Proper folding of deeply knotted proteins has a very low success rate even in structurebased models which favor formation of the native contacts but have no topological bias. By employing a structure-based model, we demonstrate that cotranslational folding on a model ribosome may enhance the odds to form trefoil knots for protein YibK without any need to introduce any non-native contacts. The ribosome is represented by a repulsive wall that keeps elongating the protein. On-ribosome folding proceeds through a a slipknot conformation. We elucidate the mechanics and energetics of its formation. We show that the knotting probability in on-ribosome folding is a function of temperature and that there is an optimal temperature for the process. Our model often leads to the establishment of the native contacts without formation of the knot.

We construct two variants of coarse-grained models of three hexaoses: one based on the centers of mass of the monomers and the other associated with the C4 atoms. The latter is found to be better defined and more suitable for studying interactions with proteins described within α-C based models. We determine the corresponding effective stiffness constants through all-atom simulations and two statistical methods. One method is the Boltzmann inversion (BI) and the other, named energy-based (EB), involves direct monitoring of energies as a function of the variables that define the stiffness potentials. The two methods are generally consistent in their account of the stiffness. We find that the elastic constants differ between the hexaoses and are noticeably different from those determined for the crystalline cellulose Iβ. The nonbonded couplings through hydrogen bonds between different sugar molecules are modeled by the Lennard-Jones potentials and are found to be stronger than the hydrogen bonds in proteins. We observe that the EB method agrees with other theoretical and experimental determinations of the nonbonded parameters much better than BI. We then consider the hexaose-Man5B catalytic complexes and determine the contact energies between their the C4-α-C atoms. These interactions are found to be stronger than the proteinic hydrogen bonds: about four times as strong for cellohexaose and two times for mannohexaose. The fluctuational dynamics of the coarse-grained complexes are found to be compatible with previous all-atom studies by Bernardi et al.

Unveiling the nanomechanical stability of the novel coronavirus (SARS-CoV-2) spike protein

We study the folding process in the shallowly knotted protein MJ0366 within two variants of a structure-based model. We observe that the resulting topological pathways are much richer than identified in previous studies. In addition to the single knot-loop events, we find novel, and dominant, two-loop mechanisms. We demonstrate that folding takes place in a range of temperatures and the conditions of most successful folding are at temperatures which are higher than those required for the fastest folding. We also demonstrate that nascent conditions are more favorable to knotting than off-ribosome folding.

We provide theoretical comparisons of the physical properties of eighteen proteins with the pathogenesis-related proteins of class 10 (PR-10) fold, which is characterized by a large hydrophobic cavity enclosed between a curved b-sheet and a variable a-helix. Our novel algorithm to calculate the volume of internal cavities within protein structures is used to demonstrate that, although the sizes of the cavities of the investigated PR-10 proteins vary significantly, their other physical properties, such as thermodynamic and mechanical parameters or parameters related to folding, are very close. The largest variations (in the order of 20%) are predicted for the optimal folding times. We show that, on squeezing, the PR-10 proteins behave differently from typical virus capsids.