Configurational diffusion down a folding funnel describes the dynamics of DNA hairpins

Abstract

Elucidating the mechanism of folding of polynucleotides depends on accurate estimates of free energy surfaces and a quantitative description of the kinetics of structure formation. Here, the kinetics of hairpin formation in single-stranded DNA are measured after a laser temperature jump. The kinetics are modeled as configurational diffusion on a free energy surface obtained from a statistical mechanical description of equilibrium melting profiles. The effective diffusion coefficient is found to be strongly temperaturedependent in the nucleation step as a result of formation of misfolded loops that do not lead to subsequent zipping. This simple system exhibits many of the features predicted from theoretical studies of protein folding, including a funnel-like energy surface with many folding pathways, trapping in misfolded conformations, and non-Arrhenius folding rates.H airpin loops are ubiquitous in single-stranded DNA and RNA. Knowing the time scales and mechanism of formation of these loops is an essential first step toward understanding the folding problem. Although the stability of hairpin loops and the kinetics of hairpin formation have been a subject of intense investigation for over 30 years (1-5), our understanding of the kinetics is limited. In particular, there is no simple physical model that describes in a consistent way both the thermodynamics and kinetics of hairpin formation. With the exception of some early work on the helix-to-coil transition, in which the kinetics were described in terms of a statistical mechanical kinetic ''zipper'' model (6, 7), the kinetics of hairpin-to-coil transition have been described more recently in terms of a two-state system with Arrhenius temperature dependence for the rates of hairpin formation and unwinding (5, 8). The equilibrium dynamics of hairpins, obtained from fluctuation correlation spectroscopy measurements of hairpins labeled with fluorescent donor and acceptor pairs (8, 9), have revealed a number of kinetic features that are not easily explained within the framework of a simple two-state analysis. First, the data of Libchaber and coworkers show that the rate coefficient corresponding to the closing of hairpins has a non-Arrhenius temperature dependence (8). Second, they report a puzzling result in which the apparent activation energy for forming hairpins with poly(dA) loops increases as the loop size increases. Third, Klenerman and coworkers report stretched exponential kinetics at temperatures well below the melting temperature (9). These observations suggest a failure of the simplest two-state analysis and require a modification of even the more rigorous kinetic ''zipper'' model in the form in which it was applied to helix-coil kinetics (6).Here we present a model for the dynamics of hairpins that is consistent with many of the apparently anomalous kinetic observations. The dynamics are described as configurational diffusion along a free energy profile that we calculate from a statistical mechanical ''zipper'' model that describes the equilibrium melt...

Defining the sequence-recognition profile of DNA-binding molecules

“…1). Previous work shows that this addition is sufficient to buffer the core of the hairpin stem against thermal end-fraying of the duplex and against deviations from B-form DNA resulting from the presence of the loop (26). There is good evidence that the core of a hairpin stem interacts with proteins and small molecule ligands indistinguishably from DNA duplexes composed of two individual complementary strands (27,28).…”

Direct observation of DNA bending/unbending kinetics in complex with DNA-bending protein IHF

“…Our T-jump spectrometer consists of a multimode Q-switched Nd:YAG laser (Continuum Surelite II, Santa Clara, CA; fwhm ϭ 6 ns, 300 mJ per pulse at 1.06 m) that is used to pump a 1-m-long Raman cell consisting of high pressure methane gas (27,48). The first Stokes line is separated from the fundamental by using a Pellin-Broca prism.…”

“…In the last decade, laser T-jump has emerged as a powerful tool whereby conformational changes in biomolecules can be monitored on time scales of submicroseconds-tomilliseconds (23)(24)(25)(26)(27)(28)(29). The T-jump measurements, in combination with stopped-flow measurements, demonstrate that the binding of IHF to its cognate DNA site involves an intermediate state with straight or, possibly, partially bent DNA (Fig.…”

RNA hairpin-folding kinetics

“…Recently, the studies of the folding kinetics for RNA hairpins (11), peptide ␤-hairpin (12)(13)(14)(15)(16)(17)(18), and DNA hairpins (19)(20)(21)(22)(23)(24)(25) have become highly active. However, despite the active efforts on the modeling of RNA folding (26)(27)(28)(29)(30)(31)(32)(33)(34)(35)(36)(37)(38)(39), quantitative analysis based on the first principle calculations has not been explored very much for RNA hairpin-folding kinetics.…”