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DNA toroids are compact torus-shaped bundles formed by one or multiple DNA molecules being condensed from the solution due to various condensing agents. It has been shown that the DNA toroidal bundles are twisted. However, the global conformations of DNA inside these bundles are still not well understood. In this study, we investigate this issue by solving different models for the toroidal bundles and performing replica-exchange molecular dynamics (REMD) simulations for self-attractive stiff polymers of various chain lengths. We find that a moderate degree of twisting is energetically favorable for toroidal bundles, yielding optimal configurations of lower energies than for other bundles corresponding to spool-like and constant radius of curvature arrangements. The REMD simulations show that the ground states of the stiff polymers are twisted toroidal bundles with the average twist degrees close to those predicted by the theoretical model. Constant-temperature simulations show that twisted toroidal bundles can be formed through successive processes of nucleation, growth, quick tightening, and slow tightening of the toroid, with the two last processes facilitating the polymer threading through the toroid's hole. A relatively long chain of 512 beads has an increased dynamical difficulty to access the twisted bundle states due to the polymer's topological constraint. Interestingly, we also observed significantly twisted toroidal bundles with a sharp U-shaped region in the polymer conformation. It is suggested that this U-shaped region makes the formation of twisted bundles easier by effectively reducing the polymer length. This effect can be equivalent to having multiple chains in the toroid.

The ribosomal exit tunnel is the primary structure affecting the release of nascent proteins at the ribosome. The ribosomal exit tunnels from different species have elements of conservation and differentiation in structural and physico-chemical properties. In this study, by simulating the elongation and escape processes of nascent proteins at the ribosomal exit tunnels of four different organisms, we show that the escape process has conserved mechanisms across the domains of life. Specifically, it is found that the escape process of proteins follows the diffusion mechanism given by a simple diffusion model, and the median escape time positively correlates with the number of hydrophobic residues and the net charge of a protein for all the exit tunnels considered. These properties hold for 12 distinct proteins considered in two slightly different and improved Gō-like models. It is also found that the differences in physico-chemical properties of the tunnels lead to quantitative differences in the protein escape times. In particular, the relatively strong hydrophobicity of E. coli's tunnel and the unusually high number of negatively charged amino acids on the tunnel's surface of H. marismortui lead to substantially slower escapes of proteins at these tunnels than at those of S. cerevisiae and H. sapiens.

We study the post-translational escape of nascent proteins at the ribosomal exit tunnel with the consideration of a real shape atomistic tunnel based on the Protein Data Bank structure of the large ribosome subunit of archeon Haloarcula marismortui. Molecular dynamics simulations employing the Go-like model for the proteins show that at intermediate and high temperatures, including a presumable physiological temperature, the protein escape process at the atomistic tunnel is quantitatively similar to that at a cylinder tunnel of length L = 72 Å and diameter d = 16 Å. At low temperatures, the atomistic tunnel, however, yields an increased probability of protein trapping inside the tunnel, while the cylinder tunnel does not cause the trapping. All-β proteins tend to escape faster than all-α proteins, but this difference is blurred on increasing the protein's chain length. A 29-residue zinc-finger domain is shown to be severely trapped inside the tunnel. Most of the single-domain proteins considered, however, can escape efficiently at the physiological temperature with the escape time distribution following the diffusion model proposed in our previous works. An extrapolation of the simulation data to a realistic value of the friction coefficient for amino acids indicates that the escape times of globular proteins are at the sub-millisecond scale. It is argued that this time scale is short enough for the smooth functioning of the ribosome by not allowing nascent proteins to jam the ribosome tunnel.

How fast a post-translational nascent protein escapes from the ribosomal exit tunnel is relevant to its folding and protection against aggregation. Here, by using Langevin molecular dynamics, we show that non-local native interactions help decrease the escape time, and foldable proteins generally escape much faster than same-length, self-repulsive homopolymers at low temperatures. The escape process, however, is slowed down by the local interactions that stabilize the α-helices. The escape time is found to increase with both the tunnel length and the concentration of macromolecular crowders outside the tunnel. We show that a simple diffusion model described by the Smoluchowski equation with an effective linear potential can be used to map out the escape time distribution for various tunnel lengths and various crowder concentrations. The consistency between the simulation data and the diffusion model, however, is found only for the tunnel length smaller than a crossover length of 90 Å-110 Å, above which the escape time increases much faster with the tunnel length. It is suggested that the length of ribosomal exit tunnel has been selected by evolution to facilitate both the efficient folding and the efficient escape of single-domain proteins. We show that macromolecular crowders lead to an increase in the escape time, and attractive crowders are unfavorable for the folding of nascent polypeptide.

Deciphering the links between amino acid sequence and amyloid fibril formation is key for understanding protein misfolding diseases. Here we use Monte Carlo simulations to study the aggregation of short peptides in a coarse-grained model with hydrophobic-polar (HP) amino acid sequences and correlated side chain orientations for hydrophobic contacts. A significant heterogeneity is observed in the aggregate structures and in the thermodynamics of aggregation for systems of different HP sequences and different numbers of peptides. Fibril-like ordered aggregates are found for several sequences that contain the common HPH pattern, while other sequences may form helix bundles or disordered aggregates. A wide variation of the aggregation transition temperatures among sequences, even among those of the same hydrophobic fraction, indicates that not all sequences undergo aggregation at a presumable physiological temperature. The transition is found to be the most cooperative for sequences forming fibril-like structures. For a fibril-prone sequence, it is shown that fibril formation follows the nucleation and growth mechanism. Interestingly, a binary mixture of peptides of an aggregation-prone and a non-aggregation-prone sequence shows the association and conversion of the latter to the fibrillar structure. Our study highlights the role of a sequence in selecting fibril-like aggregates and also the impact of a structural template on fibril formation by peptides of unrelated sequences.

We use Wang-Landau and replica exchange techniques to study the effect of an increasing stiffness on the formation of secondary structures in protein-like systems. Two possible models are considered. In both models, a polymer chain is formed by tethered beads where non-consecutive backbone beads attract each other via a square-well potential representing the tendency of the chain to fold. In addition, smaller hard spheres are attached to each non-terminal backbone bead along the direction normal to the chain to mimic the steric hindrance of side chains in real proteins. The two models, however, differ in the way bending rigidity is enforced. In the first model, partial overlap between consecutive beads is allowed. This reduces the possible bending angle between consecutive bonds thus producing an effective entropic stiffness that competes with a short-range attraction, and leads to the formation of secondary structures characteristic of proteins. We discuss the low-temperature phase diagram as a function of increasing interpenetration and find a transition from a planar, beta-like structure, to helical shape. In the second model, an energetic stiffness is explicitly introduced by imposing an infinitely large energy penalty for bending above a critical angle between consecutive bonds, and no penalty below it. The low-temperature phase of this model does not show any sign of protein-like secondary structures. At intermediate temperatures, however, where the chain is still in the coil conformation but stiffness is significant, we find the two models to predict a quite similar dependence of the persistence length as a function of the stiffness. This behaviour is rationalized in terms of a simple geometrical mapping between the two models. Finally, we discuss the effect of shrinking side chains to zero and find the above mapping to still hold true.

We investigate the interplay between post-translational folding and escape of two small single-domain proteins at the ribosomal exit tunnel by using Langevin dynamics with coarse-grained models. It is shown that at temperatures lower or near the temperature of the fastest folding, folding proceeds concomitantly with the escape process, resulting in vectorial folding and enhancement of foldability of nascent proteins. The concomitance between the two processes, however, deteriorates as temperature increases. Our folding simulations as well as free energy calculation by using umbrella sampling show that, at low temperatures, folding at the tunnel follows one or two specific pathways without kinetic traps. It is shown that the escape time can be mapped to a one-dimensional diffusion model with two different regimes for temperatures above and below the folding transition temperature. Attractive interactions between amino acids and attractive sites on the tunnel wall lead to a free energy barrier along the escape route of the protein. It is suggested that this barrier slows down the escape process and consequently promotes correct folding of the released nascent protein.

The competition between toroidal and rod-like conformations as possible ground states for DNA condensation is studied as a function of the stiffness, the length of the DNA, and the form of the long-range interactions between neighboring molecules, using analytical theory supported by Monte Carlo simulations. Both conformations considered are characterized by a local nematic order with hexagonal packing symmetry of neighboring DNA molecules, but differ in global configuration of the chain and the distribution of its curvature as it wraps around to form a condensate. The long-range interactions driving the DNA condensation are assumed to be of the form pertaining to the attractive depletion potential as well as the attractive counterion induced soft potential. In the stiffness-length plane we find a transition between rod-like to toroid condensate for increasing stiffness at a fixed chain length L. Strikingly, the transition line is found to have a L(1/3) dependence irrespective of the details of the long-range interactions between neighboring molecules. When realistic DNA parameters are used, our description reproduces rather well some of the experimental features observed in DNA condensates.

The van der Waals interaction between a lipid membrane and a substrate covered by a graphene sheet is investigated using the Lifshitz theory. The reflection coefficients are obtained for a layered planar system submerged in water. The dielectric response properties of the involved materials are also specified and discussed. Our calculations show that a graphene covered substrate can repel the biological membrane in water. This is attributed to the significant changes in the response properties of the system due to the monolayer graphene. It is also found that the van der Waals interaction is mostly dominated by the presence of graphene, while the role of the particular substrate is secondary.

We present a novel technique, based on the principle of maximum entropy, for deriving the solvation energy parameters of amino acids from the knowledge of the solvent accessible areas in experimentally determined native state structures as well as high quality decoys of proteins. We present the results of detailed studies and analyze the correlations of the solvation energy parameters with the standard hydrophobic scale. We study the ability of the inferred parameters to discriminate between the native state structures of proteins and their decoy conformations.

Proteins, chain molecules of amino acids, behave in ways which are similar to each other yet quite distinct from standard compact polymers. We demonstrate that the Flory theorem, derived for polymer melts, holds for compact protein native state structures and is not incompatible with the existence of structured building blocks such as alpha helices and beta strands. We present a discussion on how the notion of the thickness of a polymer chain, besides being useful in describing a chain molecule in the continuum limit, plays a vital role in interpolating between conventional polymer physics and the phase of matter associated with protein structures.

Comparison of properties of three domains of titin, I1, I27, and I28, in a simple geometry-based model shows that despite a high structural homology between their native states different domains show similar but distinguishable mechanical properties. Folding properties of the separate domains are predicted to be diversified which reflects sensitivity of the kinetics to the details of native structures. The Go-like model corresponding to the experimentally resolved native structure of the I1 domain is found to provide the biggest thermodynamic and mechanical stability compared to the other domains studied here. We analyze elastic, thermodynamic, and kinetic properties of several structures corresponding to the I28 domain as obtained through homology-based modeling. We discuss the ability of the models of the I28 domain to reproduce experimental results qualitatively. A strengthening of contacts that involve hydrophobic amino acids does not affect theoretical comparisons of the domains. Tandem linkages of up to five identical or different domains unravel in a serial fashion at low temperatures. We study the nature of the intermediate state that arises in the early stages of the serial unraveling and find it to qualitatively agree with the results of Marszalek et al.