Sampling

At MSL you will often need to make decisions about where in your samples to take images, and how many images to take. These decisions will have a dramatic effect on the conclusions you can reach from those images. As a result, you should have a plan for how you are going to make those decisions.

Introducing the Problem

You will almost never be able to study the entire population of objects that you are interested in. Thus, you will need to use methods that ensure that the subset that you do study are selected such that they are representative of the population you care about. If you could study the entire population of objects you would be conducting a census; since you cannot, you will be doing some form of sampling and then inferring properties of the population from that sample.

When you are designing your experiments one of the first things you need to define is the population of objects you are studying.

Examples of populations:

• All mice with mutation ABC.
• All kidneys from mice with mutation ABC.
• All cultured cells of type XYZ from mouse with mutation ABC.
• All mitochondria of cells of type XYZ from mouse with mutation ABC.

In all of these examples you would never be able to study the entire population of objects. In fact, in all of the examples those populations are potentially infinite. For the case of cells, even if you were to image all of the XYZ cells with mutation ABC in a dish that you cultured, this does not constitute the entire population, which consists of all of the cells of that type that have ever been (or ever could be) cultured. Thus, you will need to study a small subset of all of those cells, doing it in a way that the cells you do study accurately represent the full population. The way in which you decide which cells you will study is called sampling. Done properly, sampling will allow you to derive broad conclusions from a—relatively—small number of observations. Done incorrectly, poor sampling will lead to results that are not representative of the population you are trying to study.

Decisions you need to make before you get to MSL – how to cut sections

You will have to make decisions on how to sample long before you step into MSL. For example, in the—fairly common—case in which you have a tissue that you intend to cut into sections, there is the question of how to cut those sections, and which of those sections to process further. There is an entire discipline called stereology which deals with this problem. If you are in this situation, further reading is recommended.

Decisions you need to make at MSL – where to take images

Considerations if you are imaging cells in a culture

To truly take images that are representative of all images in a culture, you will need to do some form of random sampling. That is, you will need to place sampling regions randomly in the culture, and take images wherever you land. MSL can provide you tools for doing this.

Claims that images are “representative” or come from a “random sample” without any description of the procedure followed to ensure they were representative or randomly selected are very weak. All these statements usually indicate is that an observer looked around a microscope slide, saw a few things that they thought were “typical”, and took images of them. All sorts of biases (conscious or not) could creep into this kind of imaging approach.

A frequent issue is that certain potential imaging fields need to be discarded because of valid biological reasons, and in the interest of experimental efficiency. For example, some possible reasons for exclusion could be:

• There are too few cells in a field of view.
• There are too many cells in a field of view, and they are piled on top of each other.
• The majority of cells in the field of view are dead.
• The cells in the field are expressing a reporter construct at too high a level (for example: causing the reporter to be mislocalized, or the cell to die).

Excluding cells from an analysis is fine as long as the criteria by which they are excluded is clearly described and disclosed in your methods. In the examples above:

• What are the upper and lower bounds on number of cells in a field of view?
• How are dead cells identified?
• What degree of reporter expression is considered too much (10X higher than the mean?, 5X higher than the mean)?

A reviewer will want to know what fraction of potential imaging fields were rejected, to get an overall sense of how representative your results are of the entire population of cells. This is because when you exclude images from your analysis you are restricting the population of objects on which you can make inferences. In the examples above:

• If you exclude fields with few cells, you will bias your results towards cells that are growing with more neighbors, and might be exposed to a different mechanical microenvironment.
• If you exclude fields with dead cells, you might obscure the fact that your experimental intervention increases the likelihood that cells will die and will be making inferences about a specific subpopulation (cells that are resistant to your experimental intervention).
• If you exclude cells that express a reporter above a certain level you may only report a subset of the full effects that your experimental interventions can cause in your sample.

In some cases, when studying cells in culture, you may not need to worry about sampling at MSL.

One scenario where you circumvent the issue of sampling is if you decide to image a culture in its entirety. This can be accomplished on all of our scopes with motorized stages (the LSM700 and LSM710 confocals, and the IX81 and IX70 widefield systems). However, this may require a significant investment of time and money, and might be much more inefficient than a sampling approach.

Another scenario where sampling does not come into play is when the events you are studying are rare, and the cells in which those events occur are clearly identifiable. For example, if your transfection efficiency is low and you are only interested in transfected cells, or if you are only interested in cells undergoing a particular–and brief–phase in cell division. In these cases, you would simply image all cells of interest.

Considerations if you are imaging cells or features in a tissue section

When imaging in a tissue section, all of the considerations about cells in a culture apply, but there are additional concerns because tissues are spatially organized arrays of cells. Thus, you will need to figure out how to sample representatively within these non-random spatial arrays. The principles of stereology can provide guidance, and MSL can consult with you to help you set up best practices.

As with cells in culture you can circumvent these decisions by simply imaging sections in their entirety. While many MSL microscopes can perform complete imaging of very large areas (entire sections or dishes), this can be an inefficient use of resources (time, money) if you could obtain the same information by taking a few images from that section in a way that ensures they are representative. Also note also that if the sections were prepared in a way that is not representative of the population you are trying to study, imaging sections in their entirety will not fix that problem.

Considerations if you are imaging a whole organ with the light-sheet microscope

This system is specifically designed to rapidly and completely scan large samples, so there is usually no need to decide where in those samples to take images, and how many of them to take. If you are in a situation where you need to subsample, then the same considerations apply as for tissue sections, but in three dimensions. Even if you don’t need to subsample on the light-sheet you will need to ensure that your large samples are prepared in a way that makes them representative of the phenomenon under study.

Decisions you need to make at MSL – how many images to take

Once you know how you will be taking images, you need to decide on how many images to take. There is a whole branch of statistical analysis that deals with this problem, called power analysis. To perform this kind of analysis you will need some preliminary data, to estimate the variance of the parameters you will be measuring. Once you have a preliminary data set, you will need to decide what difference in that parameter you want to be able to detect, with what probability, given an estimated variance, and proposed statistical analysis. View some examples of power analysis calculators; here are some instructions for performing these calculations in the software package R.

Note that taking 3, 5, or 10 images because a postdoc from your lab told you, or because that is what everyone else in your field seems to be doing is likely a bad idea. You may end up oversampling (wasting time and money) or undersampling (not having enough sensitivity to detect differences of a given magnitude). Run a proper pilot study, do the power analysis and figure out for yourself how many images you should take. You will save time and money in the long run, and do better science along the way.

Showing What You Sampled

At some point you will have many images, and will need to decide which of these images to present to your colleagues. In a sense, you are again faced with a sampling problem, and need to make a decision to ensure that what you show is representative. Beware of picking the “best” or most extreme image as the “representative” one to include in a publication. Also, avoid using settings with much higher quality for your published image, compared to the settings used for the images you actually analyze. Both of those approaches are misleading; remember that you want a truly representative image. A good way to accomplish this when you measure things in your images is to show a dot plot with whatever parameter you measured, indicate which of those dots is the image you are showing, and ideally have that dot be one near the median or mean of the distribution of measurements. Then that image will be truly representative of the phenomenon you are studying.