The Water is Wide

Proper molecular dynamics simulations require lots of water.

What is hydrophobicity? We know it as the separation of oil and water. But what underpins the phenomenon is not any problem of oil, but peculiarities of water, which is a polar solvent. The hydrogen and oxygen comprising water have very different electronegativities, which produce a highly polar compound with partial charge separation across the H-O bond. The electrostatic attraction between these tiny charges leads water to have a networked structure with lots of attractive forces between molecules. This keeps water in a liquid state at far higher temperatures than other liquids of similar molecular mass (think of liquid nitrogen). This hydrogen bonding network also makes of water a sort of clique that expels those uncool molecules that can't hook up in the same way and participate in the bonded network. That is why oil ends up the odd droplet out, forced to stand aside while all the water molecules madly pair up and network, handing out their business cards.

Polar water forms a network that repels non-polar molecules.

These forces are crucial to protein structure and function as well. Typically, proteins that swim in the water-based cytoplasm fold with a zone of hydrophobicity on the inside, and a shell of electrically polar groups that can interact with water on the outside. One of the best known proteins is hemoglobin, which not only follows this rule, but also has an intricate mechanism of cooperativity that depends on hydrophobic interactions.

Proteins generally organize themselves with hydrophobic cores and hydrophilic exteriors.

Hemoglobin doesn't just float about by itself, but forms a tetrameric complex that cooperates in binding oxygen. When one oxygen binds to one of the four units, the other units gain affinity and bind oxygen much faster. Conversely, when carbon dioxide builds up and drives peripheral pH down, (more acidic), it drives the structure to lose affinity for oxygen, and the rest of the oxygens leave faster as well. This helps our blood efficiently unload O2 in the tissues while taking it up in the lungs. The differences between these structures (with high or low affinity for oxygen) are well known, but their detailed transitions (called allosteric, being structural changes induced by outside compounds) are not quite understood, as the structural techniques for which hemoglobin and its relatives have been pioneer molecules (principally X-ray crystallography) yield only static pictures.

Full tetramer of hemoglobin shifts between oxygen-bound and not-bound states. This structural shift has functional consequences for cooperative binding, increasing oxygen affinity once one O2 binds.

This where molecular dynamics come in. This is an entirely computational method that uses first principles of statistical mechanics and chemistry to model how a structure (known from other methods) changes with time, as it is buffeted by ambient motions of temprature, i.e. Brownian (or Einsteinian) motion. A recent paper resolved a decades-long difficulty in this field by finding that the allosteric transitions of hemoglobin are deeply intwined with hydrophobic / electronic aspects of its environment which can not be properly modeled by the standard few waters sprinkled around the structure, but need a much wider swath of solvent to become apparent. The precise issue is the spontaneous transition between these structures (the base state being called "T0" and the oxygen-accommodating state being called "R0") in the absence of oxygen. The T0 state is known to be more stable and the R0 -> T0 transition happens in 20 microseconds. But in simulations done to date, the R0 state is more stable, and the transition never happened. What was wrong?

Box sizes from cited article, showing how many or few waters are involved.

Why is the standard practice to use so few waters? They move a lot, and there are a lot of them, making it very computationally draining to add to a molecular dynamics simulation. For instance, the authors cite that their small 75 Å box contains 39,439 atoms in all, while their largest 150 Å box contains 318,911 atoms, an almost order of magnitude increase. The small box, which contains the full hemoglobin tetramer plus 10,763 water molecules is unable to simulate the conformational shift that is so well known to happen, while the larger ones are. The message from the paper is that if the waters surrounding the hemoglobin protein are not occupied by their wider network of hydrogen bonding interactions extending out into the bulk medium, then (in the simulations with small boxes) those waters tend to attack critical structural elements of the protein, at its ionic and polar self-interactions, creating a mistaken impression of instability for the T0 conformation, and generally of hemoglobin's structural dynamics. Obviously this has general implications for the molecular simulation method, which presumably can be fixed by the addition of more computers.

Idle waters do the devil's work! Right box is without hemoglobin, while the left box is with. The curves represent numbers of hydrogen bonds by waters, (X-axis), which are sharply reduced in small box sizes. Those waters then go on to pester the protein and destabilize it.

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FRET Better

New developments in short-range distance sensing technology.

Biology ultimately comes down to chemistry and structure, usually of molecules that are rather small. Seeing them has been a big challenge through the decades, and successful visualization has led to significant advances, such as the original structure of DNA, to take one example. The premier method has been X-ray crystallography, more recently superceded by electron cryomicroscopy. Both of these methods use powerful, ultra-short-wave radiation and mathematical methods to reconstruct complete structures of static molecules. In each case, the subjects have to keep very still in order to have their picture taken. While it is often possible to lock proteins of interest in more than one static conformation for these analyses, such as bound to a substrate, and then without, dynamics have to be inferred or guessed from the further application of math in the form of molecular dynamics.

NMR has been a supplementary method for small molecules, which allows some dynamic analysis, but there have also been a large number of more ad-hoc methods to gain structural insight when full structures or dynamic behavior is inaccessible, such as cross-linking, immunolabeling, complex purification, and systematic genetic mutation. One of the most magical of these non-comprehensive structure methods is Förster resonance energy transfer (FRET) between pairs of fluorescent elements. Such elements can communicate directly, via their light emissions, how close they are, and thus can give rather direct information on specific structural aspects of a molecular system in an immediate, dynamic, and convenient way.

At top, a structural schematic of light coming into one fluorescent compound (which will be the donor, on left), with the two-ring structure. This is named L-Anap, and its absorbance spectrum is shown at bottom, receiving shorter (more energetic) wavelengths. Its emission spectrum is closely related, and peaks at 494 nm. Then FRET takes place, over to the acceptor compound on a different area of the protein on the right (either HH, for the two histidines, which coordinate a copper ion, or a cysteine-tethered TETAC, which also coordinates a copper ion in a small ring. The acceptor spectrum is also shown below, with significantly lower energy absorbance- just the right gap to be an acceptor for resonant electronic excitation from the donor.

If two fluorescent molecules are close to each other, and the radiation absorbance spectrum of the acceptor is at a slightly lower energy than the emission spectrum of the donor, then instead of fluorescing away a photon, there is a good chance that the donor will transfer its electronic excitation directly, via resonance through the mediating electric field structures, to the acceptor molecule, which may (or may not) then emit the energy in its own emission wavelenght, somewhat longer than that of the donor. Obviously, this is very distance-dependant, and the distance at which the chances of resonant transfer are 50% is termed R0. This distance is surprisingly far for many pairs of robustly fluorescing molecules- on the order of 60 or 70 Ångstroms (Å), or tenths of a nanometer.

This is obviously great for some things. Photosynthesis, for instance, relies on the rapid and quantitative transfer of this kind of resonance energy from the various light-gathering antenna complexes to the photocenter where chemical reactions can take place. A recent direction in this structure field, (paper 1, 2), however, is to recognize that for detailed structure work, these distances are too far, and a finer ruler is needed. Additionally, two other issues have come up. Typical fluorophores are very direction-dependent, with large organic rings that gain excitation and generate emission preferentially in certain directions. Secondly, they are typically mounted on long tethers. Both of these properties reduce the ability to infer distances in any confident way from FRET measurements.

So the recent improvements amount to using worse fluorophores, specifically metals like copper, cobalt, and nickel, which reduce the working distance of FRET to 10 - 20 Å, and have a much more isotropic excitation profile, which is to say that they are direction-neutral, due to their simple, single-atom nature. This allows finer working distances and more accurate inferences about distance, when the intended span can be engineered to under 20 Å. For comparison, a lipid bilayer membrane is 100 Å across, and a protein alpha helix is 5.4 Å per turn, making 20 Å about 3.7 turns. One drawback to the new method is that the metal acceptors do not in turn fluoresce at a longer wavelength- they only quench the donor's fluorescence. That makes the structure professionals happy, reducing stray signals, but at the cost of some extra certainty of what is going on, not to mention some of the magic of this method.

Maltose binding protein, with maltose in pink at the center. The binding of maltose causes a well-studied structural shift from open to closed, with the top of this structure closing like a clam. Locations of studied donor and acceptor sites that were engineered into the protein are marked (black) by their amino acid position on the protein sequence.

The model system most researchers use to guage new methods is maltose binding protein, (MBP), which closes like a clam when binding the sugar maltose (pink). The amino acid positions noted 237 and 295 are about 13 Å apart in the bound state, as shown, and separate to 21 Å in the naked state. There are additional innovations in how fluorescence probes are engineered into the protein and managed, that won't be discussed. The new paper shows that, when everything is placed properly, fluorescence from the donor is cut in half as maltose is added, and if they plug all this into appropriate mathematical models of the system, they get an implied distance estimate within a couple of Ångstroms of the true values- a significant advance in accuracy for this kind of method.

Example of a result. The Y axis is fluorescence of the donor, normalized to a control case where there is no acceptor compound at all (it is tethered to a cysteine residue [cys] on the protein). When copper is added to the solution, filling the acceptor TETAC ring with its fluorescence acceptor, the signal goes to 0.6 for protein without maltose, but to 0.2 when maltose is added as well. This difference is the FRET signal: fluorescence that is lost to the acceptor by direct excitation transfer. Then DTT is added, which breaks (reduces) the cysteine bond which holds TETAC to the protein, and the donor fluorescence goes back to its original value. The X-axis is time.

While the major (comprehensive) structural methods are gaining convenience and accuracy, these extra methods of structure estimation can be lifesavers in special situations where some dynamic aspect of a system is in question. For example, another paper from this group looked at a cyclic nucleotide-gated cation channel that functions in smell, vision, and the central nervous system, being directly activated by key second messengers like cAMP. They positioned one probe on the membrane surface and another in the protein domain nearby which is a key hinge conducting the cAMP/cGMP binding signal to the channel. They found a close correlation between activity of the channels and how close their probe, and thus the hinge region, is to the membrane, thus giving a little more structural insight into this protein family.

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