On the fisher and the cubic-polynomial equations for the propagation of species properties

For precise boundary conditions of biological relevance, it is proved that the steadily propagating plane-wave solution to the Fisher equation requires the unique (eigenvalue) velocity of advance 2(Df)^1/2, whereD is the diffusivity of the mutant species andf is the frequency of selection in favor of the mutant. This rigorous result shows that a so-called “wrong equation”, i.e. one which differs from Fisher's by a term that is seemingly inconsequential for certain initial conditions, cannot be employed readily to obtain approximate solutions to Fisher's, for the two equations will often have qualitatively different manifolds of exact solutions. It is noted that the Fisher equation itself may be inappropriate in certain biological contexts owing to the manifest instability of the lowerconcentration uniform equilibrium state (UES). Depicting the persistence of a mutantdeficient spatial pocket, an exact steady-state solution to the Fisher equation is presented. As an alternative and perhaps more faithful model equation for the propagation of certain species properties through a homogeneous population, we consider a reaction-diffusion equation that features a cubic-polynomial rate expression in the species concentration, with two stable UES and one intermediate unstable UES. This equation admits a remarkably simple exact analytical solution to the steadily propagating plane-wave eigenvalue problem. In the latter solution, the sign of the eigenvelocity is such that the wave propagates to yield the “preferred” stable UES (namely, the one further removed from the unstable intermediate UES) at all spatial points ast→∞. The cubic-polynomial equation also admits an exact steady-state solution for a mutant-deficient or mutant-isolated spatial pocket. Finally, the perpetuating growth of a mutant population from an arbitrary localized initial distribution, a mathematical problem analogous to that for ignition in laminar flame theory, is studied by applying differential inequality analysis, and rigorous sufficient conditions for extinction are derived here.     

Observations of rainbow trout, Salmo gairdneri Richardson, infected with Cryptobia salmostica

Rainbow trout, Salmo gairdneri , were experimentally infected with Cryptobia salmositica . The parasitaemia was associated with increases in the size of the spleen, liver and heart (% body weight). The splenomegaly was pronounced and was often 600-fold larger. The amounts of blood lactic acid and lactic dehydrogenase in the infected and control fish were similar. However, glycogen levels of the liver, heart and epaxial muscle declined. Liver glycogen levels were most affected and decreased to values which represented 20% of the control values. The pattern of the glycogen levels of the liver, heart and epaxial muscle declined to rise to normal values by day 56 post-inoculation. Thus, the glycogen levels both paralleled the acute parasitaemia and the subsequent partial recovery of the infected fish as they tolerated a low chronic parasitaemia.     

Growth-dependent expression of a cell surface glycoprotein

The expression of the hepatocellular membrane receptor for desialylated galactose-termining glycoproteins was studied during different proliferative stages of a human hepatoma cell line. Rapidly growing cells exhibited a reduced endocytotic rate of desialylated orsomucoid as compared to non-growing cells. This reduction was shown to be the consequence of a lower concentration of active cell-surface associated receptor protein in the dividing cells.     

Mise en evidence de l'existence de sensilles chemorecepteurs sur les antennes d'un crustace mysidace cavernicole et de l'intervention de ces sensilles dans la detection d'un extrait de nourriture

The cavernicolous crustacean Antromysis juberthiei showed unexpected behavior when presented with food extract : it avoids the area of odor inflow. This avoidance reaction is reduced by removal of various combinations of antennae and disappears almost with bilateral removal of the first antennae (the aesthetasc-bearing antennules).     

Quantification of human spermatogenesis: germ cell degeneration during spermatocytogenesis and meiosis in testes from younger and older adult men

Germ cell degeneration during spermatocytogenesis and meiosis was investigated to explain the age-related decline in daily sperm production (DSP). Numbers of Types A-dark, A-pale, and B-spermatogonia, potential daily sperm production per g parenchyma (PDSP) based on type B-spermatogonia, early primary spermatocytes, and late primary spermatocytes, and DSP per g based on early spermatids were determined in 15 men aged 20 to 48 yr (mean +/- SEM, 33 +/- 2 yr) and 15 men aged 52 to 90 yr (65 +/- 3 yr). Testes obtained within 15 h of death (largely due to trauma or heart failure) were perfused vascularly with glutaraldehyde. The number of each cell type per g parenchyma was calculated as the product of the percentage of nuclei in the parenchyma times a correction factor for section thickness and nuclear diameter divided by the volume of a single nucleus of that cell type. Paired testicular weight was lower (p less than 0.01) in older men (33 +/- 3 g) than in the younger men (49 +/- 3 g). Younger and older men had similar numbers of A-dark, A-pale, and B-spermatogonia per g parenchyma. PDSP based on late primary spermatocytes and DSP based on early spermatids were lower (p less than 0.01) in older men than in younger men. In younger men, PDSP was similar (p greater than 0.05) between B-spermatogonia and late primary spermatocytes, whereas DSP measured at the spermatid level was abruptly lower than that estimated from younger cell types. Older men showed reduction in PDSP between early and late primary spermatocytes, with further reduction occurring in DSP at the spermatid level.(ABSTRACT TRUNCATED AT 250 WORDS)