An official website of the United States government
Abstract Based on polymer scaling theory and numerical evidence, Orlandini, Tesi, Janse van Rensburg and Whittington conjectured in 1996 that the limiting entropy of knot-typeKlattice polygons is the same as that for unknot polygons, and that the entropic critical exponent increases by one for each prime knot in the knot decomposition ofK. This Knot Entropy (KE) conjecture is consistent with the idea that for unconfined polymers, knots occur in a localized way (the knotted part is relatively small compared to polymer length). For full confinement (to a sphere or box), numerical evidence suggests that knots are much less localized. Numerical evidence for nanochannel or tube confinement is mixed, depending on how the size of a knot is measured. Here we outline the proof that the KE conjecture holds for polygons in the lattice tube and show that knotting is localized when a connected-sum measure of knot size is used. Similar results are established for linked polygons. This is the first model for which the knot entropy conjecture has been proved.
more »
« less
Topological descriptions of protein folding
How knotted proteins fold has remained controversial since the identification of deeply knotted proteins nearly two decades ago. Both computational and experimental approaches have been used to investigate protein knot formation. Motivated by the computer simulations of Bölinger et al. [Bölinger D, et al. (2010)PLoS Comput Biol6:e1000731] for the folding of the -knotted α-haloacid dehalogenase (DehI) protein, we introduce a topological description of knot folding that could describe pathways for the formation of all currently known protein knot types and predicts knot types that might be identified in the future. We analyze fingerprint data from crystal structures of protein knots as evidence that particular protein knots may fold according to specific pathways from our theory. Our results confirm Taylor’s twisted hairpin theory of knot folding for the -knotted proteins and the -knotted ketol-acid reductoisomerases and present alternative folding mechanisms for the -knotted phytochromes and the - and -knotted proteins.
more »
« less
- PAR ID:
- 10109472
- Publisher / Repository:
- Proceedings of the National Academy of Sciences
- Date Published:
- Journal Name:
- Proceedings of the National Academy of Sciences
- ISSN:
- 0027-8424
- Page Range / eLocation ID:
- Article No. 201808312
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
While hydrogen-rich materials have been demonstrated to exhibit high Tcsuperconductivity at high pressures, there is an ongoing search for ternary, quaternary, and more chemically complex hydrides that achieve such high critical temperatures at much lower pressures. First-principles searches are impeded by the computational complexity of solving the Eliashberg equations for large, complex crystal structures. Here, we adopt a simplified approach using electronic indicators previously established to be correlated with superconductivity in hydrides. This is used to study complex hydride structures, which are predicted to exhibit promisingly high critical temperatures for superconductivity. In particular, we propose three classes of hydrides inspired by the Fm m RH structures that exhibit strong hydrogen network connectivity, as defined through the electron localization function. The first class [RH X Y] is based on a Pm m structure showing moderately high Tc, where the Tcestimate from electronic properties is compared with direct Eliashberg calculations and found to be surprisingly accurate. The second class of structures [(RH ) X YZ] improves on this with promisingly high density of states with dominant hydrogen character at the Fermi energy, typically enhancing Tc. The third class [(R H )(R H )X YZ] improves the strong hydrogen network connectivity by introducing anisotropy in the hydrogen network through a specific doping pattern. These design principles and associated model structures provide flexibility to optimize both Tcand the structural stability of complex hydrides.more » « less
-
Abstract Building on the theory of circuit topology for intra-chain contacts in entangled proteins, we introduce tiles as a way to rigorously model local entanglements which are held in place by molecular forces. We develop operations that combine tiles so that entangled chains can be represented by algebraic expressions. Then we use our model to show that the only knot types that such entangled chains can have are$$3_1$$ ,$$4_1$$ ,$$5_1$$ ,$$5_2$$ ,$$6_1$$ ,$$6_2$$ ,$$6_3$$ ,$$7_7$$ ,$$8_{12}$$ and connected sums of these knots. This includes all proteins knots that have thus far been identified.more » « less
-
MXenes have demonstrated potential for various applications owing to their tunable surface chemistry and metallic conductivity. However, high temperatures can accelerate MXene film oxidation in air. Understanding the mechanisms of MXene oxidation at elevated temperatures, which is still limited, is critical in improving their thermal stability for high-temperature applications. Here, we demonstrate that Ti C T MXene monoflakes have exceptional thermal stability at temperatures up to 600 C in air, while multiflakes readily oxidize in air at 300 C. Density functional theory calculations indicate that confined water between Ti C T flakes has higher removal energy than surface water and can thus persist to higher temperatures, leading to oxidation. We demonstrate that the amount of confined water correlates with the degree of oxidation in stacked flakes. Confined water can be fully removed by vacuum annealing Ti C T films at 600 C, resulting in substantial stability improvement in multiflake films (can withstand 600 C in air). These findings provide fundamental insights into the kinetics of confined water and its role in Ti C T oxidation. This work enables the use of stable monoflake MXenes in high-temperature applications and provides guidelines for proper vacuum annealing of multiflake films to enhance their stability.more » « less
-
Abstract Using mass–radius composition models, small planets (R≲ 2R⊕) are typically classified into three types: iron-rich, nominally Earth-like, and those with solid/liquid water and/or atmosphere. These classes are generally expected to be variations within a compositional continuum. Recently, however, Luque & Pallé observed that potentially Earth-like planets around M dwarfs are separated from a lower-density population by a density gap. Meanwhile, the results of Adibekyan et al. hint that iron-rich planets around FGK stars are also a distinct population. It therefore remains unclear whether small planets represent a continuum or multiple distinct populations. Differentiating the nature of these populations will help constrain potential formation mechanisms. We present theRhoPopsoftware for identifying small-planet populations.RhoPopemploys mixture models in a hierarchical framework and a nested sampler for parameter and evidence estimates. UsingRhoPop, we confirm the two populations of Luque & Pallé with >4σsignificance. The intrinsic scatter in the Earth-like subpopulation is roughly half that expected based on stellar abundance variations in local FGK stars, perhaps implying M dwarfs have a smaller spread in the major rock-building elements (Fe, Mg, Si) than FGK stars. We applyRhoPopto the Adibekyan et al. sample and find no evidence of more than one population. We estimate the sample size required to resolve a population of planets with Mercury-like compositions from those with Earth-like compositions for various mass–radius precisions. Only 16 planets are needed when and . At and , however, over 154 planets are needed, an order of magnitude increase.more » « less
