An official website of the United States government
Abstract The conformation of macromolecules attached to a surface is influenced by both their excluded volume and steric forces. Here, self‐avoiding random walk simulations are used to evaluate the occurrence of various conformations as a function of the number of monomeric units to estimate the effect of conformational entropy of a tethered chain. Then, a more realistic scenario is assessed, which can more accurately reproduce the shape of a tethered macromolecule. The simulations presented here confirm that it is more likely for a polymer to undergo a collapse conformation rather than a stretched one, as a collapse conformation can be realized in more different ways. Also, they confirm the “mushroom” shape of polymers close to a surface. From this simple approach, the conformation entropy of a model 100‐unit polymer close to a surface is estimated to contribute with over 129 toward its collapse. This conformation entropy is higher than that of typical hydrogen bonds and even barriers that keep proteins folded. As such, entropic collapse of macromolecules plays an important role in realizing the mushroom shape of attached polymers and can be the driving force in protein folding, while the polypeptide chain emerges from the ribosome.
more »
« less
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.
more »
« less
- Award ID(s):
- 2004493
- PAR ID:
- 10272406
- Publisher / Repository:
- Proceedings of the National Academy of Sciences
- Date Published:
- Journal Name:
- Proceedings of the National Academy of Sciences
- Volume:
- 118
- Issue:
- 28
- ISSN:
- 0027-8424
- Page Range / eLocation ID:
- Article No. e2106380118
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
When very long polymers are trapped into multiple entropic traps created by the meshes of host hydrogels, our recent discovery shows that the guest polymer chains are entropically frozen into a nondiffusive topologically frustrated dynamical state (TFDS) at intermediate confinements. Outside the confinement boundaries of the TFDS, the guest molecules diffuse, whereas in the TFDS regime, the center of mass diffusion coefficient is essentially zero due to the macromolecule being localized into long-lived metastable states with extreme free-energy barriers for the escape of the macromolecule. However, the segmental dynamics of the macromolecule is active with hierarchical dynamics. A key assumption to explain this hierarchical segmental dynamics of the macromolecule in the TFDS regime has been that the number of monomers in the various entropic traps is polydisperse. The validity of this assumption is tested in the present paper by experimentally investigating the segmental dynamics using the ideal tetra-PEG hydrogel as the host matrix and sodium poly(styrene sulfonate) as the guest macromolecule. We find that all features of TFDS previously observed using poly(acrylamide-co-acrylate) hydrogels with the polydisperse distribution of mesh size are recovered in the present system of uniform mesh size as well. Thus, the present study, with the chemical details different from those of our previous systems, adds credence to the universality of the phenomenon of TFDS. Furthermore, the present finding suggests that the polydispersity in the number of monomers in the various entropic traps must arise from conformational fluctuations emanating from the local exchange dynamics of segments among neighboring meshes.more » « less
-
Abstract We present a theory of melting kinetics of semicrystalline polymers at temperatures above the equilibrium melting temperature, by accounting for conformational entropy of chains during melting. We have derived free energy landscapes for escape of individual chains from a lamella into the amorphous phase as a function of the characteristics of the initial lamella, such as the lamellar thickness, number of chain folds, fold‐ and lateral‐surface free energies, and mean energy of a monomer inside the lamella. We show that melting of lamellae is always accompanied by a free energy barrier which is entirely entropic in origin. In terms of the parameters characterizing the lamellae and the extent of superheating, closed‐form formulas are presented for the equilibrium melting temperature, driving force for crystallization, free energy barrier height, average expulsion time of a single chain from a lamella, and the melting velocity of lamellae. The present entropic barrier theory predicts that the dependence of melting velocity on superheating is nonlinear and non‐Arrhenius, in qualitative agreement with experimental observations reported in the literature. The derived formulas open an opportunity to further explore the role of various molecular features of semicrystalline polymers on their melting kinetics.more » « less
-
Abstract Molecular dynamics (MD) is the primary computational method by which modern structural biology explores macromolecule structure and function. Boltzmann generators have been proposed as an alternative to MD, by replacing the integration of molecular systems over time with the training of generative neural networks. This neural network approach to MD enables convergence to thermodynamic equilibrium faster than traditional MD; however, critical gaps in the theory and computational feasibility of Boltzmann generators significantly reduce their usability. Here, we develop a mathematical foundation to overcome these barriers; we demonstrate that the Boltzmann generator approach is sufficiently rapid to replace traditional MD for complex macromolecules, such as proteins in specific applications, and we provide a comprehensive toolkit for the exploration of molecular energy landscapes with neural networks.more » « less
-
The phase behavior and chain conformational structure of biphasic polyzwitterion–polyelectrolyte coacervates in salted aqueous solution are investigated with a model weak cationic polyelectrolyte, poly(2-vinylpyridine) (P2VP), whose charge fraction can be effectively tuned by pH. It is observed that increasing the pH leads to the increase of the yielding volume fraction and the water content of dense coacervates formed between net neutral polybetaine and cationic P2VP in contrast to the decrease of critical salt concentration for the onset of coacervation, where the P2VP charge fraction is reduced correspondingly. Surprisingly, a single-molecule fluorescence spectroscopic study suggests that P2VP chains upon coacervation seem to adopt a swollen or an even more expanded conformational structure at higher pH. As the hydrophobicity of P2VP chains is accompanied by a reduced charge fraction by increasing the pH, a strong pH-dependent phase and conformational behaviors suggest the shift of entropic and enthalpic contribution to the underlying thermodynamic energy landscape and chain structural dynamics of polyelectrolyte coacervation involving weak polyelectrolytes in aqueous solution.more » « less
