Protein Folding: Questions and food for thought

1. Protein Folding: Questions and food for thought Nozomi Ando Journal Club, 7.10.03

2. Outline • What are the qualities of a polymer? • What is a coil-globule transition? Hydrophobic effect? • Is protein denaturation a globule-coil transition? • Challenging the hydrophobic model: What is the Kauzmann paradox? • What are protein thermodynamics? • What is the molten globule state?

3. Ideal Polymer Coil • Proteins are linear polymers made of amino acids. Random walk distribution for ideal polymer chain: Pn(R) = [3/2pnL2]3/2exp(-3R2/2nL2) L = Kuhn length, n = # Kuhn steps, R = end-end vector RMS end-to-end distance for ideal polymer chain: <R2> 1/2 ~ n1/2 L Hooke’s Law: elasticity -TS = -kT ln W = -k (-3R2/2nL2) + const

4. Real Polymer Coil • Excluded volume effect (collisions): repulsion at small distances RMS end-to-end distance for self-avoiding random walk: <R2> 1/2 ~ n6/5 • Solvent effects: balance of repulsive effects and attractive effects (entropic elasticity) F = Urep – TS • We can immediately see how temperature is involved in ‘solvent quality’ (affinity of the polymer for the solvent).

5. Solvent Effects: Coil-Globule • In ‘good solvent’, polymer interacts with solvent. • In ‘bad solvent’, polymer prefers to interact with self. • At q point, polymer acts ideal. T > q T = q T < q Solvent quality decreases Images from: “Giant Molecules” software (Grosberg).

6. More Interactions: Nearing Folding • Monomer interaction: attractive to repulsive (red to violet). • ‘Hydrophilic’ shell (violet), ‘hydrophobic’ core (red). Cool Images from: “Giant Molecules” software (Grosberg).

7. Hydrophobic Model of Globular Proteins • Observation: many proteins have hydrophobic core. • Hydrophobic core stabilizes protein globule in water? Kliman’s experiment: solubility of 4-octanone in water as function of pressure. Kato’s experiment: volume of NIPA gels with pressure near critical T. Result: solubility (volume) increases to a max value and then decreases again with pressure. • But we observe that proteins do not refold at high pressures. We can’t explain protein unfolding with hydrophobic model.

8. Protein Folding vs. Heteropolymer Collapse • Random heteropolymer globule has some order but still has many conformations. • Protein globule exists in particular globular state (very small fluctuations). • The native protein is a frozen globule. So can we say… • the hydrophobic effect cannot be the major stabilizing force for a frozen globule? • there is cooperative effect of very specific interactions for proteins?

9. N U 2-State Equilibrium Protein Thermodynamics • Observe: heat denaturation, cold denaturation, pressure denaturation. Native protein in closed area of p-T space. • Hawley’s folding-unfolding theory: DG = GU-GN DG = DG0 – DS0(T-T0) – DCp[(T-T0)+ln(T/T0)] + DV0(p-p0) + Db/2(p-p0)2 + Da(p-p0)(T-T0) 2nd order expansion gives ellipse in p-T space. Even with third order terms, basic shape is ellipse. (Smeller)

10. DS=0 P DV=0 T Thermodynamic Changes Cp = (dH/dT)pkT Cp = T<S-<S>>2 heat capacity b = -1/V(dV/dp)TkT bV= <V-<V>>2 compressibility a = -1/V(dV/dT)pkT aV = <SV-<S><V>>2thermal expansion At high T (low P), solvent conditions become good – protein released from tight interactions. Loss in energy compensated by increase in polymeric entropy. DS>0. A high P (low T), we expect DV<0. Loss in entropy associated with hydrophobic interaction compensated by efficient packing. Drawn from Smeller (BBA 2002)

11. N U MG Molten Globule • Observe: molten globule (partially unfolded protein) has some order (secondary, tertiary) – preserved core with loose side chains; molten globule is an intermediate of native and unfolded states. • Is the molten globule a random (non-frozen) globule? • Is the molten globule a distinct phase? http://www.csn.ul.ie/~stephen/reports/unfolding.html