We will examine how the structure of a muscle's smaller constituents influences its force generating capacity. For this problem, assume a sarcomere has a diameter of 2 microns and a length of 2.7 microns, and assume a muscle fiber has a diameter of 50 microns (the length of the myofibril will vary based on the muscle).
a) Briefly describe the hierarchical structure of muscle, from the sarcomere level up to a whole muscle.
b) If we are examining a longer muscle that is half a meter long, approximately how many sarcomeres make up an entire myofibril in that muscle? Note that a myofibril is made up of sarcomeres in series. Round to the nearest thousand.
c) How many sarcomeres are in a single muscle fiber? Round to the nearest thousand or million, whichever is more appropriate.
d) For a muscle with a cross-sectional area of 1 cm², compute the following: (1) How many muscle fibers are in the whole muscle (to the nearest thousand)? (2) How many sarcomeres are in the whole muscle (to the nearest trillion)?
e) The innervation ratio for a motor unit is defined as the number of muscle fibers innervated by the motor neuron of that unit. If this muscle is comprised of 500 motor units, what is the average innervation ratio in the muscle? Round to the nearest integer.
f) If the actin–myosin filaments throughout the muscle undergo one power stroke, how much would the muscle contract in length? Assume, for each power stroke, that each sarcomere shortens by 10 nm. Round to the nearest millimeter.
g) Mammalian muscle has a specific tension of 30 N/cm² (i.e., it can generate a maximum of 30 N of active force per square centimeter of cross-sectional area). What is the peak amount of active force a single sarcomere can generate? Round to the nearest micronewton.
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