Physics, Muscles and Unbreakable Sticks

   High-school physics tells us that when an object is displaced through ds (an infinitesimal displacement) under the influence of a force F , the infinitesimal work done in the process is given by the “dot product” of the force with the infinitesimal displacement. This statement can be summarized by the well-known relation dW = F.ds   (where vectors are written in bold). The problems that one has to solve as a high-school student usually involve pumps supplying water to a tall building or a lift at a construction site carrying cement to the top floor. All that the students have to do is to multiply the gravitational force of the earth with the height of the building to calculate the work done. I have done this so many times that “W = mgh ” has now become permanently imprinted on my brain. These textbooks rarely talk about problems such as the work done by a human being (or, for that matter by any animal) while lifting objects

   Consider the case when a person holds a heavy dumb-bell stationary in front of his or her face. To keep the dumb-bell stationary, the person, using his or her muscles, has to apply an upward force to counter the downward pull of gravity.  Since the dumb-bell is stationary, or in other words ds = 0 , the work done by the person should be zero. And since no work is done by the person, his or her energy expenditure should be zero; and hence, he or she should not tire at all. This, clearly, is a contradiction!  All human beings (including Arnold Schwarzenegger), while lifting heavy weights, will sooner or later, tire. So where is the catch? 

   If one thinks for a while it is not hard to realise that the answer to this problem must lie in the mechanism with which muscles function. Even though no apparent macroscopic work is being performed, at the microscopic level, the fibres that constitute the muscles must undergo rapid movements for which work in the  sense dW = F.ds is required. Therefore, even when the weight that the person is holding is not displaced, microscopic displacements of the muscle-fibres would require work, consume energy and hence, the person would tire.

   It turns out that the Sliding Filament Model, modern molecular biologists’ explanation to muscle contraction, uses this very idea at its core. Muscles are made up of strands of fibres which are wrapped around each other. The functional unit of a muscle fibre, called a “Sarcomere”, is composed of two characteristically different protein-filaments: the “thin” filaments made up of a protein called Actin and the “thick” filaments made up of another protein called Myosin. Actin molecules have specific regions on them which have a very strong affinity to certain domains on Myosin molecules. Ordinarily, these binding sites on Actin molecules are ‘hidden’ or not accessible. But a signal from a motor-neuron, causes changes in the structure of Actin molecules, ‘unmasking’ those binding sites, to which Myosin molecules can now bind. Such interactions between Actin and Myosin are called “cross-bridges”. 

   Sarcomeres are observed to contract when the muscle which they are a part of contracts. But does that imply that the protein-fibres (Actin and Myosin filaments) which are building blocks of the Sarcomere also contract? Scientists were able to show that contraction of the Sarcomere is caused not by the contraction of its constituent filaments but by increasing the overlap of the thick and thin filaments. In the relaxed state, the two kinds of filaments overlap over a certain region. When the muscle contracts, the thick (Myosin) and thin (Actin) filaments slide against each other in opposite directions, increasing their overlap and as a consequence (see figure 1), decreasing the length of the Sarcomere. This sliding movement is achieved by bringing about a change in the structure Myosin, which causes the Actin filament to be tugged towards the centre of the Sarcomere. This is the step where work in the  sense dW = F.ds is performed and the energy required to change molecular conformations is supplied by ATP molecules- the universal “energy-currency” of life. Therefore, a person holding heavy weights tires as his/her ATP molecules get depleted.

   It is quite remarkable that with the help of molecules such as Actin and Myosin, a trained weightlifter can lift weights in the excess of 200 kg (approximately 10 to the power 25  times heavier than molecules like myosin) above their head. In each thick filament, every second, around 350 of its myosin heads form five cross-bridges. The number of thick and thin filaments in a muscle fibre and the number of muscle fibres in a muscle are so large that, molecules which are insignificant on their own, when acting together, can produce enormous forces.

   Perhaps, a thousand years down the line, children’s story-books will not have stories of sticks that cannot be broken when bunched together, but will talk about how tiny molecules, acting in tandem, can bring about events of simply astronomical relative magnitudes.

United we stand!

References:

11.      Life the Science of Biology (8^th Edition), Sadava, Heller, Orians, Purves, Hillis,

22.    www.nature.com/scitable/topicpage/the-sliding-filament-theory-of-muscle-contraction-14567666