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lecture2 - Molecular Structure Background Valence Each...

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Unformatted text preview: Molecular Structure Background Valence Each element tends to form a fixed number of bonds that depends on the number of electrons in its outer shell: Carbon and phosphorus have valence 4 Nitrogen has valence 3 Oxygen and sulphur have valence 2 Hydrogen has valence 1 Jay Taylor (ASU) APM 530 - Lecture 2 Fall 2010 1 / 20 Molecular Structure Background Notation Carbon atoms are often shown as vertices. Hydrogen atoms bound to C are often implicit. Nitrogen, Oxygen, Phosphorus, Sulphur atoms are explicit. Jay Taylor (ASU) APM 530 - Lecture 2 Fall 2010 2 / 20 Molecular Structure Background Molecules can rotate about single bonds. e- density is approximately radially symmetric about the bond. Steric hindrance of attached atoms can restrict the motion. Timescale of rotation is 10-11 sec. Jay Taylor (ASU) APM 530 - Lecture 2 Fall 2010 3 / 20 Molecular Structure Background Double bonded compounds are planar. No rotation about the double bond. Two stereoisomers: cis (same side) and trans (opposite sides). The trans isomer is usually more stable. Jay Taylor (ASU) APM 530 - Lecture 2 Fall 2010 4 / 20 Molecular Structure Background Molecular structure can be represented using Cartesian or Internal Coordinates Cartesian coordinates are used in most computations. Potential energies are often expressed in terms of internal coordinates. Jay Taylor (ASU) APM 530 - Lecture 2 Fall 2010 5 / 20 Molecular Structure Background Dihedral Angles ijkl ijk n = cos-1 ( ijk jkl ) n n jk ij = | jk| ij The dihedral angle between linked atoms i - j - k - l is the counterclockwise angle between the bond vectors kl and when ij rotated about jk. Jay Taylor (ASU) APM 530 - Lecture 2 Fall 2010 6 / 20 Molecular Structure Background Steric Interference Repulsive forces between atoms can favor certain dihedral angles. Staggered conformations are usually much more stable than eclipsed conformations. Jay Taylor (ASU) APM 530 - Lecture 2 Fall 2010 7 / 20 Molecular Structure Nucleic Acids Backbone torsion angles Backbone torsion angles control DNA/RNA bending. The angles , , are measured along the sequence P O5 C 5 C 4 C 3 O3 P. and are usually in the trans state. , and are more flexible. Jay Taylor (ASU) APM 530 - Lecture 2 Fall 2010 8 / 20 Molecular Structure Nucleic Acids Ring Puckering The pentose sugar is usually non-planar. Twist conformations have three coplanar atoms. Envelope conformations have four. Atoms displaced to the same side as C5' are endo; those on the other side are exo. Jay Taylor (ASU) APM 530 - Lecture 2 Fall 2010 9 / 20 Molecular Structure Nucleic Acids The Pseudorotation Cycle The endocyclic torsion angles 0 , , 4 are defined clockwise from the 04'-C1' bond. These approximately obey the formula: 4 j = cos P + (j - 2) , 5 where P is the phase and is the amplitude. Jay Taylor (ASU) APM 530 - Lecture 2 Fall 2010 10 / 20 Molecular Structure Nucleic Acids Glycosyl Rotation Base flipping occurs through rotation from a syn to an anti conformation. Jay Taylor (ASU) APM 530 - Lecture 2 Fall 2010 11 / 20 Molecular Structure Nucleic Acids Geometry of Helices Helix sense (handedness) Pitch Ph is the distance along the helix axis for one turn. Axial rise h is the vertical distance between adjacent base pairs. nb is the number of base pairs per turn. Unit twist is the rotation about the helix axis between adjacent base pairs: = 360 /nb . Jay Taylor (ASU) APM 530 - Lecture 2 Fall 2010 12 / 20 Molecular Structure Nucleic Acids Nucleic acid helices have a major and a minor groove. Jay Taylor (ASU) APM 530 - Lecture 2 Fall 2010 13 / 20 Molecular Structure Nucleic Acids Base pair parameters Jay Taylor (ASU) APM 530 - Lecture 2 Fall 2010 14 / 20 Molecular Structure Experimental techniques X-ray crystallography X-ray wavelengths 0.1 - 10 . A Molecular structure can be inferred from X-ray diffraction patterns produced by crystals. The amplitude of the scattered wave is proportional to the FT of the density of nuclei p( ): r qr d p( )e -i , r r where = out - in . q k k One limitation is that the molecules must usually be crystallized. Jay Taylor (ASU) APM 530 - Lecture 2 Fall 2010 15 / 20 Molecular Structure Experimental techniques Nuclear Magnetic Resonance (NMR) Structures of molecules in solution can be inferred using multidimensional NMR. Nuclei exposed to EM pulses radiate the energy at frequencies that depend on both bonded and non-bonded nuclei. Information is available for H, C-13 and N-15. NMR provides structural information about molecules in solution, but is limited to molecules with sizes < 100 kDa. Jay Taylor (ASU) APM 530 - Lecture 2 Fall 2010 16 / 20 Molecular Structure Helical structures DNA helices can have different conformations. Jay Taylor (ASU) APM 530 - Lecture 2 Fall 2010 17 / 20 Molecular Structure Helical structures Average properties of A-, B- and Z-DNA Property Handedness bps/turn Rise/bp Diameter Pitch bp inclination Sugar pucker Glycosyl rotation Major groove Minor groove A-DNA right 11 2.6 A 26 A 28 A 20 C3'-endo anti narrow & deep wide & shallow B-DNA right 10-10.5 3.4 A 20 A 34 A 0 C2'-endo anti wide & deep narrow & deep Z-DNA left 12 3.8 A 18 A 45 A -7 C2'/C3'-endo anti (C)/syn (G) convex narrow & deep Jay Taylor (ASU) APM 530 - Lecture 2 Fall 2010 18 / 20 Molecular Structure Helical structures 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 some DNA-RNA hybrids and regions of dsRNA. Z-DNA may occur transiently in negatively-supercoiled DNA and in poly(dGC)2 sequences. Jay Taylor (ASU) APM 530 - Lecture 2 Fall 2010 19 / 20 Molecular Structure Helical structures References Krebs, J. E., Goldstein, E. S. and Kilpatrick, S. T. (2011) Lewin's Genes X. Jones and Bartlett. Schlick, T. (2006) Molecular Modeling and Simulation. Springer. Jay Taylor (ASU) APM 530 - Lecture 2 Fall 2010 20 / 20 ...
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