Summary of April 23, 2013 meeting

What we planned to discuss:

Topic: Kinetic Proofreading - how the cell uses free energy to increase fidelity of translation.  We'll study a sample mechanism describing the exchange of free energy for information.

Reading: Uri Alon, An Introduction to Systems Biology, Chapter 9

Meeting Summary
As planned, we followed Uri Alon's discussion of kinetic proofreading.  In brief, Alon shows how the presence of an irreversible process can increase fidelity of translation well beyond what is expected from equilibrium binding-affinity arguments.  Alon correctly points out that an "irreversible" process requires energy input (though in reality no molecular process is truly irreversible - it's just that reverse events are highly unlikely).  In other words, the cell expends free energy to gain fidelity or information.  Personally, I think it's incredible to get some insight into this at the molecular/mechanistic level.

Because Alon's discussion is vague on the molecular players and the means of energy input, we augmented our discussion with the discussion of translation in big Alberts (Ch 6, Section on "From RNA to Protein").  The following sketches give insight into what we learned and fill out some details omitted from Alon's schemes:

Next Meeting: Tuesday, April 23, 2013 at 3:00 in 3065 BST3 (conference room)

Topic: Kinetic Proofreading - how the cell uses free energy to increase fidelity of translation.  We'll study a sample mechanism describing the exchange of free energy for information.

Reading: Uri Alon, An Introduction to Systems Biology, Chapter 9.  Contact me if you need a copy of the necessary pages.

More information: http://biops-pgh.blogspot.com/

Meeting Summary - Tuesday, Feb 19, 2013

What was scheduled ...

Topic: Free energy transduction via molecular machines.  Review of how free energy is stored and, qualitatively, transduced.  Introductory quantitative analysis of free energy transduction.

Reading: TL Hill, "Free energy transduction and biochemical cycle kinetics," Chapter 1.  This is a classic book, and chapter 1 is essential reading, nicely presented.  The rest of the book is more opaque.  The book is available cheaply in a Dover edition.  Let me know if you will not have access to a copy.

Summary
Hill's first chapter illustrates free energy transduction using a number of simple models.  The models have discrete states and simple first order kinetics - such as (i) a transporter being open to one side of a membrane or the other and being bound to ligands or not or (ii) a cycle involving binding of a substrate, catalysis, and unbinding of the product.  Every model includes one or more cycles because the proteins are re-used.  Hill identifies simple cycles (involving, for instance, binding and unbinding of a single ligand) and more complex cycles (involving, say, multiple species).

The chapter analyzes how free energy is "transduced," or transferred from one form to another.  An example of transduction is when the gradient of one type of molecule (across a membrane) is used to drive the creation of a gradient in another molecule.  Such gradients, which are out of equilibrium, store free (i.e., usable) energy.  The chapter shows that it is the complex cycles, which couple one process to another (e.g., the transport of two types of molecules), that can transduce free energy.  Simple cycles involving a single species only facilitate - really, catalyze - moving from a high free energy non-equilibrium state (e.g., gradient of A across a membrane) to an equilibrium state (matching concentrations of A on both sides of the membrane).  Effective molecular machines are those which have tightly coupled complex cycles and ineffective (i.e., slow) or inoperative simple cycles.

Summary - Tuesday, Oct 2, 2012 Meeting

Here's what we proposed to do:

• Topic: Coupled reactions and synthesis.  Biochemical processes move downhill in free energy: they too must follow the laws of physics.  To see how, we'll explore generic mechanisms of reaction coupling and a few key examples of synthesis powered by that ultimate activated carrier, ATP.
• Reading: Big Alberts, sections on reaction coupling and activated carriers (pp. 81-91 in the 4th ed.), as well as tidbits on DNA synthesis (pp. 239, 242-243), and protein synthesis (p. 339). 

Meeting Summary

We managed to get a pretty concrete sense of how a non-equilibrium (i.e., typical) ATP concentration could be coupled to a bio-synthetic reaction, forcing the latter to proceed in an unfavorable direction.  To that end, we considered in detail an example from Big Alberts Ch. 2, which is representative of some critical biosyntheses:
           A-H + B-OH --> A-B + H20

The cell forces this reaction to proceed in two steps. 
           B-OH + ATP <--> B-Pi + ADP  (fwd rate a, reverse rate b)
           A-H + B-Pi <--> A-B + Pi          (fwd rate c, reverse rate c)
First, ATP is hydrolyzed (very favorable) in a reaction that releases ADP and adds a phosphate group to B, forming a compound we'll abbreviate as B-Pi.  But B-Pi is itself "activated" in being out of equilibrium with more favorable potential products, especially the free form of Pi.  (Regarding activation, see summary April 18, 2012 meeting http://biops-pgh.blogspot.com/2012/05/biops-weds-4182012-meeting-here-was.html)  The release of Pi is then enzymatically coupled to the formation of A-B.

The preceding qualitative explanation can be made more precise by modeling the steady state of the two coupled reactions assuming reactants A-H, B-OH, and ATP are added and products A-B, ADP, and Pi are removed.  Using the rate constants from above, one finds
      d[A-B]/dt = a[B-OH][ATP] - b[B-Pi][ADP],
in terms of the steady-state concentrations.  Our basic question of whether A-B can in fact be synthesized is equivalent to whether the sign of this derivative is positive.  The sign will be positive for a sufficiently large [ATP]/[ADP] ratio.  Of course, "sufficiently large" will depend on the particular system (i.e., all rate constants) - qualitatively, on how unfavorable the synthesis of A-B truly is.

In brief, then, synthesis proceeds by harnessing energy from some carrier, which can be coupled to the desired synthesis in a clever step-wise fashion.

A very interesting example is DNA synthesis during replication, drawing on Ch. 5 from Big Alberts.  In this case, the carrier is the "incoming" nucleotide tri-phosphate itself, which makes sense.  The interesting part is that the need for potential error correction (i.e., removal of an incorrect base and attachment of correct base) actually dictates that replication should occur in the 5' to 3' direction.  As illustrated in a lovely figure in big Alberts (5-11 in my edition), if the other direction were used the phosphate groups of the incoming nucleotide would not be available to power the required attachment.

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.

ATP Synthesis, Qualitatively: Summary of July 17, 2012 Meeting

We discussed both the forward and reverse mechanisms of the F1F0 ATP synthase – i.e., both ATP synthesis and generation of rotary motion from ATP hydrolysis although limited to the F1 domain.  (Previously, Michael Grabe led our discussion of the F0 domain.)  Our discussion was based on the schematic model depicted in Berg’s textbook (http://www.ncbi.nlm.nih.gov/books/NBK22388/figure/A2538/).  While the schematic did provide a lot of qualitative insight, I think most of us felt unsatisfied with the attempt to understand a machine without at least a semi-quantitative basis.  Specifically, we know there are thermodynamically constrained relations among the various rates (for catalysis, binding, and conformational change) that would provide a much more concrete picture.  We will attempt to pursue this approach next time.

Some questions raised that we would like to address:

• What is the importance of the three-fold symmetry?  Would two sub-units be enough?  An initial answer is that only with three subunits can the directionality be ensured in the hydrolysis process.
• What is the minimal kinetic model that can explain ATP synthesis using mechanical force?  Are two subunits sufficient?
• What is the minimal kinetic model need for rotary motion?
• What insights can thermodynamically consistent kinetic models provide?

Meeting Summary - June 26, 2012

Stated Goals

Topic: More on energy transduction & use via molecular machines.  Michael Grabe will attend as a discussion leader.

Reading 

“Energy transduction in ATP synthase,” by Elston, Wang, and Oster.  Nature 391:510-513, 1998.  http://www.cnr.berkeley.edu/~goster/pdfs/FoMotor.pdf

And don't forget to keep on reading Franklin Harold's book. 

Meeting Summary - June 26, 2012 

I thought this was a very exciting meeting because, in previous meetings, we relied on cartoons and kinetic models, but now we explored a truly structural mechanism for ATP synthesis.

Michael Grabe led us through the Oster paper about the F1F0 ATP synthase, which primarily describes the transduction of a trans-membrane proton gradient into rotary motion via the F0 portion of the molecule.  The membrane-sited F0 contains rotor and stator domains.  The rotary motion is generated because Asp residues on the rotor permit or prohibit rotation depending on whether they are protonated.  (Protonation allows rotation because only charge-neutralized Asp's can exit the stator region, which covers only part of the rotor, and enter the hydrophobic membrane environment.)  The rotation is rectified and made uni-directional on average because of the much higher density of protons on the acid side of the membrane: the higher density encourages protonation of some sites over others.


The paper makes other points of interest: (1) The rotation is made quasi-mechanistic, with few backsteps, because a charged residue on the stator (Arg 210) greatly increases the barrier to rotation (in either direction).  (2) The qualitative picture just described is quantified using a Markov-state model which is simulated and apparently is consistent with experimental data.  Prof. Grabe provided a beautiful presentation of this material.

In the bigger picture, it must be understood how this rotary motion drives ATP synthesis in the F1 domain (an issue not addressed in the Oster paper).