Time-dependent ligand current into a single cell performing chemoreception

We determine the ligand current into a single spherical cell which carries a large number of receptors on its surface. Initially, this cell is placed into a medium which contains ligands at uniform concentration. The time-dependent ligand distribution is calculated, from which the time-dependent ligand current into the cell is derived. If the ligand concentration is kept constant at distances comparable to the radius of the cell the stationary state sets in at times comparable to the T1 necessary for ligands to travel a distance of the order of the radius of the cell. If the ligand concentration is kept constant at infinity the stationary state sets in at a time which is about 1000T1 for typical values of the parameters.     

Chemoreception by a cell with age-dependent receptor binding sites

The authors determine the time-dependent ligand current into a spherical cell that is covered with a large number of age-dependent receptors. These receptors can be in either of two states: active (i.e., available for ligand binding) or inactive. An active receptor turns inactive upon binding a ligand, and it can reappear as active at some later time. The transition inactive----active is treated as a probabilistic process. The ligand distribution around the cell is determined analytically in terms of this distribution at the cell surface. A set of nonlinear integral equations is derived for the distribution at the cell surface, which is solved numerically. In this way the time-dependent ligand current into the cell as well as the average active receptor population at the cell surface are determined.     

Autocrine ligand binding to cell receptors. Mathematical analysis of competition by solution "decoys".

Autocrine ligands have been demonstrated to regulate cell proliferation, cell adhesion, and cell migration in a number of different systems and are believed to be one of the underlying causes of malignant cell transformation. Binding of these ligands to their cellular receptors can be compromised by diffusive transport of ligand away from the secreting cell. Exogenous addition of antibodies or solution receptors capable of competing with cellular receptors for these autocrine ligands has been proposed as a means of inhibiting autocrine-stimulated cell behavioral responses. Such "decoys" complicate cellular binding by offering alternative binding targets, which may also be capable of aiding or abating transport of the ligand away from the cell surface. We present a mathematical model incorporating autocrine ligand production and the presence of competing cellular and solution receptors. We elucidate effects of key system parameters including ligand diffusion rate, binding rate constants, cell density, and secretion rate on the ability of solution receptors to inhibit cellular receptor binding. Both plated and suspension cell systems are considered. An approximate analytical expression relating the key parameters to the critical concentration of solution "decoys" required for inhibition is derived and compared to the numerical calculations. We find that in order to achieve essentially complete inhibition of surface receptor binding, the concentration of decoys may need to be as much as four to eight orders of magnitude greater than the equilibrium disociation constant for ligand binding to surface receptors.     

Cohort movement of different ligands and receptors in the intracellular endocytic pathway of alveolar macrophages

The rate of movement of different receptors and ligands through the intracellular endocytic apparatus was studied in alveolar macrophages. Cells were exposed to iodinated alpha-macroglobulin-protease complexes, mannose terminal glycoproteins, diferric transferrin, and maleylated proteins. By use of the diaminobenzidine density shift procedure, we demonstrated that these ligands were internalized into the same endocytic vesicle. We then compared the rates of transfer to the lysosome or recycling to the cell surface of different ligands/receptors contained in the same endosome. We found that although the rate constant for degradation was ligand specific, the lag time prior to the initiation of degradation was the same for all three ligands. We also found that molecules taken up nonspecifically by fluid-phase pinocytosis had the same lag time prior to degradation as ligands internalized via receptor-mediated endocytosis. These data suggest that different molecules within the same endocytic compartment are transferred to the lysosome (or degradative compartment) at the same rate. We measured the rate of return of receptors to the cell surface by either inactivating surface receptors by protease treatment at 0 degrees C, or by incubating cells with saturating amounts of nonradioactive ligand at 37 degrees C. We then measured the rate of appearance of "new" receptors on the cell surface. Using these approaches, we found that three different receptors were transferred from internal pools to the cell surface at the same rate. The rate of transfer was independent of whether receptors were initially occupied or unoccupied. Our observations indicate that receptor/ligands, once inside alveolar macrophages, are transported by vesicles which transfer their contents as a cohort from one compartment to another. The rate of movement of these receptors is determined by the movement of vesicles and is independent of their content.     

Interrupting autocrine ligand-receptor binding: comparison between receptor blockers and ligand decoys.

Stimulation of cell behavioral functions by ligand/receptor binding can be accomplished in autocrine fashion, where cells secrete ligand capable of binding to receptors on their own surfaces. This proximal secretion of autocrine ligands near the surface receptors on the secreting cell suggests that control of these systems by inhibitors of receptor/ligand binding may be more difficult than for systems involving exogenous ligands. Hence, it is of interest to predict the conditions under which successful inhibition of cell receptor binding by the autocrine ligand can be expected. Previous theoretical work using a compartmentalized model for autocrine cells has elucidated the conditions under which addition of solution decoys for the autocrine ligand can interrupt cell receptor/ligand binding via competitive binding of the secreted molecules (Forsten, K. E., and D. A. Lauffenburger. 1992. Biophys. J. 61:1-12.) We now apply a similar modeling approach to examine the addition of solution blockers targeted against the cell receptor. Comparison of the two alternative inhibition strategies reveals that a significantly lower concentration of receptor blockers, compared to ligand decoys, will obtain a high degree of inhibition. The more direct interruption scheme characteristic of the receptor blockers may make them a preferred strategy when feasible.     

A response calculus for immobilized T cell receptor ligands

To address the molecular mechanism of T cell receptor (TCR) signaling, we have formulated a model for T cell activation, termed the 2D-affinity model, in which the density of TCR on the T cell surface, the density of ligand on the presenting surface, and their corresponding two-dimensional affinity determine the level of T cell activation. When fitted to T cell responses against purified ligands immobilized on plastic surfaces, the 2D-affinity model adequately simulated changes in cellular activation as a result of varying ligand affinity and ligand density. These observations further demonstrated the importance of receptor cross-linking density in determining TCR signaling. Moreover, it was found that the functional two-dimensional affinity of TCR ligands was affected by the chemical composition of the ligand-presenting surface. This makes it possible that cell-bound TCR ligands, despite their low affinity in solution, are of optimal two-dimensional affinity thereby allowing effective TCR binding under physiological conditions, i.e. at low ligand densities in cellular interfaces.     

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.     

Transmembrane interactions and the mechanisms of transport of proteins across membranes

We have made observations, by double fluorescence staining of the same cell, of the distributions of surface receptors, and of intracellular actin and myosin, on cultured normal fibroblasts and other flat cells, and on lymphocytes and other rounded cells. The binding of multivalent ligands (a lectin or specific antibodies) to a cell surface receptor on flat cells clusters the cell receptors into small patches, which line up directly over the actin- and myosin-containing stress fibers inside the cell. Similar ligands binding to rounded cells can cause their surface receptors to be collected into caps on the surface, and these caps are invariably found to be associated with concentrations of actin and myosin under the capped membrane. Although these ligand-induced surface phenomena appear to be different on flat and rounded cells, we propose that in both cases clusters of receptors become linked across the membrane to actin- and myosin-containing structures. In flat cells these structures are very long stress fibers; therefore, when clusters of receptors become linked to these fibers, the clusters are immobilized. In round cells, membrane-associated actin- and myosin-containing structures are apparently much less extensive than in flat cells; therefore, clusters of receptors linked to these structures are still mobile in the plane of the membrane. We suggest that in this case the clusters are then actively collected into a cap by an analogue of the muscle sliding filament mechanism. To explain the transmembrane linkage, we propose that actin is associated with the plasma membrane as a peripheral protein which is directly or indirectly bound to an integral protein (or proteins) X of the membrane. Individual molecules of any receptor are not bound to X, but after they are specifically clustered into patches, a patch of receptors then becomes bound to S and hence to actin/myosin. Patching and capping of specific receptors on rounded cells is often accompanied by a specific endocytosis of the ligand-receptor complexes. This represents one common transport mechanism of a protein (the ligand) across the plasma membrane. The possibility is discussed that this type of endocytosis is mediated by a transmembrane linkage of the clustered receptor to actin/myosin. Another mechanism of endocytosis involves the “coated pit” structures that are observed by electron microscopy of plasma membranes. The possible relationships between an actin/myosin and a coated pit mechanism of endocytosis are explored.     

Clustering of ligand on the surface of a particle enhances adhesion to receptor-bearing cells

Human leukocytes express a receptor that mediates the binding of cells and particles coated with C3bi, a fragment of the third component of complement. Previous data indicate that the capacity of this receptor to mediate binding is regulated by changes in its aggregation state. Randomly distributed receptors bind ligand very inefficiently, but stimulation of polymorphonuclear leukocytes with phorbol esters causes a ligand-independent clustering of the receptors in the membrane, and the clustered receptors avidly bind C3bi-coated cells (1). We examined whether the aggregation state of surface-bound ligands also affects the efficiency of binding between receptors and ligands. We found that erythrocytes bearing C3bi in clusters were bound by both macrophages and polymorphonuclear leukocytes far more avidly than erythrocytes bearing the same number of ligands in random array. We made similar observations with erythrocytes coated with C3b, a ligand that is recognized by a separate receptor. Our observations show that the ability of a receptor-bearing cell to bind particles coated with the corresponding ligands is dramatically affected by the distribution of ligand on the surface of the particle. Cell-cell interactions may thus be regulated by alterations in the two-dimensional distribution of receptors and ligands on opposing cell surfaces.     

Structures of an ActRIIB:activin A complex reveal a novel binding mode for TGF-beta ligand:receptor interactions

The TGF-beta superfamily of ligands and receptors stimulate cellular events in diverse processes ranging from cell fate specification in development to immune suppression. Activins define a major subgroup of TGF-beta ligands that regulate cellular differentiation, proliferation, activation and apoptosis. Activins signal through complexes formed with type I and type II serine/threonine kinase receptors. We have solved the crystal structure of activin A bound to the extracellular domain of a type II receptor, ActRIIB, revealing the details of this interaction. ActRIIB binds to the outer edges of the activin finger regions, with the two receptors juxtaposed in close proximity, in a mode that differs from TGF-beta3 binding to type II receptors. The dimeric activin A structure differs from other known TGF-beta ligand structures, adopting a compact folded-back conformation. The crystal structure of the complex is consistent with recruitment of two type I receptors into a close packed arrangement at the cell surface and suggests that diversity in the conformational arrangements of TGF-beta ligand dimers could influence cellular signaling processes.     

Analysis of intracellular receptor/ligand sorting in endosomes

After binding to specific cell surface receptors, many extracellular ligand molecules are internalized via the process termed receptor-mediated endocytosis. Within the cell, in endosomes, a sorting process occurs: receptors and ligands are directed along various intracellular pathways. The extent of this intracellular separation of receptors from ligands has been shown experimentally to vary with receptor and ligand properties such as binding affinity and valency. In this paper, we propose and analyze a simple model mechanism for the sorting process based on binding and dissociation kinetics along with diffusive molecular transport. We show that the outcome of the sorting process can be directly linked to measurable parameters such as the intrinsic rate constants for the binding to, dissociation from, and crosslinking of receptors by ligands. We further show that this mechanism is able to account for the wide range of reported experimental observations. Manipulation of ligand and receptor properties guided by the results presented here may enable the outcome of the sorting process to be controlled.     

Three-dimensional EM structure of the ectodomain of integrin {alpha}V{beta}3 in a complex with fibronectin

Integrins are alphabeta heterodimeric cell surface receptors that mediate transmembrane signaling by binding extracellular and cytoplasmic ligands. The ectodomain of integrin alphaVbeta3 crystallizes in a bent, genuflexed conformation considered to be inactive (unable to bind physiological ligands in solution) unless it is fully extended by activating stimuli. We generated a stable, soluble complex of the Mn(2+)-bound alphaVbeta3 ectodomain with a fragment of fibronectin (FN) containing type III domains 7 to 10 and the EDB domain (FN7-EDB-10). Transmission electron microscopy and single particle image analysis were used to determine the three-dimensional structure of this complex. Most alphaVbeta3 particles, whether unliganded or FN-bound, displayed compact, triangular shapes. A difference map comparing ligand-free and FN-bound alphaVbeta3 revealed density that could accommodate the RGD-containing FN10 in proximity to the ligand-binding site of beta3, with FN9 just adjacent to the synergy site binding region of alphaV. We conclude that the ectodomain of alphaVbeta3 manifests a bent conformation that is capable of stably binding a physiological ligand in solution.     

Analysis of intracellular receptor/ligand sorting. Calculation of mean surface and bulk diffusion times within a sphere.

Cell surface receptors bind extracellular ligand molecules and transport those ligands into the cell by a process termed receptor-mediated endocytosis. Receptor and ligand molecules are sorted from one another after endocytosis, apparently within a structure consisting of intracellular vesicles and connected thin tubules. The experimental observation is that most free (unbound) ligand molecules are found in the lumen of the vesicles and receptors are located primarily within the tubules. Because equilibrium and geometric considerations do not explain this segregation, a kinetic scheme involving the passive diffusion of molecules from a vesicle into a tubule is investigated. Two possible sorting mechanisms are considered: first, that receptors are able to move into tubules more rapidly than ligand molecules due to an advantage in dimensionality and, second, that receptors diffusing into tubules are trapped there while ligands are not. Mean diffusion times for receptor and ligand movement into a tubule are calculated by solving Poisson's equation in two and three dimensions, respectively, on the surface of and within a sphere. Using estimated parameter values, we found that only the second scheme is able to account for the experimentally observed sorting. An estimate is obtained for the length of time a tubule and vesicle must be connected in order to remove a significant number of receptors into a tubule. The fraction of free ligand that is "mis-sorted" with the recycling receptor population and thus exocytosed is also determined.     

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.This work was performed under the auspices of the Department of Energy and supported by Grant AI 16465 from the National Institute of Allergy and Infectious Diseases.     

Dpp gradient formation by dynamin-dependent endocytosis: receptor trafficking and the diffusion model

Developing cells acquire positional information by reading the graded distribution of morphogens. In Drosophila, the Dpp morphogen forms a long-range concentration gradient by spreading from a restricted source in the developing wing. It has been assumed that Dpp spreads by extracellular diffusion. Under this assumption, the main role of endocytosis in gradient formation is to downregulate receptors at the cell surface. These surface receptors bind to the ligand and thereby interfere with its long-range movement. Recent experiments indicate that Dpp spreading is mediated by Dynamin-dependent endocytosis in the target tissue, suggesting that extracellular diffusion alone cannot account for Dpp dispersal. Here, we perform a theoretical study of a model for morphogen spreading based on extracellular diffusion, which takes into account receptor binding and trafficking. We compare profiles of ligand and surface receptors obtained in this model with experimental data. To this end, we monitored directly the pool of surface receptors and extracellular Dpp with specific antibodies. We conclude that current models considering pure extracellular diffusion cannot explain the observed role of endocytosis during Dpp long-range movement.     

Phorbol esters and calcium ionophores inhibit internalization and accelerate recycling of receptors in macrophages

Exposure of macrophages to phorbol esters or the calcium ionophore A23187 increases the number of several surface receptors due to recruitment of receptors from internal pools (Buys, S. S., Keogh, E. A., and Kaplan, J. (1984) Cell 38, 569-576). We have examined the mechanism by which these agents increase surface receptor number. Cells which were preloaded with either fluid phase or receptor-mediated ligands did not lose ligand following exposure to ionophore or phorbol ester. The rate of movement of ligands to the lysosome was also unaffected. These results suggest that A23187 does not induce the fusion of ligand-containing compartments with the cell surface. Ionophore treatment did, however, produce a severalfold increase in the rate at which unoccupied receptors reappear on the cell surface. These results suggest that the compartment of receptors affected by the ionophore formed subsequent to the dissociation of ligand from receptor. The altered rate of receptor reappearance was transitory (90 s), and the increase in receptor number was subsequently maintained by a decrease in the rate of internalization. Changes in the rate of receptor internalization did not correlate with changes in the rate of fluid phase pinocytosis, suggesting that the effect on receptor internalization was selective.     

Molecular and cellular mechanisms of receptor-mediated endocytosis.

In general, receptors are involved in pathways of endocytosis, either constitutive or ligand induced. These receptors cluster in clathrin-coated pits, enter the cell via clathrin-coated vesicles, pass through an acidified endosome in which the receptors and ligands are sorted, and then either recycle to the cell surface, become stored intracellularly, or are degraded in lysosomes. The internalization pathways serve a variety of functions, such as nutrient uptake, removal of activated proteins, clearance of macromolecules, opportunistic entry of certain viruses and toxins, dissociation and degradation of ligand, and receptor-level regulation. Many receptors follow more than one intracellular pathway, depending on the cell type, receptor concentration, type of ligand, ligand valency, and ligand concentration. Although endocytosis is common to all nucleated eukaryotic cells, the factors that regulate these receptor-mediated endocytic pathways are not fully understood. Defective receptors that are not capable of undergoing normal endocytosis can lead to certain disease states, as in the case of familial hypercholesteremia (FH). This review has three objectives: (i) to describe the different routes that receptors and ligands follow after internaliation; (ii) to describe the potential mechanisms which regulate the initiation and subsequent sorting of receptors and ligands so they reach their final destination; and (iii) to describe the potential functions of receptor-mediated endocytosis.     

Analysis of the steady state binding, internalization, and degradation of human interferon-alpha2

Scatchard analyses of the equilibrium binding of radiolabeled human interferon-alpha2 (huIFN-alpha2) to Madin-Darby bovine kidney cells previously exposed to subsaturating concentrations of IFN-alpha showed approximately a 50% decrease in the number of cell surface receptors and no change in the apparent dissociation constant, Kd, compared with cells not exposed to interferon. The steady state equations describing the interaction of polypeptide ligands with cell surface receptors under physiological conditions (Wiley, H.S., and Cunningham, D.D. (1981) Cell 25, 433-440) have allowed us to determine, under steady state conditions, the rate of insertion of receptors into the cell membrane, the endocytic rate constant of occupied receptors, the rate constant of turnover of unoccupied receptors, and the rate of hydrolysis of internalized ligand. Our results indicate that occupied and unoccupied interferon receptors are cleared from the cell surface at approximately the same rate. This suggests that the down-regulation of the huIFN-alpha2 receptor on Madin-Darby bovine kidney cells by huIFN-alpha2 differs from that of several other surface receptors for polypeptide hormones and growth factors analyzed on cultured cells in that the binding of huIFN-alpha2 to its receptor does not increase the rate of receptor endocytosis.     

Human NK cells in acute myeloid leukaemia patients: analysis of NK cell-activating receptors and their ligands

Natural killer (NK) cell activation is strictly regulated to ensure that healthy cells are preserved, but tumour-transformed or virus-infected cells are recognized and eliminated. To carry out this selective killing, NK cells have an ample repertoire of receptors on their surface. Signalling by inhibitory and activating receptors by interaction with their ligands will determine whether the NK cell becomes activated and kills the target cell. Here, we show reduced expression of NKp46, NKp30, DNAM-1, CD244 and CD94/NKG2C activating receptors on NK cells from acute myeloid leukaemia patients. This reduction may be induced by chronic exposure to their ligands on leukaemic blasts. The analysis of ligands for NK cell-activating receptors showed that leukaemic blasts from the majority of patients express ligands for NK cell-activating receptors. DNAM-1 ligands are frequently expressed on blasts, whereas the expression of the NKG2D ligand MICA/B is found in half of the patients and CD48, a ligand for CD244, in only one-fourth of the patients. The decreased expression of NK cell-activating receptors and/or the heterogeneous expression of ligands for major receptors on leukaemic blasts can lead to an inadequate tumour immunosurveillance by NK cells. A better knowledge of the activating receptor repertoire on NK cells and their putative ligands on blasts together with the possibility to modulate their expression will open new possibilities for the use of NK cells in immunotherapy against leukaemia.     

Differential interactions of fluorescent agonists and antagonists with the yeast G protein coupled receptor Ste2p

We describe a rapid method to probe for mutations in cell surface ligand-binding proteins that affect the environment of bound ligand. The method uses fluorescence-activated cell sorting to screen randomly mutated receptors for substitutions that alter the fluorescence emission spectrum of environmentally sensitive fluorescent ligands. When applied to the yeast α-factor receptor Ste2p, a G protein-coupled receptor, the procedure identified 22 substitutions that red shift the emission of a fluorescent agonist, including substitutions at residues previously implicated in ligand binding and at additional sites. A separate set of substitutions, identified in a screen for mutations that alter the emission of a fluorescent α-factor antagonist, occurs at sites that are unlikely to contact the ligand directly. Instead, these mutations alter receptor conformation to increase ligand-binding affinity and provide signaling in response to antagonists of normal receptors. These results suggest that receptor-agonist interactions involve at least two sites, of which only one is specific for the activated conformation of the receptor.