Summary of Aug 15, 2012 Meeting

Here were the original goals and reading ...

Topic: Kinetic models for both ATP synthesis and driven rotary motion in the F1 domain of ATP synthase.  This should round out our incomplete discussion from last time.

Reading

• Read basic ideas of “Energy Conversion by Molecular Motors Coupled to Nucleotide Hydrolysis,” by Lipowsky, Liepelt and Valleriani http://www.springerlink.com/content/7m3611514t2xv0pn/
• Section 18.4 in Berg on the ATP synthase mechanism.
• Regarding Fig. 18.32 in Berg (http://www.ncbi.nlm.nih.gov/books/NBK22388/figure/A2538/), see worksheet below get warmed up for kinetic models.

Meeting Summary - Aug 15, 2012

I believe we succeeded in achieving several goals.  We constructed relatively precise kinetic models that seemed to provide good insight into the physical mechanisms of both mechanical-force-driven ATP synthesis and high-ATP-driven rotary motion in an F1-ATPase-like machine.  Models will be shown below.  We also considered the advantages of a three-domain rotary machine in comparison to one with just two domains.  (Although a two-domain machine in principle should be capable of synthesizing ATP with mechanical driving, it does not appear capable of uni-directional rotary motion because clockwise and counter-clockwise motion are not kinetically distinguishable.)

As a warm-up, we constructed a cycle comparing ATP hydrolysis/synthesis in solution and the same reaction catalyzed by an enzyme.  Thermodynamic consistency (zero sum of free energy changes around cycle) shows that the ratio of forward and reverse catalytic rates is determined by the relative binding strengths of the enzyme to ADP-Pi and ATP. Perhaps more precisely, the relative catalytic rates and the binding strengths are manifestations of the same property - stronger binding necessarily is favored catalytically.

Some models for the F1 ATPase are shown below.  Several points should be borne in mind:

• Following Berg's notation, we assume three states:
• O = open, the only state capable of (un)binding.  ADP binding strongly favored.
• T = tight, the only catalytically efficient/fast conformation, "likes" both ADP and ATP such that [T-ADP-Pi] = [T-ATP]
• L = loose, requires specification to be consistent with the model
• The left-most and right-most states are the same: hence a rotary cycle
• The model should permit spontaneous rotation at high [ATP].
• Importantly, because all states are likely to be occupied, the thermodynamics and kinetics of any transition SHOULD BE CHARACTERIZED BY THE SUM/AVERAGE OF ALL THREE CONCURRENT TRANSITIONS.
• Please note carefully the arrow notation used.  Broad, free energy arrows point in the direction that is favored (if any) with a length proportional to Delta G.  Thus, thermodynamic consistency is easily checked by using arrow lengths and directions.  Most transitions are considered to be slow on the timescale of rotation: only filled arrows indicate fast (always reversible) transitions.

[Thanks to all our discussants and to Rory Donovan for catching errors in early models.]

The model above corresponds reasonably with Section 18.4 in Berg on the ATP synthase mechanism.  The model below, although perhaps functional in principle, causes rotation in the wrong direction compared to F1-ATPase.