DNA PACKING: Distances Between DNA Molecules in Crystals Bryson W. Finklea St. John's College DIMACS REU

Unit Cell

Asymmetric Unit Unit Cell 3x3x3 Block of Unit Cells

NDB #: bdl042 (Rasmol images) Space Group: C 2

Asymmetric Unit Unit Cell 3x3x3 Block of Unit Cells NDB #: bdl042 (Rasmol images) Space Group: C 2

NDB #: adh007 Asymmetric Unit Unit Cell 3x3x3 Block of Unit Cells (Rasmol images) Space Group: P 6 1

NDB #: adh007 Asymmetric Unit Unit Cell 3x3x3 Block of Unit Cells (Rasmol images) Space Group: P 6 1

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 ● Connecting 4 lattice points in a parallelogram gives a unit cell ● Unit cell – the basic unit that repeats in every direction ● Some unit cells are conventionally used because of their higher symmetry

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:

Generalized 3D unit cell—a parallelepiped 3D Symmetry (Unknown)

Categories of Space Groups

Proper symmetry elements in 3D: Rotation axes (by 60°, 90°, 120°, or 180°) Notated: 6, 4, 3, and 2, respectively Screw Axes (translation and rotation) Notated: 6 1, 6 2, 6 3, 6 4, 6 5 ; 4 1, 4 2, 4 3 ; 3 1, 3 2 ; and 2 1 (Translation) Proper symmetry elements in 3D: Reflection planes Glide reflection planes (reflection and translation) Inversion points Rotary inversion axes (rotation and inversion)

Symmetry operations –the actual changes carried out in relation to a symmetry element Sets of symmetry operations form algebraic groups called space groups. 230 space groups

Asymmetric Unit Unit Cell 3x3x3 Block of Unit Cells NDB #: bdl042 (Rasmol images) Space Group: C 2

Characterizing Intermolecular Contacts of DNA Data from Nucleic Acid Database (NDB): ● orthogonal coordinates of atoms in asymmetric unit ● conversion matrix from orthogonal to fractional (unit cell) coordinates ● 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 ● Measure distances between pairs of atoms in different molecules My Project

Example output from program of distances less than 3.0 angstroms: (for bdl042.pdb) UCELL MOL AT# AT RES UCELL MOL AT# AT RES DISTANCE O2 C C4* G C4* G O2 C C2 G O4* T C5* G C5* G O4* T C2 G O2P G O2P G N3 G N2 G O4* C O3* G O3* C C5* G C5* G O3* C C5* G C5* G O4* G O4* G O3* G O4* C N2 G N3 G N2 G N2 G O2P G O2P G N3 G N2 G O4* C O3* G O3* C C5* G C5* G O3* C C5* G C5* G O4* G O4* G O3* G O4* C N2 G N3 G N2 G N2 G 2.73

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

Future Work: ● Tweak output features of program ● Run program on all DNA-only files of NDB ● Characterize intermolecular contacts in different ways e.g. angle between DNA molecular axes ● Alter notation of program to run it on NDB files containing RNA, protein, and drug molecules

Acknowledgments DIMACS REU NSF Support Advisor: Wilma Olson, Department of Chemistry, Rutgers University Additional Advisor: A.R. Srinivasan, Department of Chemistry, Rutgers University (background: