A self-consistent formulation for analysis and generation of non-uniform DNA structures

A fully self-consistent formulation is described here for the analysis and generation of base-pairs in non-uniform DNA structures, in terms of various local parameters. It is shown that the internal "wedge parameters" are mathematically related to the parameters describing the base-pair orientation with respect to an external helix axis. Hence any one set of three translation and three rotation parameters are necessary and sufficient to completely describe the relative orientation of the base-pairs comprising a step (or doublet). A general procedure is outlined for obtaining an average or global helix axis from the local helix axes for each step. A graphical representation of the local helix axes in the form of a polar plot is also shown and its application for estimating the curvature of oligonucleotide structures is illustrated, with examples of both A and B type structures.     

Base sequence and helix structure variation in B and A DNA

The observed propeller twist in base-pairs of crystalline double-helical DNA oligomers improves the stacking overlap along each individual helix strand. But, as proposed by Calladine, it also leads to clash or steric hindrance between purines at adjacent base-pairs on opposite strands of the helix. This clash can be relieved by: (1) decreasing the local helix twist angle between base-pairs; (2) opening up the roll angle between base-pairs on the side on which the clash occurs; (3) separating purines by sliding base-pairs along their long axes so that the purines are partially pulled out of the stack (leading to equal but opposite alterations in main-chain torsion angle delta at the two ends of the base-pair); and (4) flattening the propeller twist of the offending base-pairs. Simple sum functions, sigma 1 through sigma 4, are defined, by which the expected local variation in helix twist, base roll angle, torsion angle delta and propeller twist may be calculated from base sequence. All four functions are quite successful in predicting the behavior of B DNA. Only the helix twist and base roll functions are applicable to A DNA, and the helix twist function begins to fail for an A helical RNA/DNA hybrid. Within these limits, the sequence-derived sum functions match the observed helix parameter variation quite closely, with correlation coefficients greater than 0.900 in nearly all cases. Implications of this sequence-derived helix parameter variation for repressor-operator interactions are considered.     

Definitions and analysis of DNA Holliday junction geometry

A number of single-crystal structures have now been solved of the four-stranded antiparallel stacked-X form of the Holliday junction. These structures demonstrate how base sequence, substituents, and drug and ion interactions affect the general conformation of this recombination intermediate. The geometry of junctions had previously been described in terms of a specific set of parameters that include: (i) the angle relating the ends of DNA duplexes arms of the junction (interduplex angle); (ii) the relative rotation of the duplexes about the helix axes of the stacked duplex arms (J_roll); and (iii) the translation of the duplexes along these helix axes (J_slide). Here, we present a consistent set of definitions and methods to accurately calculate each of these parameters based on the helical features of the stacked duplex arms in the single-crystal structures of the stacked-X junction, and demonstrate how each of these parameters contributes to an overall conformational feature of the structure. We show that the values for these parameters derived from global rather than local helical axes through the stacked bases of the duplex arms are the most representative of the stacked-X junction conformation. In addition, a very specific parameter (J_twist) is introduced which relates the relative orientation of the stacked duplex arms across the junction which, unlike the interduplex angle, is length independent. The results from this study provide a general means to relate the geometric features seen in the crystal structures to those determined in solution.     

Impact of static and dynamic A-form heterogeneity on the determination of RNA global structural dynamics using NMR residual dipolar couplings

We examined how static and dynamic deviations from the idealized A-form helix propagate into errors in the principal order tensor parameters determined using residual dipolar couplings (rdcs). A 20-ns molecular dynamics (MD) simulation of the HIV-1 transactivation response element (TAR) RNA together with a survey of spin relaxation studies of RNA dynamics reveals that pico-to-nanosecond local motions in non-terminal Watson-Crick base-pairs will uniformly attenuate base and sugar one bond rdcs by approximately 7%. Gaussian distributions were generated for base and sugar torsion angles through statistical comparison of 40 RNA X-ray structures solved to <3.0 A resolution. For a typical number (>or=11) of one bond C-H base and sugar rdcs, these structural deviations together with rdc uncertainty (1.5 Hz) lead to average errors in the magnitude and orientation of the principal axis of order that are <9% and <4 degrees, respectively. The errors decrease to <5% and <4 degrees for >or=17 rdcs. A protocol that allows for estimation of error in A-form order tensors due to both angular deviations and rdc uncertainty (Aform-RDC) is validated using theoretical simulations and used to analyze rdcs measured previously in TAR in the free state and bound to four distinct ligands. Results confirm earlier findings that the two TAR helices undergo large changes in both their mean relative orientation and dynamics upon binding to different targets.     

HELANAL: A Program to Characterize Helix Geometry in Proteins

Abstract

A detailed analysis of structural and position dependent characteristic features of helices will give a better understanding of the secondary structure formation in globular proteins. Here we describe an algorithm that quantifies the geometry of helices in proteins on the basis of their C^α atoms alone. The Fortran program HELANAL can extract the helices from the PDB files and then characterises the overall geometry of each helix as being linear, curved or kinked, in terms of its local structural features, viz. local helical twist and rise, virtual torsion angle, local helix origins and bending angles between successive local helix axes. Even helices with large radius of curvature are unambiguously identified as being linear or curved. The program can also be used to differentiate a kinked helix and other motifs, such as helix-loop-helix or a helix-turn-helix (with a single residue linker) with the help of local bending angles. In addition to these, the program can also be used to characterise the helix start and end as well as other types of secondary structures.     

Inosine.adenine base pairs in a B-DNA duplex.

The structure of the synthetic deoxydodecamer d(C-G-C-I-A-A-T-T-A-G-C-G) has been determined by single crystal X-ray diffraction techniques at 2.5A resolution. The refinement converged with a crystallographic residual, R = 0.19 and the location of 64 solvent molecules. The sequence crystallises as a B-DNA helix with 10 Watson-Crick base-pairs (4 A.T. and 6 G.C) and 2 inosine.adenine (I.A) pairs. The present work shows that in the purine.purine base-pairs the adenine adopts syn orientation with respect to the furanose moiety while the inosine is in the trans (anti) orientation. Two hydrogen bonds link the I.A. base-pair, one between N-1(I) and N-7(A), the other between O-6(I) and N-6(A). This bulky purine.purine base-pair is incorporated in the double helix at two positions with little distortion of either local or global conformation. The pairing observed in this study is presented as a model for I.A base-pairs in RNA codon-anticodon interactions and may help explain the thermodynamic stability of inosine containing base-pairs. Conformational parameters and base stacking interactions are presented and where appropriate compared with those of the native compound, d(C-G-C-G-A-A-T-T-C-G-C-G) and with other studies of oligonucleotides containing purine.purine base-pairs.     

Periodic Structurally Similar Oligomers are Found on One Side of the Axes of Symmetry in the lac,trp, and gal Operators

Abstract

Three well-defined E. coli operator regions were examined for recurring conformational deviation from a regular B-DNA helix. All three, the lac, trp, and gal, show repeats of the same set of neighboring helical twist angles. These angles recur with a periodicity equal to the helix periodicity on one side of the operator's axes of symmetry. The probability that their occurrence is random was found to be extremely small. Therefore, we propose that in addition to specific bases, repeating twist angle patterns are likely to be among the local parameters involved in repressor-operator recognition.     

Crystallographic study of one turn of G/C-rich B-DNA

The DNA decamer d(CCAGGCCTGG) has been studied by X-ray crystallography. At a nominal resolution of 1.6 A, the structure was refined to R = 16.9% using stereochemical restraints. The oligodeoxyribonucleotide forms a straight B-DNA double helix with crystallographic dyad symmetry and ten base-pairs per turn. In the crystal lattice, DNA fragments stack end-to-end along the c-axis to form continuous double helices. The overall helical structure and, notably, the groove dimensions of the decamer are more similar to standard, fiber diffraction-determined B-DNA than A-tract DNA. A unique stacking geometry is observed at the CA/TG base-pair step, where an increased rotation about the helix axis and a sliding motion of the base-pairs along their long axes leads to a superposition of the base rings with neighboring carbonyl and amino functions. Three-center (bifurcated) hydrogen bonds are possible at the CC/GG base-pair steps of the decamer. In their common sequence elements, d(CCAGGCCTGG) and the related G.A mismatch decamer d(CCAAGATTGG) show very similar three-dimensional structures, except that d(CCAGGCCTGG) appears to have a less regularly hydrated minor groove. The paucity of minor groove hydration in the center of the decamer may be a general feature of G/C-rich DNA and explain its relative instability in the B-form of DNA.     

Variability in the Geometry of RNA Double Helices Generated from Dinucleoside Building-Blocks

Abstract

A graphical method is presented for the generation of helical parameters from single-crystal structures of RNA nucleic acid fragments that are minimally dinucleosides. The method is compared with other published procedures, for a number of text examples. The RNA double helices generated from three different salts of the dinucleoside monophosphate GpC are examined in relation to the variations in helix morphology that are produced. It is shown that small differences between these GpC salts can be amplified to very distinct helix characteristics.     

Base-Stacking Interactions in Double-Helical DNA Structures: Experiment Versus Theory

Abstract

Atom-atom potential energy calculations have been undertaken for deriving stacking energies in double-helical structures. A comparison between the energy patterns of A- and B-type double-helical fragments determined by single-crystal X-ray diffraction methods versus idealized uniform models based on fiber diffraction data shows that the van der Waals stacking energy is largely sensitive to local changes in the relative orientation of adjacent base pairs. The sequence-dependent conformational variability observed in the high-resolution structures appears to be a consequence of the equipartitioning of the stacking energy along the double helix. The large energy variations expected for a uniform structure are dampened considerably in the observed structures by means of local changes in conformational features such as helix rotation and roll angles between base pairs.     

Analysis of local helix geometry in three B-DNA decamers and eight dodecamers

Local variations in B-DNA helix structure are compared among three decamers and eight dodecamers, which contain examples of all ten base-pair step types. All pairwise combinations of helix parameters are compared by linear regression analysis, in a search for internal relationships as well as correlations with base sequence. The primary conclusions are: (1) Three-center hydrogen bonds between base-pairs occur frequently in the major groove at C-C, C-A, A-A and A-C steps, but are less convincing at C-C and C-T steps in the minor groove. The requirements for large base-pair propeller are (1) that the base-pair should be A.T rather than G.C, and (2) that it be involved in a major groove three-center hydrogen bond with the following base-pair. Either condition alone is insufficient. Hence, a large propeller is expected at the leading base-pair of A-A and A-C steps, but not at A-T, T-A, C-A or C-C steps. (2) A systematic and quantitative linkage exists between helix variables twist, rise, cup and roll, of such strength that the rise between base-pairs can hardly be described as an independent variable at all. Two typical patterns of behavior are observed at steps from one base-pair to the next: high twist profile (HTP), characterized by high twist, low rise, positive cup and negative roll, and low twist profile (LTP), marked by low twist, high rise; negative cup and positive roll. Examples of HTP are steps G-C, G-A and Y-C-A-R, where Y is pyrimidine and R is purine. Examples of LTP steps are C-G, G-G, A-G and C-A steps other than Y-C-A-R. (3) The minor groove is especially narrow across the two base-pairs of the following steps: A-T, T-A, A-A and G-A. (4) In general, base step geometry cannot be correlated solely with the bases that define the step in question; the two flanking steps also must be taken into account. Hence, local helix structure must be studied in the context, not of two base-pairs: A-B, but of four: x-A-B-y. Calladine's rules, although too simple in detail, were correct in defining the length of sequence over which a given perturbation is expressed. Whereas ten different two-base steps are possible, allowing for the identity of complementary sequences, there are 136 different four-base steps. Only 33 of these 136 four-base steps are represented in the decamer and dodecamer structures solved to date, and hence it is premature to try to set up detailed structural algorithms. (5) The sugar-phosphate backbone chains of B-DNA place strong limits on sequence-induced structural variation, damping down most variables within four or five base-pairs, and preventing purine-purine anti-anti mismatches from causing bulges in the double helix. Hence, although short-range sequence-induced deformations (or deformability) are observed, long-range deformations propagated down the helix are not to be expected.     

A Refined Prediction Method for Gel Retardation of DNA Oligonucleotides from Dinucleotide Step Parameters: Reconciliation of DNA Bending Models with Crystal Structure Data

Abstract

The development and assessment of a prediction method for gel retardation and sequence dependent curvature of DNA based on dinucleotide step parameters are described. The method is formulated using the Babcock-Olson equations for base pair step geometry (1) and employs Monte Carlo simulated annealing for parameter optimization against experimental data. The refined base pair step parameters define a structural construct which, when the width of observed parameter distributions is taken into account, is consistent with the results of DNA oligonucleotide crystal structures. The predictive power of the method is demonstrated and tested via comparisons with DNA bending data on sets of sequences not included in the training set, including A-tracts with and without periodic helix phasing, phased A₄T₄ and T₄A₄ motifs, a sequence with a phased GGGCCC motif, some “unconventional” helix phasing sequences, and three short fragments of kinetoplast DNA from Crithidia fasiculata that exhibit significantly different behavior on non-denaturing polyacrylamide gels. The nature of the structural construct produced by the methodology is discussed with respect to static and dynamic models of structure and representations of bending and bendability. An independent theoretical account of sequence dependent chemical footprinting results is provided. Detailed analysis of sequences with A-tract induced axis bending forms the basis for a critical discussion of the applicability of wedge models, junction models and non A-tract, general sequence models for understanding the origin of DNA curvature at the molecular level.     

Structure of the B-DNA decamer C-C-A-A-C-G-T-T-G-G and comparison with isomorphous decamers C-C-A-A-G-A-T-T-G-G and C-C-A-G-G-C-C-T-G-G

The crystal structure of the DNA decamer C-C-A-A-C-G-T-T-G-G has been solved to a resolution of 1.4 A, and is compared with the 1.3 A structure of C-C-A-A-G-A-T-T-G-G and the 1.6 A structure of C-C-A-G-G-C-C-T-G-G. All three decamers crystallize isomorphously in space group C2 with five base-pairs per asymmetric unit, and with decamer double helices stacked atop one another along the c axis in a manner that closely approximates a continuous B helix. This efficient stacking probably accounts for the high resolution of the crystal data. Comparison of the three decamers reveals the following. (1) Minor groove width is more variable than heretofore realized. Regions of A.T base-pairs tend to be narrower than average, although two successive A.T base-pairs alone may not be sufficient to produce narrowing. The minor groove is wider in regions where BII phosphate conformations are opposed diagonally across the groove. (2) Narrow regions of minor groove exhibit a zig-zag spine of hydration, as was first seen in C-G-C-G-A-A-T-T-C-G-C-G, whereas wide regions show two ribbons of water molecules down the walls, connecting base edge N or O with sugar O-4' atoms. Regions of intermediate groove width may accommodate neither pattern of hydration well, and may exhibit a less regular pattern of hydration. (3) Base-pair stacking is virtually identical at equivalent positions in the three decamers. The unconnected step from the top of one decamer helix to the bottom of the next helix is a normal helix step in all respects, except for the absence of connecting phosphate groups. (4) BII phosphate conformation require the unstacking of the two bases linked by the phosphate, but do not necessarily follow as an inevitable consequence of unstacking. They have an influence on minor groove width as noted in point (1) above. (5) Sugar ring pseudorotation P and main-chain torsion angle delta show an excellent correlation as given by the equation: delta = 40 degrees cos (P + 144 degrees) + 120 degrees. Although centered around C-2'-endo, the conformations in these B-DNA helices are distributed broadly from C-3'-exo to O-4'-endo, unlike the tighter clustering around C-3'-endo observed in A-DNA oligomer structures.     

The Crystal Structure of d(CCCCGGGG): A New A-Form Variant with an Extended Backbone Conformation

Abstract

The crystal structure of d(CCCCGGGG) has been determined at a resolution of 2.25Å. The oligomers crystallize as A-DNA duplexes occupying crystallographic two-fold axes. The backbone conformation is, in general, similar to that observed in previously reported crystal structures of A-DNA fragments, except for the central linkage, where it adopts an extended structure resulting from all trans conformation at the P-05′-C5′-C4′ bonds. This type of conformation facilitates interstrand stacking between the guanines at the C-G site. The local helix twist at this step is very small (25°) compared to an overall average of 33.5°. The unique structure of the C-G base-pair step, namely the extended backbone and the distinct stacking geometry, may be an important feature in the recognition mechanism between double- stranded DNA molecules and restriction endonucleases such as Msp I, which cuts the sequence CCGG very specifically with a rate unaffected by neighboring base pairs.     

Structure of a B-DNA dodecamer. II. Influence of base sequence on helix structure

Detailed examination of the structure of the B-DNA dodecamer C-G-C-G-A-A-T-T-C-G-C-G, obtained by single-crystal X-ray analysis (Drew et al., 1981), reveals that the local helix parameters, twist, tilt and roll, are much more strongly influenced by base sequence than by crystal packing or any other external forces. The central EcoRI restriction endonuclease recognition site, G-A-A-T-T-C, is a B helix with an average of 9.8 base-pairs per turn. It is flanked on either side by single-base-pair steps having aspects of an A-like helix character. The dodecamer structure suggests several general principles, whose validity must be tested by other B-DNA analyses. (1) When an external bending moment is applied to a B-DNA double helix, it bends smoothly, without kinks or breaks, and with relatively little effect on local helix parameters. (2) Purine-3′,5′-pyrimidine steps open their base planes towards the major groove, pyrimidine-purine steps open toward the minor groove, and homopolymer (Pur-Pur, Pyr-Pyr) steps resist rolling in either direction. This behavior is related to the preference of pyrimidines for more negative glycosyl torsion angles. (3) CpG steps have smaller helical twist angles than do GpC, as though in compensation for their smaller intrinsic base overlap. Data on A-T steps are insufficient for generalization. (4) G.C base-pairs have smaller propellor twist than A · T, and this arises mainly from interstrand base overlap rather than the presence of the third hydrogen bond. (5) DNAase I cuts preferentially at positions of high helical twist, perhaps because of increased exposure of the backbone to attack. The correlation of the digestion patterns in solution and helical twist in the crystal argues for the essential identity of the helix structure in the two environments. (6) In the two places where the sequence TpCpG occurs, the C slips from under T in order to stack more efficiently over G. At the paired bases of this CpG step, the G and C are tilted so the angle between base planes is splayed out to the outside of the helix. This TpC is the most favored cutting site for DNAase I by a factor of 4.5 (Lomonossoff et al., 1981). (7) The EcoRI restriction endonuclease and methylase both appear to prefer a cutting site of the type purine-purine-A-T-T-pyrimidine, involving two adjacent homopolymer triplets, and this may be a consequence of the relative stiffness of homopolymer base-stacking observed in the dodecamer.     

Groove Width and Depth of B-DNA Structures Depend on Local Variation in Slide

Abstract

The groove widths of DNA helix, especially minor groove width, are generally believed to be important for recognition of DNA by various types of ligands. It has been postulated earlier that large negative propeller twist, in the AT rich regions compresses the minor groove of duplex DNA A systematic study has now been carried out by generating models with different values of local doublet and intra-basepair parameters and calculating their minor groove widths. It is found that several local doublet parameters affect the minor groove width but it depends most strongly on the local step parameters roll and slide when each parameter is considered individually. However, a detailed analysis of the various local parameters within the B-DNA family of crystal structures indicates that propeller twist and slide are most strongly correlated with the observed values of minor groove width. The groove depth is also strongly correlated with slide. Thus the local base sequence dependent variations in slide can modify both the groove width and depth and consequently determine the ligand binding properties of DNA.     

A Stochastic Model for Helix Bending in B-DNA

Abstract

Bending in double-helical B-DNA apparently occurs only by rolling adjacent base pairs over one another along their long axes. The lifting apart of ends that would be required by tilt or wedge angle contributions is too costly in free energy and does not occur. Roll angles at base steps can be positive (compression of major groove) or negative (compression of minor groove); with the former somewhat easier.

Individual steps may advance or oppose the overall direction of bend, or make lateral excursions, but the result of this series of “random roll” steps is the production of a net bending in the helix axis. Because the natural roll points for bending in a given plane occur every 5 base pairs, one would expect that double-helical DNA wrapped around a nucleosome core would exhibit bends with the same periodicity. Alternate bends might be particularly acute where the major groove faced the nucleosome core and was compressed against it.

The “annealed kinking” model proposed by Fratini et al. (J. Biol. Chem. 257, 14686 (1982) was suggested from the observation that a major bend at a natural roll point is flanked by decreasing roll angles at the steps to either side, as though local strain was being minimized by somewhat blurring the bend out rather than keeping it localized. The random walk model suggested in this paper would describe this as a decreased roll angle as the helix step rotates toward a direction perpendicular to the overall bend. Bending of DNA is seen to be a more stochastic process than had been suspected. Detailed analysis of every helix step reveals both side excursions and backward or retrograde motion, as in any random walk situation. Yet these isolated steps counteract one another, to leave behind a residuum of overall bending in a specific direction.     

Super Secondary Structure Consisting of a Polyproline II Helix and a β-Turn in Leucine Rich Repeats in Bacterial Type III Secretion System Effectors

Leucine rich repeats (LRRs) are present in over 100,000 proteins from viruses to eukaryotes. The LRRs are 20–30 residues long and occur in tandem. LRRs form parallel stacks of short β-strands and then assume a super helical arrangement called a solenoid structure. Individual LRRs are separated into highly conserved segment (HCS) with the consensus of LxxLxLxxNxL and variable segment (VS). Eight classes have been recognized. Bacterial LRRs are short and characterized by two prolines in the VS; the consensus is xxLPxLPxx with Nine residues (N-subtype) and xxLPxxLPxx with Ten residues (T-subtype). Bacterial LRRs are contained in type III secretion system effectors such as YopM, IpaH3/9.8, SspH1/2, and SlrP from bacteria. Some LRRs in decorin, fribromodulin, TLR8/9, and FLRT2/3 from vertebrate also contain the motifs. In order to understand structural features of bacterial LRRs, we performed both secondary structures assignments using four programs—DSSP-PPII, PROSS, SEGNO, and XTLSSTR—and HELFIT analyses (calculating helix axis, pitch, radius, residues per turn, and handedness), based on the atomic coordinates of their crystal structures. The N-subtype VS adopts a left handed polyproline II helix (PPII) with four, five or six residues and a type I β-turn at the C-terminal side. Thus, the N-subtype is characterized by a super secondary structure consisting of a PPII and a β-turn. In contrast, the T-subtype VS prefers two separate PPIIs with two or three and two residues. The HELFIT analysis indicates that the type I β-turn is a right handed helix. The HELFIT analysis determines three unit vectors of the helix axes of PPII (P), β-turn (B), and LRR domain (A). Three structural parameters using these three helix axes are suggested to characterize the super secondary structure and the LRR domain.     

Index to Authors,Volume 3

Abstract

Results of calculations using various empirical potentials suggest that base pair buckling, which commonly occurs in DNA crystal structures, is sufficient to eliminate the steric clash at CpG steps in B-DNA, originating from the base pair propeller twisting. The buckling is formed by an inclination of cytosines while deviations of guanines from a plane perpendicular to the double helix axis are unfavorable. The buckling is accompanied by an increased vertical separation of the base pair centers but the buckled arrangement of base pairs is at least as stable as when the vertical separation is normal and buckle zero. In addition, room is created by the increased vertical separation for the bases to propeller twist as is observed in DNA crystal structures. Further stabilization of base stacking is introduced into the buckled base pair arrangement by roll opening the base pairs into the double helix minor groove. The roll may lead to the double helix bending and liberation of guanines from the strictly perpendicular orientation to the double helix axis. The liberated guanines further contribute to the base pair buckling and stacking improvement. This work also suggests a characteristic very stable DNA structure promoted by nucleotide sequences in which runs of purines follow runs of pyrimidine bases.     

The energy of formation of internal loops in triple-helical collagen polypeptides

The sequence-dependent local destabilization in the interior of the collagen triple helix has been evaluated by means of conformational energy computations. Using a model poly(Gly-Pro-Pro) triple helix as the reference state, a method was developed for generating local loops, i.e., internal deformations, and analyzing their conformations. A seven-residue Gly-Pro-Pro-Gly-Pro-Pro-Gly fragment was replaced by the Gly-Pro-Ala-Gly-Ala-Ala-Gly sequence in one, two, or all three of the strands of the loop region. A set of loop conformations was generated in which the ends of the loop were initially fixed in the triple-helical structure. The potential energy of the entire deformed triple helix was then minimized, resulting in a variety of structures that contained deformed loops. The conformations of the triple helices at the two ends of the loops remained essentially unchanged in many of the low-energy conformations. In numerous high-energy conformations, however, the triple-helical segments were also partially or totally disrupted. The minimum-energy conformations of the whole structures were compared in terms of rms deviations of atomic coordinates with respect to the original triple helix, and of the shapes of the loops (using a distance function derived from differential geometry). Three new geometrical parameters—stretch S, kink K, and unwinding U—were defined to describe the changes in the overall orientation of the triple helices at the two ends of the loop. It is shown that, when the number of Pro residues in a short fragment is reduced, the triple helical structure can accomodate internal loops (i.e., distortions) within a 5 kcal/mol cutoff from the essentially unperturbed triple helical structure. For structures with a Gly-Pro-Ala-Gly-Ala-Ala-Gly sequence in all three strands, the probability of finding conformations with internal loops is small, i.e., 0.06. Internal loops affect the overall orientation of these structures, as measured by the helix-distortion parameters S, K, and U. © 1995 John Wiley & Sons, Inc.