Biophysics: Rough passage across a barrier

The role of solvent quality and chain stiffness on the end-to-end contact kinetics of semiflexible polymers

Motivated by loop closure during protein folding and DNA packing, we systemically studied the effects of the solvent quality and chain stiffness on the thermodynamics and kinetics of the end-to-end contact formation for semiflexible polymer chains with reactive ends by Langevin dynamics simulations. In thermodynamics, a rich variety of products of the end-to-end contact have been discovered, such as loop, hairpin, toroid, and rodlike bundle, the populations of which are dependent on the solvent quality and chain stiffness. In kinetics, the overall pathways to form the end-to-end contact have been identified. The change of solvent quality and chain stiffness can tune the roughness of energy landscape and modulate the kinetic partitioning of the end-to-end contact formation pathways, leading to differing kinetic behaviors. In good or poor solvents, the first end-to-end contact rate k _c decreases with increasing the strength of bending stiffness k _θ monotonically. In very poor solvents, however, the dependence of the logarithm of the first end-to-end contact rate ln k _c on k _θ exhibits erratic behavior, which stems from more rugged energy landscape due to the polymer chain getting trapped into the intermediate state composed of the rodlike bundles with two ends in separation. For semiflexible chains, with increasing chain length N, the rate k _c increases initially and then decreases: in good solvents, the rate k _c exhibits a power-law relationship to chain length N with an exponent of ∼-1.50 in the region of long chains, which is in good agreement with the value derived from the experiment in the asymptotic limit of large N; and in poor solvents, the rate k _c exhibits a significantly stronger chain length dependence than those observed in good solvents in the region of long chains due to frustration to form the end-to-end contact along a specific path, especially the scaling exponent between the rate k _c and chain length N is ∼-3.62 for the case of polymer chains with k _θ = 4 at the solvent quality ε _ij = 1, in accord with the value obtained from the experiments.

Transition state theory demonstrated at the micron scale with out-of-equilibrium transport in a confined environment

Transition state theory (TST) provides a simple interpretation of many thermally activated processes. It applies successfully on timescales and length scales that differ several orders of magnitude: to chemical reactions, breaking of chemical bonds, unfolding of proteins and RNA structures and polymers crossing entropic barriers. Here we apply TST to out-of-equilibrium transport through confined environments: the thermally activated translocation of single DNA molecules over an entropic barrier helped by an external force field. Reaction pathways are effectively one dimensional and so long that they are observable in a microscope. Reaction rates are so slow that transitions are recorded on video. We find sharp transition states that are independent of the applied force, similar to chemical bond rupture, as well as transition states that change location on the reaction pathway with the strength of the applied force. The states of equilibrium and transition are separated by micrometres as compared with angstroms/nanometres for chemical bonds.

Resolution of Two Sub-Populations of Conformers and Their Individual Dynamics by Time Resolved Ensemble Level FRET Measurements

Most active biopolymers are dynamic structures; thus, ensembles of such molecules should be characterized by distributions of intra- or intermolecular distances and their fast fluctuations. A method of choice to determine intramolecular distances is based on Förster resonance energy transfer (FRET) measurements. Major advances in such measurements were achieved by single molecule FRET measurements. Here, we show that by global analysis of the decay of the emission of both the donor and the acceptor it is also possible to resolve two sub-populations in a mixture of two ensembles of biopolymers by time resolved FRET (trFRET) measurements at the ensemble level. We show that two individual intramolecular distance distributions can be determined and characterized in terms of their individual means, full width at half maximum (FWHM), and two corresponding diffusion coefficients which reflect the rates of fast ns fluctuations within each sub-population. An important advantage of the ensemble level trFRET measurements is the ability to use low molecular weight small-sized probes and to determine nanosecond fluctuations of the distance between the probes. The limits of the possible resolution were first tested by simulation and then by preparation of mixtures of two model peptides. The first labeled polypeptide was a relatively rigid Pro₇ and the second polypeptide was a flexible molecule consisting of (Gly-Ser)₇ repeats. The end to end distance distributions and the diffusion coefficients of each peptide were determined. Global analysis of trFRET measurements of a series of mixtures of polypeptides recovered two end-to-end distance distributions and associated intramolecular diffusion coefficients, which were very close to those determined from each of the pure samples. This study is a proof of concept study demonstrating the power of ensemble level trFRET based methods in resolution of subpopulations in ensembles of flexible macromolecules.

Effects of the internal friction and the solvent quality on the dynamics of a polymer chain closure

Using 3D Langevin dynamics simulations, we investigate the effects of the internal friction and the solvent quality on the dynamics of a polymer chain closure. We show that the chain closure in good solvents is a purely diffusive process. By extrapolation to zero solvent viscosity, we find that the internal friction of a chain plays a non-ignorable role in the dynamics of the chain closure. When the solvent quality changes from good to poor, the mean closure time τc decreases by about 1 order of magnitude for the chain length 20 ≤ N ≤ 100. Furthermore, τc has a minimum as a function of the solvent quality. With increasing the chain length N, the minimum of τc occurs at a better solvent. Finally, the single exponential distributions of the closure time in poor solvents suggest that the negative excluded volume of segments does not alter the nearly Poisson statistical characteristics of the process of the chain closure.

Molecular origins of internal friction effects on protein-folding rates

Recent experiments on protein folding dynamics have revealed strong evidence for internal friction effects. That is, observed relaxation times are not simply proportional to the solvent viscosity as might be expected if the solvent were the only source of friction. However, a molecular interpretation of this remarkable phenomenon is currently lacking. Here, we use all-atom simulations of peptide and protein folding in explicit solvent, to probe the origin of the unusual viscosity dependence. We find that an important contribution to this effect, explaining the viscosity dependence of helix formation and the folding of a helix-containing protein, is the insensitivity of torsion angle isomerization to solvent friction. The influence of this landscape roughness can, in turn, be quantitatively explained by a rate theory including memory friction. This insensitivity of local barrier crossing to solvent friction is expected to contribute to the viscosity dependence of folding rates in larger proteins.

Structure, function, and plasticity of GABA transporters

GABA transporters belong to a large family of neurotransmitter:sodium symporters. They are widely expressed throughout the brain, with different levels of expression in different brain regions. GABA transporters are present in neurons and in astrocytes and their activity is crucial to regulate the extracellular concentration of GABA under basal conditions and during ongoing synaptic events. Numerous efforts have been devoted to determine the structural and functional properties of GABA transporters. There is also evidence that the expression of GABA transporters on the cell membrane and their lateral mobility can be modulated by different intracellular signaling cascades. The strength of individual synaptic contacts and the activity of entire neuronal networks may be finely tuned by altering the density, distribution and diffusion rate of GABA transporters within the cell membrane. These findings are intriguing because they suggest the existence of complex regulatory systems that control the plasticity of GABAergic transmission in the brain. Here we review the current knowledge on the structural and functional properties of GABA transporters and highlight the molecular mechanisms that alter the expression and mobility of GABA transporters at central synapses.