apm 530 - lecture 2 - arizona state university€¦ · jay taylor (asu) apm 530 - lecture 2 fall...

Molecular Structure Background

Valence

Each element tends to form a fixed number of bonds that depends on thenumber of electrons in its outer shell:

Carbon and phosphorus havevalence 4

Nitrogen has valence 3

Oxygen and sulphur havevalence 2

Hydrogen has valence 1

Jay Taylor (ASU) APM 530 - Lecture 2 Fall 2010 1 / 20


Notation

Carbon atoms are oftenshown as vertices.

Hydrogen atoms boundto C are often implicit.

Nitrogen, Oxygen,Phosphorus, Sulphur atomsare explicit.



Molecules can rotate about single bonds.

e− density is approximatelyradially symmetric about thebond.

Steric hindrance of attachedatoms can restrict themotion.

Timescale of rotation is∼ 10−11 sec.



Double bonded compounds are planar.

No rotation about thedouble bond.

Two stereoisomers: cis(same side) and trans(opposite sides).

The trans isomer is usuallymore stable.



Molecular structure can be represented using Cartesian or InternalCoordinates

Cartesian coordinates are used in most computations.

Potential energies are often expressed in terms of internal coordinates.



Dihedral Angles

τijkl = cos−1(~nijk · ~njkl)

~nijk =~ij × ~jk

|~ij × ~jk|

The dihedral angle between linked atoms i − j − k − l is thecounterclockwise angle between the bond vectors ~kl and ~ij whenrotated about ~jk.



Steric Interference

Repulsive forces between atoms can favor certain dihedral angles.

Staggered conformations are usually much more stable than eclipsedconformations.


Molecular Structure Nucleic Acids

Backbone torsion angles

Backbone torsion angles controlDNA/RNA bending.

The angles α, · · · , ζ are measuredalong the sequence

P → O5′ → C5′ → C4′ → C3′

→ O3′ → P.

β and δ are usually in the transstate.

α, γ and ζ are more flexible.



Ring Puckering

The pentose sugar is usuallynon-planar.

Twist conformations have threecoplanar atoms.

Envelope conformations havefour.

Atoms displaced to the sameside as C5’ are endo; those onthe other side are exo.



The Pseudorotation Cycle

The endocyclic torsion anglesτ0, · · · , τ4 are defined clockwisefrom the 04’-C1’ bond.

These approximately obey theformula:

τj = ν cos

(P +

4π

5(j − 2)

),

where P is the phase and ν isthe amplitude.



Glycosyl Rotation

Base flipping occurs through rotation from a syn to an anti conformation.



Geometry of Helices

Helix sense (handedness)

Pitch Ph is the distance along thehelix axis for one turn.

Axial rise h is the vertical distancebetween adjacent base pairs.

nb is the number of base pairs per turn.

Unit twist is the rotation about thehelix axis between adjacent base pairs:Ω = 360/nb.



Nucleic acid helices have a major and a minor groove.



Base pair parameters


Molecular Structure Experimental techniques

X-ray crystallography

X-ray wavelengths 0.1− 10 A.

Molecular structure can beinferred from X-ray diffractionpatterns produced by crystals.

The amplitude of the scatteredwave is proportional to the FTof the density of nuclei p(~r):∫

d~r p(~r)e−i~q·~r ,

where ~q = ~kout − ~kin.

One limitation is that the molecules must usually be crystallized.


Molecular Structure Experimental techniques

Nuclear Magnetic Resonance (NMR)

Structures of molecules insolution can be inferred usingmultidimensional NMR.

Nuclei exposed to EM pulsesradiate the energy at frequenciesthat depend on both bondedand non-bonded nuclei.

Information is available for H,C-13 and N-15.

NMR provides structural information about molecules in solution, but islimited to molecules with sizes < 100 kDa.


Molecular Structure Helical structures

DNA helices can have different conformations.



Average properties of A-, B- and Z-DNA

Property A-DNA B-DNA Z-DNA

Handedness right right left

bps/turn 11 10-10.5 12

Rise/bp 2.6 A 3.4 A 3.8 A

Diameter 26 A 20 A 18 A

Pitch 28 A 34 A 45 A

bp inclination 20 0 −7

Sugar pucker C3’-endo C2’-endo C2’/C3’-endo

Glycosyl rotation anti anti anti (C)/syn (G)

Major groove narrow & deep wide & deep convex

Minor groove wide & shallow narrow & deep narrow & deep



Occurrence of A-, B- and Z-DNA

B-DNA is the canonical form of DNA under physiological conditions.

A-DNA occurs at low humidity (e.g., in some crystals) and in someDNA-RNA hybrids and regions of dsRNA.

Z-DNA may occur transiently in negatively-supercoiled DNA and inpoly(dGC)2 sequences.



References

Krebs, J. E., Goldstein, E. S. and Kilpatrick, S. T. (2011) Lewin’sGenes X. Jones and Bartlett.

Schlick, T. (2006) Molecular Modeling and Simulation. Springer.


apm 530 - lecture 2 - arizona state university€¦ · jay taylor (asu) apm 530 - lecture 2 fall...

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