Empirical study of muscle contraction

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In Tools to Study Muscle Contraction we present different methods that can provide information about the most fundamental processes governing the functioning of motor proteins, some of which are taking part in muscle contractions. Science advances through an interplay between empirical observation and theoretical work. In this section we describe the theoretical assumptions guiding the empirical work on muscle contraction, thus exposing the interface between theory and experimentation, in order to understand how different methods can expand our understanding, and to design new such methods.    

Generally accepted facts about muscle contraction

The myofibril

The figure on the right shows the muscle structure down to the myofibril level. Myofibrils are about 1-2 microns in diameter and run the length of the muscle fiber. Optically, they present a striated pattern, with units called sarcomeres. Sarcomeres are only 2.3 microns long, stretching between two Z lines, and are considered the "contractile units" of the muscle cell. This striated pattern is mainly produced by the regular arrangement of two kinds of molecular filaments, called the thin and thick filaments. Every sarcomere contains 2 mirror-symmetrical structures on both sides of the M line. A cross section through one half of a sarcomere reveals a very regular arrangement of parallel thin and thick filaments, see the diagram below (from Ref.1).  



The thick filament 

Contains mostly myosin, about 300 molecules. Myosin heads spiral on the filament, with periodicity of 42.9 nm, and 14.3 nm axial distance between each head. 
The myosin head presents two lobs, 19 nm long, connected to a 156 nm long tail, with a flexible hinge in the tail 43 nm from the head.
The thick filament presents a polarity, which is reversed through the M line.  
The thick filament also contains other regulatory and structural proteins.  

Thin Filament  

Contains 350 G actin monomers, each containing 50 molecules of troponin and tropomyosin. The filament's main structure is made of 2 helical F-actin strands wound round each other with pitch of 73nm. The filament is polarized, with inverse polarization on each side the Z line.    
There are twice as many thin filaments as thick ones. 

For the contraction process, let's start with some facts. Muscles contract because myofibrils contract. This is a very well established fact, because one can make myofibrils contract individually, outside of the cellular environment. In fact, myofibrils contract because individual sarcomeres contract independently (Ref.2). 

It is also well established that during sarcomere contraction the thin and the thick filaments slide past each other, with very little change in their length compared to the entire length of the motion. In fact, thin and thick filaments are now routinely made to interact with one another in vitro, and are observed "sliding" on each other, even pulling against a load, producing work. We are doing this in our lab. The composition and the structure of the thin and thick filaments are also very well known for most species. But the precise interaction between the thin and thick filaments within the myofibril that leads to the production of work is still open for debate. 

The sliding filament model

See this video.
See this very comprehensive review: Regulation of Contraction in Striated Muscle; A. M. GORDON, E. HOMSHER, AND M. REGNIER

Other facts

About muscle flexibility: The resting muscle fiber is very flexible, and it stiffens as soon as it begins contraction.

ATP dissociation is seen during muscle contraction.

The most popular model which explains the production of work at the level of the thin and thick filaments is the so called "molecular rope pulling" model, or the cross bridge model.

Ref.1 Architecture and function in the muscle sarcomere; John M Squire
Ref.2 The mechanical behavior of individual sarcomeres of myofibrils isolated from rabbit psoas muscle; Ivan Pavlov, Rowan Novinger, and Dilson E. Rassier


Invariants

Science can be seen as the search of stable patterns in nature. The gemstones of science are invariants, which are physical quantities that are invariant under experimental conditions. A great example is the speed of light in physics. Other qualities are not considered universally invariant, but they still hold a special place in science, like the gravitational constant on Earth for instance. Why are invariants so important? Because they constitute the foundation of our models. Galilee set the stage for Newton by establishing that acceleration in a gravitational field is an invariant. In other words, a feather should fall in sync with a rock under the Earth's gravitational field, if we make abstraction of the atmosphere, or in vacuum. Later, Einstein built his special relativity theory around the speed of light as an invariant.    

The science of muscle contraction is not different in that respect. Physiologists and biophysicists are constantly looking for quantities that are invariant under experimental conditions, at least for a specific type of muscle or animal. 

The force-length relation

The force-length relation is a plot of the tension generated by a sarcomere vs its length. The figure was extracted from Ref. 1. It shows the curve with its interpretation according to the cross bridge model. It is important to mention how this data is produced experimentally.

Ref.: Length dependence of active force production in skeletal muscle, Rassier et all.

Physical properties and their measurements 

Tension

Tension is developed within a muscle fiber or a myofibril during activation if both ends are more or less rigidly attached. Tension is measured by using a displacement/force transducer usually attached to one end of the fiber. This technique can be extended to the interaction between a single actin filament with one myosin filament. In this case, very precise cantilevers or even optical tweezers are used. In any case, the total tension in the fiber is measured. In the case of a single myofibril, this total tension is equal to the tension supported by every sarcomere in series with each others, and results from the total interaction between all thin and thick filaments within the weakest half sarcomere, which is proportional to the total number of participating thin and thick filaments. 

In this video produced in our lab we show the development of tension as a bundle of myofibrils contracts during activation with a Ca2+ solution, the force redevelopment after two consecutive (user controlled) mechanical releases of tension, and the force relaxation by dropping the concentration of the Ca2+ in the solution. This movie was recorded under 60x magnification, the motion of the cantilever represents only a few microns, and the forces generated are in the nN range. Data obtained in collaboration with Dilson Rassier

Ultimately, according to the sliding filament model the instantaneous tension developed by a fiber (at different levels of muscle organization) is proportional to the average number of cross bridges bound to one actin filament, as seen in one half of a sarcomere.  
   

Stiffness/Compliance

Stiffness is the instantaneous dependence of tension on length. Compliance is just the inverse of stiffness. The stiffness of a fiber, in any state, can be measured by rapidly stretching it, while recording the tension. The stretching action must disturb much the contractile mechanism. According to the cross bridge model, this length of the stretch must not exceed ***/sarcomere, which is the length of the power stroke. The time of the stretch must be in the ms regime, faster than the cross-bridge turnover rate.  

Unanswered questions in muscle contraction

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Theoretical predictions and empirical methods for corroboration/falsification

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