The Molecular Universe

Flushed with my success in predicting the number of employees of Google, Yahoo, and Accelrys, I decided to experiment with extracting and posting news about molecular systems from various news sources. This is not completely trivial, sadly, because although many organizations like to dissemintate news, few like to do so in a manner which is helpful to others.

But, I persisted, and created a crude amalgamation of news stories which are generated automatically using rss feeds. The most important command is provided by 'XmlStartlet' which is a cunning small utility, most often encountered on Linux, which allows you to carry out automated operations on xml files, which is what rss feeds actually are.

The command in question was as follows:

...incoming rss standard in... | xml sel -t -m "///item" -c . -n

This was followed by a certain amount of massaging and processing - and the resulting web page can be seen here.

Of course, whether this page is updated regularly will depend on whether I remember to run the appropiate commands, but I'll try to do that.

I wanted to create this page to keep an eye on the way in which the media are covering and presenting the concept of molecules. In general, it is impressive how widely appreciated chemical and molecular concepts are. And every now and again, one sees a reminder that Universities and government laboratories have too many people working in their PR departments...

A while back (on 10/26/2009 to be precise) I wrote a short note where I made a mistake which no self respecting climatologist would ever make. I posted three predictions which could be tested. The article was Companies and Bacteria, contained predictions as the number of employees in one year's time at Google, Yahoo, and Accelrys. The predictions were, Google: 21,640; Yahoo: 13,960, Accelrys: 242.

Aside from marvelling at the immense number of decimal places I had decided to include, I came to wonder recently how the predictions faired against the cruel realities of corporate America, the recession, and so on. Hence, I looked up the figures.

Google, in Octorber 2010 had 23,331 employees, 'up from 21,805 full-time employees as of June 30, 2010', according to their 2010 Q3 earnings report, posted here. So the prediction of 21,640 wasn't too bad.

Yahoo, in October 2010 had 14,100 employees versus the prediction of 13,960. So, again not a bad prediction.

Finally, Accelrys in October 2010 had complicated its picture substantially by acquring Symyx. The deal resulted in a reduction in force of approximately 80 employees, according to this report. Prior to the merger, Accelrys had 358 employees. So, if we assume that half of the reduction in force occurred at Accelrys, they were left with 318 employees, versus the prediction of 242.

All in all, not too bad a set of results. Probably better than a linear projection could have achieved, anyway. (Though obviously, like a good climatologist I won't be making the mistake of testing this immediately). But, in general I would suspect that the growth form of a bacterial colony and a company would be similar, and so when making a prediction as to future company sizes, the logistics function seems reasonable. Even if the predictions are not perfect, they provide insights into what will happen. In the case of Accelrys, the declining but cash rich company obfuscated the situation by acquiring another software company. This helps to mask the decline in the basic markets served by Accelrys and conceivably could give the company a petri dish jumping means of avoiding its bacterial fate. Perhaps it can jump the species barrier altogether and start to grow!

I use a variety of computers as I go about my daily business. Naturally I pick up email along the way and many people send me Microsoft Word attachements (.doc files, if you are on a Windows system). Now, often this is not a problem, as on my main computer I have a copy of Microsoft Word. However, on other machines, I cannot read such files. That is where the Doc2Ascii.com comes in. Without fuss or complexity, Doc2Ascii.com turns .doc files into Ascii text.

Arguably, Doc2Ascii is actually easier to use than Word itself for such a conversion. Word will give you a host of messages and questions, and leaves the worrying impression that you are about to lose something if you convert to ascii format. In contrast Doc2Ascii is simple, it just does what you expect.

The output of the conversion is presented on a new web page, you can cut and paste the text straight into whichever or whatever application you like. It is very convenient, and completely free.

PETN, or PentaErythritol TetraNitrate, crops up in the news from time to time as a high explosive, often used by terrorists.

PETN's molecular structure is shown above. A central carbon atom supports four identical chains, each of which ends in a nitrate group. The resulting structure has the formula C(CH₂NO₃)₄. This form of the formula emphasizes the four identical chains which the molecule contains. You can also write the formula at C(CO₂)₄(N₂)₂4(H₂O) ₄, which emphasizes the fact the PETN molecule contains just the right ratios of carbon, nitrogen, and oxygen to form many gas molecules from each molecule of explosive.

Not only do PETN's constuents contain a host of small stable combustion products ready to be released by the appropriate detonator, the molecule is also somewhat strained, with four identical large side chains terminating at the central carbon atom.

So when suitably triggered, PETN rearranges rapidly, releasing CO₂, H₂O, and N₂, and plenty of heat, as these products are more stable than the PETN molecule itself. The result can be a devastating explosion.

Hence, PETN has been emplolyed by several terrorists, including Abdulfarouk Umar Muttalab.

Rather chillingly, when you look at the PETN molecule in three dimensions, as is shown above, at a certain orientation of the central tetrahedral carbon, the molecule takes on the shape of a swastika.

About a year ago I was talking with a scientist that I had known for many years, and was surprised to find, that he himself was surprised, that I accepted without question the concept of manmade global warming. 'You believe that global warming is manmade?', he said. 'Yes', says I, 'It's on the news!'. Global warming was and is not one of my day to day concerns, and I had blithely assumed that what was reported by the Al Gore, the BBC, Science, Nature, et al was to be believed.

The conversation induced me to check the usual sources, Wikipedia, Google, more attentive reading of the newspapers. I was hoping for a definitive answer. Rapidly, and sadly, I was forced to conclude that the situation was muddy. It was clear that there was room for debate, and it was clear that scientists themselves were not in agreement.

I was disappointed, there was no well thought through description of the situation. Instead, there was a disconcerting, and acrimonious debate. This seemed a different situation to CFCs and ozone, or acid rain, to name some recent examples where theories have been publicly analyzed, debated and confirmed.

It was surprising to see journals and magazines apparently taking sides. For example, for some reason, Bjorn Lomborg, the author of The Skepitcal Environmentalist (Robert Boyle the author of 'The Sceptical Chymist' would be flattered) and The Scientific American had somehow or other fallen out. Normally this does not happen in science. Theories are proposed and tested, scientists can reproduce each other's work (or cannot), and fairly soon, assuming a theory has merit, a consensus emerges, upon which new predictions theories can be built. Debates tend to be spirited but good natured.

What was (and is) the problem? Scientists are trying to find discernable information in a noisy and incomplete record. That is a very difficult thing to do, and assumptions can play havoc with the interpretation. Added to this is the problem that if calamity is imminent, we would like to avoid it if at all possible. These problems afflict both sides of the discussion. Uncertainty makes the trend hard to prove or disprove, and its dire consequences either in terms of environmental or financial disaster inject the same sense of impending disaster guaranteed to cement religious fervor into both camps.

So, I remained disappointed, the situation was far from clear, as my friend had suggested. The recent Climate Research Unit (CRU) 'Climategate' leaks have been an interesting addition to the discussion, however. At first I thought, these emails probably don't amount to much. I took a look at the file, though. (It is readily available on the internet: FOIA.zip is the string to search for). And I found that it is quite an explosive cache of information. There is discussion of massaging charts by combining information from different sources, which unsurprisingly greatly improves their agreement, there is discussion of deleting data, there is discussion of interfering with the independence of scientific refereeing, and a great reluctance to release information publicly. Added to this, there are sets of poorly written filtering or massaging programs and a description of a frustrating attempt to reproduce a long forgotten massaging recipe. It has to be said that this is more than a few email lines out of context. All in all, not science at its best.

So, although I am no expert in climate matters, and am therefore not really qualified to comment, I have to say that I am becoming slightly doubtful of the quality of the work that leads to the alarm over manmade global warming. The effect may very well be real, but the case has been made to seem more faith based than science based by the FOIA.zip leak.

Open information, process, and discussion would help immensely. The raw data, upon which conclusions are based, should be freely available, along with the manipulation algorithms, with all the information and algorithms stored in a revision control system, with suitable backup archiving, so that data and histories are never lost. It would also be interesting to see how predictions of the effects of global warming, which have been made since the late 1980s have faired in comparison with actual measurements.

As someone interested in science I find it a little frustrating and worrying that there is not a clear answer yet to the question 'Is human activity causing the temperature of the planet to increase significantly?'. It seems that the evidence is not yet clear, it is hard to say, one way or another, whether warming or cooling trends are significantly impacted by human activities. Hence, there is an active scientific debate. And there is also an acrimonious debate which serves to increase confusion.

Often the debaters express their opinions with passion. This caused me to wonder, how close to religious ferver have the competing sides of the climate debate come. Fortunately, Richard Brodie, has described a short set of features to look for in religions, leading to the following scoring of the pro and anti anthropomorphic global warming (AGW) groups.

A couple of explanations may help: These characteristics are the things to look for in a successful religion. For example, some prescriptions about food tend to be helpful. Feasts, rules about what to eat, what not to eat, and so on. As far as I can tell the pro- and anti-AGW groups do not make provision for strictures with respect to food. (Though one can see how this might happen if labeling of total carbon footprints were to become part of a future directive).

Religions tend to concern themselves with issues related to sex. Marriage, baptism, contraception, and so on. Again as far as I can see the AGW debaters do not make pronouncements in this direction.

The list above seems to indicate that the substantial difference between the groups is the impending crisis focus of the pro-AGW group. For the pro-AGW group, as for religions, this is likely very helpful in increasing popularity and interest in the cause. The anti-AGW group seem to have no such characteristic, and this reduces the effectiveness of their message and cause.

Personally, I think that CO₂ release into the atmosphere is symptomatic of inefficiency and waste. Energy resources are being converted into energy and a waste product that could just as easily be plastic bottles, bags, or all manner of desirable modern products. So, I would certainly advocate less CO₂ production, on the grounds of conservation of a finite resource (hydrocarbons in the ground) rather than on the grounds of a certain causative link between atmospheric CO₂ and significant warming. It happens that by conserving resources we can also mitigate the risk while the scientific and religious discussions continue.

The molecule above is one of the group of molecules collectively known as vitamin-D. Such molecules are aggressively marketed (i.e. hawked!) by the nutraceutical and food supplement industries, based on the fact that people who are severely deficient in vitamin-D, to the point of exhibiting bone weakness, also have depressed immune systems. Fortunately vitamin-D does little harm and arguably provides some benefits (see for example the nice write up provided by the Linus Pauling Institute). So, as is often the case, the nutraceutical business activity does little harm.

Industrially cholecalciferol is manufactured through the irradiation of 7-dehydrocholesterol, extracted from lanolin, with ultraviolet light. The lanolin itself is extracted from the grease in sheep wool, or from cow or pig skins. Fortunately, these sources are widely produced materials, so the price of the complex vitamin-D molecules, like cholecalciferol, are relatively low. Interesting, cholecalciferol finds a less 'healthful', or expensive, application as an additive to rat poison. For rodents, cholecalciferol increases the toxicity of anticoagulents like warfarins, which cause poisoned rats to bleed to death internally.

Two facts to keep in mind when you next purchase multivitamins: The vitamin-D component, as likely as not, was extracted from an animal skin; and rat poison was the other possible product that the cholecalciferol could have been used in.

A slight departure for TheMolecularUniverse blog, a digression on the growth of bacteria and companies.

In ideal conditions, and in the absence of competition from other creatures, disinfectants, or predators, bacteria grow until their waste products inhibit further growth. If one assumes that the initial growth rate of the bacterial colony depends on the number of bacteria present and that the effect of inhibition also increases linearly with the increasing size of the colony, you can write down a simple equation, known as the logistic, which describes the number of bacteria as a function of time.

Perhaps unsurprisingly, companies behave similarly to bacteria. When a business model which works is identified, a company will grow until its growth is limited by factors such as its ability to coordinate its employees effectively. If you plot the number of Google employees versus time, and fit the resulting data points to a logistic function, you will see a curve like the one shown below. This exercise is not in itself too surprising. You have a few data points and a sigmoidal function, the logistic, with three parameters, which can be fitted to almost any data set. The acting of fitting the actual Google employee numbers provides an estimate, with estimated uncertainties, of the intrinsic growth factor of the company (which we will label 'k'), the rate of inhibition of growth (labeled 'a'), and a fitting constant, related to the solution of the differential equation which underlies the logistic, 'b'.

The fit for Google is quite satisfactory. The fit for Yahoo is extremely good (see below). This implies that, like bacteria, companies like Google and Yahoo do one thing and eventually begin to inhibit their own growth. Despite the marketing and executive hype, Google and Yahoo aren't reinventing themselves or evolving in new money making directions, they are doing one thing and doing it until their actions become self limiting. At least, that is what this simple model suggests.

How about a company which seems to be not tending toward an equilibrium, finite size? Applying this analysis to the number of employees reported by the much smaller company Accelrys leads to the graph below. Here the k, factor relating growth to employee numbers is negative. Additionally, the quality of fit is poorer than in the case of Google or Yahoo (this can be seen by the very large estimated errors in each of the parameters). Hopefully for its customers and employees Accelrys will evolve to a different form of business model, more aligned with simple bacterial growth.

How does the logisitic function come to exist? The simple derivation is as follows: If N is the number of cells in the bacterial colony, then we speculate that the rate of change of N with respect to time is proportional to N. If we take the constant of proportionality as k, then this gives:

dN_growth/dt = kN

the rate of increase in the number of bacteria is zero when there are no bacteria, and become higher when the colony increases in size. However, this is not the complete story, as bacteria proliferate they also secrete waste products into the environment and there is therefore a counter to colony growth which depends on colony size. This factor has no effect when the colony is small, but becomes strong when the colony is large. This can be represented as another linear function of N:

inhibition factor= 1-(1/a)N

when N is zero, the inhibition factor is 1, or irrelevant, and when N is large, the inhibition factor tends toward zero. The constant a determines the gradient of the inhibition factor with respect to the number of bacteria in the colony. By multiplying the growth rate equation and the inhibition factor equation we have an expression for the overall rate of growth of the bacterial colony:

dN/dt = kN(1-(1/a)N)

or

dN/dt = kN - (k/a)N²

or

dN/dt = kN(a - N)/a

This differential equation can be solved by collecting terms with N on one side:

dN/(N(a-N)) = (k/a)dt

and making use of a partial fraction decomposition to simplify the left hand side:

dN/aN + dN/(a(a-N)) = (k/a)dt

or

dN/N + dN/(a-N) = kdt

which on integration gives:

logN - log (a-N) = kt + c

and this rearranges to:

log (N/(a-N)) = kt + c

which can be rearranged to:

N = a/(1+exp(-kt)b)

where b = exp(-c) and so is in essence the constant of integration. k is the constant of proportionality related to growth, the higher this value, the more rapid the growth for a given colony size. Inhibition is described by a, in general the smaller this factor, the more the colony is inhibited from growing by its size.

The resulting equation for colony size with time shows how a very simple model can be used to establish an understanding of growth. The fact that it is possible to apply such a model to the size of companies, as measured by their employee bases, is also interesting. It has to be said the economists prefer more linear models, and financial wizards more complicated models including the effects of size fluctuations. However, a model which provides a simple account of the factors effecting growth has appeal. In the case of a healthy company it would seem reasonable that adding more employees should increase growth. Additionally, there should also be some negative impact of adding employees, as communication overhead increases, for example, just as the bacterial colony inhibits itself through the production of waste products. Scarily, these models allow one to predict company sizes. In 2010, for example, we can estimate that Google will have 21,640 employees, Yahoo will have 13,960, and Accelrys will have 242. Unless, of course, they evolve! (These extrapolations are made in October 2009, we will have to see what happens in practice).

As Google, Yahoo, and Accelrys are public companies, they report employee counts from time to time. I have made use of the records posted by Yahoo for each company to obtain the information for the diagrams shown here, I used the 'WayBack Engine' internet archive to obtain pages for past years.

As if there were every any doubt, researchers at IBM have recently created beautiful direct images of the pentacene molecule using an Atomic Force Microscope (AFM).

Pentacene, as you can see above, contains five six-membered carbon rings in a linear chain together with their associated complement of hydrogen atoms. Pentacene is an aromatic molecule with interesting properties. Somewhat like graphite, and yet truly molecular, pentacene has electrical conductivity like graphite, and the controllability of a molecular organics. Hence there is great interest in putting pentacene to work in molecular electronic devices.

The atomic resolution of the atom positions in pentacene will come as no surprise to crystallographers. Crystallographers have been able to 'see' atoms for close to 100 years. However, crystallographers need crystals. Without a regular array of diffracting atoms, conveniently provided by nature in the form of crystals, crystallographers cannot carry out the their trade. So the atomic resolution of the atoms in a single molecule is, strangely, big news. The AFM, one day, may allow chemists to characterize individual molecules simply by tracing their connectivity. Perhaps one day it will be possible to map the binding site of a protein, or the key interaction regions of an antibody, on a molecule by molecule basis, using an AFM.

The IBM image, which you can see here, is brighter at the ends of the molecule. It is tempting to speculate that this is a result of the AFM directly sampling the molecular orbitals of the pentacene, rather than simply its electron density. Perhaps experiments are finally catching up with quantum mechanics, which have been able to see molecular orbitals for many decades!

For a while we will probably see AFM images confirming what has long been established through crystallography and quantum mechanics. However, as experience with the technique increases, and interest in vanishingly small states of matter accelerates, we will undoubtedly see surprises as scientists get up close and personal with individual molecules.

The molecule above is called Diprivan or propofol, the drug that has been linked to the death of Michael Jackson.

Propofol does not possess pain reducing qualities; however it does rapidly induce unconsciousness, forgetfulness, and an extreme detachment from the physical world. Hence it is used medically as an anesthetic. It renders patients unconscious rapidly and once the patient is 'out' additional drugs are used to suppress their sensation of pain.

Although propofol is relatively easy to synthesize from common chemical building blocks, it is a difficult drug to self administer. To avoid rapid decomposition it must be injected into the body and the dosage needs to be finely monitored and finely controlled to prevent death by heart attack or by suppression of respiration. This combination of characteristics makes the risk reward ratio from a drug abuser's perspective very unattractive. Despite the fact that propofol is difficult to self administer there have been documented cases of the abuse of the drug and these cases have been generally limited to those with medical knowledge and medical access to the drug.

Analysis of the activity of a range of molecules which contain similar chemical features has led to detailed knowledge of the origin of the pharmacological effects of Diprivan.

The propofol molecule interacts with the gamma-aminobutyric acid type A, GABA(A), receptor. The keys to the binding interaction are the hydrophilic group at the center of the molecule (shown in red in the diagram above) and two hydrophobic centers which are on either side of the hydrophilic center.

The commercial development of the propofol molecule has focused on the control of its concentration in the human body. These developments have taken the form of the careful design of the formulation of the medical emulsion which is given intravenously to patients and more recently in designing pro-drugs which are metabolized in the body to yield free propofol molecules.