Computational Modeling and Visualization of Biomolecules

Preston J. MacDougallMiddle Tennessee State University

With contributions by:Dr. Christopher E. Henze, NASA Ames Research Center

Profs. Tibor Koritsanszky and Anatoliy Volkov, MTSUDrs. Michal Chodkiewicz, Hui Yang, and Yevgeni Moskovitz, MTSU

Acknowledgments:

Funding of personnel, a dedicated cluster, andthe 4x4 3D-Hyperwall at MTSU, provided bythe Office of Science in the U.S. Department of Energy; grant #DE-SC00005094

The new Ph.D. in Computational Science has provided a home for the MTSU 3D-Hyperwall

Inter-disciplinary Research in the Department of Chemistry at MTSU

Before

After

CGI fly-through of New Science Building: http://mtsunews.com/sciencebuilding/#!

MTSU PhD program in Computational Science(www.mtsu.edu/cpsphd/)

MTSU PhD program in Molecular Biosciences(www.mtsu.edu/mbsphd/)

MTSU PhD program in Math & Science Education(www.mtsu.edu/mbsphd/)

Overview• this will be a talk about theoretical and computational chemistry without

numbers (actually, there are too many numbers, so we must visualize the data with tools from computer graphics)

• we will see different methods of visualizing the type of data generated; the good, the bad, and the beautiful!

• we will focus on electron density analysis, which offers beautiful ideas, and several visualization challenges

• EVolVis - a new molecular visualization tool, developed by an inter-disciplinary team at NASA Ames, is conceptually accessible to freshman chemistry students and helps researchers discover reactive sites in biomolecules and drugs

• a brief outline is given for a new method of rapidly generating model electron densities of very large molecules from a library of oriented pseudoatoms (Koritsanszky, Volkov and Chodkiewicz, 2011)

• we demonstrate drug-design utilization of a Hyperwall with modeling of active and inactive drug candidates

• we present initial steps toward the long-term goal of designing drugs that selectively bind to a novel target in drug-resistant bacteria

What’s the difference between “computational chemistry” and “theoretical chemistry”?

Molecules are nothing, if not nanoscale works of art.

“Molecular art” exists at many scales.

“Molecular art” also exists in our minds.Computer graphics can make our models “real”.

Beginning with wooden balls and sticks, chemists have used disparate artificial models to help visualize molecules.

New visualization techniques made possible with advances in technology are real eye-openers!

Science should lead technology, however.

One should first ask “How will molecules be modeled?” and “What properties of that model will

be most instructive when visualized?”

Y(xi)

Ihkl > r(r) <reduction: integration over all but 3 spatial dimensionsand loss of phase information

synthesis: by Fourier seriesfrom zero dimensional X-rayreflections

Computational chemists, of course,often take short-cuts to the density

orbital models S|fi|2

multipole models SK3Rl(K,r)

* *

*These short-cuts are like scaffolds. They are only a means to an end.

Y(xi)

Ihkl > r(r) <

Once you have an accurate electrondensity, either from theory or experiment,you will find that it is rather pedestrian in appearance. What then?

V

?

Y(xi)

Ihkl > r(r) <

There are three fundamentally different options*, but mixing is allowed:1. subtracting reference densities2. partitioning the density3. differentiating the total density(let’s consider option no. 3)

V

r(r)v

2r(r)

* For a broad overview, consult “A Matter of Density”, ed. N. Sukumar (Wiley, 2013)

Even simple molecules like CO can have controversial (point) “charge distributions”. Which end is negative? By considering the total

electron density, concepts such as atomic charge, bond paths and molecular structure, can be defined with reference to r(r)

(R. F. W. Bader, “Atoms in Molecules – A Quantum Theory” (Oxford Univ. Press, 1990))

In one dimension, the 2nd derivative acts like a tactile sensor:depressions and necks are + , humps and shoulders are -

The Laplacian of the total electron density has anenergetic and a “relative concentration” interpretation

Energetically, it appears in the local virial theorem:

Where,

(1/4)2r(r) = 2G(r) + V(r)

2r(r) = ¶2r(r)/¶x2 + ¶2r(r)/¶y2 + ¶2r(r)/¶z2

In Maxwell’s interpretation of theLaplacian of any scalar function,negative regions are “local concentrations”and positive regions are “local depletions.”

r(r) - rave. = -(1/10)r22r(r) + O4

where rave.is the mean value of rwithin a small sphere of radius r centered at r.

R. F. W. Bader (1931 - 2012)Chemical Eye on a Theoretical Truck

James Clerk Maxwell (1831 – 1879)

In three dimensions, the Laplacian is also like a tactile sensor:holes, or local depletions, are +, lumps, or local concentrations are -

The pattern of local concentrations and depletions in a water molecule reveals that the “charge cloud” does indeed have a “shell structure” and that the valence shell charge concentration (VSCC) has a sub-shell structure that can be mapped onto the Lewis structure of the

molecule

B3LYP M062X MP2 MP4 CCSDr θ r θ r θ r θ r θ

6-311++G(d,p) 34.22 107.40 34.19 107.25 34.30 108.09 34.27 107.71 34.25 107.536-311++G(2d,p) 34.26 106.42 34.23 106.50 34.34 107.27 34.30 106.92 34.29 106.78

6-311++G(3df,3pd) 34.25 108.54 34.20 108.79 34.30 109.47 34.27 109.03 34.25 108.88aug-cc-pVTZ 33.67 108.67 33.67 108.75 33.83 109.84 33.78 109.29 33.76 109.14aug-cc-pVQZ 33.38 107.86 33.37 108.79 33.46 109.03 - - 33.42 108.42aug-cc-pV5Z 33.40 108.14 33.31 107.63 33.43 109.23 - - - -

Standard deviation 0.43 0.84 0.43 0.97 0.43 0.96 0.25 1.12 0.39 0.98

B3LYP M062X MP2 MP4 CCSDr θ r θ r θ r θ r θ

6-311++G(d,p) 38.06 178.89 38.09 178.37 37.92 179.20 37.95 178.28 37.96 178.096-311++G(2d,p) 37.82 178.59 37.82 178.58 37.68 179.22 37.72 179.67 37.72 180.00

6-311++G(3df,3pd) 35.32 174.58 34.83 180.00 35.39 174.65 35.42 174.78 35.43 174.84aug-cc-pVTZ 36.07 178.40 36.28 178.76 36.11 177.42 36.16 176.75 36.17 176.76aug-cc-pVQZ 42.98 177.54 43.91 172.61 42.89 179.12 - - 42.97 179.66aug-cc-pV5Z 42.24 180.00 46.37 180.00 42.03 179.59 - - - -

Standard deviation 3.17 1.85 4.55 2.76 3.10 1.90 1.22 2.10 2.95 2.13

(3,+3) CP in the vicinity of Oxygen

(3,-3) CP in the vicinity of Hydrogen

Method- and basis-set-dependence of topology properties of CP in 2r

For highly symmetrical molecules, such as Cr(CO)6, Fe(CO)5, and Ni(CO)4, 2D contour plots may suffice

(MacDougall and Hall, Trans. Am. Cryst. Assoc., 26, 105 (1990))

By sacrificing all but one of the contour values in the 2D Laplacian plots, we can go 3D. “Good” at best.

Algorithms that “search and follow” (gradient paths)can visualize topological features in the 3D Laplacian and

draw “atomic graphs”

Algorithms “boosted” by NASA rocket scientists can visualize the entire VSCC (here, of oxygen in water).

It is a “separation surface” in fluid dynamics terminology(MacDougall and Henze, Theor. Chem. Acc. (2001))

EVolVis – an interactive volume visualization tool that lets one “scan” and “focus” on multiple topological features in the

Laplacian of the total electron density of molecules (either measured or computed)

• “hot” colors indicate regions of local charge concentration (“lumps” in the density) where the Laplacian is negative

• “cool” colors indicate regions of local charge depletion (“holes” in the density) where the Laplacian is positive

• color opacity is user-defined via a “transfer function editor” that tunes the amplitude, offset, variance and decay rate of overlaid Gaussians (inset)

• same visual texture applies to all molecules, using expt’l or computational densities

• More details: MacDougall and Henze, Theor. Chem. Acc., 105, 345 (2001).

This visualization tool conveys key concepts of bonding and reactivity in a manner that is in perfect concert with an intriguing statement by a pioneer in theoretical chemistry

“It is always of interest to find that some of our most modern scientific ideas have been vaguely anticipated by scientists of earlier centuries. One of the ideas of Lemery, a contemporary of Robert Boyle, is amusingly discussed in a well known history of chemistry, as follows: ‘Yet one of his theoretical conceptions was very odd, and shows how far astray a capable man may wonder, when he deserts observed facts for philosophical speculations. He thought that chemical combination between two substances, such as an acid and a base, might be accounted for by supposing that the particles of one were sharp, and those of the other porous, and that chemical combination was effected by the fitting of the points into the holes!’”

G. N. Lewis (1934)

Let’s have a “fleshed-out” look at medicinal molecules(penamecillin, A. Wagner et al, Chem. Eur. J., 10, 2977 (2004))

Ionic, covalent and polar-covalent molecules

Heavy metal molecules(cisplatin’s Pt+2 ion has a sharply defined bite angle)

Molecules that are pink and blue(this is the same molecule that was wooden before)

Splitting molecules(conventional “movies” show atoms as unchanging during

reactions, implying they are rigid, like Lego blocks)

Dancing molecules – vitamin B12 and its Co+3 ion(M. Kemp, Nature, p.588, 9 August, 2001)

Pseudo-molecules(These can be rapidly constructed from a pseudoatomic

library of highly transferable “atoms”. Here, the total charge density of the 11-mer polypeptide cyclosporin A is modeled.)

Stockholder Pseudoatom (PSA) Library Building(Koritsanszky, Volkov and Chodkiewicz, “New Directions in Pseudoatom-Based X-ray Charge Density Analysis” in “Structure and Bonding” (2011))

CSD Structure Bank (~1300)

Organic CompoundsSingle-crystal structuresR < 5%s< 0.005 ÅNo disorder / errorIdealized X-H bonds

EntryBuilder

Wave functionsPseudoatomscattering factors

Equivalencedescriptors

Atom-type Grouping

The PSA library building is a five-step procedure:

1.Selection of reference molecules containing the atoms to be included in the library.

2. Identification of and search for equivalent atoms. An automatic protocol scans the reference structures and collects equivalent atoms using different structure

descriptors and similarity measures. These descriptors include the atomic number, the local connectivity graph, bond-orders and aromaticity indices. Based on the statistical agreement of similarity measures, a decision is made for each atom, whether it belongs to an existing group or it is a new type.

3.Ab initio electronic structure calculations on reference molecules containing atoms picked up by the above protocol. The molecular densities for the current databank were generated at the B3LYP/cc-aug-pVTZ level.

4.Calculation of the RDFs. For each SPA’s of each type, the RDFs are calculated from the molecular wave functions on a fine radial grid.

5.Building the ED of the target molecule of known structure. Input atomic positions and specific criteria for matching similarity indices are used by the builder to

construct the average density and the RDFs of the first-order correction.

Atom H B C N O F Si P S ClNumber 14419 29 8223 2523 2339 114 37 78 421 196

Type 266 3 805 304 157 21 3 13 71 24

Atom types in the library (B3LYP/cc-aug-pVTZ)

Equivalence descriptors:

Atomic numberLocal connectivityBond ordersAromaticity

Parallel molecules on the NASA Ames Hyperwall(Sandstrom, Henze and Levit, Proc. of Coordinated & Multiple Views in

Exploratory Visualization (I.E.E.E., 2003))

NASA Ames Hyperwall & the MTSU 3D-Hyperwallin “Drug Design Mode”

Pharmacophores are typically modeled by featureless “features”, color-coded for H-bond donors, H-bond

acceptors, ionizing groups, hydrophobic groups etc…

Fleshed-out pharmacophores can have subtle sub-atomic features that are critical to their

inter-molecular interactions

(MacDougall and Henze, in “The Quantum Theory of Atoms in Molecules:From Solid State to DNA and Drug Design” Matta & Boyd (Wiley-VCH, 2007))

Next steps: Examine the docking of drug candidates to the ATP-binding site of E. coli DNA gyrase – a promising target in multi-drug resistant

bacteria.

Summary:

• A new molecular visualization tool has been presented. It is simple, model-independent, amenable to experiment, and makes useful predictions that are relevant to the selective binding of drug candidates to drug targets and characterizing reactive sites on any type of surface.

• Modeling tools that are based on the electron density allow input from either experiment (single crystal X-ray diffraction), or from densities that are computed to the desired accuracy from either a pseudo-atomic library and/or with ab initio methods.

• The use of a Hyperwall allows users to easily see subtle differences in reactive sites that may otherwise be lost in a sea of numerical data.

• Computer graphics technology has advanced to the point where it not only helps tell the story, it helps make it.

From WMOT News (www.wmot.org)

A Chemical Eye on AestheticsMURFREESBORO, TN (2004-11-12) MTSU

Chemistry Professor Dr. Preston MacDougall ponders the relationship between Art and Chemistry.

Other commentaries also available online at:

www.sitnews.us/MacDougall/list.html

Thanks for listening!