Transition Path Times for DNA and RNA Folding from Force Spectroscopy

Testing Landscape Theory for Biomolecular Processes with Single Molecule Fluorescence Spectroscopy

Although Kramers' theory for diffusive barrier crossing on a 1D free energy profile plays a central role in landscape theory for complex biomolecular processes, it has not yet been rigorously tested by experiment. Here we test this 1D diffusion scenario with single molecule fluorescence measurements of DNA hairpin folding. We find an upper bound of 2.5  μs for the average transition path time, consistent with the predictions by theory with parameters determined from optical tweezer measurements.

Anomalous dynamics of DNA hairpin folding

By means of computer simulations of a coarse-grained DNA model we show that the DNA hairpin zippering dynamics is anomalous; i.e., the characteristic time τ scales nonlinearly with N, the hairpin length, τ ∼ N(α) with α>1. This is in sharp contrast to the prediction of the zipper model for which τ ∼ N. We show that the anomalous dynamics originates from an increase in the friction during zippering due to the tension built in the closing strands. From a simple polymer model we get α = 1+ν ≈ 1.59 with ν being the Flory exponent, a result which is in agreement with the simulations. We discuss transition path times data where such effects should be detected.

Comparing a simple theoretical model for protein folding with all-atom molecular dynamics simulations

Advances in computing have enabled microsecond all-atom molecular dynamics trajectories of protein folding that can be used to compare with and test critical assumptions of theoretical models. We show that recent simulations by the Shaw group (10, 11, 14, 15) are consistent with a key assumption of an Ising-like theoretical model that native structure grows in only a few regions of the amino acid sequence as folding progresses. The distribution of mechanisms predicted by simulating the master equation of this native-centric model for the benchmark villin subdomain, with only two adjustable thermodynamic parameters and one temperature-dependent kinetic parameter, is remarkably similar to the distribution in the molecular dynamics trajectories.

Phosphate release coupled to rotary motion of F1-ATPase

F1-ATPase, the catalytic domain of ATP synthase, synthesizes most of the ATP in living organisms. Running in reverse powered by ATP hydrolysis, this hexameric ring-shaped molecular motor formed by three αβ-dimers creates torque on its central γ-subunit. This reverse operation enables detailed explorations of the mechanochemical coupling mechanisms in experiment and simulation. Here, we use molecular dynamics simulations to construct a first atomistic conformation of the intermediate state following the 40° substep of rotary motion, and to study the timing and molecular mechanism of inorganic phosphate (Pi) release coupled to the rotation. In response to torque-driven rotation of the γ-subunit in the hydrolysis direction, the nucleotide-free αβE interface forming the "empty" E site loosens and singly charged Pi readily escapes to the P loop. By contrast, the interface stays closed with doubly charged Pi. The γ-rotation tightens the ATP-bound αβTP interface, as required for hydrolysis. The calculated rate for the outward release of doubly charged Pi from the αβE interface 120° after ATP hydrolysis closely matches the ~1-ms functional timescale. Conversely, Pi release from the ADP-bound αβDP interface postulated in earlier models would occur through a kinetically infeasible inward-directed pathway. Our simulations help reconcile conflicting interpretations of single-molecule experiments and crystallographic studies by clarifying the timing of Pi exit, its pathway and kinetics, associated changes in Pi protonation, and changes of the F1-ATPase structure in the 40° substep. Important elements of the molecular mechanism of Pi release emerging from our simulations appear to be conserved in myosin despite the different functional motions.