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 Damk\"ohler number Da > 0.1, where the spatio-temporal correlations due to diffusive transport and ligand-receptor rebinding events dominate the dynamics of SPR systems.Comment: 21 pages, 9 figure

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

In this article, 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.Comment: 23 pages with 4 figure

Effects of receptor clustering on ligand dissociation: 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, co-receptors for FGF-2. In this paper, we develop a continuum stochastic formalism in order to (i) study how rebinding affects the dissociation of ligands from a planar substrate, and (ii) address the question of how receptor clustering influences 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 non-monotonic behavior with time. These predictions are verified via lattice Monte Carlo simulations. Comparison with experimental results suggests that the theory does not capture the complete biological system. We speculate that additional co-operative mechanisms might be present in order to increase ligand retention, and present one possible ``internal diffusion'' model.Comment: Expanded text and added figures, revised version to appear in Biophys.

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

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.National Institutes of Health (U.S.) (NIH grant HL088572)Massachusetts Lions Eye Research Fund, Inc

Simulations predict cell surface density impacts FGF-2 retention.

<p>Simulations were run for FGF-2 (1ng) added to the system (30% non-specific loss) at 0.63 mL/min pulsatile flow (1.26 mm/sec) for 5 min. (A) Cells expressed either 1×10⁴ FGFR/cell and variable densities of HSPG (○) or 2.5×10⁵ HSPG/cell and variable densities of FGFR (•) on the cell-lined hollow fibers. The amount retained within the system (bound, internalized, and fluid phase FGF-2) is shown. (B) Cells expressed 1×10⁴ FGFR/cell and 2×10³ (•,○), 2×10⁴ (▪,□), or 2×10⁵ (▴,▵) HSPG/cell on the cell-lined hollow fibers and simulation results correspond to entrance cell value at a given time. Filled symbols correspond to % of FGF-2 bound to FGFR which are simultaneously bound to HSPG and open symbols correspond to the #/cell of FGF-2 bound to FGFR and HSPG.</p