Spatiotemporal measurement of concentration-dependent diffusion coefficient

Abstract

We introduce a method to measure the concentration-dependent diffusion coefficient from a sequence of images of molecules diffusing from a source toward a sink. Generally, approaches measuring the diffusion coefficient, such as fluorescence recovery after photobleaching (FRAP), assume that the diffusion coefficient is constant. Hence, these methods cannot capture the concentration dependence of the diffusion coefficient if present. Other approaches measure the concentration-dependent diffusion coefficient from an instantaneous concentration profile and lose the temporal information. These methods make unrealistic assumptions, are not robust, and lead to 100% error. We introduce an image analysis framework that utilizes spatial and temporal information in a sequence of concentration images and numerically solves the general form of Fick's second law using radial basis functions (RBF) to measure the concentration-dependent diffusion coefficient. We term this approach as concentration image diffusimetry (CID). Our method makes no assumptions about the sink and source size and the diffusion dependence on concentration. CID is superior to existing methods in estimating spatiotemporal changes and concentration-dependent diffusion. CID also provides a statistical uncertainty quantification on the measurements using a bootstrapping approach, improving the reliability of the diffusion measurement. We assessed CID's performance using synthetically generated images. Our analysis suggests that CID accurately measures the diffusion coefficient with less than 2% error for most cases. We validated CID with FRAP experimental images and showed that CID agrees with established FRAP algorithms for samples with a constant diffusion coefficient. Finally, we demonstrate the application of CID to experimental datasets of a concentration gradient-driven protein diffusion into a tissue replicate. In conclusion, this work presents an image-based methodology that uses the spatial and temporal changes of concentration fields to measure the concentration-dependent diffusion coefficient.