Chromatin remodelers: a concise introduction for biophysicists.

Chromatin remodelers are molecular motors that act on nucleosomes: they move them along DNA or (dis-)assemble them. Despite the fact that they perform essential regulatory functions in cells-their deregulation can contribute to the development of cancers and lead to cell death-chromatin remodelers have only received meager attention in the biophysics community so far. In this short text, we attempt to present the key features of this interesting class of enzymes obtained with different experimental and theoretical methods, thereby providing a concise introduction for biophysicists to further stimulate interest in their properties.

Short-time expansion of one-dimensional Fokker-Planck equations with heterogeneous diffusion.

We formulate a short-time expansion for one-dimensional Fokker-Planck equations with spatially dependent diffusion coefficients, derived from stochastic processes with Gaussian white noise, for general values of the discretization parameter 0≤α≤1 of the stochastic integral. The kernel of the Fokker-Planck equation (the propagator) can be expressed as a product of a singular and a regular term. While the singular term can be given in closed form, the regular term can be computed from a Taylor expansion whose coefficients obey simple ordinary differential equations. We illustrate the application of our approach with examples taken from statistical physics and biophysics. Furthermore, we show how our formalism allows us to define a class of stochastic equations which can be treated exactly. The convergence of the expansion cannot be guaranteed independently from the discretization parameter α.

Counterion-controlled phase equilibria in a charge-regulated polymer solution.

We study phase equilibria in a minimal model of charge-regulated polymer solutions. Our model consists of a single polymer species whose charge state arises from protonation-deprotonation processes in the presence of a dissolved acid, whose anions serve as screening counterions. We explicitly account for variability in the polymers' charge states. Homogeneous equilibria in this model system are characterised by the total concentration of polymers, the concentration of counter-ions and the charge distributions of polymers which can be computed with the help of analytical approximations. We use these analytical results to characterise how parameter values and solution acidity influence equilibrium charge distributions and identify for which regimes uni-modal and multi-modal charge distributions arise. We then study the interplay between charge regulation, solution acidity and phase separation. We find that charge regulation has a significant impact on polymer solubility and allows for non-linear responses to the solution acidity: Re-entrant phase behaviour is possible in response to increasing solution acidity. Moreover, we show that phase separation can yield to the coexistence of local environments characterised by different charge distributions.

Nucleosome Array Deformation in Chromatin is Sustained by Bending, Twisting and Kinking of Linker DNA.

Chromatin in the nucleus undergoes mechanical stresses from different sources during the various stages of cell life. Here a trinucleosome array is used as the minimal model to study the mechanical response to applied stress at the molecular level. By using large-scale, all-atom steered-molecular dynamics simulations, we show that the largest part of mechanical stress in compression is accommodated by the DNA linkers joining pairs of nucleosomes, which store the elastic energy accumulated by the applied force. Different mechanical instabilities (Euler bending, Brazier kinking, twist-bending) can deform the DNA canonical structure, as a function of the increasing force load. An important role of the histone tails in assisting the DNA deformation is highlighted. The overall response of the smallest chromatin fragment to compressive stress leaves the nucleosome assembly with a substantial plastic deformation and localised defects, which can have a potential impact on DNA transcription, downstream signaling pathways, the regulation of gene expression, and DNA repair.

Infinite ergodicity in generalized geometric Brownian motions with nonlinear drift.

Geometric Brownian motion is an exemplary stochastic processes obeying multiplicative noise, with widespread applications in several fields, e.g., in finance, in physics, and biology. The definition of the process depends crucially on the interpretation of the stochastic integrals which involves the discretization parameter α with 0≤α≤1, giving rise to the well-known special cases α=0 (Itô), α=1/2 (Fisk-Stratonovich), and α=1 (Hänggi-Klimontovich or anti-Itô). In this paper we study the asymptotic limits of the probability distribution functions of geometric Brownian motion and some related generalizations. We establish the conditions for the existence of normalizable asymptotic distributions depending on the discretization parameter α. Using the infinite ergodicity approach, recently applied to stochastic processes with multiplicative noise by E. Barkai and collaborators, we show how meaningful asymptotic results can be formulated in a transparent way.

A one-dimensional three-state run-and-tumble model with a 'cell cycle'.

We study a one-dimensional three-state run-and-tumble model motivated by the bacterium Caulobacter crescentus which displays a cell cycle between two non-proliferating mobile phases and a proliferating sedentary phase. Our model implements kinetic transitions between the two mobile and one sedentary states described in terms of their number densities, where mobility is allowed with different running speeds in forward and backward direction. We start by analyzing the stationary states of the system and compute the mean and squared-displacements for the distribution of all cells, as well as for the number density of settled cells. The latter displays a surprising super-ballistic scaling [Formula: see text] at early times. Including repulsive and attractive interactions between the mobile cell populations and the settled cells, we explore the stability of the system and employ numerical methods to study structure formation in the fully nonlinear system. We find traveling waves of bacteria, whose occurrence is quantified in a non-equilibrium state diagram.

Brownian particles driven by spatially periodic noise.

We discuss the dynamics of a Brownian particle under the influence of a spatially periodic noise strength in one dimension using analytical theory and computer simulations. In the absence of a deterministic force, the Langevin equation can be integrated formally exactly. We determine the short- and long-time behaviour of the mean displacement (MD) and mean-squared displacement (MSD). In particular, we find a very slow dynamics for the mean displacement, scaling as [Formula: see text] with time t. Placed under an additional external periodic force near the critical tilt value we compute the stationary current obtained from the corresponding Fokker-Planck equation and identify an essential singularity if the minimum of the noise strength is zero. Finally, in order to further elucidate the effect of the random periodic driving on the diffusion process, we introduce a phase factor in the spatial noise with respect to the external periodic force and identify the value of the phase shift for which the random force exerts its strongest effect on the long-time drift velocity and diffusion coefficient.

DNA Aptamers Block the Receptor Binding Domain at the Spike Protein of SARS-CoV-2.

DNA aptamers are versatile molecular species obtained by the folding of short single-stranded nucleotide sequences, with highly specific recognition capabilities against proteins. Here we test the ability of DNA aptamers to interact with the spike (S-)protein of the SARS-CoV-2 viral capsid. The S-protein, a trimer made up of several subdomains, develops the crucial function of recognizing the ACE2 receptors on the surface of human cells, and subsequent fusioning of the virus membrane with the host cell membrane. In order to achieve this, the S1 domain of one protomer switches between a closed conformation, in which the binding site is inaccessible to the cell receptors, and an open conformation, in which ACE2 can bind, thereby initiating the entry process of the viral genetic material in the host cell. Here we show, by means of state-of-the-art molecular simulations, that small DNA aptamers experimentally identified can recognize the S-protein of SARS-CoV-2, and characterize the details of the binding process. We find that their interaction with different subdomains of the S-protein can effectively block, or at least considerably slow down the opening process of the S1 domain, thereby significantly reducing the probability of virus-cell binding. We provide evidence that, as a consequence, binding of the human ACE2 receptor may be crucially affected under such conditions. Given the facility and low cost of fabrication of specific aptamers, the present findings could open the way to both an innovative viral screening technique with sub-nanomolar sensitivity, and to an effective and low impact curative strategy.

Dipolar Poisson models in a dual view.

In this work, we study the continuum theories of dipolar-Poisson models. Both the standard dipolar-Poisson model and the dipolar-Poisson-Langevin model, which keeps the dipolar density fixed, are non-convex functionals of the scalar electrostatic potential ϕ. Applying the Legendre transform approach introduced by Maggs [Europhys. Lett. 98, 16012 (2012)], the dual functionals of these models are derived and are given by convex vector-field functionals of the dielectric displacement D and the polarization field P. We compare the convex functionals in P-space to the non-convex functionals in electric field E-space and apply them to the classic problem of the solvation of point-like ions. Since the dipolar-Poisson model does not properly describe polarization saturation, we argue that only the dipolar-Poisson-Langevin functional can be used to provide a nonlinear generalization of the harmonic polarization functional used in the theory of Marcus for the electron transfer rate to nonlinear regimes. We show that the model can be quantitatively parameterized by molecular dynamics simulations.

Pioneer transcription factors in chromatin remodeling: The kinetic proofreading view.

Pioneer transcription factors are a recently defined class of transcription factors which can bind directly to nucleosomal DNA; they play a key role in gene activation in certain pathways. Here we quantify their role in the initiation of nucleosome displacement within the kinetic proofreading scenario of chromatin remodeling. The model allows one to perform remodeling efficiency comparisons for scenarios involving different types of transcription factors and remodelers as a function of their binding and unbinding rates and concentrations. Our results demonstrate a way to fine-tune the specificity of processes that modify the chromatin structure in transcriptional initiation.

Methylation-dependent transcriptional regulation of crescentin gene (creS) by GcrA in Caulobacter crescentus.

In Caulobacter crescentus the combined action of chromosome replication and the expression of DNA methyl-transferase CcrM at the end of S-phase maintains a cyclic alternation between a full- to hemi-methylated chromosome. This transition of the chromosomal methylation pattern affects the DNA-binding properties of the transcription factor GcrA that controls the several key cell cycle functions. However, the molecular mechanism by which GcrA and methylation are linked to transcription is not fully elucidated yet. Using a combination of cell biology, genetics, and in vitro analysis, we deciphered how GcrA integrates the methylation pattern of several S-phase expressed genes to their transcriptional output. We demonstrated in vitro that transcription of ctrA from the P1 promoter in its hemi-methylated state is activated by GcrA, while in its fully methylated state GcrA had no effect. Further, GcrA and methylation together influence a peculiar distribution of creS transcripts, encoding for crescentin, the protein responsible for the characteristic shape of Caulobacter cells. This gene is duplicated at the onset of chromosome replication and the two hemi-methylated copies are spatially segregated. Our results indicated that GcrA transcribed only the copy where coding strand is methylated. In vitro transcription assay further substantiated this finding. As several of the cell cycle-regulated genes are also under the influence of methylation and GcrA-dependent transcriptional regulation, this could be a mechanism responsible for maintaining the gene transcription dosage during the S-phase.

Charge regulation radically modifies electrostatics in membrane stacks.

Motivated by biological membrane-containing organelles in plants and photosynthetic bacteria, we study charge regulation in a model membrane stack. Considering (de)protonation as the simplest mechanism of charge equilibration between the membranes and with the bathing environment, we uncover a symmetry-broken charge state in the stack with a quasiperiodic effective charge sequence. In the case of a monovalent bathing salt solution our model predicts complex, inhomogeneous charge equilibria depending on the strength of the (de)protonation reaction, salt concentration, and membrane size. Our results shed light on the basic reorganization mechanism of thylakoid membrane stacks.

Histone mark recognition controls nucleosome translocation via a kinetic proofreading mechanism: Confronting theory and high-throughput experiments.

Chromatin remodelers are multidomain enzymatic motor complexes that displace nucleosomes along DNA and hence "remodel chromatin structure," i.e., they dynamically reorganize nucleosome positions in both gene activation and gene repression. Recently, experimental insights from structural biology methods and remodeling assays have substantially advanced the understanding of these key chromatin components. Here we confront the kinetic proofreading scenario of chromatin remodeling, which proposes a mechanical link between histone residue modifications and the ATP-dependent action of remodelers, with recent experiments. We show that recent high-throughput data on nucleosome libraries assayed with remodelers from the Imitation Switch family are in accord with our earlier predictions of the kinetic proofreading scenario. We make suggestions for experimentally verifiable predictions of the kinetic proofreading scenarios for remodelers from other families.

Multivalent Thiosialosides and Their Synergistic Interaction with Pathogenic Sialidases.

Sialidases (SAs) hydrolyze sialyl residues from glycoconjugates of the eukaryotic cell surface and are virulence factors expressed by pathogenic bacteria, viruses, and parasites. The catalytic domains of SAs are often flanked with carbohydrate-binding module(s) previously shown to bind sialosides and to enhance enzymatic catalytic efficiency. Herein, non-hydrolyzable multivalent thiosialosides were designed as probes and inhibitors of V. cholerae, T. cruzi, and S. pneumoniae (NanA) sialidases. NanA was truncated from the catalytic and lectinic domains (NanA-L and NanA-C) to probe their respective roles upon interacting with sialylated surfaces and the synthetically designed di- and polymeric thiosialosides. The NanA-L domain was shown to fully drive NanA binding, improving affinity for the thiosialylated surface and compounds by more than two orders of magnitude. Importantly, each thiosialoside grafted onto the polymer was also shown to reduce NanA and NanA-C catalytic activity with efficiency that was 3000-fold higher than that of the monovalent thiosialoside reference. These results extend the concept of multivalency for designing potent bacterial and parasitic sialidase inhibitors.

A Novel Integrated Way for Deciphering the Glycan Code for the FimH Lectin.

The fimbrial lectin FimH from uro- and enteropathogenic Escherichia coli binds with nanomolar affinity to oligomannose glycans exposing Manα1,3Man dimannosides at their non-reducing end, but only with micromolar affinities to Manα1,2Man dimannosides. These two dimannoses play a significantly distinct role in infection by E. coli. Manα1,2Man has been described early on as shielding the (Manα1,3Man) glycan that is more relevant to strong bacterial adhesion and invasion. We quantified the binding of the two dimannoses (Manα1,2Man and Manα1,3Man to FimH using ELLSA and isothermal microcalorimetry and calculated probabilities of binding modes using molecular dynamics simulations. Our experimentally and computationally determined binding energies confirm a higher affinity of FimH towards the dimannose Manα1,3Man. Manα1,2Man displays a much lower binding enthalpy combined with a high entropic gain. Most remarkably, our molecular dynamics simulations indicate that Manα1,2Man cannot easily take its major conformer from water into the FimH binding site and that FimH is interacting with two very different conformers of Manα1,2Man that occupy 42% and 28% respectively of conformational space. The finding that Manα1,2Man binding to FimH is unstable agrees with the earlier suggestion that E. coli may use the Manα1,2Man epitope for transient tethering along cell surfaces in order to enhance dispersion of the infection.

The Inclusion of Water Molecules in Residue Interaction Networks Identifies Additional Central Residues.

The relevance of water molecules for the recognition and the interaction of biomolecules is widely appreciated. In this paper we address the role that water molecules associated to protein complexes play for the functional relevance of residues by considering their residue interaction networks (RINs). These are commonly defined on the basis of the amino acid composition of the proteins themselves, disregarding the solvation state of the protein. We determine properties of the RINs of two protein complexes, colicin E2/Im2 and barnase/barstar, with and without associated water molecules, using a previously developed methodology and its associated application RINspector. We find that the inclusion of water molecules in RINs leads to an increase in the number of central residues which adds a novel mechanism to the relevance of water molecules for protein function.

Mechanical evolution of DNA double-strand breaks in the nucleosome.

Double strand breaks (DSB) in the DNA backbone are the most lethal type of defect induced in the cell nucleus by chemical and radiation treatments of cancer. However, little is known about the outcomes of damage in nucleosomal DNA, and on its effects on damage repair. We performed microsecond-long molecular dynamics computer simulations of nucleosomes including a DSB at various sites, to characterize the early stages of the evolution of this DNA lesion. The damaged structures are studied by the essential dynamics of DNA and histones, and compared to the intact nucleosome, thus exposing key features of the interactions. All DSB configurations tend to remain compact, with only the terminal bases interacting with histone proteins. Umbrella sampling calculations show that broken DNA ends at the DSB must overcome a free-energy barrier to detach from the nucleosome core. Finally, by calculating the covariant mechanical stress, we demonstrate that the coupled bending and torsional stress can force the DSB free ends to open up straight, thus making it accessible to damage signalling proteins.

The Latest Twists in Chromatin Remodeling.

In its most restrictive interpretation, the notion of chromatin remodeling refers to the action of chromatin-remodeling enzymes on nucleosomes with the aim of displacing and removing them from the chromatin fiber (the effective polymer formed by a DNA molecule and proteins). This local modification of the fiber structure can have consequences for the initiation and repression of the transcription process, and when the remodeling process spreads along the fiber, it also results in long-range effects essential for fiber condensation. There are three regulatory levels of relevance that can be distinguished for this process: the intrinsic sequence preference of the histone octamer, which rules the positioning of the nucleosome along the DNA, notably in relation to the genetic information coded in DNA; the recognition or selection of nucleosomal substrates by remodeling complexes; and, finally, the motor action on the nucleosome exerted by the chromatin remodeler. Recent work has been able to provide crucial insights at each of these three levels that add new twists to this exciting and unfinished story, which we highlight in this perspective.

Nucleation of twisted and tubular states in chiral ribbons.

Bilayers of chiral molecules can self-assemble into twisted and tubular structures, as was recently shown with chiral molecular constituents such as ssDNA-amphiphiles. I show that the dynamics of the transition between these topologies is driven by a nucleation mechanism that bears a striking formal similarity to that encountered in first-order wetting and dewetting transitions. Exploiting this analogy enables the critical nuclei of the transition to be calculated.