1. Department of Chemistry
Prediction of protein functional states by multi-resolution protein modeling
Cecilia Clementi
Department of Chemistry
Rice University
Houston, Texas

2. The challenges in molecular biophysics: The “middle way”, in between a few small molecules and bulk
thermodynamics
describes the system
bulk water
…in between…
Large water clusters
Wet/Dry interfaces
Interaction with solutes
quantum chemistry gives
molecular orbitals
one water molecule
what are the relevant variables?
what is the intrinsic dimensionality?
I would like to spend just a few words on the issue of studing systems that are in between a few atoms and bulk. Consider water, that is very important in biology. If you have just one water molecule, one would approach it with quantum chemistry tools, and determine the wavefunctions that give molecular orbitals - the important quantity is the distrubution of the electrons around the nuclei, wavefunctions give that.
On the other extreme, take an Avogadro number of water molecule, we can consider it an infinite system and apply thermodynamics - the important quantities are different now, they are pressure, temperature, global variables.
In biophysics we have systems in between: consider large clusters of water molecules, that can be for instance surranding a macromolecule in solution, think wet/dry interfaces. What are the important variables?
If there are a few collective parameters (analogous to T, P in thermo), what are they?
Empirical approach
Theoretical approach
C.Clementi, Curr. Opin. Struct. Biol. 2008, vol.18(1), 10-15

3. Physicists and biochemists often perceive molecular structure and function differently
Example: representation of a Heme group
Biochemist view:
Physicist view:
Protoporphyrin ring
Central Iron
Heme group: A prosthetic group consisting of a protoporphyrin ring and a central iron (Fe) atom - A protoporphyrin ring is made up of four pyrrole rings linked by methene bridges. Four methyl, two vinyl, and two propionate side chains are attached. The iron can either be in the ferrous (Fe++) or the ferric (Fe+++) oxidation state.
1 nm
Biophysics should reconcile the two!

4. Outline Our toolbox to explore Application to characterize
protein landscapes
at multiple resolutions
Application to characterize
a protein functional state
Photoactive Yellow Protein

5. PYP transforms light into biological signal
PYP is believed to be responsible for
H.halophila's ability to respond to
blue light.
How?
PYP

6. PYP transforms light into biological signal
PYP is interesting to study because:
It is the prototype for the PAS domain
(a ubiquitous domain in signaling proteins)
Its photochemistry is directly analogous to rhodopsin
PYP
PYP’s
native state.

7. How? Basic outline of the photocycle
We know the structure of these states.
But the structure of this state is unkown.

8. How? The signaling state is elusive: PYP’s signaling state?
It’s difficult to observe experimentally
(because it partially unfolds)
It’s difficult to predict computationally
(broad range of time scales)
PYP’s
signaling state?

9. 2) All atom reconstruction 3) All atom / quantum calculations
The signalling process can be characterized using a multiscale approach:
1) Coarse Graining
2) All atom reconstruction
3) All atom / quantum calculations

10. P.Das, S.Matysiak & C.Clementi PNAS 102, 10141-10146 (2005)
The signaling state ensemble can be characterized using a multiscale approach:
1) Coarse graining
P.Das, S.Matysiak & C.Clementi PNAS 102, (2005)

11. What’s the role of a protein coarse-grained model?
Simplified models are largely used to test general ideas and principles on toy-systems
Recently they have been applied to make predictions on real protein systems
At what extent can protein coarse-grained models
be used as predictive tools on real systems?
C.Clementi, Curr. Opin. Struct. Biol. 2008, vol.18(1), 10-15

12. Building a coarse-grained protein model
met-asp-leu-tyr

13. Building a coarse-grained protein model2 i j

14. A realistic coarse-grained protein model
 1-bead per residue (Ca model)
 20 aminoacid “colors”
P.Das, S.Matysiak & C.Clementi PNAS 102, (2005)

15. We “photoactivate” the coarse grained model by
perturbing the coarse grained forcefield
at the chromophore.
Dark PYP
Photoactivated PYP
The free energy is computed as a function of the “Diffusion Coordinates”
[“Determination of reaction coordinates via locally scaled diffusion map”,
M.A.Rohrdanz, W.Zheng, M.Maggioni & C.Clementi, J.Chem.Phys. 134, (2011)]
P.J. Ledbetter, B.P. Lambeth & C.Clementi, unpublished results (2011)

16. We “photoactivate” the coarse grained model by
perturbing the coarse grained forcefield
at the chromophore.
Dark PYP
Photoactivated PYP
This perturbation has a strong effect on the free energy
landscape, creating an on pathway intermediate.
P.J. Ledbetter, B.P. Lambeth & C.Clementi, unpublished results (2011)

17. The difference is in the inclusion of non-native interactions
It is interesting to compare the results of this model (DMC) to a simpler model (GO)
DMC GO
The difference is in the inclusion of non-native interactions

18. Photoactivated PYP Dark PYP DMC model GO model
P.J. Ledbetter, B.P. Lambeth & C.Clementi, unpublished results (2011)

19. Comparison with available experimental data (on D25)
experimental data from
Bernard, et al.
Structure, 13, 953–962 (2005)‏
Fluctuations (A)
P.J. Ledbetter, B.P. Lambeth & C.Clementi, unpublished results (2011)‏

20. protein coarse-grained model?
How much can we push
a prediction from a
protein coarse-grained model?

21. How accurate is the prediction? How can we test it quantitatively ?
“activated”
minimum?
protein
“quake”
folded state ensemble
chromophore in
cis configuration
photo-isomerization
Energy
activated state
chromophore in
cis configuration
folded state ensemble
chromophore in
trans configuration
recovery
unfolded
minimum
folded
minimum

22. 2) All atom reconstruction
The signaling state ensemble can be characterized using a multiscale approach:
2) All atom reconstruction
Start from
only C-alpha atoms
Reconstruct
backbone atoms
Reconstruct
side-chain atoms
Optimize structure
(locally and globally)
A.P.Heath, L.E.Kavraki & C.Clementi, Proteins 2007, 68,

23. The signaling state ensemble can be characterized using a multiscale approach:
2) All atom reconstruction
An example rotational isomer (rotamer)
Different rotamers can be obtained by twisting around all the residue bonds.
Alpha-carbon
Along backbone…
Along backbone…
Lysine

24. 2) All atom reconstruction
The signaling state ensemble can be characterized using a multiscale approach:
2) All atom reconstruction
P.J. Ledbetter, B.P. Lambeth & C.Clementi, unpublished results (2011)

25. Problem:
photo-isomerization changes the electronic structure of the chromophore
Solution:
use quantum chemistry to correct the force field
(collaboration with Gustavo Scuseria’s
group at Rice)

26. 3) All atom/quantum computations
The signaling state ensemble can be characterized using a multiscale approach:
3) All atom/quantum computations
The chromophore is responsible for triggering conformational change.
But there are no standard force fields for this residue.
The forcefield needs to be derived from quantum chemical computations, for cis, trans and protonated forms.

27. Existing parameters are ineffective at producing the isomerization energy
Trans (ground state) results
Cis results
Amber predicts ~ 14 kcal/mol,
while pbe1pbe/6-31++G** predicts ~ 6 kcal/mol
P.J. Ledbetter & C.Clementi, unpublished results (2011)

28. Parameter Fitting Procedure
Cluster
Quantum Calculations
New parameters
MD Simulations
Goal: Converge to parameters which approximate the molecule’s free energy
P.J. Ledbetter & C.Clementi, unpublished results (2011)

29. New Parameter Fitting Procedure
Cluster
Quantum Calculations
New parameters
MD Simulations
MD Simulations
What: With initial parameters, run very long molecular dynamics simulations.
Goal: Generate an ensemble large enough for statistical properties to converge

30. New Parameter Fitting Procedure
Cluster
Quantum Calculations
New parameters
MD Simulations
Cluster
What: Select sub-ensembles by clustering the MD trajectory, using its size to estimate as a measure of free energy.
Goal: Choose a few structures on which to calculate the quantum chemical energy.

31. New Parameter Fitting Procedure
Cluster
Quantum Calculations
New parameters
MD Simulations
Quantum Calculations
What: Use Gaussian to calculate the quantum chemical energy of the molecule. (PBE1PBE 6-311G**)
Goal: Calculate the energy of the molecules in a reliable way.
P.J. Ledbetter & C.Clementi, unpublished results (2011)

32. New Parameter Fitting Procedure
Cluster
Quantum Calculations
New parameters
MD Simulations
New Parameters
Perform a least squares fit on the energy of the structures weighted by the free energy estimate by varying the parameters.
If the parameters are realistic enough, stop.
P.J. Ledbetter & C.Clementi, unpublished results (2011)

33. New Parameter Fitting Procedure
Results
P.J. Ledbetter & C.Clementi, unpublished results (2011)

34. The signalling process can be characterized using a multiscale approach:
2) All-atom reconstruction
All-atom structures
of 25 most populated
intermediate structures
1) Coarse Graining
3) QM parameter fitting
for chromophore force field

35. Diffusion dynamics from the 25 reconstructed structures
Lowest energy
structures
are solvated
P. J. Ledbetter, B.P. Lambeth & C.Clementi, unpublished results (2011)‏

36. Structural Analysis of the Results
Native (dark) state
Photoactivated ensemble
Structure, Vol. 13, 953–962, July, 2005,
P.J. Ledbetter, B.P. Lambeth & C.Clementi, unpublished results (2011)

37. How accurate is the prediction? How can we test it quantitatively ?
folded state ensemble
chromophore in
cis configuration
activated state
chromophore in
cis configuration
comparable
energy
“activated”
minimum? pR pB
Conformational
entropy
in pB
much larger
than pR pG
folded state ensemble
chromophore in
trans configuration
unfolded
minimum
folded
minimum
Next: design experimental tests
(collaboration with Thomas Kiefhaber)
P. J. Ledbetter, B.P. Lambeth & C.Clementi, unpublished results (2011)‏

38. Cecilia Clementi’s research group
Clementi’s group
Dr. Mary Rohrdanz (Rice Chemistry)
Paul Ledbetter (Rice Applied Physics)
Brad Lambeth (Rice Chem. Eng.)
Wenwei Zheng (Rice Chemistry)
Amarda Shehu (now: GMU)
Payel Das (now: IBM Watson)
Silvina Matysiak (now: U Maryland)
Collaborators:
Prof. Kathy Matthews (Rice - Biochemistry)
Prof. Lydia Kavraki (Rice - Computer Science)
Prof. Gustavo Scuseria (Rice - Chemistry)
Prof. Kurt Kremer (MPIP Mainz)
Prof. Mauro Maggioni (Duke - Math)
Graduate Students and
Postdoctoral Positions
Available
$$ NSF (CAREER CHE , CCF , CNS )
$$ Texas Advanced Technology Program ( )
$$ Norman Hackerman Welch Young Investigator Award
$$ Welch Foundation C-1570
$$ Hamill Innovation Award