Entropic barrier of topologically immobilized DNA in hydrogels

The single most intrinsic property of nonrigid polymer chains is their ability to adopt enormous numbers of chain conformations, resulting in huge conformational entropy. When such macromolecules move in media with restrictive spatial constraints, their trajectories are subjected to reductions in their conformational entropy. The corresponding free energy landscapes are interrupted by entropic barriers separating consecutive spatial domains which function as entropic traps where macromolecules can adopt their conformations more favorably. Movement of macromolecules by negotiating a sequence of entropic barriers is a common paradigm for polymer dynamics in restrictive media. However, if a single chain is simultaneously trapped by many entropic traps, it has recently been suggested that the macromolecule does not undergo diffusion and is localized into a topologically frustrated dynamical state, in apparent violation of Einstein’s theorem. Using fluorescently labeled λ-DNA as the guest macromolecule embedded inside a similarly charged hydrogel with more than 95% water content, we present direct evidence for this new state of polymer dynamics at intermediate confinements. Furthermore, using a combination of theory and experiments, we measure the entropic barrier for a single macromolecule as several tens of thermal energy, which is responsible for the extraordinarily long extreme metastability. The combined theory–experiment protocol presented here is a determination of single-molecule entropic barriers in polymer dynamics. Furthermore, this method offers a convenient general procedure to quantify the underlying free energy landscapes behind the ubiquitous phenomenon of movement of single charged macromolecules in crowded environments.

Understanding Conformational Entropy in Small Molecules

The calculation of the entropy of flexible molecules can be challenging, since the number of possible conformers grows exponentially with molecule size and many low-energy conformers may be thermally accessible. Different methods have been proposed to approximate the contribution of conformational entropy to the molecular standard entropy, including performing thermochemistry calculations with all possible stable conformations, and developing empirical corrections from experimental data. We have performed conformer sampling on over 120,000 small molecules generating some 12 million conformers, to develop models to predict conformational entropy across a wide range of molecules. Using insight into the nature of conformational disorder, our cross-validated physically-motivated statistical model can outperform common machine learning and deep learning methods, with a mean absolute error ≈4.8 J/mol•K, or under 0.4 kcal/mol at 300 K. Beyond predicting molecular entropies and free energies, the model implies a high degree of correlation between torsions in most molecules, often as- sumed to be independent. While individual dihedral rotations may have low energetic barriers, the shape and chemical functionality of most molecules necessarily correlate their torsional degrees of freedom, and hence restrict the number of low-energy conformations immensely. Our simple models capture these correlations, and advance our understanding of small molecule conformational entropy.

Structural origins of protein conformational entropy

The thermodynamics of molecular recognition by proteins is a central determinant of complex biochemistry. For over a half-century detailed cryogenic structures have provided deep insight into the energetic contributions to ligand binding by proteins1. More recently, a dynamical proxy based on NMR-relaxation methods has revealed an unexpected richness in the contributions of conformational entropy to the thermodynamics of ligand binding2,3,4,5. There remains, however, a discomforting absence of an understanding of the structural origins of fast internal motion and the conformational entropy that this motion represents. Here we report the pressure-dependence of fast internal motion within the ribonuclease barnase and its complex with the protein barstar. Distinctive clustering of the pressure sensitivity correlates with the presence of small packing defects or voids surrounding affected side chains. Prompted by this observation, we performed an analysis of the voids surrounding over 2,500 methyl-bearing side chains having experimentally determined order parameters. We find that changes in unoccupied volume as small as a single water molecule surrounding buried side chains greatly affects motion on the subnanosecond timescale. The discovered relationship begins to permit construction of a united view of the relationship between changes in the internal energy, as exposed by detailed structural analysis, and the conformational entropy, as represented by fast internal motion, in the thermodynamics of protein function.