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)
(Human Genome Project Information of the DOE)
Cube built from DNA
in nanotechnology lab
(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 atoms
Unit 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 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 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 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)
3D Symmetry
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 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)