Direct measurement of sequence-dependent transition path times and conformational diffusion in DNA duplex formation

Abstract

The conformational diffusion coefficient, D, sets the timescale for microscopic structural changes during folding transitions in biomolecules like nucleic acids and proteins. D encodes significant information about the folding dynamics such as the roughness of the energy landscape governing the folding and the level of internal friction in the molecule, but it is challenging to measure. The most sensitive measure of D is the time required to cross the energy barrier that dominates folding kinetics, known as the transition path time. To investigate the sequence dependence of D in DNA duplex formation, we measured individual transition paths from equilibrium folding trajectories of single DNA hairpins held under tension in high-resolution optical tweezers. Studying hairpins with the same helix length but with G:C base-pair content varying from 0 to 100%, we determined both the average time to cross the transition paths, τ tp , and the distribution of individual transit times, P TP (t). We then estimated D from both τ tp and P TP (t) from theories assuming one-dimensional diffusive motion over a harmonic barrier. τ tp decreased roughly linearly with the G:C content of the hairpin helix, being 50% longer for hairpins with only A:T base pairs than for those with only G:C base pairs. Conversely, D increased linearly with helix G:C content, roughly doubling as the G:C content increased from 0 to 100%. These results reveal that G:C base pairs form faster than A:T base pairs because of faster conformational diffusion, possibly reflecting lower torsional barriers, and demonstrate the power of transition path measurements for elucidating the microscopic determinants of folding.folding | DNA hairpins | energy landscapes | optical tweezers S tructure formation in biological macromolecules like proteins and nucleic acids is a complex, dynamic process. Physically, it is described in the context of energy landscape theory as a diffusive search in conformational space for the minimumenergy structure (1-3). The speed at which this search takes place at the microscopic level is set by the conformational diffusion coefficient, D. Because D plays a key role in determining the kinetics of the folding, as encapsulated in the well-known expression for rates derived by Kramers (4), it is one of the fundamental physical determinants of folding phenomena: it connects the thermodynamics encoded in the energy landscape to the dynamics of conformational changes. The properties of D relate to such key issues as internal friction in the polymer chain (5-8), roughness in the energy landscape (9-12), projection of the full phase-space for conformational dynamics onto experimental reaction coordinates (13), and "speed limits" for folding transitions (14).Despite its importance, D remains challenging to determine experimentally. Several studies have found D from the reconfiguration times for unfolded proteins or polypeptides (15-19), using fluorescence probes to measure interactions between specific locations on the polymer chain. However, few stu...

Measuring the average shape of transition paths during the folding of a single biological molecule

“…4C, yellow). The values of D returned by the fits, 6 ± 4 × 10 5 nm 2 /s for both unfolding and refolding, agreed within error with the values in the range 2-5 × 10 5 nm 2 /s found previously for this hairpin by analyzing rates (6), transition path times (9), and transition path velocities (13). Repeating this analysis for each hairpin by fitting 〈x(tjτ)〉 τ to Eq.…”

“…Fitting 〈x(tjτ)〉 τ for hairpin 30R50/T4 to Eq. 1, while fixing 2L = x 2 − x 1 , using the values of κ found from energy-landscape reconstructions (9), and treating D as a free parameter, we found good agreement with the observed shape ( Fig. 4C, yellow).…”

“…Since simulations showed that 〈x(tjτ)〉 τ provides a reasonable approximation of the analytical shape of the dominant transition path for harmonic barriers (Fig. 5A), and since the transition paths in hairpin folding are generally well-described by harmonic-barrier models (9,11,15), we fit the average shapes to the functional form of the dominant path shape for a harmonic barrier. In 1D with constant diffusion, this path shape is given by the following:…”

“…As a result, it has only recently become possible to measure transition path properties directly (3). Work to date using fluorescence and force spectroscopy has probed properties such as the average transition path time for proteins and nucleic acids (4)(5)(6)(7)(8), the variations in transit times for individual transitions (9,10), the occupancy statistics within transition paths (11,12), the distribution of velocities along the transition paths (13), and the agreement between experiment and theory for the properties measured to date (13)(14)(15).…”

Transition path time distributions

“…Transition paths are the part of the trajectories spent crossing the potential barrier connecting the two wells. Due to the very short duration of these trajectories, their experimental analysis has been a big challenge for a long time, but measurements of transition path times in nucleic acids and protein folding have been successfully performed in the past decade [6][7][8][9] . Transition paths have also attracted the attention of theorists and their properties were discussed in several papers [10][11][12][13][14][15][16][17][18][19][20][21] .…”