DNA PACKING:

Characterizing Intermolecular

Contacts of DNA

Bryson W. Finklea

St. John's College

DIMACS REU

Outline:

● Background

● Symmetry

● My Project

Outline:

● Background

● Symmetry

● My Project

Different representations of the same DNA(18 base pairs color-coded according to base identity)

Background

(http://siggy.chem.ucla.edu/~tim/chemistry/DNA.jpg)

In nature each human cell has 3 billion DNA base pairs

(about 2 meters long)

Background

(Human Genome Project Information of the DOE)

Cube built from DNAin nanotechnology lab

In nature each human cell has 3 billion DNA base pairs

(about 2 meters long)

Background

(Human Genome Project Information of the DOE) (Dr. Nadrian Seeman, Department of Chemistry, New York University)

Background

Molecular Crystals(often microscopic)*

(www.scripps.edu/newsandviews/e_20010129/chang-2.html)

*These are similar examples from proteins instead of DNA.

DNA X-Ray Diffraction Pattern*

Background

Molecular Crystals(often microscopic)*

(www.scripps.edu/newsandviews/e_20010129/chang-2.html) (http://userpage.chemie.fu-berlin.de/~psf/ifv_psfx.htm)

*These are similar examples from proteins instead of DNA.

Outline:

● Background

● Symmetry

● My Project

Crystal – a solid with regularly repeating arrangement of atoms

Unit Cell – •the basic unit of symmetry•an arrangement of atoms that repeats in every direction

3D Symmetry

(Unknown)

Example of 2D symmetry in a

wallpaper pattern

(http://www.clarku.edu/~djoyce/wallpaper/)

Example of 2D symmetry in a

wallpaper pattern

To show symmetry:

●pick a point

Example of 2D symmetry in a

wallpaper pattern

To show symmetry:

●pick a point

●find all equivalent points

Example of 2D symmetry in a

wallpaper pattern

To show symmetry:

●pick a point

●find all equivalent points

●the points form a 2D lattice

Example of 2D symmetry in a

wallpaper pattern

● Connecting 4 lattice points to form a parallelogram gives a possible unit cell

● Unit cell – the basic unit that repeats in every direction

● Different unit cells can be chosen

●But some unit cells are preferable for higher symmetry

Symmetry is defined by symmetry elements

Four possible symmetry elements in 2D:•Rotation points (by 60°, 90°, 120°, or 180°)•Reflection axes•Glide reflection axes (reflection and translation)•Inversion points•(Translation)

Symmetry operations –the actual changes carried outin relation to a symmetry element

3D Symmetry

Symmetry elements of this wallpaper group

Reflection Axis

Glide Reflection Axis

90° Rotation Point

180° Rotation Point

Example of 2D symmetry in a

wallpaper pattern

(http://www.clarku.edu/~djoyce/wallpaper/)

Symmetry elements of this wallpaper group

Reflection Axis

Glide Reflection Axis

90° Rotation Point

180° Rotation Point

Example of 2D symmetry in a

wallpaper pattern

●Unit cell

Symmetry elements of this wallpaper group

Reflection Axis

Glide Reflection Axis

90° Rotation Point

180° Rotation Point

●Asymmetric Unit –the simplest unit on which the symmetry operations can act to produce the entire symmetrical structure*

Example of 2D symmetry in a

wallpaper pattern

●Unit cell*

* Although the spirit of what I show is correct, it appears from the following website that my choice of conventional unit cell and choice of asymmetric unit may be unconventional or even wrong. See the last example in the n=4 section of the following website: http://jwilson.coe.uga.edu/EMT668/EMAT6680.F99/McCallum/WALLPA~1/SEVENT~1.HTM

Generalized 3D unit cell—a parallelepiped

3D Symmetry

(Unknown)

3D Symmetry

Crystal – a solid with regularly repeating arrangement of atoms

Unit Cell – •the basic unit of symmetry•an arrangement of atoms that repeats in every direction

(Different colors are different copies of the same asymmetric unit)

Six symmetry elements in 3D:•Rotation axes (by 60°, 90°, 120°, or 180°)•Reflection planes•Glide reflection planes (reflection and translation)•Inversion points•(Translation)

•Screw Axes (translation and rotation)•Rotary inversion axes (rotation and inversion)

Sets of symmetry operations form algebraic groups calledspace groups.

•230 space groups

3D Symmetry

Asymmetric unit Unit cell 27 adjacent unit cells

3D Symmetry

Outline:

● Background

● Symmetry

● My Project

Characterizing Intermolecular Contacts of DNA

Data from Nucleic Acid Database (NDB):●orthogonal coordinates of atoms in an asymmetric unit●equivalent positions in equation form (info from symmetry elements)●unit cell dimensions and angles

To revise a computer program to:●reconstruct coordinates of the atoms in a unit cell●…then in a 3x3x3 block of unit cells●make measurements of interesting properties of contacts between molecules of DNA (Examples: distances, angles between axes,…)

My Project

Asymmetric unit Unit cell 27 adjacent unit cells

3D Symmetry

Final Presentation:

●Details on computer program structure and images created using its output

●Specification of important DNA molecular contacts and report of findings

●Perhaps more details on mathematics of space groups, including notation used

References:

DNA for the layman:

Understanding DNA, Calladine and Drew, 3rd edition.

Symmetry in crystals, including space group theory:

Crystal Structure Analysis for Chemist and Biologists, Glusker, et al, Ch. 1, 2, and 4.

X-Ray Analysis and the Structure of Organic Molecules,Dunitz, Ch. 2.

Molecular structure databases (on web):

Nucleic Acid Database (NDB), Protein Data Bank (PDB),Cambridge Structural Database (CSB)

Acknowledgments

DIMACS REUNSF Support

Advisor:

Wilma Olson, Department of Chemistry,

Rutgers University

Additional Advisors:

A.R. Srinivasan, Department of Chemistry

Rutgers University

Andrew Colasanti, Department of Molecular BiologyRutgers University(background: http://www.karolinskaeducation.ki.se/services/courses/selection_courses_se.html)