Division Day: using PCA in cell biology

In this post I’ll describe a computational method for splitting two sides of a cell biological structure. It’s a simple method that relies on principal component analysis, otherwise known as PCA. Like all things mathematical there are some great resources on the web, if you want to understand this operation in more detail (for example, this great post by Lior Pachter). PCA can applied to many biological problems, you’ve probably seen it used to find patterns in large data sets, e.g. from proteomic studies. It can also be useful for analysing microscopy data. Since our analysis using this method is unlikely to make it into print any time soon, I thought I’d put it up on Quantixed.

Mitotic spindle in 3D. Kinetochores are green. Microtubules are red.
Mitotic spindle in 3D. Kinetochores are green. Microtubules are red.

During mitosis, a cell forms a mitotic spindle to share copied chromosomes equally to the two new cells. Our lab is working on how this process works and how it goes wrong in cancer. The chromosomes attach to the spindle via kinetochores and during prometaphase they are moved to the middle of the cell. Here, the chromosomes are organised into a disc-like structure called the metaphase plate. The disc is thin in the direction of the spindle axis, but much larger in width and height. To examine the spatial distribution of kinetochores on the plate we wanted a way to approximately separate kinetochores on one side if the plate from the other.

Kinetochores can be easily detected in 3D confocal images of mitotic cells by particle analysis. Kinetochores are easily stained and appear as bright spots that a computer can pick out (we use Imaris for this). The cartesian coordinates of each detected kinetochore were saved as csv and fed into IgorPro. A procedure could then be run which works in three steps. The code is shown at the bottom, it is wrapped in further code that deals with multiple datasets from many cells/experiments etc. The three steps are:

  1. PCA
  2. Point-to-plane
  3. Analysis on each subset

I’ll describe each step and how it works.

1. Principal component analysis

This is used to find the 3rd eigenvector, which can be used to define a plane passing through the centre of the plate. This plane is used for division.

PCAtestGIFNow, because the metaphase plate is a disc it has three dimensions, the third of which – “thickness” – is the smallest. PCA will find the principal component, i.e. the direction in which there is most variance. Orthogonal to that is the second biggest variance and orthogonal to that direction is the smallest. These directions are called eigenvectors and their magnitude is the eigenvalue. As there are three dimensions to the data we can get all three eigenvectors out and the 3rd eigenvector corresponds to thickness of the metaphase plate. Metaphase plates in cells grown on coverslips are orientated similarly, but the cells themselves are at random orientations. PCA takes no notice of this and can simply reveal the direction of the smallest dimension of a 3D structure. The movie shows this in action for a simulated data set. The black spots are arranged in a disk shape about the origin. They are rotated about x by 45° (the blue spots). We then run PCA and show the eigenvectors as unit vectors (red lines). The 3rd eigenvector is normal to the plane of division, i.e. the 1st and 2nd eigenvectors lie on the plane of division.

Also, the centroid needs to be defined. This is simply the cartesian coordinates for the average of each dimension. It is sometimes referred to as the mean vector. In the example this was the origin, in reality this will depend on the position and the overall height of the cell.

A much longer method to get the eigenvectors is to define the variance-covariance matrix (sometimes called the dispersion matrix) for each dimension, for all kinetochores and then do an eigenvector decomposition on the matrix. PCA is one command, whereas the matrix calculation would be an extra loop followed by an additional command.

2. Point-to-plane

The distance of each kinetochore to the plane that we defined is calculated. If it is a positive value then the kinetochore lies on the same side as the normal vector (defined above). If it is negative then it is on the other side. The maths behind how to do this are in section 10.3.1 of Geometric Tools for Computer Graphics by Schneider & Eberly (starting on p. 374). Google it, there is a PDF version on the web. I’ll save you some time, you just need one equation that defines a plane,


Where the unit normal vector is [a b c] and a point on the plane is [x y z]. We’ll use the coordinates of the centroid as a point on the plane to find d. Now that we know this, we can use a similar equation to find the distance of any point to the plane,


Results for each kinetochore are used to sort each side of the plane into separate waves for further calculation. In the movie below, the red dots and blue dots show the positions of the kinetochores on either side of the division plane. It’s a bit of an optical illusion, but the cube is turning in a right hand fashion.


3. Analysis on each subset

Now that the data have been sorted, separate calculations can be carried out on each. In the example, we were interested in how the kinetochores were organised spatially and so we looked at the distance to nearest neighbour. This is done by finding the Euclidean distance from each kinetochore to every other kinetochore and putting the lowest value for each kinetochore into a new wave. However, this calculation can be anything you want. If there are further waves that specify other properties of the kinetochores, e.g. brightness, then these can be similarly processed here.

Other notes

The code in its present form (not very streamlined) was fast and could be run on every cell from a number of experiments, reading out positional data for 10,000 kinetochores in ~2 s. For QC it is possible to display the two separated coordinated sets to check that the division worked fine (see above). The power of this method is that it doesn’t rely on imaging spindle poles or anything else to work out the orientation of the metaphase plate. It works well for metaphase cells, but cells with any misaligned chromosomes ruin the calculation. It is possible to remove these and still fit the plane, but for our analysis we focused on cells at metaphase with a defined plate.

What else can it be used for?

Other structures in the cell can be segregated in a similar way. For example, the Golgi apparatus has a trans and a cis side, which could be similarly divided (although using the 2nd eigenvector as normal to the plane, rather than the 3rd).

Acknowledgements: I’d like to thank A.G. at WaveMetrics Inc. for encouraging me to try PCA rather than my dispersion matrix approach.



If you want to use it, the code is available here (it seems I can only upload PDF at wordpress.com). I used pygments for annotation.

The post title comes from “Division Day” a great single by Elliott Smith.

Sticky End

We have a new paper out! You can access it here.

The work was mainly done by Cristina Gutiérrez Caballero, a post-doc in the lab. We had some help from Selena Burgess and Richard Bayliss at the University of Leicester, with whom we have an ongoing collaboration.

The paper in a nutshell

We found that TACC3 binds the plus-ends of microtubules via an interaction with ch-TOG. So TACC3 is a +TIP.

What is a +TIP?

EB3 (red) and TACC3 (green) at the tips of microtubules in mitotic spindle

This is a term used to describe proteins that bind to the plus-ends of microtubules. Microtubules are a major component of the cell’s cytoskeleton. They are polymers of alpha/beta-tubulin that grow and shrink, a feature known as dynamic instability. A microtubule has polarity, the fast growing end is known as the plus-end, and the slower growing end is referred to as the minus-end. There are many proteins that bind to the plus-end and these are termed +TIPs.

OK, so what are TACC3 and ch-TOG?

They are two proteins found on the mitotic spindle. TACC3 is an acronym for transforming acidic coiled-coil protein 3, and ch-TOG stands for colonic hepatic tumour overexpressed gene. As you can tell from the names they were discovered due to their altered expression in certain human cancers. TACC3 is a well-known substrate for Aurora A kinase, which is an enzyme that is often amplified in cancer. The ch-TOG protein is thought to be a microtubule polymerase, i.e. an enzyme that helps microtubules grow. In the paper, we describe how TACC3 and ch-TOG stick together at the microtubule end. TACC3 and ch-TOG are at the very end of the microtubule, they move ahead of other +TIPs like “end-binding proteins”, e.g. EB3.

What is the function of TACC3 as a +TIP?

We think that TACC3 is piggybacking on ch-TOG while it is acting as a polymerase, but any biological function or consequence of this piggybacking was difficult to detect. We couldn’t see any clear effect on microtubule dynamics when we removed or overexpressed TACC3. We did find that loss of TACC3 affects how cells migrate, but this is not likely to be due to a change in microtubule dynamics.

I thought TACC3 and ch-TOG were centrosomal proteins…

In the paper we look again at this and find that there are different pools of TACC3, ch-TOG and clathrin (alone and in combination) and describe how they reside in different places in the cell. Although ch-TOG is clearly at centrosomes, we don’t find TACC3 at centrosomes, although it is on microtubules that cluster near the centrosomes at the spindle pole. TACC3 is often described as a centrosomal protein in lots of other papers, but this is quite misleading.

What else?

NeonCellWe were on the cover – whatever that means in the digital age! We imaged a cell expressing tagged EB3 proteins, EB3 is another +TIP. We coloured consecutive frames different colours and the result looked pretty striking. Biology Open picked it as their cover, which we were really pleased about. Our paper is AOP at the moment and so hopefully they won’t change their mind by the time it appears in the next issue.


This is the second paper that we have deposited as a preprint at bioRxiv (not counting a third paper that we preprinted after it was accepted). I was keen to preprint this particular paper because we became aware that two other groups had similar results following a meeting last summer. Strangely, a week or so after preprinting and submitting to a journal, a paper from a completely different group appeared with a very similar finding! We’d been “scooped”. They had found that the Xenopus homologue of TACC3 was a +TIP in retinal neuronal cultures. The other group had clearly beaten us to it, having submitted their paper some time before our preprint. The reviewers of our paper complained that our data was no longer novel and our paper was rejected. This was annoying because there were lots of novel findings in our paper that weren’t in theirs (and vice versa). The reviewers did make some other constructive suggestions that we incorporated into the manuscript. We updated our preprint and then submitted to Biology Open. One advantage of the preprinting process is that the changes we made can be seen by all. Biology Open were great and took a decision based on our comments from the other journal and the changes we had made in response to them. Their decision to provisionally accept the paper was made in four days. Like our last experience publishing in Biology Open, it was very positive.


Gutiérrez-Caballero, C., Burgess, S.G., Bayliss, R. & Royle, S.J. (2015) TACC3-ch-TOG track the growing tips of microtubules independently of clathrin and Aurora-A phosphorylation. Biol. Open doi:10.1242/​bio.201410843.

Nwagbara, B. U., Faris, A. E., Bearce, E. A., Erdogan, B., Ebbert, P. T., Evans, M. F., Rutherford, E. L., Enzenbacher, T. B. and Lowery, L. A. (2014) TACC3 is a microtubule plus end-tracking protein that promotes axon elongation and also regulates microtubule plus end dynamics in multiple embryonic cell types. Mol. Biol. Cell 25, 3350-3362.

The post title is taken from the last track on The Orb’s U.F.Orb album.

Tips from the blog III – violin plots

Having recently got my head around violin plots, I thought I would explain what they are and why you might want to use them.

There are several options when it comes to plotting summary data. I list them here in order of granularity, before describing violin plots and how to plot them in some detail.

Bar chart

kdebarThis is the mainstay of most papers in my field. Typically, a bar representing the mean value that’s been measured is shown with an error bar which shows either the standard error of the mean, the standard deviation, or more rarely a confidence interval. The two data series plotted in all cases is the waiting time for Old Faithful eruptions (waiting), a classic dataset from R. I have added some noise to waiting (waiting_mod) for comparison. I think it’s fair to say that most people feel that the bar chart has probably had its day and that we should be presenting our data in more informative ways*.

Pros: compact, easy to tell differences between groups

Cons: hides the underlying distribution, obscures the n number

Box plot

kdeboxThe box plot – like many things in statistics – was introduced by Tukey. It’s sometimes known as a Tukey plot, or a box-and-whiskers plot. The idea was to give an impression of the underlying distribution without showing a histogram (see below). Histograms are great, but when you need to compare many distributions they do not overlay well and take up a lot of space to show them side-by-side. In the simplest form, the “box” is the interquartile range (IQR, 25th and 75th percentiles) with a line to show the median. The whiskers show the 10th and 90th percentiles. There are many variations on this theme: outliers can be shown or not, the whiskers may show the limits of the dataset (or something else), the boxes can be notched or their width may represent the sample size…

Pros: compact, easy to tell differences between groups, shows normality/skewness

Cons: hides multimodal data, sometimes obscures the n number, many variations


kdehistoA histogram is a method of showing the distribution of a dataset and was introduced by Pearson. The number of observations within a bin are counted and plotted. The ‘bars’ sit next to each other, because the variable being measured is continuous. The variable being measured is on the x-axis, rather than the category (as in the other plots).

Often the area of all the bars is normalised to 1 in order to assess the distributions without being confused by differences in sample size. As you can see here, “waiting” is bimodal. This was hidden in the bar chart and in the bot plot.

Related to histograms are other display types such as stemplots or stem-and-leaf plots.

Pros: shows multimodal data, shows normality/skewness clearly

Cons: not compact, difficult to overlay, bin size and position can be misleading

Scatter dot plot

kdescatterIt’s often said that if there are less than 10 data points, then best practice is to simply show the points. Typically the plot is shown together with a bar to show the mean (or median) and maybe with error bars showing s.e.m., s.d., IQR. There are a couple of methods of plotting the points, because they need to be scattered in x value in order to be visualised. Adding random noise is one approach, but this looks a bit messy (top). A symmetrical scatter can be introduced by binning (middle) and a further iteration is to bin the y values rather than showing their true location (bottom). There’s a further iteration which constrains the category width and overlays multiple points, but again the density becomes difficult to see.

These plots still look quite fussy, the binned version is the clearest but then we are losing the exact locations of the points, which seems counterintuitive. Another alternative to scattering the dots is to show a rug plot (see below) where there is no scatter.

Pros: shows all the observations

Cons: can be difficult to assess the distribution

Violin plot

kdeviolinThis type of plot was introduced in the software package NCSS in 1997 and described in this paper: Hintze & Nelson (1998) The American Statistician 52(2):181-4 [PDF]. As the title says, violin plots are a synergism between box plot and density trace. A thin box plot is shown together with a symmetrical kernel density estimate (KDE, see explanation below). The point is to be able to quickly assess the distribution. You can see that the bimodality of waiting in the plot, but there’s no complication of lots of points just a smooth curve to see the data.

Pros: shows multimodal data, shows normality/skewness unambiguously

Cons: hides n, not familiar to many readers.

* Why is the bar chart so bad and why should I show my data another way?

425px-Anscombe's_quartet_3.svgThe best demonstration of why the bar chart is bad is Anscombe’s Quartet (the figure to the right is taken from the Wikipedia page). These four datasets are completely different, yet they all have the same summary statistics. The point is, you would never know unless you plotted the data. A bar chart would look identical for all four datasets.

Making Violin Plots in IgorPro

I wanted to make Violin Plots in IgorPro, since we use Igor for absolutely everything in the lab. I wrote some code to do this and I might make some improvements to it in the future – if I find the time! This was an interesting exercise, because it meant forcing myself to understand how smoothing is done. What follows below is an aide memoire, but you may find it useful.

What is a kernel density estimate?

A KDE is a non-parametric method to estimate a probability density function of a variable. A histogram can be thought of as a simplistic non-parametric density estimate. Here, a rectangle is used to represent each observation and it gets bigger the more observations are made.

What’s wrong with using a histogram as a KDE?

hist1The following examples are taken from here (which in turn are taken from the book by Bowman and Azzalini described below). A histogram is simplistic. We lose the location of each datapoint because of binning. Histograms are not smooth and the estimate is very sensitive to the size of the bins and also the starting location of the first bin. The histograms to the right show the same data points (in the rug plot).

hist2Using the same bin size, they result in very different distributions depending on where the first bin starts. My first instinct to generate a KDE was to simply smooth a histogram, but this is actually quite inaccurate as it comes from a lossy source. Instead we need to generate a real KDE.

How do I make a KDE?

optsmoothTo do this we place a kernel (a Gaussian is commonly used) at each data point. The rationale behind this is that each observation can be thought of as being representative of a greater number of observations. It sounds a bit bizarre to assume normality to estimate a density non-parametrically, but it works. We can sum all of the kernels to give a smoothed distribution: the KDE. Easy? Well, yes as long as you know how wide to make the kernels. To do this we need to find the bandwidth, h (also called the smoothing parameter).

undersmoothIt turns out that this is not completely straightforward. The answer is summarised in this book: Bowman & Azzalini (1997) Applied Smoothing Techniques for Data Analysis. In the original paper on violin plots, they actually do not have a good solution for selecting h for drawing the violins, and they suggest trying several different values for h. They recommend starting at ~15% of the data range as a good starting point. Obviously if you are writing some code, the process of selecting h needs to be automatic.

oversmoothOptimising h is necessary because if h is too large, the estimate with be oversmoothed and features will be lost. If is too small, then it will be undersmoothed and bumpy. The examples to the right (again, taken from Bowman & Azzalini, via this page) show examples of undersmoothed, oversmoothed and optimal smoothing.

An optimal solution to find h is

\(h = \left(\frac{4}{3n}\right)^{\frac{1}{5}}\sigma\)

This is termed Silverman’s rule-of-thumb. If smoothing is needed in more than one dimension, the multidimensional version is

\(h = \left\{\frac{4}{\left(p+2\right)n}\right\}^{\frac{1}{\left(p+4\right)}}\sigma\)

bowman3dYou might need multidimensional smoothing to contextualise more than one parameter being measured. The waiting data used above describes the time to wait until the next eruption from Old Faithful. The duration of the eruption is measured, and also the wait to the next eruption can be extracted, giving three parameters. These can give a 3D density estimate as shown here in the example.

The Bowman & Azzalini recommend that, if the distribution is long-tailed, using the median absolute deviation estimator is robust for \(\sigma\).


where \(\tilde\mu\) is the median of the sample. All of this is something you don’t need to worry about if you use R to plot violins, the implementation in there is rock solid having been written in S plus and then ported to R years ago. You can even pick how the h selection is done from sm.density, or even modify the optimal h directly using hmult.

To get this working in IgorPro, I used some code for 1D KDE that was already on IgorExchange. It needed a bit of modification because it used FastGaussTransform to sum the kernels as a shortcut. It’s a very fast method, but initially gave an estimate that seemed to be undersmoothed. I spent a while altering the formula for h, hence the detail above. To cut a long story short, FastGaussTransform uses Taylor expansion of the Gauss transform and it just needed more terms to do this accurately. This is set with the /TET flag. Note also, that in Igor the width of a Gauss is sigma*2^1/2.

OK, so how do I make a Violin for plotting?

I used the draw tools to do this and placed the violins behind an existing box plot. This is necessary to be able to colour the violins (apparently transparency is coming to Igor in IP7). The other half of the violin needs to be calculated and then joined by the DrawPoly command. If the violins are trimmed, i.e. cut at the limits of the dataset, then this required an extra point to be added. Without trimming, this step is not required. The only other issue is how wide the violins are plotted. In R, the violins are all normalised so that information about n is lost. In the current implementation, box width is 0.1 and the violins are normalised to the area under the curve*(0.1/2). So, again information on n is lost.

Future improvements

Ideas for developments of the Violin Plot method in IgorPro

  • incorporate it into the ipf for making boxplots so that it is integrated as an option to ‘calculate percentiles’
  • find a better solution for setting the width of the violin
  • add other bandwidth options, as in R
  • add more options for colouring the violins

What do you think? Did I miss something? Let me know in the comments.


Bowman, A.W. & Azzalini, A. (1997) Applied Smoothing Techniques for Data Analysis : The Kernel Approach with S-Plus Illustrations: The Kernel Approach with S-Plus Illustrations. Oxford University Press.

Hintze, J.L. & Nelson, R.D. (1998) Violin plots: A Box Plot-Density Trace Synergism. The American Statistician, 52:181-4.

Joining A Fanclub

When I started this blog, my plan was to write about interesting papers or at least blog about the ones from my lab. This post is a bit of both.

I was recently asked to write a “Journal Club” piece for Nature Reviews Molecular Cell Biology, which is now available online. It’s paywalled unfortunately. It’s also very short, due to the format. For these reasons, I thought I’d expand a bit on the papers I highlighted.

I picked two papers from Dick McIntosh’s group, published in J Cell Biol in the early 1990s as my subject. The two papers are McDonald et al. 1992 and Mastronarde et al. 1993.

Almost everything we know about the microanatomy of mitotic spindles comes from classical electron microscopy (EM) studies. How many microtubules are there in a kinetochore fibre? How do they contact the kinetochore? These questions have been addressed by EM. McIntosh’s group in Boulder, Colorado have published so many classic papers in this area, but there are many more coming from Conly Rieder, Alexey Khodjakov, Bruce McEwen and many others. Even with the advances in light microscopy which have improved spatial resolution (resulting in a Nobel Prize last year), EM is the only way to see individual microtubules within a complex subcellular structure like the mitotic spindle. The title of the piece, Super-duper resolution imaging of mitotic microtubules, is a bit of a dig at the fact that EM still exceeds the resolution available from super-resolution light microscopy. It’s not the first time that this gag has been used, but I thought it suited the piece quite well.

There are several reasons to highlight these papers over other electron microscopy studies of mitotic spindles.

It was the first time that 3D models of microtubules in mitotic spindles were built from electron micrographs of serial sections. This allowed spatial statistical methods to be applied to understand microtubule spacing and clustering. The software that was developed by David Mastronarde to do this was later packaged into IMOD. This is a great software suite that is actively maintained, free to download and is essential for doing electron microscopy. Taking on the same analysis today would be a lot faster, but still somewhat limited by cutting sections and imaging to get the resolution required to trace individual microtubules.

kfibreThe paper actually showed that some of the microtubules in kinetochore fibres travel all the way from the pole to the kinetochore, and that interpolar microtubules invade the bundle occasionally. This was an open question at the time and was really only definitively answered thanks to the ability to digitise and trace individual microtubules using computational methods.

The final thing I like about these papers is that it’s possible to reproduce the analysis. The methods sections are wonderfully detailed and of course the software is available to do similar work. This is in contrast to most papers nowadays, where it is difficult to understand how the work has been done in the first place, let alone to try and reproduce it in your own lab.

David Mastronarde and Dick McIntosh kindly commented on the piece that I wrote and also Faye Nixon in my lab made some helpful suggestions. There’s no acknowledgement section, so I’ll thank them all here.


McDonald, K. L., O’Toole, E. T., Mastronarde, D. N. & McIntosh, J. R. (1992) Kinetochore microtubules in PTK cells. J. Cell Biol. 118, 369—383

Mastronarde, D. N., McDonald, K. L., Ding, R. & McIntosh, J. R. (1993) Interpolar spindle microtubules in PTK cells. J. Cell Biol. 123, 1475—1489

Royle, S.J. (2015) Super-duper resolution imaging of mitotic microtubules. Nat. Rev. Mol. Cell. Biol. doi:10.1038/nrm3937 Published online 05 January 2015

The post title is taken from “Joining a Fanclub” by Jellyfish from their classic second and final LP “Spilt Milk”.

A Day In The Life II

I have been doing paper of the day (#potd) again in 2014. See my previous post about this.

My “rules” for paper of the day are:

  1. Read one paper each working day.
  2. If I am away, or reviewing a paper for a journal or colleague, then I get a pass.
  3. Read it sufficiently to be able to explain it to somebody else, i.e. don’t just scan the abstract and look at the figures. Really read it and understand it. Scan and skim as many other papers as you normally would!
  4. Only papers reporting primary research count. No reviews/opinion pieces etc.
  5. If it was really good or worth telling people about – tweet about it.
  6. Make a simple database in Excel – this helps you keep track, make notes about the paper (to see if you meet #3) and allows you to find the paper easily in the future (this last point turned out to be very useful).

This year has been difficult, especially sticking to #3. My stats for 2014 are:

  • 73% success rate. Down from 85% in 2013
  • Stats errors in 36% of papers I read!
  • 86% of papers were from 2014

Following last year, I wasn’t so surprised by the journals that the papers appeared in:

  1. eLife
  2. J Cell Biol
  3. Mol Biol Cell
  4. Dev Cell
  5. Nature Methods
  6. J Cell Sci
  7. J Neurosci
  8. Nature Cell Biol
  9. Traffic
  10. Curr Biol
  11. Nature
  12. Nature Comm
  13. Science

According to my database I only read one paper in Cell this year. I certainly have lots of them in “Saved for later” in Feedly (which is a black hole from which papers rarely emerge to be read). It’s possible that the reason Cell, Nature and Science are low on the list is that I might quickly glance at papers in those journals but not actually read them for #potd. Last year eLife was at number 9 and this year it is at number 1. This journal is definitely publishing a lot of exciting cell biology and also the lens format is very nice for reading.

I think I’ll try to continue this in 2015. The main thing it has made me realise is how few papers I read (I mean really read). I wonder if students and postdocs are actually the main consumers of the literature. If this is correct, do PIs rely on “subsistence reading”, i.e. when they write their own papers and check the immediate literature? Is their deep reading done only during peer reviewing other people’s work? Or do PIs rely on a constant infusion of the latest science at seminars and at meetings?

Insane In The Brain

Back of the envelope calculations for this post.

An old press release for a paper on endocytosis by Tom Kirchhausen contained this fascinating factoid:

The equivalent of the entire brain, or a football field of membrane, is turned over every hour

If this is true it is absolutely staggering. Let’s check it out.

A synaptic vesicle is ~40 nm in diameter. So the surface area of 1 vesicle is

\(4 \pi r^2\)

which is 5026 nm2, or 5.026 x 10-15 m2.

Synaptic vesicles in the presynaptic terminal (asterisk).
Synaptic vesicles in the presynaptic terminal (asterisk)

Now, an American football field is 5350 m2 (including both endzones), this is the equivalent of 1.065 x 1018 synaptic vesicles.

It is estimated that the human cortex has 60 trillion synapses. This means that each synapse would need to internalise 17742 vesicles to retrieve the area of membrane equivalent to one football field.

The factoid says this takes one hour. This membrane load equates to each synapse turning over 296 vesicles in one minute, which is 4.93 vesicles per second.

Tonic activity of neurons differs throughout the brain and actually 5 Hz doesn’t sound too high (feel free to correct me on this). We’ve only considered cortical neurons, so the factoid seems pretty plausible!

For an actual football field, i.e. Association Football. The calculation is slightly more complicated. This is because there is no set size for football pitches. In England, the largest is apparently Manchester City (7598 m2) while the smallest actually belongs to the greatest football team in the world, Crewe Alexandra (5518 m2).

Gresty Road. Small but perfectly formed

A brain would hoover up Man City’s ground in an hour if each synapse turned over 7 vesicles per second, while Gresty Road would only take 5 vesicles per second.

What is less clear from the factoid is whether a football field really equates to an “entire brain”. Bionumbers has no information on this. I think this part of the factoid may come from a different bit of data which is that clathrin-mediated endocytosis in non-neuronal cells can internalise the equivalent of the entire surface area of the cell in about an hour. I wonder whether this has been translated to neurons for the purposes of the quote. Either way, it is an amazing factoid that the brain can turnover this huge amount of membrane in such a short space of time.

So there you have it: quanta quantified on quantixed.

The post title is from “Insane In The Brain” by Cypress Hill from the album Black Sunday.

Half Right

I was talking to a speaker visiting our department recently. While discussing his postdoc work from years ago, he told me about the identification of the sperm factor that causes calcium oscillations in the egg at fertilisation. It was an interesting tale because the group who eventually identified the factor – now widely accepted as PLCzeta – had earlier misidentified the factor, naming it oscillin.

The oscillin paper was published in Nature in 1996 and the subsequent (correct) paper was published in Development in 2002. I wondered what the citation profiles of these papers looks like now.


As you can see there was intense interest in the first paper that quickly petered out, presumably when people found out that oscillin was a contaminant and not the real factor. The second paper on the other hand has attracted a large number of citations and continues to do so 12 years later – a sign of a classic paper. However, the initial spike in citations was not as high as the Nature paper.

The impact factor of Nature is much higher than that of Development. I’ve often wondered if this is due to a sociological phenomenon: people like to cite Cell/Nature/Science papers rather than those at other journals and this bumps up the impact factor. Before you comment, yes I know there are other reasons, but the IFs do not change much over time and I wonder whether journal hierarchy explains the hardiness of IFs over time. Anyway, these papers struck me as a good test of the idea… Here we have essentially the same discovery, reported by the same authors. The only difference here is the journal (and that one paper is six years after the other). Normally it is not possible to test if the journal influences citations because a paper cannot erased and republished somewhere else. The plot suggests that Nature papers inherently attract much more cites than those in Development, presumably because of the exposure of publishing there. From the graph, it’s not difficult to see that even if a paper turns out not to be right, it can still boost the IF of the journal during the window of assessment. Another reason not to trust journal impact factors.

I can’t think of any way to look at this more systematically to see if this phenomenon holds true. I just thought it was interesting, so I’ll leave it here.

The post title is taken from Half Right by Elliott Smith from the posthumous album New Moon. Bootlegs have the title as Not Half Right, which would also be appropriate.

My Favorite Things

I realised recently that I’ve maintained a consistent iTunes library for ~10 years. For most of that time I’ve been listening exclusively to iTunes, rather than to music in other formats. So the library is a useful source of information about my tastes in music. It should be possible to look at who are my favourite artists, what bands need more investigation, or just to generate some interesting statistics based on my favourite music.

Play count is the central statistic here as it tells me how often I’ve listened to a certain track. It’s the equivalent of a +1/upvote/fave/like or maybe even a citation. Play count increases by one if you listen to a track all the way to the end. So if a track starts and you don’t want to hear it and you skip on to the next song, there’s no +1. There’s a caveat here in that the time a track has been in the library, influences the play count to a certain extent – but that’s for another post*. The second indicator for liking a track or artist is the fact that it’s in the library. This may sound obvious, but what I mean is that artists with lots of tracks in the library are more likely to be favourite artists compared to a band with just one or two tracks in there. A caveat here is that some artists do not have long careers for a variety of reasons, which can limit the number of tracks actually available to load into the library. Check the methods at the foot of the post if you want to do the same.

What’s the most popular year? Firstly, I looked at the most popular year in the library. This question was the focus of an earlier post that found that 1971 was the best year in music. The play distribution per year can be plotted together with a summary of how many tracks and how many plays in total from each year are in the library. There’s a bias towards 90s music, which probably reflects my age, but could also be caused by my habit of collecting CD singles which peaked as a format in this decade. The average number of plays is actually pretty constant for all years (median of ~4), the mean is perhaps slightly higher for late-2000s music.

Favourite styles of music: I also looked at Genre. Which styles of music are my favourite? I plotted the total number of tracks versus the total number of plays for each Genre in the library. Size of the marker reflects the median number of plays per track for that genre. Most Genres obey a rule where total plays is a function of total tracks, but there are exceptions. Crossover, Hip-hop/Rap and Power-pop are highlighted as those with an above average number of plays. I’m not lacking in Power-pop with a few thousand tracks, but I should probably get my hands on more Crossover or Hip-Hop/Rap.


Using citation statistics to find my favourite artists: Next, I looked at who my favourite artists are. It could be argued that I should know who my favourite artists are! But tastes can change over a 10 year period and I was interested in an unbiased view of my favourite artists rather than who I think they are. A plot of Total Tracks vs Mean plays per track is reasonably informative. The artists with the highest plays per track are those with only one track in the library, e.g. Harvey Danger with Flagpole Sitta. So this statistic is pretty unreliable. Equally, I’ve got lots of tracks by Manic Street Preachers but evidently I don’t play them that often. I realised that the problem of identifying favourite artists based on these two pieces of information (plays and number of tracks) is pretty similar to assessing scientists using citation metrics (citations and number of papers). Hirsch proposed the h-index to meld these two bits of information into a single metric, the h-index. It’s easily computed and I already had an Igor procedure to calculate it en masse, so I ran it on the library information.

Before doing this, I consolidated multiple versions of the same track into one. I knew that I had several versions of the same track, especially as I have multiple versions of some albums (e.g. Pet Sounds = 3 copies = mono + stereo + a capella), the top offending track was “Baby’s Coming Back” by Jellyfish, 11 copies! Anyway, these were consolidated before running the h-index calculation.

The top artist was Elliott Smith with an h-index of 32. This means he has 32 tracks that have been listened to at least 32 times each. I was amazed that Muse had the second highest h-index (I don’t consider myself a huge fan of their music) until I remembered a period where their albums were on an iPod Nano used during exercise. Amusingly (and narcissistically) my own music – the artist names are redacted – scored quite highly with two out of three bands in the top 100, which are shown here. These artists with high h-indeces are the most consistently played in the library and probably constitute my favourite artists, but is the ranking correct?

The procedure also calculates the g-index for every artist. The g-index is similar to the h-index but takes into account very highly played tracks (very highly cited papers) over the h threshold. For example, The Smiths h=26. This could be 26 tracks that have been listened to exactly 26 times or they could have been listened to 90 times each. The h-index cannot reveal this, but the g-index gets to this by assessing average plays for the ranked tracks. The Smiths g=35. To find the artists that are most-played-of-the-consistently-most-played, I subtracted h from g and plotted the Top 50. This ranked list I think most closely represents my favourite artists, according to my listening habits over the last ten years.


Track length: Finally, I looked at the track length. I have a range of track lengths in the library, from “You Suffer” by Napalm Death (iTunes has this at 4 s, but Wikipedia says it is 1.36 s), through to epic tracks like “Blue Room” by The Orb. Most tracks are in the 3-4 min range. Plays per track indicates that this track length is optimal with most of the highly played tracks being within this window. The super-long tracks are rarely listened to, probably because of their length. Short tracks also have higher than average plays, probably because they are less likely to be skipped, due to their length.

These were the first things that sprang to mind for iTunes analysis. As I said at the top, there’s lots of information in the library to dig through, but I think this is enough for one post. And not a pie-chart in sight!

Methods: the library is in xml format and can be read/parsed this way. More easily, you can just select the whole library and copy-paste it into TextEdit and then load this into a data analysis package. In this case, IgorPro (as always). Make sure that the interesting fields are shown in the full library view (Music>Songs). To do everything in this post you need artist, track, album, genre, length, year and play count. At the time of writing, I had 21326 tracks in the library. For the “H-index” analysis, I consolidated multiple versions of the same track, giving 18684 tracks. This is possible by concatenating artist and the first ten characters of the track title (separated by a unique character) and adding the play counts for these concatenated versions. The artist could then be deconvolved (using the unique character) and used for the H-calculation. It’s not very elegant, but seemed to work well. The H-index and G-index calculations were automated (previously sort-of-described here), as was most of the plot generation. The inspiration for the colour coding is from the 2013 Feltron Report.

* there’s an interesting post here about modelling the ideal playlist. I worked through the ideas in that post but found that it doesn’t scale well to large libraries, especially if they’ve been going for a long time, i.e. mine.

The post title is taken from John Coltrane’s cover version of My Favorite Things from the album of the same name. Excuse the US English spelling.

Belly Button Window

A bit of navel gazing for this post. Since moving the blog to wordpress.com in the summer, it recently accrued 5000 views. Time to analyse what people are reading…

blogstatsThe most popular post on the blog (by a long way) is “Strange Things“, a post about the eLife impact factor (2824 views). The next most popular is a post about a Twitter H-index, with 498 views. The Strange Things post has accounted for ~50% of views since it went live (bottom plot) and this fraction seems to be creeping up. More new content is needed to change this situation.

I enjoy putting blog posts together and love the discussion that follows from my posts. It’s also been nice when people have told me that they read my blog and enjoy my posts. One thing I didn’t expect was the way that people can take away very different messages from the same post. I don’t know why I found this surprising, since this often happens with our scientific papers! Actually, in the same way as our papers, the most popular posts are not the ones that I would say are the best.

Wet Wet Wet: I have thought about deleting the Strange Things post, since it isn’t really what I want this blog to be about. An analogy here is the Scottish pop-soul outfit Wet Wet Wet who released a dreadful cover of The Troggs’ “Love is All Around” in 1994. In the end, the band deleted the single in the hope of redemption, or so they said. Given that the song had been at number one for 15 weeks, the damage was already done. I think the same applies here, so the post will stay.

Directing Traffic: Most people coming to the blog are clicking on links on Twitter. A smaller number come via other blogs which feature links to my posts. A very small number come to the blog via a Google search. Google has changed the way it formats the clicks and so most of the time it is not possible to know what people were searching for. For those that I can see, the only search term is… yes, you’ve guessed it: “elife impact factor”.

Methods: WordPress stats are available for blog owners via URL formatting. All you need is your API key and (obviously) your blog address.

Instructions are found at http://stats.wordpress.com/csv.php

A basic URL format would be: http://stats.wordpress.com/csv.php?api_key=yourapikey&blog_uri=yourblogaddress replacing yourapikey with your API key (this can be retrieved at https://apikey.wordpress.com) and yourblogaddress with your blog address e.g. quantixed.wordpress.com

Various options are available from the first page to get the stats in which you are  interested. For example, the following can be appended to the second URL to get a breakdown of views by post title for the past year:


The format can be csv, json or xml depending on how your preference for what you want to do next with the information.

The title is from “Belly Button Window” by Jimi Hendrix, a posthumous release on the Cry of Love LP.

What The World Is Waiting For

The transition for scientific journals from print to online has been slow and painful. And it is not yet complete. This week I got an RSS alert to a “new” paper in Oncogene. When I downloaded it, something was familiar… very familiar… I’d read it almost a year ago! Sure enough, the AOP (ahead of print or advance online publication) date for this paper was September 2013 and here it was in the August 2014 issue being “published”.

I wondered why a journal would do this. It is possible that delaying actual publication would artificially boost the Impact Factor of a journal because there is a delay before citations roll in and citations also peak after two years. So if a journal delays actual publication, then the Impact Factor assessment window captures a “hotter” period when papers are more likely to generate more citations*. Richard Sever (@cshperspectives) jumped in to point out a less nefarious explanation – the journal obviously has a backlog of papers but is not allowed to just print more papers to catch up, due to page budgets.

There followed a long discussion about this… which you’re welcome to read. I was away giving a talk and missed all the fun, but if I may summarise on behalf of everybody: isn’t it silly that we still have pages – actual pages, made of paper – and this is restricting publication.

I wondered how Oncogene got to this position. I retrieved the data for AOP and actual publication for the last five years of papers at Oncogene excluding reviews, from Pubmed. Using oncogene[ta] NOT review[pt] as a search term. The field DP has the date published (the “issue date” that the paper appears in print) and PHST has several interesting dates including [aheadofprint]. These could be parsed and imported into IgorPro as 1D waves. The lag time from AOP to print could then be calculated. I got 2916 papers from the search and was able to get data for 2441 papers.

OncogeneLagTimeYou can see for this journal that the lag time has been stable at around 300 days (~10 months) for issues published since 2013. So a paper AOP in Feb 2012 had to wait over 10 months to make it into print. This followed a linear period of lag time growth from mid-2010.

I have no links to Oncogene and don’t particularly want to single them out. I’m sure similar lags are happening at other print journals. Actually, my only interaction with Oncogene was that they sent this paper of ours out to review in 2011 (it got two not-negative-but-admittedly-not-glowing reviews) and then they rejected it because they didn’t like the cell line we used. I always thought this was a bizarre decision: why couldn’t they just decide that before sending it to review and wasting our time? Now, I wonder whether they were not keen to add to their increasing backlog of papers at their journal? Whatever the reason, it has put me off submitting other papers there.

I know that there are good arguments for continuing print versions of journals, but from a scientist’s perspective the first publication is publication. Any subsequent versions are simply redundant and confusing.

*Edit: Alexis Verger (@Alexis_Verger) pointed me to a paper which describes that, for neuroscience journals, the lag time has increased over time. Moreover, the authors suggest that this is for the purpose of maximising Journal Impact Factor.

The post title comes from the double A-side Fools Gold/What The World Is Waiting For by The Stone Roses.