Elastic-mathematical theory of cells and mitochondria in swelling process the membranous stresses and modulus of elasticity of the egg cell of sea urchin, Strongylocentrotus purpuratus.

To the revolution-ellipsoidal and spherical membranous shell (cell mitochondrion) are introduced the equations for the calculation of both the modulus of elasticity (Young's modulus) and the stresses, which exist at the membrane. The existing pressure difference between the inner and outer surface of the membrane is calculated in the dilution of seawater media in the osmotic steady state. The experimental results are obtained by using egg cells of the sea urchin, Strongylocentrotus purpuratus. Up to the specific volume of the egg cell (V(E) approximately 35.10(-8) cm(3)) Boyle-van't Hoff's law is valid (defined as the subelastic range) beyond that the elastic stresses exist (elastic range). For the maximum value of the stresses existing at the cell wall one obtains sigma approximately 5.5.10(6) dyne/cm(2) and for the modulus of elasticity E = 1.0.10(7) dyne/cm(2), which is constant when the value of relative strain epsilon(nu) > 15%. The breaking limit by an approximate calculation is sigma(U) approximately 11.10(6) dyne/cm(2). The membrane is assumed to be convoluted and its hypothetical degree of folding was calculated unk = 34%. The results are compared with the values existing in the literature and other types of cells are found to have values of elasticity in the same range as values of the membrane of S. purpuratus. Both compression and cell elastometer methods are criticized and in certain cases results of these methods are considered to belong to the subelastic domain.