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Muscle Contraction
Proteins convert chemical energy, a scalar quantity, to motion, a vector quantity. How?
I. The ATPase cycle
ATP serves as the fuel for motion by undergoing hydrolysis in the presence of myosin
(either whole myosin, the head (S1 region), or heavy meromyosin). The kcat for
hydrolysis in this case is 0.1 s-1. This represents a fairly slow hydrolysis rate, and
consequently if ATP hydrolysis in the presence of myosin were the only factor governing
motion, everyone would move rather slowly.
It turns out that adding actin to the myosin, forming actomyosin, increases the kcat of ATP
hydrolysis to 10-20 s-1, a 1-200 fold rate increase over myosin alone. As we will see, this
increase is due to an increase in the rate of Pi release from myosin. This finding explains
the need for the observed cross bridges between actin and myosin.
Since both myosin and actomyosin can bind and hydrolyze ATP, and actin can bind to both
free myosin and to the myosin.ATP complex, the process of ATP hydrolysis in the presence
of actin and myosin occurs as a cycle in which actin can bind to and dissociate from myosin
at each different step. Here, M = myosin, A.M = actomyosin, T = ATP, D = ADP, and Pi =
inorganic phosphate. All of the K's are given as association constants (even if the step
actually involves a dissociation), so that all of the K's have the same units. ∆G°’ is the
standard free energy change for the forward reaction, and kf is the rate of the forward
reaction.
K1=1011M-1
∆G°': -15.4 kcal/mol
kf : 106M-1s-1
K5=~1
0
200s-1
K7=~1
0
20s-1
K9=10 M-1
+1.4
0.1s-1
K11=105M-1
+7
Σ∆G°'= -7
1s-1
D
T
Pi
M <====> M.T <====> M.D.PiR <====> M.D.PiN <====> M.D <====> M
A.M <====> A.M.T <====> A.M.D.PiR <====>A.M.D.PiN <====>A. M.D <====>A. M
T
D
Pi
K4=107M-1
K6=~1
K8=~1
K10=10-1 M-1
K12=103M-1
∆G°': -9.8 kcal/mol
0
0
-1.4
+4.2 Σ∆G°'= -7
kf : 106M-1s-1
200s-1
20s-1
100s-1
1000s-1
If we first look at just the top line of the above cycle, where myosin is hydrolyzing ATP in
the absence of actin, then we see that ATP has a high affinity for myosin; K1 is a very large
number and the associated free energy change is enormous. It is actually in this step
(where ATP is binding to myosin) that the free energy to drive the hydrolysis is released.
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The actual hydrolysis step has a ∆G°’ of 0, and the dissociation of both the Pi and ADP have
a positive ∆G°’. However, the sum of the free energy change for the overall reaction has
the expected value of -7 kcal/mol. So, the binding of ATP to myosin is rapid and releases a
great deal of free energy.
The hydrolysis of the terminal P of ATP goes through a SN1 reaction. The Pi that is formed
is tightly bound to the myosin head and is initially in a refractory state, PiR. After a
conformational change in the myosin head, the Pi enters the nonrefractory, or PiN , state.
The overall rate of hydrolysis of ATP by myosin is slowed down by the slow rate of Pi
dissociation from the M.D.PiN complex. Thus, in the absence of actin, Pi loss is the ratelimiting step. It occurs at a rate of 0.1 s-1 . (Since the release of Pi is the rate-limiting step,
the hydrolysis of ATP by myosin alone shows burst-phase kinetics. See Problem Set 3,
Question 2.)
Now let us look at the bottom row of reactions: the hydrolysis of ATP by actomyosin. The
free energy change associated with the overall reaction is still -7 kcal/mol as expected, but
now less of the free energy change is associated with the binding of ATP to actomyosin and
more from the release of Pi. The other steps have not changed appreciably. Actomyosin
loses Pi rapidly (at a rate of 20s-1 ), so that the overall reaction is no longer limited by the
release of Pi but by the conformational change allowing Pi R to become PiN . (Consequently,
the hydrolysis of actomyosin will not show burst-phase kinetics.)
In muscle, ATP hydrolysis does not occur by simply following across the bottom set of
reactions. We must also consider the relative affinity of myosin for actin at each step. It is
perhaps easier to consider a simplified form of the above cycle with all of the same steps
but with only relative rate constants and binding affinities. A diagrammatic figure is also
shown on the next page to help you follow through these steps.
fast
fast
slow
T
M <====> M.T <====> M.D.PiR
High
Low
Low
very slow
fast
D
Pi
.
.
.
<====> M D PiN <====> M D <====> M
Low
High
A.M <====> A.M.T <====> A.M.D.PiR <====>A.M.D.PiN <====>A. M.D <====>A. M
T
D
Pi
fast
fast
slow
fast
fast
Since myosin alone has a high affinity for actin, let us begin at A.M (the state seen in rigor
mortis). The concentration of ATP is very high in a muscle cell, and so ATP rapidly binds
to form A .M .T. However, the affinity of M.T for actin is much lower, and so the myosin
will largely dissociate from actin at this point. Now, the M.T will quickly hydrolyze its
ATP to give bound ADP and PiR.
3
+
-
power stroke conf. change
ADP
back to where we started,
but moved one actin over
towards Z line
fast
+
D
Pi
ADP (rigor mortis)
Start here:
ADP
fast
productive
interaction
with actin
fast
ATP
DPiN
ATP
fast
slow
rate-limiting
conf. change to
cock myosin head
DPiR
non-productive
interaction
with actin
DPiR
The M .D.PiR complex still has a low affinity for actin and so may try
to form an interaction, but will not be able to form a strong interaction. The
conformational change in myosin causing the conversion of PiR to Pi N is what “cocks” the
myosin head for the power stroke. This is slow, about 20s-1 . Once it occurs, the M.D.PiN
complex still has a low affinity for actin, BUT only when the A.M .D.PiN complex is formed
can Pi release occur at a rapid rate. This drives myosin to bind actin even though the
relative affinity of myosin for actin is weak. Once Pi is released, however, then a
conformational change in myosin can occur which will allow for tight binding. This is the
power stroke! The conformational change in myosin involves a change in the relation
between the myosin head and tail, corresponding to a 5-10 nm displacement of the lever
arm. Actin must be complexed to myosin for muscle movement to occur. After the power
stroke, ADP is released to give AM and the cycle can begin again.
If you look at V&V p. 1247 Fig. 34-65 and MBOC p.852 Fig. 16-91, you’ll notice that their
models are slightly different from the one just discussed. However, the model presented
in class is now thought to more accurately reflect what is occurring in the ATP cycle and is
the one which you should know.
So how close is this model to reality? Three experimental methods have been used to test
this model of the ATPase cycle: in vitro motility, analysis of crystal structures, and
mutations of the myosin lever arm.
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II. In vitro motility
A motility assay verifies that myosin heads move around on actin filaments. The
experiment consists of covering a polystyrene bead with S1 myosin fragments and the
adding a fluorescently labeled actin cable. The actin cable moves with respect to the beads
at a rate of about 5µm/s, which is fairly fast. However, if the conditions are manipulated
such that only one myosin-covered bead contacts a single actin cable, the rate of movement
is about 0.2 µm/s.
In a more complex version of the experiment, beads are also attached to the ends of an
actin cable, and infrared laser beams are used to trap the beads, and therefore the actin
cable, in place. Instead of covering the original bead with S1 fragments, a low amount of
S1 is used so that only one head attaches to each bead. Similarly, a low concentration of
ATP is used so that only one ATP molecule binds to each head. With this set-up, each
actin cable is associated with only one myosin-conjugated bead, and the movement of the
actin is measured using the actin-conjugated reporter beads. These steps demonstrate that
myosin moves 5-10 nm after it interacts with actin.
If the laser energy is increased, myosin tries to move the actin (relative to itself), but since
the laser energy restrains the actin’s movement, the force associated with the restraint is
measured. This force turns out to be 4-8 picoNewtons (pN).
So are these force and displacement values consistent with the energy supplied by the
hydrolysis of one molecule of ATP? A few calculations prove that they are (this is purely
for your interest).
First, ∆G = -12 kcal/mole = 16 x 10 -21 cal/molecule for ATP hydrolysis.
At the same time, 1 pN x a 10 nm displacement = 2.5 x 10-21 calories.
Since the average force observed is 5 pN, the total energy for the 10 nm displacement is 5 x
2.5 X 10-21 calories = 12.5 x 10-21 calories (or 5 x 10-13 ergs), which is indeed approximately
the amount of energy supplied by the hydrolysis of a molecule of ATP. (Hydrolysis of a
single ATP to ADP and Pi actually releases about 8.3 x 10-13 ergs which would make muscle
contraction about 60% efficient. For converting scalar energy to movement, this is a great
efficiency rate! Man-made engines are nowhere near this good.)
III. Structure of myosin
The crystal structure of myosin (see V&V p. 1238 Fig. 34-53) shows the head has a 25 kD
domain at the N-terminus, and a 50 kD region that protrudes from and wraps around the
25 kD domain. A cleft between two parts of the 50 kD region forms the ATP-binding site,
and actin binds on the other side of the cleft. The essential and the regulatory light chains
are attached at the C-terminus, and a lever arm is observed at the region where the light
chains are bound. The lever arm is long enough to allow for the observed 10 nm
displacement.
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The structure gives insight into why actin falls off when ATP binds to myosin. At first, the
ATP cleft is open, but the Pγ end of ATP is occluded due to the presence of actin at the back
of the 50 kD region. Thus, as ATP opens this side of the cleft, the actin falls off. ATP gets
trapped from the other side, and hydrolysis of the Pγ occurs. In this state actin can only
attach weakly to myosin and comes on and off. The hydrolyzed Pi then leaves through the
side of the cleft it opened, and once it’s gone the cleft closes and actin can bind tightly again.
This alternation between the closed and open cleft states should remind you of the twostate model of hemoglobin.
IV. Mutation of the lever arm
Since the lever arm is thought to determine the length of myosin displacement, what
happens if the lever arm is shortened or lengthened by DNA mutations? It turns out that
the shorter the lever arm, the slower the rate of movement. Similarly, making the arm
longer by adding an extra light chain site increases the rate. The effect of changing the
lever arm length is independent of ATP hydrolysis, since the rate of ATP hydrolysis is
constant among all the mutants.
V. Relation of ATP hydrolysis and movement rates to myosin head structure
The myosin head has two loop regions, loop 1 which is part of the ATP-binding site and
loop 2 which is part of the actin binding site. It has been observed that the rate of ATP
hydrolysis varies among species, and it turns out that the explanation for this is the
variation in the sequence of loop 2. Thus interchanging loop 2 between animals changes
their overall rates of ATP hydrolysis by changing how actin interacts with myosin. Loop 1
mutations, on the other hand, affect the movement velocity since they seem to be
involved in the "hand-over-hand" movement of myosin down an actin filament. Loop 1
mutations do not necessarily change the A.M-ATPase activity however. There can also be
mutations in the ATP binding cleft that affect the dissociation of tightly bound actinmyosin complex by ATP. (Don’t worry about the “tc” and “ts” that were mentioned in
lecture.)
These features are important for insuring that ATP hydrolysis doesn’t occur without an
intermediate step to prevent actomyosin dissociation, and therefore for insuring that
myosin only moves forward.