EXCOGITO, an Extensible Coarse-Graining Toolbox for the Investigation of Biomolecules by Means of Low-Resolution Representations.

Bottom-up coarse-grained (CG) models proved to be essential to complement and sometimes even replace all-atom representations of soft matter systems and biological macromolecules. The development of low-resolution models takes the moves from the reduction of the degrees of freedom employed, that is, the definition of a mapping between a system's high-resolution description and its simplified counterpart. Even in the absence of an explicit parametrization and simulation of a CG model, the observation of the atomistic system in simpler terms can be informative: this idea is leveraged by the mapping entropy, a measure of the information loss inherent to the process of coarsening. Mapping entropy lies at the heart of the extensible coarse-graining toolbox, EXCOGITO, developed to perform a number of operations and analyses on molecular systems pivoting around the properties of mappings. EXCOGITO can process an all-atom trajectory to compute the mapping entropy, identify the mapping that minimizes it, and establish quantitative relations between a low-resolution representation and the geometrical, structural, and energetic features of the system. Here, the software, which is available free of charge under an open-source license, is presented and showcased to introduce potential users to its capabilities and usage.

Quality assessment and community detection methods for anonymized mobility data in the Italian Covid context.

We discuss how to assess the reliability of partial, anonymized mobility data and compare two different methods to identify spatial communities based on movements: Greedy Modularity Clustering (GMC) and the novel Critical Variable Selection (CVS). These capture different aspects of mobility: direct population fluxes (GMC) and the probability for individuals to move between two nodes (CVS). As a test case, we consider movements of Italians before and during the SARS-Cov2 pandemic, using Facebook users' data and publicly available information from the Italian National Institute of Statistics (Istat) to construct daily mobility networks at the interprovincial level. Using the Perron-Frobenius (PF) theorem, we show how the mean stochastic network has a stationary population density state comparable with data from Istat, and how this ceases to be the case if even a moderate amount of pruning is applied to the network. We then identify the first two national lockdowns through temporal clustering of the mobility networks, define two representative graphs for the lockdown and non-lockdown conditions and perform optimal spatial community identification on both graphs using the GMC and CVS approaches. Despite the fundamental differences in the methods, the variation of information (VI) between them assesses that they return similar partitions of the Italian provincial networks in both situations. The information provided can be used to inform policy, for example, to define an optimal scale for lockdown measures. Our approach is general and can be applied to other countries or geographical scales.

Thermal properties of knotted block copolymer rings with charged monomers subjected to short-range interactions.

The thermal properties of coarse-grained knotted copolymer rings fluctuating in a highly screening solution are investigated on a simple cubic lattice using the Wang-Landau Monte Carlo algorithm. The rings contain two kinds of monomers A and B with opposite charges that are subjected to short-range interactions. In view of possible applications in medicine and the construction of intelligent materials, it is shown that the behavior of copolymer rings can be tuned by changing both their monomer configuration and topology. We find several phase transitions depending on the monomer distribution. They include the expansion and collapse of the knotted polymer as well as rearrangements leading to metastable states. The temperatures at which these phase transitions are occurring and other features can be tuned by changing the topology of the system. The processes underlying the observed transitions are identified. In knots formed by diblock copolymers, two different classes of behaviors are detected depending on whether there is an excess of monomers of one kind or not. Moreover, we find that the most stable compact states are formed by copolymers in which units of two A monomers are alternated by units of two B monomers. Remarkably, these compact states are in a lamellar phase. The transition from the lamellar to the expanded state produces in the specific heat capacity a narrow and high peak that is centered at temperatures that are much higher than those of the peaks observed in all other monomer distributions.

Scaling properties of RNA as a randomly branching polymer.

Formation of base pairs between the nucleotides of a ribonucleic acid (RNA) sequence gives rise to a complex and often highly branched RNA structure. While numerous studies have demonstrated the functional importance of the high degree of RNA branching-for instance, for its spatial compactness or interaction with other biological macromolecules-RNA branching topology remains largely unexplored. Here, we use the theory of randomly branching polymers to explore the scaling properties of RNAs by mapping their secondary structures onto planar tree graphs. Focusing on random RNA sequences of varying lengths, we determine the two scaling exponents related to their topology of branching. Our results indicate that ensembles of RNA secondary structures are characterized by annealed random branching and scale similarly to self-avoiding trees in three dimensions. We further show that the obtained scaling exponents are robust upon changes in nucleotide composition, tree topology, and folding energy parameters. Finally, in order to apply the theory of branching polymers to biological RNAs, whose length cannot be arbitrarily varied, we demonstrate how both scaling exponents can be obtained from distributions of the related topological quantities of individual RNA molecules with fixed length. In this way, we establish a framework to study the branching properties of RNA and compare them to other known classes of branched polymers. By understanding the scaling properties of RNA related to its branching structure, we aim to improve our understanding of the underlying principles and open up the possibility to design RNA sequences with desired topological properties.

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.

Comparing equilibration schemes of high-molecular-weight polymer melts with topological indicators.

Recent theoretical studies have demonstrated that the behaviour of molecular knots is a sensitive indicator of polymer structure. Here, we use knots to verify the ability of two state-of-the-art algorithms-configuration assembly and hierarchical backmapping-to equilibrate high-molecular-weight (MW) polymer melts. Specifically, we consider melts with MWs equivalent to several tens of entanglement lengths and various chain flexibilities, generated with both strategies. We compare their unknotting probability, unknotting length, knot spectra, and knot length distributions. The excellent agreement between the two independent methods with respect to knotting properties provides an additional strong validation of their ability to equilibrate dense high-MW polymeric liquids. By demonstrating this consistency of knotting behaviour, our study opens the way for studying topological properties of polymer melts beyond time and length scales accessible to brute-force molecular dynamics simulations.

Protein design under competing conditions for the availability of amino acids.

Isolating the properties of proteins that allow them to convert sequence into the structure is a long-lasting biophysical problem. In particular, studies focused extensively on the effect of a reduced alphabet size on the folding properties. However, the natural alphabet is a compromise between versatility and optimisation of the available resources. Here, for the first time, we include the impact of the relative availability of the amino acids to extract from the 20 letters the core necessary for protein stability. We present a computational protein design scheme that involves the competition for resources between a protein and a potential interaction partner that, additionally, gives us the chance to investigate the effect of the reduced alphabet on protein-protein interactions. We devise a scheme that automatically identifies the optimal reduced set of letters for the design of the protein, and we observe that even alphabets reduced down to 4 letters allow for single protein folding. However, it is only with 6 letters that we achieve optimal folding, thus recovering experimental observations. Additionally, we notice that the binding between the protein and a potential interaction partner could not be avoided with the investigated reduced alphabets. Therefore, we suggest that aggregation could have been a driving force in the evolution of the large protein alphabet.

Identification of Protein Functional Regions.

Protein sequence stores the information relative to both functionality and stability, thus making it difficult to disentangle the two contributions. However, the identification of critical residues for function and stability has important implications for the mapping of the proteome interactions, as well as for many pharmaceutical applications, e. g. the identification of ligand binding regions for targeted pharmaceutical protein design. In this work, we propose a computational method to identify critical residues for protein functionality and stability and to further categorise them in strictly functional, structural and intermediate. We evaluate single site conservation and use Direct Coupling Analysis (DCA) to identify co-evolved residues both in natural and artificial evolution processes. We reproduce artificial evolution using protein design and base our approach on the hypothesis that artificial evolution in the absence of any functional constraint would exclusively lead to site conservation and co-evolution events of the structural type. Conversely, natural evolution intrinsically embeds both functional and structural information. By comparing the lists of conserved and co-evolved residues, outcomes of the analysis on natural and artificial evolution, we identify the functional residues without the need of any a priori knowledge of the biological role of the analysed protein.

Design of Protein-Protein Binding Sites Suggests a Rationale for Naturally Occurring Contact Areas.

Molecular recognition is a critical process for many biological functions and consists in noncovalent binding of different molecules, such as protein-protein, antigen-antibody, and many others. The host-guest molecules involved often show a shape complementarity, and one of the leading specifications for molecular recognition is that the interaction should ideally be specific, i.e. the host should strongly bind exclusively to one selected guest. Our work focuses on the role played by the chemical heterogeneity and the steric compatibility on the specificity power of the binding site between two proteins. We tackle the problem computationally, reducing the complexity of the system by simulating a protein and a surface-like element, that shapes part of the protein and represents the binding site of an interaction partner. We investigate four systems, differing in terms of binding site size. A significant result is that, despite the fact that protein and surface chemical sequences are interdependent and simultaneously generated to stabilize the bound folded structure, the protein is stable in the folded conformation even in the absence of the surface-like partner for all investigated systems. We observe that an increase of the surface area results in a significant increase of the binding affinity. Interestingly, our data suggest the presence of upper and lower limits for the maximum and minimum area size available for a binding site. Our data match the experimental observation of such limits (750-1500 Å2 ( Arkin and Wells Nat. Rev. Drug Discov. 2004 , 3 , 301 - 317 ) and provide a rationale for them: the extent of the binding site area is limited by the value of the binding constant. For large contact areas, at physiological conditions, the binding is orders of magnitude stronger ( K a > 1040 L/mol) than what is typically observed in natural biological processes. Conversely, the smallest surface tested is just the minimal size to allow for specific binding.

Implementing efficient concerted rotations using Mathematica and C code⋆.

In this article we demonstrate a general and efficient metaprogramming implementation of concerted rotations using Mathematica. Concerted rotations allow the movement of a fixed portion of a polymer backbone with fixed bending angles, like a protein, while maintaining the correct geometry of the backbone and the initial and final points of the portion fixed. Our implementation uses Mathematica to generate a C code which is then wrapped in a library by a Python script. The user can modify the Mathematica notebook to generate a set of concerted rotations suited for a particular backbone geometry, without having to write the C code himself. The resulting code is highly optimized, performing on the order of thousands of operations per second.

KymoKnot: A web server and software package to identify and locate knots in trajectories of linear or circular polymers.

The KymoKnot software package and web server identifies and locates physical knots or proper knots in a series of polymer conformations. It is mainly intended as an analysis tool for trajectories of linear or circular polymers, but it can be used on single instances too, e.g. protein structures in PDB format. A key element of the software package is the so-called minimally interfering chain closure algorithm that is used to detect physical knots in open chains and to locate the knotted region in both open and closed chains. The web server offers a user-friendly graphical interface that identifies the knot type and highlights the knotted region on each frame of the trajectory, which the user can visualize interactively from various viewpoints. The dynamical evolution of the knotted region along the chain contour is presented as a kymograph. All data can be downloaded in text format. The KymoKnot package is licensed under the BSD 3-Clause licence. The server is publicly available at http://kymoknot.sissa.it/kymoknot/interactive.php .

Author Correction: The role of directional interactions in the designability of generalized heteropolymers.

A correction to this article has been published and is linked from the HTML and PDF versions of this paper. The error has not been fixed in the paper.

Compactness of viral genomes: effect of disperse and localized random mutations.

Genomes of single-stranded RNA viruses have evolved to optimize several concurrent properties. One of them is the architecture of their genomic folds, which must not only feature precise structural elements at specific positions, but also allow for overall spatial compactness. The latter was shown to be disrupted by random synonymous mutations, a disruption which can consequently negatively affect genome encapsidation. In this study, we use three mutation schemes with different degrees of locality to mutate the genomes of phage MS2 and Brome Mosaic virus in order to understand the observed sensitivity of the global compactness of their folds. We find that mutating local stretches of their genomes' sequence or structure is less disruptive to their compactness compared to inducing randomly-distributed mutations. Our findings are indicative of a mechanism for the conservation of compactness acting on a global scale of the genomes, and have several implications for understanding the interplay between local and global architecture of viral RNA genomes.

The role of directional interactions in the designability of generalized heteropolymers.

Heteropolymers are important examples of self-assembling systems. However, in the design of artificial heteropolymers the control over the single chain self-assembling properties does not reach that of the natural bio-polymers, and in particular proteins. Here, we introduce a sufficiency criterion to identify polymers that can be designed to adopt a predetermined structure and show that it is fulfilled by polymers made of monomers interacting through directional (anisotropic) interactions. The criterion is based on the appearance of a particular peak in the radial distribution function, that we show being a universal feature of all designable heteropolymers, as it is present also in natural proteins. Our criterion can be used to engineer new self-assembling modular polymers that will open new avenues for applications in materials science.

Discretized knot motion on a tensioned fiber induced by transverse waves.

Topological entanglement is a ubiquitous feature of many biological as well as artificial polymers and fibers. While the equilibrium properties of entangled chains have been the subject of several studies, little is known about their out-of-equilibrium behavior. Here, we address the problem of a stretched knotted fiber driven by a periodic force applied to one of its termini. We show that the onset of standing waves kinetically traps the knot in spatially localized states where the amplitude of the oscillations is maximal, while the knot normal diffusive dynamics is replaced by a discrete jump dynamics.

Role of Bending Energy and Knot Chirality in Knot Distribution and Their Effective Interaction along Stretched Semiflexible Polymers.

Knots appear frequently in semiflexible (bio)polymers, including double-stranded DNA, and their presence can affect the polymer's physical and functional properties. In particular, it is possible and indeed often the case that multiple knots appear on a single chain, with effects which have only come under scrutiny in the last few years. In this manuscript, we study the interaction of two knots on a stretched semiflexible polymer, expanding some recent results on the topic. Specifically, we consider an idealization of a typical optical tweezers experiment and show how the bending rigidity of the chain-And consequently its persistence length-Influences the distribution of the entanglements; possibly more importantly, we observe and report how the relative chirality of the otherwise identical knots substantially modifies their interaction. We analyze the free energy of the chain and extract the effective interactions between embedded knots, rationalizing some of their pertinent features by means of simple effective models. We believe the salient aspect of the knot⁻knot interactions emerging from our study will be present in a large number of semiflexible polymers under tension, with important consequences for the characterization and manipulation of these systems-Be they artificial or biologica in origin-And for their technological application.

Synonymous mutations reduce genome compactness in icosahedral ssRNA viruses.

Recent studies have shown that single-stranded (ss) viral RNAs fold into more compact structures than random RNA sequences with similar chemical composition and identical length. Based on this comparison, it has been suggested that wild-type viral RNA may have evolved to be atypically compact so as to aid its encapsidation and assist the viral assembly process. To further explore the compactness selection hypothesis, we systematically compare the predicted sizes of >100 wild-type viral sequences with those of their mutants, which are evolved in silico and subject to a number of known evolutionary constraints. In particular, we enforce mutation synonynimity, preserve the codon-bias, and leave untranslated regions intact. It is found that progressive accumulation of these restricted mutations still suffices to completely erase the characteristic compactness imprint of the viral RNA genomes, making them in this respect physically indistinguishable from randomly shuffled RNAs. This shows that maintaining the physical compactness of the genome is indeed a primary factor among ssRNA viruses' evolutionary constraints, contributing also to the evidence that synonymous mutations in viral ssRNA genomes are not strictly neutral.

Computational study on the progressive factorization of composite polymer knots into separated prime components.

Using Monte Carlo simulations and advanced knot localization methods, we analyze the length and distribution of prime components in composite knots tied on freely jointed rings. For increasing contour length, we observe the progressive factorization of composite knots into separated prime components. However, we observe that a complete factorization, equivalent to the "decorated ring" picture, is not obtained even for rings of contour lengths N ≃ 3 N(0), about tens of times the most probable length of the prime knots tied on the rings. The decorated ring hypothesis has been used in the literature to justify the factorization of composite knot probabilities into the knotting probabilities of their prime components. Following our results, we suggest that such a hypothesis may not be necessary to explain the factorization of the knotting probabilities, at least when polymers excluding volume is not relevant. We rationalize the behavior of the system through a simple one-dimensional model in which prime knots are replaced by slip links randomly placed on a circle, with the only constraint being that the length of the loops has the same distribution as that of the length of the corresponding prime knots.

Driving knots on DNA with AC/DC electric fields: topological friction and memory effects.

The dynamical properties of entangled polyelectrolytes are investigated theoretically and computationally for a proposed novel micromanipulation setup. Specifically, we investigate the effects of DC and AC electric fields acting longitudinally on knotted DNA chains, modelled as semiflexible chains of charged beads, under mechanical tension. We consider various experimentally accessible values of the field amplitude and frequency as well as several of the simplest knot types. In particular, we consider both torus and twist knots because they are respectively known to be able or unable to slide along macroscopic threads and ropes. Strikingly, this qualitative distinction disappears in this microscopic context because all the considered knot types acquire a systematic drift in the direction of the electric force. Notably, the knot drift velocity and diffusion coefficient in zero field (both measurable also experimentally) can be used to define a characteristic "frictional" lengthscale for the various knot types. This previously unexplored length provides valuable information on the extent of self-interactions in the nominal knotted region. It is finally observed that the motion of a knot can effectively follow the AC field only if the driving period is larger than the knot relaxation time (for which the self-diffusion time provides an upper bound). These results suggest that salient aspects of the intrinsic dynamics of knots in DNA chains could be probed experimentally by means of external, time-dependent electric fields.

Multiscale entanglement in ring polymers under spherical confinement.

The interplay of geometrical and topological entanglement in semiflexible knotted polymer rings confined inside a spherical cavity is investigated by using advanced numerical methods. By using stringent and robust algorithms for locating knots, we characterize how the knot length l(k) depends on the ring contour length L(c) and the radius of the confining sphere R(c). In the no- and strong-confinement cases, we observe weak knot localization and complete knot delocalization, respectively. We show that the complex interplay of l(k), L(c), and R(c) that seamlessly bridges these two limits can be encompassed by a simple scaling argument based on deflection theory. The same argument is used to rationalize the multiscale character of the entanglement that emerges with increasing confinement.