Receptor clustering on a cell surface. II. theory of receptor cross-linking by ligands bearing two chemically distinct functional groups

Leveraging Covalency to Stabilize Ternary Complex Formation For Cell-Cell "Induced Proximity"

Recent advances in the field of translational chemical biology use diverse "proximity-inducing" synthetic modalities to elicit new modes of "event driven" pharmacology. These include mechanisms of targeted protein degradation and immune clearance of pathogenic cells. Heterobifunctional "chimeric" compounds like Proteolysis TArgeting Chimeras (PROTACs) and Antibody Recruiting Molecules (ARMs) leverage these mechanisms, respectively. Both systems function through the formation of reversible "ternary" or higher-order biomolecular complexes. Critical to function are key parameters, such as bifunctional molecule affinity for endogenous proteins, target residence time, and turnover. To probe the mechanism and enhance function, covalent chemical approaches have been developed to kinetically stabilize ternary complexes. These include electrophilic PROTACs and Covalent Immune Recruiters (CIRs), the latter designed to uniquely enforce cell-cell induced proximity. Inducing cell-cell proximity is associated with key challenges arising from a combination of steric and/or mechanical based destabilizing forces on the ternary complex. These factors can attenuate the formation of ternary complexes driven by high affinity bifunctional/proximity inducing molecules. This Account describes initial efforts in our lab to address these challenges using the CIR strategy in antibody recruitment or receptor engineered T cell model systems of cell-cell induced proximity. ARMs form ternary complexes with serum antibodies and surface protein antigens on tumor cells that subsequently engage immune cells via Fc receptors. Binding and clustering of Fc receptors trigger immune cell killing of the tumor cell. We applied the CIR strategy to convert ARMs to covalent chimeras, which "irreversibly" recruit serum antibodies to tumor cells. These covalent chimeras leverage electrophile preorganization and kinetic effective molarity to achieve fast and selective covalent engagement of the target ternary complex protein, e.g., serum antibody. Importantly, covalent engagement can proceed via diverse binding site amino acids beyond cysteine. Covalent chimeras demonstrated striking functional enhancements compared to noncovalent ARM analogs in functional immune assays. We revealed this enhancement was in fact due to the increased kinetic stability and not concentration, of ternary complexes. This finding was recapitulated using analogous CIR modalities that integrate peptidic or carbohydrate binding ligands with Sulfur(VI) Fluoride Exchange (SuFEx) electrophiles to induce cell-cell proximity. Mechanistic studies in a distinct model system that uses T cells engineered with receptors that recognize covalent chimeras or ARMs, revealed covalent receptor engagement uniquely enforces downstream activation signaling. Finally, this Account discusses potential challenges and future directions for adapting and optimizing covalent chimeric/bifunctional molecules for diverse applications in cell-cell induced proximity.

A general model of multivalent binding with ligands of heterotypic subunits and multiple surface receptors

Multivalent cell surface receptor binding is a ubiquitous biological phenomenon with functional and therapeutic significance. Predicting the amount of ligand binding for a cell remains an important question in computational biology as it can provide great insight into cell-to-cell communication and rational drug design toward specific targets. In this study, we extend a mechanistic, two-step multivalent binding model. This model predicts the behavior of a mixture of different multivalent ligand complexes binding to cells expressing various types of receptors. It accounts for the combinatorially large number of interactions between multiple ligands and receptors, optionally allowing a mixture of complexes with different valencies and complexes that contain heterogeneous ligand units. We derive the macroscopic predictions and demonstrate how this model enables large-scale predictions on mixture binding and the binding space of a ligand. This model thus provides an elegant and computationally efficient framework for analyzing multivalent binding.

Optimal ligand discrimination by asymmetric dimerization and turnover of interferon receptors

In multicellular organisms, antiviral defense mechanisms evoke a reliable collective immune response despite the noisy nature of biochemical communication between tissue cells. A molecular hub of this response, the interferon I receptor (IFNAR), discriminates between ligand types by their affinity regardless of concentration. To understand how ligand type can be decoded robustly by a single receptor, we frame ligand discrimination as an information-theoretic problem and systematically compare the major classes of receptor architectures: allosteric, homodimerizing, and heterodimerizing. We demonstrate that asymmetric heterodimers achieve the best discrimination power over the entire physiological range of local ligand concentrations. This design enables sensing of ligand presence and type, and it buffers against moderate concentration fluctuations. In addition, receptor turnover, which drives the receptor system out of thermodynamic equilibrium, allows alignment of activation points for ligands of different affinities and thereby makes ligand discrimination practically independent of concentration. IFNAR exhibits this optimal architecture, and our findings thus suggest that this specialized receptor can robustly decode digital messages carried by its different ligands.

First-order 'hyper-selective' binding transition of multivalent particles under force

Multivalent particles bind to targets via many independent ligand-receptor bonding interactions. This microscopic design spans length scales in both synthetic and biological systems. Classic examples include interactions between cells, virus binding, synthetic ligand-coated micrometer-scale vesicles or smaller nano-particles, functionalised polymers, and toxins. Equilibrium multivalent binding is a continuous yet super-selective transition with respect to the number of ligands and receptors involved in the interaction. Increasing the ligand or receptor density on the two particles leads to sharp growth in the number of bound particles at equilibrium. Here we present a theory and Monte Carlo simulations to show that applying mechanical force to multivalent particles causes their adsorption/desorption isotherm on a surface to become sharper and more selective, with respect to variation in the number of ligands and receptors on the two objects. When the force is only applied to particles bound to the surface by one or more ligands, then the transition can become infinitely sharp and first-order-a new binding regime which we term 'hyper-selective'. Force may be imposed by, e.g. flow of solvent around the particles, a magnetic field, chemical gradients, or triggered uncoiling of inert oligomers/polymers tethered to the particles to provide a steric repulsion to the surface. This physical principle is a step towards 'all or nothing' binding selectivity in the design of multivalent constructs.

Biorecognition: A key to drug-free macromolecular therapeutics

This review highlights a new paradigm in macromolecular nanomedicine - drug-free macromolecular therapeutics (DFMT). The effectiveness of the new system is based on biorecognition events without the participation of low molecular weight drugs. Apoptosis of cells can be initiated by the biorecognition of complementary peptide/oligonucleotide motifs at the cell surface resulting in the crosslinking of slowly internalizing receptors. B-cell CD20 receptors and Non-Hodgkin lymphoma (NHL) were chosen as the first target. Exposing cells to a conjugate of one motif with a targeting ligand decorates the cells with this motif. Further exposure of decorated cells to a macromolecule (synthetic polymer or human serum albumin) containing multiple copies of the complementary motif as grafts results in receptor crosslinking and apoptosis induction in vitro and in vivo. The review focuses on recent developments and explores the mechanism of action of DFMT. The altered molecular signaling pathways demonstrated the great potential of DFMT to overcome rituximab resistance resulting from either down-regulation of CD20 or endocytosis and trogocytosis of rituximab/CD20 complexes. The suitability of this approach for the treatment of blood borne cancers is confirmed. In addition, the widespread applicability of DFMT as a new concept in macromolecular therapeutics for numerous diseases is exposed.

Dissecting FcγR Regulation through a Multivalent Binding Model

Many immune receptors transduce activation across the plasma membrane through their clustering. With Fcγ receptors (FcγRs), this clustering is driven by binding to antibodies of differing affinities that are in turn bound to multivalent antigen. As a consequence of this activation mechanism, accounting for and rationally manipulating immunoglobulin (Ig)G effector function is complicated by, among other factors, differing affinities between FcγR species and changes in the valency of antigen binding. In this study, we show that a model of multivalent receptor-ligand binding can effectively account for the contribution of IgG-FcγR affinity and immune complex valency. This model in turn enables us to make specific predictions about the effect of immune complexes of defined composition. In total, these results enable both rational immune complex design for a desired IgG effector function and the deconvolution of effector function by immune complexes.

Quantitative Analysis of Ligand Induced Heterodimerization of Two Distinct Receptors

The induced dimerization of two distinct receptors through a heterobifunctional inducer is prevalent among all levels of cellular signaling processes, yet its complexity poses difficulty for systematic quantitative analysis. This paper first shows how to calculate the amount of any possible complex or monomer of heteroligand and two receptors present at equilibrium. The theory is subsequently applied to the determination of three independent equilibrium parameters involved in the rapamycin induced FKBP and FRB dimerization, in which all parameters were simultaneously estimated using one set of fluorescence resonance energy transfer (FRET) experiments. A MATLAB script is provided for parametric fitting.

A comprehensive mathematical model for three-body binding equilibria

Three-component systems are often more complex than their two-component counterparts. Although the reversible association of three components in solution is critical for a vast array of chemical and biological processes, no general physical picture of such systems has emerged. Here we have developed a general, comprehensive framework for understanding ternary complex equilibria, which relates directly to familiar concepts such as EC50 and IC50 from simpler (binary complex) equilibria. Importantly, application of our model to data from the published literature has enabled us to achieve new insights into complex systems ranging from coagulation to therapeutic dosing regimens for monoclonal antibodies. We also provide an Excel spreadsheet to assist readers in both conceptualizing and applying our models. Overall, our analysis has the potential to render complex three-component systems--which have previously been characterized as "analytically intractable"--readily comprehensible to theoreticians and experimentalists alike.

Stochastic models of receptor oligomerization by bivalent ligand

In this paper, we develop stochastic models of receptor binding by a bivalent ligand. A detailed kinetic study allows us to analyse the role of cross-linking in cell activation by receptor oligomerization. We show how oligomer formation could act to buffer intracellular signalling against stochastic fluctuations. In addition, we put forward the hypothesis that formation of long linear oligomers increases the range of ligand concentration to which the cell is responsive, whereas formation of closed oligomers increases ligand concentration specificity. Thus, different physiological functions requiring different degrees of specificity to ligand concentration would favour formation of oligomers with different lengths and geometries. Furthermore, provided that ligand concentration specificity is taken as a design principle, our model enables us to estimate parameters, such as the minimum proportion of receptors, that must engage in oligomer formation in order to trigger a cellular response.

The kinetics of analyte capture on nanoscale sensors

This article presents a number of kinetic analyses related to binding processes relevant to capture of target analyte species in nanoscale cantilever-type devices designed to detect small concentrations of biomolecules. The overall analyte capture efficiency is a crucial measure of the ultimate sensitivity of such devices, and a detailed kinetic analysis tells us how rapidly such measurements may be made. We have analyzed the capture kinetics under a variety of conditions, including the possibility of so-called surface-enhanced ligand capture. One of the modalities studied requires ligand capture through a cross-linking mechanism, and it was found that this mode may provide a robust and sensitive approach to biomolecular detection. For the two modalities studied, we find that detection of specific biomolecules down to concentration levels of 1 nM or less appear to be quite feasible for the device configurations studied.

A quantitative approach for studying IgE-FcepsilonRI aggregation

Aggregation of cell surface receptors is a ubiquitous means of initiating signal transduction in many cellular systems. In this manuscript, we describe a combined theoretical and experimental approach based on multiparameter flow cytometry for measuring the time course of ligand induced aggregation of IgE-FcepsilonRI on RBL cells. By fluorescently labeling both the ligand and surface IgE (sIgE), we have developed an assay that permits us to simultaneously measure both occupancy of sIgE combining sites and association of antigen with the cell surface. This allows for a direct calculation of the degree of receptor aggregation present on the cell. By employing new mixing technologies developed for flow cytometry, we are able to look at aggregation in the sub second time domain. To extend our work, we have synthesized a new set of chemically well defined ligands (of valences 1-3) to use as probes in our studies. We show that the magnitude of the cellular response is dramatically increased as the valence of our ligand is raised from two to three.

Quantifying aggregation of IgE-FcepsilonRI by multivalent antigen

Aggregation of cell surface receptors by multivalent ligand can trigger a variety of cellular responses. A well-studied receptor that responds to aggregation is the high affinity receptor for IgE (FcepsilonRI), which is responsible for initiating allergic reactions. To quantify antigen-induced aggregation of IgE-FcepsilonRI complexes, we have developed a method based on multiparameter flow cytometry to monitor both occupancy of surface IgE combining sites and association of antigen with the cell surface. The number of bound IgE combining sites in excess of the number of bound antigens, the number of bridges between receptors, provides a quantitative measure of IgE-FcepsilonRI aggregation. We demonstrate our method by using it to study the equilibrium binding of a haptenated fluorescent protein, 2,4-dinitrophenol-coupled B-phycoerythrin (DNP25-PE), to fluorescein isothiocyanate-labeled anti-DNP IgE on the surface of rat basophilic leukemia cells. The results, which we analyze with the aid of a mathematical model, indicate how IgE-FcepsilonRI aggregation depends on the total concentrations of DNP25-PE and surface IgE. As expected, we find that maximal aggregation occurs at an optimal antigen concentration. We also find that aggregation varies qualitatively with the total concentration of surface IgE as predicted by an earlier theoretical analysis.

The kinetics of bivalent ligand-bivalent receptor aggregation: ring formation and the breakdown of the equivalent site approximation

When bivalent ligands capable of bridging binding sites on two different receptors interact with bivalent receptors, aggregates form. The aggregates can be of two types: chains (open structures containing n receptors, n-1 doubly bound ligands and 0, 1, or 2 singly bound ligands) and rings (closed structures containing n receptors and n doubly bound ligands). Both types of aggregates have been detected experimentally. In general, to determine the time dependence of the concentration of any particular aggregate requires solving an infinite set of coupled ordinary differential equations (ODEs). Perelson and DeLisi [19] showed that great simplification results if all receptor binding sites are equivalent, i.e., the binding properties of a site on a receptor are independent of the size of the aggregate the receptor is in. If only chains form, the problem reduces to solving two coupled ODEs for the concentrations of singly and doubly bound ligands. From the solutions to these ODEs, the time dependence of the entire aggregate size distribution can be determined. We show that the equivalent site approximation as formulated by Perelson and DeLisi [19] is incompatible with ring formation. We then present a modified equivalent site approximation that is useful if chains of any size can form but rings above a certain size (k) cannot. We show how to reduce the resulting infinite set of coupled ODEs to a closed system of at most 4k + 2 ODEs for the ligand concentrations, the ring concentrations, and the concentrations of all chains up to size k. Although we can only predict the kinetics of aggregate formation for aggregates of size k or less, at equilibrium the modified equivalent site approximation yields the complete aggregate size distribution.

The effect of co-operativity on the equilibrium binding of symmetric bivalent ligands to antibodies: theoretical results with application to histamine release from basophils

A theory for the co-operative binding of bivalent ligands to cell surface or solution antibody is presented. The theory treats both negative co-operativity, where the binding of a ligand to one site on an antibody makes it more difficult to bind to the second site, and positive co-operativity, where the binding of a ligand to one site on an antibody makes it easier to bind to the second site. Candidates for bivalent ligands exhibiting negative co-operativity (caused probably by steric hindrance) are certain anti-immunoglobulin antibodies. We show how to calculate the amount of ligand bound, the fraction of antibody in cross-links (i.e. in ligand-antibody aggregates) and the fraction of antibody in any size ligand-antibody aggregate. With sample calculations it is demonstrated that there can be major differences in the binding and cross-linking properties of co-operative and non-co-operative bivalent ligands. We discuss how the theory can be used to analyze experiments where human basophils or rat basophilic leukemia cells are exposed to bivalent ligands that bind co-operatively to immunoglobulin E.

A method for determining whether the descending limb of a biphasic histamine release curve reflects insufficient cross-linking

We introduce a kinetic method for determining whether the descending limb of a biphasic histamine release dose-response curve is the result of insufficient cross-linking, and delineate conditions under which it is applicable. The method involves examining kinetic curves showing for various fixed antigen concentrations the cumulative amount of histamine release as a function of time. From the slope of the kinetic curves measured at some fixed time one determines how the rate of release depends on concentration. We show under very general conditions that if the dose-response curve for histamine release reaches a peak, and then decreases over a concentration interval in which the rate of release does not decline, then the decline in the dose-response curve cannot be due to insufficient cross-linking. Consequently, a characteristic feature of antigen-excess inhibition of histamine release due to mechanisms other than insufficient cross-linking is the crossing of a kinetic curve generated at a suboptimal antigen concentration by a kinetic curve generated at a supraoptimal antigen concentration. We show that the technique is easily executed experimentally and provide kinetic evidence-suggesting that the rabbit basophils the antigen-excess inhibition of histamine release by bis-benzylpenicilloyl-1,6-diaminohexane (BPO2) is due to insufficient cross-linking, whereas the antigen-excess inhibition observed with ovalbumin probably is due to more complete desensitization mechanisms.

Theory of equilibrium binding of a bivalent ligand to cell surface antibody: the effect of antibody heterogeneity on cross-linking

We investigate the equilibrium binding of symmetric bivalent ligands to a heterogeneous population of symmetric bivalent cell surface receptors. The receptors are heterogeneous in their binding affinities (equilibrium binding constants) for the ligand. For any distribution of receptor binding affinities we show how to calculate the total concentration of receptors that are cross-linked by the ligand, i.e., the concentration of cell surface aggregates composed of two or more receptors, as well as the concentration of any given aggregate. We show that certain qualitative properties of cross-linking which hold for homogeneous antibody populations fail to hold in the heterogeneous case. We use our results to interpret certain in vitro experiments in which synthetic bivalent haptens are used to trigger histamine release from basophils which have on their surface antibody specific for the hapten.