The motion of a single molecule,the lambda-receptor,in the bacterial outer membrane

Using optical tweezers and single particle tracking, we have revealed the motion of a single protein, the lambda-receptor, in the outer membrane of living Escherichia coli bacteria. We genetically modified the lambda-receptor placing a biotin on an extracellular site of the receptor in vivo. The efficiency of this in vivo biotinylation is very low, thus enabling the attachment of a streptavidin-coated bead binding specifically to a single biotinylated lambda-receptor. The bead was used as a handle for the optical tweezers and as a marker for the single particle tracking routine. We propose a model that allows extraction of the motion of the protein from measurements of the mobility of the bead-molecule complex; these results are equally applicable to analyze bead-protein complexes in other membrane systems. Within a domain of radius approximately 25 nm, the receptor diffuses with a diffusion constant of (1.5 +/- 1.0) x 10(-9) cm(2)/s and sits in a harmonic potential as if it were tethered by an elastic spring of spring constant of ~1.0 x 10(-2) pN/nm to the bacterial membrane. The purpose of the protein motion might be to facilitate transport of maltodextrins through the outer bacterial membrane.     

Detection of membrane protein two-dimensional crystals in living cells

It is notoriously difficult to grow membrane protein crystals and solve membrane protein structures. Improved detection and screening of membrane protein crystals are needed. We have shown here that second-order nonlinear optical imaging of chiral crystals based on second harmonic generation can provide sensitive and selective detection of two-dimensional protein crystalline arrays with sufficiently low background to enable crystal detection within the membranes of live cells. The method was validated using bacteriorhodopsin crystals generated in live Halobacterium halobium bacteria and confirmed by electron microscopy from the isolated crystals. Additional studies of alphavirus glycoproteins indicated the presence of localized crystalline domains associated with virus budding from mammalian cells. These results suggest that in vivo crystallization may provide a means for expediting membrane protein structure determination for proteins exhibiting propensities for two-dimensional crystal formation.     

Modeling electrically active viscoelastic membranes

The membrane protein prestin is native to the cochlear outer hair cell that is crucial to the ear's amplification and frequency selectivity throughout the whole acoustic frequency range. The outer hair cell exhibits interrelated dimensional changes, force generation, and electric charge transfer. Cells transfected with prestin acquire unique active properties similar to those in the native cell that have also been useful in understanding the process. Here we propose a model describing the major electromechanical features of such active membranes. The model derived from thermodynamic principles is in the form of integral relationships between the history of voltage and membrane resultants as independent variables and the charge density and strains as dependent variables. The proposed model is applied to the analysis of an active force produced by the outer hair cell in response to a harmonic electric field. Our analysis reveals the mechanism of the outer hair cell active (isometric) force having an almost constant amplitude and phase up to 80 kHz. We found that the frequency-invariance of the force is a result of interplay between the electrical filtering associated with prestin and power law viscoelasticity of the surrounding membrane. Paradoxically, the membrane viscoelasticity boosts the force balancing the electrical filtering effect. We also consider various modes of electromechanical coupling in membrane with prestin associated with mechanical perturbations in the cell. We consider pressure or strains applied step-wise or at a constant rate and compute the time course of the resulting electric charge. The results obtained here are important for the analysis of electromechanical properties of membranes, cells, and biological materials as well as for a better understanding of the mechanism of hearing and the role of the protein prestin in this mechanism.     

New insights of membrane environment effects on MscL channel mechanics from theoretical approaches

The prokaryotic mechanosensitive channel of large conductance (MscL) is a remarkable integral membrane protein. During hypo-osmotic shock, it responses to membrane tension through large conformational changes, that lead to an open state of the pore. The structure of the channel from Mycobacterium tuberculosis has been resolved in the closed state. Numerous experiments have attempted to trap the channel in its open state but they did not succeed in obtaining a structure. A gating mechanism has been proposed based on different experimental data but there is no experimental technique available to follow this process in atomic details. In addition, it has been shown that a decrease of the lipid bilayer thickness lowered MscL activation energy and stabilized a structurally distinct closed channel intermediate. Here, we use atomistic molecular dynamics simulations to investigate the effect of the lipid bilayer thinning on our model of the structure of the Escherichia coli. We thoroughly analyze simulations of the channel embedded in two pre-equilibrated membranes differing by their hydrophobic tail length (DMPE and POPE). The MscL structure remains stable in POPE, whereas a distinct structural state is obtained in DMPE in response to hydrophobic mismatch. This latter is obtained by tilts and kinks of the transmembrane helices, leading to a widening and a diminution of the channel height. Part of these motions is guided by a competition between solvent and lipids for the interaction with the periplasmic loops. We finally conduct a principal component analysis of the simulation and compare anharmonic motions with harmonic ones, previously obtained from a coarse-grained normal mode analysis performed on the same structural model. Significant similarities exist between low-frequency harmonic motions and those observed with essential dynamics in DMPE. In summary, change in membrane thickness permits to accelerate the conformational changes involved in the mechanics of the E. coli channel, providing a closed structural intermediate en route to the open state. These results give clues for better understanding why the channel activation energy is lowered in a thinner membrane.     

Thermal fluctuations of red blood cell membrane via a constant-area particle-dynamics model

We describe a model of the mechanical properties of the cell plasma membrane using a finite-temperature particle-dynamics simulation of the whole cell, in which a two-dimensional network of virtual particles embedded in a three-dimensional closed surface represents the membrane. The particles interact via harmonic potential and dihedral angle potential and are subject to a constant area constraint. The evolution of the positions of the particles yields the equilibrium state of the membrane and allows determination of the membrane thermal fluctuations and the elastic moduli. We show that time-averaging of the cell-model configurations allows quantitative comparison with experimental data on membrane fluctuations and elastic moduli of the red blood cell.     

A multiscale approach to the elastic moduli of biomembrane networks

We develop equilibrium fluctuation formulae for the isothermal elastic moduli of discrete biomembrane models at different scales. We account for the coupling of large stretching and bending strains of triangulated network models endowed with harmonic and dihedral angle potentials, on the basis of the discrete-continuum approach presented in Schmidt and Fraternali (J Mech Phys Solids 60:172-180, 2012). We test the proposed equilibrium fluctuation formulae with reference to a coarse-grained molecular dynamics model of the red blood cell (RBC) membrane (Marcelli et al. in Biophys J 89:2473-2480, 2005; Hale et al. in Soft Matter 5:3603-3606, 2009), employing a local maximum-entropy regularization of the fluctuating configurations (Fraternali et al. in J Comput Phys 231:528-540, 2012). We obtain information about membrane stiffening/softening due to stretching, curvature, and microscopic undulations of the RBC model. We detect local dependence of the elastic moduli over the RBC membrane, establishing comparisons between the present theory and different approaches available in the literature.     

Response to a pure tone in a nonlinear mechanical-electrical-acoustical model of the cochlea

In this article, a nonlinear mathematical model is developed based on the physiology of the cochlea of the guinea pig. The three-dimensional intracochlear fluid dynamics are coupled to a micromechanical model of the organ of Corti and to electrical potentials in the cochlear ducts and outer hair cells (OHC). OHC somatic electromotility is modeled by linearized piezoelectric relations whereas the OHC hair-bundle mechanoelectrical transduction current is modeled as a nonlinear function of the hair-bundle deflection. The steady-state response of the cochlea to a single tone is simulated in the frequency domain using an alternating frequency time scheme. Compressive nonlinearity, harmonic distortion, and DC shift on the basilar membrane (BM), tectorial membrane (TM), and OHC potentials are predicted using a single set of parameters. The predictions of the model are verified by comparing simulations to available in vivo experimental data for basal cochlear mechanics. In particular, the model predicts more amplification on the reticular lamina (RL) side of the cochlear partition than on the BM, which replicates recent measurements. Moreover, small harmonic distortion and DC shifts are predicted on the BM, whereas more significant harmonic distortion and DC shifts are predicted in the RL and TM displacements and in the OHC potentials.     

Phase separation and bistability in a three-dimensional model for protein domain formation at biomembranes

Proteins in living cells interact with membranes. They may bind to or unbind from the membrane to the cytosol depending on the lipid composition of the membrane and their interaction with cytosolic enzymes. Moreover, proteins can accumulate at the membrane and assemble in spatial domains. Here, a simple model of protein cycling at biomembranes is studied, when the total number of proteins is conserved. Specifically, we consider the spatio-temporal dynamics of MARCKS proteins and their interactions with enzymes facilitating translocation from and rebinding to the membrane. The model exhibits two qualitatively different mechanisms of protein domain formation: phase separation related to a long-wave instability of a membrane state with homogeneous protein coverage and stable coexistence of two states with different homogeneous protein coverage in bistable media. We evaluate the impact of the cytosolic volume on the occurrence of protein pattern formation by simulations in a three-dimensional model. We show that the explicit treatment of the volume in the model leads to an effective rescaling of the reaction rates. For a simplified model of protein cycling, we can derive analytical expressions for the rescaling coefficients and verify them by direct simulations with the complete three-dimensional model.     

Teaching an old dog new tricks: A lipid membrane-based electric immunosensor for real-time probing of the spike S1 protein subunit from SARS-CoV-2

Fast, cheap, and easy to implement point-of-care testing for various pathogens constituted a game changer in past years due to its potential for early disease diagnosis. Herein, we report on the proof-of-concept of a simple method enabling in vitro detection of a structural spike protein subunit from the SARS-CoV-2 (S₁) in aqueous samples. At the core of this discovery lies the well-known paradigm of monitoring the capacitive current across a reconstituted zwitterionic lipid membrane subjected to a periodic transmembrane potential, followed by the real-time spectral analysis enabling the extraction of the second harmonic of the capacitive current. Subsequent changes in the amplitude of this harmonic recorded during lipid membrane–S₁ interactions were correlated with alterations induced in the inner membrane potential profile by the S₁ protein subunit adsorption, and were shown to be augmented by ionic strength, the presence of a specific monoclonal antibody designed against the S₁ subunit and the angiotensin-converting enzyme 2 (ACE2) protein receptor, and uninhibited by the presence of other human serum proteins.     

Spring-loaded model revisited: paramyxovirus fusion requires engagement of a receptor binding protein beyond initial triggering of the fusion protein

During paramyxovirus entry into a host cell, receptor engagement by a specialized binding protein triggers conformational changes in the adjacent fusion protein (F), leading to fusion between the viral and cell membranes. According to the existing paradigm of paramyxovirus membrane fusion, the initial activation of F by the receptor binding protein sets off a spring-loaded mechanism whereby the F protein progresses independently through the subsequent steps in the fusion process, ending in membrane merger. For human parainfluenza virus type 3 (HPIV3), the receptor binding protein (hemagglutinin-neuraminidase [HN]) has three functions: receptor binding, receptor cleaving, and activating F. We report that continuous receptor engagement by HN activates F to advance through the series of structural rearrangements required for fusion. In contrast to the prevailing model, the role of HN-receptor engagement in the fusion process is required beyond an initiating step, i.e., it is still required even after the insertion of the fusion peptide into the target cell membrane, enabling F to mediate membrane merger. We also report that for Nipah virus, whose receptor binding protein has no receptor-cleaving activity, the continuous stimulation of the F protein by a receptor-engaged binding protein is key for fusion. We suggest a general model for paramyxovirus fusion activation in which receptor engagement plays an active role in F activation, and the continued engagement of the receptor binding protein is essential to F protein function until the onset of membrane merger. This model has broad implications for the mechanism of paramyxovirus fusion and for strategies to prevent viral entry.     

Quantitative predictions of a noncarrier model for glucose transport across the human red cell membrane

There is an increasing amount of experimental data on transport across biological membranes which cannot be readily accommodated by classical mobile carrier models. We propose models for membrane transport based upon current concepts in molecular enzymology, in which the membrane component involved in transport is an oligomeric protein which undergoes substrate-induced conformational changes. A number of paradoxical observations on glucose transport in the human erythrocyte are explained if the protein involved is a tetramer possessing two classes of binding sites with different affinities for glucose. We develop in detail a particular model of this type, the internal transfer model, in which transport occurs by transfer of substrate from one subunit to another of the protein. The fit of the predictions of the internal transfer model with most of the experimental data is very good. Those data which cannot be fitted by the model cannot be accounted for by any presently available model. We extend our model qualitatively to include the sodium-activated cotransport systems for sugars and amino acids.     

Nonlinear sorting, curvature generation, and crowding of endophilin N-BAR on tubular membranes

The curvature of biological membranes is controlled by membrane-bound proteins. For example, during endocytosis, the sorting of membrane components, vesicle budding, and fission from the plasma membrane are mediated by adaptor and accessory proteins. Endophilin is a peripherally binding membrane protein that functions as an endocytic accessory protein. Endophilin's membrane tubulation capacity is well known. However, to understand the thermodynamic and mechanical aspects of endophilin function, experimental measurements need to be compared to quantitative theoretical models. We present measurements of curvature sorting and curvature generation of the endophilin A1 N-BAR domain on tubular membranes pulled from giant unilamellar vesicles. At low concentration, endophilin functions primarily as a membrane curvature sensor; at high concentrations, it also generates curvature. We determine the spontaneous curvature induced by endophilin and observe sigmoidal curvature/composition coupling isotherms that saturate at high membrane tensions and protein solution concentrations. The observation of saturation is supported by a strong dependence of lateral diffusion coefficients on protein density on the tether membrane. We develop a nonlinear curvature/composition coupling model that captures our experimental observations. Our model predicts a curvature-induced phase transition among two states with varying protein density and membrane curvature. This transition could act as a switch during endocytosis.     

Energy landscape of a native protein: Jumping-among-minima model

We have investigated energy landscape of human lysozyme in its native state by using principal component analysis and a model, jumping-among-minima (JAM) model. These analyses are applied to 1 nsec molecular dynamics trajectory of the protein in water. An assumption embodied in the JAM model allows us to divide protein motions into intra-substate and inter-substate motions. By examining intra-substate motions, it is shown that energy surfaces of individual conformational substates are nearly harmonic and mutually similar. As a result of principal component analysis and JAM model analysis, protein motions are shown to consist of three types of collective modes, multiply hierarchical modes, singly hierarchical modes, and harmonic modes. Multiply hierarchical modes, the number of which accounts only for 0.5% of all modes, dominate contributions to total mean-square atomic fluctuation. Inter-substate motions are observed only in a small-dimensional subspace spanned by the axes of multiplyhierarchical and singly hierarchical modes. Inter-substate motions have two notable time components: faster component seen within 200 psec and slower component. The former involves transitions among the conformational substates of the low-level hierarchy, whereas the latter involves transitions of the higher level substates observed along the first four multiply hierarchical modes. We also discuss dependence of the subspace, which contains conformational substates, on time duration of simulation. Proteins 33:496–517, 1998. © 1998 Wiley-Liss, Inc.     

Independent mobility of proteins and lipids in the plasma membrane of Escherichia coli

Fluidity is essential for many biological membrane functions. The basis for understanding membrane structure remains the classic Singer‐Nicolson model, in which proteins are embedded within a fluid lipid bilayer and able to diffuse laterally within a sea of lipid. Here we report lipid and protein diffusion in the plasma membrane of live cells of the bacterium Escherichia coli, using Fluorescence Recovery after Photobleaching (FRAP) and Total Internal Reflection Fluorescence (TIRF) microscopy to measure lateral diffusion coefficients. Lipid and protein mobility within the membrane were probed by visualizing an artificial fluorescent lipid and a simple model membrane protein consisting of a single membrane‐spanning alpha‐helix with a Green Fluorescent Protein (GFP) tag on the cytoplasmic side. The effective viscosity of the lipid bilayer is strongly temperature‐dependent, as indicated by changes in the lipid diffusion coefficient. Surprisingly, the mobility of the model protein was unaffected by changes in the effective viscosity of the bulk lipid, and TIRF microscopy indicates that it clusters in segregated, mobile domains. We suggest that this segregation profoundly influences the physical behaviour of the protein in the membrane, with strong implications for bacterial membrane function and bacterial physiology.     

Molecular dynamics simulations and membrane protein structure quality

Despite a growing repertoire of membrane protein structures (currently ∼120 unique structures), considerations of low resolution and crystallization in the absence of a lipid bilayer require the development of techniques to assess the global quality of membrane protein folds. This is also the case for assessment of, e.g. homology models of human membrane proteins based on structures of (distant) bacterial homologues. Molecular dynamics (MD) simulations may be used to help evaluate the quality of a membrane protein structure or model. We have used a structure of the bacterial ABC transporter MsbA which has the correct transmembrane helices but an incorrect handedness and topology of their packing to test simulation methods of quality assessment. An MD simulation of the MsbA model in a lipid bilayer is compared to a simulation of another bacterial ABC transporter, BtuCD. The latter structure has demonstrated good conformational stability in the same bilayer environment and over the same timescale (20 ns) as for the MsbA model simulation. A number of comparative analyses of the two simulations were performed to assess changes in the structural integrity of each protein. The results show a significant difference between the two simulations, chiefly due to the dramatic structural deformations of MsbA. We therefore propose that MD could become a useful quality control tool for membrane protein structural biology. In particular, it provides a way in which to explore the global conformational stability of a model membrane protein fold.     

Lipid Fingerprints and Cofactor Dynamics of Light-Harvesting Complex II in Different Membranes

Plant light-harvesting complex II (LHCII) is the key antenna complex for plant photosynthesis. We present coarse-grained molecular dynamics simulations of monomeric and trimeric LHCII in a realistic thylakoid membrane environment based on the Martini force field. The coarse-grained protein model has been optimized with respect to atomistic reference simulations. Our simulations provide detailed insights in the thylakoid lipid fingerprint of LHCII which compares well with experimental data from membrane protein purification. Comparing the monomer and trimeric LHCII reveals a stabilizing effect of trimerization on the chromophores as well as the protein. Moreover, the average chromophore distance shortens in the trimer leading to stronger excitonic couplings. When changing the native thylakoid environment to a model membrane the protein flexibility remains constant, whereas the chromophore flexibility is reduced. Overall, the presented LHCII model lays the foundation to investigate the μs dynamics of this key antenna protein of plants.     

Physical model of contractile ring initiation in dividing cells

We present a physical mechanism to describe initiation of the contractile ring during cell division. The model couples the membrane curvature with the contractile forces produced by protein clusters attached to the membrane. These protein clusters are mobile on the membrane and possess either an isotropic or an anisotropic spontaneous curvature. Our results show that under these conditions the contraction force gives rise to an instability that corresponds in a closed cellular system to the initiation of the contractile ring. We find a quantization of this process at distinct length-scales, which we compare to available data for different types of eukaryote cells.     

A kinetic model for the internal motions of proteins: diffusion between multiple harmonic wells.

The dynamics of collective protein motions derived from Molecular Dynamics simulations have been studied for two small model proteins: initiation factor I and the B1 domain of Protein G. First, we compared the structural fluctuations, obtained by local harmonic approximations in different energy minima, with the ones revealed by large scale molecular dynamics (MD) simulations. It was found that a limited set of harmonic wells can be used to approximate the configurational fluctuations of these proteins, although any single harmonic approximation cannot properly describe their dynamics. Subsequently, the kinetics of the main (essential) collective protein motions were characterized. A dual-diffusion behavior was observed in which a fast type of diffusion switches to a much slower type in a typical time of about 1-3 ps. From these results, the large backbone conformational fluctuations of a protein may be considered as "hopping" between multiple harmonic wells on a basically flat free energy surface.     

Regulation of protein mobility in cell membranes: a dynamic corral model

We analyze a two-state stochastic corral model for regulation of protein diffusion in a cell membrane. This model could mimic control of protein transport in the membrane by the cytoskeleton. The dynamic corral acts as a gate which when open permits an otherwise trapped protein to escape to a neighboring corral in the cytoskeletal network. We solve for the escape rate over a wide range of parameters of the model, and compare these results with Monte Carlo simulations. Upon introducing measured values of the model parameters for Band 3 in erythrocyte membranes, we are able to estimate the value for one unknown parameter, the average rate at which the corral closes. The ratio of calculated closing rate to measured opening rate is roughly 100:1, consistent with a gating mechanism whereby protein mobility is regulated by dissociation and reassociation of segments of the cytoskeletal network.