Molecular Modelling - part of ``Bioinformatik von RNA- und ... · Molecular Modelling atoms are...
Transcript of Molecular Modelling - part of ``Bioinformatik von RNA- und ... · Molecular Modelling atoms are...
Molecular Modellingpart of “Bioinformatik von RNA- und Proteinstrukturen”
Sonja Prohaska
Computational EvoDevoUniversity Leipzig
Leipzig, SS 2011
Sonja Prohaska Molecular Modelling
Protein Structure
levels or organizationPrimary structure: sequence of amino acids (from N- toC-terminus)Secondary structure: β-sheets and α-helicesTernary structure: arrangement of secondary structureelements into foldsQuaternary structure: assoziation of polypeptide changesinto one protein
proteins can be unfolded and refolded
conformation is assumed to be the thermodynamicallyprefered one
mathematical models should allow to predict proteinstructure from the protein sequence
→ Molecular Modelling
Sonja Prohaska Molecular Modelling
Anfinsen’s dogma and Levinthal’s paradox
Anfinsen’s dogma
The native structure of a protein is determined only by theprotein’s amino acid sequence.
The native structure is a unique, stable and kineticallyaccessible minimum of the free energy.
Levinthal’s paradox
The number of possible conformations available to agiven protein is astronomically large.
A polypeptide chain of 100 residues will have 99 peptidebonds, and therefore 198 different phi and psi bond angles.If each of these bond angles can be in one of three stableconformations, the protein may fold into a maximum of 3198
different conformations.
Sonja Prohaska Molecular Modelling
Folding Funnel
Sonja Prohaska Molecular Modelling
Primary Structure
A polypeptide is a single linear polymer chain of amino acidsbonded together by peptide bonds between the carboxyl andamino groups of adjacent amino acid residues.
During the condensation reaction a water molecule is releasedper formed peptide bond.
Sonja Prohaska Molecular Modelling
Polypeptide chain characteristics
The peptide bond is planar due to its double bond character.
Sonja Prohaska Molecular Modelling
Polypeptide chain characteristics
dihedral/torsion angles
bond N − Cα Cα − C1 C1 − Nangle φ (phi) ψ (psi) ω (omega)
cis 0◦
trans 180◦
right-handed α-helix −57◦−47◦
antiparallel β-sheet −139◦ +135◦
parallel β-sheet −119◦ +113◦
Possible combinations of φ and ψ values are visualized inRamachandran plots (see next slides).
Sonja Prohaska Molecular Modelling
Secondary Structure Elements I
Parallel and anti-parallel β-strands can form β-sheets.
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Secondary Structure Elements II
Hydrogen bonds between every N-H group and the oxygen of aC=O group four amino acids down the chain hold the α-helicesin shape.
Sonja Prohaska Molecular Modelling
Molecular Modelling
atoms are point charges with an associated mass
collective mathematical expression is the potential function
subsumes energetic contributions from multiple physicalforces
and between (all) pairs of atoms (“pair potential”)
reprecented as force field
molecular mechanics minimizes the (static) potentialenergy
molecular dynamics models the behaviour of the systemover time
Sonja Prohaska Molecular Modelling
Forces that determine protein structure
bonded energy contributionbond lengthsbond anglestorsion angles
non-bonded energy contributionvan der Waals forceselectrostatic interactions
conjugated system distortion
hydrogen bonds
solvent
E total = Ebond + Eangle + E torsion + EWaals + Ecoulomb
Sonja Prohaska Molecular Modelling
Bond length, angle and torsion
Penalty for molecule geometry deviating from optimal.
Ebondij =
12
kbondij (rij − r0
ij )2 (1)
Eangleijk =
12
kangleijk (θijk − θ0
ijk)2 (2)
E torsionijkl =
12
Vn(1 + cos nφijkl) (3)
r0ij ... optimal bond lengthθ0
ijk ... optimal valence angleVn ... height of the torsional barrierφijkl ... torional anglek ... constants
Sonja Prohaska Molecular Modelling
van der Waals forces
The Lennard-Jones potential is a simple model toapproximates the interaction between a pair of neutral atoms.
EvanderWaalsij =
Aij
rij12 −
Bij
rij6 (4)
Sonja Prohaska Molecular Modelling
electrostatic interactions
Coulomb’s law describes the electrostatic interaction betweenelectrically charged atoms. The dipole interactions of amidegroups along the protein backbone has a significant influenceon the overall conformation.
Ecoulombij =
1kcoul
ij
qiqj
rij(5)
rij ... distance between atoms i and jqi ,qj ... partial changes on atoms i and jkcoul
ij ... constant
Sonja Prohaska Molecular Modelling
AMBER Force Field
Assisted Model Building with Energy Refinement (AMBER) –represents a functional form of force fields as well as amolecular dynamics software package.
E total =∑
Ebondij +
∑Eangle
ijk +∑
E torsionijkl +
∑EvanderWaals
ij +∑
Ecoulombij
Sonja Prohaska Molecular Modelling
Energy terms for Hydrogen bonds
H O CN HN O
C
Ehydroij =
Cij
rij12 −
Dij
rij10 (6)
The equation takes only the distance of i (H on H-Donor) and j(O on H-Aceptor) into account but not the angle.
Sonja Prohaska Molecular Modelling
Literature
Biophysical Chemistry, Part I: The conformation of biologicalmacromolecules by Charles R. Cantor and Paul R. Schimmel;W. H. Freeman and Company, 12. edition, 2002; Chapter 5:“Conformational analysis and forces that determine proteinstructure”, p252-309.
Sonja Prohaska Molecular Modelling