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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. Background. Different representations of the same DNA

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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


Background

Different representations of the same DNA

(18 base pairs color-coded according to base identity)

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


Background

In nature each human cell has

3 billion DNA base pairs

(about 2 meters long)

(Human Genome Project Information of the DOE)


Background

In nature each human cell has

3 billion DNA base pairs

(about 2 meters long)

Cube built from DNA

in nanotechnology lab

(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.


Background

Molecular Crystals

(often microscopic)*

DNA X-Ray Diffraction Pattern*

(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


3D Symmetry

  • Crystal –

  • a solid with regularly repeating arrangement of atomsUnit Cell –

  • the basic unit of symmetry

  • an arrangement of atoms

  • that repeats in every direction

(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


3D Symmetry

  • Symmetry is defined bysymmetry 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 out

  • in relation to a symmetry element


Example of 2D symmetry in a

wallpaper pattern

Reflection Axis

Glide Reflection Axis

90° Rotation Point

180° Rotation Point

Symmetry elements of this wallpaper group

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


Example of 2D symmetry in a

wallpaper pattern

  • Unit cell

Reflection Axis

Glide Reflection Axis

90° Rotation Point

180° Rotation Point

Symmetry elements of this wallpaper group


Example of 2D symmetry in a

wallpaper pattern

  • Unit cell*

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

Reflection Axis

Glide Reflection Axis

90° Rotation Point

180° Rotation Point

Symmetry elements of this wallpaper group

* 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


3D Symmetry

Generalized 3D unit cell—a parallelepiped

(Unknown)


3D Symmetry

  • Crystal –

  • a solid with regularly repeating arrangement of atomsUnit 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)


3D Symmetry

  • Six symmetry elementsin 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 called

  • space groups.

  • 230 space groups


3D Symmetry

Asymmetric unit Unit cell 27 adjacent unit cells


Outline:

  • Background

  • Symmetry

  • My Project


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,…)


3D Symmetry

Asymmetric unit Unit cell 27 adjacent unit cells


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 REU

NSF Support

Advisor:

Wilma Olson, Department of Chemistry,

Rutgers University

Additional Advisors:

A.R. Srinivasan, Department of Chemistry

Rutgers University

Andrew Colasanti, Department of Molecular Biology

Rutgers University

(background: http://www.karolinskaeducation.ki.se/services/courses/selection_courses_se.html)


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