Thermo: A brief Intro I.Microstates and Global States II.Probability III. Equilibrium IV. Free energy surfaces

Microstate Microstate: Specify the molecule are uniquely as possible In a quantum description this could include: Electronic state Vibrational and rotational quantum numbers Spin states Position of all atoms We do CLASSICAL descriptions positions of all atoms defines a microstate (defer discussion of surroundings)

Global Global: A (user-defined) sum over a set of microstates Often a sum over sets that cannot be distinguished somehow: due to experimental limitations Due to similarity of structure Due to similarity of function Common uses: Folded vs. unfolded Folded vs. unfolded vs. intermediate different functional states

Population: Microstate When we have multiple states, they appear in different populations depending on their energies: N. B. The bottom is the canonical partition function. Assuming near equilibrium and a large system Each microstate has its own population. Notes: This can be proven; those of you in physics/physical chemistry probably will do so or have done so already. This is also the high T limit of the fermi-dirac and Bose-Einstein distributions

Population: Global When we have multiple states, they appear in different populations depending on their energies: Each global state has its own sum over microstates. This is sometimes represented by, Where  j is now considered as a global state energy.

Probability and the partition function When we have multiple states, they appear in different populations depending on their energies: The bottom is the canonical partition function, Q.

Equilibrium We assume equilibrium, What is equilibrium? Does equilibrium mean stasis? {pressure and temperature over ~200ps in ~130,000 atoms system}

Fluctuations Different physical properties fluctuate differently {pressure and temperature over 10ns in ~130,000 atoms system} Fluctuations (in macroscopic quantities) occur during equilibrium The fluctuation-dissapation thm says that we can perturb a structure, and that relaxation from that perturbation is equivalent to relaxation from the same fluctuation

Fluctuations Larger systems: lesser fluctuations: ~16,000 atoms vs. ~130,000

(Gibb’s) Free Energy The most fundamental quantity in biological stat mech: Different reps:  G=-K B TN ln Q  G=-RT ln K G=H-TS ->  G=  H-T  S

Free Energy Surface Free energy as a function of something Tells us about minima, and saddle point (transition points) In principle, given a free energy surface we can deduce the behavior of the system over time Erogodic principle: Given sufficient times, all microstates will be sampled regardless of initial conditions Proteins generally are regarded as having special free energy surfaces

Free Energy Surface Proteins generally are regarded as having special free energy surfaces folding funnel with a well-defined global minima This “minima” is a global state that may consist of substates that are well-connected, or not. Still an open question

Flexibility Experiment: the thermodynamics of HEWL and a mutant missing a disulfide bond were studied with scanning microcalorimetry. Both proteins have the same enthaply of unfolding, and had “two-state” behavior, but there is a difference in the entropy of unfolding. Where does the entropy change come from? The x-ray structures show essentially the same structures and interactions.