Ligand Receptor Binding Rate Kinetics via K-Space Image Correlation Spectroscopy: An in Silico Study

Abstract

To achieve a fundamental understanding of intra-cellular signalling pathways, it will be necessary to measure the rates of reaction between chemically reacting and interacting macromolecules. The magnitude of binding rates plays a very important molecular regulatory role in a range of systems including the binding of antigens to T-cell receptors, which can lead to differing immune-responses, as well as rates of hydrolysis of GTPs with Rac or Rho proteins, which lead to temporal changes in actin filament lengths and cell motility. Here, we develop an image correlation technique which may be used to study such systems in conjunction with fluorescence microscopy. We simulate receptors diffusing in 2D with diffusion coefficients varying from 0 to 10 pixels2/frame. Receptors are only visible as point emitters when a fluorescent ligand is bound to the receptor; ligand binding kinetics are created by turning receptors ‘on' or ‘off' with average life-times varying from 3 to 20 frames drawn from a negative exponential distribution. Photobleaching is similarly incorporated by permanently turning diffusing receptors ‘off' after average times varying from 20 to 400 frames. The image time-series is generated by convolving a Gaussian function of fixed radius with the point emitter distribution to create 128x128 pixel images with background noise added to give a signal to noise ratio of 3. We use k-space image correlation spectroscopy (kICS) and develop a two-state kinetic binding model with freely diffusing receptors on a 2D membrane to capture the membrane binding kinetics of the image time-series. We show that kICS can accurately recover on/off binding rates at the 95% confidence level for over 75% of simulations. Typically, percentage errors are less than 30% for weak photobleaching and within 60% for strong photobleaching effects.