Measuring fast stochastic displacements of bio-membranes with dynamic optical displacement spectroscopy

Membrane Fluctuation Model for Understanding the Effect of Receptor Nanoclustering on the Activation of Natural Killer Cells through Biomechanical Feedback

We investigated the role of ligand clustering and density in the activation of natural killer (NK) cells. To that end, we designed reductionist arrays of nanopatterned ligands arranged with different cluster geometries and densities and probed their effects on NK cell activation. We used these arrays as an artificial microenvironment for the stimulation of NK cells and studied the effect of the array geometry on the NK cell immune response. We found that ligand density significantly regulated NK cell activation while ligand clustering had an impact only at a specific density threshold. We also rationalized these findings by introducing a theoretical membrane fluctuation model that considers biomechanical feedback between ligand-receptor bonds and the cell membrane. These findings provide important insight into NK cell mechanobiology, which is fundamentally important and essential for designing immunotherapeutic strategies targeting cancer.

Measuring sub-nanometer undulations at microsecond temporal resolution with metal- and graphene-induced energy transfer spectroscopy

Out-of-plane fluctuations, also known as stochastic displacements, of biological membranes play a crucial role in regulating many essential life processes within cells and organelles. Despite the availability of various methods for quantifying membrane dynamics, accurately quantifying complex membrane systems with rapid and tiny fluctuations, such as mitochondria, remains a challenge. In this work, we present a methodology that combines metal/graphene-induced energy transfer (MIET/GIET) with fluorescence correlation spectroscopy (FCS) to quantify out-of-plane fluctuations of membranes with simultaneous spatiotemporal resolution of approximately one nanometer and one microsecond. To validate the technique and spatiotemporal resolution, we measure bending undulations of model membranes. Furthermore, we demonstrate the versatility and applicability of MIET/GIET-FCS for studying diverse membrane systems, including the widely studied fluctuating membrane system of human red blood cells, as well as two unexplored membrane systems with tiny fluctuations, a pore-spanning membrane, and mitochondrial inner/outer membranes.

Nanoscale Bending Dynamics in Mixed-Chain Lipid Membranes

Lipids that have two tails of different lengths are found throughout biomembranes in nature, yet the effects of this asymmetry on the membrane properties are not well understood, especially when it comes to the membrane dynamics. Here we study the nanoscale bending fluctuations in model mixed-chain 14:0–18:0 PC (MSPC) and 18:0–14:0 PC (SMPC) lipid bilayers using neutron spin echo (NSE) spectroscopy. We find that despite the partial interdigitation that is known to persist in the fluid phase of these membranes, the collective fluctuations are enhanced on timescales of tens of nanoseconds, and the chain-asymmetric lipid bilayers are softer than an analogous chain-symmetric lipid bilayer with the same average number of carbons in the acyl tails, di-16:0 PC (DPPC). Quantitative comparison of the NSE results suggests that the enhanced bending fluctuations at the nanosecond timescales are consistent with experimental and computational studies that showed the compressibility moduli of chain-asymmetric lipid membranes are 20% to 40% lower than chain-symmetric lipid membranes. These studies add to growing evidence that the partial interdigitation in mixed-chain lipid membranes is highly dynamic in the fluid phase and impacts membrane dynamic processes from the molecular to mesoscopic length scales without significantly changing the bilayer thickness or area per lipid.

Lipid Membrane Flexibility in Protic Ionic Liquids

Here, we determine by neutron spin echo spectrometry (NSE) how the flexibility of egg lecithin vesicles depends on solvent composition in two protic ionic liquids (PILs) and their aqueous mixtures. In combination with small-angle neutron scattering (SANS), dynamic light scattering (DLS), and fluorescent probe microscopy, we show that the bending modulus is up to an order of magnitude lower than in water but with no change in bilayer thickness or nonpolar chain composition. This effect is attributed to the dynamic association and exchange of the IL cation between the membrane and bulk liquid, which has the same origin as the underlying amphiphilic nanostructure of the IL solvent itself. This provides a new mechanism by which to tune and control lipid membrane behavior.

Investigating the entropic nature of membrane-mediated interactions driving the aggregation of peripheral proteins

Peripheral membrane-associated proteins are known to accumulate on the surface of biomembranes as a result of membrane-mediated interactions. For a pair of rotationally-symmetric curvature-inducing proteins, membrane mechanics at the low-temperature limit predicts pure repulsion. On the other hand, temperature-dependent entropic forces arise between pairs of stiff-binding proteins suppressing membrane fluctuations. These Casimir-like interactions have thus been suggested as candidates for attractive forces leading to aggregation. With dense assemblies of peripheral proteins on the membrane, both these abstractions encounter short-range and multi-body complications. Here, we make use of a particle-based membrane model augmented with flexible peripheral proteins to quantify purely membrane-mediated interactions and investigate their underlying nature. We introduce a continuous reaction coordinate corresponding to the progression of protein aggregation. We obtain free energy and entropy landscapes for different surface concentrations along this reaction coordinate. In parallel, we investigate time-dependent estimates of membrane entropy corresponding to membrane undulations and coarse-grained director field and how they change dynamically with protein aggregation. Congruent outcomes of the two approaches point to the conclusion that for low surface concentrations, interactions with an entropic nature may drive the aggregation. But at high concentrations, enthalpic contributions due to concerted membrane deformation by protein clusters are dominant.

The interplay between membrane topology and mechanical forces in regulating T cell receptor activity

T cells are critically important for host defense against infections. T cell activation is specific because signal initiation requires T cell receptor (TCR) recognition of foreign antigen peptides presented by major histocompatibility complexes (pMHC) on antigen presenting cells (APCs). Recent advances reveal that the TCR acts as a mechanoreceptor, but it remains unclear how pMHC/TCR engagement generates mechanical forces that are converted to intracellular signals. Here we propose a TCR Bending Mechanosignal (TBM) model, in which local bending of the T cell membrane on the nanometer scale allows sustained contact of relatively small pMHC/TCR complexes interspersed among large surface receptors and adhesion molecules on the opposing surfaces of T cells and APCs. Localized T cell membrane bending is suggested to increase accessibility of TCR signaling domains to phosphorylation, facilitate selective recognition of agonists that form catch bonds, and reduce noise signals associated with slip bonds.

Integrin-Functionalised Giant Unilamellar Vesicles via Gel-Assisted Formation: Good Practices and Pitfalls

Giant unilamellar vesicles (GUV) are powerful tools to explore physics and biochemistry of the cell membrane in controlled conditions. For example, GUVs were extensively used to probe cell adhesion, but often using non-physiological linkers, due to the difficulty of incorporating transmembrane adhesion proteins into model membranes. Here we describe a new protocol for making GUVs incorporating the transmembrane protein integrin using gel-assisted swelling. We report an optimised protocol, enumerating the pitfalls encountered and precautions to be taken to maintain the robustness of the protocol. We characterise intermediate steps of small proteoliposome formation and the final formed GUVs. We show that the integrin molecules are successfully incorporated and are functional.

Axial line-scanning stimulated emission depletion fluorescence correlation spectroscopy

Investigating the dynamics and interactions of biomolecules within or attached to membranes of living cells is crucial for understanding biology at the molecular level. In this pursuit, classical, diffraction-limited optical fluorescence microscopy is widely used, but it faces limitations due to (1) the heterogeneity of biomembranes on the nanoscale and (2) the intrinsic motion of membranes with respect to the focus. Here we introduce a new confocal microscopy-based fluctuation spectroscopy technique aimed at alleviating these two problems, called axial line-scanning stimulated emission depletion fluorescence correlation spectroscopy (axial ls-STED-FCS). Axial line scanning by means of a tunable acoustic gradient index of refraction lens provides a time resolution of a few microseconds, which is more than two orders of magnitude greater than that of conventional, lateral line-scanning fluorescence correlation spectroscopy (typically around 1 ms). Using STED excitation, the observation area on the membrane can be reduced 10-100 fold, resulting in sub-diffraction spatial resolution and the ability to study samples with densely labeled membranes. Due to these attractive properties, we expect that the axial ls-STED-FCS will find wide application, especially in the biomolecular sciences.

Digital holographic microscopy evaluation of dynamic cell response to electroporation

Phase-derived parameters and time autocorrelation functions were used to analyze the behavior of murine B16 cells exposed to different amplitudes of electroporation pulses. Cells were observed using an off-axis digital holographic microscope equipped with a fast camera. Series of quantitative phase images of cells were reconstructed and further processed using MATLAB codes. Projected area, dry mass density, and entropy proved to be predictors for permeabilized cells that swell or collapse. Autocorrelation functions of phase fluctuations in different regions of the cell showed a good correlation with the local effectiveness of permeabilization.

On the control of dispersion interactions between biological membranes and protein coated biointerfaces

HYPOTHESIS

Interaction of cellular membranes with biointerfaces is of vital importance for a number of medical devices and implants. Adhesiveness of these surfaces and cells is often regulated by depositing a layer of bovine serum albumin (BSA) or other protein coatings. However, anomalously large separations between phospholipid membranes and the biointerfaces in various conditions and buffers have been observed, which could not be understood using available theoretical arguments.

METHODS

Using the Lifshitz theory, we here evaluate the distance-dependent Hamaker coefficient describing the dispersion interaction between a biointerface and a membrane to understand the relative positioning of two surfaces. Our theoretical modeling is supported by experiments where the biointerface is represented by a glass substrate with deposited BSA and protein layers. These biointerfaces are allowed to interact with giant unilamellar vesicles decorated with polyethylene glycol (PEG) using PEG lipids to mimic cellular membranes and their pericellular coat.

RESULTS

We demonstrate that careful treatment of the van der Waals interactions is critical for explaining the lack of adhesiveness of the membranes with protein-decorated biointerfaces. We show that BSA alone indeed passivates the glass, but depositing an additional protein layer on the surface BSA, or producing multiple layers of proteins and BSA results in repulsive dispersion forces responsible for 100 nm large equilibrium separations between the two surfaces.

Delivery of the Radionuclide 131I Using Cationic Fusogenic Liposomes as Nanocarriers

Liposomes are highly biocompatible and versatile drug carriers with an increasing number of applications in the field of nuclear medicine and diagnostics. So far, only negatively charged liposomes with intercalated radiometals, e.g., ⁶⁴Cu, ^99mTc, have been reported. However, the process of cellular uptake of liposomes by endocytosis is rather slow. Cellular uptake can be accelerated by recently developed cationic liposomes, which exhibit extraordinarily high membrane fusion ability. The aim of the present study was the development of the formulation and the characterization of such cationic fusogenic liposomes with intercalated radioactive [¹³¹I]I^- for potential use in therapeutic applications. The epithelial human breast cancer cell line MDA-MB-231 was used as a model for invasive cancer cells and cellular uptake of [¹³¹I]I^- was monitored in vitro. Delivery efficiencies of cationic and neutral liposomes were compared with uptake of free iodide. The best cargo delivery efficiency (~10%) was achieved using cationic fusogenic liposomes due to their special delivery pathway of membrane fusion. Additionally, human blood cells were also incubated with cationic control liposomes and free [¹³¹I]I^-. In these cases, iodide delivery efficiencies remained below 3%.

Detection of sub-degree angular fluctuations of the local cell membrane slope using optical tweezers

Normal thermal fluctuations of the cell membrane have been studied extensively using high resolution microscopy and focused light, particularly at the peripheral regions of a cell. We use a single probe particle attached non-specifically to the cell-membrane to determine that the power spectral density is proportional to (frequency)-5/3 in the range of 5 Hz to 1 kHz. We also use a new technique to simultaneously ascertain the slope fluctuations of the membrane by relying upon the determination of pitch motion of the birefringent probe particle trapped in linearly polarized optical tweezers. In the process, we also develop the technique to identify pitch rotation to a high resolution using optical tweezers. We find that the power spectrum of slope fluctuations is proportional to (frequency)-1, which we also explain theoretically. We find that we can extract parameters like bending rigidity directly from the coefficient of the power spectrum particularly at high frequencies, instead of being convoluted with other parameters, thereby improving the accuracy of estimation. We anticipate this technique for determination of the pitch angle in spherical particles to high resolution as a starting point for many interesting studies using the optical tweezers.

Large-scale simulation of biomembranes incorporating realistic kinetics into coarse-grained models

Biomembranes are two-dimensional assemblies of phospholipids that are only a few nanometres thick, but form micrometre-sized structures vital to cellular function. Explicit molecular modelling of biologically relevant membrane systems is computationally expensive due to the large number of solvent particles and slow membrane kinetics. Coarse-grained solvent-free membrane models offer efficient sampling but sacrifice realistic kinetics, thereby limiting the ability to predict pathways and mechanisms of membrane processes. Here, we present a framework for integrating coarse-grained membrane models with continuum-based hydrodynamics. This framework facilitates efficient simulation of large biomembrane systems with large timesteps, while achieving realistic equilibrium and non-equilibrium kinetics. It helps to bridge between the nanometer/nanosecond spatiotemporal resolutions of coarse-grained models and biologically relevant time- and lengthscales. As a demonstration, we investigate fluctuations of red blood cells, with varying cytoplasmic viscosities, in 150-milliseconds-long trajectories, and compare kinetic properties against single-cell experimental observations.

Estimation of parameters from time traces originating from an Ornstein-Uhlenbeck process

In this article, we develop a Bayesian approach to estimate parameters from time traces that originate from an overdamped Brownian particle in a harmonic potential, or Ornstein-Uhlenbeck process (OU). We show that least-square fitting the autocorrelation function, which is often the standard way of analyzing such data, is significantly underestimating the confidence intervals of the fitted parameters. Here, we develop a rigorous maximum likelihood theory that properly captures the underlying statistics. From the analytic solution, we found that there exists an optimal measurement spacing (Δt=0.7968τ) that maximizes the statistical accuracy of the estimate for the decay-time τ of the process for a fixed number of samples N, which plays a similar role than the Nyquist-Shannon theorem for the OU process. To support our claims, we simulated time series with subsequent application of least-square and our maximum likelihood method. Our results suggest that it is quite dangerous to apply least-squares to autocorrelation functions both in terms of systematic deviations from the true parameter values and an order-of-magnitude underestimation of confidence intervals. To see whether our findings apply to other methods where autocorrelation functions are typically fitted by least-squares, we explored the analysis of membrane fluctuations and fluorescence correlation spectroscopy. In both cases, least-square fits exhibit systematic deviations from the true parameter values and significantly underestimate their confidence intervals. This fact emphasizes the need for the development of proper maximum likelihood approaches for such methods. In summary, our results have strong implications for parameter estimation for processes that result in a single exponential decay in the autocorrelation function. Our analysis can directly be applied to single-component dynamic light scattering experiments or optical trap calibration experiments.

Spontaneous cellular vibratory motions of osteocytes are regulated by ATP and spectrin network

Vibration at high frequency has been demonstrated to be anabolic for bone and embedded osteocytes. The response of osteocytes to vibration is frequency-dependent, but the mechanism remains unclear. Our previous computational study using an osteocyte finite element model has predicted a resonance effect involving in the frequency-dependent response of osteocytes to vibration. However, the cellular spontaneous vibratory motion of osteocytes has not been confirmed. In the present study, the cellular vibratory motions (CVM) of osteocytes were recorded by a custom-built digital holographic microscopy and quantitatively analyzed. The roles of ATP and spectrin network in the CVM of osteocytes were studied. Results showed the MLO-Y4 osteocytes displayed dynamic vibratory motions with an amplitude of ~80 nm, which is relied both on the ATP content and spectrin network. Spectrum analysis showed several frequency peaks in CVM of MLO-Y4 osteocytes at 30 Hz, 39 Hz, 83 Hz and 89 Hz. These peak frequencies are close to the commonly used effective frequencies in animal training and in-vitro cell experiments, and show a correlation with the computational predictions of the osteocyte finite element model. These results implicate that osteocytes are dynamic and the cellular dynamic motion is involved in the cellular mechanotransduction of vibration.

Statistical Mechanics of an Elastically Pinned Membrane: Equilibrium Dynamics and Power Spectrum

In biological settings, membranes typically interact locally with other membranes: the extracellular matrix in the exterior or internal cellular structures such as the cytoskeleton, locally pinning the membrane. Characterizing the dynamical properties of such interactions presents a difficult task. Significant progress has been achieved through simulations and experiments, yet analytical progress in modeling pinned membranes has been impeded by the complexity of governing equations. Here, we circumvent these difficulties by calculating analytically the time-dependent Green's function of the operator governing the dynamics of an elastically pinned membrane in a hydrodynamic surrounding and subject to external forces. This enables us to calculate the equilibrium power spectral density for an overdamped membrane pinned by an elastic, permanently attached spring subject to thermal excitations. By considering the effects of the finite experimental resolution on the measured spectra, we show that the elasticity of the pinning can be extracted from the experimentally measured spectrum. Membrane fluctuations can thus be used as a tool to probe mechanical properties of the underlying structures. Such a tool may be particularly relevant in the context of cell mechanics, in which the elasticity of the membrane's attachment to the cytoskeleton could be measured.

Plasmonic imaging of subcellular electromechanical deformation in mammalian cells

A membrane potential change in cells is accompanied with mechanical deformation. This electromechanical response can play a significant role in regulating action potential in neurons and in controlling voltage-gated ion channels. However, measuring this subtle deformation in mammalian cells has been a difficult task. We show a plasmonic imaging method to image mechanical deformation in single cells upon a change in the membrane potential. Using this method, we have studied the electromechanical response in mammalian cells and have observed the local deformation within the cells that are associated with cell-substrate interactions. By analyzing frequency dependence of the response, we have further examined the electromechanical deformation in terms of mechanical properties of cytoplasm and cytoskeleton. We demonstrate a plasmonic imaging approach to quantify the electromechanical responses of single mammalian cells and determine local variability related to cell-substrate interactions.

Cholesterol Depletion by MβCD Enhances Cell Membrane Tension and Its Variations-Reducing Integrity

Cholesterol depletion by methyl-β-cyclodextrin (MβCD) remodels the plasma membrane’s mechanics in cells and its interactions with the underlying cytoskeleton, whereas in red blood cells, it is also known to cause lysis. Currently it’s unclear if MβCD alters membrane tension or only enhances membrane-cytoskeleton interactions—and how this relates to cell lysis. We map membrane height fluctuations in single cells and observe that MβCD reduces temporal fluctuations robustly but flattens spatial membrane undulations only slightly. Utilizing models explicitly incorporating membrane confinement besides other viscoelastic factors, we estimate membrane mechanical parameters from the fluctuations’ frequency spectrum. This helps us conclude that MβCD enhances membrane tension and does so even on ATP-depleted cell membranes where this occurs despite reduction in confinement. Additionally, on cholesterol depletion, cell membranes display higher intracellular heterogeneity in the amplitude of spatial undulations and membrane tension. MβCD also has a strong impact on the cell membrane’s tenacity to mechanical stress, making cells strongly prone to rupture on hypo-osmotic shock with larger rupture diameters—an effect not hindered by actomyosin perturbations. Our study thus demonstrates that cholesterol depletion increases membrane tension and its variability, making cells prone to rupture independent of the cytoskeletal state of the cell.

A gradient-based, GPU-accelerated, high-precision contour-segmentation algorithm with application to cell membrane fluctuation spectroscopy

We present a novel intensity-gradient based algorithm specifically designed for nanometer-segmentation of cell membrane contours obtained with high-resolution optical microscopy combined with high-velocity digital imaging. The algorithm relies on the image oversampling performance and computational power of graphical processing units (GPUs). Both, synthetic and experimental data are used to quantify the sub-pixel precision of the algorithm, whose analytic performance results comparatively higher than in previous methods. Results from the synthetic data indicate that the spatial precision of the presented algorithm is only limited by the signal-to-noise ratio (SNR) of the contour image. We emphasize on the application of the new algorithm to membrane fluctuations (flickering) in eukaryotic cells, bacteria and giant vesicle models. The method shows promising applicability in several fields of cellular biology and medical imaging for nanometer-precise boundary-determination and mechanical fingerprinting of cellular membranes in optical microscopy images. Our implementation of this high-precision flicker spectroscopy contour tracking algorithm (HiPFSTA) is provided as open-source at www.github.com/michaelmell/hipfsta.

Membrane fluctuations and acidosis regulate cooperative binding of 'marker of self' protein CD47 with the macrophage checkpoint receptor SIRPα

Cell-cell interactions that result from membrane proteins binding weakly in trans can cause accumulations in cis that suggest cooperativity and thereby an acute sensitivity to environmental factors. The ubiquitous 'marker of self' protein CD47 binds weakly to SIRPα on macrophages, which leads to accumulation of SIRPα (also known as SHPS-1, CD172A and SIRPA) at phagocytic synapses and ultimately to inhibition of engulfment of 'self' cells - including cancer cells. We reconstituted this macrophage checkpoint with GFP-tagged CD47 on giant vesicles generated from plasma membranes and then imaged vesicles adhering to SIRPα immobilized on a surface. CD47 diffusion is impeded near the surface, and the binding-unbinding events reveal cooperative interactions as a concentration-dependent two-dimensional affinity. Membrane fluctuations out-of-plane link cooperativity to membrane flexibility with suppressed fluctuations in the vicinity of bound complexes. Slight acidity (pH 6) stiffens membranes, diminishes cooperative interactions and also reduces 'self' signaling of cancer cells in phagocytosis. Sensitivity of cell-cell interactions to microenvironmental factors - such as the acidity of tumors and other diseased or inflamed sites - can thus arise from the collective cooperative properties of flexible membranes.This article has an associated First Person interview with the first author of the paper.

Broken detailed balance and non-equilibrium dynamics in living systems: a review

Living systems operate far from thermodynamic equilibrium. Enzymatic activity can induce broken detailed balance at the molecular scale. This molecular scale breaking of detailed balance is crucial to achieve biological functions such as high-fidelity transcription and translation, sensing, adaptation, biochemical patterning, and force generation. While biological systems such as motor enzymes violate detailed balance at the molecular scale, it remains unclear how non-equilibrium dynamics manifests at the mesoscale in systems that are driven through the collective activity of many motors. Indeed, in several cellular systems the presence of non-equilibrium dynamics is not always evident at large scales. For example, in the cytoskeleton or in chromosomes one can observe stationary stochastic processes that appear at first glance thermally driven. This raises the question how non-equilibrium fluctuations can be discerned from thermal noise. We discuss approaches that have recently been developed to address this question, including methods based on measuring the extent to which the system violates the fluctuation-dissipation theorem. We also review applications of this approach to reconstituted cytoskeletal networks, the cytoplasm of living cells, and cell membranes. Furthermore, we discuss a more recent approach to detect actively driven dynamics, which is based on inferring broken detailed balance. This constitutes a non-invasive method that uses time-lapse microscopy data, and can be applied to a broad range of systems in cells and tissue. We discuss the ideas underlying this method and its application to several examples including flagella, primary cilia, and cytoskeletal networks. Finally, we briefly discuss recent developments in stochastic thermodynamics and non-equilibrium statistical mechanics, which offer new perspectives to understand the physics of living systems.

High-Affinity Ligands Can Trigger T Cell Receptor Signaling Without CD45 Segregation

How T cell receptors (TCRs) are triggered to start signaling is still not fully understood. It has been proposed that segregation of the large membrane tyrosine phosphatase CD45 from engaged TCRs initiates signaling by favoring phosphorylation of immunoreceptor tyrosine-based activation motifs (ITAMs) in the cytoplasmic domains of CD3 molecules. However, whether CD45 segregation is important to initiate triggering is still uncertain. We examined CD45 segregation from TCRs engaged to anti-CD3 scFv with high or low affinity and with defined molecular lengths on glass-supported lipid bilayers using total internal reflection microscopy. Both short and elongated high-affinity anti-CD3 scFv effectively induced similar calcium mobilization, Zap70 phosphorylation, and cytokine secretion in Jurkat T cells but CD45 segregated from activated TCR microclusters significantly less for elongated versus short anti-CD3 ligands. In addition, at early times, triggering cells with both high and low affinity elongated anti-CD3 scFv resulted in similar degrees of CD3 co-localization with CD45, but only the high-affinity scFv induced T cell activation. The lack of correlation between CD45 segregation and early markers of T cell activation suggests that segregation of CD45 from engaged TCRs is not mandatory for initial triggering of TCR signaling by elongated high-affinity ligands.

Tracking fast cellular membrane dynamics with sub-nm accuracy in the normal direction

Cellular membranes are important biomaterials with highly dynamic structures. Membrane dynamics plays an important role in numerous cellular processes, but precise tracking it is challenging due to the lack of tools with a highly sensitive and fast detection capability. Here we demonstrate a broad bandwidth optical imaging technique to measure cellular membrane displacements in the normal direction at sub-nm level detection limits and 20 μs temporal resolution (1 Hz-50 kHz). This capability allows us to study the intrinsic cellular membrane dynamics over a broad temporal and spatial spectrum. We measured the nanometer-scale stochastic fluctuations of the plasma membrane of HEK-293 cells, and found them to be highly dependent on the cytoskeletal structure of the cells. By analyzing the fluctuations, we further determine the mechanical properties of the cellular membranes. We anticipate that the method will contribute to the understanding of the basic cellular processes, and applications, such as mechanical phenotyping of cells at the single-cell level.

Membrane-Mediated Cooperativity of Proteins

Besides direct protein-protein interactions, indirect interactions mediated by membranes play an important role for the assembly and cooperative function of proteins in membrane shaping and adhesion. The intricate shapes of biological membranes are generated by proteins that locally induce membrane curvature. Indirect curvature-mediated interactions between these proteins arise because the proteins jointly affect the bending energy of the membranes. These curvature-mediated interactions are attractive for crescent-shaped proteins and are a driving force in the assembly of the proteins during membrane tubulation. Membrane adhesion results from the binding of receptor and ligand proteins that are anchored in the apposing membranes. The binding of these proteins strongly depends on nanoscale shape fluctuations of the membranes, leading to a fluctuation-mediated binding cooperativity. A length mismatch between receptor-ligand complexes in membrane adhesion zones causes repulsive curvature-mediated interactions that are a driving force for the length-based segregation of proteins during membrane adhesion.

Mapping Cell Membrane Fluctuations Reveals Their Active Regulation and Transient Heterogeneities

Shape fluctuations of the plasma membrane occur in all cells, are incessant, and are proposed to affect membrane functioning. Although studies show how membrane fluctuations are affected by cellular activity in adherent cells, their spatial regulation and the corresponding change in membrane mechanics remain unclear. In this article, we study how ATP-driven activities and actomyosin cytoskeleton impact basal membrane fluctuations in adherent cells. Using interference imaging, we map height fluctuations within single cells and compare the temporal spectra with existing theoretical models to gain insights about the underlying membrane mechanics. We find that ATP-dependent activities enhance the nanoscale z fluctuations but stretch out the membrane laterally. Although actin polymerization or myosin-II activity individually enhances fluctuations, the cortex in unperturbed cells stretches out the membrane and dampens fluctuations. Fitting with models suggest this dampening to be due to confinement by the cortex. However, reduced fluctuations on mitosis or on ATP-depletion/stabilization of cortex correlate with increased tension. Both maps of fluctuations and local temporal autocorrelation functions reveal ATP-dependent transient short-range (<2 μm) heterogeneities. Together, our results show how various ATP-driven processes differently affect membrane mechanics and hence fluctuations, while creating distinct local environments whose functional role needs future investigation.

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 κ_eff, a new expression for the effective surface tension σ_eff = σ - εk_BT/(2a_p) where k_BT is the thermal energy, a_p 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 σ_eff = 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 σ_eff 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 = σ_effR²/κ_eff > 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 σ_eff in simulations cannot but enhance our understanding of shape transitions of vesicles and cells.

The Affinity of Elongated Membrane-Tethered Ligands Determines Potency of T Cell Receptor Triggering

T lymphocytes are important mediators of adoptive immunity but the mechanism of T cell receptor (TCR) triggering remains uncertain. The interspatial distance between engaged T cells and antigen-presenting cells (APCs) is believed to be important for topological rearrangement of membrane tyrosine phosphatases and initiation of TCR signaling. We investigated the relationship between ligand topology and affinity by generating a series of artificial APCs that express membrane-tethered anti-CD3 scFv with different affinities (OKT3, BC3, and 2C11) in addition to recombinant class I and II pMHC molecules. The dimensions of membrane-tethered anti-CD3 and pMHC molecules were progressively increased by insertion of different extracellular domains. In agreement with previous studies, elongation of pMHC molecules or low-affinity anti-CD3 scFv caused progressive loss of T cell activation. However, elongation of high-affinity ligands (BC3 and OKT3 scFv) did not abolish TCR phosphorylation and T cell activation. Mutation of key amino acids in OKT3 to reduce binding affinity to CD3 resulted in restoration of topological dependence on T cell activation. Our results show that high-affinity TCR ligands can effectively induce TCR triggering even at large interspatial distances between T cells and APCs.

Binding equilibrium and kinetics of membrane-anchored receptors and ligands in cell adhesion: Insights from computational model systems and theory

The adhesion of cell membranes is mediated by the binding of membrane-anchored receptor and ligand proteins. In this article, we review recent results from simulations and theory that lead to novel insights on how the binding equilibrium and kinetics of these proteins is affected by the membranes and by the membrane anchoring and molecular properties of the proteins. Simulations and theory both indicate that the binding equilibrium constant [Formula: see text] and the on- and off-rate constants of anchored receptors and ligands in their 2-dimensional (2D) membrane environment strongly depend on the membrane roughness from thermally excited shape fluctuations on nanoscales. Recent theory corroborated by simulations provides a general relation between [Formula: see text] and the binding constant [Formula: see text] of soluble variants of the receptors and ligands that lack the membrane anchors and are free to diffuse in 3 dimensions (3D).

Cell-sized liposome doublets reveal active tension build-up driven by acto-myosin dynamics

Cells modulate their shape to fulfill specific functions, mediated by the cell cortex, a thin actin shell bound to the plasma membrane. Myosin motor activity, together with actin dynamics, contributes to cortical tension. Here, we examine the individual contributions of actin polymerization and myosin activity to tension increase with a non-invasive method. Cell-sized liposome doublets are covered with either a stabilized actin cortex of preformed actin filaments, or a dynamic branched actin network polymerizing at the membrane. The addition of myosin II minifilaments in both cases triggers a change in doublet shape that is unambiguously related to a tension increase. Preformed actin filaments allow us to evaluate the effect of myosin alone while, with dynamic actin cortices, we examine the synergy of actin polymerization and myosin motors in driving shape changes. Our assay paves the way for a quantification of tension changes triggered by various actin-associated proteins in a cell-sized system.

Nanometric thermal fluctuations of weakly confined biomembranes measured with microsecond time-resolution

We probe the bending fluctuations of bio-membranes using highly deflated giant unilamellar vesicles (GUVs) bound to a substrate by a weak potential arising from generic interactions. The substrate is either homogeneous, with GUVs bound only by the weak potential, or is chemically functionalized with a micro-pattern of very strong specific binders. In both cases, the weakly adhered membrane is seen to be confined at a well-defined distance above the surface while it continues to fluctuate strongly. We quantify the fluctuations of the weakly confined membrane at the substrate proximal surface as well as of the free membrane at the distal surface of the same GUV. This strategy enables us to probe in detail the damping of fluctuations in the presence of the substrate, and to independently measure the membrane tension and the strength of the generic interaction potential. Measurements were done using two complementary techniques - dynamic optical displacement spectroscopy (DODS, resolution: 20 nm, 10 μs), and dual wavelength reflection interference contrast microscopy (DW-RICM, resolution: 4 nm, 50 ms). After accounting for the spatio-temporal resolution of the techniques, an excellent agreement between the two measurements was obtained. For both weakly confined systems we explore in detail the link between fluctuations on the one hand and membrane tension and the interaction potential on the other hand.