A quantitative analysis of elastic, entropic, electrostatic, and osmotic forces within relaxed skinned muscle fibers
Maughan, D.W.; Godt, R.E.
Biophysics of Structure and Mechanism 7(1): 17-40
The elastic behavior of mechanically skinned skeletal muscle fibers in relaxing solution is modelled using equations developed by Flory (1953) for the elasticity of non-biological polymers. Mechanically, the relaxed skinned fiber is considered to be a semi-crystalline network of inextensible polymer chains, which are periodically cross-linked and which are bathed in an aqueous medium. We consider (1) configurational elastic forces in the network, (2) entropic forces due to mixing of polymer and water, (3) electrostatic forces due to fixed charges on the muscle proteins and mobile charges in the bathing solution, and (4) compressive forces due to large colloids in the bathing solution. Van der Waals forces are not considered since calculations show that they are probably negligible under our conditions. We derive an expression which relates known quantities (ionic strength, osmotic compressive pressure, and fiber width), experimentally estimated quantities (fixed charge density and volume fraction of muscle proteins), and derived quantities (concentration of cross-links and a parameter reflecting the interaction energy between protein and water). The model was tested by comparison with observed changes in skinned fiber width under a variety of experimental conditions which included changes in osmotic compressive pressure, pH, sarcomere length, and ionic strength. Over a wide range of compressive pressure (0-36 atm) the theory predicted the nonlinear relation between fiber width and logarithm of pressure. The direction and magnitude of the decrease in width when pH was decreased to 4 could be modelled assuming the fixed charge density on the protein network was 0.34 moles of electrons per liter protein, a value in accordance with the estimates of others. The relation between width and sarcomere length over the complete range of compressive pressures could be modelled with the assumption that the number of cross-links increases somewhat with sarcomere length. Changes of width with ionic strength were modelled assuming that increasing salt concentration both increased the electrostatic shielding of fixed charges and decreased the number of cross-links. The decrease of fiber width in 1% glutaraldehyde was modelled by assuming that the concentration of crosslinks increased by some 10%. The theory predicted the order of magnitude but not the detailed shape of the passive tension-length relation which may indicate that, as with non-biological polymers, the theory does not adequately describe the behavior of semi-crystalline networks at high degrees of deformation. In summary, the theory provides a semiquantitative approach to an understanding of the nature and relative magnitudes of the forces underlying the mechanical behavior of relaxed skinned fibers. It indicates, for instance, that when fibers are returned to near their in vivo size with 3% PVP, the forces in order of their importance are: (elastic forces) approximately (entropic forces) greater than (electrostatic forces) approximately (osmotic compressive forces).