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Computational Modeling and Visualization of Biomolecules. Preston J. MacDougall Middle Tennessee State University With contributions by: Dr. Christopher E. Henze, NASA Ames Research Center Profs. Tibor Koritsanszky and Anatoliy Volkov, MTSU

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computational modeling and visualization of biomolecules

Computational Modeling and Visualization of Biomolecules

Preston J. MacDougall

Middle Tennessee State University

With contributions by:

Dr. Christopher E. Henze, NASA Ames Research Center

Profs. Tibor Koritsanszky and Anatoliy Volkov, MTSU

Drs. Michal Chodkiewicz, Hui Yang, and Yevgeni Moskovitz, MTSU

acknowledgments
Acknowledgments:

Funding of personnel, a dedicated cluster, and

the 4x4 3D-Hyperwall at MTSU, provided by

the 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
Inter-disciplinary Research in the Department of Chemistry at MTSU

After

Before

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 Computational Science(www.mtsu.edu/cpsphd/)
mtsu phd program in molecular biosciences www mtsu edu mbsphd
MTSU PhD program in Molecular Biosciences(www.mtsu.edu/mbsphd/)
mtsu phd program in math science education www mtsu edu mbsphd
MTSU PhD program in Math & Science Education(www.mtsu.edu/mbsphd/)
overview
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
What’s the difference between “computational chemistry” and “theoretical chemistry”?
molecular art also exists in our minds computer graphics can make our models real
“Molecular art” also exists in our minds.Computer graphics can make our models “real”.
slide12
Beginning with wooden balls and sticks, chemists have used disparate artificialmodels to help visualize molecules.
slide14

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?”

slide15

Computational chemists, of course,

often take short-cuts to the density

*

*

multipole models

SK3Rl(K,r)

orbital models

S|fi|2

Ihkl

Y(xi)

> r(r) <

reduction: integration over

all but 3 spatial dimensions

and loss of phase information

synthesis: by Fourier series

from zero dimensional X-ray

reflections

*These short-cuts are like scaffolds.

They are only a means to an end.

slide16

Once you have an accurate electron

density, either from theory or experiment,

you will find that it is rather pedestrian in

appearance. What then?

Ihkl

Y(xi)

> r(r) <

V

?

slide17

There are three fundamentally different options*, but mixing is allowed:

subtracting reference densities

partitioning the density

differentiating the total density

(let’s consider option no. 3)

Ihkl

Y(xi)

> r(r) <

v

(r)

V

2(r)

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

slide18

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

slide19

In one dimension, the 2nd derivative acts like a tactile sensor:

depressions and necks are + , humps and shoulders are -

slide20
The Laplacian of the total electron density has anenergetic and a “relative concentration” interpretation

Energetically, it appears in the local

virial theorem:

(1/4)2(r) = 2G(r) + V(r)

Where,

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

R. F. W. Bader (1931 - 2012)

Chemical Eye on a Theoretical Truck

In Maxwell’s interpretation of the

Laplacian of any scalar function,

negative regions are “local concentrations”

and positive regions are “local depletions.”

(r) - ave. = -(1/10)r22(r) + O4

where ave.is the mean value of 

within a small sphere of radius r

centered at r.

James Clerk Maxwell (1831 – 1879)

slide21
In three dimensions, the Laplacian is also like a tactile sensor:holes, or local depletions, are +, lumps, or local concentrations are -
slide22

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

slide23

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

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

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

slide24

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))

slide25
By sacrificing all but one of the contour values in the 2D Laplacian plots, we can go 3D. “Good” at best.
slide26
Algorithms that “search and follow” (gradient paths)can visualize topological features in the 3D Laplacian and draw “atomic graphs”
slide27

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))

slide28

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).
slide29

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)

slide30
Let’s have a “fleshed-out” look at medicinal molecules(penamecillin, A. Wagner et al, Chem. Eur. J., 10, 2977 (2004))
slide34
Splitting molecules(conventional “movies” show atoms as unchanging during reactions, implying they are rigid, like Lego blocks)
slide36

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.)

slide37

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 Compounds
  • Single-crystal structures
  • R < 5%
  • < 0.005 Å
  • No disorder / error
  • Idealized X-H bonds

Entry

Builder

Equivalence

descriptors

Pseudoatom

scattering factors

Wave functions

Atom-type Grouping

slide38

The PSA library building is a five-step procedure:

  • Selection of reference molecules containing the atoms to be included in the library.
  • 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.
  • 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.
  • 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.
  • 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.
slide39

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

Equivalence descriptors:

Atomic number

Local connectivity

Bond orders

Aromaticity

slide40

Parallel molecules on the NASA Ames Hyperwall(Sandstrom, Henze and Levit, Proc. of Coordinated & Multiple Viewsin Exploratory Visualization (I.E.E.E., 2003))

slide42

Pharmacophores are typically modeled by featureless “features”, color-coded for H-bond donors, H-bond acceptors, ionizing groups, hydrophobic groups etc…

slide43
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))

slide44

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
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.
slide46
From WMOT News (www.wmot.org)

A Chemical Eye on Aesthetics

MURFREESBORO, 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!