Byron Goldstein

Extending the range of rate constants available from BIACORE: interpreting mass transport-influenced binding data.

Surface-based binding assays are often influenced by the transport of analyte to the sensor surface. Using simulated data sets, we test a simple two-compartment model to see if its description of transport and binding is sufficient to accurately analyze BIACORE data. First we present a computer model that can generate realistic BIACORE data. This model calculates the laminar flow of analyte within the flow cell, its diffusion both perpendicular and parallel to the sensor surface, and the reversible chemical reaction between analyte and immobilized reactant. We use this computer model to generate binding data under a variety of conditions. An analysis of these data sets with the two-compartment model demonstrates that good estimates of the intrinsic reaction rate constants are recovered even when mass transport influences the binding reaction. We also discuss the conditions under which the two-compartment model can be used to determine the diffusion coefficient of the analyte. Our results illustrate that this model can significantly extend the range of association rate constants that can be accurately determined from BIACORE.

BioNetGen: software for rule-based modeling of signal transduction based on the interactions of molecular domains

BioNetGen allows a user to create a computational model that characterizes the dynamics of a signal transduction system, and that accounts comprehensively and precisely for specified enzymatic activities, potential post-translational modifications and interactions of the domains of signaling molecules. The output defines and parameterizes the network of molecular species that can arise during signaling and provides functions that relate model variables to experimental readouts of interest. Models that can be generated are relevant for rational drug discovery, analysis of proteomic data and mechanistic studies of signal transduction.

Mathematical and computational models of immune-receptor signalling

The process of signalling through receptors of the immune system involves highly connected networks of interacting components. Understanding the often counter-intuitive behaviour of these networks requires the development of mathematical and computational models. Here, we focus on the application of these models to understand signalling through immune receptors that are involved in antigen recognition. Simple models, which ignore the details of the signalling machinery, have provided considerable insight into how ligand–receptor binding properties affect signalling outcomes. Detailed models, which include specific molecular components and interactions beyond the ligand and receptor, are difficult to develop but have already provided new mechanistic understanding and uncovered relationships that are difficult to detect by experimental observation alone. They offer hope that models might eventually predict the full spectrum of signalling behaviour.

Investigation of Early Events in FcεRI-Mediated Signaling Using a Detailed Mathematical Model

Aggregation of FcεRI on mast cells and basophils leads to autophosphorylation and increased activity of the cytosolic protein tyrosine kinase Syk. We investigated the roles of the Src kinase Lyn, the immunoreceptor tyrosine-based activation motifs (ITAMs) on the β and γ subunits of FcεRI, and Syk itself in the activation of Syk. Our approach was to build a detailed mathematical model of reactions involving FcεRI, Lyn, Syk, and a bivalent ligand that aggregates FcεRI. We applied the model to experiments in which covalently cross-linked IgE dimers stimulate rat basophilic leukemia cells. The model makes it possible to test the consistency of mechanistic assumptions with data that alone provide limited mechanistic insight. For example, the model helps sort out mechanisms that jointly control dephosphorylation of receptor subunits. In addition, interpreted in the context of the model, experimentally observed differences between the β- and γ-chains with respect to levels of phosphorylation and rates of dephosphorylation indicate that most cellular Syk, but only a small fraction of Lyn, is available to interact with receptors. We also show that although the β ITAM acts to amplify signaling in experimental systems where its role has been investigated, there are conditions under which the β ITAM will act as an inhibitor.

Activated TCRs remain marked for internalization after dissociation from pMHC

To assess the roles of serial engagement and kinetic proofreading in T cell receptor (TCR) internalization, we have developed a mathematical model of this process. Our determination of TCR down-regulation for an array of TCR mutants, interpreted in the context of the model, has provided new information about peptide-induced TCR internalization. The amount of TCR down-regulation increases to a maximum value and then declines as a function of the half-life of the bond between the TCR and peptide–major histocompatibility complex (pMHC). The model shows that this behavior, which reflects competition between serial engagement and kinetic proofreading, arises only if it is postulated that activated TCRs remain marked for internalization after dissociation from pMHC. The model also predicts that because of kinetic proofreading, the range of TCR-pMHC–binding half-lives required for T cell activation depends on the concentrations and localization of intracellular signaling molecules. We show here that kinetic proofreading provides an explanation for the different requirements for activation observed in naïve and memory T cells.

The influence of transport on the kinetics of binding to surface receptors: application to cells and BIAcore

Accurate estimation of biomolecular reaction rates from binding data, when ligands in solution bind to receptors on the surfaces of cells or biosensors, requires an understanding of the contributions of both molecular transport and reaction. Efficient estimation of parameters requires relatively simple models. In this review, we give conditions under which various transport effects are negligible and identify simple binding models that incorporate the effects of transport, when transport cannot be neglected. We consider effects of diffusion of ligands to cell or biosensor surfaces, flow in a BIAcore biosensor, and distribution of receptors in a dextran layer above the sensor surface. We also give conditions under which soluble receptors can be expected to compete effectively with surface‐bound receptors. Copyright

Approximating the effects of diffusion on reversible reactions at the cell surface: ligand-receptor kinetics

We consider the problem of determining the time dependence of the bound ligand concentration for the reversible binding of a diffusing monovalent ligand to receptors uniformly distributed over the surface of a spherical cell. We start by formulating a boundary value problem that captures the essential physics of this situation. We then introduce a systematic approximation scheme based on the method of weighted residuals. By this means we convert the initial boundary value problem into a simpler problem that requires solving only a small number of ordinary differential equations. We show how, at the lowest order of approximation, the method can be used to obtain modified chemical rate equations where, in place of fundamental rate constants, effective rate coefficients appear. These rate coefficients are functions of the ligand diffusion coefficient, the cell radius, the receptor density and other variables. We compare exact and approximate solutions and discuss under what conditions the approximate equations can be used. We also apply the method of weighted residuals to obtain approximate descriptions of the binding kinetics when (1) there are two different cell surface receptor populations that bind the ligand and (2) the cell secretes a ligand that can bind back to receptors on the cell (autocrine binding).

Competition between solution and cell surface receptors for ligand. Dissociation of hapten bound to surface antibody in the presence of solution antibody

We present a joint theoretical and experimental study on the effects of competition for ligand between receptors in solution and receptors on cell surfaces. We focus on the following experiment. After ligand and cell surface receptors equilibrate, solution receptors are introduced, and the dissociation of surface bound ligand is monitored. We derive theoretical expressions for the dissociation rate and compare with experiment. In a standard dissociation experiment (no solution receptors present) dissociation may be slowed by rebinding, i.e., at high receptor densities a ligand that dissociates from one receptor may rebind to other receptors before separating from the cell. Our theory predicts that rebinding will be prevented when S much greater than N2Kon/(16 pi 2D a4), where S is the free receptor site concentration in solution, N the number of free surface receptor sites per cell, Kon the forward rate constant for ligand-receptor binding in solution, D the diffusion coefficient of the ligand, and a the cell radius. The predicted concentration of solution receptors needed to prevent rebinding is proportional to the square of the cell surface receptor density. The experimental system used in these studies consists of a monovalent ligand, 2,4-dinitrophenyl (DNP)-aminocaproyl-L-tyrosine (DCT), that reversibly binds to a monoclonal anti-DNP immunoglobulin E (IgE). This IgE is both a solution receptor and, when anchored to its high affinity Fc epsilon receptor on rat basophilic leukemia (RBL) cells, a surface receptor. For RBL cells with 6 x 10(5) binding sites per cell, our theory predicts that to prevent DCT rebinding to cell surface IgE during dissociation requires S much greater than 2,400 nM. We show that for S = 200-1,700 nM, the dissociation rate of DCT from surface IgE is substantially slower than from solution IgE where no rebinding occurs. Other predictions are also tested and shown to be consistent with experiment.

Equilibrium Thermodynamics of Cell-Cell Adhesion Mediated by Multiple Ligand-Receptor Pairs

In many situations, cell-cell adhesion is mediated by multiple ligand-receptor pairs. For example, the interaction between T cells and antigen-presenting cells of the immune system is mediated not only by T cell receptors and their ligands (peptide-major histocompatibility complex) but also by binding of intracellular adhesion molecules. Interestingly, these binding pairs have different resting lengths. Fluorescent labeling reveals segregation of the longer adhesion molecules from the shorter T cell receptors in this case. Here, we explore the thermal equilibrium of a general cell-cell interaction mediated by two ligand-receptor pairs to examine competition between the elasticity of the cell wall, nonspecific intercellular repulsion, and bond formation, leading to segregation of bonds of different lengths at equilibrium. We make detailed predictions concerning the relationship between physical properties of the membrane and ligand-receptor pairs and equilibrium pattern formation, and suggest experiments to refine our understanding of the system. We demonstrate our model by application to the T cell/antigen-presenting-cell system and outline applications to natural killer cell adhesion.

Calculations show substantial serial engagement of T cell receptors.

The serial engagement model provides an attractive and plausible explanation for how a typical antigen presenting cell, exhibiting a low density of peptides recognized by a T cell, can initiate T cell responses. If a single peptide displayed by a major histocompatibility complex (MHC) can bind, sequentially, to different T cell receptors (TCR), then a few peptides can activate many receptors. To date, arguments supporting and questioning the prevalence of serial engagement have centered on the down-regulation of TCR after contact of T cells with antigen presenting cells. Recently, the existence of serial engagement has been challenged by the demonstration that engagement of TCR can down-regulate nonengaged bystander TCR. Here we show that for binding and dissociation rates that characterize interactions between T cell receptors and peptide-MHC, substantial serial engagement occurs. The result is independent of mechanisms and measurements of receptor down-regulation. The conclusion that single peptide-MHC engage many TCR, before diffusing out of the contact region between the antigen-presenting cell and the T cell, is based on a general first passage time calculation for a particle alternating between states in which different diffusion coefficients govern its transport.