Doing big science: Brian Schmidt and his measurement of the accelerating universe
I recently had the good fortune to see a freshly-minted Australian Nobel-prizewinner speak. Brian Schmidt from the Australian National University arrived in all his Swedish pomp-and-glory to give his first post-Prize public talk at Monash about his role in figuring out that the universe is still accelerating like a crazy man.
He’s a well-regarded speaker and it was greatly entertaining to see him talk, with his zesty American accent and his generous appetite for wine and other good things of life. Mulling over his talk, I got to thinking about how one goes about doing big science, like measuring the speed of the entire friggin universe.
I. The Richard Hamming approach to science
If you’ve never read the essay on research by Richard Hamming "You and your research", do yourself a favor and read it now for you will never find a collection of such earthy advice for doing top-knotch research.
There are many gems in that essay but one that struck me was the observation that the guys who had serial spectacular success in research were guys who are always thinking about the big problems in their field. However an important distinction was they were not actively working on the problems because typically the tools available were just not good enough to solve the problems at any given time. This makes sense as otherwise they probably would have been solved already. These guys were smart enough to know where the walls of innovation were but not dumb enough to bash their foreheads continually against the bricks of failure.
Nevertheless, the reason that these guys ultimately succeeded was that they also shared another trait, that of openess – these are guys who loved to meet other researchers and find out about new methods, no matter how crazy. Actually, especially the crazy methods. These were the guys who were able to see before any else how some crazy new method from that overlooked discipline could be exploited to solve one of the great problems of their own. They then had the strength of will to drop everything else and go for it.
During Brian Schmidt’s talk, an actual decent question was asked at question time, "what was the key idea or moment that ultimately led to the measurement of the accelerating universe". Schmidt’s answer was instructive, "…it was the realization that the type 1A supernovae could be used to measure the universe and that we had the technology to look for it."
This was exactly how great science is done according to Richard Hamming. Earlier in the talk Brian Schmidt admitted that the measurement of the universe was something he had been fascinated since he was a young lad. But desire and great intellect was not enough. Schmidt pinpointed the source of his great work as the moment of recognition that a new method could be used to solve a great problem in his field. Schmidt was uniquely gifted in recognizing that a new way had opened up in the intersection of a new theory of supernovae and the development of new machines – large-array telescopes and improved scientific workstations.
He didn’t come up with either the theory or the tools, but he made a shotgun wedding of the two. And that is why he won the prize.
II. Rare measurements
In undergrad physics they teach you this rather quaint model of experimental measurement where you’re supposed to repeat the measurement a kadjillion times and then calculate the mean and standard deviation from a statistical grind of your table of numbers. Looking back over a career in science, I now find this a rather souless way of looking at measurements. It replaces a deep understanding of the instrument and the theory behind the measurement with a blind and inelegant method of brute-force statistics to determine the error.
Indeed I believe there is a serious issue that a standard physics education fails to teach statistics properly but that is an issue for another time.
The reality is that in actual science, and in particular cutting edge science like the measurement of the acceleration of the universe, what you measure is much more ephemeral than anything you will ever encounter in Physics 101. Physics labs are toy experiments that are deliberately designed to make obviously repeatable measurements. In actual research, if you can’t get someone to accept the validity of one single measurement, making a thousand of them won’t make them change their mind. In some great experiments of the past, only one measurement was ever made.
A case in point is the set of measurements that got Brian Schmidt the Nobel Prize. What he was trying to measure, in the 90s, was the properties of a trulyb epheremal event – the explosion of a white dwarf star in a binary system, the so-called type IA supernovae. Because the theoretical model puts very stringent bounds on the masses of white dwarf stars, the maximum luminosity of this explosion had very uniform characteristics. Thus the distance and speed of these objects could be gauged by comparing the observed explosion to the theoretical explosion in a still place.
Schmidt and his large international group of rag-bag astronomers rescanned the entire sky with the large array telescopes to look specifically for these binary star systems at their moment of death. That is, not only did they re-scan the entire sky, but they had to do this over several intervals to capture the explosion from binary star to supernovae. His group pushed the puny (in comparison to today’s iPhones) workstations to their limits as they processed what would have been enormous images of gigabytes in size to look for that rare event – a supernovae explosion that happened at the right moment in the past so that the light hit the earth just when the telescope was pointing at it.
The paper that came out presented only a handful of such events. After years of searching and untold amount of image processing, they were lucky to find even these little needles in their observational haystack. The speeds of these explosions of these stars were plotted in the paper with gloriously large error bars. These bars are not calculated using statistical standard deviations but derived from deep calculations of the limits of the instruments and the theory behind the instruments.
Still, it has to be pointed that a major reason that the results were accepted pretty quickly was that there was another team (producing another winner of the Prize) that was measuring exactly the same thing, albeit on other telescopes. The fact that both groups found the same thing pretty much sealed the deal. Here is actually a case where it was better to have a competitor working on the same project, rather than live in abject fear of being scooped. Indeed, this represents a general principle of calculation before the days of generally available computers. Often, long and involved computations done by hand had be done by two different people. Only if both get the same result, will it be accepted as the answer. This ought to be a working principle in the measurement of fancy new objects.
III. The role of theory
You might think that the work behind a Nobel prize in the year 2012 astrophysics would involve some fancy new theoretical physics. The surprising thing listening to Schmidt’s talk was how thoroughly bog-standard the theory was. Indeed Schmidt spent the bulk of the introduction expaining Einstein’s theory of general relativity, which was introduced to the world in 1915. Specifically, he only invoked the totally uniform solution of the equations of general relativity, which is the easiest of all solutions, and solved immediately by Einstein. In some ways, what was most surprising was what was not discussed in the talk. No M-branes. No superstrings. No 11-dimensional universes.
Indeed, the most important piece of theory was probably the models of the explosion of white dwarf stars. From what I understand, these models involved at the lowest level, neutrino physics in the standard model. This is good solid astrophysics married to particle physics from the 1970s.
Of course, having won a Nobel Prize, Schmidt had earnt the right to speculate like a crazy mountain hermit drunk on cactus juice and he did so rather entertainingly, warning of the fearful death of the universe as space has stretched so far apart in the distant future that every atom will live forever alone. Then there is the other possibility that whatever is the magic source of dark energy, will continually churn out energy as the universe expands and so the universe will be filled with stuff.
Nevertheless, the point I want to make is that great science doesn’t need need fancy new theories, but rather, a deep appreciation of old theories and damn clever ways of measuring new things.
A Fundamental Breakthrough in Protein Folding
In my humble opinion, the biggest paper in protein folding from the last few years just got published in the wee hours of 2011. It is Protein 3D Structure Computed from Evolutionary Sequence Variation from Debora Marks, Lucy Colwell and colleagues (and when I say colleague I mean Chris Sander, which you should all know as a co-author of DSSP). This paper proves the tremendous result that the key structural contacts in a protein structure can be derived from a multiple sequence alignment. And that these contacts are sufficient to generate reliable structures of the protein. And big proteins at that.
I heard on the grapevine that this paper had a difficult passage to publication. I was both surprised and not surprised by this. I was surprised because this is such a fundamental result, it should have have been published in a top-tier journal.
But I was also not surprised because this paper pushes into a direction different to the mainstream of protein folding. The salient point of the paper is that you should be able to predict a reliable lo-res structure for any protein sequence with only a few hours computation on a standard desktop computer. No wonder some of the referees got hot-and-bothered and proved an obstacle to publication. (I can sort of understand this as the accepted test of protein-folding algorithms is CASP. Nevertheless, I’ve read many protein-folding papers and few offer novel fundamental approaches such as this). After all, wasn’t protein folding supposed to be a computationally difficult problem requiring massive computational resources? Still I am glad it got published in PLoS ONE (arguably the top open-access journal), as anybody can now read it [flips bird at closed-wall publishing].
What I am particularly excited about in this paper, is that it brings together quite a few different strands of research in protein folding into one powerful theorem, some of which I have worked in. The paper invokes results from contact analysis of protein structures, phylogenetic analysis of multiple sequence analysis, measures of coevolution, and the practical problem of generating structures from distance constraints.
The real breakthrough in this paper is the identification of a sufficiently robust measure of coevolution in a structural alignment of a protein family. Although coevolution in structural alignments had been studied before, it was really the work of Rama Ranganathan that got people excited by showing that coevolution analysis could predict mutations that had genuine experimental ramifications. Using his SCA measure to identify key contact pairs, Ranganathan identified position pairs in the PDZ domain that, when mutated, generated measurable experimental changes. Nevertheless, many of the other predicted top correlated pairs from SCA were ambiguous, with no easy interpretation. There appeared to be a lot of noise in the SCA measure.
Since then, many different coevolution measures have been proposed, each with their own points of ambiguities. The measure used in this paper has appeared to resolve the ambiguities of all previous measures. The origin of the measure used in the current paper was proposed in 2009 by Martin Weigt and colleagues, called Direct Coupling Analysis. This was a much more sophisticated measure of covevolution than previous measures. It defined the observed correlations as the result of much richer probability model of pair couplings which involve the calculation of a set of hidden parameters. Solving this model involved the use of some heavy-duty machine-learning techniques. And it was slooooow. This work was used to analyse inter-domain coupling between two protein families that were known to interact.
Finally, in mid 2011, Weigt released a new version of his measure which improved the performance of DCA by orders of magnitude. This was used to show that the pairs identified by DCA were in fact, native contact pairs in the corresponding crystal structure. Let me pause right here. This is a massive result. The impressive singal-to-noise of the DCA measure is a huge improvements over all previous measures of coevolution.
Still, this begs the question as to how significant were the contacts identified by DCA. Are they sufficient to define the structure of the protein? This is where the current paper comes in, and the answer is a resounding YES. This consitutes the great finding in this paper. Fortunately for Marks, Colwell and friends, all the technology needed to prove this result had already been developed. For instance, the work of two labs I’ve worked in has been instrumental in honing the insights of contact analysis. Ken Dill has shown contacts can define a well-defined protein-folding landscape. Michael Lappe has shown that only a paltry 8% of native contacts can be used to reconstruct the structure of a protein to 5 Å. As well, the NMR community have developed robust algorithms to generate structures from distance constraints, such as that in the venerable program CNS.
Marks, Colwell and friends showed that the highly correlated pairs identified with the DCA measure of coevolution, when used as native-contact distance-constraints, generates structures that are within 3-5 Å of the native structure for a diverse bunch of protein families, some as long as ~250 amino acids. (You should read the paper to get a bigger handle on the accuracy) This is a stunning accuracy compared to other ab-initio protein folding algorithms, given that it works across a diverse bunch of proteins, requries only a few hours of calculations on a single machine, and is incredibly robust.
Of course, the lower limit of accuracy of 3 Å is probably the best that one would expect from this method. Since coevolution identifies contacts that are common in a protein family, you would only expect native contacts to be derived from this method that is common to all the proteins in a family. Highly variable regions will not leave a sufficently strong evolutionary trace.
This method is incredibly exciting because it has worked with longer proteins than other methods (~250 amino acids), with a greater chance of attacking even longer proteins. Much as I admire the work of David Baker’s Rosetta for fragment-based folding and D. E. Shaw’s Desmond for brute-force MD based folding, these methods have been restricted to small proteins of 100 amino acids or less, with no clear indication that these methods can elegantly break beyond the complexity wall to larger proteins.
Besides, both these systems are based on old insights. The breakthrough of Rosetta’s fragment analysis is 10 years old. Desmond is a technical marvel but rests on a modeling approach that’s more than 30 years old. I’ve been working on coevolution analysis for the last 5 years, so I know well the morass of statistical aberrations in the analysis of covariation of multiple sequence alginments. The clarity of the DCA measure of coevolution represents a genuine modern breakthrough using highly sexy machine-learning techniques, and the robust nature of the results should make it the canonical method for generating accurate lo-res structures of any protein sequence.
Books Read 2011
I started this year with the good intention of writing a paragraph or three for each book I read. A short review so to speak. I managed for about 15 books up to April. It’s too much work to write about what I just read. Easier to read something new. So here’s my reading list for this year (managed to read a lot of technical shit):
[*] greatly enjoyed
[x] deeply annoying in some way
1. Stendhal, The Red and the Black
2. Steig Larson, The Girl who kicked the Hornet’s Nest
3.* Neil Howe and William Strauss, The Fourth Turning
5.* Edith Wharton, “Age of Innocence”.
6.* Gary Taubes, “Why we get Fat”
7. Nathan Haren & Mike Cliffe Jones, “Beyond Blogging”
8. Jules Verne, “Voyage au Centre du Monde”
9.* Rino Breerbaart, “Song Logic”
11. Mario Vargas Llosa, “Aunt Julia and the Scriptwriter”
12. Henry James, “Portrait of a Lady”
13.x “Persian Fire”, Tim Holland
14. “La Chartreuse de Parme”, Stendhal
15. Clay Shirky, “Cognitive Surplus”
16.* Collette, “Cheri”
17.x Tea Obreht, “The Tiger’s Wife”
18.* Simon Schama, “The Power of Art”
19.* Aristotle, “Poetics”
20.* Simon Schama, “Rembrandt’s Eyes”
21. David Foster Wallace, “Consider the Lobster”
22. Micheal Lewis, “The Big Short“
23. Edward L. Glaeser, “Triumph of the City”
24.x E.L. Doctorow, “Ragtime”
25.* Barry Strauss, “The Trojan War”
26.* Patrick White, “Tree of Man”
27. William Bengston, “The Energy Cure”
28.* John Man, “Alpha Beta: How 26 Letters Shaped the Western World”
29. Vanessa Veselka, “Zazen”
30.* Alex Ross, “Listen to This”
31.* Andrei Alexandrescu, “The D Programming Language”
32. Hugh Mckay, “What Makes Us Tick”
33. Clifford Pickover, “Archimedes to Hawking: Laws of Science”
34. G.R.R. Martin, “The Game of Thrones”
35. Barry Strauss, “The Battle at Salamis”
36.* Alberto Miguel, “A History of Reading”
37.* David Sloan Wilson “Darwin’s Cathedral”
38. Colin Wright,“Networking Awesomely”
39.* Joey Comeau, “The Girl who couldn’t Come”
40.* Tina Fey, “Bossypants”
41. John Kenneth Galbraith, “The Great Crash 1929”
42.x Fiona McGregor, “Indelible Ink”
43. Ethan Marcotte, “Responsive Web Design”
44. Richard Ellis, “Aquagenesis”
45. William Calvin, “A Brief History of the Mind”
46.* Miles Franklin, “My Brilliant Career”
52. Michael Lewis, “Boomerang”
53. Jim Collins and Morten T. Hansen, “Great by Choice”
54.* Karen Armstrong, “The Great Transformation”
55. Marshall Rosenberg, “Non-Violent Communication”
56.* Norman Wade. “The Faith Instinct”
57.* Charles Pinter, “The Theory of Abstract Algebra”
58.* Piela, “Ideas in Quantum Chemistry”
59. Keith McFarland, “The Breakthrough Company”
60. Mark Sisson, “The Primal Blueprint”
61.* Lisa See, “Shanghai Girls”
62.* M. G. Bulmer, “Principles of Statistics”
Magic Numbers and unit conversions in Structural Biology
If you end up doing any kind of energy calculation in proteins or organic chemistry – and that includes messing around with Molecular Dynamic trajectories – you may end up dealing with actual numbers.
And that means you’ll have to get your head around physical units and their conversions.
I’ve spent days trying to figure out magic numbers in equations and source-code. Diving into the guts of someone else’s source-code is not the nicest place to figure such things out. Do it enough, and you’ll start seeing the same numbers pop up everywhere. As I’ve never seen anyone bother to describe some very common magic numbers in biochemistry, I’ll list a bunch of them right here.
First let’s get acquainted with the standard units:
- positions of atoms and molecules are always expressed in Ångstroms which is 10-10 m. Ånstroms are preferred because the radius of a hydrogen atom is ~1.0 Å, a useful magnitude to describe molecules. That’s why PDB protein structure files use Ångstroms.
- masses are expressed in Da, which is g·mol-1 or 10-3 kg·mol-1 (where mol-1 is 1.0 / 6.02×10-23). This unit is the work-horse of chemistry and the masses of atoms (or at least their protons) can almost be pulled directly out of the periodic table. Once again, the mass of a hydrogen nucleus is ~1.0 Da.
- charges are expressed in multiples of e (the charge of an electron). A hydrogen nucleus has charge +1 e.
- energy is usually expressed kcal·mol-1, which biochemists and nutritions use but not engineers of physicists. At room temperature, 300 K, the average kinetic energy available to most atoms is about 1 kcal·mol-1. The hydrogen bond binding energy is about 2 kcal·mol-1.
These units are pretty universal across a whole bunch of structural biology programs, and are chosen because they have a reasonable order of magnitudes for biological molecules at room temperatures. This is important to avoid overflow and underflow problems in floating-point operations.
Where magic numbers come in is making all the other physical properties match this set of units. One of the most common calculations is the electrostatic interaction. Namely the electrostatic potential energy k·q1·q2/r.
Now, we ideally would like the result in kcal·mol-1. Given that q1 and q2 are in e, and r is in Å, this imposes a set of unit conversions on k (=1/4πε) which gives the magic number k = 332.24.
You will see this everywhere, and the first place I saw it was in the ubiquitous secondary structure evaluation program DSSP that defines hydrogen bonds in terms of the electrostatic energy calculated by this equation for bacbkone O and H atoms.
Since the energy and distance units are fixed, this means that the calculated force units are, not in terms of Newtons, but in terms kcal·mol-1Å-1. This is because forces in MD are mostly central forces taken from the energy potentials where F = dE/dr.
Notice I’ve said nothing about time. There is no particular consensus on what time units are used in Molecular Dynamics simulations.Some MD simulations choose fs (10-15 s) as this is the smallest time-step, which allows ~10 steps for the fastest vibrations (bond vibrations involving H atoms). Others choose ps (10-12 s) as this is closer to what can be observed with experiment.
Even with ps, this causes problems with velocities, due in part to the floating point representation. In NAMD, velocity values are stored in the PDB which has only 3 decimal figures in the coordinate fields. Given that velocities are outputed as Å/ps, the 3 decimal places lose a lot of precision. As a result NAMD multiplies the velocities by 10 before storing. So you have to divide by 10 when you read NAMD velocities.
But the programs mess around with time and velocity units internally, ostensibly to avoid a single floating point multiplication in the main loop. In both NAMD and AMBER, the kinetic energy E = 0.5·m·v2 is stored as kcal·mol-1. If time was stored as ps or fs, then the kinetic energy calculation would require a unit conversion to get kcal·mol-1.
In NAMD, the base time unit is fs (10-15 s). As mass is in Da and position is in Ånstroms, directly plugging these values in the kinetic energy calculation results in an energy unit that is 2388.45897 kcal·mol-1. To abstract away that 2388.45897, they find the square root of 2388.46, so that can you can slide one square root each into one of the velocities in the v2 term in the kinetic energy. The velocity is of course, distance/time. Since they don’t want to mess around with the distances in Ångstroms, they divide their time (which is in fs) by the NAMD magic time-factor of √ 2388.45897 = 48.89. Now you can plug it all in 0.5·m·(d/t)2 and get the energy directly in kcal·mol-1.
In AMBER on the other hand, the base time unit is ps (10-12 s). AMBER too, uses Da and Å. Plugging these time, mass and distance units in gives the kinetic energy as 0.00238846 kcal·mol-1. In this case, AMBER takes the square root of the inverse of this number which is 418.68. They multiply time (in ps) by the AMBER magic time-factor of √418.6 = 20.46.
Two different MD packages. In one, you multiply time by 20.46. In the other, you divide time by 48.89. Same problem, two magic numbers.
New Look, Mobile Friendly
I’ve been meaning to do this for a while, I’ve updated the look of the blog.
The previous design was inspired by an old design of über minimalist Ev Bogue. Back then I was wandering around the world as a nomadic minimalist.
I’ve since been folded back in academia and it’s time for a change. The new look has two goals:
1. Emphasise the article nature of most of my (longish) posts
2. Responsive-Web-Design
Resize the window and make it real narrow. You will see the design collapse into a linear layout. Perfect for reading on a mobile† device.
†I really mean iPhones, but I need to stay in the good books of @pansapien.
The infidelity of the theoretical protein backbone
Problems in protein simulations are often reduced to one of two categories:
- do we have a sufficiently accurate model of atomic interactions?
- have we sufficiently explored the conformational space of our proteins?
If you talk to molecular modellers, they will try to tell you the problem lies wholly in conformational sampling. It is an article of their faith that force-fields are good enough. Our erstwhile modeller can then claim that the problem lies not in software but in hardware. It’s just that their computers are too slow to finish their simulations properly.
Well, I beg to differ. One major flaw in atomic force-fields, which has been swept under the carpet, is that atomic force-fields fail to properly model the protein backbone. And they’ve failed to do so, for decades.
Experimentalists have devoted much effort in understanding the protein backbone conformations, precisely because getting the backbone right has a disproportionate effect in determining the conformation of a protein from electron diffraction maps. The first thing crystallographers worry about is the Ramachandran plot of their derived structure.
The Ramachandran plot is the allowed conformations of the φ/ψ angles of the protein backbone (I have a detailed introduction to the Ramachandran plot, which you can play with in my Ramachandran Plot Explorer)
Crystallographers have studied intensely the Ramachandran plot for decades. The original Ramachandran plot was first constructed in 1963 (Ramachandran et al 1963 JMB 7:95) which identified the two broad regions – the β-strand region in the top-left, and the α-helical region in the bottom-left:
Today’s standard Ramachandran Plot is averaged over tens of thousands of high-resolution protein structures and provides a statistically controlled measurement of the protein backbone conformational space. Packages that evaluate this – PROCHECK and MOLPROBITY – are standard diagnostic tools. No crystallographer would dream of releasing a structure of a protein if their Ramachandran plot did not validate against these diagnostics.
Here’s Janet Thornton’s classic PROCHECK map of the Ramachandran plot (Laskowski et al 1993 J App Crys 26:283). Here we can see the diagonal shape of the α-helical region, and the appearance of the semi-allowed regions, as well as an articulation of the left-handed α-helical regions:
Probably the most used is Jane Richardon’s MOLPROBITY describing the contour lines for the allowed regions of the Ramachandran plot (Lovell et al 2003 Proteins 50:437):
The fine structure in the standard Ramachandran plot identifies the conformations of the more complicated motifs in protein topology – β-hairpin turns, α-helical turns, γ-turns and β-bulges (disclosure – I worked on the Ramachandran plot for 8 years ~ 4 papers). These motifs require very specific backbone conformations in the Ramachandran plot in order to provide the correct intra-atomic interactions.
It is disheartening to learn that for decades, force-field developers have basically ignored all this experimental work on the protein backbone. Instead, our pointy-headed friends have turned to quantum-mechanical calculation of the energies and conformations of small amino-acids in vacuum, rather than to study the backbone conformations of, like, actual proteins. As a result, you will find that the Ramachandran plot calculated with classic force-fields completely misses out all the fine structure of the standard experimental Ramachandran plot.
Here’s an early force-field from 1984 (Weiner et al 1984 JACS 106:765), which doesn’t even match the original 1963 Ramachandran calculation. Instead, the strong minimum corresponds to the formation of an internal hydrogen-bond – the γ-turn, which is rarely seen in real protein structures. This minimum however, appears in virtually any vacuum QM calculation. The right-handed α-region is in the wrong place:
This level of wrongness doesn’t improve in 1995 (Cornell et al 1995 JACS 117:5179), by which time Peter Kollman had taken over force-field development for AMBER. This is particularly bad since by 1995, PROCHECK had already become de rigeur amongst crystallographers:
Meanwhile, Alexander MacKerrell and Martin Karplus (MacKerell et al 1998 J Phys Cem B 102:3586), who are plugging along with CHARMM, don’t do much better:
One reason that force-field developers have not been so concerned about the crystallographic protein backbone, is that molecular-dynamics simulations have focused mainly on folded proteins. In folded conformations, many mutually reinforcing intra-molecular interactions in the compact folded state can compensate for the poor modelling of the backbone.
However, if the simulation involves any kind of disorder in the protein chain – loops, peptides, and protein folding – the simulation will crap out. Wait, you say, but force-field developers do test their force-fields against flexible backbones. If you read their papers carefully though, you will find that these test don’t go beyond calculating α-helical propensities versus β-strand propensities. Arguably a more realistic challenge would be to reproduce complicated motifs such as β-hairpin turns, γ-turns, or α-helical turns. These turns have very well-defined conformations. That no such molecular-dynamics model can reproduce these turns at any level of accuracy really needs to be mentioned.
If I might hazard a guess to why ab initio protein folding using “physically realistic” models has failed so badly, I would hazard that the crappy modelling of the protein backbone might play a part. Taking the “nucleus” view of protein folding, the formation of turns and kinks are crucial in defining the tertiary structure. The reason is that it is the reversal of the chain generated by turns that bring the correct pieces of secondary structure together. As well, β-bulges and helix caps control the extent of secondary structure. These are typically generated by the fine structure regions of the Ramachandran plot. If your model force-field can’t generate all the fine structure of the observed Ramachandran plot, you will never get these turns and bulges in the right place, and thus miss out on the correct tertiary structure.
I think one of the main reason that David Baker’s Rosetta program for protein-folding has been so successful was that he found a way to overcome the crappy force-field modelling of the backbone. Rather than try to fix a broken thing, he bypassed the problem altogether by constructing a library of statistically probable local fragment conformations (Bystroff 1998 JMB 281:565). In Rosetta, certain high scoring short sequences are assigned φ/ψ angles direct from the fragment library. These are based on crystal structures, and not on some artificially wrong force-field. By identifying correct chain reversals from the very beginning, Rosetta searches in the right valleys in the conformational space.
I am happy though, to report that after decades of mis-placed faith in quantum-mechanical purity, force-field developers have been dashed back onto the beach of experimental data. Recent updates of force-fields have started to incorporate experimental corrections to the backbone force-field parameters.
Here’s the popular CHARMM 22 forcefield (C22) is shown on the left, giving a crappy Ramachandran plot. In 2004, Alexander MacKerell added a grid-based φ/ψ term (CMAP) to the CHARMM 22 (C22) force field (Mackerell 2004 J Comput Chem 25:1584). The corrected CMAP Ramachandran plot (on the right) shows that the grid-based correction turns a very crappy Ramachandran plot into something that at least might look acceptable to a crysallographer:
In a similar vein, Carlos Simmerling added some experimental tweaks to AMBER in 2006 (Hornak et al., 2006, 65:712). Compared to the crystallographer’s PDB (left), the tweaked AMBER Ramachandran plot (right) fixes some things but is still poor in the α-helical region:
The irony is that as the force-field developers have turned to experiment rather than rely on quantum chemistry calculations, quantum chemists are starting to get a grip on the Ramachandran plot. A quantum mechanical calculation of the alanine dipeptide using DFT with a sophisticated solvent model (Tsai et al., 2009, J Phys chem B, 113:309), gives the first decent ab initio calculation of the Ramachandran plot:
As we’re starting to have success in folding proteins using unbiased long-time MD (Shaw et al 2010 Science 330:341), some might think that our backbone atrocities have now been eliminated. But as these proteins have very simple topologies (WW domain), the turns don’t need to be so well defined. I’m guessing this won’t scale to more complicated topologies. Large topologies such as the β-sheets of serpins will require perfect modelling of the intervening β-hairpin, which still can’t be done.
I have long held the view that until we can reproduce the local fragments of Rosetta in unbiased MD with some future force-field, we cannot say that we have modelled the backbone properly. Until then, we will continue to suffer the bloated claims of our pointy-headed force-field friends.
Some English pronunciation tips
Although I learnt English as a second language, I now wear it like a well-worn glove. But in science, there are tons of made-up poly-syllabic words, and I occassionally trip over some of them, such as: equilibrate, equilibrium and equilibration.
However, I’ve been learning a bunch of languages the last few years, and through doing that, it’s thrown English pronunciation in relief. I’m starting to get a conscious handle on English pronunciation, and I’ve discovered some useful rules that were not apparent to me before:
- English is an accented language. There is one emphasized syllable in every polysyllabic word, unlike say, Chinese or French where there are no syllable stresses. In Chinese each syllable is delineated quite clearly, giving a staccato feel, whereas in French, you tend to slide or slur over syllables in a word.
- for two syllable verbs, the emphasis is on the second syllable
- for two syllable nouns, the emphasis is on the first syllable
- for words of three or more syllables, the emphasis is on the second or third last syllable. How to decide? Well, vowels are typically classed as long (dipthongs such as ‘oe’, or the long ‘i’ as in ‘sheep’) or short. If the second-last syllable is long, the emphasis lies there.
- if the second-last syllable is short, then the emphasis falls on the third-last syllable.
- A really surprising thing in English is the glottal stop. Consider the word kitten. Pronounce it slowly and you will voice the ‘tt’ – KIT-ten. But if you start speaking quickly, the ‘tt’ will not actually be voiced and a swallowed sound is made instead – KI’en. Glottal stops happens all over the place
- In the Australian and English accents, the r at the end of the words are not voiced, although I’ve found that most monolinguistic Australians swear that they can hear an r when they pronounce such words.
- English unlike most other European languages has something called sentence stress. That is you actually speed up over most of the sentence and slow down for the key part of the sentence, such as the object. If you don’t do this rolling sentence stress, you end up sounding quite mechanical.
So now I can prounce these words without embarrassment. It’s e-QUI-li-brate, e-qui-li-BRA-tion and e-qui-LI-bri-um.
Swimming, Running, Hunting, and Meditating: the Evolutionary Origin of Mystical States
I’ve wondered often at how mystical states came about, states of mind that takes us out of the every day, such as the samadhi of buddhist meditation, or the zone of the long-distance runner. Assume, for argument sake, that such mystical states are an intrinsic part of our human heritage, then they must have evolved from a mental substratum dating back to a more primordial existence. The question then arises as to what possible use our distant quasi-monkey ancestors might have had for mystical-like states or mind.
Or to rephrase it another way, is there some kind of biological function that would require the evolution of mystical-like state of mind?
To explore this, we need a reasonable map of the evolution of humans from our common ancestor with other apes. First though, we need to define the set of features that distinguish us from the other apes. I think a reasonable set is: bipedalism, sweating, loss of hair, large brains, spoken symbolic language and hunting. How did these evolve and for what reason?
Although there is no official consensus to the answer, based on my reading around the topic, I’d hazard a guess that it happened in 2 basic stages, the first happening around 3-4 million years leading to the Aquatic Ape, and then later, around 2 million years ago, another transition resulted in the Running Ape, with the final pieces snapping in place with modern humans popping up around 200,000 years ago. By thinking through these transitions, I hope to identify the key adaptations that laid the foundation for modern states of mystical experiences.
The Aquatic Ape
What is clear is that permanent bipedalism happened around 3-4 million years ago. That’s when we first find fossils of bipedal ancestors like Australopithecus. Careful analysis of the gait from the skeletal remains suggests that Australopithecus could walk but not run (Bramble & Lieberman, 2004, Nature 432:345 [PDF]). The brain is small, like a typical monkey brain, and it’s probably safe to say that Australopithecus was not a tool user.
Surprisingly, another key feature that evolved with Australopithecus is the loss of body hair. Now you might be surprised by this because hair (or the lack of it) isn’t preserved well in the fossil record, but recent compelling evidence comes from a rather ingenious bioinformatics analysis (Reed and coworkers, BMC Biology 2007, 5:7). This analysis focuses on, of all things, human hair lice. It turns out that humans, unlike other apes, have, not one, but two types of hair lice, one living in head hair and the other living in pubic hair. Chimps and gorillas on the other hand, have only one. The reason that humans have two types of hair lice arises from our nakedness over most of our bodies, and thus the two colonies of lice are isolated and have evolved separately. Indeed, it turns our head lice is related to chimp hair lice, whilst our pubic hair lice is related to gorilla hair lice.
The argument then is that when we lost our hair was when our hair lice split into two species (I first came across this idea in a wonderful Nova documentary about human origins). The bioinformatic study found that the two types of human lice shared a common ancestor around 3-4 million years ago, very close to the age of Australopithecus fossils. This suggests that Australopithecus was a butt-naked ape, every bit as hairless as we are, meaning that most artistic renderings of Australopithecus covered with monkey fur is wrong (for some gorgeous reconstructed images of our ancestors).
And if Australopithecus was naked, he probably sweated as well. It thus appears that 3-4 million years ago, our ancestors started walking on two legs about the same time that they lost most of their body hair and developed a sweating mechanism. What possible biological reason would result in these features?
In the case where one species evolve features quite different to their near relatives (other apes), I prefer explanations of evolutionary adaption that identify an environmental or functional factor that is markedly different from that which could be applied to their relatives. So the savannah ape theory is out, because there are plenty of other primates that live in the savannah but never needed to loose their hair or walk on two legs. Hunting or tool theory is also not particularly compelling as chimps are also known to use tools, hunt and eat meat. And neither is standing on tippy toes to look further out.
The only theory that fits the criteria of unique environmental factor is Alister Hardy’s much maligned Aquatic Ape Theory that postulates that our ancestors spent some time evolving in water (Elaine Morgan, Scars of Evolution). One of the compelling attributes of the Aquatic Ape Theory is that the putative response of our ancestors to the water environment is incredibly similar to responses found in other aquatic mammals. This is convergent evolution, and makes the Aquatic Ape Theory rather attractive to my eyes.
In the Aquatic ape, swimming provides an excellent reason to lose the fur, in order to stream-line the body for swimming. Evolving in a water environment answers all sorts of interesting questions about our physiologies. Although we now have reasonably effective sweating mechanisms, we do tend to lose an awful lot of salt when we sweat. How did this happen? If we did lose our hair, and evolved sweating in sea water, then the loss of salt was not a problem at all.
More importantly, evolving in water solves one of the biggest conundrums of bipedalism: how to offset the huge physiological demands to walk continuously on two legs with a skeleton designed for knuckle-walking. Wading on two legs in water immediately takes away the physiological demands of bipedalism, with the immediate benefit of allowing breathing at much greater depths. Walking on two legs, however, is not unique to humans. For instance, although the bonobo monkey walks mostly on all fours, it can occasionally walk on two legs (Youtube clip), and has been observed to wade through rivers to get food. It is not hard to imagine Australopithecus as an accentuated version of the bonobo monkey that lost its hair.
The Running Ape
Nevertheless, the aquatic ape theory only accounts for the features found in Australopithecus. The other features of modern humans developed in the descendants of Australopithecus.
It’s been suggested that the Pleistocene cooling that happened around 2.5 million years ago might have driven the Aquatic Ape back onto dry land. And about 2 million years, we start finding fossils of Homo Erectus, arguably the first ancestor that is physiologically very much like us. Analysis of the skeletal structure suggests that Erectus could run quite well (Bramble & Lieberman, 2004, Nature 432:345). There is a much better proportion of the legs for running. There is now a ridge at the back of the skull that attaches a tell-tale tendon for stabilizing the head during running. This tendon is also found in other mammals that run. Erectus was a Running Ape.
Crude stone arrow heads are also found with the fossils suggesting that Homo Erectus was a hunter, and ate meat. So here, we have a Running Ape that uses crude arrow-heads to hunt. However, it’s always puzzled me how Homo Erectus could hunt with such crappy weapons. We can run, yes, but not really as fast as other mammalian predators like tigers and wolves, certainly not fast enough to chase down zebras or antelope, and throw crappy spear heads at them.
I found the answer to this conundrum in Christopher McDougall’s Born to Run, which is a wonderful and encyclopedic book on long distance running. There, I came across the phenomenon of persistence hunting, an ancient method of hunting fleet-footed mammals. Persistence hunting is an ancient method of hunting that has almost died out. It is carried out by Kalahari bushmen (Youtube clip), and Australian aboriginal tribes. Persistence hunting works by basically running an animal to exhaustion over several hours of continuous running at roughly marathon pace. Although slow over short distances, humans are actually quite efficient runners over long distances. Hunting occurs by chasing a animal and not letting it rest, so after several hours, the animal collapses exhaustion. That’s when our Running Ape can get close enough to basically stab the animal to death with a crude spear head. The skill in persistence hunting lies in the stamina required for the long-distance running and the ability tracking the prey over a vast area.
The reason that humans can outrun four-legged ruminants over a long distance turns out to be due to a surprising reason: sweating. Humans are one of the few mammals that sweat for cooling, and this turns out to be incredibly advantageous for long-distance running in hot scorched conditions. Most mammals cool by panting, which is incompatible with running. They overheat if they run long distances without stopping. In contrast, our Running Ape ancestor could maintain a steady pace whilst the liquid glistening on their naked skins keeps their bodies from overheating. Fianlly, the hunted mammal overheats, and collapses from exhaustion.
It was first proposed by David Carrier in 1984 (Current Anthropology, Vol 25) that persistence hunting was the adaptation that drove the evolution of Homo Erectus. But the most satisfying feature of the persistence hunting theory is that it provides a direct evolutionary link to the Aquatic Ape Theory. The unique physiological feature that allowed Homo Erectus to outrun its prey, was its ability to sweat to keep cool whilst running. This particular feature already exists as an evolutionary byproduct of our Aquatic Ape ancestors. Out of all the primates, only a descendent of the Aquatic Ape – one who had lost its hair and could sweat – would adapt to the new form of persistence hunting.
The Mental Requirements of Persistence Hunting
Now that we’ve established that persistence hunting may be the key driving adaptation for Homo Erectus, we can start exploring the cognitive demands of persistence hunting. Here, I believe, we’ll find the evolutionary origins of mystical states of mind. From my reading of the literature, there seems to be three major cognitive developments required for persistence hunting:
1) an intrinsic reward for the action of running
2) a heightened awareness of the overall environment
3) ability to mimic the psyche of the animal prey
1) In studies of societies that undertake persistence hunting, it was found that hunters during the hunt often fall into a quasi-mystical state of euphoria. Running is considered effortless and enjoyable in itself. Considering that recorded hunts can last up to 8 hours, there is a tremendous delayed gratification involved. Thus, it is necessary to evolve an intrinsic reward for the running itself, in order to motivate our persistence hunter to carry out this otherwise exhausting activity. As such, our ancestor’s brains evolved natural endorphins that are released with the physiological markers of long-distance running, such as regular intense breathing, and rhythmic motion.
2) For persistence hunting to work, the hunters must isolate and chase down a single animal. If you get mixed up and chase after different animals, you will not be able to exhaust it to collapse. Thus, one of the crucial abilities of a successful hunter is to track an animal over the landscape during an entire 8 hour run. The hunter has to develop the cognitive ability to maintain awareness of the prey in the vast expanse of the landscape. This is different to other mammalian predators, who only need to maintain direct visual contact as they run down their prey directly. The Hunting Ape must have developed an expansion of consciousness that defocuses from what is in front of you, diffuse over the vast expanse of the landscape in order to locate the prey anywhere on the horizon over the many hours of a chase.
3) Over a given chase, the hunters often lose sight of the animal, and no clear tracks are discernible. In such instances, the advantage goes to the hunter who could figure out which way the animal was likely to have gone. Our ancestors had to do it without tools such as GPS, satellite tracking, or knowledge of evolution. Instead, our ancestors found a short circuit to this information by evolving the ability to be “possessed” by the animal, or cognitively inhabiting the mind and thinking of the animal. Indeed, this is how modern day persistence hunters operate to predict the movement of the prey even when the trail was lost completely.
Mysticism is an Evolutionary Spandrel
In evolution, the arrival of a new trait opens up new direction for change. The trait may not have been directly selected for, just the accident of some other trait. Such traits then get appropriated for other biological functions. This is called an evolutionary spandrel, a term coined by Steven J. Gould, where he refers to architectural spandrels, spaces created by the intersection of arches, which were a byproduct of building dome structures, but appropriated for distinctive decorative elements found in many christian churches.
The unusual cooling method evolved in the Aquatic Ape, is a spandrel, as sweating allowed one of its descendants to develop into an efficient Running Ape, who learnt how to evolve a method of persistence hunting.
We modern humans have constructed societies (even global ones) that far outnumber the small bands of ~150 individuals that our paleolithic ancestors lived in. In order to cope with societies of such great density, it’s my hypothesis that various religions were able to exploit the unique mental states of persistence hunting to re-orientating individuals to live more harmoniously in large numbers. In order words, the cognitive developments in persistence hunting are spandrels, which have been repurposed for religious spirituality.
De-centered States of Self
One obvious example is the runner’s high described in the literature of long-distance running. Most runners experience a natural high after about 20 minutes of running, where euphoria takes over and the runner feels like she can run forever. This has obvious relation to the need to motivate our Running Apes ancestors to run a lot in order to hunt and eat.
There are also many examples of athletes who report that in certain instances, they experience what is now known as the “zone”, where coordination and activity reaches a de-centered state, where everything just flows effortless. I would like to argue that this is invoking the primordial state of mind that is induced when a persistence hunter needs to de-center his consciousness over a vast landscape in order to keep track of his prey. I believe that this state of consciousness has been appropriated by modern spiritual practices to develop a de-centered sense of self. Practitioners who can experience is particular state of mind are much more functional in a heightened world of internecine conflict.
Practices such as yoga, tai-chi, and meditation tap into this ancient circuit to induce the euphoria and de-centered state of self originally evolved for persistent hunting. What is interesting is that these yoga and tai-chi focus on the body, perhaps identifying the muscles and motions that best elicits these states. As one of the most important aspects of long-distance running is the mastery of controlled efficient breathing, is it not surprising that yoga and meditation focus so much on the breath in order to elicit these states?
Possession by animal spirits
The other key cognitive development of persistence hunting is the ability to inhabit the mentality of the animal prey, which might better be described as possession by animal spirits. This kind of possession is almost a quintessential description of shamanic modes of thought, and provides a rather interesting interpretation of the cave paintings of paleolithic hunters. The purpose of these beautiful paintings, mainly of large wild animals, and rarely of human figures, have remained largely unexplained. Looking at it from the perspective of persistence hunting, however, these paintings become a natural expression of that key process of inhabiting the soul of the animal prey during a long and difficult persistence hunt.
This ability to inhabit the mind of other animals, opens up vast new potential for cognition. I believe that animal possession is the basis of a multitude of mystical states of minds, such as demonic possession, oracular prophecy, speaking in tongues, spirit channeling and charismatic prophecy. Evolution gave our Running Ape ancestor the ability to be possessed by the animal he was chasing down. This has bestowed on our minds, the cognitive potential to be invaded by the consciousness of all manner of strange beings outside of ourselves.
The GPCR-G complex: the canonical structure of Cell Signaling (with interactive guide)
Perhaps you’ve heard of the new structure of the GPCR-G complex. It’s a seminal breakthrough, and I concur with Curious Wavefunction in that it’s worthy of a Nobel prize.
So noobs, why is it important? According to some estimates, some 30% of our proteins are membrane proteins and the reason that they are so many is that membrane proteins are where most of the signal processors between our cells are found.
Our multi-cellularity depends on a constant cascade of information, as signaling molecules flow back and forth across different types of cell. Spatially, it’s much easier for a signaling molecule to hit something on the 2D surface of the membrane than to tunnel through and search for the target within the body of a cell. Signals that hit the membrane, propagate through the membrane courtesy of an adaptor molecule. The signaling molecule, an agonist, will hit the adaptor from the extra-cellular side, which activates the adaptor. The adaptor will in turn activate other proteins on the inside of the cell, which in turn will cause the cell to change. The precision of the adaptor in converting outside to inside signals communicates information between cells. These signal adaptors thus encode our multi-cellularity as organisms.
The most common architecture for such signaling adaptors is the G Protein-Coupled Receptor (GPCR). They include receptors that are responsible for seeing, smelling, hormones and neurotransmitters. The GPCR binds molecules from the outside of the cell, and then switches on a matching G-protein inside of the cell. The G-proteins are so called because they use GTP as a timer (the same G in DNA). The activated GPCR forces the G-protein to bind a new GTP molecule, which activates the G-protein. When the G-protein is released, it will then bind to all sorts of targets, setting off new cell states. The G-protein shuts down when the GTP spontaneously breaks down into the rather inert form of GDP. It will then wait for the next GPCR activation.
This GPCR-G interaction is thus the cornerstone interaction of cell signaling.
Now of course, we’d like to fuck around with this process, and we do, considering that over 30% of modern pharmaceutical drugs target a GPCR protein in our bodies. But designing such drugs is an imprecise process, full of random trial-and-error procedures. If we were know to how the GPCR-G interaction happens at atomic detail, then we may understand how these drugs actually work, with the hope of designing better ones.
The Nature paper from the Kobilka lab at Standford reports the crystallization of the GPCR complexed to a G protein [3sn6]. It’s almost academic which GPCR protein it is, but it’s the Β2-adrenergic receptor complex, which binds to to adrenalin.
[For those of you with Chrome/Safarit/Firefox(recent) you will see an interactive widget for the structure below. Click the arrows on the top, or go straight to the Jolecule page where you can add your own annotations]
What the Kobilka lab had to do to get the thing to crystallize is nothing short of phenomenal. Membrane protein crystallography is hard enough as it is. The greasy surface of the membrane proteins designed to slide into the greasy membrane do not crystallize easily. Here, they had to crystallize a membrane protein stuck to many different cytosolic proteins, which makes it even harder still. They had to identify an agonist (or trigger for binding) that would work in the mutant complex. They replaced the entire unstructured C-terminal of the GPCR with a whole lysozyme insert. They must have sieved through an interminable number of trials to find a nanobody (a truncated antibody) that would bind the different pieces of the G-protein sufficiently so that the complex would survive the crystallization process. As well, they would have to induce the right kind of lipid to form an intact micelles around the membrane region.
Phew.
The structure is beautiful, in the sense that it fits what the biochemistry tells us and gives a clear mechanical view of how it works. One fantastic result is that we see that the G-protein is splayed open when bound to the GPCR. The two domains of Gα – Gα-helical cause it’s mainly helical and Gα-Ras cause it’s a Ras-like domain – are found completely opened. The GTP binding site is completely exposed.
In the unbound form of Gα [1AZT], the binding site is complete closed over as the two domains, Gα-helical and Gα-Ras are closed over each other.
This structure also shows how the G-protein is inserted into the GPCR, especially the orientation of the A5-helix. This rationalizes known mutation experiments, and suggests many new ones. This structure provides incredible detail, but more importantly, it provides a molecular template to study all the other myriad signals that flow in-and-out of our cells. It is sobering indeed to gaze at the interaction that allowed our unicellular ancestors to cross-talk their way into our multi-cellular glory.
