Chromatin structure from high resolution microscopy: Scaling laws and microphase separation.

Recent advances in experimental fluorescence microscopy allow high accuracy determination (resolution of 50 nm) of the three-dimensional physical location of multiple (up to ∼10^{2}) tagged regions of the chromosome. We investigate publicly available microscopy data for two loci of the human Chr21 obtained from multiplexed fluorescence in situ hybridization (FISH) methods for different cell lines and treatments. Inspired by polymer physics models, our analysis centers around distance distributions between different tags with the aim being to unravel the chromatin conformational arrangements. We show that for any specific genomic site, there are (at least) two different conformational arrangements of chromatin, implying coexisting distinct topologies which we refer to as phase α and phase ß. These two phases show different scaling behaviors: the former is consistent with a crumpled globule, while the latter indicates a confined, but more extended conformation, such as a looped domain. The identification of these distinct phases sheds light on the coexistence of multiple chromatin topologies and provides insights into the effects of cellular context and/or treatments on chromatin structure.

Influence of the Quantum Capacitance on Electrolyte Conductivity through Carbon Nanotubes.

In recent experiments, unprecedentedly large values for the conductivity of electrolytes through carbon nanotubes (CNTs) have been measured, possibly owing to flow slip and a high pore surface charge density whose origin remains debated. Here, we model the coupling between the CNT quantum capacitance and the classical electrolyte-filled pore one and study how electrolyte transport is modulated when a gate voltage is applied to the CNT. Our work shows that under certain conditions the quantum capacitance is lower than the pore one due to the finite quasi-1D CNT electronic density of states and therefore controls the CNT surface charge density that dictates the confined electrolyte conductivity. The dependence of the computed surface charge and conductivity on reservoir salt concentration and gate voltage is thus intimately related to the electronic properties of the CNT. This approach provides key insight into why metallic CNTs have larger experimentally measured conductivities than semiconducting ones.

Impact of Single-Walled Carbon Nanotube Functionalization on Ion and Water Molecule Transport at the Nanoscale.

Nanofluidics has a very promising future owing to its numerous applications in many domains. It remains, however, very difficult to understand the basic physico-chemical principles that control the behavior of solvents confined in nanometric channels. Here, water and ion transport in carbon nanotubes is investigated using classical force field molecular dynamics simulations. By combining one single walled carbon nanotube (uniformly charged or not) with two perforated graphene sheets, we mimic single nanopore devices similar to experimental ones. The graphitic edges delimit two reservoirs of water and ions in the simulation cell from which a voltage is imposed through the application of an external electric field. By analyzing the evolution of the electrolyte conductivity, the role of the carbon nanotube geometric parameters (radius and chirality) and of the functionalization of the carbon nanotube entrances with OH or COO- groups is investigated for different concentrations of group functions.

Physical modeling of ribosomes along messenger RNA: Estimating kinetic parameters from ribosome profiling experiments using a ballistic model.

Gene expression is the synthesis of proteins from the information encoded on DNA. One of the two main steps of gene expression is the translation of messenger RNA (mRNA) into polypeptide sequences of amino acids. Here, by taking into account mRNA degradation, we model the motion of ribosomes along mRNA with a ballistic model where particles advance along a filament without excluded volume interactions. Unidirectional models of transport have previously been used to fit the average density of ribosomes obtained by the experimental ribo-sequencing (Ribo-seq) technique in order to obtain the kinetic rates. The degradation rate is not, however, accounted for and experimental data from different experiments are needed to have enough parameters for the fit. Here, we propose an entirely novel experimental setup and theoretical framework consisting in splitting the mRNAs into categories depending on the number of ribosomes from one to four. We solve analytically the ballistic model for a fixed number of ribosomes per mRNA, study the different regimes of degradation, and propose a criterion for the quality of the inverse fit. The proposed method provides a high sensitivity to the mRNA degradation rate. The additional equations coming from using the monosome (single ribosome) and polysome (arbitrary number) ribo-seq profiles enable us to determine all the kinetic rates in terms of the experimentally accessible mRNA degradation rate.

Relaxation time asymmetry in stator dynamics of the bacterial flagellar motor.

The bacterial flagellar motor is the membrane-embedded rotary motor, which turns the flagellum that provides thrust to many bacteria. This large multimeric complex, composed of a few dozen constituent proteins, is a hallmark of dynamic subunit exchange. The stator units are inner-membrane ion channels that dynamically bind to the peptidoglycan at the rotor periphery and apply torque. Their dynamic exchange is a function of the viscous load on the flagellum, allowing the bacterium to adapt to its local environment, although the molecular mechanisms of mechanosensitivity remain unknown. Here, by actively perturbing the steady-state stator stoichiometry of individual motors, we reveal a stoichiometry-dependent asymmetry in stator remodeling kinetics. We interrogate the potential effect of next-neighbor interactions and local stator unit depletion and find that neither can explain the observed asymmetry. We then simulate and fit two mechanistically diverse models that recapitulate the asymmetry, finding assembly dynamics to be particularly well described by a two-state catch-bond mechanism.

Competition between Born solvation, dielectric exclusion, and Coulomb attraction in spherical nanopores.

The recent measurement of a very low dielectric constant, ε, of water confined in nanometric slit pores leads us to reconsider the physical basis of ion partitioning into nanopores. For confined ions in chemical equilibrium with a bulk of dielectric constant ε_{b}>ε, three physical mechanisms, at the origin of ion exclusion in nanopores, are expected to be modified due to this dielectric mismatch: dielectric exclusion at the water-pore interface (with membrane dielectric constant, ε_{m}<ε), the solvation energy related to the difference in Debye-Hückel screening parameters in the pore, κ, and in the bulk κ_{b}, and the classical Born solvation self-energy proportional to ε^{-1}-ε_{b}^{-1}. Our goal is to clarify the interplay between these three mechanisms and investigate the role played by the Born contribution in ionic liquid-vapor (LV) phase separation in confined geometries. We first compute analytically the potential of mean force (PMF) of an ion of radius R_{i} located at the center of a nanometric spherical pore of radius R. Computing the variational grand potential for a solution of confined ions, we then deduce the partition coefficients of ions in the pore versus R and the bulk electrolyte concentration ρ_{b}. We show how the ionic LV transition, directly induced by the abrupt change of the dielectric contribution of the PMF with κ, is favored by the Born self-energy and explore the decrease of the concentration in the pore with ε both in the vapor and liquid states. Phase diagrams are established for various parameter values and we show that a signature of this phase transition can be detected by monitoring the total osmotic pressure as a function of R. For charged nanopores, these exclusion effects compete with the electrostatic attraction that imposes the entry of counterions into the pore to enforce electroneutrality. This study will therefore help in deciphering the respective roles of the Born self-energy and dielectric mismatch in experiments and simulations of ionic transport through nanopores.

Supercoiled DNA and non-equilibrium formation of protein complexes: A quantitative model of the nucleoprotein ParBS partition complex.

ParABS, the most widespread bacterial DNA segregation system, is composed of a centromeric sequence, parS, and two proteins, the ParA ATPase and the ParB DNA binding proteins. Hundreds of ParB proteins assemble dynamically to form nucleoprotein parS-anchored complexes that serve as substrates for ParA molecules to catalyze positioning and segregation events. The exact nature of this ParBS complex has remained elusive, what we address here by revisiting the Stochastic Binding model (SBM) introduced to explain the non-specific binding profile of ParB in the vicinity of parS. In the SBM, DNA loops stochastically bring loci inside a sharp cluster of ParB. However, previous SBM versions did not include the negative supercoiling of bacterial DNA, leading to use unphysically small DNA persistences to explain the ParB binding profiles. In addition, recent super-resolution microscopy experiments have revealed a ParB cluster that is significantly smaller than previous estimations and suggest that it results from a liquid-liquid like phase separation. Here, by simulating the folding of long (≥ 30 kb) supercoiled DNA molecules calibrated with realistic DNA parameters and by considering different possibilities for the physics of the ParB cluster assembly, we show that the SBM can quantitatively explain the ChIP-seq ParB binding profiles without any fitting parameter, aside from the supercoiling density of DNA, which, remarkably, is in accord with independent measurements. We also predict that ParB assembly results from a non-equilibrium, stationary balance between an influx of produced proteins and an outflux of excess proteins, i.e., ParB clusters behave like liquid-like protein condensates with unconventional "leaky" boundaries.

Physical Modeling of a Sliding Clamp Mechanism for the Spreading of ParB at Short Genomic Distance from Bacterial Centromere Sites.

Bacterial ParB partitioning proteins involved in chromosomes and low-copy-number plasmid segregation are cytosine triphosphate (CTP)-dependent molecular switches. CTP-binding converts ParB dimers to DNA clamps, allowing unidimensional diffusion along the DNA. This sliding property has been proposed to explain the ParB spreading over large distances from parS centromere sites where ParB is specifically loaded. We modeled such a "clamping and sliding" mechanism as a typical reaction-diffusion system, compared it to the F plasmid ParB DNA binding pattern, and found that it can account neither for the long range of ParB binding to DNA nor for the rapid assembly kinetics observed in vivo after parS duplication. Also, it predicts a strong effect on the F plasmid ParB binding pattern from the presence of a roadblock that is not observed in ChIP-sequencing (ChIP-seq). We conclude that although "clamping and sliding" can occur at short distances from parS, another mechanism must apply for ParB recruitment at larger genomic distances.

ATP-Driven Separation of Liquid Phase Condensates in Bacteria.

Liquid-liquid phase-separated (LLPS) states are key to compartmentalizing components in the absence of membranes; however, it is unclear whether LLPS condensates are actively and specifically organized in the subcellular space and by which mechanisms. Here, we address this question by focusing on the ParABS DNA segregation system, composed of a centromeric-like sequence (parS), a DNA-binding protein (ParB), and a motor (ParA). We show that parS and ParB associate to form nanometer-sized, round condensates. ParB molecules diffuse rapidly within the nucleoid volume but display confined motions when trapped inside ParB condensates. Single ParB molecules are able to rapidly diffuse between different condensates, and nucleation is strongly favored by parS. Notably, the ParA motor is required to prevent the fusion of ParB condensates. These results describe a novel active mechanism that splits, segregates, and localizes non-canonical LLPS condensates in the subcellular space.

A conserved mechanism drives partition complex assembly on bacterial chromosomes and plasmids.

Chromosome and plasmid segregation in bacteria are mostly driven by ParABS systems. These DNA partitioning machineries rely on large nucleoprotein complexes assembled on centromere sites (parS). However, the mechanism of how a few parS-bound ParB proteins nucleate the formation of highly concentrated ParB clusters remains unclear despite several proposed physico-mathematical models. We discriminated between these different models by varying some key parameters in vivo using the F plasmid partition system. We found that "Nucleation & caging" is the only coherent model recapitulating in vivo data. We also showed that the stochastic self-assembly of partition complexes (i) is a robust mechanism, (ii) does not directly involve ParA ATPase, (iii) results in a dynamic structure of discrete size independent of ParB concentration, and (iv) is not perturbed by active transcription but is by protein complexes. We refined the "Nucleation & caging" model and successfully applied it to the chromosomally encoded Par system of Vibrio cholerae, indicating that this stochastic self-assembly mechanism is widely conserved from plasmids to chromosomes.

Role of charge regulation and flow slip in the ionic conductance of nanopores: An analytical approach.

The number of precise conductance measurements in nanopores is quickly growing. To clarify the dominant mechanisms at play and facilitate the characterization of such systems for which there is still no clear consensus, we propose an analytical approach to the ionic conductance in nanopores that takes into account (i) electro-osmotic effects, (ii) flow slip at the pore surface for hydrophobic nanopores, (iii) a component of the surface charge density that is modulated by the reservoir pH and salt concentration c_{s} using a simple charge regulation model, and (iv) a fixed surface charge density that is unaffected by pH and c_{s}. Limiting cases are explored for various ranges of salt concentration and our formula is used to fit conductance experiments found in the literature for carbon nanotubes. This approach permits us to catalog the different possible transport regimes and propose an explanation for the wide variety of currently known experimental behavior for the conductance versus c_{s}.

Voltage-activated transport of ions through single-walled carbon nanotubes.

Ionic transport through single-walled carbon nanotubes (SWCNTs) is promising for many applications but remains both experimentally challenging and highly debated. Here we report ionic current measurements through microfluidic devices containing one or several SWCNTs of diameter of 1.2 to 2 nm unexpectedly showing a linear or a voltage-activated I-V dependence. Transition from an activated to a linear behavior, and stochastic fluctuations between different current levels were notably observed. For linear devices, the high conductance confirmed with different chloride salts indicates that the nanotube/water interface exhibits both a high surface charge density and flow slippage, in agreement with previous reports. In addition, the sublinear dependence of the conductance on the salt concentration points toward a charge-regulation mechanism. Theoretical modelling and computer simulations show that the voltage-activated behavior can be accounted for by the presence of local energy barriers along or at the ends of the nanotube. Raman spectroscopy reveals strain fluctuations along the tubes induced by the polymer matrix but displays insufficient doping or variations of doping to account for the apparent surface charge density and energy barriers revealed by ion transport measurements. Finally, experimental evidence points toward environment-sensitive chemical moieties at the nanotube mouths as being responsible for the energy barriers causing the activated transport of ions through SWCNTs within this diameter range.

A variational approach to the liquid-vapor phase transition for hardcore ions in the bulk and in nanopores.

We employ a field-theoretical variational approach to study the behavior of ionic solutions in the grand canonical ensemble. To describe properly the hardcore interactions between ions, we use a cutoff in Fourier space for the electrostatic contribution of the grand potential and the Carnahan-Starling equation of state with a modified chemical potential for the pressure one. We first calibrate our method by comparing its predictions at room temperature with Monte Carlo results for excess chemical potential and energy. We then validate our approach in the bulk phase by describing the classical "ionic liquid-vapor" phase transition induced by ionic correlations at low temperature, before applying it to electrolytes at room temperature confined to nanopores embedded in a low dielectric medium and coupled to an external reservoir of ions. The ionic concentration in the nanopore is then correctly described from very low bulk concentrations, where dielectric exclusion shifts the transition up to room temperature for sufficiently tight nanopores, to high concentrations where hardcore interactions dominate which, as expected, modify only slightly this ionic "capillary evaporation."

Ionic transport through sub-10 nm diameter hydrophobic high-aspect ratio nanopores: experiment, theory and simulation.

Fundamental understanding of ionic transport at the nanoscale is essential for developing biosensors based on nanopore technology and new generation high-performance nanofiltration membranes for separation and purification applications. We study here ionic transport through single putatively neutral hydrophobic nanopores with high aspect ratio (of length L = 6 µm with diameters ranging from 1 to 10 nm) and with a well controlled cylindrical geometry. We develop a detailed hybrid mesoscopic theoretical approach for the electrolyte conductivity inside nanopores, which considers explicitly ion advection by electro-osmotic flow and possible flow slip at the pore surface. By fitting the experimental conductance data we show that for nanopore diameters greater than 4 nm a constant weak surface charge density of about 10(-2) C m(-2) needs to be incorporated in the model to account for conductance plateaus of a few pico-siemens at low salt concentrations. For tighter nanopores, our analysis leads to a higher surface charge density, which can be attributed to a modification of ion solvation structure close to the pore surface, as observed in the molecular dynamics simulations we performed.

Slow closure of denaturation bubbles in DNA: twist matters.

The closure of long equilibrated denaturation bubbles in DNA is studied using Brownian dynamics simulations. A minimal mesoscopic model is used where the double helix is made of two interacting bead-spring freely rotating strands, with a nonzero torsional modulus in the duplex state, κ(φ)=200 to 300k(B)T. For DNAs of lengths N=40 to 100 base pairs (bps) with a large initial bubble in their middle, long closure times of 0.1 to 100µs are found. The bubble starts winding from both ends until it reaches a ≈10 bp metastable state due to the large elastic energy stored in the bubble. The final closure is limited by three competing mechanisms depending on κ(φ) and N: arms diffusion until their alignment, bubble diffusion along the DNA until one end is reached, or local Kramers process (crossing over a torsional energy barrier). For clamped ends or long DNAs, the closure occurs via this last temperature-activated mechanism, yielding a good quantitative agreement with the experiments.

The vapor-liquid interface potential of (multi)polar fluids and its influence on ion solvation.

The interface between the vapor and liquid phase of quadrupolar-dipolar fluids is the seat of an electric interfacial potential whose influence on ion solvation and distribution is not yet fully understood. To obtain further microscopic insight into water specificity we first present extensive classical molecular dynamics simulations of a series of model liquids with variable molecular quadrupole moments that interpolates between SPC/E water and a purely dipolar liquid. We then pinpoint the essential role played by the competing multipolar contributions to the vapor-liquid and the solute-liquid interface potentials in determining an important ion-specific direct electrostatic contribution to the ionic solvation free energy for SPC/E water-dominated by the quadrupolar and dipolar parts-beyond the dominant polarization one. Our results show that the influence of the vapor-liquid interfacial potential on ion solvation is strongly reduced due to the strong partial cancellation brought about by the competing solute-liquid interface potential.

Mesoscopic models for DNA stretching under force: New results and comparison with experiments.

Single-molecule experiments on double-stranded B-DNA stretching have revealed one or two structural transitions, when increasing the external force. They are characterized by a sudden increase of DNA contour length and a decrease of the bending rigidity. The nature and the critical forces of these transitions depend on DNA base sequence, loading rate, salt conditions and temperature. It has been proposed that the first transition, at forces of 60-80 pN, is a transition from B to S-DNA, viewed as a stretched duplex DNA, while the second one, at stronger forces, is a strand peeling resulting in single-stranded DNAs (ssDNA), similar to thermal denaturation. But due to experimental conditions these two transitions can overlap, for instance for poly(dA-dT). In an attempt to propose a coherent picture compatible with this variety of experimental observations, we derive an analytical formula using a coupled discrete worm-like chain-Ising model. Our model takes into account bending rigidity, discreteness of the chain, linear and non-linear (for ssDNA) bond stretching. In the limit of zero force, this model simplifies into a coupled model already developed by us for studying thermal DNA melting, establishing a connection with previous fitting parameter values for denaturation profiles. Our results are summarized as follows: i) ssDNA is fitted, using an analytical formula, over a nano-Newton range with only three free parameters, the contour length, the bending modulus and the monomer size; ii) a surprisingly good fit on this force range is possible only by choosing a monomer size of 0.2 nm, almost 4 times smaller than the ssDNA nucleobase length; iii) mesoscopic models are not able to fit B to ssDNA (or S to ss) transitions; iv) an analytical formula for fitting B to S transitions is derived in the strong force approximation and for long DNAs, which is in excellent agreement with exact transfer matrix calculations; v) this formula fits perfectly well poly(dG-dC) and λ-DNA force-extension curves with consistent parameter values; vi) a coherent picture, where S to ssDNA transitions are much more sensitive to base-pair sequence than the B to S one, emerges. This relatively simple model might allow one to further study quantitatively the influence of salt concentration and base-pairing interactions on DNA force-induced transitions.

Ionic exclusion phase transition in neutral and weakly charged cylindrical nanopores.

A field theoretic variational approach is introduced to study ion penetration into water-filled cylindrical nanopores in equilibrium with a bulk reservoir [S. Buyukdagli, M. Manghi, and J. Palmeri, Phys. Rev. Lett. 105, 158103 (2010)]. It is shown that an ion located in a neutral pore undergoes two opposing mechanisms: (i) a deformation of its surrounding ionic cloud of opposite charge, with respect to the reservoir, which increases the surface tension and tends to exclude ions from the pore, and (ii) an attractive contribution to the ion self-energy due to the increased screening with ion penetration of the repulsive image forces associated with the dielectric jump between the solvent and the pore wall. For pore radii around 1 nm and bulk concentrations lower than 0.2 mol/l, this mechanism leads to a first-order phase transition, similar to capillary "evaporation," from an ionic-penetration state to an ionic-exclusion state. The discontinuous phase transition exists within the biological concentration range (∼0.15 mol/l) for small enough membrane dielectric constants (ε(m) < 5). In the case of a weakly charged pore, counterion penetration exhibits a nonmonotonic behavior and is characterized by two regimes: at low reservoir concentrations or small pore radii, coions are excluded and counterions enter the pore to enforce electroneutrality; dielectric repulsion (image forces) remain strong and the counterion partition coefficient decreases with increasing reservoir concentration up to a characteristic value. For larger reservoir concentrations, image forces are screened and the partition coefficient of counterions increases with the reservoir concentration, as in the neutral pore case. Large surface charge densities (>2 × 10(-3) e/nm(2)) suppress the discontinuous transition by reducing the energy barrier for ion penetration and shifting the critical point toward very small pore sizes and reservoir concentrations. Our variational method is also compared to a previous self-consistent approach and yields important quantitative corrections. The role of the curvature of dielectric interfaces is highlighted by comparing ionic penetration into slit and cylindrical pores. Finally, a charge regulation model is introduced in order to explain the key effect of pH on ionic exclusion and explain the origin of observed time-dependent nanopore electric conductivity fluctuations and their correlation with those of the pore surface charge.

Variational approach for electrolyte solutions: from dielectric interfaces to charged nanopores.

A variational theory is developed to study electrolyte solutions, composed of interacting pointlike ions in a solvent, in the presence of dielectric discontinuities and charges at the boundaries. Three important and nonlinear electrostatic effects induced by these interfaces are taken into account: surface charge induced electrostatic field, solvation energies due to the ionic cloud, and image-charge repulsion. Our variational equations thus go beyond the mean-field theory, or weak coupling limit, where thermal fluctuations overcome electrostatic correlations, and allows one to reach the opposite strong coupling limit, where electrostatic interactions induced by interfaces dominate. The influence of salt concentration, ion valency, dielectric jumps, and surface charge is studied in two geometries. (i) A single neutral dielectric interface (e.g., air-water or electrolyte-membrane) with an asymmetric electrolyte. A charge separation and thus an electrostatic field get established due to the different image-charge repulsions for coions and counterions. Both charge distributions and surface tension are computed and compared to previous approximate calculations. For symmetric electrolyte solutions close to a charged surface, two zones are characterized. In the first one, in contact with the surface and with size proportional to the logarithm of the coupling parameter, strong image forces and strong coupling impose a total ion exclusion, while in the second zone the mean-field approach applies. (ii) A symmetric electrolyte confined between two dielectric interfaces as a simple model of ion rejection from nanopores in membranes. The competition between image-charge repulsion and attraction of counterions by the membrane charge is studied. For small surface charge, the counterion partition coefficient decreases with increasing pore size up to a critical pore size, contrary to neutral membranes. For larger pore sizes, the whole system behaves like a neutral pore. For strong coupling and small pore size, coion exclusion is total and the counterion partition coefficient is solely determined by global electroneutrality. A quantitative comparison is made with a previous approach, where image and surface charge effects were smeared out in the pore. It is shown that the variational method allows one to go beyond the constant Donnan potential approximation, with deviations stronger at high ion concentrations or small pore sizes. The prediction of the variational method is also compared with MC simulations and good agreement is observed.

Ionic capillary evaporation in weakly charged nanopores.

Using a variational field theory, we show that an electrolyte confined to a neutral cylindrical nanopore traversing a low dielectric membrane exhibits a first-order ionic liquid-vapor pseudo-phase-transition from an ionic-penetration "liquid" phase to an ionic-exclusion "vapor" phase, controlled by nanopore-modified ionic correlations and dielectric repulsion. For weakly charged nanopores, this pseudotransition survives and may shed light on the mechanism behind the rapid switching of nanopore conductivity observed in experiments.