How Large is an α-Helix? Studies of the Radii of Gyration of Helical Peptides by Small-angle X-ray Scattering and Molecular Dynamics

Using synchrotron radiation and the small-angle X-ray scattering technique we have measured the radii of gyration of a series of alanine-based α-helix-forming peptides of the composition Ace-(AAKAA)_n-GY-NH₂, n=2–7, in aqueous solvent at 10(±1) °C. In contrast to other techniques typically used to study α-helices in isolation (such as nuclear magnetic resonance and circular dichroism), small-angle X-ray scattering reports on the global structure of a molecule and, as such, provides complementary information to these other, more sequence-local measuring techniques. The radii of gyration that we measure are, except for the 12-mer, lower than the radii of gyration of ideal α-helices or helices with frayed ends of the equivalent sequence-length. For example, the measured radius of gyration of the 37-mer is 14.2(±0.6) Å, which is to be compared with the radius of gyration of an ideal 37-mer α-helix of 17.6 Å. Attempts are made to analyze the origin of this discrepancy in terms of the analytical Zimm–Bragg–Nagai (ZBN) theory, as well as distributed computing explicit solvent molecular dynamics simulations using two variants of the AMBER force-field. The ZBN theory, which treats helices as cylinders connected by random walk segments, predicts markedly larger radii of gyration than those measured. This is true even when the persistence length of the random walk parts is taken to be extremely short (about one residue). Similarly, the molecular dynamics simulations, at the level of sampling available to us, give inaccurate values of the radii of gyration of the molecules (by overestimating them by around 25% for longer peptides) and/or their helical content. We conclude that even at the short sequences examined here (≤37 amino acid residues), these α-helical peptides behave as fluctuating semi-broken rods rather than straight cylinders with frayed ends.

Introduction

The α-helix is the most prevalent secondary structural element in proteins.¹ However, in the absence of stabilizing tertiary interactions, α-helices rarely persist in isolation. One of the notable exceptions is a series of alanine-based, helix-forming peptides introduced by Robert Baldwin and his group.2, 3, 4 The study of these peptides has significantly furthered our understanding of the stability of α-helices,4, 5, 6 helical preference of individual amino acids,7, 8, 9 the role of helix-termination signals6, 10 and the kinetics of α-helix folding.¹¹ In addition, these peptides have been studied extensively by computer simulations, which lead to a more detailed microscopic picture of α-helix folding and dynamics in general.12, 13, 14, 15, 16, 17, 18, 19, 20

The two most commonly used techniques to study α-helices in isolation, CD and NMR, are predominantly short distance-range techniques. They report on the local structure and dynamics of polypeptides while giving limited information on the long-range ordering and correlations. On the other hand, the small angle X-ray scattering technique (SAXS),²¹ with molecular radius of gyration as its principal readout, is a long-range technique. It reports on the global structure of a molecule and, as such, gives information complementary to that obtained by CD, NMR and other local techniques. This ability of SAXS to probe the long-range structure in polypeptides is shared by electron paramagnetic resonance²² and fluorescence resonance energy transfer23, 24 techniques, but with greater accuracy compared to these methods. In this study, we have used SAXS to measure the radii of gyration of six α-helix-forming peptides with composition Ace-(AAKAA)_n-GY-NH₂ (n=2–7) in aqueous solvent. The measured radii of gyration are smaller than those of the equivalent ideal α-helices or α-helices with frayed ends. This difference is analyzed in terms of the Zimm–Bragg–Nagai (ZBN) analytical theory²⁵ and explicit solvent molecular dynamics (MD) simulations using world-wide distributed computing. The ZBN theory has been very successful in describing the behavior of long homopolymeric helices under various conditions,²⁶ but fails to account for the low radii of gyration measured here. The ZBN theory describes helices as cylinders connected by random walk segments. It combines the standard Zimm–Bragg helix-coil theory²⁷ with the statistics of ideal random walks. However, even if the persistence length of the random walk segments is taken to be very short (one amino acid), the ZBN theory predicts radii of gyration that are significantly larger than the values obtained by SAXS. The explicit solvent MD simulations described here were performed using distributed computing techniques and two variants of the AMBER force-field with a hope of finding a microscopic explanation for the low radii of gyration observed in the experiment. However, at the level of sampling used in this study (50 independent 50 ns long trajectories for each peptide and each force field), the radii of gyration of the simulated peptides deviate from the measured values, especially for the longest peptides where they are overestimated significantly. In addition, the secondary structure content from simulations deviates from the estimates based on CD. This suggests that capturing the behavior of flexible peptides is an area where modern atomistic force-fields could be improved. Our SAXS results are most consistent with alanine-based polypeptides adopting fluctuating semi-broken helix conformations, and are somewhat at odds with the picture of helices as straight cylinders with frayed ends.