A Hitch-Hiker’s Guide to Molecular Thermodynamics What really makes proteins fold and ligands bind Alan Cooper Amsterdam: November 2002 Chemistry Department Joseph Black Building, Glasgow University Glasgow G12 8QQ, Scotland

“Concepts and tools for medicinal chemists” + 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 - T  S 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

Both enthalpy and entropy are integral functions of heat capacity... ….from which  G =  H - T.  S So  C p 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  C p is the key - if we can understand heat capacity effects, then we can understand everything else. And  C p 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-T  S  G=-RTln(K) Δ G must negative for a reaction to take place. Δ G = 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 Δ G is 0; but lets pretend…) If we make G=18.6 for [A] (again, this is nonsence because we cannot know G, only Δ G) (so, G is 1.38 bigger for [A] which means better for [B]) then [B] becomes 10 times bigger than [A].

 G=  H-T  S 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-T  S Good for Δ S: Entropy of water. Bad for Δ S: Entropy of protein.