Review session this Wednesday 10/11 from 7-9 pm in Lawrence 115

Some cleanup

The stability of a structure is determined by many offsetting terms

• Folding is driven by:
  • Favorable hydrogen bonds (helix makes hydrogen bonds) (enthalpy)
  • Hydrophobic effect (a helix has a surface area less than that of the unfolded state) (entropy)
• Folding is opposed by:
  • Competing hydrogen bonds with water (enthalpy)
  • Loss of conformational entropy

The experimental value for $\Delta H^{\circ\prime}$ is $-41\ kJ\cdot mol^{-1}$. Assuming $8$ hydrogen bonds actually form and that the hydrogen bonds are the main contribution to $\Delta H^{\circ\prime}$, what is each hydrogen bond “worth” in the helix? Why might this be different from the value we used above?

$-41/8 = -5.1\ kJ\cdot mol^{-1}$

Less than $-20\ kJ \cdot mol^{-1}$ because these hydrogen bonds compete with water hydrogen bonds

Key point. You have to consider both unfolded and folded

$\Delta H^{\circ \prime} = \color{blue}{H^{\circ \prime}_{prot-prot}} - \color{red}{H^{\circ \prime}_{prot-water}}$

$\Delta H^{\circ \prime} = \color{blue}{8 \times -25.1} \color{red}{-8 \times -20.0} = -41 \ kJ\cdot mol^{-1}$

$-41 \ kJ\cdot mol^{-1}$ is correct enthalpy to use, not $-5.1$ like I did Friday

How does this play out for $\Delta S$?

From calculation

$\Delta S^{\circ \prime} = Rln(N_{helix}/N_{unfolded})$

$\Delta S^{\circ \prime} = -0.22\ kJ \cdot mol^{-1} K^{-1}$

From experiment

$\Delta G^{\circ \prime} = \Delta H^{\circ \prime} - T \Delta S^{\circ \prime}$

$\Delta G^{\circ \prime} - \Delta H^{\circ \prime} = -T \Delta S^{\circ \prime}$

$\frac{\Delta G^{\circ \prime} - \Delta H^{\circ \prime}}{-T} = \Delta S^{\circ \prime}$

$\Delta S^{\circ \prime} = \frac{-3.5 --41}{-300} = -0.125\ kJ \cdot mol^{-1} \cdot K^{-1}$

It is less entropically unfavorable to collapse helix than you might expect because of the hydrophobic effect

Key point. You have to consider both water and protein

$\Delta S^{\circ \prime}_{helix} = \color{blue}{S^{\circ \prime}_{helix}} - \color{red}{S^{\circ \prime}_{unfolded}}$

$\Delta S^{\circ \prime}_{hphobe} = \color{blue}{S^{\circ \prime}_{folded\ surface}} - \color{red}{S^{\circ \prime}_{unfolded \ surface}}$

$\Delta S^{\circ \prime} = \Delta S^{\circ \prime}_{helix} + \Delta S^{\circ \prime}_{hphobe}$

$-0.125 = -0.22 + \Delta S^{\circ \prime}_{hphobe}$

$0.095 \ kJ \cdot mol^{-1} \cdot K^{-1}= \Delta S^{\circ \prime}_{hphobe}$

Hydrophobic effect makes favorable entropic contribution to folding

Where does $S = Rln(N)$ come from, anyway?

Proline and glycine are both known as "secondary structure breakers"

Why might this be the case?

Proline uses the backbone nitrogen as part of its R-group. No hydrogen bonds + kink

Glycine has a H for an R-group. It's floppy and entropically expensive to immobilize

Disulfide bonds form between ___________ residues. These _________ [covalent|ionic|hydrogen bond] interactions ____________ [stabilize|destabilize] protein structure

Disulfide bonds form between cysteine residues. These covalent interactions stabilize protein structure

The Protein Folding Problem

2017-10-09

Conceptual goals

• Understand that the folded structure of the protein is the free energy minimum for the chain

Skill goals

• Manipulate thermodynamic equations describing protein stability to calculate contributions of different forces
• Reason correctly about interactions by thinking correctly about both sides of a reaction coordinate

• A 100 amino acid protein will have 198 peptide bonds. If each bond can take 3 possible conformations, how many conformations are there?
• If each bond rotates every nanosecond, how long would it take for the protein to sample all possible structures?

• $3^{198} = 3\times 10^{94}$ conformations
• $3\times 10^{94}\ conf \times \frac{1 \times 10^{-9} \ s}{conf} = 3 \times 10^{89} \ s$
• $9 \times 10^{77} years$

Real proteins fold in milliseconds

What does this tell us about protein folding?

Folding does not proceed by random search.

Proteins fold by a biased search.

Previous steps set up next steps

• Local elements fold (like secondary structure) fold
• These folded elements change environment of rest of chain
• Other local parts of the structure fold
• Settles in to a final 3D fold

This is known as a "folding funnel"

We can follow folding directly with Hydrogen-Deuterium Exchange Mass Spectrometry

We can follow structural intermdiates with molecular dynamics simulations

We can design proteins from scratch

George Rose is a well-known protein folder at Johns Hopkins

He is giving a seminar at 2 pm today, in Willamette 240.

Fun fact: cookies and coffee at 1:45

Fun other fact: George calls funnels the F-word

Summary

• To understand biochemical reactions, you need to account for both sides of the reaction
• To understand biochemical reactions, you need to account for biomolecules and water
• Proline, Glycine and Cysteine are special amino acids, altering secondary structure (Pro,Gly) or forming covalent bonds (Cys)
• Proteins do not fold randomly, but follow a "folding funnel" to the lowest energy state