Raibatak Das

A Hidden Markov Model for Single Particle Tracks Quantifies Dynamic Interactions between LFA-1 and the Actin Cytoskeleton

The extraction of hidden information from complex trajectories is a continuing problem in single-particle and single-molecule experiments. Particle trajectories are the result of multiple phenomena, and new methods for revealing changes in molecular processes are needed. We have developed a practical technique that is capable of identifying multiple states of diffusion within experimental trajectories. We model single particle tracks for a membrane-associated protein interacting with a homogeneously distributed binding partner and show that, with certain simplifying assumptions, particle trajectories can be regarded as the outcome of a two-state hidden Markov model. Using simulated trajectories, we demonstrate that this model can be used to identify the key biophysical parameters for such a system, namely the diffusion coefficients of the underlying states, and the rates of transition between them. We use a stochastic optimization scheme to compute maximum likelihood estimates of these parameters. We have applied this analysis to single-particle trajectories of the integrin receptor lymphocyte function-associated antigen-1 (LFA-1) on live T cells. Our analysis reveals that the diffusion of LFA-1 is indeed approximately two-state, and is characterized by large changes in cytoskeletal interactions upon cellular activation.

A Role for Rebinding in Rapid and Reliable T Cell Responses to Antigen

Experimental work has shown that T cells of the immune system rapidly and specifically respond to antigenic molecules presented on the surface of antigen-presenting-cells and are able to discriminate between potential stimuli based on the kinetic parameters of the T cell receptor-antigen bond. These antigenic molecules are presented among thousands of chemically similar endogenous peptides, raising the question of how T cells can reliably make a decision to respond to certain antigens but not others within minutes of encountering an antigen presenting cell. In this theoretical study, we investigate the role of localized rebinding between a T cell receptor and an antigen. We show that by allowing the signaling state of individual receptors to persist during brief unbinding events, T cells are able to discriminate antigens based on both their unbinding and rebinding rates. We demonstrate that T cell receptor coreceptors, but not receptor clustering, are important in promoting localized rebinding, and show that requiring rebinding for productive signaling reduces signals from a high concentration of endogenous pMHC. In developing our main results, we use a relatively simple model based on kinetic proofreading. However, we additionally show that all our results are recapitulated when we use a detailed T cell receptor signaling model. We discuss our results in the context of existing models and recent experimental work and propose new experiments to test our findings.

Toll-like receptor ligands sensitize B-cell receptor signalling by reducing actin-dependent spatial confinement of the receptor

Integrating signals from multiple receptors allows cells to interpret the physiological context in which a signal is received. Here we describe a mechanism for receptor crosstalk in which receptor-induced increases in actin dynamics lower the threshold for signalling by another receptor. We show that the Toll-like receptor ligands lipopolysaccharide and CpG DNA, which are conserved microbial molecules, enhance signalling by the B-cell antigen receptor (BCR) by activating the actin-severing protein cofilin. Single-particle tracking reveals that increased severing of actin filaments reduces the spatial confinement of the BCR within the plasma membrane and increases BCR mobility. This allows more frequent collisions between BCRs and greater signalling in response to low densities of membrane-bound antigen. These findings implicate actin dynamics as a means of tuning receptor signalling and as a mechanism by which B cells distinguish inert antigens from those that are accompanied by indicators of microbial infection.

Dynamic Regulation of CD45 Lateral Mobility by the Spectrin-Ankyrin Cytoskeleton of T Cells

The leukocyte common antigen, CD45, is a critical immune regulator whose activity is modulated by cytoskeletal interactions. Components of the spectrin-ankyrin cytoskeleton have been implicated in the trafficking and signaling of CD45. We have examined the lateral mobility of CD45 in resting and activated T lymphocytes using single-particle tracking and found that the receptor has decreased mobility caused by increased cytoskeletal contacts in activated cells. Experiments with cells that have disrupted βΙ spectrin interactions show decreased cytoskeletal contacts in resting cells and attenuation of receptor immobilization in activated cells. Applying two types of population analyses to single-particle tracking trajectories, we find good agreement between the diffusion coefficients obtained using either a mean squared displacement analysis or a hidden Markov model analysis. Hidden Markov model analysis also reveals the rate of association and dissociation of CD45-cytoskeleton contacts, demonstrating the importance of this analysis for measuring cytoskeleton binding events in live cells. Our findings are consistent with a model in which multiple cytoskeletal contacts, including those with spectrin and ankyrin, participate in the regulation of CD45 lateral mobility. These interactions are a major factor in CD45 immobilization in activated cells. Furthermore, cellular activation leads to CD45 immobilization by reduction of the CD45-cytoskeleton dissociation rate. Short peptides that mimic spectrin repeat domains alter the association rate of CD45 to the cytoskeleton and cause an apparent decrease in dissociation rates. We propose a model for CD45-cytoskeleton interactions and conclude that the spectrin-ankyrin-actin network is an essential determinant of immunoreceptor mobility.

Analysis of membrane-localized binding kinetics with FRAP

Interactions between plasma membrane-associated proteins on interacting cells are critical for many important biological processes. Few experimental techniques, however, can accurately determine the association and the dissociation rates between such interacting pairs when the two molecules diffuse on apposing membranes or lipid bilayers. In this study, we give a theoretical description of how and when fluorescence recovery after photobleaching (FRAP) experiments can be used to quantify these reaction rates. We analyze the effect of binding on FRAP recovery curves with a reaction–diffusion model and systematically identify different regimes in the parameter space of the association and the dissociation constants for which the full model simplifies into equivalent one-parameter models. Based on this analysis, we propose an experimental protocol that may be used to identify the kinetic parameters of binding in the appropriate parameter regime. We present simulated experiments illustrating our protocol and lay down guidelines for parameter estimation.

Modeling Effect of a γ-Secretase Inhibitor on Amyloid-β Dynamics Reveals Significant Role of an Amyloid Clearance Mechanism

Aggregation of the small peptide amyloid beta (Aβ) into oligomers and fibrils in the brain is believed to be a precursor to Alzheimer’s disease. Aβ is produced via multiple proteolytic cleavages of amyloid precursor protein (APP), mediated by the enzymes β- and γ-secretase. In this study, we examine the temporal dynamics of soluble (unaggregated) Aβ in the plasma and cerebral-spinal fluid (CSF) of rhesus monkeys treated with different oral doses of a γ-secretase inhibitor. A dose-dependent reduction of Aβ concentration was observed within hours of drug ingestion, for all doses tested. Aβ concentration in the CSF returned to its predrug level over the monitoring period. In contrast, Aβ concentration in the plasma exhibited an unexpected overshoot to as high as 200% of the predrug concentration, and this overshoot persisted as late as 72 hours post-drug ingestion. To account for these observations, we proposed and analyzed a minimal physiological model for Aβ dynamics that could fit the data. Our analysis suggests that the overshoot arises from the attenuation of an Aβ clearance mechanism, possibly due to the inhibitor. Our model predicts that the efficacy of Aβ clearance recovers to its basal (pretreatment) value with a characteristic time of >48 hours, matching the time-scale of the overshoot. These results point to the need for a more detailed investigation of soluble Aβ clearance mechanisms and their interaction with Aβ-reducing drugs.

Real-time semiclassical initial value method and threshold tunneling probabilities

Abstract The semiclassical initial value representation (SCIVR) approach to tunneling is applied to a barrier which does not have a harmonic component and vanishes asymptotically. The lack of a harmonic approximation near the barrier top combined with the use of the primitive Van Vleck–Gutzwiller approximation provides a fairly stringent test for the SCIVR approach. In this paper we show that the primitive IVR performs rather well in obtaining the threshold tunneling probabilities for the nonharmonic barrier. In particular, we demonstrate that the threshold tunneling probabilities are reliable even in situations wherein the cutoff distances are large enough for tunneling loops to be formed.