Folding kinetics of an entangled protein.

The possibility of the protein backbone adopting lasso-like entangled motifs has attracted increasing attention. After discovering the surprising abundance of natively entangled protein domain structures, it was shown that misfolded entangled subpopulations might become thermosensitive or escape the homeostasis network just after translation. To investigate the role of entanglement in shaping folding kinetics, we introduce a novel indicator and analyze simulations of a coarse-grained, structure-based model for two small single-domain proteins. The model recapitulates the well-known two-state folding mechanism of a non-entangled SH3 domain. However, despite its small size, a natively entangled antifreeze RD1 protein displays a rich refolding behavior, populating two distinct kinetic intermediates: a short-lived, entangled, near-unfolded state and a longer-lived, non-entangled, near-native state. The former directs refolding along a fast pathway, whereas the latter is a kinetic trap, consistently with known experimental evidence of two different characteristic times. Upon trapping, the natively entangled loop folds without being threaded by the N-terminal residues. After trapping, the native entangled structure emerges by either backtracking to the unfolded state or threading through the already formed but not yet entangled loop. Along the fast pathway, trapping does not occur because the native contacts at the closure of the lasso-like loop fold after those involved in the N-terminal thread, confirming previous predictions. Despite this, entanglement may appear already in unfolded configurations. Remarkably, a longer-lived, near-native intermediate, with non-native entanglement properties, recalls what was observed in cotranslational folding.

Dynamic and facilitated binding of topoisomerase accelerates topological relaxation.

How type 2 Topoisomerase (TopoII) proteins relax and simplify the topology of DNA molecules is one of the most intriguing open questions in genome and DNA biophysics. Most of the existing models neglect the dynamics of TopoII which is expected of proteins searching their targets via facilitated diffusion. Here, we show that dynamic binding of TopoII speeds up the topological relaxation of knotted substrates by enhancing the search of the knotted arc. Intriguingly, this in turn implies that the timescale of topological relaxation is virtually independent of the substrate length. We then discover that considering binding biases due to facilitated diffusion on looped substrates steers the sampling of the topological space closer to the boundaries between different topoisomers yielding an optimally fast topological relaxation. We discuss our findings in the context of topological simplification in vitro and in vivo.

The rise and fall of branching: A slowing down mechanism in relaxing wormlike micellar networks.

A mean-field kinetic model suggests that the relaxation dynamics of wormlike micellar networks is a long and complex process due to the problem of reducing the number of free end-caps (or dangling ends) while also reaching an equilibrium level of branching after an earlier overgrowth. The model is validated against mesoscopic molecular dynamics simulations and is based on kinetic equations accounting for scission and synthesis processes of blobs of surfactants. A long relaxation time scale is reached with both thermal quenches and small perturbations of the system. The scaling of this relaxation time is exponential with the free energy of an end cap and with the branching free energy. We argue that the subtle end-recombination dynamics might yield effects that are difficult to detect in rheology experiments, with possible underestimates of the typical time scales of viscoelastic fluids.

Aging of living polymer networks: a model with patchy particles.

Microrheology experiments show that viscoelastic media composed by wormlike micellar networks display complex relaxations lasting seconds even at the scale of micrometers. By mapping a model of patchy colloids with suitable mesoscopic elementary motifs to a system of worm-like micelles, we are able to simulate its relaxation dynamics, upon a thermal quench, spanning many decades, from microseconds up to tens of seconds. After mapping the model to real units and to experimental scission energies, we show that the relaxation process develops through a sequence of non-local and energetically challenging arrangements. These adjustments remove undesired structures formed as a temporary energetic solution for stabilizing the thermodynamically unstable free caps of the network. We claim that the observed scale-free nature of this stagnant process may complicate the correct quantification of experimentally relevant time scales as the Weissenberg number.

Folding Rate Optimization Promotes Frustrated Interactions in Entangled Protein Structures.

Many native structures of proteins accomodate complex topological motifs such as knots, lassos, and other geometrical entanglements. How proteins can fold quickly even in the presence of such topological obstacles is a debated question in structural biology. Recently, the hypothesis that energetic frustration might be a mechanism to avoid topological frustration has been put forward based on the empirical observation that loops involved in entanglements are stabilized by weak interactions between amino-acids at their extrema. To verify this idea, we use a toy lattice model for the folding of proteins into two almost identical structures, one entangled and one not. As expected, the folding time is longer when random sequences folds into the entangled structure. This holds also under an evolutionary pressure simulated by optimizing the folding time. It turns out that optmized protein sequences in the entangled structure are in fact characterized by frustrated interactions at the closures of entangled loops. This phenomenon is much less enhanced in the control case where the entanglement is not present. Our findings, which are in agreement with experimental observations, corroborate the idea that an evolutionary pressure shapes the folding funnel to avoid topological and kinetic traps.

Rings in random environments: sensing disorder through topology.

In this paper we study the role of topology in DNA gel electrophoresis experiments via molecular dynamics simulations. The gel is modelled as a 3D array of obstacles from which half edges are removed at random with probability p, thereby generating a disordered environment. Changes in the microscopic structure of the gel are captured by measuring the electrophoretic mobility of ring polymers moving through the medium, while their linear counterparts provide a control system as we show they are insensitive to these changes. We show that ring polymers provide a novel, non-invasive way of exploiting topology to sense microscopic disorder. Finally, we compare the results from the simulations with an analytical model for the non-equilibrium differential mobility, and find a striking agreement between simulation and theory.

Interpretable Machine Learning of Amino Acid Patterns in Proteins: A Statistical Ensemble Approach.

Explainable and interpretable unsupervised machine learning helps one to understand the underlying structure of data. We introduce an ensemble analysis of machine learning models to consolidate their interpretation. Its application shows that restricted Boltzmann machines compress consistently into a few bits the information stored in a sequence of five amino acids at the start or end of α-helices or ß-sheets. The weights learned by the machines reveal unexpected properties of the amino acids and the secondary structure of proteins: (i) His and Thr have a negligible contribution to the amphiphilic pattern of α-helices; (ii) there is a class of α-helices particularly rich in Ala at their end; (iii) Pro occupies most often slots otherwise occupied by polar or charged amino acids, and its presence at the start of helices is relevant; (iv) Glu and especially Asp on one side and Val, Leu, Iso, and Phe on the other display the strongest tendency to mark amphiphilic patterns, i.e., extreme values of an effective hydrophobicity, though they are not the most powerful (non)hydrophobic amino acids.

Generalized virial equation for nonlinear multiplicative Langevin dynamics: Application to laser-cooled atoms.

The virial theorem, and the equipartition theorem in the case of quadratic degrees of freedom, are handy constraints on the statistics of equilibrium systems. Their violation is instrumental in determining how far from equilibrium a driven system might be. We extend the virial theorem to nonequilibrium conditions for Langevin dynamics with nonlinear friction and multiplicative noise. In particular, we generalize it for confined laser-cooled atoms in the semiclassical regime. The resulting relation between the lowest moments of the atom position and velocity allows to measure in experiments how dissipative the cooling mechanism is. Moreover, its violation can reveal the departure from a strictly harmonic confinement or from the semiclassical regime.

Radiomics and deep learning methods for the prediction of 2-year overall survival in LUNG1 dataset.

In this study, we tested and compared radiomics and deep learning-based approaches on the public LUNG1 dataset, for the prediction of 2-year overall survival (OS) in non-small cell lung cancer patients. Radiomic features were extracted from the gross tumor volume using Pyradiomics, while deep features were extracted from bi-dimensional tumor slices by convolutional autoencoder. Both radiomic and deep features were fed to 24 different pipelines formed by the combination of four feature selection/reduction methods and six classifiers. Direct classification through convolutional neural networks (CNNs) was also performed. Each approach was investigated with and without the inclusion of clinical parameters. The maximum area under the receiver operating characteristic on the test set improved from 0.59, obtained for the baseline clinical model, to 0.67 ± 0.03, 0.63 ± 0.03 and 0.67 ± 0.02 for models based on radiomic features, deep features, and their combination, and to 0.64 ± 0.04 for direct CNN classification. Despite the high number of pipelines and approaches tested, results were comparable and in line with previous works, hence confirming that it is challenging to extract further imaging-based information from the LUNG1 dataset for the prediction of 2-year OS.

Fibril elongation mechanisms of HET-s prion-forming domain: topological evidence for growth polarity.

The prion-forming C-terminal domain of the fungal prion HET-s forms infectious amyloid fibrils at physiological pH. The conformational switch from the nonprion soluble form to the prion fibrillar form is believed to have a functional role, as HET-s in its prion form participates in a recognition process of different fungal strains. On the basis of the knowledge of the high-resolution structure of the prion forming domain HET-s(218-289) in its fibrillar form, we here present a numerical simulation of the fibril growth process, which emphasizes the role of the topological properties of the fibrillar structure. An accurate thermodynamic analysis of the way an intervening HET-s chain is recruited to the tip of the growing fibril suggests that elongation proceeds through a dock and lock mechanism. First, the chain docks onto the fibril by forming the longest ß-strands. Then, the re-arrangement in the fibrillar form of all the rest of the molecule takes place. Interestingly, we also predict that one side of the HET-s fibril is more suitable for sustaining its growth with respect to the other. The resulting strong polarity of fibril growth is a consequence of the complex topology of HET-s fibrillar structure, as the central loop of the intervening chain plays a crucially different role in favoring or not the attachment of the C-terminus tail to the fibril, depending on the growth side.