Philippos K. Tsourkas

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.

Discrimination of membrane antigen affinity by B cells requires dominance of kinetic proofreading over serial engagement.

B-cell receptor signaling in response to membrane-bound antigen increases with antigen affinity, a process known as affinity discrimination. We use computational modeling to show that B-cell affinity discrimination requires that kinetic proofreading predominate over serial engagement. We find that if B-cell receptors become signaling-capable immediately upon antigen binding, which results in decreasing serial engagement as affinity increases, then increasing affinity can lead to weaker signaling. Rather, antigen must stay bound to B-cell receptors for a threshold time of several seconds before becoming signaling-capable, a process similar to kinetic proofreading. This process overcomes the loss in serial engagement due to increasing antigen affinity, and replicates the monotonic increase in B-cell signaling with increasing affinity that has been observed in B-cell activation experiments. This finding matches well with the experimentally observed time (∼20 s) required for the B-cell receptor signaling domains to undergo antigen and lipid raft-mediated conformational changes that lead to Src-family kinase recruitment. We hypothesize that the physical basis for a threshold time of antigen binding might lie in the formation timescale of B-cell receptor dimers. The time required for dimer formation decreases with increasing antigen affinity, thereby resulting in shorter threshold antigen binding times as affinity increases. Such an affinity-dependent kinetic proofreading requirement results in affinity discrimination very similar to that observed in biological experiments. B-cell affinity discrimination is critical to the process of affinity maturation and the production of high-affinity antibodies, and thus our results have important implications in applications such as vaccine design.

Modeling of B cell Synapse Formation by Monte Carlo Simulation Shows That Directed Transport of Receptor Molecules Is a Potential Formation Mechanism

The formation of the protein segregation structure known as the “immunological synapse” in the contact region between B cells and antigen presenting cells appears to precede antigen (Ag) uptake by B cells. The mature B cell synapse consists of a central cluster of B cell receptor/Antigen (BCR/Ag) complexes surrounded by a ring of LFA-1/ICAM-1 complexes. In this study, we used an in silico model to investigate whether cytoskeletally driven transport of molecules toward the center of the contact zone is a potential mechanism of immunological synapse formation in B cells. We modeled directed transport by the cytoskeleton in an effective manner, by biasing the diffusion of molecules toward the center of the contact zone. Our results clearly show that biased diffusion of BCR/Ag complexes on the B cell surface is sufficient to produce patterns similar to experimentally observed immunological synapses. This is true even in the presence of significant membrane deformation as a result of receptor–ligand binding, which in previous work we showed had a detrimental effect on synapse formation at high antigen affinity values. Comparison of our model’s results to those of experiments shows that our model produces synapses for realistic length, time, and affinity scales. Our results also show that strong biased diffusion of free molecules has a negative effect on synapse formation by excluding BCR/Ag complexes from the center of the contact zone. However, synapses may still form provided the bias in diffusion of free molecules is an order-of-magnitude weaker than that of BCR/Ag complexes. We also show how diffusion trajectories obtained from single-molecule tracking experiments can generate insight into the mechanism of synapse formation.

Monte Carlo study of B-cell receptor clustering mediated by antigen crosslinking and directed transport.

It is known from experiments that in the presence of soluble antigen, B-cell receptors (BCRs) assemble into microclusters and then collect into a macrocluster known as a ‘cap’. However, the mechanisms of BCR cluster formation during recognition of soluble antigens remain unclear. In previous work, we demonstrated that effective intrinsic attractions among BCRs can lead to the formation of small microclusters of BCR molecules. The effective intrinsic attractions could be caused by multivalent antigen binding, association with lipid rafts, or other biochemical factors. In the present study, we have developed and studied a Monte Carlo model of BCR clustering mediated by explicit binding and crosslinking of soluble bivalent antigens. Antigen crosslinking is shown to microcluster BCRs in an affinity-dependent manner and also in a biologically relevant timescale; however, antigen crosslinking alone does not appear to be sufficient for the formation of a single macrocluster of receptor molecules. We show that directed transport of BCRs is needed to drive the formation of large macroclusters. We constructed a simple model of directed transport, where BCR molecules diffuse towards the largest cluster or towards a random BCR microcluster, which results in a single macrocluster of receptor molecules. The mechanisms for both types of directed transport are compared using network-based metrics. We also develop and use appropriate network measures to analyze the effect of BCR and antigen concentration on BCR clustering, the stability of the formed clusters over time and the size of BCR–antigen crosslinked chains.

Monte Carlo Investigation of Diffusion of Receptors and Ligands that Bind Across Opposing Surfaces

Studies of receptor diffusion on a cell surface show a variety of behaviors, such as diffusive, sub-diffusive, or super-diffusive motion. However, most studies to date focus on receptor molecules diffusing on a single cell surface. We have previously studied receptor diffusion to probe the molecular mechanism of receptor clustering at the cell–cell junction between two opposing cell surfaces. Here, we characterize the diffusion of receptors and ligands that bind to each other across two opposing cell surfaces, as in cell–cell and cell–bilayer interactions. We use a Monte Carlo method, where receptors and ligands are simulated as independent agents that bind and diffuse probabilistically. We vary receptor–ligand binding affinity and plot the molecule-averaged mean square displacement (MSD) of ligand molecules as a function of time. Our results show that MSD plots are qualitatively different for flat and curved interfaces, as well as between the cases of presence and absence of directed transport of receptor–ligand complexes toward a specific location on the interface. Receptor–ligand binding across two opposing surfaces leads to transient sub-diffusive motion at early times provided the interface is flat. This effect is entirely absent if the interface is curved, however, in this instance we observe sub-diffusive motion. In addition, a decrease in the equilibrium value of the MSD occurs as affinity increases, something which is absent for a flat interface. In the presence of directed transport of receptor–ligand complexes, we observe super-diffusive motion at early times for a flat interface. Super-diffusive motion is absent for a curved interface, however, in this case we observe a transient decrease in MSD with time prior to equilibration for high-affinity values.