Medical Physiology 2006

Problem Set 2:  Cellular Physiology II:  Action Potentials / Muscle:

 

 

Part I: Action Potentials

 

At the axon hillock of a neuron at rest, ENa = +50 mV, EK = -100 mV and Vm = -70 mV.   The resting membrane conductances are gNa = 10 nS, gK = 100 nS (ignore Cl- conductance).  A nearly instantaneous rise in the Na+ conductance elicits an action potential.

 

1.   What is the minimum Na+ conductance that is sufficient to attain threshold?  (Hint:  recall that threshold is attained when the inward [depolarizing] current just exceeds the outward [hyperpolarizing] current.)

 

 

During the hyperpolarizing after-potential, the K+ conductance rises to 1000 nS, and Vm = ­-90 mV.

 

2.   Can a second action potential be generated during this time (yes/no, why/why not)?

 

 

3.   If a second action can be generated, then what Na+ conductance would produce the inward current sufficient to attain threshold?

 

 

 

Part II:  Muscle Physiology

 

4.   EC coupling involves transmission of a the muscle fiber action potential down the t-tubules, with subsequent release of Ca++ from the sarcoplasmic reticulum.  This process initiates muscle contraction in as little as several milliseconds, owing to short diffusion distances (i.e., the sarcoplasmic reticulum surrounds individual myofibrils).  If this process did not occur, and the Ca++ necessary for binding to troponin came solely from the extracellular medium (after all, there is a large inward driving force for Ca++ entry into the fiber), how long would it take for the action potential to trigger contraction of the sarcomeres—especially in myofibrils near the center of the fiber?   Assume that a “typical” fiber has a diameter of 100 mm, and also assume that the diffusion constant for Ca++ is 10-5 cm2/sec.

 

5.   Electron micrographs from a newly discovered species show that the skeletal-muscle filaments are 1.7 mm in length, the bare zone is 0.3 mm in length, and the thin filaments (measured from end to end with the Z-disk in the middle) are 2.2 mm in length.  From these measurements, accurately construct the active force length-tension relationship of the muscle.

 

 

 

6.   As bones grow, muscle lengths adjust in order to always operate in the peak range of their length-tension curve.  If the filament lengths remain constant throughout growth, and assuming that maximum force development of a muscle doesn’t change during a period of growth, what does this imply regarding number of sarcomeres, myofibrils, etc.? 

 

Repeated exercise of a muscle results in increased muscle growth via fiber hypertrophy (the number of fibers don’t change).  What does this imply regarding number of sarcomeres, myofibrils, etc., resulting from exercise?  If the maximum force development of a muscle should double as a result of strength training, then how would this affect the muscles diameter (assume the muscle is roughly cylindrical in shape)?