1.-Muscle architecture 4.-Titin architecture and muscle elasticity 2.- Actin-myosin interactions and force generation 3.-Transverse tubules and calcium release Readings: 1.- Goldman YE. (1998) Wag the tail: structural dynamics of actomyosin. Cell. Apr 3;93(1): Huxley AF, Taylor RE. (1958) Local activation of striated muscle fibres. J Physiol. Dec 30;144(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 Aug 29;418(6901): Muscle contraction

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 cm 2 /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

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. ( X ) “feet”

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? Will titin also break if we pull it too far? The elasticity of a metal spring results from the stretching of the bonds between the metal atoms. Is this how titin works?

Gold wire A metal wire in a spring extends by bond stretching and breaks by irreversibly disrupting its atomic arrangements elastic extension (reversible) plastic extension (irreversible)

Electron micrographs of isolated titin molecules

Photodiode (Force) mirrors laser cantilever protein linear actuator (extension) We can stretch a single protein and measure how does the restoring force changes with the extension..

detector can measure pico-Newton forces Actuator can extend a molecule by fractions of a nano-meter

How much is a pico ( ) Newton of Force? Rice grain mouse Madonna Steam engine N pico Newtonsnano Newtons Protein unfolding kT Force that ruptures a covalent bond Newtonsmega Newtons micro Newtons Average force exerted over 1 nm by thermal motion

If we stretch a single titin protein we obtain force-extension curves that is very different from Hooke’s law. Force (pN) Extension (nm) titin protein a very thin metal spring

Robert Brown ( ), a botanist, reported in 1828 his observation that pollen grains in water underwent incessant motion. To understand how titin works, we must first understand Brownian 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= k B T

Large particle moving slowly at an average velocity v, on a random path of steps of length l (green pollen grain) Small particles moving fast (red water molecules) Einstein and Smoluchowski viewed Brownian motion from an atomistic and probabilistic point of view l

d t1t1 t2t2 Motion in a straight line

d l t1t1 t2t2 Brownian motion A. Einstein, 1906

A computer simulation of the Einstein-Smoluchowski view of Brownian motion

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

Austrian physicist who established the relationship between entropy and the statistical analysis of molecular motions Ludwig Boltzman ( ) Polymers move towards situations that permit the largest number of conformations

Simulation of a polymer increasing its entropy as it shrinks from a more extended conformation Increased entropy makes polymers look crooked and pushes them to collapse

For a polymer made of N segments of equal length l, the contour length is defined as: l

A polymer looks like the path of a particle in Brownian motion l

The contour length, L c, 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? Answer :.

If we stretch a single titin protein we obtain force-extension curves that are perfectly explained by the Brownian collapse theories! Force (pN) Extension (nm) titin protein

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 ubiquitinA 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. Coiled part Folded modules Engineered titin-like protein

Unfolding of folded titin modules prevents rupture when the coiled region is overextended Coiled region

Brownian motion explains muscle elasticity in humans We may be able to test and design better titin molecules Helps understand the effect of mutations on the elasticity Conclusions