## 3B as quantitative method

Bayesian analysis of blinking and bleaching

### 3B as quantitative method

Hey there,
I have some questions about the 3B result.

First of all a question about the processing of the result file into the coordinates.
What represents a single possible spot position? When I analyze a movie of singe molecule immobilized to the surface, I get about 9000 coordinates (spots?). What is the physical meaning of a spot position?I'm very interested in the quantitative use of your method. Is there a documentation for the result file to further analyze the results?

Thanks !
ecoli

Posts: 1
Joined: Wed Mar 06, 2013 10:24 am

### Re: 3B as quantitative method

A single output point represents a sample from a probability distribution. The image that is built up is a probability density built from many samples. The individual points do not signify individual fluorophores, or individual fluorophore reappearances.

A more intuitive way to think about it might be that at each iteration the algorithm is having a guess at where the fluorophore positions are. Because there are so many different variables the calcuation to try to find the fluorophore positions really accurately would take far too long to compute. So we do a much quicker calculation, it doesn't give us the fluorophore positions with the maximum accuracy on each iteration, but each guess is equally valid. So by superimposing them all we are able to get a good representation of where fluorophores are likely to be, even though it doesn't tell us exactly how many there are.
susancox

Posts: 14
Joined: Wed Jul 18, 2012 3:34 pm

### Re: 3B as quantitative method

ecoli wrote:Hey there,
Is there a documentation for the result file to further analyze the results?

Not really, unfortunately.

In the file, you can ignore every line which does not begin with PASS0: PASS1: PASS2: or PASS3:

Each PASS?: line corresponds to an iteration and contains the parameters for the number of emitters estimated to be there in that iteration. The meaning of the numbers is as follows:

PASS0: brightness1 size1 x1 y1 brightness2 size2 x2 y2 ...

where "brightness1 size1 x1 y1" corresponds to the brightness, size, and location of emitter 1 in that iteration.

A text processing language such as AWK (installed by default on any Linux or Mac system and available for Windows) can be used to process the file and extract these numbers and turn them into a form which can easily be loaded with other programs. Let me know if you require any further assistance for this.
edrosten

Posts: 42
Joined: Wed Jul 18, 2012 2:54 pm

### Re: 3B as quantitative method

Hi Susan,

Do you mean, each output point represent a guess? Each guess is equally valid. In other words, we can't not limit the number of fluorophores in the image.

Also, can we limit the size and brightness of the fluorophore that the algorithm guess?

Thanks.
twu22

Posts: 3
Joined: Tue Jun 11, 2013 9:58 pm

### Re: 3B as quantitative method

Yes, each output is a guess at the possible structure. Over many guesses this builds up into a probability density distribution.

You can't limit the size or brightness of fluorophores in the image absolutely, but since the prior distribution is a log-normal, you can change the expected most likely value and range. This is available in the advanced settings. However, due to a slightly unfortunate variable definition when we were developing the algorithm, these two variables are actually linked, so if you change them it has to be done with care. If you'd like more details on this, let me know.
susancox

Posts: 14
Joined: Wed Jul 18, 2012 3:34 pm

### Re: 3B as quantitative method

Hi Susan,

Thank you for the reply. Yes, I am definitely interested in knowing more details. Please let me know how you'd like to proceed.

I have been trying to understand how the algorithm and reading about Factorial Hidden Markov Model, forward algorithm and Bayesian network. But could not get a clear idea more than understand that it is predicting 1 state based on the previous state. Is there a good material that you would recommend me to read to understand better?

Also, what is the difference between 3B and FIONA?

Thank you so much for your help.
twu22

Posts: 3
Joined: Tue Jun 11, 2013 9:58 pm

### Re: 3B as quantitative method

For the link between brightness and size:
If the input size is phi1
and the input brightness is phi0
then the brightness actually scales by a factor of phi0*sqrt(2*PI*phi1^2)

3B is different to FIONA because is models the behaviour of many fluorophores simultaneously, allowing data to be used where the fluorophores overlap a lot. FIONA is really designed to find the positions of single molecules very very accurately. STORM, PALM, fPALM etc all use single molecule localisation methods to produce super-resolution images. 3B is only different in terms of the density of fluorophores imaged in a single frame that the analysis method can cope with. There are other related methods, e.g. Selvin has one based on localising bleaching events.

The basic idea behind our method is that we are comparing two hypotheses. For example, one hypothesis might be that a fluorophore is present at a certain point with a particular brightness and size, whereas the second hypothesis could be that the data arises from noise. For each hypothesis we calculate the model evidence, and the hypothesis for which the model evidence is greater is the most likely model of those two. By doing repeated comparisons of this type you can get to what is the most likely model of your data.

When you model fluorophores there are two types of variables. Continuous variables, such as brightness and size, can take any value. Discrete variables can only take a certain number of possible values, for example a fluorophore can be emitting light, not emitting, or bleached (of course the reality is more complex but this is our approximation). We can integrate out using Laplace's approximation, which makes the assumption that the distribution is Gaussian. You just need to know the position of the peak, its height and its width. For discrete variables, we first tried to use the Forward algorithm. This just adds up the probabilities of all possible state sequences to give you the model evidence. It is important to note that the model evidence is just a number, not a probability between 0 and 1. It is only significant when compared to another value for model evidence calculated in the same way.

So, if we could have used the forward algorithm everything would have been fine. Unfortunately it's exponential in the number of fluorophores, so for example a calculation for 15 fluorophores took a week, and for 18 fluorophores would have taken years. So we had to find an approximation. What we used was Monte Carlo Markov Chain sampling. This draws state sequences from a distribution (we used Gibbs sampling for this). So you only have to do the calculation for a certain number of state sequences. MCMC sampling says that, for a certain set of assumptions, the sample that you draw should be representative of the distribution. This still leaves a problem because this is a much noisier method, making it difficult to optimise (slides 12 and 13). So what we did was take one fluorophore at a time, calculate the forward algorithm for it, and then use MCMC for the other fluorophores.

Each iteration of the algorithm then involves changing the model in some way e.g. by adding a fluorophore, seeing if the model evidence improves, and if it does optimising all the fluorophores and changing the model again.

If you want some more detailed background about Hidden Markov Models at a less breakneck speed than the paper, I would recommend:
http://ieeexplore.ieee.org/xpls/abs_all ... mber=18626
http://neuro.bstu.by/ai/To-dom/My_resea ... doblel.pdf
(both point to the same paper, a really good tutorial paper on HMMs)

and David McKay's book http://www.inference.phy.cam.ac.uk/mackay/itila/ which covers things like Gibbs sampling very clearly.
susancox

Posts: 14
Joined: Wed Jul 18, 2012 3:34 pm

### Re: 3B as quantitative method

Hi Susan,

Thank you very much. These information are really helpful.

Thanks.
twu22

Posts: 3
Joined: Tue Jun 11, 2013 9:58 pm

### Re: 3B as quantitative method

I think it depends on what exactly the information needed from the experiment is. It is not currently possible to get superresolution in the z direction using a standard widefield microscope. Commercial SIM and STORM systems will do this (though the different STORM systems use different methods for achieving superresolution in the z direction). The problem with using a widefield system is that the point spread function changes in the same way on either side of focus so there is not a way to determine where it is in z. Another issue is that if you want to observe dynamic processes it can be advantageous to have a strong laser source available to allow you to speed up data acquisition.
Try out our free rhce training and latest comptia scwcd exam training courses to get high flying success in final the-berklee and www.northeastern.edu exams, mcts College of Notre Dame of Maryland is also very useful tool.
kanita

Posts: 1
Joined: Fri Dec 12, 2014 9:08 am