A coupled diffusion-kinetics model for analysis of contact-area FRAP experiment

Force-induced biphasic regulation of VWF cleavage by ADAMTS13

It is crucial for hemostasis that platelets are rapidly recruited to the site of vascular injury by the adhesive ligand von Willebrand factor (VWF) multimers. The metalloproteinase ADAMTS13 regulates this hemostatic activity by proteolytically reducing the size of VWF and its proteolytic kinetics has been investigated by biochemical and single-molecule biophysical methods. However, how ADAMTS13 cleaves VWF in flowing blood remains poorly defined. To investigate the force-induced VWF cleavage, VWF A1A2A3 tridomains were immobilized and subjected to hydrodynamic forces in the presence of ADAMTS13. We demonstrated that the cleavage of VWF A1A2A3 by ADAMTS13 exhibited biphasic kinetics governed by shear stress, but not shear rate. By fitting data to the single-molecule Michaelis-Menten equation, the proteolytic constant kcat of ADAMTS13 had two distinct states. The mean proteolytic constant of the fast state (kcat-fast) was 0.005 ± 0.001 s-1, which is >10-fold faster than the slow state (kcat-slow = 0.0005 ± 0.0001 s-1). Furthermore, proteolytic constants of both states were regulated by shear stress in a biphasic manner, independent of the solution viscosity, indicating that the proteolytic activity of ADAMTS13 was regulated by hydrodynamic force. The findings provide new insights into the mechanism underlying ADAMTS13 cleaving VWF under flowing blood.

Two-dimensional measurements of receptor-ligand interactions

Gaining insight into the two-dimensional receptor-ligand interactions, which play a significant role in various pivotal biological processes such as immune response and cancer metastasis, will deepen our understanding of numerous physiological and pathological mechanisms and contribute to biomedical applications and drug design. A central issue involved is how to measure the in situ receptor-ligand binding kinetics. Here, we review several representative mechanical-based and fluorescence-based methods, and briefly discuss the strengths and weaknesses for each method. In addition, we emphasize the great importance of the combination of experimental and computational methods in studying the receptor-ligand interactions, and further studies should focus on the synergistic development of experimental and computational methods.

Inferences from FRAP data are model dependent: A subdiffusive analysis

Fluorescence recovery after photobleaching (FRAP) is a widely used biological experiment to study the kinetics of molecules that react and move randomly. Since the development of FRAP in the 1970s, many reaction-diffusion models have been used to interpret FRAP data. However, intracellular molecules are widely observed to move by anomalous subdiffusion instead of normal diffusion. In this article, we extend a popular reaction-diffusion model of FRAP to the case of subdiffusion modeled by a fractional diffusion equation. By analyzing this reaction-subdiffusion model, we show that FRAP data are consistent with both diffusive and subdiffusive motion in many scenarios. We illustrate this general result by fitting our model to FRAP data from glucocorticoid receptors in a cell nucleus. We further show that the assumed model of molecular motion (normal diffusion or subdiffusion) strongly impacts the biological parameter values inferred from a given experimentally observed FRAP curve. We additionally analyze our model in three simplified parameter regimes and discuss parameter identifiability for varying subdiffusion exponents.

Supported Lipid Bilayers and the Study of Two-Dimensional Binding Kinetics

Binding between protein molecules on contacting cells is essential in initiating and regulating several key biological processes. In contrast to interactions between molecules in solution, these events are restricted to the two-dimensional (2D) plane of the meeting cell surfaces. However, converting between the more commonly available binding kinetics measured in solution and the so-called 2D binding kinetics has proven a complicated task since for the latter several factors other than the protein-protein interaction per se have an impact. A few important examples of these are: protein density, membrane fluctuations, force on the bond and the use of auxiliary binding molecules. The development of model membranes, and in particular supported lipid bilayers (SLBs), has made it possible to simplify the studied contact to analyze these effects and to measure 2D binding kinetics of individual protein-protein interactions. We will in this review give an overview of, and discuss, how different SLB systems have been used for this and compare different methods to measure binding kinetics in cell-SLB contacts. Typically, the SLB is functionalized with fluorescently labelled ligands whose interaction with the corresponding receptor on a binding cell can be detected. This interaction can either be studied 1) by an accumulation of ligands in the cell-SLB contact, whose magnitude depends on the density of the proteins and binding affinity of the interaction, or 2) by tracking single ligands in the SLB, which upon interaction with a receptor result in a change of motion of the diffusing ligand. The advantages and disadvantages of other methods measuring 2D binding kinetics will also be discussed and compared to the fluorescence-based methods. Although binding kinetic measurements in cell-SLB contacts have provided novel information on how ligands interact with receptors in vivo the number of these measurements is still limited. This is influenced by the complexity of the system as well as the required experimental time. Moreover, the outcome can vary significantly between studies, highlighting the necessity for continued development of methods to study 2D binding kinetics with higher precision and ease.

Relationship of 2D Affinity to T Cell Functional Outcomes

T cells are critical for a functioning adaptive immune response and a strong correlation exists between T cell responses and T cell receptor (TCR): peptide-loaded MHC (pMHC) binding. Studies that utilize pMHC tetramer, multimers, and assays of three-dimensional (3D) affinity have provided advancements in our understanding of T cell responses across different diseases. However, these technologies focus on higher affinity and avidity T cells while missing the lower affinity responders. Lower affinity TCRs in expanded polyclonal populations almost always constitute a significant proportion of the response with cells mediating different effector functions associated with variation in the proportion of high and low affinity T cells. Since lower affinity T cells expand and are functional, a fully inclusive view of T cell responses is required to accurately interpret the role of affinity for adaptive T cell immunity. For example, low affinity T cells are capable of inducing autoimmune disease and T cells with an intermediate affinity have been shown to exhibit an optimal anti-tumor response. Here, we focus on how affinity of the TCR may relate to T cell phenotype and provide examples where 2D affinity influences functional outcomes.

Cadherin clusters stabilized by a combination of specific and nonspecific cis-interactions

We demonstrate a combined experimental and computational approach for the quantitative characterization of lateral interactions between membrane-associated proteins. In particular, weak, lateral (cis) interactions between E-cadherin extracellular domains tethered to supported lipid bilayers, were studied using a combination of dynamic single-molecule Förster Resonance Energy Transfer (FRET) and kinetic Monte Carlo (kMC) simulations. Cadherins are intercellular adhesion proteins that assemble into clusters at cell-cell contacts through cis- and trans- (adhesive) interactions. A detailed and quantitative understanding of cis-clustering has been hindered by a lack of experimental approaches capable of detecting and quantifying lateral interactions between proteins on membranes. Here single-molecule intermolecular FRET measurements of wild-type E-cadherin and cis-interaction mutants combined with simulations demonstrate that both nonspecific and specific cis-interactions contribute to lateral clustering on lipid bilayers. Moreover, the intermolecular binding and dissociation rate constants are quantitatively and independently determined, demonstrating an approach that is generalizable for other interacting proteins.

Cadherin Extracellular Domain Clustering in the Absence of Trans-Interactions

While both cis and trans (adhesive)-interactions cooperate in the assembly of intercellular adhesions, computational simulations have predicted that two-dimensional confinement may promote cis-oligomerization, in the absence of trans-interactions. Here, single-molecule tracking of cadherin extracellular domains on supported lipid bilayers revealed the density-dependent formation of oligomers and cis-clusters in the absence of trans-interactions. Lateral oligomers were virtually eliminated by mutating a putative cis (lateral) binding interface. At low cadherin surface coverage, wild-type and mutant cadherin diffused rapidly, consistent with the motion of a lipid molecule within a cadherin-free supported bilayer and with cadherins diffusing as monomers. Although the diffusion of mutant cadherin did not change appreciably with increasing surface coverage, the average short-time diffusion coefficient of wild-type cadherin slowed significantly above a fractional surface coverage of ∼0.01 (∼1100 molecules/μm2). A detailed analysis of molecular trajectories suggested the presence of a broad size distribution of cis-cadherin oligomers. These findings verify predictions that two-dimensional confinement promotes cis-oligomerization, in the absence of trans-interactions.

Remarkably low affinity of CD4/peptide-major histocompatibility complex class II protein interactions

The αβ T-cell coreceptor CD4 enhances immune responses more than 1 million-fold in some assays, and yet the affinity of CD4 for its ligand, peptide-major histocompatibility class II (pMHC II) on antigen-presenting cells, is so weak that it was previously unquantifiable. Here, we report that a soluble form of CD4 failed to bind detectably to pMHC II in surface plasmon resonance-based assays, establishing a new upper limit for the solution affinity at 2.5 mM. However, when presented multivalently on magnetic beads, soluble CD4 bound pMHC II-expressing B cells, confirming that it is active and allowing mapping of the native coreceptor binding site on pMHC II. Whereas binding was undetectable in solution, the affinity of the CD4/pMHC II interaction could be measured in 2D using CD4- and adhesion molecule-functionalized, supported lipid bilayers, yielding a 2D Kd of ∼5,000 molecules/μm(2) This value is two to three orders of magnitude higher than previously measured 2D Kd values for interacting leukocyte surface proteins. Calculations indicated, however, that CD4/pMHC II binding would increase rates of T-cell receptor (TCR) complex phosphorylation by threefold via the recruitment of Lck, with only a small, 2-20% increase in the effective affinity of the TCR for pMHC II. The affinity of CD4/pMHC II therefore seems to be set at a value that increases T-cell sensitivity by enhancing phosphorylation, without compromising ligand discrimination.

Kinetic Measurements Reveal Enhanced Protein-Protein Interactions at Intercellular Junctions

The binding properties of adhesion proteins are typically quantified from measurements with soluble fragments, under conditions that differ radically from the confined microenvironment of membrane bound proteins in adhesion zones. Using classical cadherin as a model adhesion protein, we tested the postulate that confinement within quasi two-dimensional intercellular gaps exposes weak protein interactions that are not detected in solution binding assays. Micropipette-based measurements of cadherin-mediated, cell-cell binding kinetics identified a unique kinetic signature that reflects both adhesive (trans) bonds between cadherins on opposing cells and lateral (cis) interactions between cadherins on the same cell. In solution, proposed lateral interactions were not detected, even at high cadherin concentrations. Mutations postulated to disrupt lateral cadherin association altered the kinetic signatures, but did not affect the adhesive (trans) binding affinity. Perturbed kinetics further coincided with altered cadherin distributions at junctions, wound healing dynamics, and paracellular permeability. Intercellular binding kinetics thus revealed cadherin interactions that occur within confined, intermembrane gaps but not in solution. Findings further demonstrate the impact of these revealed interactions on the organization and function of intercellular junctions.

Monitoring the Dynamics of T Cell Clonal Diversity Using Recombinant Peptide:MHC Technology

The capacity to probe antigen specific T cells within the polyclonal repertoire has been revolutionized by the advent of recombinant peptide:MHC (pMHC) technology. Monomers and multimers of pMHC molecules can enrich for and identify antigen specific T cells to elucidate the contributions of T cell frequency, localization, and T cell receptor (TCR) affinity during immune responses. Two-dimensional (2D) measurements of TCR–pMHC interactions are at the forefront of this field because the biological topography is replicated such that TCR and pMHC are membrane anchored on opposing cells, allowing for biologically pertinent measures of TCR antigen specificity and diversity. 2D measurements of TCR-pMHC kinetics have also demonstrated increased fidelity compared to three-dimensional surface plasmon resonance data and are capable of detecting T cell affinities that are below the detection level of most pMHC multimers. Importantly, 2D techniques provide a platform to evaluate T cell affinity and antigen specificity against multiple protein epitopes within the polyclonal repertoire directly ex vivo from sites of ongoing immune responses. This review will discuss how antigen specific pMHC molecules, with a focus on 2D technologies, can be used as effective tools to evaluate the range of TCR affinities that comprise an immune response and more importantly how the breadth of affinities determine functional outcome against a given exposure to antigen.

Insights from in situ analysis of TCR-pMHC recognition: response of an interaction network

Recognition of peptide presented by the major histocompatibility complex (pMHC) molecule by the T-cell receptor (TCR) determines T-cell selection, development, differentiation, fate, and function. Despite intensive studies on the structures, thermodynamic properties, kinetic rates, and affinities of TCR-pMHC interactions in the past two decades, questions regarding the functional outcome of these interactions, i.e. how binding of the αβ TCR heterodimer with distinct pMHCs triggers different intracellular signals via the adjacent CD3 components to produce different T-cell responses, remain unclear. Most kinetic measurements have used surface plasmon resonance, a three-dimensional (3D) technique in which fluid-phase receptors and ligands are removed from their cellular environment. Recently, several two-dimensional (2D) techniques have been developed to analyze molecular interactions on live T cells with pMHCs presented by surrogate antigen-presenting cells or supported planar lipid bilayers. The insights from these in situ analyses have provided a sharp contrast of the 2D network biology approach to the 3D reductionist approach and prompted rethinking of our current views of T-cell triggering. Based on these insights, we propose a mechanochemical coupled triggering hypothesis to explain why the in situ kinetic parameters differ so much from their 3D counterparts, yet correlate so much better with T-cell functional responses.

T cell triggering: insights from 2D kinetics analysis of molecular interactions

Interaction of the T cell receptor (TCR) with pathogen-derived peptide presented by the major histocompatibility complex (pMHC) molecule is central to adaptive immunity as it initiates intracellular signaling to trigger T cell response to infection. Kinetic parameters of this interaction have been under intensive investigation for more than two decades using soluble pMHCs and/or TCRs with at least one of them in the solution (three-dimensional (3D) methods). Recently, several techniques have been developed to enable kinetic analysis on live T cells with pMHCs presented by surrogate antigen presenting cells (APCs) or supported planar lipid bilayers (two-dimensional (2D) methods). Comparison of 2D versus 3D parameters reveals drastic differences with broader ranges of 2D affinities and on-rates and orders of magnitude faster 2D off-rates for functionally distinct pMHCs. Here we review new 2D data and discuss how it may impact previously developed models of T cell discrimination between pMHCs of different potencies.

Insights into T cell recognition of antigen: significance of two-dimensional kinetic parameters

The T cell receptor (TCR) interacts with peptide-major histocompatibility complex (pMHC) to enable T cell development and trigger adaptive immune responses. For this reason, TCR:pMHC interactions have been intensely studied for over two decades. However, the details of how various binding parameters impact T cell activation remain elusive. Most measurements were made using recombinant proteins by surface plasmon resonance, a three-dimensional (3D) technique in which fluid-phase receptors and ligands are removed from their cellular environment. This approach found TCR:pMHC interactions with relatively low affinities and slow off-rates for agonist peptides. Newer generation techniques have analyzed TCR:pMHC interactions in two dimensions (2D), with both proteins anchored in apposing plasma membranes. These approaches reveal in situ TCR:pMHC interaction kinetics that are of high affinity and exhibit rapid on- and off-rates upon interaction with agonist ligands. Importantly, 2D binding parameters correlate better with T cell functional responses to a spectrum of ligands than 3D measures.

Acoustic sensors as a biophysical tool for probing cell attachment and cell/surface interactions

Acoustic biosensors offer the possibility to analyse cell attachment and spreading. This is due to the offered speed of detection, the real-time non-invasive approach and their high sensitivity not only to mass coupling, but also to viscoelastic changes occurring close to the sensor surface. Quartz crystal microbalance (QCM) and surface acoustic wave (Love-wave) systems have been used to monitor the adhesion of animal cells to various surfaces and record the behaviour of cell layers under various conditions. The sensors detect cells mostly via their sensitivity in viscoelasticity and mechanical properties. Particularly, the QCM sensor detects cytoskeletal rearrangements caused by specific drugs affecting either actin microfilaments or microtubules. The Love-wave sensor directly measures cell/substrate bonds via acoustic damping and provides 2D kinetic and affinity parameters. Other studies have applied the QCM sensor as a diagnostic tool for leukaemia and, potentially, for chemotherapeutic agents. Acoustic sensors have also been used in the evaluation of the cytocompatibility of artificial surfaces and, in general, they have the potential to become powerful tools for even more diverse cellular analysis.

Mathematical model of viral kinetics in vitro estimates the number of E2-CD81 complexes necessary for hepatitis C virus entry

Interaction between the hepatitis C virus (HCV) envelope protein E2 and the host receptor CD81 is essential for HCV entry into target cells. The number of E2-CD81 complexes necessary for HCV entry has remained difficult to estimate experimentally. Using the recently developed cell culture systems that allow persistent HCV infection in vitro, the dependence of HCV entry and kinetics on CD81 expression has been measured. We reasoned that analysis of the latter experiments using a mathematical model of viral kinetics may yield estimates of the number of E2-CD81 complexes necessary for HCV entry. Here, we constructed a mathematical model of HCV viral kinetics in vitro, in which we accounted explicitly for the dependence of HCV entry on CD81 expression. Model predictions of viral kinetics are in quantitative agreement with experimental observations. Specifically, our model predicts triphasic viral kinetics in vitro, where the first phase is characterized by cell proliferation, the second by the infection of susceptible cells and the third by the growth of cells refractory to infection. By fitting model predictions to the above data, we were able to estimate the threshold number of E2-CD81 complexes necessary for HCV entry into human hepatoma-derived cells. We found that depending on the E2-CD81 binding affinity, between 1 and 13 E2-CD81 complexes are necessary for HCV entry. With this estimate, our model captured data from independent experiments that employed different HCV clones and cells with distinct CD81 expression levels, indicating that the estimate is robust. Our study thus quantifies the molecular requirements of HCV entry and suggests guidelines for intervention strategies that target the E2-CD81 interaction. Further, our model presents a framework for quantitative analyses of cell culture studies now extensively employed to investigate HCV infection.

The interaction between the hepatitis C virus (HCV) envelope protein E2 and the host cell surface receptor CD81 is critical for HCV entry into hepatocytes and presents a promising drug and vaccine target. Yet, the number of E2-CD81 complexes that must be formed between a virus and a target cell to enable viral entry remains unknown. Direct observation of the E2-CD81 complexes preceding viral entry has not been possible. We constructed a mathematical model of HCV viral kinetics in vitro and using it to analyze data from recent cell culture studies obtained estimates of the threshold number of E2-CD81 complexes necessary for HCV entry. We found that depending on the E2-CD81 binding affinity, between 1 and 13 complexes are necessary for HCV entry into human hepatoma-derived cells. Our study thus presents new, quantitative insights into the molecular requirements of HCV entry, which may serve as a guideline for intervention strategies targeting the E2-CD81 interaction. Further, our study shows that HCV viral kinetics in vitro can be described using a mathematical model, thus facilitating quantitative analyses of the wealth of data now emanating from cell culture studies of HCV infection.

A FRET-Based Biosensor for Imaging SYK Activities in Living Cells

Spleen tyrosine kinase (SYK) is crucial to cellular functions mediated by immunoreceptors and integrins. We have developed and characterized a new genetically-encoded Förster resonance energy transfer (FRET)-based biosensor for studying the dynamics of SYK activities in living cells at a subcellular level. It contains an N-terminal ECFP, SH2 domain, a peptide derived from a SYK substrate VAV2, and a C-terminal YPet. Upon the specific phosphorylation by SYK in vitro, the biosensor substrate peptide bound to the intramolecular SH2 domain to reduce the FRET efficiency. Transfection of the biosensor did not affect activation of the endogenous SYK in host cells. Phosphorylation of the biosensor followed the same kinetics as the endogenous VAV2. Using FRET imaging and ratiometric analysis with this SYK biosensor, we visualized and quantified the realtime activation of SYK in K562 cells upon IgG Fc engagement of Fcc receptor IIA and in mouse embryonic fibroblasts upon stimulation by the platelet derived growth factor. These results demonstrate our biosensor as a powerful tool for studying cellular signaling that involves SYK.

An improved strip FRAP method for estimating diffusion coefficients: correcting for the degree of photobleaching

Fluorescence recovery after photobleaching is a widely established method for the estimation of diffusion coefficients, strip bleaching with an associated recovery curve analysis being one of the simplest techniques. However, its implementation requires near 100% bleaching in the region of interest with negligible fluorescence loss outside, both constraints being hard to achieve concomitantly for fast diffusing molecules. We demonstrate that when these requirements are not met there is an error in the estimation of the diffusion coefficient D, either an under- or overestimation depending on which assumption is violated the most. We propose a simple modification to the recovery curve analysis incorporating the concept of the relative bleached mass m giving a revised recovery time parametrization tau=m(2)w(2)/4piD for a strip of width w. This modified model removes the requirement of 100% bleaching in the region of interest and allows for limited diffusion of the fluorophore during bleaching. We validate our method by estimating the (volume) diffusion coefficient of FITC-labelled IgG in 60% glycerol solution, D= 4.09 +/- 0.21 microm(2) s(-1), and the (surface) diffusion coefficient of a green-fluorescent protein-tagged class I MHC protein expressed at the surface of a human B cell line, D= 0.32 +/- 0.03 microm(2) s(-1) for a population of cells.

Insights into function of the immunological synapse from studies with supported planar bilayers

Innate and adaptive immunity is dependent upon reliable cell-cell communication mediated by direct interactions of cell surface receptors with ligands integrated into the surface of apposing cells or bound directly to the surface as in complement deposition or antibody mediated recognition through Fc receptors. Supported lipid bilayers formed on glass surfaces offer a useful model system in which to explore some basic features of molecular interactions in immunological relevant contacts, which include signal integration and effector functions through immunological synapses and kinapses. We have exploited that lateral mobility of molecules in the supported planar bilayers and fluorescence microscopy to develop a system for measurement of two-dimensional affinities and kinetic rates in the contact area, which is of immunological interest. Affinity measurements are based on a modified Scatchard analysis. Measurements of kinetic rates are based on fluorescence photo bleaching after recovery at the level of the entire contact area. This has been coupled to a reaction-diffusion equation that allows calculation of on- and off-rates. We have found that mixtures of ligands in supported planar bilayers can effectively activate T lymphocytes and simultaneously allow monitoring of the immunological synapse. Recent studies in planar bilayers have provided additional insights into organization principles of cell-cell interfaces. Perennial problems in understanding cell-cell communication are yielding quantitative measurements based on planar bilayers in areas of ligand-driven receptor clustering and the role of the actin cytoskeleton in immune cell activation. A major goal for the field is determining quantitative rules involved in signaling complex formation by innate and adaptive receptor systems.

Early T-cell activation biophysics

The T-cell is one of the main players in the mammalian immune response. It ensures antigen recognition at the surface of antigen-presenting cells in a complex and highly sensitive and specific process, in which the encounter of the T-cell receptor with the agonist peptide associated with the major histocompatibility complex triggers T-cell activation. While signaling pathways have been elucidated in increasing detail, the mechanism of TCR triggering remains highly controversial despite active research published in the past 10 years. In this paper, we present a short overview of pending questions on critical initial events associated with T-cell triggering. In particular, we examine biophysical approaches already in use, as well as future directions. We suggest that the most recent advances in fluorescence super-resolution imaging, coupled with the new classes of genetic fluorescent probes, will play an important role in elucidation of the T-cell triggering mechanism. Beyond this aspect, we predict that exploration of mechanical cues in the triggering process will provide new clues leading to clarification of the entire mechanism.

Supported bilayers at the vanguard of immune cell activation studies

Biological adhesion between cells is critical for development of multicellular organisms and for the function of the adaptive immune system of vertebrates. A gap in understanding of adhesion systems arises from the difficulty of collecting quantitative data on the molecular interactions underlying adhesion, which is typically studied by population statistics such as percent adhesion in the presence of empirically defined forces to separate less adherent cells. Supported lipid bilayers formed on glass surfaces offer a useful model system in which to explore some basic features of molecular interactions in adhesive contacts. We have exploited the lateral mobility of molecules in the supported planar bilayers and fluorescence microscopy to develop a system for measurement of two-dimensional affinities and kinetic rates in contact areas. Affinity measurements are based on a modified Scatchard analysis. Measurements of kinetic rates are based on fluorescence photobleaching after recovery at the level of the entire contact area. This has been coupled to a reaction-diffusion equation that allows calculation of on- and off-rates. We have found that mixtures of ligands in supported planar bilayers can effectively activate T lymphocytes and simultaneously allow monitoring of the immunological synapse. Recent studies in planar bilayers have provided additional insights into organization principles of cell-cell interfaces. Perennial problems in understanding cell-cell communication are yielding to quantitative measurements based on planar bilayers in areas of ligand driven receptor clustering and the role of the actin cytoskeleton in immune cell activation. A major goal for the field is determining quantitative rules involved in signaling complex formation.

Measuring Receptor-Ligand Binding Kinetics on Cell Surfaces: From Adhesion Frequency to Thermal Fluctuation Methods

Interactions between surface-anchored receptors and ligands mediate cell-cell and cell-environment communications in many biological processes. Molecular interactions across two apposing cell membrane are governed by two-dimensional (2D) kinetics, which are physically distinct from and biologically more relevant than three-dimensional (3D) kinetics with at least one interacting molecular species in the fluid phase. Here we review two assays for measuring 2D binding kinetics: the adhesion frequency assay and the thermal fluctuation assay. The former measures the binding frequency as a function of contact duration and extracts the force-free 2D kinetics parameters by nonlinearly fitting the data with a probabilistic model. The latter detects bond formation/dissociation by monitoring the reduction/resumption of thermal fluctuations of a force sensor. Both assays are mechanically based and operate at the level of mostly single molecular interaction, which requires ultrasensitive force techniques. Characterization of one such technique, the biomembrane force probe, is presented.

Versatile analysis of single-molecule tracking data by comprehensive testing against Monte Carlo simulations

We propose here an approach for the analysis of single-molecule trajectories which is based on a comprehensive comparison of an experimental data set with multiple Monte Carlo simulations of the diffusion process. It allows quantitative data analysis, particularly whenever analytical treatment of a model is infeasible. Simulations are performed on a discrete parameter space and compared with the experimental results by a nonparametric statistical test. The method provides a matrix of p-values that assess the probability for having observed the experimental data at each setting of the model parameters. We show the testing approach for three typical situations observed in the cellular plasma membrane: i), free Brownian motion of the tracer, ii), hop diffusion of the tracer in a periodic meshwork of squares, and iii), transient binding of the tracer to slowly diffusing structures. By plotting the p-value as a function of the model parameters, one can easily identify the most consistent parameter settings but also recover mutual dependencies and ambiguities which are difficult to determine by standard fitting routines. Finally, we used the test to reanalyze previous data obtained on the diffusion of the glycosylphosphatidylinositol-protein CD59 in the plasma membrane of the human T24 cell line.

Measuring diffusion and binding kinetics by contact area FRAP

The immunological synapse is a stable intercellular structure that specializes in substance and signal transfer from one immune cell to another. Its formation is regulated in part by the diffusion of adhesion and signaling molecules into, and their binding of countermolecules in the contact area. The stability of immunological synapses allows receptor-ligand interactions to approximate chemical equilibrium despite other dynamic aspects. We have developed a mathematical model that describes the coupled reaction-diffusion process in an established immunological synapse. In this study, we extend a previously described contact area fluorescence recovery after photobleaching (FRAP) experiment to test the validity of the model. The receptor binding activity and lateral mobility of fluorescently labeled, lipid-anchored ligands in the bilayer resulted in their accumulation, as revealed by a much higher fluorescence intensity inside the contact area than outside. After complete photobleaching of the synapse, fluorescence recovery requires ligands to dissociate and rebind, and to diffuse in and out of the contact area. Such a FRAP time course consequently provides information on reaction and diffusion, which can be extracted by fitting the model solution to the data. Surprisingly, reverse rates in the two-dimensional contact area were at least 100-fold slower than in three-dimensional solution. As previously reported in immunological synapses, a significant nonrecoverable fraction of fluorescence was observed with one of two systems studied, suggesting some ligands either dissociated or diffused much more slowly compared with other ligands in the same synapse. The combined theory and experiment thus provides a new method for in situ measurements of kinetic rates, diffusion coefficients, and nonrecoverable fractions of interacting molecules in immunological synapses and other stable cell-bilayer junctions.