A2AR Binding Kinetics in the Ligand Depletion Regime.

Ligand binding plays a fundamental role in stimulating the downstream signaling of membrane receptors. Here, ligand-binding kinetics of the full-length human adenosine A2A receptor (A2AR) reconstituted in detergent micelles were measured using a fluorescently labeled ligand via fluorescence anisotropy. Importantly, to optimize the signal-to-noise ratio, these experiments were conducted in the ligand depletion regime. In the ligand depletion regime, the assumptions used to determine analytical solutions for one-site binding models for either one or two ligands in competition are no longer valid. We therefore implemented a numerical solution approach to analyze kinetic binding data as experimental conditions approach the ligand depletion regime. By comparing the results from the numerical and the analytical solutions, we highlight the ligand-receptor ratios at which the analytical solution begins to lose predictive accuracy. Using the numerical solution approach, we determined the kinetic rate constants of the fluorescent ligand, FITC-APEC, and those for three unlabeled ligands using competitive association experiments. The association and dissociation rate constants of the unlabeled ligands determined from the competitive association experiments were then independently validated using competitive dissociation data. Based on this study, a numerical solution is recommended to determine kinetic ligand-binding parameters for experiments conducted in the ligand-depletion regime.

Ligand-receptor binding kinetics in surface plasmon resonance cells: a Monte Carlo analysis.

Surface plasmon resonance (SPR) chips are widely used to measure association and dissociation rates for the binding kinetics between two species of chemicals, e.g., cell receptors and ligands. It is commonly assumed that ligands are spatially well mixed in the SPR region, and hence a mean-field rate equation description is appropriate. This approximation however ignores the spatial fluctuations as well as temporal correlations induced by multiple local rebinding events, which become prominent for slow diffusion rates and high binding affinities. We report detailed Monte Carlo simulations of ligand binding kinetics in an SPR cell subject to laminar flow. We extract the binding and dissociation rates by means of the techniques frequently employed in experimental analysis that are motivated by the mean-field approximation. We find major discrepancies in a wide parameter regime between the thus extracted rates and the known input simulation values. These results underscore the crucial quantitative importance of spatio-temporal correlations in binary reaction kinetics in SPR cell geometries, and demonstrate the failure of a mean-field analysis of SPR cells in the regime of high Damköhler number [Formula: see text], where the spatio-temporal correlations due to diffusive transport and ligand-receptor rebinding events dominate the dynamics of SPR systems.

Facilitated diffusion of VEGF165 through descemet's membrane with sucrose octasulfate.

Vascular endothelial growth factor A (VEGF-A) is a promoter of neovascularization and thus a popular therapeutic target for diseases involving excessive growth of blood vessels. In this study, we explored the potential of the disaccharide sucrose octasulfate (SOS) to alter VEGF165 diffusion through Descemet's membrane. Descemet's membranes were isolated from bovine eyes and used as a barrier between two chambers of a diffusion apparatus to measure VEGF transport. Diffusion studies revealed a dramatic increase in VEGF165 transport in the presence of SOS, with little diffusion of VEGF165 across the membrane over a 10-h time course in the absence of SOS. Diffusion studies with VEGF121, a non-heparin binding variant of VEGF, showed robust diffusion with or without SOS. To determine a possible mechanism, we measured the ability of SOS to inhibit VEGF interactions with extracellular matrix (ECM), using cell-free and cell surface binding assays. Binding studies showed SOS had no effect on VEGF165 binding to either heparin-coated plates or endothelial cell surfaces at less than mg/ml concentrations. In contrast, we show that SOS inhibited VEGF165 binding to fibronectin in a dose dependent manner and dramatically accelerated the rate of release of VEGF165 from fibronectin. SOS also inhibited the binding of VEGF165 to fibronectin-rich ECM deposited by vascular smooth muscle cells. These results suggest that fibronectin-rich extracellular matrices serve as barriers to VEGF165 diffusion by providing a network of binding sites that can trap and sequester the protein. Since the content of Descemet's membrane is typical of many basement membranes it is possible that they serve throughout the body as formidable barriers to VEGF165 diffusion and tightly regulate its bioavailability and distribution within tissues.

Complex receptor-ligand dynamics control the response of the VEGF system to protease injury.

BACKGROUND: Vascular homeostasis and response to injury are dependent on the coordinated activity of growth factors such as vascular endothelial growth factor-A (VEGF). VEGF signaling is mediated by VEGF receptors 1 (VEGFR1) and 2 (VEGFR2). VEGF also binds to extracellular matrix (ECM) and neuropilin (NP), a cell surface glycoprotein that enhances VEGF binding to VEGFR2 while inhibiting VEGF-VEGFR1 interactions. Proteases such as neutrophil elastase release VEGF bound to ECM; however, this results in proteolytic processing of VEGF to a smaller species termed VEGF fragment (VEGFf). We hypothesized that the generation and presence of VEGFf would have significant effects on the binding distribution of VEGF. RESULTS: We show that VEGFf, unlike VEGF, does not bind ECM, fibronectin, or NP-1. Using computational simulations, we find that excess VEGFf can lead to increased binding of VEGF to VEGFR2 through VEGFf binding to VEGFR1 and subsequent liberation of NP-1. We show experimentally that VEGF-induced migration has a biphasic response to conversion of VEGF to VEGFf. Simulations suggest that a simple change in VEGFR1 or VEGFR2 complexes are unlikely to be responsible and that a more complex integration of signals is more likely involved. CONCLUSIONS: These findings suggest that proteolytic damage at sites of tissue injury and inflammation has the potential to modulate the VEGF system through a complex process and highlight the need for quantitative analysis to reveal mechanisms of growth factor control.

Endothelial cell capture of heparin-binding growth factors under flow.

Circulation is an important delivery method for both natural and synthetic molecules, but microenvironment interactions, regulated by endothelial cells and critical to the molecule's fate, are difficult to interpret using traditional approaches. In this work, we analyzed and predicted growth factor capture under flow using computer modeling and a three-dimensional experimental approach that includes pertinent circulation characteristics such as pulsatile flow, competing binding interactions, and limited bioavailability. An understanding of the controlling features of this process was desired. The experimental module consisted of a bioreactor with synthetic endothelial-lined hollow fibers under flow. The physical design of the system was incorporated into the model parameters. The heparin-binding growth factor fibroblast growth factor-2 (FGF-2) was used for both the experiments and simulations. Our computational model was composed of three parts: (1) media flow equations, (2) mass transport equations and (3) cell surface reaction equations. The model is based on the flow and reactions within a single hollow fiber and was scaled linearly by the total number of fibers for comparison with experimental results. Our model predicted, and experiments confirmed, that removal of heparan sulfate (HS) from the system would result in a dramatic loss of binding by heparin-binding proteins, but not by proteins that do not bind heparin. The model further predicted a significant loss of bound protein at flow rates only slightly higher than average capillary flow rates, corroborated experimentally, suggesting that the probability of capture in a single pass at high flow rates is extremely low. Several other key parameters were investigated with the coupling between receptors and proteoglycans shown to have a critical impact on successful capture. The combined system offers opportunities to examine circulation capture in a straightforward quantitative manner that should prove advantageous for biologicals or drug delivery investigations.

A computational model of FGF-2 binding and HSPG regulation under flow.

A novel convection-diffusion-reaction model is developed to simulate fibroblast growth factor (FGF-2) binding to cell surface receptors (FGFRs) and heparan sulfate proteoglycans (HSPGs) under flow conditions within a cylindrical-shaped vessel or capillary. The model consists of a set of coupled nonlinear partial differential equations (PDEs) and a set of coupled nonlinear ordinary differential equations (ODEs). The time-dependent PDE system is discretized and solved by a second-order implicit Euler scheme using the finite volume method. The ODE system is solved by a stiff ODE solver VODE using backward differencing formulation (BDF). The transient solution of FGF-2, FGFR, HSPG, and their bound complexes for three different flow rates are computed and presented. Simulation results indicate that the model can predict growth factor transport and binding to receptors with/without the presence of heparan sulfate, as well as the effect of flow rate on growth factor-receptor binding. Our computational model may provide a useful means to investigate the impact of fluid flow on growth factor dynamics, and ultimately, signaling within the circulation.

Using quantitative fluorescence microscopy to probe organelle assembly and membrane trafficking.

With current light microscopy and laboratory-level computational capability, many questions in organelle assembly and membrane trafficking that were once treated in a qualitative manner can now be treated quantitatively. We present here an overview of the principles involved in doing quantitative fluorescence microscopy. We illustrate these with examples drawn from our work with the Golgi apparatus and endosomes in cultured mammalian cells. The principles themselves can be applied to any system.

A catalytic role of heparin within the extracellular matrix.

We investigated the mechanism by which heparin enhances the binding of vascular endothelial growth factor (VEGF) to the extracellular matrix protein fibronectin. In contrast to other systems, where heparin acts as a protein scaffold, we found that heparin functions catalytically to modulate VEGF binding site availability on fibronectin. By measuring the binding of VEGF and heparin to surface-immobilized fibronectin, we show that substoichiometric amounts of heparin exposed cryptic VEGF binding sites within fibronectin that remain available after heparin removal. Measurement of association and dissociation kinetics for heparin binding to fibronectin indicated that the interaction is rapid and transient. We localized the heparin-responsive element to the C-terminal 40-kDa Hep2 domain of fibronectin. A mathematical model of this catalytic process was constructed that supports a mechanism whereby the heparin-induced conformational change in fibronectin is accompanied by release of heparin. Experiments with endothelial extracellular matrix suggest that this process may also occur within biological matrices. These results indicate a novel mechanism whereby heparin catalyzes the conversion of fibronectin to an open conformation by transiently interacting with fibronectin and progressively hopping from molecule to molecule. Catalytic activation of the extracellular matrix might be an important mechanism for heparin to regulate function during normal and disease states.

Control of growth factor networks by heparan sulfate proteoglycans.

Growth factor binding to transmembrane protein receptors is generally understood to initiate cell signaling. Receptor binding of heparin-binding growth factors (HB-GFs), such as fibroblast growth factor-2 (FGF-2), is regulated by interactions with heparan sulfate proteoglycans. While there is some specificity for binding to heparan sulfate, overlap in sites for different growth factors may allow for cross regulation. Here we demonstrate, using experiments and computer simulations, that the HB-GFs FGF-2 and heparin-binding EGF-like growth factor (HB-EGF) can cross regulate receptor binding of the other despite having unique receptors. The ability of HSPG to stabilize HB-GF receptor binding is critical for competing growth factors to modulate receptor binding with both enhanced and reduced binding possible depending on this stabilization process. HSPG density and affinity for HB-GF are also critical factors for HB-GF cross regulation. Simulations further reveal that HB-GF can regulate receptor binding of non-HB-GFs such as EGF even when the two proteins share no binding sites when other HB-GF are present within the network. Proliferation studies demonstrate potentiation of HB-EGF-induced growth by FGF-2 indicating that competition networks can alter biological response. Exogenous manipulation of cellular responses to growth factors in complex living systems will require understanding the HSPG-controlled network.

Sucrose octasulfate regulates fibroblast growth factor-2 binding, transport, and activity: potential for regulation of tumor growth.

The antithrombotic activity of heparin has largely been credited with the success found in some cancer treatment by heparin. There are, however, many potent growth factors involved in tumor and blood vessel growth that bind to heparin with high affinity and their regulation by heparin may play a role in heparin's efficacy. We therefore chose to study the activity of a heparin analog, sucrose octasulfate (SOS), which has been similarly shown to interact with heparin-binding growth factors. Using mouse melanoma and lung carcinoma models, we demonstrate in vivo inhibition of tumor growth by SOS. SOS, however, showed little effect in coagulation assays indicating that this activity was not a primary mechanism of action for this molecule. Studies were then performed to assess the effect of SOS on basic fibroblast growth factor (FGF-2) activity, a growth factor which promotes tumor and blood vessel growth and is produced by B16 melanoma cells. SOS potently inhibited FGF-2 binding to endothelial cells and stripped pre-bound FGF-2 from cells. SOS also regulated FGF-2 stimulated proliferation. Further, SOS facilitated FGF-2 diffusion through Descemet's membrane, a heparan sulfate-rich basement membrane from the cornea, suggesting a possible role in FGF-2 clearance. Our results suggest that molecules such as SOS have the potential to remove growth factors from tumor microenvironments and the approach offers an attractive area for further study.

Self-consistent theory of reversible ligand binding to a spherical cell.

Ligand binding to receptors is the initial event in many signaling processes, and a quantitative understanding of this interaction is important for modeling cell behavior. In this paper, we study the kinetics of reversible ligand binding to receptors on a spherical cell surface using a self-consistent stochastic theory. Binding, dissociation, diffusion and rebinding of ligands are incorporated into the theory in a systematic manner. We derive explicitly the time evolution of the ligand-bound receptor fraction p(t) in various regimes. Contrary to the commonly accepted view, we find that the well-known Berg-Purcell scaling for the association rate is modified as a function of time. Specifically, the effective on-rate changes non-monotonically as a function of time and equals the intrinsic rate at very early as well as late times, while being approximately equal to the Berg-Purcell value at intermediate times. The effective dissociation rate, as it appears in the binding curve or measured in a dissociation experiment, is strongly modified by rebinding events and assumes the Berg-Purcell value except at very late times, where the decay is algebraic and not exponential. In equilibrium, the ligand concentration everywhere in the solution is the same and equals its spatial mean, thus ensuring that there is no depletion in the vicinity of the cell. Implications of our results for binding experiments and numerical simulations of ligand-receptor systems are also discussed.

Autocrine production of insulin-like growth factor-I (IGF-I) affects paracellular transport across epithelial cells in vitro.

Autocrine production of growth factors can have significant effects on cell activity. We report for the first time that autocrine production of insulin-like growth factor-I (IGF-I) alters paracellular transport across bovine mammary epithelial cells in vitro. Paracellular transport was assessed by measuring phenol red transport across mammary alveolar cells-large T antigen (MAC-T cells) derived from parental mammary epithelial cells, cultured on porous membranes and compared with two different transfected MAC-T cell lines that constitutively secrete IGF-I. Phenol red transport was essentially blocked in parental cell culture after six days, while IGF-I secreting cells provided essentially no barrier. Surprisingly, neither co-culture studies between parental and IGF-I-secreting cells nor addition of exogenous IGF-I or IGF-binding protein-3 reversed the phenol red transport properties. IGF-I-secreting cells did however express lower levels of the junction components occludin and E-cadherin than parental cells, suggesting that localized autocrine IGF-I activity might lead to increased permeability via changes in both the tight and adherens junction protein levels.

Design and application of an oscillatory compression device for cell constructs.

Mechanical compression has been shown to impact cell activity; however a need for a single device to perform a broader range of parametric studies exists. We have developed an oscillatory displacement controlled device to uniaxially strain cell constructs under both static and dynamic compression and used this device to investigate gene expression in cell constructs. The device has a wide stroke (0.25-4 mm) and frequency range (0.1-3 Hz) and several loading waveforms are possible. Alginate cellular constructs with embedded equine chondrocytes were tested and viability was maintained for the 24 h test period. Off-line mechanical testing is described and a modulus value of 18.2 +/- 1.3 kPa found for alginate disks which indicates the level of stress achieved with this deformation profile. Static (15% strain) and dynamic (15% strain, 1 Hz, triangle waveform) testing of chondrocyte constructs was performed and static compression showed significantly higher collagen II expression than dynamic using quantitative RT-PCR. In contrast, differences in matrix metalloproteinase-3 (MMP-3) expression were statistically insignificant. These studies indicate the utility of our device for studying cell activity in response to compression and suggest further studies regarding how the load and strain spectrum impact chondrocyte activity.

Both post-Golgi and intra-Golgi cycling affect the distribution of the Golgi phosphoprotein GPP130.

Golgi phosphoprotein, GPP130, a cis Golgi protein, is representative of proteins cycling between the Golgi apparatus and endosomes in a pH-sensitive manner. The present qualitative data are insufficient to distinguish the relative contributions of Golgi and endosomal processes in regulating the cycling of such proteins. We have taken a quantitative approach to analyze GPP130 distribution in response to pH perturbation. We have used Shiga-like toxin B fragment, a protein that traffics from the cell surface and Golgi apparatus by the late endosomal bypass pathway, as a probe to highlight one aspect of GPP130 cycling and similarly the trafficking of tsO45-green fluorescent protein (GFP) between the Golgi apparatus and the plasma membrane to treat that aspect of GPP130 cycling in isolation. Overall, we conclude from quantitative analysis and simulations that treatment of HeLa cells with the pH perturbant, monensin, affects GPP130 cycling at several stages with effects on (i) intra-Golgi cycling, (ii) trans Golgi to endosome transport and (iii) endosome to Golgi transport. Our analysis indicates that the effect is greatest at the trans Golgi, the most acidic portion of the Golgi apparatus. In sum, multiple, regulated steps affect the trafficking of GPP130.

Alginate encapsulation impacts the insulin-like growth factor-I system of monolayer-expanded equine articular chondrocytes and cell response to interleukin-1beta.

Alginate hydrogel culture has been shown to reestablish chondrocytic phenotype following monolayer expansion; however, previous studies have not adequately addressed how culture conditions affect the signaling systems responsible for chondrocyte metabolic activity. Here we investigate whether chondrocyte culture history influences the insulin-like growth factor-I (IGF-I) signaling system and its regulation by interleukin-1 (IL-1). Articular chondrocytes (ACs) from equine stifle joints were expanded by serial passage and were either encapsulated in alginate beads or maintained in monolayer culture for 10 days. Alginate-derived cells (ADCs) and monolayer-derived cells (MDCs) were then plated at high density, stimulated with IL-1beta (1 and 10 ng/mL) or IGF-I (50 ng/mL) for 48 h, and assayed for levels of type I IGF receptor (IGF-IR), IGF binding proteins (IGFBPs), and endogenously secreted IGF-I. Intermediate alginate culture yielded relatively low IGF-IR levels that increased in response to IL-1beta, whereas higher receptor levels on MDCs were reduced by cytokine. MDCs also secreted substantially more IGFBP-2, the predominant binding protein in conditioned media (CM), though IL-1beta suppressed levels for both cell populations. Concentrations of autocrine/paracrine IGF-I paralleled IGFBP-2 secretion. Disparate basal levels of IGF-IR and IGFBP-2, but not IGF-I, were attributed to relative transcript expression. Systemic differences coincided with varied effects of IL-1beta and IGF-I on cell growth and type I collagen expression. We conclude that culture strategy impacts the IGF-I signaling system of ACs, potentially altering their capacity to mediate cartilage repair. Consideration of hormonal regulators may be an essential element to improve chondrocyte culture protocols used in tissue engineering applications.

Enhanced insulin-like growth factor-I (IGF-I) cell association at reduced pH is dependent on IGF binding protein-3 (IGFBP-3) interaction.

The cellular microenvironment impacts how signals are transduced by cells and plays a key role in tissue homeostasis. Although pH is generally well regulated, there are a number of situations where acidosis occurs and our work addresses how low pH impacts cell association of insulin-like growth factor-I (IGF-I) in the presence of IGF binding protein-3 (IGFBP-3). We have previously shown that IGF-I cell binding was enhanced in the presence of IGFBP-3 at low pH and now show that this binding is IGFBP-mediated as it is inhibited by Y60L-IGF-I, a mutant with reduced affinity for the IGF receptor (IGF-IR), and unaffected by insulin, which binds but not IGFBPs. Using surface plasmon resonance (SPR), we show that direct binding between IGF-I and IGFBP-3 is pH sensitive. Despite this, the key step in the process appears to be IGFBP-3 cell surface association as Long-R(3)-IGF-I, a mutant with reduced affinity for IGFBPs, shows a similar increase in cell association at pH 5.8 in the presence of IGFBP-3 but does not exhibit pH-dependent binding by SPR. Further, analysis indicates a large increase in low-affinity binding sites for IGF-I in the presence of IGFBP-3 and an elimination of IGF-I enhanced binding when a non-cell associating mutant of IGFBP-3 is added in place of IGFBP-3. That the IGFBP-3-mediated binding localizes IGF-I away from IGF-IR is suggested by triton-solubility testing and indicates additional complexities to IGF-I regulation by IGFBP-3. Identifying the pH-dependent binding partner(s) for IGFBP-3 is a necessary next step in deciphering this process.

Transcriptional and proteolytic regulation of the insulin-like growth factor-I system of equine articular chondrocytes by recombinant equine interleukin-1beta.

Interleukin-1 (IL-1) and insulin-like growth factor-I (IGF-I), which have opposing effects on matrix metabolism within articular cartilage, are thought to play prominent roles in the pathogenesis of osteoarthritis. To better understand the link between these anabolic (IGF-I) and catabolic (IL-1) stimuli, we examined exogenous IL-1 regulation of the IGF-I signaling system of articular chondrocytes (ACs). Equine ACs from non-arthritic stifle joints were expanded in monolayer culture, encapsulated for 10 days in alginate beads, and stimulated as high-density monolayers with recombinant equine IL-1beta (0, 1, 10 ng/ml) for 48 h. IL-1beta enhanced expression of IGF-IR levels, as determined by both [125I]-IGF-I binding studies and Western blotting, while reducing the concentration of endogenous IGF-I detected in conditioned media by radioimmunoassay. Western ligand blotting revealed that chondrocytes primarily secreted IGF binding proteins (IGFBPs) with molecular weights of 28-30 and 32-34 kDa, which were identified as IGFBPs 5 and 2, respectively, and that IL-1beta treatment diminished IGFBP-2, the prominent homolog in conditioned media. Northern blot analysis suggested IL-1beta regulation of IGF-I and, to some extent, IGF-IR was mediated by transcription; however, the cytokine did not affect IGFBP-2 expression. To test for evidence of proteolysis by matrix metalloproteinases (MMPs), additional cultures were co-incubated with inhibitors for MMPs 2/9, 3, and 8. IGFBP-2 suppression was partially reversed by gelatinase (MMP-2/9) inhibition. In summary, these findings further delineate the role of IL-1 as a key regulator of the IGF-I system within articular cartilage, demonstrating that regulation occurs through both direct (transcriptional) and indirect (proteolytic) mechanisms.

Regulation of insulin-like growth factor-I (IGF-I) delivery by IGF binding proteins and receptors.

Delivery of growth factors via the bloodstream for the treatment of various diseases is regulated in part by interactions with cell surface binding elements. Understanding the kinetics of growth factor binding and transport by cells would, therefore, be advantageous. This report quantifies the binding, internalization, and transport of insulin-like growth factor-I (IGF-I) across bovine aortic endothelial cells (BAEC) cultured in vitro. Binding analysis indicated that IGF binding proteins (IGFBPs), primarily localized with the extracellular matrix, were the primary IGF-I binding elements in our system, with twice as many binding sites (8.0 +/- 1.9 x 10(4) per cell) as IGF-I receptors (IGF-IR) (3.9 +/- 0.6 x 10(4) per cell). Internalization of IGF-I by IGF-IR, but not IGFBPs, was detected, however both receptor and IGFBP binding were shown to inhibit rather than enhance the transport of intact IGF-I, albeit in different ways. IGFBPs retained IGF-I in the apical region while IGF-IR binding led to protein degradation. Based on our computational modeling and experimental data, we hypothesize that IGFBPs could function as a reservoir for IGF-I, sequestering it for later release and transport, and that this reservoir function of the IGFBPs could be used to promote controlled localized delivery of IGF-I.

The steady-state distribution of glycosyltransferases between the Golgi apparatus and the endoplasmic reticulum is approximately 90:10.

Several lines of evidence support a novel model for Golgi protein residency in which these proteins cycle between the Golgi apparatus and the endoplasmic reticulum (ER). However, to preserve the functional distinction between the two organelles, this pool of ER-resident Golgi enzymes must be small. We quantified the distribution for two Golgi glycosyltransferases in HeLa cells to test this prediction. We reasoned that best-practice, quantitative solutions would come from treating images as data arrays rather than pictures. Using deconvolution and computer calculated organellar boundaries, the Golgi fraction for both endogenous beta1,4-galactosyltransferase and UDP-N-acetylgalactosamine:polypeptide N-acetylgalactosaminyltransferase 2 fused with green fluorescent protein (GFP) was 91% by fluorescence microscopy. Immunogold labeling followed by electron microscopy and model analysis yielded a similar value. Values reflect steady-state conditions, as inclusion of a protein synthesis inhibitor had no effect. These data strongly suggest that the fluorescence of a GFP chimera with an organellar protein can be a valid indicator of protein distribution and more generally that fluorescent microscopy can provide a valid, rapid approach for protein quantification. In conclusion, we find the ER pool of cycling Golgi glycosyltransferases is small and approximately 1/100 the concentration found in the Golgi apparatus.

Effects of receptor clustering on ligand dissociation kinetics: theory and simulations.

Receptor-ligand binding is a critical first step in signal transduction and the duration of the interaction can impact signal generation. In mammalian cells, clustering of receptors may be facilitated by heterogeneous zones of lipids, known as lipid rafts. In vitro experiments show that disruption of rafts significantly alters the dissociation of fibroblast growth factor-2 (FGF-2) from heparan sulfate proteoglycans (HSPGs), co-receptors for FGF-2. In this article, we develop a continuum stochastic formalism to address how receptor clustering might influence ligand rebinding. We find that clusters reduce the effective dissociation rate dramatically when the clusters are dense and the overall surface density of receptors is low. The effect is much less pronounced in the case of high receptor density and shows nonmonotonic behavior with time. These predictions are verified via lattice Monte Carlo simulations. Comparison with FGF-2-HSPG experimental results is made and suggests that the theory could be used to analyze similar biological systems. We further present an analysis of an additional cooperative internal-diffusion model that might be used by other systems to increase ligand retention when simple rebinding is insufficient.