Muscle contraction
1.-Muscle architecture
2.- Actin-myosin interactions and force generation
3.-Transverse tubules and calcium release
4.-Titin architecture and muscle elasticity
Readings:
1.-Goldman YE. (1998) Wag the tail: structural dynamics of actomyosin. Cell. Apr
3;93(1):1-4.
2.- Huxley AF, Taylor RE. (1958) Local activation of striated muscle fibres. J
Physiol. Dec 30;144(3):426-41.
3.-Li H, Linke WA, Oberhauser AF, Carrion-Vazquez M, Kerkvliet JG, Lu H,
Marszalek PE, Fernandez JM. (2002) Reverse engineering of the giant muscle
protein titin. Nature. 2002 Aug 29;418(6901):998-1002.
Keywords:
Sarcomere
I band, A band, Z line
Sliding filaments
Myosin, actin, titin
Tranverse tubular network
Calcium release, Troponin complex
Ryanodine and Dihydropyridine receptors
Problems:
1.-Muscle contraction triggered by an action potential has a latency
of less than 10 ms for a 1 mm in thick, single frog muscle fiber.
Is it plausible to claim that the calcium ions that trigger contraction
enter mainly through the plasma membrane of the muscle fiber?
In your answer consider that calcium ions move inside cells
with a diffusion coefficient D in the range of 10-7 cm2/s.
2.-Describe the full sequence of events that start with a nerve impulse
arriving at the neuromuscular junction, through muscle contraction and
ending with relaxation of the muscle fiber. Write short one line descriptions
of each event.
3.-The longest PEVK region of titin is about 2000 aa long. The contribution
that a single aa makes to the contour length of the PEVK region is 0.36 nm.
In thermal equilibrium calculate (roughly) the end-to-end length of this protein.
Calculate its maximal extension and draw the force-extension relationship
that you expect to observe.
Testing the sliding filaments hypothesis
Relaxed
Contracting
“feet”
Electron micrograph of a longitudinal section of a muscle fiber
showing a full triad and also the connections (“feet”) between
the T tubules and the sarcoplasmic reticulum. (180 000X )
Mechanisms of Ca2+ removal from the cytoplasm.
The elasticity of muscle is due to the Brownian motion driven
collapse of a protein named titin
Sprinter Brian Lewis
Muscle can contract and also can extend elastically
The elasticity of muscle results from the properties of a giant
protein named Titin (from Titan!)
Titin has a coiled region
(PEVK) and a region folded
into individual modules (I):
Machina Carnis
Is the elasticity of titin like that of a spring?
The elasticity of a metal spring results
from the stretching of the bonds between
the metal atoms.
Is this how titin works?
Will titin also break
if we pull it too far?
A metal wire in a spring extends by bond stretching and breaks by
irreversibly disrupting its atomic arrangements
Gold wire
elastic extension
(reversible)
plastic extension
(irreversible)
Electron micrographs of isolated titin molecules
We can stretch a single protein and measure how does
the restoring force changes with the extension.
mirrors
laser
Photodiode (Force)
cantilever
protein
linear actuator (extension)
.
detector can measure pico-Newton forces
Actuator can extend
a molecule by fractions
of a nano-meter
How much is a pico (10-12) Newton of Force?
Steam engine
Protein unfolding
mouse
pico Newtons
N
-12
10
nano Newtons
-9
10
Newtons
micro Newtons
-6
10
kT
-3
10
1
mega Newtons
10
3
Rice grain
Average force
exerted over 1 nm
by thermal motion
Force that ruptures
a covalent bond
Madonna
6
10
If we stretch a single titin protein we obtain
force-extension curves that is very different from Hooke’s law.
Force (pN)
a very thin metal spring
Extension (nm)
titin protein
To understand how titin works,
we must first understand Brownian motion.
Robert Brown (1773-1858 ), a
botanist, reported in 1828 his
observation that pollen grains in
water underwent incessant motion.
A single pollen grain observed with
a microscope is being moved about
by mysterious forces.
Temperature is a measure of the average kinetic energy of
the molecules in a material.
Increasing the temperature increases the translational
motion of molecules.
The average kinetic energy of each molecules is related to
temperature by the relationship:
E= kBT
Small particles moving fast
(red water molecules)
Einstein and Smoluchowski
viewed Brownian motion from
an atomistic and probabilistic
point of view
l
Large particle moving slowly at an
average velocity v, on a random path
of steps of length l (green pollen grain)
t1
Motion in a straight line
d  v(t2  t1 )
d
t2
d  lv(t  t )
2
1
A. Einstein, 1906
t2
l
Brownian motion
d
t1
A computer simulation of the Einstein-Smoluchowski
view of Brownian motion
d ~ t
Titin is a polymer.
What does Brownian motion do
to a polymer?
The linking of many individual molecules called monomers
………
Results in the formation of a POLYMER
Polymers then, are freely jointed segments with
complex chemical groups branching out on the sides.
Polymers can have many
different conformations
Making a simple toy polymer
joints
Polymers move towards situations that
permit the largest number of conformations
Ludwig Boltzman
(1844-1906)
Austrian physicist who
established the relationship
between entropy and the
statistical analysis of
molecular motions
Entropy  lnnumber of conformations 
Increased entropy makes polymers look crooked
and pushes them to collapse
Simulation of a polymer increasing its entropy as it shrinks from
a more extended conformation
For a polymer made of N segments
of equal length l, the contour length
is defined as:
Lc  N  l
l
A polymer looks like the path of a particle
in Brownian motion
l
d  lv(t2  t1 )  lLc
The contour length, Lc, of a single DNA double helix molecule
from a human or an animal can be up to one meter long!
1 meter
How long would
the DNA molecule
be if it moved
randomly with
Brownian motion?
Lc  1m
l  10 m
7
Answer:
d  Lc l  0.0003m
.
If we stretch a single titin protein we obtain
force-extension curves that are perfectly explained
by the Brownian collapse theories!
Force (pN)
titin protein
Extension (nm)
Ok, so we have discovered that muscle elasticity
results from the Brownian motion of titin.
What happens to titin if we stretch it too much?
Will it brake like the metal spring?
No! Certain parts of titin will just reversibly unfold.
Folded proteins have a bonded structure that helps them
resist the constant bombardment caused by Brownian motion.
Small protein ubiquitin
A cartoon representation
The Bonded structure is dynamic, as it gets bombarded,
the structure bends and bonds break and reform
If we apply a mechanical force to a protein,
we can trigger unfolding.
Proteins can unfold and extend
under forces of just a few pico Newtons!
If we then relax the force, we can observe folding!
We can understand how titin works by engineering
a protein that imitates its properties.
Engineered titin-like protein
Coiled part
Folded modules
Unfolding of folded titin modules prevents
rupture when the coiled region is overextended
Coiled region
Conclusions
Brownian motion explains muscle elasticity in humans
Helps understand the effect of mutations
on the elasticity
We may be able to test and design
better titin molecules