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26 September 2003

Moving matter: Fun things to do with your computer

by Marty Carlson

What would you want to look at if you could "see" a molecule, and watch it move in its native environment, as it interacts with matter around it? Due to the similarity of the atomic scale to the wavelengths we would try to use for this, it’s actually a little difficult with current technology. How about a close second? With the advent of cheap, fast computers, we can now do things that forward-looking chemists may have dreamed about only fifty years ago. We can virtually visualize atoms and molecules with some sense of scale, and even visualize the interaction between matter, between atoms, and molecules! Today forward-looking chemists are using, and developing these tools.

Forward-looking chemists
(Click image to enlarge)

I am looking into this because of my own interest in the interactions that lead to degradation of lipids. My day job is as a chemist investigating the response of vegetable oils (lipids) to formulation (mixing with things). This formulation is meant to help the vegetable oils defend against oxidation, hydrolysis, freezing, boiling and wearing metal surfaces. For more on this you may like to refer back to "Tribology: What is it, and what does it do for us?" from 08 August 2003. Many formulation chemists take the approach of choosing what others have found to work, but I want to know how, and why. So I took this path recently, one that I am clearly an amateur at, to try and gain some insight.

Having done this I thought I’d share what I found with my fellow amateur scientists here. I’ll link you to some of the resources available to amateur scientists for molecular visualization and computational chemistry that I’ve found, in the link section at the end of this paper and I’ll show you what I was able to put together over a few weekends for myself. It sounds heady, and it is. These are powerful tools, things that you can do at home, right now, for the cost of this computer and this internet hookup.

Some basics of atomic interaction

First some basic information on the nature of interactions at this scale, some things you may have learned in chemistry class or in reading on your own. When two atoms approach each other they experience forces. These forces are due to the interaction of these two atoms, and, according to current thinking, would even be measurable at infinite distances if they weren’t swamped out by nearer interactions.

Computer-generated molecules coming
and going in a computer-generated
cell membrane (blue - largely lipids).

Repulsion. At very close distances two atoms will experience repulsive forces from the electrons that surround them pushing away from the like charges of the electrons that surround the other. If they get close enough, overcoming the repulsive force of the electrons, they will even experience the strong nuclear force, a very powerful repulsive force. Just for the record, that’s nu-cle-er, not nu-cu-lar. If this force is overcome you will actually have nuclear fusion, with the release of energy we have heard so much about in the hydrogen bomb, or the stars.

Attraction. When they aren’t being repulsed, atoms are busy being attracted. The attractive forces have to do with the electrons around the atoms. There may be a shortage of them in one atom so that it is charged, or ionic, or it may be that the atom would just like another electron to fill what is called a valence shell, while another is willing to share an extra. But there is no counterpart to the strong nuclear force in attraction and so the force profile between the atoms, with distance between them, ends up looking like this.

Energy Well Graph
(Click to enlarge)

The reaction coordinate. I left some values on the axis just for your curiosity, but the important point is that the y-axis is energy, and at the low point the energy of this system is "minimized". The x-axis is the distance that separates the two atoms, or the reaction coordinate If the two atoms represented here get too close together they are up against a steep energy wall as you can see on the left of the graph, while at the right there is a much more shallow wall

In nature, as you probably know, energy is minimized. Water flows downhill, electrons flow in a circuit toward a positive charge, etc. These two atoms will have a tendency to be at the distance represented by the low point of this "energy well".

From this deceptively simple graph comes much real information. For example, where peaks will appear on a spectrograph, how much energy it will take to break a bond or how much is released when one is formed, and more, but as they say, these issues are outside the scope of this article. Look again at the graph, and understand it. This is key.

Visualization programs

A computer program, given a set of z, y, and x coordinates, can be made to display them for us, but you knew this. If a number is added to each of the x-coordinate values then the item, let’s say it’s a molecule, will appear to move along the x-axis. The molecule will be rotated in three dimensions if it’s x, y, and z values are modified with a bit of trigonometry. For those of you who will want to try this for yourselves, here are the actual functions. Go through and apply these to the x, y, z coordinates of your item and it will rotate!

Rotation about the X-axis

NewY = CurrentZ * Sin(XAngle) + CurrentY * Cos(XAngle)

NewZ = CurrentZ * Cos(XAngle) - CurrentY * Sin(XAngle)

NewX = LastX

Rotation about the Y-axis

NewX = CurrentX * Cos(YAngle) - CurrentZ * Sin(YAngle)

NewZ = CurrentX * Sin(YAngle) + CurrentZ * Cos(YAngle)

NewY = CurrentY

Rotation about the Z-axis

NewX = CurrentX * Cos(ZAngle) + CurrentY * Sin(ZAngle)

NewY = -CurrentX * Sin(ZAngle) + CurrentY * Cos(ZAngle)

NewZ = CurrentZ

There are many programs (free!) on the web that will perform all of these functions for you. My personal favorite is Rasmol because it is small, fast and largely flawless, but I will include options at the end of this paper and you’ll want to choose which is best for you... or play with all of them. I’ll even throw in my own source code as a starting point/demonstration for those of you VB programmers who’d like to build your own at home.

Data!

What will you look at? There is a great deal of xyz data available for molecules from small ones like water with three atoms, to ones like peroxidase C1A, an enzyme with over 17,000 atoms! As you may guess, these are made in ways ranging from manually, with the use of a text editor and/or spreadsheet to the importation of computerized x-ray crystallography data.

More and more, there is calculated data that is output from energy minimization programs. These programs take, as their starting points, data about how the shape (or conformation) that a molecule might take, and calculate other possible conformations. More on this next.

What energy minimization programs do

There are excellent energy minimization programs available on the internet. The bottom line is this: These programs calculate where the bottom of that energy well is in the graph you scrutinized a moment ago.

This may seem easy for a computer to do, given the right mathematical relationships, for just one pair of atoms interacting. First, let me disabuse you of this thought. The Time-Dependant Schrödinger equation, which governs this interaction, is included below, again for you do-it-yourselfers. The function Psi will be different for every type of interaction, the Hamiltonian operator on the left is simple enough but on the right there’s also a partial derivative where its time-dependence is carried out. To do this calculation, for any atomic interaction much above a couple of beryllium atoms, will probably take time on your local super computer! (For you masochists I direct you to the source of the graph above and this formula; Quantum Chemistry and Molecular Spectroscopy, by Clifford E. Dykstra)

The Time-Dependant Schrödinger Equation

Fortunately there have been some very good approximations developed. For example, in the 1950s a physical chemist named Sir John Edward Lennard-Jones derived a set of interaction parameters from his understanding of Van der Waals interactions (electrons - see the middle and right side of the Energy Well graph above).

Now we have an approximation for the function for the interaction of a single set of atoms. But in a system of atoms each of the atoms will effect the others. Here the computer’s iterative power is used. It is able to go through, to iterate these calculations, for the entire set of interactions. As you can see in the two pictures below, where we have hundreds of atoms, as the water molecules (small red with white attachments) are drawn toward the oxygen atoms on the trioleate molecule’s backbone, the bend in the left leg of the trioleate increases.

For the simulation here I used a Monte Carlo algorithm provided with the "Tinker" set of algorithms, and a program I wrote in Visual Basic. The system of atoms and bonds was defined using a set of parameters called Lennard-Jones parameters. These are the approximations I mentioned above. These pictures are actually just two consecutive frames of a set of a thousand and the end result is that you see a movie representing this overall motion.

The steps are these:

1. Find or make your atoms of interest.

• The file is in ascii, with x, y, z coordinates, bonding, atom names (carbon, hydrogen...) and references to approximation parameters.

2. If you want more than one molecule then combine the sets of individual atom data from step one into a larger file for the system you wish to study.

• For example, I combined one water molecule file into one of 27 water molecules. Then I combined two of these files with one of a trioleate molecule which had I built in an Excel spreadsheet. Tricky, but doable.

3. Run the algorithm on the file.

• This, like the previous two steps, depends on your choice of program for the exact syntax.

4. View and interpret the results.

• More on this next.

Play the movie (.mov file) of 54 water molecules
attacking a trioleate molecule’s backbone

So what... ?

So what did I get from this particular simulation and four weekend’s work? I already knew a couple of things about my trioleate molecule, and I was able to extend what I knew in these ways:

1. I knew that it could be hydrolyzed at the glycerol backbone. Again, the mechanism of this reaction is beyond the scope of this article, but I have put an H in the image below (my molecular data displayed in Rasmol, which has a nice rendering engine) showing that the water molecules are indeed attacking in the way expected. This wasn’t a surprise, but it was fun to see it in action. What I did find interesting was the way the single water molecule I am pointing to is straddling two oxygens on the trioleate molecule, and will eventually split into an H+ and an -OH to break one of the two related bonds... hydrolysis.

2. I also know that the point about midway down the oleate leg has a double bond. This point is vulnerable to oxidation. See how the water molecules are actually bending the leg (a cis conformation) so that the double bond is more exposed to oxidizing species that may exist in the system? This suggests that when there is water in this system (there almost always is) and you are worried about oxidation (and you almost always are since you don’t want your foods, or your biodegradable hydraulic fluid, to spoil), you will need to address this.

Just show me the links please

Well this is what I am doing with it now. You’ll probably dream up some neat things yourself. Here are just a few resource links that I’ve come across recently, but there are more, many more. Have fun!

Visualization:

Rasmol - http://www.bernstein-plus-sons.com/software/rasmol/

Chime Plug-in - http://www.mdlchime.com/

Protein Explorer - http://www.umass.edu/microbio/rasmol/

Forcefield Explorer - http://dasher.wustl.edu/ffe/

Energy minimization:

Tinker - http://dasher.wustl.edu/tinker/

Pymol - http://pymol.sourceforge.net/

Molecular Data:

Protein Data Bank - http://www.rcsb.org/pdb/

PDB Sum - http://www.biochem.ucl.ac.uk/bsm/pdbsum/

NIH Molecules R Us - http://molbio.info.nih.gov/cgi-bin/pdb

My program in VisualBasic 4.0:

- - You will want to read the file "readme.txt" as soon as you get it! - -

Click here to download my program in a compressed file (1.7 MBytes)

VB Source - mrc@frontiernet.net

C++ Source - mrc@frontiernet.net