1. The document outlines topics related to DNA geometry including one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) representations as well as circular DNA topology and measures like writhe, twist, and linking number. 2. It describes the NAB software package for modeling DNA and its energy model that considers torsion, curvature, twist, tilt, and roll. 3. The document discusses accuracy issues in modeling DNA and visualization techniques like overlapped and narrowed views as well as probability densities from methods like NMR.

1. Outline of Talk
DNA Geometry
1D, 2D, 3D
Circular DNA Topology
Writhe, Twist and Linking
The NAB package
C language extension
DNA Energy Model
Torsion and Curvature
Twist, Tilt, and Roll
Writhing DNA with NAB
Mechanisms
Pictures

2. Linear(1D) DNA
Sequence of 4 units – A,C,G,T
Huge
Human 2.9GB
Yeast 13MB
Bacteria 4MB
Virus 50KB
Information in 6 reading frames
of 3 bases per amino acid for proteins
1 2 3 1… ->
ACGT…
TGCA…
4 6 5 4… <-
(Information in 1 base for ncRNA )

3. Annotated 1D Diagram
‘5 ‘3 Additional Information:
P 1. The PSPS chain
SA--TS strong
P P 2. The AT,CG are
SC=GS relatively weak
P P 3. Alignment between
SG=CS bases adds
P P stability
ST--AS 4. AT and CG
. . proportions
. . 5. Statistical
. . goldmine
. P 6. Easy data
‘3 ‘5

4. 2D DNA Chain Diagram
What’s right: Rappe 5.2
All atom connectivity
Lengths and some angles(flats)

5. 2D DNA Base Pair Diagram
Calladine 2.11
What’s right:
Hydrogen bond connectivity
2D base/base orientation

6. What’s missing from 2D models?
Phosphate and Carbon tetrahedral angles
Calladine 1.10
Boyd 2.11

7. XYZ information in PDB format
HEADER DEOXYRIBONUCLEIC ACID 17-OCT-97 1AXP
TITLE DNA DUPLEX CONTAINING A PURINE-RICH STRAND, NMR, 6
COMPND 2 MOLECULE: DNA (D(GAAGAGAAGC)(DOT)D(GCTTCTCTTC));
....
ATOM 1 O5* G A 1 2.572 -5.361 -5.523
ATOM 2 C5* G A 1 2.872 -5.631 -4.170
ATOM 3 C4* G A 1 4.132 -4.868 -3.744
ATOM 4 O4* G A 1 3.880 -3.473 -3.810
ATOM 5 C3* G A 1 4.513 -5.195 -2.294
ATOM 6 O3* G A 1 5.928 -5.200 -2.189
ATOM 7 C2* G A 1 3.871 -4.032 -1.546
ATOM 8 C1* G A 1 4.110 -2.898 -2.538
ATOM 9 N9 G A 1 3.190 -1.757 -2.329
ATOM 10 C8 G A 1 1.818 -1.752 -2.355
ATOM 11 N7 G A 1 1.283 -0.577 -2.179
ATOM 12 C5 G A 1 2.377 0.267 -2.026
Problems:
Accuracy problems because of vibrations
Methods: NMR,…
Conditions: crystals,temperature
Visualization
Overloaded view
Narrowing view
Which is truth? - Seduction

8. Accuracy – Probability Densities
ORTEP-
Oak Ridge Thermal
Ellipsoid Program
Jeffery 11.10

9. Characteristics of Relaxed DNA
Width - 18 Angstroms
Between base pairs – 6 Angstroms
34 degrees rotation between bps
10-12 bases per rotation
The twisted ladder

10. DNA Basepair
Reference Frame

11. Torsion Angles
Nucleic Acids
Proteins Fletterick

12. Circular DNA – Plasmids
Examples:
APU83788 2439 bp
BACPSTK1 1883 bp
PHIPPF1 1509 bp
PBR323( drug resistance) 4KB
PM2 virus DNA 9-10KB
Yeast 2u Circle 6.3KB
F factor(E.coli fertility) 93KB
Human Mitochondria 16KB
Choroplast 154KB
Circular DNA can constrain twists,
Linear DNA will relax to default.

13. NAB – Nucleic Acid Builder – 1998
Thomas J. Macke and David Case

14. NAB Extensions to the C language
Lex/Yacc preprocessor
Source distribution
Datatypes and language extensions
Molecule Awk/Perl strings
Residue Hashed arrays
Atom
Functions
Rigid Body Transformations
Distance Geometry
Molecular Mechanics
Builtin PDB information through
libraries of molecules
Examples
DNA plasmids*
RNA pseudoknotting
Protein
Nucleosome

15. Flowchart NAB Writhing Program
Steps
1. Input, sequence, compute reference structure
2. Input, twist, compute twisted structure
3. All Atom XYZ ->
Reference Frame and Twist, Tilt  Roll
or curvature and torsion
K. Monte Carlo Loop Minimization
Local change
Global change
Energy decrease?
N-1. Optimal Twist, Tilt and Roll ->
or Curvature and Torsion
All Atom XYZ
N. Output – writhed DNA

16. Energy Models - Fated to succeed
1.Curvature and Torsion(Schlick)
Energy = Es + Eb + Et + Ee
nk
Es(stretching) = h/2  (li-l0)2
i=1
nk
Eb(bending) = g/2  i
2
i=1
nk
Et(torsion) = C/(2l)  (i,i+1- 0)2
i=1
Ee(electrostatic) nk
Ee= ((v2l0
2)/D)  exp(-krij)/rij
j > i+1

17. . Twist, Tilt and Roll
E= .5kBT  [ k1 [k0(Twi-Tw0) + (Roi-Ro0)]2
+k2 [k0(Twi-Tw0) - (Roi-Ro0)]2
+k3 [ (Tli-Tl0) ]2 ]

18. Monte Carlo Movements
1.Local - small rotation 
r_n = r
a_n = a
b_n = cos()* b + sin() * c
c_n = - sin() * b + cos() * c
2.Global - crankshaft movement



19. Model Limitations – Reductionist’s bane
1. Electronegativity-Water,Mg++, Ca++, Na+
Coulomb attraction/repulsion
2. Sequence dependent energy
3. Monte Carlo replacements
a.Conjugate gradient
b.Verlet algorithm
4. Accouchements/Attachments
(DNA is never naked)

20. The Folding Problem
Input: 1D sequence(Protein,DNA,RNA)
Model0 - beads on a string
…
ModelK(Search Space Reduction)
...
ModelN – all atom
Minimization
Output: 3D structure
Comparison to known results

21. Credits
Hong Qian
– for suggesting this problem
Dan Beard
– for starting for this as an
Chem575 exercise
David Case and Thomas Mack
– for removing a lot of the
programming details