��������������� Last class... 1. Sequence - {Folding} - Structure - Dynamics - Function paradigm: perspective for the course 2. Molecular structure: representation, conformational changes, conformational ensembles, conformer selection 3. Steric effect or hard-sphere approximation: preferred (allowed) versus not-preferred (disallowed) conformations; application to monosaccharides and peptides; Ramachandran map
��������������� Population of molecules in different energy wells Nature (2011) 477:111 Curr. Opin. Struct. Biol. (2011) 21:426 L99A L99A,G113A, L99A,G113A R119P Helicobacter pylori SlyD PDB id 2KR7
��������������� Population of molecules in different energy wells Experimental approach ♦ ♦ ♦ ♦ Exhaustive cataloging is not guaranteed ♦ Limited by the sensitivity of the technique ♦ ♦ ♦ ♦ “Minor” and “transient” conformations are especially ♦ ♦ ♦ difficult to capture Computational approach ♦ Exhaustive search is possible only for “small” molecules ♦ ♦ ♦ ♦ Compute energies for all the conformers ♦ ♦ ♦ ♦ Calculate “population” based on the partition function ♦ ♦ ♦ ♦ ♦ Validate by comparing with experimental data ♦ ♦ ♦ ♦ ♦ ♦ Limitation: computation of energies - functions used and empirical parameters
��������������� Vicinal coupling constants Vicinal NMR spectrum atoms � � �� Bonded atoms Chemical shift ( δ δ , ppm) δ δ Geminal atoms Residual dipolar couplings derived from NMR spectroscopy can also be used for comparing experimental and computational data on preferred conformations Angew. Chem. Int. Ed. (2011) 50:7222
��������������� Karplus equation: 3 J and torsion angle Karplus, M. (1959) J. Chem. Phys. 30:11-15 ( ) cos 2 φ = φ + φ + J A B cos C A, B and C are empirically determined parameters These are different for different types of molecules For a given 3 J , more than one value of φ φ φ φ (torsion angle) is possible Torsion angle (deg.)
��������������� Comparing with experimental data Vicinal coupling constant 3 J from NMR spectroscopy Tetrahedron (2007) 63:2622
��������������� Comparing with experimental data J. Mol. Struct. (2005) 734:211 Let us assume that this molecule exists in (only) two conformations “aa” conformation: H1 and H2 are axial “ee” conformation: H1 and H2 are equatorial Both “aa” and “ee” represent ensembles Number of molecules in “aa” conformation is n aa Number of molecules in “ee” conformation is n ee
��������������� Comparing with experimental data J. Mol. Struct. (2005) 734:211 H1 and H2 are equatorial in “ee” conformation, gauche with respect to each other, 3 J H1,H2 will be “low” (denoted as J ee ) H1 and H2 are axial in “aa” conformation, trans with respect to each other, 3 J H1,H2 will be “high” (denoted as J aa )
��������������� Comparing with experimental data J. Mol. Struct. (2005) 734:211 Observed coupling constant: J obs J obs is a weighted sum of J aa and J ee = + + = 1 J n J n J n n obs aa aa ee ee aa ee ∆ n E aa = − ∆ = − exp E E E aa ee n RT ee
��������������� Conformational analysis: illustrative example Seven carbon monosaccharides OH OH OMe MeO HO MeO HO HO OMe HO HO HO Methyl 5-O-Methyl- α α α -D- α Methyl 5-O-Methyl- β β -D- β β glycero -D- glycero -D-guloseptanoside idoseptanoside Carbohydr. Res. (2006) 341:2927
��������������� Conformational analysis: illustrative example 1. Generate as many different conformations as possible We know standard bond lengths and bond angles Variations in torsion angles lead to different conformations Internal coordinates can be converted to Cartesian coordinates 2. For each conformation, calculate energy Using quantum chemical methods Using empirically derived parameters Equations for calculating energy due to different non-covalent interactions (e.g., Coulomb’s lab for calculating electrostatic interactions) will be discussed later
��������������� Relative energies of different conformers Me 5-O-Me- α α -D- glycero -D-idoseptanoside α α Conformer Relative energy Minimum number (in kcal/mol) type 6 0.00 Global 10 0.61 Local 1 1.84 Local 15 2.71 Local 1. Other higher energy conformers also exist 2. Energy -- quantum chemical methods (coordinates are from supplementary information file) Carbohydr. Res. (2006) 341:2927
��������������� Population of different conformers − E partition function i exp RT = f − i E ∑ j exp j RT R = 1.98 cal/mol.K Conf. # E i exp. term f i T = 298 K 6 0.00 1.000 0.709 10 0.61 0.356 0.253 1 1.84 0.044 0.031 15 2.71 0.010 0.007 (total 1.410 1.000) Carbohydr. Res. (2006) 341:2927
��������������� Calculated and experimental coupling constants Me 5-O-Me- α α -D- glycero -D-idoseptanoside α α �������� ����� ����� ����� ����� �������� ����� �������� ��� ���� ��� ���� ��� ��� ����� � � ��� ���� ���� ���� ���� ���� ��� � � ��� ���� ���� ���� ���� ���� ��� � � ��� ���� ���� ���� ���� ���� ��� � � ��� ���� ���� ���� ���� ���� ��� � � ��� ���� ���� ���� ���� ���� ���� illustrative values from supplementary information file = + + + + + + J obs n J n J n J n J n J n J ... 1 1 2 2 2 2 3 3 4 4 5 5 Carbohydr. Res. (2006) 341:2927
��������������� Conformational analysis: illustrative example Different protonated forms of L-Phenylalanine J. Comput. Chem. (2012) 33:44
��������������� Conformational analysis: illustrative example J. Comput. Chem. (2012) 33:44
��������������� Conformational analysis: illustrative example J. Comput. Chem. (2012) 33:44
��������������� Maltose: Glc- α α α 1,4-Glc α $������ ����!&'(� ���������� �����"���� $���������������) ������ ����$���� *�����+�"���� �� ��$����+�������"�������, �*������-����� �� #����� �������������*������% ����!�"���� ������"��� #���� ���$���� ������$$�� ���% ����!�"���� ������"��� # ���$������� ��$$�� ���% ����!�"���� #���� ���$$�� ���%
��������������� Dealing with complexity Model systems (transferability?) Reductionistic approach break the system into smaller, constituent components study these components individually / separately (limitation: non-linearity)
��������������� Data from model systems 1. How accurate are the calculated energies? Empirically derived parameters are used in molecular mechanics to calculate energies. Errors in these parameters. Ab initio methods – calculated energies are dependent on the underlying theory, basis set used, conformation chosen. Energy also depends on how the environment is treated (solvent, dielectric constant, ...) 2. How appropriate is the model system (Ala-Met-Ala)? Protein context may be different from that of a tripeptide. 3. How representative is the dataset? Proteins considered in the dataset may not be a true representation
��������������� Summary • Conformational analysis - which conformers are predominant? • What is the population of different conformers • Small molecules - relatively easier • Compute energies of different conformers using quantum chemical methods • Compare calculated coupling constants with experimental data to validate the computed populations • Residual dipolar couplings have also been used for comparison • Macromolecules are complex - need to use model systems • Question of ‘transferability’ of data derived from model systems
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