Interfacial water on collagen nanoribbons by 3D AFM.

Collagen is the most abundant structural protein in mammals. Type I collagen in its fibril form has a characteristic pattern structure that alternates two regions called gap and overlap. The structure and properties of collagens are highly dependent on the water and mineral content of the environment. Here, we apply 3D AFM to characterize at angstrom-scale resolution the interfacial water structure of collagen nanoribbons. For a neutral tip, the interfacial water structure is characterized by the oscillation of the water particle density distribution with a value of 0.3 nm (hydration layers). The interfacial structure does not depend on the collagen region. For a negatively charged tip, the interfacial structure might depend on the collagen region. Hydration layers are observed in overlap regions, while in gap regions, the interfacial solvent structure is dominated by electrostatic interactions. These interactions generate interlayer distances of 0.2 nm.

A coarse-grained approach to model the dynamics of the actomyosin cortex.

BACKGROUND: The dynamics of the actomyosin machinery is at the core of many important biological processes. Several relevant cellular responses such as the rhythmic compression of the cell cortex are governed, at a mesoscopic level, by the nonlinear interaction between actin monomers, actin crosslinkers, and myosin motors. Coarse-grained models are an optimal tool to study actomyosin systems, since they can include processes that occur at long time and space scales, while maintaining the most relevant features of the molecular interactions. RESULTS: Here, we present a coarse-grained model of a two-dimensional actomyosin cortex, adjacent to a three-dimensional cytoplasm. Our simplified model incorporates only well-characterized interactions between actin monomers, actin crosslinkers and myosin, and it is able to reproduce many of the most important aspects of actin filament and actomyosin network formation, such as dynamics of polymerization and depolymerization, treadmilling, network formation, and the autonomous oscillatory dynamics of actomyosin. CONCLUSIONS: We believe that the present model can be used to study the in vivo response of actomyosin networks to changes in key parameters of the system, such as alterations in the attachment of actin filaments to the cell cortex.

Intrinsic structure perspective for MIPS interfaces in two-dimensional systems of active Brownian particles.

Suspensions of active Brownian particles (ABPs) undergo motility-induced phase separation (MIPS) over a wide range of mean density and activity strength, which implies the spontaneous aggregation of particles due to the persistence of their direction of motion, even in the absence of an explicit attraction. Both similarities and qualitative differences have been obtained when the MIPS is analysed in the same terms as a liquid-gas phase coexistence in an equilibrium attractive system. Negative values of the mechanical surface tension have been reported, from the total forces across the interface, while stable fluctuations of the interfacial line could be interpreted as a positive capillary surface tension; in equilibrium liquid surfaces, these two magnitudes are equal. We present here the analysis of 2D-ABP interfaces in terms of the intrinsic density and force profiles, calculated with the particle distance to the instantaneous interfacial line. Our results provide new insight into the origin of MIPS from the local rectification of the random active force on the particles near the interface. As has been reported, this effect acts as an external potential that produces a pressure gradient across the interface, such that the mechanical surface tension of the MIPS cannot be described as that of equilibrium coexisting phases; however, our analysis shows that most of that effect comes from the tightly caged particles at the dense (inner) side of the MIPS interface, rather than from the free moving particles at the outer side that collide with the dense cluster. Moreover, a clear correlation appears between the decay of the hexatic order parameter at the dense slab and the end of the MIPS as the strength of the active force is lowered. We show that, using the strong active forces required for MIPS, the interfacial structure and properties are very similar for ABPs with purely repulsive interactions (the Weeks-Chandler-Andersen-Lennard-Jones (WCA-LJ) model truncated at its minimum) and when the interaction includes a range of the LJ attractive force.

Layering and capillary waves in the structure factor of liquid surfaces.

Within the extended Capillary Wave Theory (ECWT), to extract the bending modulus of a liquid surface from the total structure factor of the interfacial region requires to separate the capillary waves (CW) signal from a non-CW background. Some years ago, Höfling and Dietrich (HD), working in the strict grazing incidence limit qz = 0, proposed a background that combines the liquid and vapor bulk structure factors in the amounts set by Gibbs's plane. We contrast that proposal with Molecular Dynamics (MD) simulations of the Lennard-Jones model analyzed with the Intrinsic Sampling Method (ISM). The study is extended to qz ≠ 0, to test the stronger consistency requirements of the ECWT and the experimental conditions; it shows a good MD-ECWT matching although we need some fine tuning over HD proposal. Then, the agreement with the ISM result for the surface bending modulus is good and that provides an interpretation, in terms of the molecular layering at the liquid edge, for the fluctuating surface represented by the CW signal in the surface structure factor, both for MD simulations and surface diffraction experiments.

Tip Charge Dependence of Three-Dimensional AFM Mapping of Concentrated Ionic Solutions.

A molecular scale understanding of the organization and structure of a liquid near a solid surface is currently a major challenge in surface science. It has implications across different fields from electrochemistry and energy storage to molecular biology. Three-dimensional AFM generates atomically resolved maps of solid-liquid interfaces. The imaging mechanism behind those maps is under debate, in particular, for concentrated ionic solutions. Theory predicts that the observed contrast should depend on the tip's charged state. Here, by using neutrally, negatively, and positively charged tips, we demonstrate that the 3D maps depend on the tip's polarization. A neutral tip will explore the total particle density distribution (water and ions) while a charged tip will reveal the charge density distribution. The experimental data reproduce the key findings of the theory.

Density functional analysis of atomic force microscopy in a dense fluid.

We present a density functional (DF) analysis for the entropic force in Atomic Force Microscopy (AFM) across the layers of a dense fluid. Previous theoretical analysis, based on the ideal gas entropy, was apparently supported by the similarity in the oscillatory decay for the force and density profile. We point out that such similarity is a generic DF result, which carries no information on the interface, since the decaying mode is characteristic of the bulk fluid correlation. The truly interfacial information, from the layering measured by AFM, comes in its amplitude and not in the decay mode. With our rigorous study of a simple hard sphere model, we find semiempirical clues to disentangle the role of the tip radius and to relate the amplitude of the molecular layering to the oscillatory force on the AFM tip.

A MOF@COF Composite with Enhanced Uptake through Interfacial Pore Generation.

Herein, we describe a new class of porous composites comprising metal-organic framework (MOF) crystals confined in single spherical matrices made of packed covalent-organic framework (COF) nanocrystals. These MOF@COF composites are synthesized through a two-step method of spray-drying and subsequent amorphous (imine-based polymer)-to-crystalline (imine-based COF) transformation. This transformation around the MOF crystals generates micro- and mesopores at the MOF/COF interface that provide far superior porosity compared to that of the constituent MOF and COF components added together. We report that water sorption in these new pores occurs within the same pressure window as in the COF pores. Our new MOF@COF composites, with their additional pores at the MOF/COF interface, should have implications for the development of new composites.

Density correlation in liquid surfaces: Bedeaux-Weeks high order terms and non capillary wave background.

We present Molecular Dynamics (MD) simulations of liquid-vapor surfaces, and their Intrinsic Sampling Method analysis, to get a quantitative test for the theoretical prediction of the capillary wave (CW) effects on density correlation done by Bedeaux and Weeks (BW) in 1985. The results are contrasted with Wertheim's proposal which is the first term in BW series and are complemented with a (formally defined and computational accessible) proposal for the background of non-CW fluctuations. Our conclusion is that BW theory is both accurate and needed since it may differ significantly from Wertheim's proposal. We discuss the implications for the analysis of experimental X-ray surface diffraction data and MD simulations.

Capillary waves as eigenmodes of the density correlation at liquid surfaces.

We analyze the density correlations in a liquid-vapor surface to establish a quantitative connection between the Density Functional (DF) formalism, Molecular Dynamic (MD) simulations, and the Capillary Wave (CW) theory. Instead of the integrated structure factor, we identify the CW fluctuations as eigenmodes of the correlation function. The square-gradient DF approximation appears as fully consistent with the use of the thermodynamic surface tension to describe the surface fluctuations for any wavevector because it misses the upper cutoff in the surface Hamiltonian from the merging of the CW mode with the non-CW band. This mesoscopic cutoff may be accurately predicted from the main peak in the structure factor of the bulk liquid. We explore the difference between the full density-density correlation mode and the bare CW that represents the correlation between the corrugation of the intrinsic surface and the density at the interfacial region. The non-local decay of the CW effects, predicted from DF analysis and observed in MD simulations with the intrinsic sampling method, is found to characterize the bare CW fluctuations, which also require a wavevector-dependent surface tension.

Deconstructing Temperature Gradients across Fluid Interfaces: The Structural Origin of the Thermal Resistance of Liquid-Vapor Interfaces.

The interfacial thermal resistance determines condensation-evaporation processes and thermal transport across material-fluid interfaces. Despite its importance in transport processes, the interfacial structure responsible for the thermal resistance is still unknown. By combining nonequilibrium molecular dynamics simulations and interfacial analyses that remove the interfacial thermal fluctuations we show that the thermal resistance of liquid-vapor interfaces is connected to a low density fluid layer that is adsorbed at the liquid surface. This thermal resistance layer (TRL) defines the boundary where the thermal transport mechanism changes from that of gases (ballistic) to that characteristic of dense liquids, dominated by frequent particle collisions involving very short mean free paths. We show that the thermal conductance is proportional to the number of atoms adsorbed in the TRL, and hence we explain the structural origin of the thermal resistance in liquid-vapor interfaces.

A computer simulation approach to quantify the true area and true area compressibility modulus of biological membranes.

We present a new computational approach to quantify the area per lipid and the area compressibility modulus of biological membranes. Our method relies on the analysis of the membrane fluctuations using our recently introduced coupled undulatory (CU) mode [Tarazona et al., J. Chem. Phys. 139, 094902 (2013)], which provides excellent estimates of the bending modulus of model membranes. Unlike the projected area, widely used in computer simulations of membranes, the CU area is thermodynamically consistent. This new area definition makes it possible to accurately estimate the area of the undulating bilayer, and the area per lipid, by excluding any contributions related to the phospholipid protrusions. We find that the area per phospholipid and the area compressibility modulus features a negligible dependence with system size, making possible their computation using truly small bilayers, involving a few hundred lipids. The area compressibility modulus obtained from the analysis of the CU area fluctuations is fully consistent with the Hooke's law route. Unlike existing methods, our approach relies on a single simulation, and no a priori knowledge of the bending modulus is required. We illustrate our method by analyzing 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine bilayers using the coarse grained MARTINI force-field. The area per lipid and area compressibility modulus obtained with our method and the MARTINI forcefield are consistent with previous studies of these bilayers.

Depolymerization dynamics of individual filaments of bacterial cytoskeletal protein FtsZ.

We report observation and analysis of the depolymerization filaments of the bacterial cytoskeletal protein FtsZ (filament temperature-sensitive Z) formed on a mica surface. At low concentration, proteins adsorbed on the surface polymerize forming curved filaments that close into rings that remain stable for some time before opening irreversibly and fully depolymerizing. The distribution of ring lifetimes (T) as a function of length (N), shows that the rate of ring aperture correlates with filament length. If this ring lifetime is expressed as a bond survival time, (T(b) ≡ NT), this correlation is abolished, indicating that these rupture events occur randomly and independently at each monomer interface. After rings open irreversibly, depolymerization of the remaining filaments is fast, but can be slowed down and followed using a nonhydrolyzing GTP analogue. The histogram of depolymerization velocities of individual filaments has an asymmetric distribution that can be fit with a computer model that assumes two rupture rates, a slow one similar to the one observed for ring aperture, affecting monomers in the central part of the filaments, and a faster one affecting monomers closer to the open ends. From the quantitative analysis, we conclude that the depolymerization rate is affected both by nucleotide hydrolysis rate and by its exchange along the filament, that all monomer interfaces are equally competent for hydrolysis, although depolymerization is faster at the open ends than in central filament regions, and that all monomer-monomer interactions, regardless of the nucleotide present, can adopt a curved configuration.

Torsion and curvature of FtsZ filaments.

FtsZ filaments participate in bacterial cell division, but it is still not clear how their dynamic polymerization and shape exert force on the underlying membrane. We present a theoretical description of individual filaments that incorporates information from molecular dynamic simulations. The structure of the crystallized Methanococcus jannaschii FtsZ dimer was used to model a FtsZ pentamer that showed a curvature and a twist. The estimated bending and torsion angles between monomers and their fluctuations were included in the theoretical description. The MD data also permitted positioning the curvature with respect to the protein coordinates and allowed us to explore the effect of the relative orientation of the preferred curvature with respect to the surface plane. We find that maximum tension is attained when filaments are firmly attached and oriented with their curvature perpendicular to the surface and that the twist serves as a valve to release or to tighten the tension exerted by the curved filaments on the membrane. The theoretical model also shows that the presence of torsion can explain the shape distribution of short filaments observed by Atomic Force Microscopy in previously published experiments. New experiments with FtsZ covalently attached to lipid membranes show that the filament on-plane curvature depends on lipid head charge, confirming the predicted monomer orientation effects. This new model underlines the fact that the combination of the three elements, filament curvature, twist and the strength and orientation of its surface attachment, can modulate the force exerted on the membrane during cell division.

Intrinsic fluid interfaces and nonlocality.

We present results of an extensive molecular dynamics simulation of the structure and fluctuations of a liquid-gas interface, close to its triple point, in a system with cutoff Lennard-Jones interactions. The equilibrium density profile, averaged and (shape dependent) constrained intrinsic density profiles together with the fluctuations of the interfacial shape are extracted using an intrinsic sampling method. The correlation between fluctuations in the interfacial shape and in the intrinsic density show that the latter is not due to rigid translations of some underlying profile, as is most commonly assumed. Instead, over the whole range of wavelengths from the system size down to the molecular diameter, we see wave-vector dependent behavior in good agreement with a nonlocal interfacial Hamiltonian theory specifying the shape dependence of the intrinsic profiles.

Thermal fluctuations and bending rigidity of bilayer membranes.

We present a new scheme to estimate the elastic properties of biological membranes in computer simulations. The method analyzes the thermal fluctuations in terms of a coupled undulatory mode, which disentangle the mixing of the mesoscopic undulations and the high-q protrusions. This approach makes possible the accurate estimation of the bending modulus both for membranes under stress and in tensionless conditions; it also extends the applicability of the fluctuation analysis to the small membrane areas normally used in atomistic simulations. Also we clarify the difference between the surface tension imposed in simulations through a pressure coupling barostat, and the surface tension that can be extracted from the analysis of the low wave vector dependence of the coupled undulatory fluctuation spectrum. The physical analysis of the peristaltic mode is also refined, by separating the bulk and protrusions contributions. We illustrate the procedure by analyzing 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine and 1,2-dipalmitoyl-sn-glycero-3-phosphocholine bilayers. The bending moduli obtained from our analysis, shows good agreement with available experiments.

Functional thermo-dynamics: a generalization of dynamic density functional theory to non-isothermal situations.

We present a generalization of Density Functional Theory (DFT) to non-equilibrium non-isothermal situations. By using the original approach set forth by Gibbs in his consideration of Macroscopic Thermodynamics (MT), we consider a Functional Thermo-Dynamics (FTD) description based on the density field and the energy density field. A crucial ingredient of the theory is an entropy functional, which is a concave functional. Therefore, there is a one to one connection between the density and energy fields with the conjugate thermodynamic fields. The connection between the three levels of description (MT, DFT, FTD) is clarified through a bridge theorem that relates the entropy of different levels of description and that constitutes a generalization of Mermin's theorem to arbitrary levels of description whose relevant variables are connected linearly. Although the FTD level of description does not provide any new information about averages and correlations at equilibrium, it is a crucial ingredient for the dynamics in non-equilibrium states. We obtain with the technique of projection operators the set of dynamic equations that describe the evolution of the density and energy density fields from an initial non-equilibrium state towards equilibrium. These equations generalize time dependent density functional theory to non-isothermal situations. We also present an explicit model for the entropy functional for hard spheres.

The structure of ionic aqueous solutions at interfaces: an intrinsic structure analysis.

We investigate the interfacial structure of ionic solutions consisting of alkali halide ions in water at concentrations in the range 0.2-1.0 molal and at 300 K. Combining molecular dynamics simulations of point charge ion models and a recently introduced computational approach that removes the averaging effect of interfacial capillary waves, we compute the intrinsic structure of the aqueous interface. The interfacial structure is more complex than previously inferred from the analysis of mean profiles. We find a strong alternating double layer structure near the interface, which depends on the cation and anion size. Relatively small changes in the ion diameter disrupt the double layer structure, promoting the adsorption of anions or inducing the density enhancement of small cations with diameters used in simulation studies of lithium solutions. The density enhancement of the small cations is mediated by their strong water solvation shell, with one or more water molecules "anchoring" the ion to the outermost water layer. We find that the intrinsic interfacial electrostatic potential features very strong oscillations with a minimum at the liquid surface that is ∼4 times stronger than the electrostatic potential in the bulk. For the water model employed in this work, SPC/E, the electrostatic potential at the water surface is ∼-2 V, equivalent to ∼80 k(B)T (for T = 300 K), much stronger than previously considered. Furthermore, we show that the utilization of the intrinsic surface technique provides a route to extract ionic potentials of mean force that are not affected by the thermal fluctuations, which limits the accuracy of most past approaches including the popular umbrella sampling technique.

Bending Modulus of Lipid Membranes from Density Correlation Functions.

The bending modulus κ quantifies the elasticity of biological membranes in terms of the free energy cost of increasing the membrane corrugation. Molecular dynamics (MD) simulations provide a powerful approach to quantify κ by analyzing the thermal fluctuations of the lipid bilayer. However, existing methods require the identification and filtering of non-mesoscopic fluctuation modes. State of the art methods rely on identifying a smooth surface to describe the membrane shape. These methods introduce uncertainties in calculating κ since they rely on different criteria to select the relevant fluctuation modes. Here, we present a method to compute κ using molecular simulations. Our approach circumvents the need to define a mesoscopic surface or an orientation field for the lipid tails explicitly. The bending and tilt moduli can be extracted from the analysis of the density correlation function (DCF). The method introduced here builds on the Bedeaux and Weeks (BW) theory for the DCF of fluctuating interfaces and on the coupled undulatory (CU) mode introduced by us in previous work. We test the BW-DCF method by computing the elastic properties of lipid membranes with different system sizes (from 500 to 6000 lipid molecules) and using coarse-grained (for POPC and DPPC lipids) and fully atomistic models (for DPPC). Further, we quantify the impact of cholesterol on the bending modulus of DPPC bilayers. We compare our results with bending moduli obtained with X-ray diffraction data and different computer simulation methods.

Adhesive transitions in Newton black films: a computer simulation study.

We report molecular dynamics simulations of Newton black films (NBFs), ultra thin films of aqueous solutions stabilized with two monolayers of ionic surfactants, sodium dodecyl sulfate. We show that at low water content conditions and areas per surfactant corresponding to experimental estimates in NBFs, homogeneous films undergo an adhesion "transition," which results in a very thin adhesive film coexisting with a thicker film. We identify the adhesive film with the equilibrium structure of the Newton black film. We provide here a direct microscopic view of the formation of these important structures, which have been observed in experimental studies of emulsions and foams. We also report a detailed investigation of the structural properties and interfacial fluctuation spectrum of the adhesive film. Our analysis relies on the definition of an "intrinsic surface," which is used to remove the averaging effect that the capillary waves have on the film properties.

Bacterial cell division: modeling FtsZ assembly and force generation from single filament experimental data.

The bacterial cytoskeletal protein FtsZ binds and hydrolyzes GTP, self-aggregates into dynamic filaments and guides the assembly of the septal ring on the inner side of the membrane at midcell. This ring constricts the cell during division and is present in most bacteria. Despite exhaustive studies undertaken in the last 25 years after its discovery, we do not yet know the mechanism by which this GTP-dependent self-aggregating protein exerts force on the underlying membrane. This paper reviews recent experiments and theoretical models proposed to explain FtsZ filament dynamic assembly and force generation. It highlights how recent observations of single filaments on reconstituted model systems and computational modeling are contributing to develop new multiscale models that stress the importance of previously overlooked elements as monomer internal flexibility, filament twist and flexible anchoring to the cell membrane. These elements contribute to understand the rich behavior of these GTP consuming dynamic filaments on surfaces. The aim of this review is 2-fold: (1) to summarize recent multiscale models and their implications to understand the molecular mechanism of FtsZ assembly and force generation and (2) to update theoreticians with recent experimental results.