Saturday, July 21, 2018

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.