Ligand rebinding: self-consistent mean-field theory and numerical simulations applied to surface plasmon resonance studies

Abstract

Rebinding of dissociated ligands from cell surface proteins can confound quantitative measurements of dissociation rates important for characterizing the affinity of binding interactions. This can be true also for in vitro techniques such as surface plasmon resonance (SPR). We present experimental results using SPR for the interaction of insulin-like growth factor-I (IGF-I) with one of its binding proteins, IGF binding protein-3 (IGFBP-3), and show that the dissociation, even with the addition of soluble heparin in the dissociation phase, does not exhibit the expected exponential decay characteristic of a 1:1 binding reaction. We thus consider the effect of (multiple) rebinding events and, within a self-consistent mean-field approximation, we derive the complete mathematical form for the fraction of bound ligands as a function of time. We show that, except for very low association rate and surface coverage, this function is non-exponential at all times, indicating that multiple rebinding events strongly influence dissociation even at early times. We compare the mean-field results with numerical simulations and find good agreement, although deviations are measurable in certain cases. Our analysis of the IGF-I-IGFBP-3 data indicates that rebinding is prominent for this system and that the theoretical predictions fit the experimental data well. Our results provide a means for analyzing SPR biosensor data where rebinding is problematic and a methodology to do so is presented.1 Present Address: Max Planck Institut für Physik komplexer Systeme, Nöthnitzer Stra e 38, 01187 Dresden, Germany. (i) IntroductionSignal transduction via transmembrane receptor proteins is initiated by extracellular binding with specific proteins known as growth factors. These interactions tend to be of high affinity and, in many systems, are regulated by binding proteins present in the extracellular environment. Insulin-like growth factor-I (IGF-I) constitutes one prominent example of such a growth factor. Cell signaling is transmitted by direct interaction with the IGF-I receptor but this binding can be impacted by solution and cell-associated IGF binding proteins (IGFBPs), of which there are at least six. Quantification of the interactions of IGF-I with IGFBPs is critical if one is to understand how changes in expression and secretion will impact IGF-I signaling. Surface plasmon resonance (SPR) is one technique amenable to such measurements. SPR is an optical sensor technique that has the advantage of being able to take real-time measurements using low concentrations of unlabeled biologicals [reviewed in Cooper 2003].Quantification of IGF-I interactions with both cell surface receptors and IGFBPs using SPR has been performed as a means of evaluating and predicting the competition between these molecules for IGF-I. Studies have used immobilized IGF-I [Wong et al. 1999;Dubaquie and Lowman 1999;Galanis et al. 2001;Fong et al. 2002; Vorwerk et al. 2002], IGF-I receptor [Jansson et al. 1997], or IGFBPs [Heding et al. 1996Jansson et al. ...

A Catalytic Role of Heparin within the Extracellular Matrix

“…A simple exponential dissociation model, where rebinding of heparin to fibronectin is not included, failed to fit the data, despite the presence of high concentrations of unlabeled heparin. The rebinding model, which fits our transient data well, would predict that a molecule of heparin that dissociates from fibronectin will rebind to the fibronectin matrix many times prior to diffusing to the bulk solution (42).…”

“…Assuming that unlabeled heparin equilibrates quickly, we replace h with h*, its equilibrium value. If p(0) Ͻ Ͻ 1, the resulting differential equation can be solved (42) to yield the following,…”

Allovalency revisited: An analysis of multisite phosphorylation and substrate rebinding

“…͑12͒, two kinetic regimes are observed that depend on the relative size of the receptor as determined by ␥ = a / ͑a + ͒. First, if ͑1 − ␥͒ Ӷ ␥ ͱ s, ͑13͒ ͑e.g., the radius of gyration of the disordered protein is small compared to the radius of the region to which it binds to its targeted substrate, Ϸ 0 and ␥ ϳ 1͒, then the overall kinetics of ligand dissociation that are modified as a result of rebinding events behave in a similar fashion to that of the onedimensional case 15 as shown in the Appendixes. This can be seen by taking the → 0 ͑i.e., ␥ → 1͒ limit of Eq.…”

“…28 Many mechanisms have been proposed ͑and some tested͒ that can account for switchlike dose responses involving proteins with multisite phosphorylations. 15,22,29 In the language of our model, such effects would result in having a complex, nonlinear relationship with n and 0 . It may be interesting to explore how these mechanisms containing phenomena such as decoy phosphorylation, entropically driven binding, or electrostatics may couple to the effects of ligand rebinding as studied here.…”

“…The formalism was developed by Gopalakrishnan et al 15 who investigated the effects of a ligand binding to a collection of receptors on a planar surface in the context of surface plasmon resonance studies. Although our approach is similar in many regards, there are some subtleties that distinguish the two approaches and they are discussed within our treatment.…”