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).

May 15, 2012 Meeting

Our stated goal ...

Topic: Energy transduction & use via molecular machines - pumping/transport, coupled reactions.  Cells use a set of closely related non-equilibrium mechanisms to get things done.  We want to understand the (simple) underlying kinetic mechanisms and discuss a few examples.

Reading (see References): Read about active transport in your favorite book.  Some choices:

• Alberts, Ch. 11
• Baby Alberts, Ch 12
• Berg, Ch 13, Section 14.1

Meeting summary - Tues, May 15 meeting

We attempted to address the question, “How does driven (coupled) transport work?”  Thus, for example, how can a difference in ion concentrations across a membrane be used to drive the flow of some small molecule across that membrane? 

Our discussion focused around Fig. 13.11 of Berg which shows a putative cycle of states for coupled transport.  The key element in the cycle is the coupling of binding and conformational change.  From a physics point of view, a cycle appears to be reversible, so it is necessary to understand how a cycle can be driven.  In our discussion, we used equilibrium as a reference point.  In equilibrium there is equal flow in both directions around a cycle and so no active pumping can occur.  But if a (non-equilbirium) uni-directional  flow can be added at any point in the cycle, the cycle will be driven in the direction of  that flow.  (Here flow refers to flow through the space of states, which typically also will imply flow of matter.)

Our abstract discussion of cycles suggested that there is no reason why the same basic description could not be used to explain both “symporters”  and “antiporters” – that is, where the physical flow of the driven species is in the same direction or opposite that of the driving species.

We also discussed how a uni-directional chemical reaction (e.g., hydrolysis of ATP) could be used for active transport if it can be coupled to a suitable conformational change in a transporter.  A cycle related to that of Berg Fig. 13.11 can be drawn.  In principle, any “activated” (out-of-equilibrium) molecule/carrier can be used to drive transport.

Our discussion did not probe the structural mechanisms by which binding events can be couple to conformational changes suitable for transport.  Hopefully we will cover this next time.

April 18, 2012 meeting

BIOPS Weds 4/18/2012 meeting

Here was the original plan:

Topic: Comparative energy production in bacteria, plants, animals (roughly)

Reading (see References):

• Mid-level (start here): Baby Alberts [Alberts-2004] Ch 14 or Berg [Berg-2002] Ch 18.
• Does anyone have a recommendation for bacteria?  Ch 14 of Harris [Harris-1995] has some info.
• Most technical: Your favorite bioenergetics book, perhaps [Harris-1995] DA Harris, Bioenergetics at a glance or [Nicholls-1992] DG Nichools and SJ Ferguson, Bioenergetics. Any biochemistry book will have chapters on oxidative phosphorylation, photosynthesis, etc -- e.g., [Berg-2002].  Also fat Alberts [Alberts-2002] Ch 14. 
• General: Keep on reading Harold, Way of the Cell

In the end, we did some comparative study of different types of organisms, but our main focus was on common/general physical mechanisms of energy "production".  Of course, energy is never produced but really transduced -- converted from one form to another.

Here is a summary of what we discussed.  (Those who attended were rewarded with fresh donuts from Peace, Love, & Little Donuts!)

In common among all cell types

• Use of ATP as primary energy currency
• ATP produced by F1F0ATPase (most cells)
• ATP synthesis driven by proton gradient (difference in proton concentrations) across a membrane
• Proton gradient produced by redox processes starting from ‘high energy electron’ carriers
• Use of ‘activated carriers’ (see below), which are molecules that store free energy under cellular conditions

Differences among cell types

• Mechanisms for pumping protons
• Carriers of high-energy electrons
• Krebs/citric acid cycle produces electron carriers to maximize energy extraction from glucose
• Original source of energy – bacteria are much more flexible in getting food
• Light, for plants and photosynthetic bacteria
• Hydrocarbons, for animal cells (originally produced by other cells)
• Other sources for extreme-philes??
• Aerobic respiration, where molecular oxygen is the ultimate receptor of high-energy electrons, is much more efficient than anaerobic respiration.

Activated carriers (common among cell types)

Definition: a “kinetically stable” molecule (reactant) that is out of equilibrium with respect to a reaction it can undergo to form product(s); examples: ATP → ADP + Pi, NADH → NAD+ + e-; the carrier is out of equilibrium in that there is a dearth of product relative to reactant compared to what would hold in equilibrium under cellular conditions; cell maintains ‘activation’ of the carrier by continually producing it and limiting the overall amount reacting by the amount of catalyst (enzyme) available.  See Berg p. 383, 386]

• ATP (and perhaps other carriers) not only is kinetically stable for a long time (days) but is highly activated (stores a lot of free energy, being far from equilibrium) when both ATP and ADP are at similar concentrations.  See Harris p. 20.
• Components of the redox chain can be considered activated carriers, wherein typical reactions involve the gain/loss of protons and electrons
• In eukaryotic cells, both sugars and fats are converted to the common activated carrier acetyl CoA, which is used to drive the citric acid cycle and ultimately the proton gradient.

Proton pumping (common among cell types)

We reviewed several mechanisms of proton pumping across membrane.  All are driven by a net flow of electrons from higher to lower free energy.  Terminology here is non-standard.  See section “electron-transport chains and proton pumping” in Ch. 14 of baby Alberts.

• Implicit/virtual proton pumping.  A trans-membrane protein catalyzes two nearly simultaneous reactions at its two ends.  At one end, a carrier is catalyzed to release a proton and electron.  The proton is released into solution and the electron is ‘conducted’ by tunneling through the protein.  At the other end, the electron joins with a proton from solution and attaches to a different (lower free energy) carrier.  See Harris Ch. 24.
• Looping.  Quinone/quinol (Q/QH2) species are mobile within the membrane and can shuttle protons from one side to the other using redox reactions similar to those just described.  Q species must loop back and forth.  See Harris Ch 24.
• Direct proton pumping via alternating access mechanism.  See Harris Ch 25.

Improving our forum - suggestions & to-do list

Any ideas for making this better.

My initial thoughts
* Compile topic-specific reading lists (book-and-chapter or paper).  This would be ongoing and not just what was assigned the first time.

PHYSICAL PRINCIPLES OF CELL BOLOGY

This thread is meant to include key principles we have gleaned.

ENERGY STORAGE - The cell stores energy not by having "fuels" which are "burned" but rather by maintaining processes (reactions/flows) out of equilibrium.  A key example is that [ATP] is maintained much higher than the value to which it would equilibrate given the ADP and Pi in the cell.  ATP is an example of an 'activated carrier', but there are numerous others.  Besides carrier molecules, energy is also stored by out-of-equilibrium gradients across membranes -- such as of ions and protons. In fact, ATP synthesis is driven by non-equilibrium proton [H+] concentrations maintained across the appropriate membrane.

ENERGY TRANSDUCTION - Energy is regularly converted among different carriers and 'devices' in the cell.  A sequence of activated carriers with high-energy electrons create a proton gradient, which in turn is used to generate ATP.  The constant downhill flow of (free) energy - from original source (food or light) to cellular waste - keeps the cell operating in an orderly way.  The flow of energy provides the power for information to flow in a single direction -- e.g., from a signal outside the cell to the nucleus.