Diffusion and Camera-Noise Modelling for Analysis of Single-Particle Tracking Movies

Abstract: Interactions between T-cells and other body cells is an essential part of the immune system. It involves the binding between surface receptors of the two cells. Specifically, T-cell receptors (TCRs) bind onto pMHC (peptide-loaded major histocompatibility complex) molecules on the partnering cell surface. This way, a cell signal from the TCR to the nucleus can be initiated. Depending on the "message" of the signal, cells may respond in various ways. While it has been found that the signal message is dependent on how, where and when the signalling occurs, the interaction details and kinetics remain largely unclear. A specific observable that has been found experimentally is the average time duration of a binding event, called the "lifetime" of the interaction. To measure biophysical parameters in practise, e.g. diffusion constants or lifetimes, is not as straightforward as it may appear. In here, we consider an experimental setup which utilises fluorescence microscopy in a controlled environment. The TCRs are allowed to move on a supported lipid bilayer (mimicking a real cell membrane) and have been labelled with a fluorescent dye. The partnering pMHCs are free to move on the surfaces of live T-cells. As such, the motion of these proteins is effectively two-dimensional and the resultant pMHC trajectories can be imaged with a fluorescence microscopy setup with a suitable camera. After tracking the particles in a tracking program, we are left with data in the form of single-particle tracks. At this point, most conventional methods start by trying to estimate the diffusion constants (corresponding to free or bound TCR, respectively). For instance, this can be done with a usual mean-square-displacement analysis. Despite the importance of this data analysis step, many of its difficulties are often overlooked. These include systematic bias, such as tracking errors in the form of dot detection and dot linking. Moreover, there are uncharted errors involved in the analysis procedures and it is hard to assess the reliability and associated errors of estimated parameters. In this study, we assess the ability of analysis methods for estimating diffusion constants and the fraction of steps spent in a free versus a bound state. To be able to estimate the errors on parameter estimates and potential biases in these, we analyse tracking data from synthetic movies. To this end, we include the diffusive motion, binding as well as photon statistics and camera-induced noise in the imaging system. As a benefit, the synthetic movies allow us to test and assess less conventional analysis methods on the data. In particular, we test a hidden Markov model analysis scheme and systematically compare it to a step-size distribution analysis. Furthermore, reliable simulated results could help us mitigate the uncertainty involved in the analyses by indicating sound experimental modifications. This can be done by calibrating all simulation parameters to agree with experiments, such that whatever errors and biases we obtain when analysing synthetic movies, will correspond well to those obtained with experimental movies.