Observing the base-by-base search for native structure along transition paths during the folding of single nucleic acid hairpins

Nonlinear effects in optical trapping of titanium dioxide and diamond nanoparticles

Optical trapping in biophysics typically uses micron-scale beads made of materials like polystyrene or glass to probe the target of interest. Using smaller beads made of higher-index materials could increase the time resolution of these measurements. We characterized the trapping of nanoscale beads made of diamond and titanium dioxide (TiO2) in a single-beam gradient trap. Calculating theoretical expectations for the trapping stiffness of these beads, we found good agreement with measured values. Trap stiffness was significantly higher for TiO2 beads, owing to notable enhancement from nonlinear optical effects, not previously observed for continuous-wave trapping. Trap stiffness was over 6-fold higher for TiO2 beads than polystyrene beads of similar size at 70 mW laser power. These results suggest that diamond and TiO2 nanobeads can be used to improve time resolution in optical tweezers measurements.

Microscopic origin of diffusive dynamics in the context of transition path time distributions for protein folding and unfolding

Experimentally measured transition path time distributions are usually analyzed theoretically in terms of a diffusion equation over a free energy barrier. It is though well understood that the free energy profile separating the folded and unfolded states of a protein is characterized as a transition through many stable micro-states which exist between the folded and unfolded states. Why is it then justified to model the transition path dynamics in terms of a diffusion equation, namely the Smoluchowski equation (SE)? In principle, van Kampen has shown that a nearest neighbor Markov chain of thermal jumps between neighboring microstates will lead in a continuum limit to the SE, such that the friction coefficient is proportional to the mean residence time in each micro-state. However, the practical question of how many microstates are needed to justify modeling the transition path dynamics in terms of an SE has not been addressed. This is a central topic of this paper where we compare numerical results for transition paths based on the diffusion equation on the one hand and the nearest neighbor Markov jump model on the other. Comparison of the transition path time distributions shows that one needs at least a few dozen microstates to obtain reasonable agreement between the two approaches. Using the Markov nearest neighbor model one also obtains good agreement with the experimentally measured transition path time distributions for a DNA hairpin and PrP protein. As found previously when using the diffusion equation, the Markov chain model used here also reproduces the experimentally measured long time tail and confirms that the transition path barrier height is ∼3k_BT. This study indicates that in the future, when attempting to model experimentally measured transition path time distributions, one should perhaps prefer a nearest neighbor Markov model which is well defined also for rough energy landscapes. Such studies can also shed light on the minimal number of microstates needed to unravel the experimental data.

TPP Riboswitch Populates Holo-Form-like Structure Even in the Absence of Cognate Ligand at High Mg2+ Concentration

Riboswitches are noncoding RNA that regulate gene expression by folding into specific three-dimensional structures (holo-form) upon binding by their cognate ligand in the presence of Mg²⁺. Riboswitch functioning is also hypothesized to be under kinetic control requiring large cognate ligand concentrations. We ask the question under thermodynamic conditions, can the riboswitches populate structures similar to the holo-form only in the presence of Mg²⁺ and absence of cognate ligand binding. We addressed this question using thiamine pyrophosphate (TPP) riboswitch as a model system and computer simulations using a coarse-grained model for RNA. The folding free energy surface (FES) shows that with the initial increase in Mg²⁺ concentration ([Mg²⁺]), the aptamer domain (AD) of TPP riboswitch undergoes a barrierless collapse in its dimensions. On further increase in [Mg²⁺], intermediates separated by barriers appear on the FES, and one of the intermediates has a TPP ligand-binding competent structure. We show that site-specific binding of the Mg²⁺ aids in the formation of tertiary contacts. For [Mg²⁺] greater than physiological concentration, AD folds into a structure similar to the crystal structure of the TPP holo-form even in the absence of the TPP ligand. The folding kinetics shows that TPP AD populates an intermediate due to the misalignment of two arms present in the structure, which acts as a kinetic trap, leading to larger folding timescales. The predictions of the intermediate structures from the simulations are amenable for experimental verification.