Calculating Molarity part 2: Vaccine structure

I’ve continued to think about this post at Respectful Insolence. You may already have read my previous post on this subject. I had a short conversation with Orac by email about the previous post; he had asked me what I thought about the alterations he made after thinking about my objections. One thing I answered that I thought he might add has sort of stuck with me and I think is worthy of a post of its own. What do you know, two posts in one week! This one may not be tremendously long, but it’s important and it bolsters the thesis written in that post on Respectful Insolence. They are about minimizing the contamination; this is true, but I would actually modify it by saying that you have to know what you’re looking at before you claim it’s a problem.

My previous writing here has been directed at my fellow skeptics and could be used by antivaccine advocates to attack people whose efforts I normally support. I would rather my efforts be focused at the greater good: namely to support vaccines. I don’t write often about my specific research expertise, but I’m mainly a soft matter researcher and I have a great deal of experience with colloids, nanoparticles and liquid crystals. This paper they’re talking about is my cup of tea! More than that, I’ve spent time at the university electron microscopy lab using SEM and elemental analysis in the form of EDS, shooting electron beams at precipitates obtained from colloidal suspensions.

I feel that the strategy of showing that vaccine contaminants are extraordinarily minor and not nearly as large as the antivaccine efforts try to claim is a good effort, but might also be the wrong strategy for tackling this science, particularly when screwing up the math. A part of my reason for feeling this way is that the argument is actually hinging on the existence, or not, of particulate objects in the preparations that the antivaxxers are examining. The paper that Orac (and, in a quotation, Skeptical Raptor) are looking at, is focusing on the spurious occurrence of a small particle content revealed in vaccine samples under SEM examination. The antivaxxers are counting and reporting particles found in SEM, of which they are reporting highly dispersive values: very few in some, many in others. They are also reporting instances where EDS shows unexpected metal content, like gold and others. Here, Orac notes that the particles are typically so few that they should be considered negligible and that’s fair… question is, what is the nature of these particles? And, should we take the antivaxxer EDS results seriously? It seems poor form for me to criticize my fellow skeptics and to not turn my attention against the subject that are analyzing –to allay my own conscience, I have to open my mouth! I therefore spent a bit of time of my own looking at the paper they were analyzing “New Quality-Control Investigations on Vaccines: Micro- and Nanocontamination.” I won’t link to it directly because I have no respect for it.

I’ll deal with the EDS first.


This picture is from

EDS is another spectroscopy technique that is sometimes called electron fluorescence. You shoot an electron beam (or X-ray) at a sample with the deliberate intent of knocking a deep orbital electron out of the atom. A higher energy shell electron will then drop down into the vacant orbital and emit an X-ray at the transition energy between the two orbitals. The spectrometer then detects the emitted X-rays. Because atoms have differing transition energies due to the depth of their shells, you can identify the element based on the X-ray frequencies emitted. A precondition for seeing this X-ray spectrum is that your impinging electron beam must be at sufficiently high energy to knock a deep shell electron up into the continuum, ionizing the atom and that energy might actually be considerable. There is also a confounder in that a lot of atoms have EDS peaks at fairly similar energies, meaning that it can be hard sometimes to distinguish them.

Here is a periodic table containing EDS peaks from Jeol:


Now, when you perform SEM, you spread your sample onto a conductive substrate and observe it in a fair vacuum. To generate an SEM image, the electron beam is rastered in a point across an area in the sample and an off-angle detector detects electron scatter. You’re literally trying to puff electrons up into the space over the sample by bombarding the surface. The substrate is usually conductive in order to replenish ejected electrons. The direction the ejection puff travels depends on the topography of the surface and the off-angle positioning of the detector means that some surfaces face the detector and give bright puffs while surfaces facing away do not. This gives the dimensionality to SEM images. Many SEM samples are sputtered with a layer of gold to improve contrast by introducing a material that is electron dense, but a system with the intent to use EDS would actually be directed at naked samples. With SEM, you always have to remember that the electron beam is intrinsically erosive and damaging. The beam doesn’t just bounce off the surface, it penetrates into the sample to a depth that I’ve heard called the interaction volume. The interaction volume is regulated by the accelerating voltage of the electron beam: higher accelerating voltages means deeper interacting volumes. Crisp SEM images that show clear surface features are usually obtained with low accelerating voltages which limit the interacting volume to only surface features of the sample. SEM images obtained at higher accelerating voltages take on a sort of translucent cast because the beam penetrates into the sample and interacts with an interior volume.

The combination of EDS with SEM is a little tricky. In SEM, EDS gains its excitation from the imaging electron beam of the system. Now, what makes this tricky is that samples like protein antigens in a vaccine are predominantly carbon and have low electron density, making them low contrast. You hit the sample at low accelerating voltages to see surface features. If you try to do EDS, you must hit the sample with electrons at energies sufficient to eject deep orbital electrons: it depends on the depth of that atom’s potential and on which electron is ejected, but atoms like gold can have deeper orbitals than atoms like carbon, meaning larger energies are needed to resolve deeper gold atom orbital transitions. Energies favorable to SEM imaging are sometimes very low compared to the energies needed to hit the EDS ejection energies. When you switch to EDS from imaging, you must be aware that you’re gaining a deeper penetration depth from the larger interaction volume of the beam. If your sample is thin and has low electron density, like carbonaceous biological molecules, you can easily be shooting through the sample and hitting the substrate, whatever that might be.

This can be a serious confounder because you don’t necessarily know where your signal is coming from. In the article commented on by Orac, the authors mention that they’re using an aluminum stub as an SEM mount, but they also talk about aluminum hydroxide and aluminum phosphate. The EDS aluminum signal is sensitive only to the aluminum atoms: you can’t know if the signal is coming from the mount or the sample! How do they know that the phosphate signal isn’t from phosphate buffered saline? That’s a common medical buffer that shows up in vaccine preparation. You can’t know if the material you’re looking at is aluminum phosphate from EDS or SEM.

As I mentioned, you also have to contend with close spacing of EDS peaks: if you look at that periodic table linked above, there’s a lot of overlap. To know gold, for certain, you really need to hit a couple of its EDS peaks to make certain you aren’t misreading the signal (all the peaks you get will have a gaussian width, meaning that you might have a broad signal that covers a number of peaks.) And, at least in the figure presented by Orac, they’re making their calls based on single peak identifications. This in addition to the other potential confounders Orac brought up: exogenous grit and the possibility that they’re reusing their SEM stub for other experiments. How can they be certain they aren’t getting spurious signals?

For EDS, I would be careful about making calls without having some means of independent analysis… like knowing what materials are supposed to be present and possibly hiring out elemental analysis of the sample. Will the gold or zirconium appear in the second analysis? Remember, science depends on being able to reproduce a result… if it was always spurious, a good tale is not being able to make it dance the second time around! Reporting everything doesn’t always mean that you know what you’re looking at. When I was doing EDS more routinely, I had a devil of a time hitting Titanium over Silicon and Gold signals… I knew titanium was present because I put it there, but I had trouble hitting it or ascribing it to specific particles in the SEM image. The EDS would not routinely allow me to reproduce an observation before the sample simply exploded while I was pounding high energy electrons into it.

Referring directly to the crank paper myself and I note that they make some extremely complicated mineral calls in their tables from the EDS data. Again, be aware that EDS is only sensitive to atoms specifically: you can’t know if Aluminum signals are aluminum phosphate or aluminum hydroxide or aluminum from the SEM stub. To know mineral crystals, you need precision ratios of the contents or X-ray diffraction or maybe Raman analysis of the mineral’s crystal lattice.

From their SEM imagery, it looks to me like they’re using a very strong voltage, which is confirmed in their methods section. They claim to be using voltages between 10 kV and 30 kV. These are very high voltages. For good surface resolution of a proteinaceous sample, I restricted myself to around 1 kV to 5 kV and sometimes below 1 kV and found that I was cutting holes through the specimen for much higher than that. Let me actually quote a piece of their methods for sample mounting:

A drop of about 20 microliter of vaccine is released from
the syringe on a 25-mm-diameter cellulose filter (Millipore,
USA), inside a flow cabinet. The filter is then deposited on an
Aluminum stub covered with an adhesive carbon disc.

They put a cellulose filter from Millipore into this SEM. I would have dried directly onto a clean silicon substrate. Here are the appropriate specimen mounts from Ted Pella. Note that the specimen mounts are not cellulose. Cellulose filters are used for a completely different purpose from normal SEM specimen mounts and, really importantly, you can’t efficiently clean a cellulose filter before putting your sample onto it. And, since these filters are actually designed to easily collect dust and grit as a part of their function, it is actually kind of difficult to get crap off of them. Without a control showing that their filters are clean of dust, there’s no way to be certain that this article isn’t actually a long survey examining the dust and foreign crap that can be found impregnating cellulose filters since the SEM acceleration voltages are unquestionably high enough to be cutting through a thin, low contrast biological layer on the top.

I won’t say more about the EDS.

So, I wanted also to address the particulate discussion a bit more directly too.

First off, from the paper directly, there is no real effort at reproduction or control. The source of the particles mentioned could be the carbon adhesive, the cellulose membrane or the vaccine sample. Having thought about it, I personally would bet on that cellulose: you don’t use them this way! They claim to be making preparations in a flow hood to keep dust out, but that doesn’t mean the dust isn’t already on any of the components being brought into the hood.

I stand by my original criticism of Orac’s post that these particles can’t be effectively quantified by molarity: those shown in the paper are all clearly micron scale objects, meaning that they have relatively large mass in and of themselves and constitute significant quantities of material. A better concentration unit for describing them would be mg/mL. I repeat that we don’t know the source of these objects for certain because the experiment is performed without true replication! If the vaccines are the source, the authors should have been able to perform a simple filtration of a vaccine specimen by a 0.22 um or 0.1 um filter and show that this drastically reduces contamination because many of their micrographs are of objects that should not have passed through such a filter… but they did no comparable experiment.

As I’ve been thinking about it, there are a couple potential different particles that could be observed under these conditions. The first is dust, as already detailed. The second possible source is vaccine components, but from a non-contaminating perspective. Orac used a quote by Skeptical Raptor who was rebutting the idea of Aluminum hydroxide being a strong contaminant by again mistaking particles for molecules. I won’t get into his difficulty calculating concentration since it was similar to what happened to Orac, but he was speaking about Aluminum hydroxide being a chemical that is a tiny fraction of a nanogram in a vaccine and therefore much less than environmental exposure to aluminum. I know I probably annoyed Orac with my thoughts about this as I was thinking out loud, but Aluminum hydroxide is not any sort of contaminant in the Cervarix vaccine friend Raptor was talking about: it’s the Adjuvant! Here’s a product insert for a Cervarix vaccine.


In this vaccine, I found that there is approximately 500 ug of Aluminum hydroxide adjuvant added per 0.5 mL vaccine dose. If you look in the Aluminum hydroxide MSDS, there is no LD50 for this compound, no cancinogen warnings and no other special health precautions from chronic exposure –it irritates your eyes from contact, but what doesn’t? It got a 1 as a chemical hazard. Antivaxxers are crazy about being anti-aluminum based upon more decades old information that has since been rebutted, but for all intents and purposes, this material is pretty harmless. One special thing about it is that it’s actually very insoluble unless you drop an acid or a strong base on it, meaning that it should be no surprise if it’s a particulate in a neutral physiological pH vaccine (Ksp = 3×10^-34)! In vaccine design, and I haven’t spent a huge amount of time looking, but the main point of the adjuvant is to cause the antigen to be retained at the site of injection for a prolonged time so that the body can be exposed to it for a longer period. The adjuvant adheres the vaccine antigen and, by being an insoluble particle, it lodges in your tissues upon injection and stays there, holding the antigen with it. I found immunology papers on pubmed calling this establishment of a ‘immune depot’ for stimulating immune cells. Over a prolonged period, the insoluble Ksp will allow this compound to gradually dissolve and release the antigen out of the injection site, but Aluminum hydroxide will never have a very high concentration in the body as a whole: that’s what Ksp says, that the soluble phase of the salt components can be no greater than about 2.4 nM, which is well below established exposure limits recommended in the MSDS of between 30 nM and 100 nM (by my calculation).

But, if you look at vaccine adjuvant under SEM, it will be a colloidal particle with a core of Aluminum in the EDS! You can even see examples of this in the target paper itself: the SEM in figure 1 looks like a colloid fractal (they call it a ‘crystals’, but it looks like a precipitate deposition fractal), and the colloids are probably aluminum hydroxide particles caked with antigen protein (again, EDS can’t distinguish between  aluminum hydroxide mixed with PBS and aluminum phosphate, contrary to what the caption says). And, these colloids are INTENDED TO BE THERE by the manufacture of the vaccine. Note, this is a structure designed into the vaccine to help prolong the immune response.

I’ve been debating the source of the singleton particles that the authors of this paper take many SEM pictures of in the remainder of their work. They are mostly not regular enough to be designed nanoparticles or precipitate colloids and they often look like dust (Orac mentions as much). I’ve been skeptical of the sample preparation practices outlined in the paper: I think adding the cellulose membrane to the sample is asking for trouble. You use substrates in SEM to avoid contaminant issues and to provide surfaces that are easily cleaned prior to use. The cellulose polymer and vaccine antigens are all low contrast… at 30 kV accelerating voltage, the SEM could actually be interacting down into the volume of the filter (as I mentioned above). If this isn’t dust sitting on the filter prior to dropping the vaccine onto it, it might also be dust dropped randomly into the cellulose monomer during the manufacturing process and trapped there while polymerizing the membrane. The filter won’t care about most of this sort of contamination because the polymer will immobilize it. Another possibility, but the paper tests almost no hypotheses for purposes of error checking, so we’ll never know.

Overall, I found that paper incompetent. There’s no reason to take it seriously. I hope that my writing this blog post will help balance the previous post which attacked science advocates for misusing the science.

Calculating Molarity (mole/L)

As a preface to this post, I want to make doubly clear my stance on vaccines. There is no good scientific evidence to support the notion that vaccination is in any way an unsafe practice or that it is responsible for any manner of health problem above and beyond the diseases that vaccines protect against. Vaccination is the single most powerful health intervention created in the last 150 years of medicine. There is, in my opinion, some potential for this post to be used to damage the credibility of a person who I believe to be a necessary positive force in the Healthcare scene and I want to make it clear that this was not the intention of my writing here. Orac is a tireless advocate for science and for clear, skeptical thought in general and I respect him quite deeply for the time he puts in and for putting up with the static he puts up with.

That said, I believe that science advocacy is a double edged sword: if you didn’t get it right, it can come back to bite you.

I love Respectful Insolence, but I’ve got to ding Orac for failing to calculate molarity correctly. He is profoundly educated, but I think he’s a surgeon and not a physicist. We all have our weak points! (Thank heaven above I’m not ever in the operating room with the knife!)

In this post, which he may now have edited for correctness (and it seems he has), he makes the following statement:

More importantly, look at the numbers of precipitates found per sample. It ranges from two to 1,821.

O.M.G.! 1,821 particles! Holy crap! That’s horrible! The antivaxers are right that vaccines are hopelessly contaminated!

No. They. Are. Not.

Look at it this way. This is what was found in 20 μl (that’s microliters) of liquid. That’s 0.00002 liters. That means, in a theoretical liter of the vaccine, the most that one would find is 91,050,000 (9.105 x 107) particles! Holy hell! That’s a lot. We should be scared, shouldn’t we? well, no. Let’s go back to our homeopathy knowledge and look at Avogadro’s number. One mole of particles = 6.023 x 1023. So divide 91,050,000 by Avogadro’s number, and you’ll get the molarity of a solution of 91,050,000 particle in a liter, as a 1 M solution would contain 6.023 x 1023 particles. So what’s the concentration:

1.512 x 10-16 M. that’s 0.15 femtomolar (fM) (or 150 altomolar), an incredibly low concentration. And that’s the highest amount the investigators found.

Anybody see the mistake? Let’s start here: Avogadro’s number is a scaling constant for a linear relationship and it has a unit! The units on this number are atoms(or molecules) per mole. It converts a number of atoms or molecules into a number of moles.

‘Moles’ is a convenient person-sized number that is standardized around ‘molecular weight,’ which is a weight unit that arbitrarily says that a single carbon atom has a weight of ’12’ and results in atomic hydrogen having a weight of ‘1.’ That’s atomic mass units (or AMU), which is usually very convenient for calculating relative weights of molecules by adding up all the AMU of their atomic constituents. To use molarity, we usually need a molecular weight in the form of Daltons, or grams/mole. Grams per mole says that it takes this many grams in mass of a substance for that substance to contain a single mole’s worth of molecules (or atoms) where it is then implicit that the number of molecules or atoms is Avogadro’s number.

‘Mole’ is extremely special. It refers to a collection of objects that are atomically identical! If you have a mole of a kind of protein, it means that you have 6.02 x 10^23 number of this kind of identical object. If you make a comparison between two proteins, the same molar number of each with a different molecular weight is a different overall mass. Consider Insulin (5808 g/mole) compared to the 70S Ribosome (2,500,000 g/mole)… one mole of Insulin would weigh 5.8 kg while one mole of 70S Ribosome would weigh 2.5 metric tons!!! If they have roughly the average density of proteins, what would be the volume of 1 mole of 70S ribosome as compared to 1 mole of Insulin? It would be 430 times greater for the Ribosome; 2900 L for 70S Ribosome while Insulin is about 6 L!

Notice something here: an object with a big molecular weight occupies a bigger volume than the same object of a smaller molecular weight… regardless of the fact that they are at the same molarity. Molarity as a number depends strongly on the molecular weight of the substance in question in order to mean anything at all. For the Ribosome, the same molar concentration as for Insulin means a solution containing a much larger amount of solute.

In the post in question on Respectful Insolence, Orac is talking about a paper which observes particulate matter derived from vaccine specimens in an SEM. It is clear from the authorship and publication of the paper that the intent is to find fault in vaccines based upon the contents of materials examined by this probing… from what little I know about the paper, it does not seem to be producing any information that is truly that informative. But, you can’t fault a paper on a point that may not actually be as flawed as an initial interpretation would imply. The paper reports number of particles observed per 20 uL of a solvent. They find as many as 1,821 particles per 20 uL. We are not told for certain what these particles are composed of except that the investigators aren’t sure and shot an overpower EDS at everything and reported even the spurious results. Orac scales up this number to 1L to get 90.1 x 10^7 particles and then divides by Avogadro’s number to find what proportion this is of one mole of these particles, never mind that we don’t know how big the particles are in terms of molecular weight or how dense in volume per mass. He declares it to be a tenth of a femtomole and runs on with how tiny the concentration is. As I initially wrote this, I focused on the gleeful way in which Orac does his deconstruction in large part because it really isn’t a valid thing to laugh at when the deconstruction is not properly done.

Here is how someone of my background approaches the same series of observations. I can see from the micrograph in the blog post that the scale bar is something like 2 mm (2000 microns)… the objects in question are maybe tens to hundreds of microns in size. Let’s make a physicist supposition here and think about it: pulling this out of my ass, I’ll claim these are 1,821 approximately spherical identical particles of sodium chloride, each of 40 microns diameter. That gives a volume of 4/3*Pi*20^3 um^3 or 1.9 x 10^-12 m^3 per particle and 3.5 x 10^-9 m^3 for the whole collection of particles. Now, density usually is given in terms of g/cm^3 or g/mL… there are 100 cm per meter and you must convert three times to cube it, so 3.5 x 10^-9 x 100^3 = 3.5 x 10^-3 cm^3. Wait a minute, we’re now at a volume of 3.5 uL!!! Did you see that? A cubic centimeter is a mL and 0.0035 mL is 3.5 uL, or 17% of the original 20 uL sample volume! What molarity is this? The density of sodium chloride is 2.16 g/mL or 2.16 mg/uL… which is 7.56 mg. That’s 7.56 mg of salt dissolved in 20 uL. The molecular weight of sodium chloride is 58.44 g/mole or 58.44 mg/mmole, which gives .129 mmole. From this .129 mmole in .02 mL is 6.47 mmole/mL.

That’s 6.47 mole/L……. 6.47 M!!!!

Let’s pause for a second. Is that femtomolar?

Orac missed the science here! I initially wrote that he should be apologizing for it, but I’ve revised this so that my respect for his work is more apparent. The volume of these particles and their composition is everything. A single particle with a molecular weight in the gigadaltons or teradaltons range is suddenly a very substantial mass in low particle number. If these particles are as I specified and composed of simple salt, they are at a molarity that is abruptly appreciable. If we make these into tiny balls of Ricin, that’s unquestionably a fatally toxic quantity!

As with all things, dose makes the poison and there’s no Ricin in evidence, but this argument Orac has made about concentration, in this particular case is catastrophically wrong. A femtomole of a big particle that can be dissolved could be a large dose!

I forgive him and I love his blog, but let this be a lesson… you don’t just divide by Avogadro’s number in order to get meaningful concentrations!