A Hitch-Hiker’s Guide to Molecular Thermodynamics

What really makes proteins fold and ligands bind

Alan Cooper

Amsterdam: November 2002

Chemistry DepartmentJoseph Black Building, Glasgow UniversityGlasgow G12 8QQ, Scotland

“Concepts and tools for medicinal chemists”

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What makes this protein fold, and what controls its

stability ?

“Concepts and tools for medicinal chemists”

+

What makes this protein fold, and what controls its

stability ?

What are the thermodynamic forces responsible for ligand binding ? Can we use them to

design better ligands ?

“ Concepts and tools for medicinal chemists”

Microcalorimetry: analytical uses for

biomolecular interactions and

stability

Thermodynamic homeostasis,

compensation; hydrogen-bonded

lattices…

...the role of water in biomolecular

interactions

There is a natural tendency for all things (even atoms & molecules) to roll downhill - to fall to lower energy.

H wants to be negative

This is opposed (at the molecular level) by the equally natural tendency for thermal/Brownian motion (otherwise known as “entropy”) to make things go the other way…

…and this effect gets bigger as the temperature increases.

T.S wants to be positive

A bluffer’s guide to Thermodynamic Equilibrium…

Thermodynamic Equilibrium, expressed in terms of the Gibbs Free Energy change, reflects just the balance between these opposing tendencies…

G = H - TS

Equilibrium is reached when these two forces just balance (G = 0).

The standard free energy change, G, is just another way of expressing the equilibrium constant, or affinity (K) for any process, on a logarithmic scale…

G = -RTlnK

H(T) = H(Tref) + Tref

T

Cp .dT

S(T) = S(Tref) + Tref

T

(Cp /T).dT

Both enthalpy and entropy are integral functions of heat capacity...

….from which G = H - T.S

So Cp is the key - if we can understand heat capacity effects, then we can understand everything else.

Calorimetric techniques...

• Differential scanning calorimetry (DSC)

• Isothermal titration calorimetry (ITC)

• Pressure perturbation calorimetry (PPC)

So, what is the role of water?

So Cp is the key - if we can understand heat capacity effects, then we can understand everything else. And Cp is largely determined by the interactions between water and the macromolecule(s).

In figure b many more waters are free than in a. And free waters are happy waters!

G=H-TS G=-RTln(K)

Δ G must negative for a reaction to take place. ΔG = 1.38 kCal/Mole means a factor 10 difference in an equilibrium.

Example:A <==> B [A] = [B] G=17.2 for [A] and for [B], so

we have a 50/50 equilibrium (it is impossible to know that G=17.2, we can only know that ΔG is 0; but lets pretend…)

If we make G=18.6 for [A] (again, this is nonsence because we

cannot know G, only ΔG) (so, G is 1.38 bigger for [A] which means better for [B]) then [B] becomes 10 times bigger than [A].

G=H-TS

Good for Δ H: 1) Contacts in protein (H-bonds, Van der Waals

interactions, salt bridges, aromatic stacking, etc).2) H-bonds between water molecules

Bad for Δ H: 1) H-bonds between water and part of protein that gets

buried.

G=H-TS

Good for Δ S: Entropy of water.

Bad for Δ S: Entropy of protein.