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Register a new userExploring the correlation between the folding rates of proteins and the entanglement of their native states
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The folding of a protein towards its native state is a rather complicated process. However there are empirical evidences that the folding time correlates with the contact order, a simple measure of the spatial organisation of the native state of the protein. Contact order is related to the average length of the main chain loops formed by amino acids which are in contact. Here we argue that folding kinetics can be influenced also by the entanglement that loops may undergo within the overall three dimensional protein structure. In order to explore such possibility, we introduce a novel descriptor, which we call maximum intrachain contact entanglement. Specifically, we measure the maximum Gaussian entanglement between any looped portion of a protein and any other non-overlapping subchain of the same protein, which is easily computed by discretized line integrals on the coordinates of the $C_{alpha}$ atoms. By analyzing experimental data sets of two-state and multistate folders, we show that also the new index is a good predictor of the folding rate. Moreover, being only partially correlated with previous methods, it can be integrated with them to yield more accurate predictions.
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Loops are abundant in native RNA structures and proliferate close to the unfolding transition. By including a statistical weight ~ l^{-c} for loops of length l in the recursion relation for the partition function, we show that the calculated heat capacity depends sensitively on the presence and value of the exponent c, even of short t-RNA. For homo-RNA we analytically calculate the critical temperature and critical exponents which exhibit a non-universal dependence on c.
Stochastic simulations of coarse-grained protein models are used to investigate the propensity to form knots in early stages of protein folding. The study is carried out comparatively for two homologous carbamoyltransferases, a natively-knotted N-acetylornithine carbamoyltransferase (AOTCase) and an unknotted ornithine carbamoyltransferase (OTCase). In addition, two different sets of pairwise amino acid interactions are considered: one promoting exclusively native interactions, and the other additionally including non-native quasi-chemical and electrostatic interactions. With the former model neither protein show a propensity to form knots. With the additional non-native interactions, knotting propensity remains negligible for the natively-unknotted OTCase while for AOTCase it is much enhanced. Analysis of the trajectories suggests that the different entanglement of the two transcarbamylases follows from the tendency of the C-terminal to point away from (for OTCase) or approach and eventually thread (for AOTCase) other regions of partly-folded protein. The analysis of the OTCase/AOTCase pair clarifies that natively-knotted proteins can spontaneously knot during early folding stages and that non-native sequence-dependent interactions are important for promoting and disfavoring early knotting events.
Water plays a fundamental role in protein stability. However, the effect of the properties of water on the behaviour of proteins is only partially understood. Several theories have been proposed to give insight into the mechanisms of cold and pressure denaturation, or the limits of temperature and pressure above which no protein has a stable, functional state, or how unfolding and aggregation are related. Here we review our results based on a theoretical approach that can rationalise the water contribution to protein solutions free energy. We show, using Monte Carlo simulations, how we can rationalise experimental data with our recent results. We discuss how our findings can help develop new strategies for the design of novel synthetic biopolymers or possible approaches for mitigating neurodegenerative pathologies.
Chiral heteropolymers such as larger globular proteins can simultaneously support multiple length scales. The interplay between different scales brings about conformational diversity, and governs the structure of the energy landscape. Multiple scales produces also complex dynamics, which in the case of proteins sustains live matter. However, thus far no clear understanding exist, how to distinguish the various scales that determine the structure and dynamics of a complex protein. Here we propose a systematic method to identify the scales in chiral heteropolymers such as a protein. For this we introduce a novel order parameter, that not only reveals the scales but also probes the phase structure. In particular, we argue that a chiral heteropolymer can simultaneously display traits of several different phases, contingent on the length scale at which it is scrutinized. Our approach builds on a variant of Kadanoffs block-spin transformation that we employ to coarse grain piecewise linear chains such as the C$alpha$ backbone of a protein. We derive analytically and then verify numerically a number of properties that the order parameter can display. We demonstrate how, in the case of crystallographic protein structures in Protein Data Bank, the order parameter reveals the presence of different length scales, and we propose that a relation must exist between the scales, phases, and the complexity of folding pathways.
The phase-separation occurring in a system of mutually interacting proteins that can bind on specific sites of a chromatin fiber is here investigated. This is achieved by means of extensive Molecular Dynamics simulations of a simple polymer model which includes regulatory proteins as interacting spherical particles. Our interest is particularly focused on the role played by phase-separation in the formation of molecule aggregates that can join distant regulatory elements, such as gene promoters and enhancers, along the DNA. We find that the overall equilibrium state of the system resulting from the mutual interplay between binding molecules and chromatin can lead, under suitable conditions that depend on molecules concentration, molecule-molecule and molecule-DNA interactions, to the formation of phase-separated molecular clusters allowing robust contacts between regulatory sites. Vice-versa, the presence of regulatory sites can promote the phase-separation process. Different dynamical regimes can generate the enhancer-promoter contact, either by cluster nucleation at binding sites or by bulk spontaneous formation of the mediating cluster to which binding sites are successively attracted. The possibility that such processes can explain experimental live-cell imaging data measuring distances between regulatory sites during time is also discussed.
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