No Arabic abstract
In single molecule laser optical tweezer (LOT) pulling experiments a protein or RNA is juxtaposed between DNA handles that are attached to beads in optical traps. The LOT generates folding trajectories under force in terms of time-dependent changes in the distance between the beads. How to construct the full intrinsic folding landscape (without the handles and the beads) from the measured time series is a major unsolved problem. By using rigorous theoretical methods---which account for fluctuations of the DNA handles, rotation of the optical beads, variations in applied tension due to finite trap stiffness, as well as environmental noise and the limited bandwidth of the apparatus---we provide a tractable method to derive intrinsic free energy profiles. We validate the method by showing that the exactly calculable intrinsic free energy profile for a Generalized Rouse Model, which mimics the two-state behavior in nucleic acid hairpins, can be accurately extracted from simulated time series in a LOT setup regardless of the stiffness of the handles. We next apply the approach to trajectories from coarse grained LOT molecular simulations of a coiled-coil protein based on the GCN4 leucine zipper, and obtain a free energy landscape that is in quantitative agreement with simulations performed without the beads and handles. Finally, we extract the intrinsic free energy landscape from experimental LOT measurements for the leucine zipper, which is independent of the trap parameters.
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 T scales non-linearly with N, the hairpin length: T ~ N^a with a>1. This is in sharp contrast with the prediction of the zipper model for which T ~ 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 a = 1+ nu = 1.59 with nu the Flory exponent, a result which is in agreement with the simulations. We discuss transition path times data where such effects should be detected.
The folding pathway and rate coefficients of the folding of a knotted protein are calculated for a potential energy function with minimal energetic frustration. A kinetic transition network is constructed using the discrete path sampling approach, and the resulting potential energy surface is visualized by constructing disconnectivity graphs. Owing to topological constraints, the low-lying portion of the landscape consists of three distinct regions, corresponding to the native knotted state and to configurations where either the N- or C-terminus is not yet folded into the knot. The fastest folding pathways from denatured states exhibit early formation of the N-terminus portion of the knot and a rate-determining step where the C-terminus is incorporated. The low-lying minima with the N-terminus knotted and the C-terminus free therefore constitute an off-pathway intermediate for this model. The insertion of both the N- and C-termini into the knot occur late in the folding process, creating large energy barriers that are the rate limiting steps in the folding process. When compared to other protein folding proteins of a similar length, this system folds over six orders of magnitude more slowly.
We propose an improved prediction method of the tertiary structures of $alpha$-helical membrane proteins based on the replica-exchange method by taking into account helix deformations. Our method allows wide applications because transmembrane helices of native membrane proteins are often distorted. In order to test the effectiveness of the present method, we applied it to the structure predictions of glycophorin A and phospholamban. The results were in accord with experiments.
The knowledge of the Free Energy Landscape topology is the essential key to understand many biochemical processes. The determination of the conformers of a protein and their basins of attraction takes a central role for studying molecular isomerization reactions. In this work, we present a novel framework to unveil the features of a Free Energy Landscape answering questions such as how many meta-stable conformers are, how the hierarchical relationship among them is, or what the structure and kinetics of the transition paths are. Exploring the landscape by molecular dynamics simulations, the microscopic data of the trajectory are encoded into a Conformational Markov Network. The structure of this graph reveals the regions of the conformational space corresponding to the basins of attraction. In addition, handling the Conformational Markov Network, relevant kinetic magnitudes as dwell times or rate constants, and the hierarchical relationship among basins, complete the global picture of the landscape. We show the power of the analysis studying a toy model of a funnel-like potential and computing efficiently the conformers of a short peptide, the dialanine, paving the way to a systematic study of the Free Energy Landscape in large peptides.
Test experiments of hybridization in DNA microarrays show systematic deviations from the equilibrium isotherms. We argue that these deviations are due to the presence of a partially hybridized long-lived state, which we include in a kinetic model. Experiments confirm the model predictions for the intensity vs. free energy behavior. The existence of slow relaxation phenomena has important consequences for the specificity of microarrays as devices for the detection of a target sequence from a complex mixture of nucleic acids.