Ligand configurational entropy and protein

bindingChia-en A. Chang, Wei Chen, and Michael K. Gilson – PNAS(2007)

Presented by Christopher Williams

Remember K*?

Uses conformational entropy of side chains to better predict redesign mutations

What about ligands?

Entropy is lost on binding How much? What kind? Do we care?

Configurational Entropy

Configurational Entropy

Conformational Entropy Vibrational Entropy

Configurational Entropy

Conformational Entropy Vibrational Entropy

Configurational Entropy

Conformational Entropy Vibrational Entropy

Rotation/ Translation

Torsion

Angle Bending

Bond Stretching

Energy Well

More Wells

Wider Well

Higher Conform

ational Entro

py

Higher Vibrational Entropy

How to measure entropy

S = k ln(W)k = Boltzman constantW = Multiplicity

j

The test case

Amprenavir, an HIV protease inhibitor

Results

Configurational entropy loss on binding: 26.4 kcal/mol

# of accessible conformations in solution: 960 # of accessible conformations bound: 1

ΔS = RT ln(960)

Conformational entropy contribution: 4.1 kcal/mol

Results

Configuational entropy loss on binding: 26.4 kcal/mol

Entropy loss: torsion only: 12.2 kcal/mol Entropy loss: rotation/translation only: 15.7

kcal/mol

12.2 + 15.7 = 27.9 != 26.7 kcal/mol

Configurational Entropy

Conformational Entropy Vibrational Entropy

Rotation/ Translation

Torsion

Angle Bending

Bond StretchingThere is correlation among the “separate” components of configurational entropy

Proof?

Similar results were returned by a separate analysis“Quasiharmonic analysis” – essentially an MD

approachCompare 11.6 kcal/ mol to 12.3 kcal/mol

Cannot test in wetlebCannot yet measure separate components of

entropy

Predictions and Observations

Configurational entropy has a similar magnitude effect to electrostatics or hydrophobics ~25 kcal/molDoes not include proteinVaries by ligandVaries by tightness of binding

Predictions and Observations

Vibrational entropy loss dominatesNot conformational/rotamer lossThis challenges conventional thinking

Certain atom centers are more prone to vibrational entropysp3 versus ring structures

Applications to design

Optimizing drugsEntropy loss inhibits bindingRigid ligands have less entropy to lose

Applications to design

Improving Scoring FunctionsCurrent functions overweight conformational

entropy, underweight vibrationalVaries by ligand

Applications to design

Computational savingsVibrational entropy dominatesMay not have to enumerate every minumum

Chia-en A. Chang, Wei Chen, & Michael K. Gilson. Ligand configurational entropy and protein binding. 2007 PNAS 104(5):1534-1539

Questions

Mining Minima

Margin of Error: ± 0.8 kcal/mol

q.e.d