An incredibly efficient rotary
molecular motor
in our cells!
Laura Orian
Molecular fluctuations and kinetic processes
Corso di Dottorato in scienze Molecolari
AA 2015-2016
Linear molecular motors: generating movement along a filamentous structure.
Examples are myosin along an actin filament, dynein along a microtubule,
RNA polymerase along DNA.
Rotary molecular motors: generating a torque.
Examples are: bacterial flagellar motor;
F0F1-ATP synthase which comprises two rotary motors, one driven by proton flow
(F0 motor) and the other by ATP hydrolysis (F1 motor) in one molecule.
Rotor and stator are combined in the rotary motor.
The focus of this lecture will be F1 motor.
ATP synthase is ubiquitous from bacteria to plants and animals. It is a membrane-spanning
enzyme that produces ATP using proton flow across the membrane.
F0 is a transmembrane portion
F1 is a protruding globular catalytic moiety
When protons flow through F0 from
top to bottom, ATP is synthesised in F1.
Viceversa when ATP is hydrolysed in F1,
protons are pumped back, from bottom
to top, against an electrochemical
gradient.
HOW IS THE PROTON FLOW THROUGH
F0 COUPLED TO THE SYNTHESISHYDROLYSIS OF ATP IN F1?
F0
F1
The motor enzyme F0F1-ATP synthase of mitochondria uses the
proton-motive force across the mitochondrial membranes to make
ATP from ADP and P (H2PO4-).
AMAZING: in cellular conditions the hydrolysis reaction is favored
by a factor 2x105!
But F0F1-ATP synthase is not a conventional enzyme, which increases
the rate of reaction without shifting the equilibrium position,
but rather a catalytic motor, which can drive a
reaction away from equilibrium by harnessing an external force!
Boyer’s idea (1981): the coupling is mechanical: F0 is a motor driven by
proton flow; F1 is another motor driven by ATP hydrolysis. The two
have a common shaft.
When the free energy obtained from the downward flow of protons is
greater than the free energy of ATP hydrolysis, F0 rotates the shaft in
its genuine direction and F1 is forced to rotate in its reverse direction,
and thus ATP is synthesised.
Boyer’s idea came from the experiment:
F1 can be isolated and it only hydrolyses ATP. Hence this isolated
enzyme is called F1-ATPase.
F1-ATPase
It consists of five type of subunits in the stoichiometry of 3 3 .
 3  3  suffice for ATPase activity (and for rotation).
Each  subunit contributes one catalytic site for the synthesis-hydrolysis of ATP;
the catalytic sites reside at the interface between  and  subunit. On each  three
non catalytic nucleotide binding sites exist.
 subunit is indespensable for the catalysis, but lacks three fold symmetry. Thus to interact
with the three  subunits it must rotate.
This revolutionary idea was supported in 1994 by Walker with a three dimensional
structure.
red 
green 
black 
Setting up experiments to prove the rotation
•Cross-linkage of a residue on  to one .
•Then cutting the link the enzyme was allowed to catalyze ATP
hydrolysis (F1: Duncan 1995) or synthesis (F1F0: Zhou 1997).
•After that the residue was again crosslinked to one .
This second crosslinking was found to be any of the three  subunits.
•Attaching a fluorescent dye to  (Haesler 1998):
the orientation of the fluorofore was detected with time resolved
polarization measurements during ATP hydrolysis.
But….the sense of rotation was not assessed univocally!
Single molecule approach: To prove that F1-ATPase is a rotary
motor that consistently rotates in a unique direction one can
image the rotation of a single F1 molecule under a microscope
(Noji 1997, Yasuda 1998).
EXPERIMENT:
The subcomplex 3 3  derived from a thermophilic bacterium was
fixed on a glass surface through His residues at the bottom of the
 subunits. A µm long actin filament was attached through the
protruding portion of  above the hexamer. The actin was labelled
to be fluorescent and oberved under a fluorescence microscope.
When ATP was infused, the filament began to rotate!
Noji 1997, Yasuda 1998
Some filaments made hundreds of rotations counterclockwise without reversal.
Most of the filaments did not rotate because:
1. The filaments stick to the surface (F1 is only 10 nm thick and the actin is 1µm).
2. F1 ATPase tends to be inhibited by its reaction product MgADP (see biochemical section)
3. Protein molecules on a surface are often damaged or denatured.
The actin rotates like a propeller, the  subunit slides against the 3 3 stator
over unlimited angles.
F1ATPase is indeed the smallest rotary motor (10 nm)!
Other studies demonstrated that  is likely part of the rotor and  of the stator.
The rotation was always found counterclockwise.
Very important: reducing ATP concentration the rotation becomes stepwise (120 deg)!
Mechanical properties of the F1 motor
To rotate the actin filament at the observed speed (40 rad s-1) the motor has to
produce an enormous torque, i.e. 40 pN nm.
N  
4 3
L
3

  L

ln

0
.
447
  2r 

  

L and r are the length and
radius of the filament.
 friction coefficient
F1 produces a constant torque.
The points fall on the calculated lines
assuming a constant torque (straight line)
The range is 20nM – 2mM (ATP conc)
and 0.1-10 rev s-1.
At low ATP conc low rate of ATP binding
With longer actin  higher friction
The mechanical work done in a 120 deg step is:
Torque (40) x 2/3 rad (120 deg)= 80 pN nm
This value is close to the free energy obtained from hydrolysis of one ATP molecule in
intracellular conditions.
G  G0  kBT ln
[ ADP][ Pi ]
[ ATP]
G0 (-50 pN nm) standard change per molecule for ATP hydrolysis at ph 7.
KBT 4.1 pN nm at room temperature
[ATP] and [Pi] are 10-3 M
G changes from -100 pN nm to -90 pN nm when [ADP] changes from 10 µM
to 100 µM.
The F1 motor appears to work at an efficiency close to 100%.
Individual steps for a 1µm filament
rotating at 0.2 µM ATP concentration are
superimposed. The thick cyan line shows
the average. The speed is approx constant.
Red and pink are in rapid succession
showing the linearity.
Constant speed implies a constant torque
over the stepping angle 120 deg.
The slope indicates that the torque is about
44 pN nm, which, if derived form an angle-dependent
potential energy
V
 N

The fact that the motor produces a constant torque and constant work per step,
irrespective of the load (actin length), speed and [ATP] concentration is rationalized
if ATP binding and hydrolysis produces the rotational potential!
IMPORTANT: this experimental potential is an effective potential: the chemical state
of bound nucleotides changes while the motor makes one step and thus V does not
correspond to a single chemical state and there will be several chemical states during one
mechanical step, each with a different potential.
The torque of 44 pN nm is at submicromolar ATP; in tri-site regime (2mM ATP) a
similar torque of 40 pN nm is deduced!
Possible mechanisms of rotation
Analogy with a DC (direct current) motor
The motor is powered with unidirectional current; continuous anticlockwise rotation
is assured by three pairs of switches on the shaft (commutators) which alternate the
polarity of the stator magnet. The rotor is a static magnet. The three stator magnets
never have the same polarity at the same time. The DC motor becomes a generator if the
rotor shaft is forced to rotate clockwise. The efficiency is close to 95%.
A three pole DC motor. The commutators on the shaft control the polarity of stator
magnets such that the shaft rotates continuously counterclockwise
Switch based F1 model
North
South
NB No distinction
between ATP,
ADP and Pi;
see biochemistry.
The side of  facing the empty beta is the North pole; an empty  is
the South pole and a nucleotide carrying  is the North pole and
attracts the South face of . Reciprocally the South face of 
augments the affinity of  for a nucleotide and the
North face decreases its affinity.
Commutators are required for rotation: Binding/release of ATP is
allowed for  when on the pink side, binding release of ADP is
allowed when on the green side.
Switch-less F1 model
North
South
The kinetics of coordination of nucleotide can be programmed even
without switches.
The position of the magnetic pole in  changes depending on the
bound nucleotide. When the pole is close to to the South face of  the
affinity for the nucletoides is higher.
Molecular mechanism of ATP hydrolysis in F1-ATPase
The hydrolysis of a nucleotide triphosphate (NTP) into a nucleotide diphosphate (NDP)
and an inorganic phosphate (P1) is one of the most fundamental reactions in protein
functions and generates approximately 45 kj mol-1.
Despite its biological importance the chemical mechanism of the catalytic activity and
the hydrolysis reaction itself remains obscure.
Issues: kinetic experiments with mutants provide a catalytic rate constant which can
include not only hydrolysis reaction rate but also other components associated,
for example to ligand binding/unbinding and protein conformational changes.
The mutations lead to protein structural disorder.
A clear interpretation of the kinetic data is not possible.
Purely theoretical approaches (QM calculations) are difficult, (highly polar electronic
nature of the triphosphate substrate and the binding pocket) and require
experimental verification.
In F1-ATPase single molecule observation of the rotation of the  subunit allows
to distinguish the elementary step of the ATP hydrolysis (Hayashi 2012)
Proposed mechanism
POD: P-O bond dissociation
PT: proton transfer
HBR: hydrogen bond rearrangements
of the three water molecules
Energies are in kj mol-1
The kinetics of ATP hydrolysis
Issues: presence of three catalytic sites (and three not catalytic sites also binding a nucleotide)
and MgADP inhibition.
Extremely low ATP concentrations: uni-site regime.
This kinetics has been described by Cunningham and Cross in 1988:
Uni-site catalysis has been reported
in 1998 also when rotation is inhibited;
but this does not exclude that rotation
might occur with uni-site catalysis.
Binding a second ATP increases the hydrolysis rate by 103 factor (bi-site regime at
submicromolar ATP)
At higher ATP concentrations it has been suggested that three site catalysis occurs.
but a Michaelis Menten model is not able to reproduce the kinetics (effect of
MgADP inhibition?).
Most of the efforts are in the bi-site catalysis where rotation has been observed.
ATP red 60 µM
ATP green 0.6 µM
ATP black 2mM
MgADP inhibition
Observation: the rotation was suspended in solution without attaching actin.
On the basis of the amount of hydrolysed ATP, the rate of hydrolysis gradually dereased
to less than half the initial value.
This is called MgADP inhibition, where the hydrolysis product, i.e. MgADP, is tightly bound
to a catalytic site (Boyer 2000).
The inhibition is not complete because slow binding of ATP to non catalytic sistes displaces
the tightly bound ADP from the catalytic sites.
Under certain conditions the hydrolysis becomes triphasic: full activity in the initial phase,
slows down due to inhibition and then is partially recovered to an intermediate rate.
Thus during kinetics measurement ATP is immediately regenerated, to avoid inhibition
as much as possible. This phenomenon economizes the consumption of ATP in the cells, but
makes the analysis of ATP kinetics more complex.
It is important to note that the Walker structure is likely an inhibited structure,
which represents a stable form of the enzyme.
How many molecules of ATP are consumed per turn?
Below 1 µM where ATP binding is rate limiting, three ATP molecules are
consumed per turn (Yasuda 1998), although the agreement is not perfect due to
MgADP inhibition.
Each 120 deg step is driven by the hydrolysis of an ATP molecule.
Very likely one ATP binds to one site and another one is released from a different site.
We have no proof that each hydrolysis is accompanied by rotation (futile
consumption of ATP).
To summarize:
• F1 ATPase is a rotary motor made of a single molecule and
ATP is the energy source
• 3 3  suffice for rotation and ATP hydrolysis.  is the rotor and the hexamer is the stator.
• The rotation of  is counterclockwise when viewed from F0 side
• The motor rotates in discrete 120 deg steps at low ATP concentrations
• The F1 motor produces a constant torque of 40 pN nm over a large range of speed
and load and ATP concentrations.
• The mechanical work in each step is also constant except for statistical variations
and amounts to 80-90 pN nm
• Hydrolysis of one ATP molecule suffices for one step
• The energy conversion efficiency approaches 100%
• Bi-site catalysis supports rotation. At high ATP concentration three site catalysis
gives the same torque.
More recent perspectives:
The pathway for ATP hydrolysis is not simply the pathway for ATP synthesis in reverse…
(Karplus 2005).
Although the essential features of Boyer model are retained, cyclical conversion of the
 subunits is invoked from an open state abel to bind a nucleotide weakly to a tight
State with the highest affinity for ATP to a loose state from which ATP can be released.