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.     

Hemopexin-mediated heme uptake by liver. Characterization of the interaction of heme-hemopexin with isolated rabbit liver plasma membranes

Plasma membranes isolated from rabbit liver retain the ability to interact specifically with heme-hemopexin. In this system, apohemopexin does not compete effectively with heme-hemopexin for binding. The membranes bind heme-hemopexin complexes with high affinity (KD = 6.8 X 10(-7) M) and with an apparent capacity of 2.3 pmol/mg of membrane protein. These membranes also retain the ability to remove heme from heme-hemopexin. The release of heme reaches a plateau after 15-30 min at 30 degrees C and does not involve metabolic energy, proteolysis of hemopexin or pH gradients. The apohemopexin formed is rapidly released from the membranes. The accumulation of heme is saturable and is affected by pH and temperature with maximum uptake occurring between pH 5.5 and 6.5 and at 30 degrees C. Interestingly, much more heme (approximately 25 pmol/mg of membrane protein) is accumulated than hemopexin at saturation, implying that the receptor can turn over several times and that a heme-binding component exists in the rabbit liver plasma membrane.     

Sulphamerazine toxicity in cut-throat trout broodfish Salmo clarki (Richardson)

Treatment of cut-throat trout broodfish Salmo clarki (Richardson) with Sulphamerazine at 220 mg/kg (10 g/100 1b) of fish/day for 14 days resulted in severe kidney histopathology and increased mortality among males. Experimental data presented showed that cut-throat trout broodfish were extremely sensitive to Sulphamerazine toxicity. Hydropic degeneration of renal tubule epithelium and haemorrhage into tubule lumens were observed in kidneys of both male and female trout, but was more severe in the former. Death, which occurred only in males, was correlated with spawning stress and impaired renal function.     

Viscoelasticity of packed erythrocyte suspensions subjected to low amplitude oscillatory deformation.

Concentrated adult erythrocyte suspensions were subjected to low amplitude oscillatory shear in a Weissenberg rheogoniometer equipped with a cone-and-plate assembly. The dynamic viscoelastic properties of the suspension were measured over a broad range of frequency by a numerical solution that accounted for fluid inertia. Variation of shear amplitude and cell volume percent, and comparison of buffered saline, plasma, and dextran as suspending media showed that the cellular elements had undergone small bending and shearing deformations. Studies of normal adult erythrocytes, hypotonically swollen cells, temperature-altered cells, and erythrocyte ghosts suggested that the method was evaluating membrane material properties. The normal membrane was found to exhibit a shear rate dependent elastic modulus that increased by more than a factor of 20 over a frequency range from 0.0076 Hz to 60 Hz. The membrane viscosity showed a substantial drop with frequency indicative of a frequency thinning phenomenon. At high frequency of deformation the viscous response of normal erythrocytes was no longer indicative of a membrane property due to the dominant influence of the internal hemoglobin solution. The studies generally supported the ability of the method to quantify relative membrane material properties and detect changes in membrane structure.     

Ventilatory responses to specific CNS hypoxia in sleeping dogs.

Our study was concerned with the effect of brain hypoxia on cardiorespiratory control in the sleeping dog. Eleven unanesthetized dogs were studied; seven were prepared for vascular isolation and extracorporeal perfusion of the carotid body to assess the effects of systemic [and, therefore, central nervous system (CNS)] hypoxia (arterial PO(2) = 52, 45, and 38 Torr) in the presence of a normocapnic, normoxic, and normohydric carotid body during non-rapid eye movement sleep. A lack of ventilatory response to systemic boluses of sodium cyanide during carotid body perfusion demonstrated isolation of the perfused carotid body and lack of other significant peripheral chemosensitivity. Four additional dogs were carotid body denervated and exposed to whole body hypoxia for comparison. In the sleeping dog with an intact and perfused carotid body exposed to specific CNS hypoxia, we found the following. 1) CNS hypoxia for 5-25 min resulted in modest but significant hyperventilation and hypocapnia (minute ventilation increased 29 +/- 7% at arterial PO(2) = 38 Torr); carotid body-denervated dogs showed no ventilatory response to hypoxia. 2) The hyperventilation was caused by increased breathing frequency. 3) The hyperventilatory response developed rapidly (<30 s). 4) Most dogs maintained hyperventilation for up to 25 min of hypoxic exposure. 5) There were no significant changes in blood pressure or heart rate. We conclude that specific CNS hypoxia, in the presence of an intact carotid body maintained normoxic and normocapnic, does not depress and usually stimulates breathing during non-rapid eye movement sleep. The rapidity of the response suggests a chemoreflex meditated by hypoxia-sensitive respiratory-related neurons in the CNS.     

Social status and reproductive success of male Macaca fascicularis

Dominant males of nonseasonally breeding species should have more opportunity than seasonal breeders to monopolize access to estrous females and thus enhance their reproductive success. They may also use other strategies for maximizing reproductive success such as producing offspring by relatively high ranking females. To test these hypotheses, the paternity of 35 (80%) of 44 Macaca fascicularis offspring, born over a 28-month period, was established using electrophoretically and serologically defined genetic markers. The social ranks of each of the seven potential fathers and 26 potential mothers were determined by recording outcomes of dyadio agonistic interactions. No evidence could be found to support either hypothesis. Further, in view of previously reported significant, positive correlations between male social rank and sexual activity rates in this study group, sexual activity rates do not appear to predict the number of offspring a male sires in this species.