Locality of contacts determines the subdiffusion exponents in polymeric models of chromatin.

Loop extrusion by motor proteins mediates the attractive interactions in chromatin on the length scale of megabases, providing the polymer with a well-defined structure and at the same time determining its dynamics. The mean-square displacement of chromatin loci varies from a Rouse-like scaling to a more constrained subdiffusion, depending on cell type, genomic region, and time scale. With a simple polymeric model, we show that such a Rouse-like dynamics occurs when the parameters of the model are chosen so that contacts are local along the chain, while in the presence of nonlocal contacts we observe subdiffusion at short time scales with exponents smaller than 0.5. Such exponents are independent of the detailed choice of the parameters and build a master curve that depends only on the mean locality of the resulting contacts. We compare the loop-extrusion model with a polymeric model with static links, showing that also in this case only the presence of nonlocal contacts can produce low-exponent subdiffusion. We interpret these results in terms of a simple analytical model.

Cohesin and CTCF control the dynamics of chromosome folding.

In mammals, interactions between sequences within topologically associating domains enable control of gene expression across large genomic distances. Yet it is unknown how frequently such contacts occur, how long they last and how they depend on the dynamics of chromosome folding and loop extrusion activity of cohesin. By imaging chromosomal locations at high spatial and temporal resolution in living cells, we show that interactions within topologically associating domains are transient and occur frequently during the course of a cell cycle. Interactions become more frequent and longer in the presence of convergent CTCF sites, resulting in suppression of variability in chromosome folding across time. Supported by physical models of chromosome dynamics, our data suggest that CTCF-anchored loops last around 10 min. Our results show that long-range transcriptional regulation might rely on transient physical proximity, and that cohesin and CTCF stabilize highly dynamic chromosome structures, facilitating selected subsets of chromosomal interactions.

Key interaction patterns in proteins revealed by cluster expansion of the partition function.

The native conformation of structured proteins is stabilized by a complex network of interactions. We analyzed the elementary patterns that constitute such network and ranked them according to their importance in shaping protein sequence design. To achieve this goal, we employed a cluster expansion of the partition function in the space of sequences and evaluated numerically the statistical importance of each cluster. An important feature of this procedure is that it is applied to a dense finite system. We found that patterns that contribute most to the partition function are cycles with even numbers of nodes, while cliques are typically detrimental. Each cluster also gives a contribute to the sequence entropy, which is a measure of the evolutionary designability of a fold. We compared the entropies associated with different interaction patterns to their abundances in the native structures of real proteins.

Polymer Folding Simulations from Hi-C Data.

In the absence of a clear molecular understanding of the mechanism that stabilizes specific contacts in interphasic chromatin, we resort to the principle of maximum entropy to build a polymeric model based on the Hi-C data of the specific system one wants to study. The interactions are set by an iterative Monte Carlo algorithm to reproduce the average contacts summarized by the Hi-C map. The study of the ensemble of conformations generated by the algorithm can report a much richer set of information than the experimental map alone, including colocalization of multiple sites, fluctuations of the contacts, and kinetical properties.

The denatured state of HIV-1 protease under native conditions.

The denatured state of several proteins has been shown to display transient structures that are relevant for folding, stability, and aggregation. To detect them by nuclear magnetic resonance (NMR) spectroscopy, the denatured state must be stabilized by chemical agents or changes in temperature. This makes the environment different from that experienced in biologically relevant processes. Using high-resolution heteronuclear NMR spectroscopy, we have characterized several denatured states of a monomeric variant of HIV-1 protease, which is natively structured in water, induced by different concentrations of urea, guanidinium chloride, and acetic acid. We have extrapolated the chemical shifts and the relaxation parameters to the denaturant-free denatured state at native conditions, showing that they converge to the same values. Subsequently, we characterized the conformational properties of this biologically relevant denatured state under native conditions by advanced molecular dynamics simulations and validated the results by comparison to experimental data. We show that the denatured state of HIV-1 protease under native conditions displays rich patterns of transient native and non-native structures, which could be of relevance to its guidance through a complex folding process.

Managing Experimental 3D Structures in the Beyond-Rule-of-5 Chemical Space: The Case of Rifampicin.

The beyond-Rule-of-5 (bRo5) chemical space is a source of new oral drugs and includes large and flexible compounds. Because of their size and conformational variability, bRo5 molecules assume different privileged conformations in the compartments of human body, i. e., they can exhibit chameleonic properties. The elucidation of the ensemble of 3D structures explored by such molecules under different conditions is therefore critical to check the role played by chameleonicity to modulate cell permeability. Here we characterized the conformational ensembles of rifampicin, a bRo5 drug, in polar and nonpolar solvents and in the solid state. We performed NMR experiments, analyzed their results with a novel algorithm and set-up a pool of ad hoc in silico strategies to investigate crystallographic structures retrieved from the CSD. Moreover, a polarity descriptor often related to permeability (SA-3D-PSA) was calculated for all the conformers and its variation with the environment analyzed. Results showed that the conformational behavior of rifampicin in solution and in the solid state is not superposable. The identification of dynamic intramolecular hydrogen bonds can be assessed by NMR spectroscopy but not by X-ray structures. Moreover, SA-3D-PSA revealed that dynamic IMHBs do not provide rifampicin with chameleonic properties. Overall, this study highlights that the peculiarity of rifampicin, which is cell permeable probably because of the presence of static IMHBs but is devoid of any chameleonic behavior, can be assessed by a proper analysis of experimental 3D structures.

HP1 drives de novo 3D genome reorganization in early Drosophila embryos.

Fundamental features of 3D genome organization are established de novo in the early embryo, including clustering of pericentromeric regions, the folding of chromosome arms and the segregation of chromosomes into active (A-) and inactive (B-) compartments. However, the molecular mechanisms that drive de novo organization remain unknown1,2. Here, by combining chromosome conformation capture (Hi-C), chromatin immunoprecipitation with high-throughput sequencing (ChIP-seq), 3D DNA fluorescence in situ hybridization (3D DNA FISH) and polymer simulations, we show that heterochromatin protein 1a (HP1a) is essential for de novo 3D genome organization during Drosophila early development. The binding of HP1a at pericentromeric heterochromatin is required to establish clustering of pericentromeric regions. Moreover, HP1a binding within chromosome arms is responsible for overall chromosome folding and has an important role in the formation of B-compartment regions. However, depletion of HP1a does not affect the A-compartment, which suggests that a different molecular mechanism segregates active chromosome regions. Our work identifies HP1a as an epigenetic regulator that is involved in establishing the global structure of the genome in the early embryo.

Evolution of frustrated and stabilising contacts in reconstructed ancient proteins.

Energetic properties of a protein are a major determinant of its evolutionary fitness. Using a reconstruction algorithm, dating the reconstructed proteins and calculating the interaction network between their amino acids through a coevolutionary approach, we studied how the interactions that stabilise 890 proteins, belonging to five families, evolved for billions of years. In particular, we focused our attention on the network of most strongly attractive contacts and on that of poorly optimised, frustrated contacts. Our results support the idea that the cluster of most attractive interactions extends its size along evolutionary time, but from the data, we cannot conclude that protein stability or that the degree of frustration tends always to decrease.

Effective model of loop extrusion predicts chromosomal domains.

An active loop-extrusion mechanism is regarded as the main out-of-equilibrium mechanism responsible for the structuring of megabase-sized domains in chromosomes. We developed a model to study the dynamics of the chromosome fiber by solving the kinetic equations associated with the motion of the extruder. By averaging out the position of the extruder along the chain, we build an effective equilibrium model capable of reproducing experimental contact maps based solely on the positions of extrusion-blocking proteins. We assessed the quality of the effective model using numerical simulations of chromosomal segments and comparing the results with explicit-extruder models and experimental data.

MicroRNA-222 Regulates Melanoma Plasticity.

Melanoma is one of the most aggressive and highly resistant tumors. Cell plasticity in melanoma is one of the main culprits behind its metastatic capabilities. The detailed molecular mechanisms controlling melanoma plasticity are still not completely understood. Here we combine mathematical models of phenotypic switching with experiments on IgR39 human melanoma cells to identify possible key targets to impair phenotypic switching. Our mathematical model shows that a cancer stem cell subpopulation within the tumor prevents phenotypic switching of the other cancer cells. Experiments reveal that hsa-mir-222 is a key factor enabling this process. Our results shed new light on melanoma plasticity, providing a potential target and guidance for therapeutic studies.

Molecular Recognition between Cadherins Studied by a Coarse-Grained Model Interacting with a Coevolutionary Potential.

Studying the conformations involved in the dimerization of cadherins is highly relevant to understand the development of tissues and its failure, which is associated with tumors and metastases. Experimental techniques, like X-ray crystallography, can usually report only the most stable conformations, missing minority states that could nonetheless be important for the recognition mechanism. Computer simulations could be a valid complement to the experimental approach. However, standard all-atom protein models in explicit solvent are computationally too demanding to search thoroughly the conformational space of multiple chains composed of several hundreds of amino acids. To reach this goal, we resorted to a coarse-grained model in implicit solvent. The standard problem with this kind of model is to find a realistic potential to describe its interactions. We used coevolutionary information from cadherin alignments, corrected by a statistical potential, to build an interaction potential, which is agnostic about the experimental conformations of the protein. Using this model, we explored the conformational space of multichain systems and validated the results comparing with experimental data. We identified dimeric conformations that are sequence specific and that can be useful to rationalize the mechanism of recognition between cadherins.

Assessing the accuracy of direct-coupling analysis for RNA contact prediction.

Many noncoding RNAs are known to play a role in the cell directly linked to their structure. Structure prediction based on the sole sequence is, however, a challenging task. On the other hand, thanks to the low cost of sequencing technologies, a very large number of homologous sequences are becoming available for many RNA families. In the protein community, the idea of exploiting the covariance of mutations within a family to predict the protein structure using the direct-coupling-analysis (DCA) method has emerged in the last decade. The application of DCA to RNA systems has been limited so far. We here perform an assessment of the DCA method on 17 riboswitch families, comparing it with the commonly used mutual information analysis and with state-of-the-art R-scape covariance method. We also compare different flavors of DCA, including mean-field, pseudolikelihood, and a proposed stochastic procedure (Boltzmann learning) for solving exactly the DCA inverse problem. Boltzmann learning outperforms the other methods in predicting contacts observed in high-resolution crystal structures.

Coarse Graining of a Giant Molecular System: The Chromatin Fiber.

The chromatin fiber is a complex polymer whose conformational properties are quite important to regulate gene transcription. One cannot but resort to coarse-grained models to describe the structure and the dynamics of this system on the length scale of the cellular nucleus. Bulk biological data can be used within the framework of the principle of maximum entropy to generate a realistic interaction potential that can be used to sample the equilibrium state of the fiber. The analysis of the structure and of the dynamics of the fiber can be correlated with its biological function, thus providing interesting results about transcriptional regulation.

DamC reveals principles of chromatin folding in vivo without crosslinking and ligation.

Current understanding of chromosome folding is largely reliant on chromosome conformation capture (3C)-based experiments, where chromosomal interactions are detected as ligation products after chromatin crosslinking. To measure chromosome structure in vivo, quantitatively and without crosslinking and ligation, we implemented a modified version of DNA adenine methyltransferase identification (DamID) named DamC, which combines DNA methylation-based detection of chromosomal interactions with next-generation sequencing and biophysical modeling of methylation kinetics. DamC performed in mouse embryonic stem cells provides the first in vivo validation of the existence of topologically associating domains (TADs), CTCF loops and confirms 3C-based measurements of the scaling of contact probabilities. Combining DamC with transposon-mediated genomic engineering shows that new loops can be formed between ectopic and endogenous CTCF sites, which redistributes physical interactions within TADs. DamC provides the first crosslinking- and ligation-free demonstration of the existence of key structural features of chromosomes and provides novel insights into how chromosome structure within TADs can be manipulated.

Determination of Structural Ensembles of Flexible Molecules in Solution from NMR Data Undergoing Spin Diffusion.

Spin diffusion is a formidable problem when interpreting NMR data of chemical compounds. We developed a method to reconstruct the conformational ensemble of flexible molecules displaying spin diffusion, which minimizes the subjective bias in the interpretation of experimental data and which can be used routinely to obtain sets of structures with the correct thermodynamic weights. We showed in the case of a flexible molecule that the correct conformational ensemble is quite different from that obtained with standard methods.

Molecular mechanisms of heterogeneous oligomerization of huntingtin proteins.

There is still no successful strategy to treat Huntington's disease, an inherited autosomal disorder associated with the aggregation of mutated forms of the huntingtin protein containing polyglutamine tracts with more than 36 repeats. Recent experimental evidence is challenging the conventional view of the disease by revealing transcellular transfer of mutated huntingtin proteins which are able to seed oligomers involving wild type forms of the protein. Here we decipher the molecular mechanism of this unconventional heterogeneous oligomerization by performing discrete molecular dynamics simulations. We identify the most probable oligomer conformations and the molecular regions that can be targeted to destabilize them. Our computational findings are complemented experimentally by fluorescence-lifetime imaging microscopy/fluorescence resonance energy transfer (FLIM-FRET) of cells co-transfected with huntingtin proteins containing short and large polyglutamine tracts. Our work clarifies the structural features responsible for heterogeneous huntingtin aggregation with possible implications to contrast the prion-like spreading of Huntington's disease.

Spontaneous domain formation in disordered copolymers as a mechanism for chromosome structuring.

Motivated by the problem of domain formation in chromosomes, we studied a co-polymer model where only a subset of the monomers feel attractive interactions. These monomers are displaced randomly from a regularly-spaced pattern, thus introducing some quenched disorder in the system. Previous work has shown that in the case of regularly-spaced interacting monomers this chain can fold into structures characterized by multiple distinct domains of consecutive segments. In each domain, attractive interactions are balanced by the entropy cost of forming loops. We show by advanced replica-exchange simulations that adding disorder in the position of the interacting monomers further stabilizes these domains. The model suggests that the partitioning of the chain into well-defined domains of consecutive monomers is a spontaneous property of heteropolymers. In the case of chromosomes, evolution could have acted on the spacing of interacting monomers to modulate in a simple way the underlying domains for functional reasons.

A method for partitioning the information contained in a protein sequence between its structure and function.

Proteins employ the information stored in the genetic code and translated into their sequences to carry out well-defined functions in the cellular environment. The possibility to encode for such functions is controlled by the balance between the amount of information supplied by the sequence and that left after that the protein has folded into its structure. We study the amount of information necessary to specify the protein structure, providing an estimate that keeps into account the thermodynamic properties of protein folding. We thus show that the information remaining in the protein sequence after encoding for its structure (the 'information gap') is very close to what needed to encode for its function and interactions. Then, by predicting the information gap directly from the protein sequence, we show that it may be possible to use these insights from information theory to discriminate between ordered and disordered proteins, to identify unknown functions, and to optimize artificially-designed protein sequences.

An implementation of the maximum-caliber principle by replica-averaged time-resolved restrained simulations.

Inferential methods can be used to integrate experimental informations and molecular simulations. The maximum entropy principle provides a framework for using equilibrium experimental data, and it has been shown that replica-averaged simulations, restrained using a static potential, are a practical and powerful implementation of such a principle. Here we show that replica-averaged simulations restrained using a time-dependent potential are equivalent to the principle of maximum caliber, the dynamic version of the principle of maximum entropy, and thus may allow us to integrate time-resolved data in molecular dynamics simulations. We provide an analytical proof of the equivalence as well as a computational validation making use of simple models and synthetic data. Some limitations and possible solutions are also discussed.

A Combined NMR-Computational Study of the Interaction between Influenza Virus Hemagglutinin and Sialic Derivatives from Human and Avian Receptors on the Surface of Transfected Cells.

The development of small-molecule inhibitors of influenza virus Hemagglutinin could be relevant to the opposition of the diffusion of new pandemic viruses. In this work, we made use of Nuclear Magnetic Resonance (NMR) spectroscopy to study the interaction between two derivatives of sialic acid, Neu5Ac-α-(2,6)-Gal-β-(1⁻4)-GlcNAc and Neu5Ac-α-(2,3)-Gal-β-(1⁻4)-GlcNAc, and hemagglutinin directly expressed on the surface of recombinant human cells. We analyzed the interaction of these trisaccharides with 293T cells transfected with the H5 and H1 variants of hemagglutinin, which thus retain their native trimeric conformation in such a realistic environment. By exploiting the magnetization transfer between the protein and the ligand, we obtained evidence of the binding event, and identified the epitope. We analyzed the conformational features of the glycans with an approach combining NMR spectroscopy and data-driven molecular dynamics simulations, thus obtaining useful information for an efficient drug design.