutagenesis, advances in theory, the expansion of the Protein Data Bank and new experimental techniques. Helical peptides in solution form a vast number of structures, including fully helical, fully coiled and partly helical. To interpret peptide results quantitatively it is essential to use a helix/coil model that includes the stabilities of all these conformations. Our models now include terms for helix interiors, capping, side-chain interactions, N-termini and 3(10)-helices. The first three amino acids in a helix (N1, N2 and N3) and the preceding N-cap are unique, as their amide NH groups do not participate in backbone hydrogen bonding. We surveyed their structures in proteins and measured their amino acid preferences. The results are predominantly rationalized by hydrogen bonding to the free NH groups. Stabilizing side-chain-side-chain energies, including hydrophobic interactions, hydrogen bonding and polar/non-polar interactions, were measured accurately in helical peptides. Helices in proteins show a preference for having approximately an integral number of turns so that their N- and C-caps lie on the same side. There are also strong periodic trends in the likelihood of terminating a helix with a Schellman or alpha L C-cap motif. The kinetics of alpha-helix folding have been studied with stopped-flow deep ultraviolet circular dichroism using synchrotron radiation as the light source; this gives a far superior signal-to-noise ratio than a conventional instrument. We find that poly(Glu), poly(Lys) and alanine-based peptides fold in milliseconds, with longer peptides showing a transient overshoot in helix content.

Effect of the N2 residue on the stability of the alpha-helix for all 20 amino acids.

N2 is the second position in the alpha-helix. All 20 amino acids were placed in the N2 position of a synthetic helical peptide (CH(3)CO-[AXAAAAKAAAAKAAGY]-NH(2)) and the helix content was measured by circular dichroism spectroscopy at 273K. The dependence of peptide helicity on N2 residue identity has been used to determine a free-energy scale by analysis with a modified Lifson-Roig helix-coil theory that includes a parameter for the N2 energy (n2). The rank order of DeltaDeltaG((relative to Ala)) is Glu(-), Asp(-) > Ala > Glu(0), Leu, Val, Gln, Thr, Ile, Ser, Met, Asp(0), His(0), Arg, Cys, Lys, Phe > Asn, > Gly, His(+), Pro, Tyr. The results correlate very well with N2 propensities in proteins, moderately well with N1 and helix interior preferences, and not at all with N-cap preferences. The strongest energetic effects result from interactions with the helix dipole, which favors negative charges at the helix N terminus. Hydrogen bonds to side chains at N2, such as Gln, Ser, and Thr, are weak, despite occurring frequently in protein crystal structures, in contrast to the N-cap position. This is because N-cap hydrogen bonds are close to linear, whereas N2 hydrogen bonds have poor geometry. These results can be used to modify protein stability rationally, help design helices, and improve prediction of helix location and stability.

Effect of the N1 residue on the stability of the alpha-helix for all 20 amino acids.

N1 is the first residue in an alpha-helix. We have measured the contribution of all 20 amino acids to the stability of a small helical peptide CH(3)CO-XAAAAQAAAAQAAGY-NH(2) at the N1 position. By substituting every residue into the N1 position, we were able to investigate the stabilizing role of each amino acid in an isolated context. The helix content of each of the 20 peptides was measured by circular dichroism (CD) spectroscopy. The data were analyzed by our modified Lifson-Roig helix-coil theory, which includes the n1 parameter, to find free energies for placing a residue into the N1 position. The rank order for free energies is Asp(-), Ala > Glu(-) > Glu(0) > Trp, Leu, Ser > Asp(0), Thr, Gln, Met, Ile > Val, Pro > Lys(+), Arg, His(0) > Cys, Gly > Phe > Asn, Tyr, His(+). N1 preferences are clearly distinct from preferences for the preceding N-cap and alpha-helix interior. pK(a) values were measured for Asp, Glu, and His, and protonation-free energies were calculated for Asp and Glu. The dissociation of the Asp proton is less favorable than that of Glu, and this reflects its involvement in a stronger stabilizing interaction at the N terminus. Proline is not energetically favored at the alpha-helix N terminus despite having a high propensity for this position in crystal structures. The data presented are of value both in rationalizing mutations at N1 alpha-helix sites in proteins and in predicting the helix contents of peptides.

Rotamer strain energy in protein helices - quantification of a major force opposing protein folding.

It is widely believed that the dominant force opposing protein folding is the entropic cost of restricting internal rotations. The energetic changes from restricting side-chain torsional motion are more complex than simply a loss of conformational entropy, however. A second force opposing protein folding arises when a side-chain in the folded state is not in its lowest-energy rotamer, giving rotameric strain. chi strain energy results from a dihedral angle being shifted from the most stable conformation of a rotamer when a protein folds. We calculated the energy of a side-chain as a function of its dihedral angles in a poly(Ala) helix. Using these energy profiles, we quantify conformational entropy, rotameric strain energy and chi strain energy for all 17 amino acid residues with side-chains in alpha-helices. We can calculate these terms for any amino acid in a helix interior in a protein, as a function of its side-chain dihedral angles, and have implemented this algorithm on a web page. The mean change in rotameric strain energy on folding is 0.42 kcal mol-1 per residue and the mean chi strain energy is 0.64 kcal mol-1 per residue. Loss of conformational entropy opposes folding by a mean of 1.1 kcal mol-1 per residue, and the mean total force opposing restricting a side-chain into a helix is 2.2 kcal mol-1. Conformational entropy estimates alone therefore greatly underestimate the forces opposing protein folding. The introduction of strain when a protein folds should not be neglected when attempting to quantify the balance of forces affecting protein stability. Consideration of rotameric strain energy may help the use of rotamer libraries in protein design and rationalise the effects of mutations where side-chain conformations change.

Is polyproline II helix the killer conformation? A Raman optical activity study of the amyloidogenic prefibrillar intermediate of human lysozyme.

The amyloidogenic prefibrillar partially denatured intermediate of human lysozyme, prepared by heating the native protein to 57 degrees C at pH 2.0, was studied using Raman optical activity (ROA). A positive band in the room temperature ROA spectrum of the native protein at approximately 1345 cm(-1), assigned to a hydrated form of alpha-helix, is not present in that of the prefibrillar intermediate, where a new strong positive band at approximately 1318 cm(-1) appears instead that is assigned to the poly(l-proline) II (PPII)-helical conformation. A sharp negative band at approximately 1241 cm(-1) in the native protein, assigned to beta-strand, shows little change in the ROA spectrum of the prefibrillar intermediate. The disappearance of a positive ROA band at approximately 1551 cm(-1) assigned to vibrations of tryptophan side-chains indicates that major conformational changes have occurred among the five tryptophan residues present in human lysozyme, four of which are located in the alpha-domain. The various ROA data suggest that a substantial loss of tertiary structure has occurred in the prefibrillar intermediate and that this is located more in the alpha-domain than in the beta-domain. There is no evidence for any increase in beta-structure. The ROA spectrum of hen lysozyme, which does not form amyloid fibrils so readily, remains much more native-like on heating to 57 degrees C at pH 2.0. The thermal behaviour of the alanine-rich alpha-helical peptide AK21 in aqueous solution was found to be similar to that of human lysozyme. Hydrated alpha-helix therefore appears to readily undergo a conformational change to PPII structure on heating, which may be a key step in the conversion of alpha-helix into beta-sheet in the formation of amyloid fibrils in human lysozyme. Since it is extended, flexible, lacks intrachain hydrogen bonds and is fully hydrated in aqueous solution, PPII helix has the appropriate characteristics to be implicated as a critical conformational element in many conformational diseases. Disorder of the PPII type may be a sine qua non for the formation of regular fibrils; whereas the more dynamic disorder of the random coil may lead only to amorphous aggregates.

Determination of alpha-helix N1 energies after addition of N1, N2, and N3 preferences to helix/coil theory.

Surveys of protein crystal structures have revealed that amino acids show unique structural preferences for the N1, N2, and N3 positions in the first turn of the alpha-helix. We have therefore extended helix-coil theory to include statistical weights for these locations. The helix content of a peptide in this model is a function of N-cap, C-cap, N1, N2, N3, C1, and helix interior (N4 to C2) preferences. The partition function for the system is calculated using a matrix incorporating the weights of the fourth residue in a hexamer of amino acids and is implemented using a FORTRAN program. We have applied the model to calculate the N1 preferences of Gln, Val, Ile, Ala, Met, Pro, Leu, Thr, Gly, Ser, and Asn, using our previous data on helix contents of peptides Ac-XAKAAAAKAAGY-CONH2. We find that Ala has the highest preference for the N1 position. Asn is the most unfavorable, destabilizing a helix at N1 by at least 1.4 kcal mol(-1) compared to Ala. The remaining amino acids all have similar preferences, 0.5 kcal mol(-1) less than Ala. Gln, Asn, and Ser, therefore, do not stabilize the helix when at N1.

Inhibition of toxicity in the beta-amyloid peptide fragment beta -(25-35) using N-methylated derivatives: a general strategy to prevent amyloid formation.

beta-(25-35) is a synthetic derivative of beta-amyloid, the peptide that is believed to cause Alzheimer's disease. As it is highly toxic and forms fibrillar aggregates typical of beta-amyloid, it is suitable as a model for testing inhibitors of aggregation and toxicity. We demonstrate that N-methylated derivatives of beta-(25-35), which in isolation are soluble and non-toxic, can prevent the aggregation and inhibit the resulting toxicity of the wild type peptide. N-Methylation can block hydrogen bonding on the outer edge of the assembling amyloid. The peptides are assayed by Congo red and thioflavin T binding, electron microscopy, and a 3-(4, 5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide (MTT) toxicity assay on PC12 cells. One peptide (Gly(25) N-methylated) has properties similar to the wild type, whereas five have varying effects on prefolded fibrils and fibril assembly. In particular, beta-(25-35) with Gly(33) N-methylated is able to completely prevent fibril assembly and to reduce the toxicity of prefolded amyloid. With Leu(34) N-methylated, the fibril morphology is altered and the toxicity reduced. We suggest that the use of N-methylated derivatives of amyloidogenic peptides and proteins could provide a general solution to the problem of amyloid deposition and toxicity.

Periodicity in alpha-helix lengths and C-capping preferences.

We surveyed 299 high resolution, non-homologous protein crystal structures for alpha-helix lengths and capping preferences. We find that helices show a preference to have close to an integral number of turns. Helices can be usefully subdivided into either "favoured length" with 6, 7, 10, 11, 13, 14, 17, 18, 21, 22, 24, 25, 28, 29 or 31 residues, or "disfavoured length" with 8, 9, 12, 15, 16, 19, 20, 23, 26, 27 or 30 residues. Favoured length helices have their N and C-caps on the same side of the helix so they can lie on the protein surface. There is no significant difference in amino acid preferences at the N terminus between favoured and disfavoured length helices. At the C terminus, favoured length helices prefer non-polar side-chains at C4 and polar amino acid residues at C2, while disfavoured length helices prefer non-polar amino acid residues at C2. There are strong periodic trends in the likelihood of terminating a helix with a Schellman or alphaL C-capping motif. These can be rationalised by the preference for a non-polar side-chain at C3 with these motifs, favouring placing C3 on the buried side of the helix. We suggest that algorithms aiming to predict helices or C-capping in proteins should include a weight for the helix length.

The alpha-helix folds on the millisecond time scale.

It has long been believed that nucleation of the alpha-helix is a very fast reaction, occurring in around 10(-7) s. We show here that helix nucleation, in fact, takes place on the millisecond time scale. The rate of alpha-helix nucleation in two polyalanine-based peptides and in lysine and glutamic acid homopolymers was measured directly by stopped-flow deep UV CD with synchrotron radiation as the light source. Synchrotron radiation CD gives far superior signal to noise than a conventional instrument. The 16-aa AK peptide folds with first-order kinetics and a rate constant of 15 s-1 at 0 degrees C. The rate-determining step is presumably the initiation of a new helix, which occurs at least 10(5) times slower than expected. Helix folding occurs in at least two steps on the millisecond time scale for the longer peptides, with a transient overshoot of helix content significantly greater than at equilibrium, similar to that seen in the folding of several proteins. We suggest that the overshoot is caused by the formation of a single long helix followed by its breakage into the two or more helices present at equilibrium.

Side-chain structures in the first turn of the alpha-helix.

The first three residues at the N terminus of the alpha-helix are called N1, N2 and N3. We surveyed 2102 alpha-helix N termini in 298 high-resolution, non-homologous protein crystal structures for N1, N2 and N3 amino acid and side-chain rotamer propensities and hydrogen-bonding patterns. We find strong structural preferences that are unique to these sites. The rotamer distributions as a function of amino acid identity and position in the helix are often explained in terms of hydrogen-bonding interactions to the free N1, N2 and N3 backbone NH groups. Notably, the "good N2" amino acid residues Gln, Glu, Asp, Asn, Ser, Thr and His preferentially form i, i or i,i+1 hydrogen bonds to the backbone, though this is hindered by good N-caps (Asp, Asn, Ser, Thr and Cys) that compete for these hydrogen bond donors. We find a number of specific side-chain to side-chain interactions between N1 and N2 or between the N-cap and N2 or N3, such as Arg(N-cap) to Asp(N2). The strong energetic and structural preferences found for N1, N2 and N3, which differ greatly from positions within helix interiors, suggest that these sites should be treated explicitly in any consideration of helical structure in peptides or proteins.

Addition of side-chain interactions to 3(10)-helix/coil and alpha-helix/3(10)-helix/coil theory.

An increasing number of experimental and theoretical studies have demonstrated the importance of the 3(10)-helix/ alpha-helix/coil equilibrium for the structure and folding of peptides and proteins. One way to perturb this equilibrium is to introduce side-chain interactions that stabilize or destabilize one helix. For example, an attractive i, i + 4 interaction, present only in the alpha-helix, will favor the alpha-helix over 3(10), while an i, i + 4 repulsion will favor the 3(10)-helix over alpha. To quantify the 3(10)/alpha/coil equilibrium, it is essential to use a helix/coil theory that considers the stability of every possible conformation of a peptide. We have previously developed models for the 3(10)-helix/coil and 3(10)-helix/alpha-helix/ coil equilibria. Here we extend this work by adding i, i + 3 and i, i + 4 side-chain interaction energies to the models. The theory is based on classifying residues into alpha-helical, 3(10)-helical, or nonhelical (coil) conformations. Statistical weights are assigned to residues in a helical conformation with an associated helical hydrogen bond, a helical conformation with no hydrogen bond, an N-cap position, a C-cap position, or the reference coil conformation plus i, i + 3 and i, i + 4 side-chain interactions. This work may provide a framework for quantitatively rationalizing experimental work on isolated 3(10)-helices and mixed 3(10)-/alpha-helices and for predicting the locations and stabilities of these structures in peptides and proteins. We conclude that strong i, i + 4 side-chain interactions favor alpha-helix formation, while the 3(10)-helix population is maximized when weaker i, i + 4 side-chain interactions are present.

Free energies of amino acid side-chain rotamers in alpha-helices, beta-sheets and alpha-helix N-caps.

Scales have previously been determined for the entropic cost of restricting amino acid side-chain rotations upon protein folding, giving the rule of thumb that the entropic cost of restricting a single side-chain bond is approximately 0.5 kcal mol-1. However, this result does not consider the distinct preferences shown by amino acid side-chains for particular side-chain chi1 angles in the folded protein. For example, Glu in an alpha-helix has chi1 4% gauche- (g-), 39% trans (t) and 58% gauche+ (g+) showing that it is most favourable to restrict Glu chi1 as g+ in a helix while g- is least favoured. The change in side-chain conformational entropy is the same in both cases, but the free energy of each rotamer is different. Here, we determine the energies of every amino acid chi1 rotamer in alpha-helices, beta-sheets and alpha-helix N-caps and each chi1chi2 rotamer pair in helices and sheets. The calculation uses observed rotamer distributions in secondary structure and the coil state, together with experimentally determined free energy changes for secondary structure formation. The results are sets of rotamer energies within a secondary structure that can be directly compared to each other. For example, we conclude that Tyr is the most stable residue in a beta-sheet if only the trans rotamer is accessible; if only the gauche- conformation is available, Thr would be the most stabilising. Previously published scales of amino acid preferences for secondary structure are weighted averages of rotamer energies and therefore imply that Thr is the most stabilising substitution in a beta-sheet in any side-chain conformation. Both side-chain conformational entropies and intrinsic secondary structure preferences are subsumed within our data; the results presented here should therefore be used in preference to both side-chain conformational entropies and intrinsic secondary structure preferences when the rotamer occupied in the folded state is known. The results may be useful in protein engineering, simulations of binding and folding, prediction of protein stability and peptide binding energies, and identification of incorrectly folded structures.

Hydrogen bonding interactions between glutamine and asparagine in alpha-helical peptides.

We have measured the strength of a Gln-Asn side-chain-side-chain interaction spaced i, i+4 in an alpha-helix by placing pairs of interacting residues in the middle, N and C termini of Ala-based peptides. Experimental helicities for peptides containing Gln-Asn spaced i, i+4, as measured by circular dichroism, are considerably higher than those of a peptide with Gln-Asn spaced i, i+5, and that predicted by a modified form of Lifson-Roig helix-coil transition theory that does not include side-chain interactions. A model that includes side-chain-side-chain interactions successfully fits the experimental data and gives a free energy of interaction of between -0.4 and -0.7 kcal mol-1. This favourable interaction is evident in a statistical survey of alpha-helices from a set of non-homologous crystal structures. The Asn-Gln orientation has an interaction energy of less than that of Gln-Asn and close to zero. This difference shows that the free energy of interaction is sensitive to the geometry of the interacting groups. Because i, i+4 interactions can occur only when the side-chain chi1 angle of residue i is trans and that of residue i+4 is gauche+, and because side-chains are free to rotate in peptides, we have corrected interaction free energies from this and other studies to remove the conformational entropy cost of placing them in these conformations so that they are comparable with studies of hydrogen bonding in mutant proteins. The corrected DeltaG is -1 kcal mol-1, which is slightly lower than that reported for hydrogen bonds in folded proteins; however, this value is similar to that for hydrophobic i, i+4 interactions in peptides. We conclude that even in highly mobile, surface-exposed regions, hydrogen bonds can significantly stabilise proteins, provided that their geometric requirements can be achieved.

Improving the efficiency of the genetic code by varying the codon length--the perfect genetic code.

The function of DNA is to specify protein sequences. The four-base "alphabet" used in nucleic acids is translated to the 20 base alphabet of proteins (plus a stop signal) via the genetic code. The code is neither overlapping nor punctuated, but has mRNA sequences read in successive triplet codons until reaching a stop codon. The true genetic code uses three bases for every amino acid. The efficiency of the genetic code can be significantly increased if the requirement for a fixed codon length is dropped so that the more common amino acids have shorter codon lengths and rare amino acids have longer codon lengths. More efficient codes can be derived using the Shannon-Fano and Huffman coding algorithms. The compression achieved using a Huffman code cannot be improved upon. I have used these algorithms to derive efficient codes for representing protein sequences using both two and four bases. The length of DNA required to specify the complete set of protein sequences could be significantly shorter if transcription used a variable codon length. The restriction to a fixed codon length of three bases means that it takes 42% more DNA than the minimum necessary, and the genetic code is 70% efficient. One can think of many reasons why this maximally efficient code has not evolved: there is very little redundancy so almost any mutation causes an amino acid change. Many mutations will be potentially lethal frame-shift mutations, if the mutation leads to a change in codon length. It would be more difficult for the machinery of transcription to cope with a variable codon length. Nevertheless, in the strict and narrow sense of coding for protein sequences using the minimum length of DNA possible, the Huffman code derived here is perfect.

Structures of N-termini of helices in proteins.

We have surveyed 393 N-termini of alpha-helices and 156 N-termini of 3(10)-helices in 85 high resolution, non-homologous protein crystal structures for N-cap side-chain rotamer preferences, hydrogen bonding patterns, and solvent accessibilities. We find very strong rotamer preferences that are unique to N-cap sites. The following rules are generally observed for N-capping in alpha-helices: Thr and Ser N-cap side chains adopt the gauche - rotamer, hydrogen bond to the N3 NH and have psi restricted to 164 +/- 8 degrees. Asp and Asn N-cap side chains either adopt the gauche - rotamer and hydrogen bond to the N3 NH with psi = 172 +/- 10 degrees, or adopt the trans rotamer and hydrogen bond to both the N2 and N3 NH groups with psi = 1-7 +/- 19 degrees. With all other N-caps, the side chain is found in the gauche + rotamer so that the side chain does not interact unfavorably with the N-terminus by blocking solvation and psi is unrestricted. An i, i + 3 hydrogen bond from N3 NH to the N-cap backbone C = O in more likely to form at the N-terminus when an unfavorable N-cap is present. In the 3(10)-helix Asn and Asp remain favorable N-caps as they can hydrogen bond to the N2 NH while in the trans rotamer; in contrast, Ser and Thr are disfavored as their preferred hydrogen bonding partner (N3 NH) is inaccessible. This suggests that Ser is the optimum choice of N-cap when alpha-helix formation is to be encouraged while 3(10)-helix formation discouraged. The strong energetic and structural preferences found for N-caps, which differ greatly from positions within helix interiors, suggest that N-caps should be treated explicitly in any consideration of helical structure in peptides or proteins.