Extracting diffusion dynamics from the fluctuations in photothermal images


This is a guest post by Dan Nieves, who was until recently a joint member of Raphael and Dave’s labs. Dan has moved as far as he could go from us: he is now residing in Sydney at the EMBL Australia node for Single Molecule Science at the University of New South Wales.

Today, our paper from my time at Liverpool “Photothermal Raster Image Correlation Spectroscopy (PhRICS) of gold nanoparticles in solution and on live cells was published in the new Royal Society open-access journal, Royal Society Open Science.  This journal is committed to an open peer-review system, thus, the review history and referees comments are viewable alongside the article, and also post publication peer-review in the form of a comments section below the paper is facilitated. Additionally, the data that supports the conclusions of the paper are (and have to be) readily accessible (here at Figshare). This is exciting, as not only are the discussions between authors and referees are available to everyone, but you can also join in the discussion fully after publication with access to the primary data. Therefore, the critical evaluation/re-evaluation of the work is totally encouraged and should never stop!

Our paper describes the development of an extension of photothermal heterodyne imaging; a technique used to detect and image single gold nanoparticles much smaller than the diffraction limit at high signal to noise via scattering induced by laser light absorption (nice explanation here). The extension employs fast raster-scan imaging of the sample in which fluctuations, or “streaks” (top panels, Fig.1), are observed due to the movement of nanoparticles through the detection volume during the scan. From these fluctuations it is possible to extract how fast the nanoparticles are moving from the application of image correlation analyses.  In our particular case, we applied the raster image correlation spectroscopy (RICS) method, developed in the lab of Enrico Gratton (original paper here). Briefly, after acquiring many raster scan images; the images are then spatially correlated with themselves by shifting the image pixel by pixel in all directions (x and y in this case) and calculating the correlation function.  This means repeating fluctuations within the image, i.e., nanoparticle diffusion, will be reflected in the time it takes for the spatial correlation to decay, for example, the spatial correlations for movement of slow moving objects decays quite differently to that of fast moving objects (lower panels, Fig.1). From the spatial correlations the diffusion behavior, such as the diffusion coefficient, can be extracted.  In our case, I applied the analysis to photothermal images of 8.8nm gold nanoparticles diffusing in solutions of different viscosity to verify the PhRICS approach (Fig.1). Here, we were able to extract the diffusion coefficients of the nanoparticles in the different solutions. The advantage of this approach compared to the current photothermal heterodyne techniques for probing diffusion (photothermal tracking and absorption correlation spectroscopy) is that not only can we acquire rapidly information on fast diffusion dynamics, but we can also observe the distribution of nanoparticles over the relatively large area of the image (≈ 40 μm2).



Fig.1 – Example of gold nanoparticle diffusion in solutions of different viscosity (top panel) with the corresponding spatial correlations (bottom panel).

We then turned our attention to the use of the technique to observe the diffusion of fibroblast growth factors labelled with gold nanoparticles on live cells. FGFs are involved in a wide range of essential biological processes from the formation of morphogen gradients and signalling to homeostatic control of glucose and phosphate levels.  Here, 8.8 nm gold nanoparticles were used to covalently label single fibroblast growth factor 2 proteins (FGF2-NP: via this method), and then incubated with live rat mammary fibroblast cells (Fig.2).  It was observed previously in our lab that there is significant heterogeneity in FGF2 distribution and diffusion in the pericellular matrix when bound to heparan sulphate. We found the diffusion coefficient of the FGF2-NP could be extracted, and that diffusion measurements were variable depending on the area imaged.  Additionally, it is apparent that the image data contained much more information than we could extract using the simple diffusion model applied.  The observation of the formation and dissolution of intense peaks within the images, added to the 2D-movement of such peaks from image to image (see Movie1), gives more insight into the dynamic long range restructuring of the pericellular matrix of live cells at “short” (μs and ms) and “longer” (secs and mins) timescales.


Fig.2 – Photothermal image of rat mammary fibroblast incubated with 600 pM of FGF2-NP.  Blue boxes indicate the areas where PhRICS imaging was performed on the cell.


Movie1 – PhRICS image series from box 5 in Fig.2

The paper is now available at the Royal Society Open Science , and if your interest has been piqued thus far, I strongly encourage you check the paper out.  Better still would be for you to engage in the post-publication comments section should you have any questions, comments or suggestions.


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