There and back again: bridging meso- and nano-scales to understand lipid vesicle patterning.

We describe a complete methodology to bridge the scales between nanoscale molecular dynamics and (micrometer) mesoscale Monte Carlo simulations in lipid membranes and vesicles undergoing phase separation, in which curving molecular species are furthermore embedded. To go from the molecular to the mesoscale, we notably appeal to physical renormalization arguments enabling us to rigorously infer the mesoscale interaction parameters from its molecular counterpart. We also explain how to deal with the physical timescales at stake at the mesoscale. Simulating the as-obtained mesoscale system enables us to equilibrate the long wavelengths of the vesicles of interest, up to the vesicle size. Conversely, we then backmap from the meso- to the nano-scale, which enables us to equilibrate in turn the short wavelengths down to the molecular length-scales. By applying our approach to the specific situation of patterning a vesicle membrane, we show that macroscopic membranes can thus be equilibrated at all length-scales in achievable computational time offering an original strategy to address the fundamental challenge of timescale in simulations of large bio-membrane systems.

Protein overexpression can induce the elongation of cell membrane nanodomains.

In cell membranes, proteins and lipids are organized into submicrometric nanodomains of varying sizes, shapes, and compositions, performing specific functions. Despite their biological importance, the detailed morphology of these nanodomains remains unknown. Not only can they hardly be observed by conventional microscopy due to their small size, but there is no full consensus on the theoretical models to describe their structuring and their shapes. Here, we use a combination of analytical calculations and Monte Carlo simulations based upon a model coupling membrane composition and shape to show that increasing protein concentration leads to an elongation of membrane nanodomains. The results are corroborated by single-particle tracking measurements on HIV receptors, whose level of expression in the membrane of specifically designed living cells can be tuned. These findings highlight that protein abundance can modulate nanodomain shape and potentially their biological function. Beyond biomembranes, this mesopatterning mechanism is of relevance in several soft-matter systems because it relies on generic physical arguments.

Statistical physics and mesoscopic modeling to interpret tethered particle motion experiments.

Tethered particle motion experiments are versatile single-molecule techniques enabling one to address in vitro the molecular properties of DNA and its interactions with various partners involved in genetic regulations. These techniques provide raw data such as the tracked particle amplitude of movement, from which relevant information about DNA conformations or states must be recovered. Solving this inverse problem appeals to specific theoretical tools that have been designed in the two last decades, together with the data pre-processing procedures that ought to be implemented to avoid biases inherent to these experimental techniques. These statistical tools and models are reviewed in this paper.

Domain formation in bicomponent vesicles induced by composition-curvature coupling.

Lipid vesicles composed of a mixture of two types of lipids are studied by intensive Monte Carlo numerical simulations. The coupling between the local composition and the membrane shape is induced by two different spontaneous curvatures of the components. We explore the various morphologies of these biphasic vesicles coupled to the observed patterns such as nano-domains or labyrinthine mesophases. The effect of the difference in curvatures, the surface tension, and the interaction parameter between components is thoroughly explored. Our numerical results quantitatively agree with the previous analytical results obtained by Gueguen et al. [Eur. Phys. J. E 37, 76 (2014)] in the disordered (high temperature) phase. Numerical simulations allow us to explore the full parameter space, especially close to and below the critical temperature, where analytical results are not accessible. Phase diagrams are constructed and domain morphologies are quantitatively studied by computing the structure factor and the domain size distribution. This mechanism likely explains the existence of nano-domains in cell membranes as observed by super-resolution fluorescence microscopy.

How does temperature impact the conformation of single DNA molecules below melting temperature?

The double stranded DNA molecule undergoes drastic structural changes during biological processes such as transcription during which it opens locally under the action of RNA polymerases. Local spontaneous denaturation could contribute to this mechanism by promoting it. Supporting this idea, different biophysical studies have found an unexpected increase in the flexibility of DNA molecules with various sequences as a function of the temperature, which would be consistent with the formation of a growing number of locally denatured sequences. Here, we take advantage of our capacity to detect subtle changes occurring on DNA by using high throughput tethered particle motion to question the existence of bubbles in double stranded DNA under physiological salt conditions through their conformational impact on DNA molecules ranging from several hundreds to thousands of base pairs. Our results strikingly differ from previously published ones, as we do not detect any unexpected change in DNA flexibility below melting temperature. Instead, we measure a bending modulus that remains stable with temperature as expected for intact double stranded DNA.

Dependence of DNA Persistence Length on Ionic Strength and Ion Type.

Even though the persistence length L_{P} of double-stranded DNA plays a pivotal role in cell biology and nanotechnologies, its dependence on ionic strength I lacks a consensual description. Using a high-throughput single-molecule technique and statistical physics modeling, we measure L_{P} in the presence of monovalent (Li^{+}, Na^{+}, K^{+}) and divalent (Mg^{2+}, Ca^{2+}) metallic and alkyl ammonium ions, over a large range 0.5 mM≤I≤5 M. We show that linear Debye-Hückel-type theories do not describe even part of these data. By contrast, the Netz-Orland and Trizac-Shen formulas, two approximate theories including nonlinear electrostatic effects and the finite DNA radius, fit our data with divalent and monovalent ions, respectively, over the whole I range. Furthermore, the metallic ion type does not influence L_{P}(I), in contrast to alkyl ammonium monovalent ions at high I.

Fluctuation tension and shape transition of vesicles: renormalisation calculations and Monte Carlo simulations.

It has been known for long that the fluctuation surface tension of membranes r, computed from the height fluctuation spectrum, is not equal to the bare surface tension σ, which is introduced in the theory either as a Lagrange multiplier to conserve the total membrane area or as an external constraint. In this work we relate these two surface tensions both analytically and numerically. They are also compared to the Laplace tension γ, and the mechanical frame tension τ. Using the Helfrich model and one-loop renormalisation calculations, we obtain, in addition to the effective bending modulus κeff, a new expression for the effective surface tension σeff = σ - εkBT/(2ap) where kBT is the thermal energy, ap the projected cut-off area, and ε = 3 or 1 according to the allowed configurations that keep either the projected area or the total area constant. Moreover we show that the crumpling transition for an infinite planar membrane occurs for σeff = 0, and also that it coincides with vanishing Laplace and frame tensions. Using extensive Monte Carlo (MC) simulations, triangulated membranes of vesicles made of N = 100-2500 vertices are simulated within the Helfrich theory. As compared to alternative numerical models, no local constraint is applied and the shape is only controlled by the constant volume, the spontaneous curvature and σ. It is shown that the numerical fluctuation surface tension r is equal to σeff both with radial MC moves (ε = 3) and with corrected MC moves locally normal to the fluctuating membrane (ε = 1). For finite vesicles of typical size R, two different regimes are defined: a tension regime for [small sigma, Greek, circumflex]eff = σeffR2/κeff > 0 and a bending one for -1 < [small sigma, Greek, circumflex]eff < 0. A shape transition from a quasi-spherical shape imposed by the large surface energy, to more deformed shapes only controlled by the bending energy, is observed numerically at [small sigma, Greek, circumflex]eff ≃ 0. We propose that the buckling transition, observed for planar supported membranes in the literature, occurs for [small sigma, Greek, circumflex]eff ≃ -1, the associated negative frame tension playing the role of a compressive force. Hence, a precise control of the value of σeff in simulations cannot but enhance our understanding of shape transitions of vesicles and cells.

Probing a label-free local bend in DNA by single molecule tethered particle motion.

Being capable of characterizing DNA local bending is essential to understand thoroughly many biological processes because they involve a local bending of the double helix axis, either intrinsic to the sequence or induced by the binding of proteins. Developing a method to measure DNA bend angles that does not perturb the conformation of the DNA itself or the DNA-protein complex is a challenging task. Here, we propose a joint theory-experiment high-throughput approach to rigorously measure such bend angles using the Tethered Particle Motion (TPM) technique. By carefully modeling the TPM geometry, we propose a simple formula based on a kinked Worm-Like Chain model to extract the bend angle from TPM measurements. Using constructs made of 575 base-pair DNAs with in-phase assemblies of one to seven 6A-tracts, we find that the sequence CA6CGG induces a bend angle of 19° ± 4°. Our method is successfully compared to more theoretically complex or experimentally invasive ones such as cyclization, NMR, FRET or AFM. We further apply our procedure to TPM measurements from the literature and demonstrate that the angles of bends induced by proteins, such as Integration Host Factor (IHF) can be reliably evaluated as well.

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."

DNA denaturation bubbles: free-energy landscape and nucleation/closure rates.

The issue of the nucleation and slow closure mechanisms of non-superhelical stress-induced denaturation bubbles in DNA is tackled using coarse-grained MetaDynamics and Brownian simulations. A minimal mesoscopic model is used where the double helix is made of two interacting bead-spring rotating strands with a prescribed torsional modulus in the duplex state. We demonstrate that timescales for the nucleation (respectively, closure) of an approximately 10 base-pair bubble, in agreement with experiments, are associated with the crossing of a free-energy barrier of 22 kBT (respectively, 13 kBT) at room temperature T. MetaDynamics allows us to reconstruct accurately the free-energy landscape, to show that the free-energy barriers come from the difference in torsional energy between the bubble and duplex states, and thus to highlight the limiting step, a collective twisting, that controls the nucleation/closure mechanism, and to access opening time scales on the millisecond range. Contrary to small breathing bubbles, those more than 4 base-pair bubbles are of biological relevance, for example, when a pre-existing state of denaturation is required by specific DNA-binding proteins.

Mixed lipid bilayers with locally varying spontaneous curvature and bending.

A model of lipid bilayers made of a mixture of two lipids with different average compositions on both leaflets, is developed. A Landau Hamiltonian describing the lipid-lipid interactions on each leaflet, with two lipidic fields ψ 1 and ψ 2, is coupled to a Helfrich one, accounting for the membrane elasticity, via both a local spontaneous curvature, which varies as C 0 + C 1(ψ 1 - ψ 2/2), and a bending modulus equal to κ 0 + κ 1(ψ 1 + ψ 2)/2. This model allows us to define curved patches as membrane domains where the asymmetry in composition, ψ 1 - ψ 2, is large, and thick and stiff patches where ψ 1 + ψ 2 is large. These thick patches are good candidates for being lipidic rafts, as observed in cell membranes, which are composed primarily of saturated lipids forming a liquid-ordered domain and are known to be thick and flat nano-domains. The lipid-lipid structure factors and correlation functions are computed for globally spherical membranes and planar ones and for a whole set of parameters including the surface tension and the coupling in the two leaflet compositions. Phase diagrams are established, within a Gaussian approximation, showing the occurrence of two types of Structure Disordered phases, with correlations between either curved or thick patches, and an Ordered phase, corresponding to the divergence of the structure factor at a finite wave vector. The varying bending modulus plays a central role for curved membranes, where the driving force κ 1 C 0 (2) is balanced by the line tension, to form raft domains of size ranging from 10 to 100 nm. For planar membranes, raft domains emerge via the cross-correlation with curved domains. A global picture emerges from curvature-induced mechanisms, described in the literature for planar membranes, to coupled curvature- and bending-induced mechanisms in curved membranes forming a closed vesicle.

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.

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.

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.

Probing DNA conformational changes with high temporal resolution by tethered particle motion.

The tethered particle motion (TPM) technique informs about conformational changes of DNA molecules, e.g. upon looping or interaction with proteins, by tracking the Brownian motion of a particle probe tethered to a surface by a single DNA molecule and detecting changes of its amplitude of movement. We discuss in this context the time resolution of TPM, which strongly depends on the particle-DNA complex relaxation time, i.e. the characteristic time it takes to explore its configuration space by diffusion. By comparing theory, simulations and experiments, we propose a calibration of TPM at the dynamical level: we analyze how the relaxation time grows with both DNA contour length (from 401 to 2080 base pairs) and particle radius (from 20 to 150 nm). Notably we demonstrate that, for a particle of radius 20 nm or less, the hydrodynamic friction induced by the particle and the surface does not significantly slow down the DNA. This enables us to determine the optimal time resolution of TPM in distinct experimental contexts which can be as short as 20 ms.

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.

Statistical mechanics and dynamics of two supported stacked lipid bilayers.

The statistical physics and dynamics of double supported bilayers are studied theoretically. The main goal in designing double supported lipid bilayers is to obtain model systems of biomembranes: the upper bilayer is meant to be almost freely floating, the substrate being screened by the lower bilayer. The fluctuation-induced repulsion between membranes and between the lower membrane and the wall are explicitly taken into account using a Gaussian variational approach. It is shown that the variational parameters, the "effective" adsorption strength, and the average distance to the substrate, depend strongly on temperature and membrane elastic moduli, the bending rigidity, and the microscopic surface tension, which is a signature of the crucial role played by membrane fluctuations. The range of stability of these supported membranes is studied, showing a complex dependence on bare adsorption strengths. In particular, the experimental conditions of having an upper membrane slightly perturbed by the lower one and still bound to the surface are found. Included in the theoretical calculation of the damping rates associated with membrane normal modes are hydrodynamic friction by the wall and hydrodynamic interactions between both membranes.