Last class... 1. Sequence - {Folding} - Structure - Dynamics - - - PowerPoint PPT Presentation

• 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

Last class...

• Population of molecules in different energy wells
• Curr. Opin. Struct.
• Biol. (2011) 21:426

L99A L99A,G113A L99A,G113A, R119P Nature (2011) 477:111

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

Bonded atoms Geminal atoms Vicinal atoms NMR spectrum Chemical shift (δ δ δ δ, ppm)

• 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

• ( )

C B A J + + = φ φ φ cos cos2

Karplus, M. (1959) J. Chem. Phys. 30:11-15

Karplus equation: 3J and torsion angle

Torsion angle (deg.)

A, B and C are empirically determined parameters These are different for different types of molecules For a given 3J, more than one value of φ φ φ φ (torsion angle) is possible

• Comparing with experimental data

Vicinal coupling constant 3J 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 naa Number of molecules in “ee” conformation is nee

• Comparing with experimental data
• J. Mol. Struct. (2005) 734:211

H1 and H2 are equatorial in “ee” conformation, gauche with respect to each other, 3JH1,H2 will be “low” (denoted as Jee) H1 and H2 are axial in “aa” conformation, trans with respect to each other, 3JH1,H2 will be “high” (denoted as Jaa)

• ee

aa ee aa ee aa ee ee aa aa

• bs

E E E RT E n n n n J n J n J − = ∆       ∆ − = = + + = exp 1 Comparing with experimental data

• J. Mol. Struct. (2005) 734:211

Observed coupling constant: Jobs Jobs is a weighted sum of Jaa and Jee

• Methyl 5-O-Methyl-β

β β β-D- glycero-D-guloseptanoside

Conformational analysis: illustrative example

Methyl 5-O-Methyl-α α α α-D- glycero-D- idoseptanoside

Seven carbon monosaccharides

• Carbohydr. Res. (2006) 341:2927

OH HO HO HO OMe MeO OH HO HO HO OMe MeO

• 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

• 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

Relative energies of different conformers

(coordinates are from supplementary information file)

Me 5-O-Me-α α α α-D-glycero-D-idoseptanoside

• Carbohydr. Res. (2006) 341:2927

• Population of different conformers

∑

       −      − =

j j i i

RT E RT E f exp exp

• Conf. #

Ei

• exp. term

fi 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) R = 1.98 cal/mol.K T = 298 K partition function

• Carbohydr. Res. (2006) 341:2927

• Calculated and experimental coupling constants
• illustrative values from supplementary information file

Me 5-O-Me-α α α α-D-glycero-D-idoseptanoside

• Carbohydr. Res. (2006) 341:2927

...

5 5 4 4 3 3 2 2 2 2 1 1

+ + + + + + = J n J n J n J n J n J n Jobs

• 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

• J. Comput. Chem. (2012) 33:44

Conformational analysis: illustrative example

• Maltose: Glc-α

α α α1,4-Glc

!" "

# $ $$ %

$ !&'( " $) $ *+" $+", *- !" "

# $ $$ %

!"

# $$ % # *%

• 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

• Conformer selection

Unique conformer selection of human growth- regulatory lectin galectin-1 for ganglioside GM1 versus bacterial toxins H-C Siebert et al., (2003) Biochemistry 42:14762

*) *)

&.$ /$ / / /&.$

Is predominant conformer also “active” conformer?

• 0 $$ &.$α

α α α+/β β β β+/$ 1 123 4 *)$ #56+%+#+% 4 #7+%+#57+5% 23& 89 * #+%+#57+% // : * #+%+#5;+% :/ #;+5%+#57+6% :/ < )* *= #+%+#57+;% 482 $ 4 #7+;%+#57+6% >0! *?"3$* )#%@77

#φ φ φ φ+ψ ψ ψ ψ% #φ φ φ φ+ψ ψ ψ ψ% #φ φ φ φ+ψ ψ ψ ψ% #φ φ φ φ+ψ ψ ψ ψ%

Conformer selection

Is predominant conformer also “active” conformer?

• #5+%

#5+% #5+% #5+% #57+% A$ #5+% 1 #5+% #5;+6% /β β β β+/&.$ *?"3$* )#%@77

Conformer selection

Is predominant conformer also “active” conformer?

• Conformer selection

Biologically active conformation need not be the global minimum not even be local minimum NeuAc-α α α α2,3-Gal-β β β β1,4-Glc-β β β β1, (Sialyllactose)

&.$ /$ /

• Conformer selection
• Light color: major conformer found in

solution

• Dark color: microtubule-bound

conformation From Chem. Eur. J. (2008) 14:7557

• Proc. Natl. Acad. Sci. (USA) (2009) 106:3071

Figure 1

Probing conformer populations in vivo / in cells

Dynamic activation of caspase-1 Model proposed based on available experimental evidence

• Proc. Natl. Acad. Sci. (USA) (2009) 106:3071

Figure 1

Probing conformer populations in vivo / in cells

• Trap the protein in one of the conformations using

irreversible active-site inhibitors or allosteric compounds

• Use such ‘conformationally locked’ protein to raise

conformation-specific antibodies

• Conformational transitions

? $ * ) * $ <$** )$ * B$ " $ * )" *

∆ ∆ ∆ ∆/.3

.

$ *

3

∆ ∆ ∆ ∆/

.→3

∆ ∆ ∆ ∆/

3→.

• 

       ∆ − = RT G h T K k

B #

exp

Rate constant for conformational interconversions

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 60 120 180 240 300 360

Energy (kcal/mol) Torsion angle

Planck's constant = 6.626 × 10-34 m2 kg s-1 (J s) Boltzmann constant = 1.381 × 10-23 m2 kg s-2 K-1 (J K-1)

• Vibrations and conformational transitions

<!<α α α α22#%

2< +#% ") B@;7 #$ ** ) *%

* *

C$-*

D

$ * " $- " #*"% " $- " #*"%

• *
• *
• *E

$ $

8 $<$ 3)$")A.?9)CF<G 9)C+;

• Reaction coordinate

Potential energy ZZa EZa EZa EZa EZs EEa

ZZa, EZa, EZs, EEa: different conformers

1 2 3 1 2 3 1 2 3

1: Vacuum (ε ε ε εr = 1.) 2: CHCl3 (ε ε ε εr = 4.9) 3: DMSO (ε ε ε εr = 46.7)

• J. Mol. Struct. (2009) 938:97-110

HC = C – C ≡ N CO-CH3 NH-N(CH3)2

H )$ ) ) &<B$ $) I" $ $) ." $$

Dependence of energy on environment

• Time scale of conformational inter-conversions

“conformational averaging” Interpretation of experimental results

Ergodic hypothesis

Equivalence of time and ensemble averages

• Summary
• Lowest energy or predominant conformer - NEED NOT be the

biologically active conformer

• Different conformers of a molecule may be ‘biologically

relevant’ in different ‘context’

• Conformers interconvert among themselves
• Ergodic hypothesis states the equivalence of time and ensemble

averages