Cursor analysis in the RICS page

RICS page

Cursor Analysis menu entry

Purpose: to perform the RICS analysis of a small region of an image as the cursor is dragged on the image. A one component diffusion analysis is also performed.

Use

Load an image stack to be analyzed. Select a ROI analysis size of 64 (any other size will work, but we suggest using a small size).

On the main RICS page menu select “cursor analysis”. The following menu should appear


You must select a type of analysis and then toggle the cursor analysis. The cursor analysis is active when the Select analysis is checked.

As you drag the cursor on the screen (image 1), in image 3 you will see the RICS function corresponding to the cursor position. In the caption of image 3 the result of the diffusion (one component) analysis is shown.

You must initialize the fit to be in a reasonable range. To initialize the fit, just press fit in the RICS page menu. Fill up the variables as needed. One example is shown below. These values will be used as a starting point for the cursor analysis.


The cursor analysis is intended to be a fast way to explore an image. If you want to systematically analyze the image and store the results of the RICS analysis in a file, then use the “Scan analysis” menu.

Tutorial on immobile subtraction in RICS

 

The RICS technique is sensitive to fluctuations in a relatively fast time scale. The fluctuations can be due to diffusion of molecules or to changes of fluorescence intensity due to binding-unbinding to fixed locations or similar processes. The basis of the RICS calculation is the 2D image correlation. This operation is sensitive to the spatial distribution of the fluorescence. Since we are interested in the fluctuating molecules, not in the distribution of fluorescence due to immobile molecules, we must subtract this distribution so that what is left is the distribution of the fluctuation particles. This is done using the Spatial correlation -<average> entry in the tools menu of the RICS screen.

 

The subtraction operation is performed according to the following algorithm

 

 

ICS indicates the image correlation operation, I_i(x,y) is the intensity of frame is the average frame, i.e., the average (pixel by pixel) of the entire stack. This is the image of the immobile fraction. a is the average of all values of the stack. Clearly, if there is no immobile fraction there is nothing to subtract according to the above formula because =a. If there is an immobile fraction with intensity different than the average, then there is something to subtract. The question is about what modifications, if any, the subtraction operation causes in the RICS parameters G(0,0) and the diffusion coefficients. The diffusion coefficients are not modified, since the immobile part is not contributing to the correlated fluctuations. Instead the G(0,0) value could be modified since the average intensity is modified after the subtraction operation. However, the average intensity, for the purpose of the calculation of the number of particles, was wrong from the very beginning. Let us evaluate if the correction bring us closer to the expected value.

 

Assume that we have a "sea" of diffusing particles and that we add immobile features to the overall intensity (if there are part of the image outside the cell, the intensity will be smaller in these regions. If the intensity in a give pixel is given by the sum of the mobile part and the immobile part, then the subtraction algorithm should re-establish the proper DC level provide we know exactly the amount of the immobile fraction. This scenario is schematically illustrated in the figure below.

 

 

 

In the example above, after the correction, the average value of the image is shifted up with respect to the "true" value, resulting in a smaller value of G(0,0). In the case in which we have parts outside the cell with lower intensity, the average is shifted down. The amount of "overshoot" or "undershoot" of the correction depends on the total integral of the bright and dark spots. Few bright spots will modify very little the G(0,0) of the mobile part. In principle, we could evaluate the average intensity only in the region where there are no bright of dark features and use that value as the average intensity. This procedure has not been yet implemented in SimFCS. We estimate that in normal situations, the G(0,0) obtained after subtraction of the immobile part is within factors of 2 of the "true" value.

 

 

Subtraction of a slowly varying bright image features.

 

In many experiments cells move, causing a slow change of the intensity at one pixel. Subtracting the average intensity at that pixel does not remove completely the slowly moving quasi-immobile features. This results in additional spatial correlations that overwhelm the correlations due to the RICS effect. In this case, it is better to subtract the average image calculated using only a limited number of frames and then update the average image according to the frame that needs to be subtracted. This procedure results in a very efficient removal of the slowly varying intensity at a pixel. The following figure illustrates how this operation works for one pixel.

 

 

The red curve indicates the slowly varying intensity at one pixel. Assume that we have 60 frames in our file. The movement of the cell causes variations of the intensity over the scale of about 10 frames. You select the method of moving average immobile fraction subtraction as shown in the figure below. Set the moving average field to 10. The average of the first 10 frames is calculated. Then this average is subtracted from the 5^th frame, since this frame corresponds to the center of the moving average window. The ICS of the subtracted frame is calculated. Then we advance to the following frame. We recalculate the moving average by shifting the moving window by one frame unit. The operation is repeated until 5 frames are left. At this point the operation terminates and the resulting ICS function is displayed.

 

 

The minimum value of the moving average segment is 2. We suggest to use relatively small values for the moving average, between 5 and 20, since the half of the window is subtracted at the beginning and at the end of the stack. If you use larger values, you will analyze only few frames. For example, if you have 60 frames and you use a moving average of 40, the analysis is only performed from frame 20 to frame 40, i.e., only uses 20 out of the 60 frames.