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.

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.

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.

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.

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.

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.

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.

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.

Ionic current inversion in pressure-driven polymer translocation through nanopores.

We predict streaming current inversion with multivalent counterions in hydrodynamically driven polymer translocation events from a correlation-corrected charge transport theory including charge fluctuations around mean-field electrostatics. In the presence of multivalent counterions, electrostatic many-body effects result in the reversal of the DNA charge. The attraction of anions to the charge-inverted DNA molecule reverses the sign of the ionic current through the pore. Our theory allows for a comprehensive understanding of the complex features of the resulting streaming currents. The underlying mechanism is an efficient way to detect DNA charge reversal in pressure-driven translocation experiments with multivalent cations.

Influence of slip on the Rayleigh-Plateau rim instability in dewetting viscous films.

A dewetting viscous film develops a characteristic fluid rim at its receding edge due to mass conservation. In the course of the dewetting process, the rim becomes unstable via an instability of Rayleigh-Plateau type. An important difference exists between this classic instability of a liquid column and the rim instability in a thin film as the growth of the rim is continuously fueled by the receding film. We explain how the development and macroscopic morphology of the rim instability are controlled by the slip of the film on the substrate. A single thin-film model captures quantitatively the characteristics of the complete evolution of the rim observed in the experiments.

Dipolar correlations in structured solvents under nanoconfinement.

We study electrostatic correlations in structured solvents confined to nanoscale systems. We derive variational equations of Netz-Orland type for a model liquid composed of finite size dipoles. These equations are solved for both dilute solvents and solvents at physiological concentrations in a slit nanopore geometry. Correlation effects are of major importance for the dielectric reduction and anisotropy of the solvent resulting from dipole image interactions and also lead to a reduction of van der Waals attractions between low dielectric bodies. Finally, by comparison with other recently developed self-consistent theories and experiments, we scrutinize the effect of solvent-membrane interactions on the differential capacitance of the charged liquid in contact with low dielectric substrates. The interfacial solvent depletion driven by solvent-image interactions plays the major role in the observed low values of the experimental capacitance data, while non-locality associated with the extended charge structure of solvent molecules only brings a minor contribution.

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.

Structure and mechanical characterization of DNA i-motif nanowires by molecular dynamics simulation.

We studied the structure and mechanical properties of DNA i-motif nanowires by means of molecular dynamics computer simulations. We built up to 230 nm-long nanowires, based on a repeated TC5 sequence from crystallographic data, fully relaxed and equilibrated in water. The unusual C⋅C(+) stacked structure, formed by four ssDNA strands arranged in an intercalated tetramer, is here fully characterized both statically and dynamically. By applying stretching, compression, and bending deformations with the steered molecular dynamics and umbrella sampling methods, we extract the apparent Young's and bending moduli of the nanowire, as well as estimates for the tensile strength and persistence length. According to our results, the i-motif nanowire shares similarities with structural proteins, as far as its tensile stiffness, but is closer to nucleic acids and flexible proteins, as far as its bending rigidity is concerned. Furthermore, thanks to its very thin cross section, the apparent tensile toughness is close to that of a metal. Besides their yet to be clarified biological significance, i-motif nanowires may qualify as interesting candidates for nanotechnology templates, due to such outstanding mechanical properties.

A dynamical model of oocyte maturation unveils precisely orchestrated meiotic decisions.

Maturation of vertebrate oocytes into haploid gametes relies on two consecutive meioses without intervening DNA replication. The temporal sequence of cellular transitions driving eggs from G2 arrest to meiosis I (MI) and then to meiosis II (MII) is controlled by the interplay between cyclin-dependent and mitogen-activated protein kinases. In this paper, we propose a dynamical model of the molecular network that orchestrates maturation of Xenopus laevis oocytes. Our model reproduces the core features of maturation progression, including the characteristic non-monotonous time course of cyclin-Cdks, and unveils the network design principles underlying a precise sequence of meiotic decisions, as captured by bifurcation and sensitivity analyses. Firstly, a coherent and sharp meiotic resumption is triggered by the concerted action of positive feedback loops post-translationally activating cyclin-Cdks. Secondly, meiotic transition is driven by the dynamic antagonism between positive and negative feedback loops controlling cyclin turnover. Our findings reveal a highly modular network in which the coordination of distinct regulatory schemes ensures both reliable and flexible cell-cycle decisions.

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.

Kinetic control of nucleosome displacement by ISWI/ACF chromatin remodelers.

Chromatin structure is dynamically organized by chromatin remodelers, motor protein complexes which move and remove nucleosomes. The regulation of remodeler action has recently been proposed to underlie a kinetic proofreading scheme which combines the recognition of histone-tail states and the ATP-dependent loosening of DNA around nucleosomes. Members of the ISWI-family of remodelers additionally recognize linker length between nucleosomes. Here, we show that the additional proofreading step involving linker length alone is sufficient to promote the formation of regular arrays of nucleosomes. ATP-dependent remodeling by bidirectional motors is shown to reinforce positioning as compared to statistical positioning.

Signal propagation of the MAPK cascade in Xenopus oocytes: role of bistability and ultrasensitivity for a mixed problem.

The MAPK signaling cascade is nowadays understood as a network module highly conserved across species. Its main function is to transfer a signal arriving at the plasma membrane to the cellular interior. Current understanding of 'how' this is achieved involves the notions of ultrasensitivity and bistability which relate to the nonlinear dynamics of the biochemical network, ignoring spatial aspects. Much less, indeed, is so far known about the propagation of the signal through the cytoplasm. In this work we formulate, starting from a Michaelis-Menten model for the MAPK cascade in Xenopus oocytes, a reaction-diffusion model of the cascade. We study this model in one space dimension. Basing ourselves on previous general results on reaction diffusion models, we particularly study for our model the conditions for signal propagation. We show that the existence of a propagating front depends sensitively on the initial and boundary conditions at the plasma membrane. Possible biological consequences of this finding are discussed.

Kinetic proofreading in chromatin remodeling: the case of ISWI/ACF.

For activation or repression of genes in eukaryotic organisms, the chromatin structure has to be adapted. This action is performed at least in part by dedicated motor proteins, the chromatin remodeling complexes. Recently, investigators have shown some interest in explaining how specific nucleosomes are targeted for chromatin remodeling. For this purpose, two kinetic proofreading scenarios for gene activation and repression have been put forward. We reanalyze both scenarios and show their common points and differences. Further, we propose that in gene repression by ISWI/ACF remodelers, which involves the generation of regular nucleosomal arrays, an additional proofreading step may be active.