Protein folding mediated by Protein folding mediated by solvation: Watersolvation: Water

expulsion and formation of the expulsion and formation of the hydrophobichydrophobic

core occur after the structural core occur after the structural collapsecollapse

Max ShokhirevMax Shokhirev

BIOC585

December 2007

Margaret S. Cheung, Angel E. Garcı´a, and Jose´ N. Onuchic

Department of Physics, University of California at San Diego Received 11/26/2001

Energy Landscape/Funnel Energy Landscape/Funnel TheoryTheory

•Levinthal paradox1:

•Statistically, it would take 1030 seconds for proteins to sample all possible 3D conformations in a random manner.

•In reality the number of allowed conformations is considerably smaller since folding follows the path of least energetic frustration.

http://www.lsbu.ac.uk/water/images/wetsurf.gif

1) C. Levinthal, J. Chem. Phys. 65, 44 (1968)

Energy Landscape/Funnel Energy Landscape/Funnel TheoryTheory

• Traditionally we can apply this model to protein folding if the energy funnel for the protein is relatively smooth. – Fast folding– Simple folding mechanism– Independent folders

A concern…A concern…

• What about solvent effects?– Solvent effects are incorporated implicitly in

previous energetically unrestricted models– This means that (de)solvation effects of the

hydrophobic core are not taken into consideration in the potentials.

Protein (De)solvationProtein (De)solvation

• Hilson et al. showed that forcing water into the hydrophobic core of ß-protein leads to increased folding times1,2.

• Hummer et al. calculated the effect of solvation on free-energy of simple alkane molecules, and that the PMF between two methane-like particles exhibits two minima3:– Van der Waals distance between the

particles– Solvent separated minimum distance

1) Hillson, N., Onuchic, J. N. & Garcı´a, A. E. (1999) Proc. Natl. Acad. Sci. USA 96, 14848–14853.2) Garcı´a, A. E., Hillson, N. & Onuchic, J. N. (2000) Prog. Theor. Phys. Suppl. 138, 282–291.3) Hummer, G., Garde, S., Garcı´a, A. E., Paulaitis, M. E. & Pratt, L. R. (1998) Proc. Natl. Acad. Sci. USA 95, 1552–1555.

Can we incorporate desolvation?

A Minimalist Model for A Minimalist Model for Water-Mediated InteractionWater-Mediated Interaction

Native ContactsNative Contacts Pseudo ContactPseudo Contact

No ContactNo Contact

• Gō-like potential was used– only attractive interactions are assigned

to the native contacts (bond, angle, dihedral, LJ, electrostatic, and etc.)

– repulsive interactions are assigned to the nonnative contacts (desolvation potential)• Two possible contacts for non-local

interactions

A Minimalist Model for A Minimalist Model for Water-Mediated InteractionWater-Mediated Interaction

Multicanonical Sampling

• Adding non-native interaction perturbs the energy funnel.– No longer energetically unfrustrated since desolvation

barrier is relatively high.

• Cononical sampling rarely samples energies high enough to cross local energy barriers since energy comes from normal distribution.

• Instead use a uniform energy distribution function that allows for frequent high energies, and then simply “fix” the data at the end (Multicanonical).

Q and “pseudo” QQ and “pseudo” Q

• Q– Folding parameter used to quantify native

contacts (How close are we to the “native” form?)

• Pseudo Q– Folding parameter used to quantify solvation

contacts (What is the degree of solvation?)

• Normalized

Applying the model to the SH3 Applying the model to the SH3 family of proteinsfamily of proteins

http://www.answers.com/topic/1shg-sh3-domain-png

Free Energy vs Q and pseudo QFree Energy vs Q and pseudo QHigh Free EnergyHigh Free Energy

Low Free EnergyLow Free Energy

Figure 2B

High Free High Free EnergyEnergy

Low Free Low Free EnergyEnergy

Figure B,E

Red = nativeRed = nativeBlue = Blue = Water contactWater contact

Figure 2B-E

Two step folding process…Two step folding process…• First step involves a structural

collapse toward a nearly native ensemble (τ1). – Mediated by the expulsion of 23

water molecules from the diverging turn and distal loop.

Two step folding process…Two step folding process… • Second step involves water

expulsion from the hydrophobic core (τ2). – Mediated by the cooperative

expulsion of 17 water molecules

Cooperative Water Expulsion from Cooperative Water Expulsion from Hydrophobic CoreHydrophobic Core

Figure 2C

Specific Heat ComparisonSpecific Heat Comparison

Conclusions…Conclusions…• Folding process of SH3 protein has two steps

– structure-search collapse to a nearly-native ensemble

• Corresponds well to experimental data1,2

• Insights into general folding mechanism

– “desolvation” step

• This can be achieved using a minimalist model – Gō-like model with a“desolvation” feature in the

tertiary contacts pair potential – multicanonical sampling required.

1) Zhang, O. & Forman-Kay, J. D. (1997) Biochemistry 36, 3959–3970.2) Mok, Y.-K., Kay, C. M., Kay, L. E. & Forman-Kay, J. (1999) J. Mol. Biol. 289, 619–638.

Thank you…Thank you…

“Protein folding mediated by solvation: water expulsion and formation of the hydrophobic core occur after the structural collapse.”

Cheung MS, García AE, Onuchic JN. Proc Natl Acad Sci U S A. 2002;99(2):685-90.