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.     

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.     

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)     

Radiometric assay for cytochrome P-450-catalyzed progesterone 16 alpha-hydroxylation and determination of an apparent isotope effect

In the course of studies on the oxygenation of steroids by purified P-450 cytochromes, particularly rabbit liver microsomal cytochrome P-450 form 3b, a rapid and reliable radiometric assay has been devised for progesterone 16 alpha-hydroxylation. In view of the lack of a commercially available, suitably tritiated substrate, [1,2,6,7,16,17-3H]progesterone was treated with alkali to remove the label from potential hydroxylation sites other than the 16 alpha position. The resulting [1,7,16-3H]progesterone was added to a reconstituted enzyme system containing cytochrome P-450 form 3b, NADPH-cytochrome P-450 reductase, and NADPH, and the rate of 16 alpha-hydroxylation was measured by the formation of 3H2O. This reaction was shown to be linear with respect to time and to the cytochrome P-450 concentration. An apparent tritium isotope effect of 2.1 was observed by comparison of the rates of formation of tritium oxide and 16 alpha-hydroxyprogesterone, and the magnitude of the isotope effect was confirmed by an isotope competition assay in which a mixture of [1,7,16-3H]progesterone and [4-14C]progesterone was employed.     

Identity cards for patients infected with HIV?

Dr A C Srivastava has written to us to describe a case that raises the suggestion that people infected with the human immuno-deficiency virus (HIV) should carry identity cards. We asked two physicians, a general practitioner working with patients with the acquired immune deficiency syndrome (AIDS), and a general practitioner with a special interest in medical ethics to respond to the broad issues raised by Dr Srivastava''s letter.     

A predictive model for freshwater bioassessment (Mondego River,Portugal)

We sampled macroinvertebrates at 75 locations in the Mondego river catchment, Central Portugal, and developed a predictive model for water quality assessment of this basin, based on the Reference Condition Approach. Sampling was done from June to September 2001. Fifty-five sites were identified as “Reference sites” and 20 sites were used as “Test sites” to test the model. At each site we also measured 40 habitat variables to characterize water physics and chemistry, habitat type, land use, stream hydrology and geographic location. Macroinvertebrates were generally identified to species or genus level; a total of 207 taxa were found. By Unweighted Pair Group Method with Arithmetic mean (UPGMA) clustering and analysis of species contribution to similarities percentage (SIMPER), two groups of reference sites were established. Using Discriminant Analysis (stepwise forward), four variables correctly predicted 78% of the reference sites to the appropriate group: stream order, pool quality, substrate quality and current velocity. Test sites’ environmental quality was established from their relative distance to reference sites, in MDS ordination space, using a series of bands (BEAST methodology). The model performed well at upstream sites, but at downstream sites it was compromised by the lack of reference sites. As with the English RIVPACS predictive model, the Mondego model should be continually improved with the addition of new reference sites. The adaptation of the Mondego model methodology to the Water Framework Directive is possible and would consist mainly of the integration of the WFD typology and increasing the number of ellipses that define quality bands. Handling editor: K. Martens