A mathematical model for dynamics of CD40 clustering

Ligand bound-receptors in a signalosome complex trigger signals to determine cellular functions. Upon ligand binding, the ligand–receptor complexes form clusters on cell membrane. Guided by the previous experimental reports on the cluster formation of CD40, a trans membrane receptor for CD40-ligand, we built a minimal model of the receptor cluster formation. In this model, we studied co-operative and non-co-operative clustering of a maximum of four CD40 molecules assuming a positive mediator of clustering such as cholesterol to be present in both cases. We observed that co-operative interactions between CD40 molecules resulted in more of the largest CD40 clusters than that observed with the non-co-operatively interacting CD40 molecules. We performed global sensitivity analysis on the model parameters and the analyses suggested that cholesterol influenced only the initial stage of the co-operatively clustering CD40 molecules but it affects both the initial and the final stages in case of the non-co-operatively clustering CD40 molecules. Robustness analyses revealed that in both co-operative and non-co-operative interactions, the higher order clusters beyond a critical size are more robust with respect to alterations in the environmental parameters including the cholesterol. Thus, the role of co-operative and non-co-operative interactions in environment-influenced receptor clustering is reported for the first time.     

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.     

Residence time of receptor-ligand complexes and its effect on biological function

The formation and duration of binary receptor-ligand complexes are fundamental to many physiologic processes. Most often, the effectiveness of interaction between a receptor and its ligand is quantified in terms of closed system, equilibrium affinity measurements, such as IC50 and Kd. In the context of in vivo biology, however, the extent and duration of responses to receptor-ligand interactions depend greatly on the time period over which the ligand is in residence on its receptor. Here we define receptor-ligand complex residence time in quantitative terms and describe its significance to biological function. Examples of the importance of residence time are presented for natural ligands of different receptor types. The impact of residence time on the optimization of potential ligands as drugs for human medicine is also described.     

Increased mobility of major histocompatibility complex I-peptide complexes decreases the sensitivity of antigen recognition

CD8(+) cytotoxic T lymphocytes (CTL) can recognize and kill target cells expressing only a few cognate major histocompatibility complex (MHC) I-peptide complexes. This high sensitivity requires efficient scanning of a vast number of highly diverse MHC I-peptide complexes by the T cell receptor in the contact site of transient conjugates formed mainly by nonspecific interactions of ICAM-1 and LFA-1. Tracking of single H-2K(d) molecules loaded with fluorescent peptides on target cells and nascent conjugates with CTL showed dynamic transitions between states of free diffusion and immobility. The immobilizations were explained by association of MHC I-peptide complexes with ICAM-1 and strongly increased their local concentration in cell adhesion sites and hence their scanning by T cell receptor. In nascent immunological synapses cognate complexes became immobile, whereas noncognate ones diffused out again. Interfering with this mobility modulation-based concentration and sorting of MHC I-peptide complexes strongly impaired the sensitivity of antigen recognition by CTL, demonstrating that it constitutes a new basic aspect of antigen presentation by MHC I molecules.     

Studies on stimulus-response coupling in human neutrophils. II. Relationships between the effects of changes of external ionic composition on the properties of N-formylmethionylleucylphenylalanine receptors and on the respiratory and secretory responses

Studies were carried out on the mechanism responsible for the enhancement of the respiratory and secretory responses to N-formylmethionylleucylphenylalanine (fMet-Leu-Phe) exhibited by human neutrophils suspended in Na+-free, high-K+ buffered solution. The results demonstrate that: (a) the variation of Na+ concentration in the suspending solution induces in human neutrophils a marked modification of the recognition apparatus for the chemotactic peptide fMet-Leu-Phe, the lack of or low concentration of this ion increasing the number of the receptors and their specific affinity for the ligand; (b) the greater respiratory burst and secretion induced by fMet-Leu-Phe in human neutrophils suspended in Na+-free, high-K+ medium are due to the increased formation of receptor-ligand complexes at the cell membrane; (c) the greater respiratory response is partially due also to a higher efficiency of these receptor-ligand complexes. The molecular mechanism by which Na+ exerts a regulative role on the properties of the recognition apparatus for the chemotactic peptide and its possible significance are discussed.     

Mechanical modulation of receptor-ligand interactions at cell-cell interfaces

Cell surface receptors have been extensively studied because they initiate and regulate signal transduction cascades leading to a variety of functional cellular outcomes. An important class of immune receptors (e.g., T-cell antigen receptors) whose ligands are anchored to the surfaces of other cells remain poorly understood. The mechanism by which ligand binding initiates receptor phosphorylation, a process termed “receptor triggering”, remains controversial. Recently, direct measurements of the (two-dimensional) receptor-ligand complex lifetimes at cell-cell interface were found to be smaller than (three-dimensional) lifetimes in solution but the underlying mechanism is unknown. At the cell-cell interface, the receptor-ligand complex spans a short intermembrane distance (15 nm) compared to long surface molecules (LSMs) whose ectodomains span >40 nm and these LSMs include phosphatases (e.g., CD45) that dephosphorylate the receptor. It has been proposed that size-based segregation of LSMs from a receptor-ligand complex is a mechanism of receptor triggering but it is unclear whether the mechanochemistry supports such small-scale segregation. Here we present a nanometer-scale mathematical model that couples membrane elasticity with the compressional stiffness and lateral mobility of LSMs. We find robust supradiffusive segregation of LSMs from a single receptor-ligand complex. The model predicts that LSM redistribution will result in a time-dependent tension on the complex leading to a decreased two-dimensional lifetime. Interestingly, the model predicts a nonlinear relationship between the three- and two-dimensional lifetimes, which can enhance the ability of receptors to discriminate between similar ligands.     

Obligatory role for cooperative signaling by pre-TCR and Notch during thymocyte differentiation

The first checkpoint during T cell development, known as beta selection, requires the successful rearrangement of the TCR-beta gene locus. Notch signaling has been implicated in various stages during T lymphopoiesis. However, it is unclear whether Notch receptor-ligand interactions are necessary during beta selection. Here, we show that pre-TCR signaling concurrent with Notch receptor and Delta-like-1 ligand interactions are required for the survival, proliferation, and differentiation of mouse CD4(-)CD8(-) thymocytes to the CD4(+)CD8(+) stage. Furthermore, we address the minimal signaling requirements underlying beta selection and show a hierarchical positioning of key proximal signaling molecules. Collectively, our results demonstrate an essential role for Notch receptor-ligand interactions in enabling the autonomous signaling capacity of the pre-TCR complex.     

Morphology of cell-substratum adhesion. Influence of receptor heterogeneity and nonspecific forces.

Many cell types modulate growth, differentiation, and motility through changes in cell substrate adhesion, including regulation of focal contact formation. Clustering of cell surface adhesion receptors is an essential early step in the development of focal contacts, and thus may influence cell physiology. In this paper, we present a theoretical framework to examine how cell surface chemistry affects receptor clustering. Our one-dimensional tape-peeling model couples the equations of mechanical equilibrium for a cell membrane with kinetic receptor-ligand binding relations. We considered two distinct model scenarios: Adhesion mediated by multiple receptor-ligand interactions of different length and specific binding of a single receptor type occurs in the presence of van der Waals attraction and nonspecific repulsion. In each case, nonuniform (wave-like) membrane morphologies are observed in certain parameter ranges that support the clustering of adhesion receptors. The formation of these morphologies is described in terms of a balance of membrane stresses; when cell-surface potential as a function of separation distance is symmetric between two potential energy minima, nonuniform morphologies are obtained. Increases in the chemical binding energy between receptor and ligand (e.g., increases in ligand density) or decreases in the membrane rigidity result in smaller wavelengths for nonuniform interfaces. Additionally, we show wave-like geometries appear only when the mechanical compliance of receptor-ligand bonds is within an intermediate range, and examine how the mobility of "repellers"--glycocalyx molecules that exert a nonspecific repulsive force--influences membrane morphology. We find fully mobile repellers always redistribute to prevent nonuniform morphologies.     

The membrane anchor influences ligand binding two-dimensional kinetic rates and three-dimensional affinity of FcgammaRIII (CD16)

Kinetic rates and affinity are essential determinants for biological processes that involve receptor-ligand binding. By using a micropipette method, we measured the kinetics of human Fcgamma receptor III (CD16) interacting with IgG when the two molecules were bound to apposing cellular membranes. CD16 is one of only four eukaryotic receptors known to exist natively in both the transmembrane (TM, CD16a) and glycosylphosphatidylinositol (GPI, CD16b) isoforms. The biological significance of this anchor isoform coexistence is not clear. Here we showed that the anchor influenced kinetic rates; compared with CD16a-TM, CD16a-GPI bound faster and with higher affinities to human and rabbit IgGs but slower and with lower affinity to murine IgG2a. The same differential affinity patterns were observed using soluble IgG ligands. A monoclonal antibody bound CD16a-GPI with higher affinity than CD16a-TM, whereas another monoclonal antibody reacted strongly with CD16a-TM but weakly with CD16a-GPI. No major differential glycosylation between the two CD16a isoforms was detected by SDS-polyacrylamide gel electrophoresis analysis. We suggest a conformational difference as the mechanism underlying the observed anchor effect, as it cannot be explained by the differing diffusivity, flexibility, orientation, height, distribution, or clustering of the two molecules on the cell membrane. These data demonstrate that a covalent modification of an Ig superfamily receptor at the carboxyl terminus of the ectodomain can have an impact on ligand binding kinetics.     

Mannose-specific endocytosis receptor of alveolar macrophages: demonstration of two functionally distinct intracellular pools of receptor and their roles in receptor recycling

Receptor-mediated endocytosis of rat preputial beta-glucuronidase and the glycoconjugate mannose-BSA by rat alveolar macrophages is inhibited by chloroquine and ammonium chloride. We have previously reported that these drugs cause a loss of cell surface binding activity and that they do not inhibit internalization of receptor ligand complexes when incubated with cells at 37 degrees C. In this report we more clearly delineate the intracellular site of weak base inhibition of receptor recycling and the mechanism of that inhibition. From our analysis of the kinetics of ligand transport we conclude that there are two functionally distinct intracellular pools of receptor. One of these, the cycling pool, is not sensitive to the presence of weak bases, and receptor-ligand complexes return from this pool to the cell surface intact. The second pool is responsible for the time-dependent intracellular delivery of ligand to acid vesicles, which is inhibited by weak bases. Chloroquine and ammonium chloride appear to inhibit the dissociation of receptor-ligand complexed in this second pool and thereby the production of free receptors for the continuation of receptor-mediated endocytosis. We examine the internalization and binding of ligand in normal and paraformaldehyde-treated cells and find that these are strongly affected by pH. In particular, the dissociation rate of receptor ligand complexes is enhanced greater than 7.5 fold by lowering the medium pH from 7 to 6. From these results we propose that weak bases raise the pH of acid intracellular compartments, slowing the rate of receptor-ligand dissociation and thereby reducing the cellular pool of free receptors available for further uptake of ligand. In addition, we demonstrate that receptor-ligand complexes cannot return to the cell surface from the amine-sensitive (acid) intracellular pool that led us to call this the nonreleasable pool. This final observation indicates that receptor movements through these two pools are functionally distinct processes.     

Detection of liposome membrane viscosity perturbations with ratiometric molecular rotors

Molecular rotors are a form of fluorescent intramolecular charge-transfer complexes that can undergo intramolecular twisting motion upon photoexcitation. Twisted-state formation leads to non-radiative relaxation that competes with fluorescence emission. In bulk solutions, these molecules exhibit a viscosity-dependent quantum yield. On the molecular scale, the fluorescence emission is a function of the local free volume, which in turn is related to the local micro-viscosity. Membrane viscosity, and the inverse; fluidity, are characteristic terms used to describe the ease of movement withing the membrane. Often, changes in membrane viscosity govern intracellular processes and are indicative of a disease state. Molecular rotors have been used to investigate viscosity changes in liposomes and cells, but accuracy is affected by local concentration gradients and sample optical properties. We have developed self-calibrating ratiometric molecular rotors to overcome this challenge and integrated the new molecules into a DLPC liposome model exposed to the membrane-fluidizing agent propanol. We show that the ratiometric emission intensity linearly decreases with the propanol exposure and that the ratiometric intensity is widely independent of the total liposome concentration. Conversely, dye concentration inside liposomes influences the sensitivity of the system. We suggest that the new self-calibrating dyes can be used for real-time viscosity sensing in liposome systems with the advantages of lifetime measurements, but with low-cost steady-state instrumentation.     

Formation of stable homomeric and transient heteromeric bone morphogenetic protein (BMP) receptor complexes regulates Smad protein signaling

The type I and type II bone morphogenetic protein receptors (BMPRI and BMPRII) are present at the plasma membrane as monomers and homomeric and heteromeric complexes, which are modulated by ligand binding. The complexes of their extracellular domains with ligand were shown to form heterotetramers. However, the dynamics of the oligomeric interactions among the full-length receptors in live cell membranes were not explored, and the roles of BMP receptor homodimerization were unknown. Here, we investigated these issues by combining patching/immobilization of an epitope-tagged BMP receptor at the cell surface with measurements of the lateral diffusion of a co-expressed, differently tagged BMP receptor by fluorescence recovery after photobleaching (FRAP). These studies led to several novel conclusions. (a) All homomeric complexes (without or with BMP-2) were stable on the patch/FRAP time scale (minutes), whereas the heterocomplexes were transient, a difference that may affect signaling. (b) Patch/FRAP between HA- and myc-tagged BMPRII combined with competition by untagged BMPRIb showed that the heterocomplexes form at the expense of homodimers. (c) Stabilization of BMPRII·BMPRIb heterocomplexes (but not homomeric complexes) by IgG binding to same-tag receptors elevated phospho-Smad formation both without and with BMP-2. These findings suggest two mechanisms that may suppress the tendency of preformed BMP receptor hetero-oligomers to signal without ligand: (a) competition between homo- and heterocomplex formation, which reduces the steady-state level of the latter, and (b) the transient nature of the heterocomplexes, which limits the time during which BMPRI can be phosphorylated by BMPRII in the heterocomplex.     

Morphology of cell-substratum adhesion

Many cell types modulate growth, differentiation, and motility through changes in cell substrate adhesion, including regulation of focal contact formation. Clustering of cell surface adhesion receptors is an essential early step in the development of focal contacts, and thus may influence cell physiology. In this paper, we present a theoretical framework to examine how cell surface chemistry affects receptor clustering. Our one-dimensional tape-peeling model couples the equations of mechanical equilibrium for a cell membrane with kinetic receptor-ligand binding relations. We considered two distinct model scenarios: Adhesion mediated by multiple receptor-ligand interactions of different length and specific binding of a single receptor type occurs in the presence of van der Waals attraction and nonspecific repulsion. In each case, nonuniform (wave-like) membrane morphologies are observed in certain parameter ranges that support the clustering of adhesion receptors. The formation of these morphologies is described in terms of a balance of membrane stresses; when cell-surface potential as a function of separation distance is symmetric between two potential energy minima, nonuniform morphologies are obtained. Increases in the chemical binding energy between receptor and ligand (e.g., increases in ligand density) or decreases in the membrane rigidity result in smaller wavelengths for nonuniform interfaces. Additionally, we show wave-like geometries appear only when the mechanical compliance of receptor-ligand bonds is within an intermediate range, and examine how the mobility of “repellers”—glycocalyx molecules that exert a nonspecific repulsive force—influences membrane morphology. We find fully mobile repellers always redistribute to prevent nonuniform morphologies.     

Receptor dissociation constants and the information entropy of membranes coding ligand concentration

The binding of ligands to receptor proteins embedded in cell membranes drives cellular responses that involve either second messenger cascades or directly gated ion channels. It is known that a single class of receptor proteins expresses approximately 98% of its graded response to ligand concentrations over four orders of magnitude, where the response is measured by the equilibrium proportion of bound ligand-receptor complexes. This four-decadic concentration range is centered on a logarithmic scale around logK, where K is the dissociation constant defined by the ratio of ligand-receptor unbinding (k-) to binding (k+) rates. Remarkably, this four-decadic concentration range is intrinsic to all homogeneous ligand-receptor (or, equivalently, enzyme-substrate) systems. Thus, adapting the sensitivity of cell membranes to narrower or wider ranges of ligand concentrations, respectively, requires multivalent receptors or heterogeneous populations of receptors. Here we use a normalized Shannon-Weaver measure of information entropy to represent the efficiency of coding over given concentrations for membranes containing a population of univalent receptors with a specified distribution of dissociation constants, or a homogeneous population of strongly cooperative multivalent receptors. Assuming a specified level of resolution in the response of cellular or neural systems downstream from the membrane that 'read' the ligand concentration 'code', we calculate the range of concentrations over which the coding efficiency of the membrane itself is maximized. Our results can be used to hypothesize the number of receptor types associated with the membranes of particular cells. For example, from data in the literature, we conclude that the response of most general olfactory sensory neurons can be explained in terms of a homogeneous population of receptor proteins, while the response of pheromone sensory neurons is satisfactorily explained by the presence of two types of membrane receptor protein with pheromone-binding dissociation constants that have values at least one to two orders of magnitude apart.     

Studies on stimulus-response coupling in human neutrophils: II. Relationships between the effects of changes of external ionic composition on the properties of N-formylmethionylleucylphenylalanine receptors and on the respiratory and secretory responses

Studies were carried out on the mechanism responsible for the enhancement of the respiratory and secretory responses to N-formylmethionylleucylphenylalanine (fMet-Leu-Phe) exhibited by human neutrophils suspended in Na⁺-free, high-K⁺ buffered solution. The results demonstrate that: (a) the variation of Na⁺ concentration in the suspending solution induces in human neutrophils a marked modification of the recognition apparatus for the chemotactic peptide fMet-Leu-Phe, the lack of or low concentration of this ion increasing the number of the receptors and their specific affinity for the ligand; (b) the greater respiratory burst and secretion induced by fMet-Leu-Phe in human neutrophils suspended in Na⁺-free, high-K⁺ medium are due to the increased formation of receptor-ligand complexes at the cell membrane; (c) the greater respiratory response is partially due also to a higher efficiency of these receptor-ligand complexes. The molecular mechanism by which Na⁺ exerts a regulative role on the properties of the recognition apparatus for the chemotactic peptide and its possible significance are discussed.     

Intrinsic Selectivity of Notch 1 for Delta-like 4 Over Delta-like 1

Notch signaling makes critical contributions to cell fate determination in all metazoan organisms, yet remarkably little is known about the binding affinity of the four mammalian Notch receptors for their three Delta-like and two Jagged family ligands. Here, we utilized signaling assays and biochemical studies of purified recombinant ligand and receptor molecules to investigate the differences in signaling behavior and intrinsic affinity between Notch1-Dll1 and Notch1-Dll4 complexes. Systematic deletion mutagenesis of the human Notch1 ectodomain revealed that epidermal growth factor (EGF) repeats 6–15 are sufficient to maintain signaling in a reporter assay at levels comparable with the full-length receptor, and identified important contributions from EGF repeats 8–10 in conveying an activating signal in response to either Dll1 or Dll4. Truncation studies of the Dll1 and Dll4 ectodomains showed that the MNNL-EGF3 region was both necessary and sufficient for full activation. Plate-based and cell binding assays revealed a specific, calcium-dependent interaction between cell-surface and recombinant Notch receptors and ligand molecules. Finally, direct measurement of the binding affinity of Notch1 EGF repeats 6–15 for Dll1 and Dll4 revealed that Dll4 binds with at least an order of magnitude higher affinity than Dll1. Together, these studies give new insights into the features of ligand recognition by Notch1, and highlight how intrinsic differences in the biochemical behavior of receptor-ligand complexes can influence receptor-mediated responses of developmental signaling pathways.     

Matched sizes of activating and inhibitory receptor/ligand pairs are required for optimal signal integration by human natural killer cells

It has been suggested that receptor-ligand complexes segregate or co-localise within immune synapses according to their size, and this is important for receptor signaling. Here, we set out to test the importance of receptor-ligand complex dimensions for immune surveillance of target cells by human Natural Killer (NK) cells. NK cell activation is regulated by integrating signals from activating receptors, such as NKG2D, and inhibitory receptors, such as KIR2DL1. Elongating the NKG2D ligand MICA reduced its ability to trigger NK cell activation. Conversely, elongation of KIR2DL1 ligand HLA-C reduced its ability to inhibit NK cells. Whereas normal-sized HLA-C was most effective at inhibiting activation by normal-length MICA, only elongated HLA-C could inhibit activation by elongated MICA. Moreover, HLA-C and MICA that were matched in size co-localised, whereas HLA-C and MICA that were different in size were segregated. These results demonstrate that receptor-ligand dimensions are important in NK cell recognition, and suggest that optimal integration of activating and inhibitory receptor signals requires the receptor-ligand complexes to have similar dimensions.