Monte Carlo study of single molecule diffusion can elucidate the mechanism of B cell synapse formation

B cell receptors have been shown to cluster at the intercellular junction between a B cell and an antigen-presenting cell in the form of a segregated pattern of B cell receptor/antigen complexes known as an immunological synapse. We use random walk-based theoretical arguments and Monte Carlo simulations to study the effect of diffusion of surface-bound molecules on B cell synapse formation. Our results show that B cell synapse formation is optimal for a limited range of receptor-ligand complex diffusion coefficient values, typically one-to-two orders of magnitude lower than the diffusion coefficient of free receptors. Such lower mobility of receptor-ligand complexes can significantly affect the diffusion of a tagged receptor or ligand in an affinity dependent manner, as the binding/unbinding of such receptor or ligand molecules crucially depends on affinity. Our work shows how single molecule tracking experiments can be used to estimate the order of magnitude of the diffusion coefficient of receptor-ligand complexes, which is difficult to measure directly in experiments due to the finite lifetime of receptor-ligand bonds. We also show how such antigen movement data at the single molecule level can provide insight into the B cell synapse formation mechanism. Thus, our results can guide further single molecule tracking experiments to elucidate the synapse formation mechanism in B cells, and potentially in other immune cells.     

Spatial range of autocrine signaling: modeling and computational analysis

Autocrine loops formed by growth factors and their receptors have been identified in a large number of developmental, physiological, and pathological contexts. In general, the spatially distributed and recursive nature of autocrine signaling systems makes their experimental analysis, and often even their detection, very difficult. Here, we combine Brownian motion theory, Monte Carlo simulations, and reaction-diffusion models to analyze the spatial operation of autocrine loops. Within this modeling framework, the ability of autocrine cells to recapture the endogenous ligand and the distances traveled by autocrine ligands are explicitly related to ligand diffusion coefficients, density of surface receptors, ligand secretion rate, and rate constants of ligand binding and endocytic internalization. Applying our models to study autocrine loops in the epidermal growth factor receptor system, we find that autocrine loops can be highly localized--even at the level of a single cell. We demonstrate how the variations in molecular and cellular parameters may "tune" the spatial range of autocrine signals over several orders of magnitude: from microns to millimeters. We argue that this versatile regulation of the spatial range of autocrine signaling enables autocrine cells to perceive a broad spectrum of environmental information.     

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.     

Some models of the evolution of altruistic behaviour between siblings

When a fluid membrane, containing mobile receptors for some ligand, is placed in a diffusion gradient of that ligand, the receptors will redistribute to become more concentrated in those regions of the membrane which are associated with the higher concentrations of ligand. The thermodynamics of this effect are developed. The significance of this effect as a possible step in the transduction of the orientational information content of a diffusion gradient to a cell is discussed. It is pointed out that fluid membrane receptors should potentially be more sensitive transducers of the orientational information content of the gradient than would fixed membrane receptors, and that the transduction sensitivity will rise as the number of ligand binding sites per receptor rises.     

Predicting novel binding modes of agonists to β adrenergic receptors using all-atom molecular dynamics simulations

Understanding the binding mode of agonists to adrenergic receptors is crucial to enabling improved rational design of new therapeutic agents. However, so far the high conformational flexibility of G protein-coupled receptors has been an obstacle to obtaining structural information on agonist binding at atomic resolution. In this study, we report microsecond classical molecular dynamics simulations of β(1) and β(2) adrenergic receptors bound to the full agonist isoprenaline and in their unliganded form. These simulations show a novel agonist binding mode that differs from the one found for antagonists in the crystal structures and from the docking poses reported by in silico docking studies performed on rigid receptors. Internal water molecules contribute to the stabilization of novel interactions between ligand and receptor, both at the interface of helices V and VI with the catechol group of isoprenaline as well as at the interface of helices III and VII with the ethanolamine moiety of the ligand. Despite the fact that the characteristic N-C-C-OH motif is identical in the co-crystallized ligands and in the full agonist isoprenaline, the interaction network between this group and the anchor site formed by Asp(3.32) and Asn(7.39) is substantially different between agonists and inverse agonists/antagonists due to two water molecules that enter the cavity and contribute to the stabilization of a novel network of interactions. These new binding poses, together with observed conformational changes in the extracellular loops, suggest possible determinants of receptor specificity.     

A method to measure receptor binding of ligands with low affinity : Application to plasma proteins binding assay with hemopoietic cells

A gradient has been developed for separating free ligand from ligand bound to cells growing in suspension. This method can be used with all kinds of ligand but it is particularly useful for those ligands having the tiresome tendency to adhere to the cells non-specifically or to polymerize by themselves. This is the case of fibronectin, fibrinogen, immunoglobulins and many other plasma proteins. The gradient consists of two layers: an upper aqueous phase and a lower hydrophobic organic phase. The aqueous phase, a sucrose buffer, allows the cells to become well dispersed before they enter the hydrophobic phase which excludes the free ligand efficiently. This reduces non-specific binding and allows the accurate measurement of specific binding which could not be obtained with a gradient made of a single phase. Depending upon the size and the density of the cells, and the nature of the ligand, the assay method can be modified by changing the density or the nature of the hydrophilic and hydrophobic phases.     

Localization of receptors in lipid rafts can inhibit signal transduction

Processes of cell survival, division, differentiation, and death are guided by the binding of signal molecules to receptors, which activates intracellular signaling networks and ultimately elicits genetic, biochemical, or biomechanical responses within the cell. While intracellular mechanisms for these processes have been well studied, little attention has been given to the role extracellular ligand transport and binding may play in signal initiation. Recent studies have found that the localization of receptors in lipid rafts is critical for the functions of many signaling pathways. By concentrating membrane components, rafts may promote essential interactions for signaling. Lipid rafts can also have negative effects on signaling, but mechanisms remain elusive. We propose that raft-mediated receptor clustering can reduce signaling by prolonging the diffusion of ligands to their receptors. We quantify this effect using a simple diffusion-limited binding model that accounts for the spatial distribution of lipid rafts and receptors on the cell surface. We find that receptor clustering can reduce the apparent rate of receptor binding by up to 80%, consistent with observed increases in epidermal growth factor (EGF) binding by up to 100% following disruption of lipid rafts (Pike and Casey 2002 Biochemistry 41:10315-10322; Roepstorff et al. 2002 J Biol Chem 277:18954-18960). Failure to account for the effects of receptor clustering on rates of ligand binding can skew the interpretation of current methods of cancer diagnosis and treatment. Finally, we discuss how the activation of particular signaling pathways can change over time, depending, in part, on the overall level and spatial distribution of the receptors.     

Displacement Reactions Employing Heterologous Tracer Ligands in Peptide Receptor Studies: A Review

Abstract

Heterologous tracer ligands used in displacement studies with peptide-receptor systems may become unsuitable to these aims for several reasons. (1) The forms of binding isotherms for the tracer and for the ligand under investigation are different. The Schild plot and similar schemes are then not applicable. Possible modifications of the computational methods are indicated. (2) The rate of dissociation from the receptor is slowed, until almost irreversible. In such cases, there is no chance for displacement studies. (3) Large discrepancy in rate constants, or dramatically different distribution coefficients between binding system and water, for the two ligands mimic irreversible binding to receptors in a pharmacological experiment. Adjustment of ligand concentrations (control of association rate) may help in some instances.     

Kinetics of large-ligand binding to one-dimensional lattices: theory of irreversible binding

Exact solutions are obtained for the time dependence of the extent of irreversible binding of ligands that cover more than one lattice site to a homogeneous one-dimensional lattice. The binding may be cooperative or noncooperative and the lattice either finite or infinite. Although the form of the solution is most convenient when the ligand concentration is buffered, exact numerical or approximate analytical solutions, including upper and lower bounds, can be derived for the case of variable ligand concentration as well. The physical reason behind the relative simplicity of the kinetics of irreversible as opposed to reversible binding in such systems is discussed.     

Low density lipoprotein receptor-related protein and gp330 bind similar ligands, including plasminogen activator-inhibitor complexes and lactoferrin, an inhibitor of chylomicron remnant clearance.

The low density lipoprotein receptor-related protein/alpha 2-macroglobulin receptor (LRP) and gp330, two members of the low density lipoprotein receptor gene family, share a multitude of cysteine-rich repeats. LRP has been shown to act as an endocytosis-mediating receptor for several ligands, including protease-antiprotease complexes and plasma lipoproteins. The former include alpha 2-macroglobulin-protease complexes and plasminogen activator inhibitor-activator complexes. The latter include chylomicron remnant-like particles designated beta-very low density lipoproteins (beta-VLDL) complexed with apoprotein E or lipoprotein lipase. The binding specificity of gp330 is unknown. In the current studies we show that gp330 from rat kidney membranes binds several of these ligands on nitrocellulose blots. We also show that both LRP and gp330 bind an additional ligand, bovine lactoferrin, which is known to inhibit the hepatic clearance of chylomicron remnants. Lactoferrin blocked the LRP-dependent stimulation of cholesteryl ester synthesis in cultured human fibroblasts elicited by apoprotein E-beta-VLDL or lipoprotein lipase-beta-VLDL complexes. Cross-competition experiments in fibroblasts showed that the multiple ligands recognize at least three distinct, but partially overlapping sites on the LRP molecule. Binding of all ligands to LRP and gp330 was inhibited by the 39-kDa protein, which co-purifies with the two receptors, suggesting that the 39-kDa protein is a universal regulator of ligand binding to both receptors. The correlation of the inhibitory effects of lactoferrin in vivo and in vitro support the notion that LRP functions as a chylomicron remnant receptor in liver. LRP and gp330 share a multiplicity of binding sites, and both may function as endocytosis-mediating receptors for a large number of ligands in different organs.     

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.     

Mathematical modelling and computational study of two-dimensional and three-dimensional dynamics of receptor–ligand interactions in signalling response mechanisms

Cell signalling processes involve receptor trafficking through highly connected networks of interacting components. The binding of surface receptors to their specific ligands is a key factor for the control and triggering of signalling pathways. But the binding process still presents many enigmas and, by analogy with surface catalytic reactions, two different mechanisms can be conceived: the first mechanism is related to the Eley–Rideal (ER) mechanism, i.e. the bulk-dissolved ligand interacts directly by pure three-dimensional (3D) diffusion with the specific surface receptor; the second mechanism is similar to the Langmuir–Hinshelwood (LH) process, i.e. 3D diffusion of the ligand to the cell surface followed by reversible ligand adsorption and subsequent two-dimensional (2D) surface diffusion to the receptor. A situation where both mechanisms simultaneously contribute to the signalling process could also occur. The aim of this paper is to perform a computational study of the behavior of the signalling response when these different mechanisms for ligand-receptor interactions are integrated into a model for signal transduction and ligand transport. To this end, partial differential equations have been used to develop spatio-temporal models that show trafficking dynamics of ligands, cell surface components, and intracellular signalling molecules through the different domains of the system. The mathematical modeling developed for these mechanisms has been applied to the study of two situations frequently found in cell systems: (a) dependence of the signal response on cell density; and (b) enhancement of the signalling response in a synaptic environment.     

A kinetic model for virus binding which involves release of cell-bound virus-receptor complexes

A general kinetic mechanism is presented for reversible binding of viruses to cells followed by an irreversible step that initiates the delivery of the viral genome. A novel feature is additional pathways for the release of both virus-occupied and unoccupied receptors from cells. Due to one simplifying assumption, it does not apply at low receptor densities. However, it is sufficiently general to be applicable to ligand binding and internalization for those systems in which ligand diffusion is rate limiting. Three different versions of the model fit the usual kinetic data for the binding of an eclipse mutant of bacteriophage phi X174 to Escherichia coli. However, in each case binding to cell-bound receptors is irreversible. Therefore, this explains the apparent failure of this system to obey the Law of Mass Action. One version of the model also predicts that the release rate of lipopolysaccharide receptors from the outer membrane may be significantly lowered when virus is bound to these receptors.     

Spatio-temporal dependence of the signaling response in immune-receptor trafficking networks regulated by cell density: a theoretical model

Cell signaling processes involve receptor trafficking through highly connected networks of interacting components. The binding of surface receptors to their specific ligands is a key factor for the control and triggering of signaling pathways. In most experimental systems, ligand concentration and cell density vary within a wide range of values. Dependence of the signal response on cell density is related with the extracellular volume available per cell. This dependence has previously been studied using non-spatial models which assume that signaling components are well mixed and uniformly distributed in a single compartment. In this paper, a mathematical model that shows the influence exerted by cell density on the spatio-temporal evolution of ligands, cell surface receptors, and intracellular signaling molecules is developed. To this end, partial differential equations were used to model ligand and receptor trafficking dynamics through the different domains of the whole system. This enabled us to analyze several interesting features involved with these systems, namely: a) how the perturbation caused by the signaling response propagates through the system; b) receptor internalization dynamics and how cell density affects the robustness of dose-response curves upon variation of the binding affinity; and c) that enhanced correlations between ligand input and system response are obtained under conditions that result in larger perturbations of the equilibrium ligand + surface receptor [Please see text] ligand - receptor complex. Finally, the results are compared with those obtained by considering that the above components are well mixed in a single compartment.     

Determinants of ligand binding specificity in the glial cell line-derived neurotrophic factor family receptor alpha S

The glial cell line-derived neurotrophic factor (GDNF) family comprise a subclass of cystine-knot superfamily ligands that interact with a multisubunit receptor complex formed by the c-Ret tyrosine kinase and a cystine-rich glycosyl phosphatidylinositol-anchored binding subunit called GDNF family receptor alpha (GFRalpha). All four GDNF family ligands utilize c-Ret as a common signaling receptor, whereas specificity is conferred by differential binding to four distinct GFRalpha homologues. To understand how the different GFRalphas discriminate ligands, we have constructed a large set of chimeric and truncated receptors and analyzed their ligand binding and signaling capabilities. The major determinant of ligand binding was found in the most conserved region of the molecule, a central domain predicted to contain four conserved alpha helices and two beta strands. Distinct hydrophobic and positively charged residues in this central region were required for binding of GFRalpha1 to GDNF. Interaction of GFRalpha1 and GFRalpha2 with GDNF and neurturin required distinct subsegments within this central domain, which allowed the construction of chimeric receptors that responded equally well to both ligands. C-terminal segments adjacent to the central domain are necessary and have modulatory function in ligand binding. In contrast, the N-terminal domain was dispensable without compromising ligand binding specificity. Ligand-independent interaction with c-Ret also resides in the central domain of GFRalpha1, albeit within a distinct and smaller region than that required for ligand binding. Our results indicate that the central region of this class of receptors constitutes a novel binding domain for cystine-knot superfamily ligands.