Dimensional analysis in mathematical biology I. General discussion

Dimensional analysis is discussed from the viewpoint of its basic group properties and shown to be an algebraic Abelian group that is useful for analysis of physical measurements. The application of the method to various types of equations and the formulation of previously unclassified dimensions are discussed. Functional dimensional analysis is applied to the problems of cell size and biomass proliferation; future applications are also noted. A number of dimensionless terms have been formulated for cellular physiochemical phenomena. They apparently represent the first systematic study of biological dimensionless numbers recorded in the literature. A dimensionless proliferation law is suggested. A brief analysis of the physical dimensionality associated with information measures is carried out. Entropy and “information” are shown to be completely different in their dimensional meaning; other informational measures of possible interest in biology are proposed. The dimensional coding and computor analysis of biomathematical equations is suggested.     

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GTP gamma S stimulation of endosome fusion suggests a role for a GTP-binding protein in the priming of vesicles before fusion.

Guanosine 5'-(3-O-thio)triphosphate (GTP gamma S), a non-hydrolyzable analogue of GTP, inhibits in vitro fusion among early endocytic vesicles in the presence of high concentrations of cytosol. In this report we show that fusion is remarkably stimulated by GTP gamma S under conditions where cytosolic components are the limiting factors for the process. The amount of cytosolic factors required for maximal fusion activity is several-fold decreased by the presence of GTP gamma S. Moreover, preincubation of vesicles in the presence of cytosol and GTP gamma S allows fusion to proceed even in the absence of cytosol. Our results indicate that a GTP-binding protein facilitates the binding of cytosolic factor(s) required for endosome fusion to the endosomal membrane and stabilizes a dilution-resistant intermediate of the fusion process.     

Reconstitution of endosomal proteolysis in a cell-free system. Transfer of immune complexes internalized via Fc receptors to an endosomal proteolytic compartment

The presence of acid proteases in the endosomal compartment of macrophages has been recently demonstrated (Diment, S., Leech, M. S., and Stahl, P. D. (1988) J. Biol. Chem. 263, 6901-6907). This proteolytic activity allows the early degradation of ligands internalized by receptor-mediated endocytosis. To study the early steps that initiate the proteolytic processing of ligands, immune complexes formed with anti-dinitrophenol monoclonal IgG and radiolabeled dinitrophenol-derivatized bovine serum albumin were bound at 4 degrees C to Fc receptors of J774 macrophages. Cells were allowed to internalize immune complexes bound to the plasma membrane for different periods of time at 37 degrees C. Vesicle preparations generated from these cells were incubated in vitro at acidic pH to allow the hydrolysis of ligands located in protease-positive compartments. Ligand hydrolysis was observed after about 5 min of internalization, suggesting that at earlier times immune complexes were located in protease-free vesicles. Upon incubation of cell lysates under conditions that support in vitro endosome-endosome fusion, early protease-free endosomes containing ligand acquire proteolytic activity. Reconstitution of fusion-dependent proteolysis required energy, ions, membrane-associated factors, and cytosol. Cytosol was inactivated by incubation with N-ethylmaleimide. The proteolytic compartment formed upon in vitro incubation colocalized with endosomes in the light region of a Percoll gradient. Reconstitution was also achieved using an endosomal preparation separated from lysosomes in a Percoll gradient. Our results indicate that a fusion step between newly formed endocytic vesicles and a light density, protease-positive compartment triggers the proteolytic processing of ligands internalized by receptor-mediated endocytosis.     

Emission of volatile sulfur compounds from spruce trees

Spruce (Picea Abies L.) trees from the same clone were supplied with different, but low, amounts of plant available sulfate in the soil (9.7-18.1 milligrams per 100 grams of soil). Branches attached to the trees were enclosed in a dynamic gas exchange cuvette and analyzed for the emission of volatile sulfur compounds. Independent of the sulfate supply in the soil, H₂S was the predominant reduced sulfur compound continuously emitted from the branches with high rates during the day and low rates in the night. In the light, as well as in the dark, the rates of H₂S emission increased exponentially with increasing water vapor flux from the needles. Approximately 1 nanomole of H₂S was found to be emitted per mole of water. When stomata were closed completely, only minute emission of H₂S was observed. Apparently, H₂S emission from the needles is highly dependent on stromatal aperture, and permeation through the cuticle is negligible. In several experiments, small amounts of dimethylsulfide and carbonylsulfide were also detected in a portion of the samples. However, SO₂ was the only sulfur compound consistently emitted from branches of spruce trees in addition to H₂S. Emission of SO₂ mainly proceeded via an outburst starting before the beginning of the light period. The total amount of SO₂ emitted from the needles during this outburst was correlated with the plant available sulfate in the soil. The diurnal changes in sulfur metabolism that may result in an outburst of SO₂ are discussed.     

Dual staining of natural bacterioplankton with 4',6-diamidino-2-phenylindole and fluorescent oligonucleotide probes targeting kingdom-level 16S rRNA sequences.

A method for quantifying eubacterial cell densities in dilute communities of small bacterioplankton is presented. Cells in water samples were stained with 4',6-diamidino-2-phenylindole (DAPI), transferred to gelatin-coated slides, and hybridized with rhodamine-labeled oligonucleotide probes specific for kingdom-level 16S rRNA sequences. Between 48 and 69% of the cells captured on membrane filters were transferred to gelatin-coated slides. The number of DAPI-stained cells that were visualized with eubacterial probes varied from 35 to 67%. Only 2 to 4% of these cells also fluoresced following hybridization with a probe designed to target a eukaryotic 16S rRNA sequence. Between 0.1 and 6% of the bacterioplankton in these samples were autofluorescent and may have been mistaken as cells that hybridized with fluorescent oligonucleotide probes. Dual staining allows precise estimates of the efficiency of transfers of cells to gelatin films and can be used to measure the percentage of the total bacterioplankton that also hybridize with fluorescent oligonucleotide probes, indicating specific phylogenetic groups.     

cis-trans isomers of lycopene and beta-carotene in human serum and tissues.

Since cis or trans isomers of carotenoids may have different biological reactivities, the isomeric composition of lycopene and beta-carotene was measured in serum and seven human tissues. In addition to all-trans lycopene, at least three cis-isomers (9-, 13-, and 15-cis) were present, accounting for more than 50% of total lycopene. 13- and 15-cis-beta-carotene, however, were present at only 5% of the all-trans isomer. In addition, 9-cis-beta-carotene was present in tissue samples but not in serum. There were interindividual differences in carotenoid levels of the different tissue types, but liver, adrenal gland, and testes always contained significantly higher amounts of the carotenoids than kidney, ovary, and fat; carotenoids in brain stem tissue were below the detection limit. beta-Carotene was the major carotenoid in liver, adrenal gland, kidney, ovary, and fat, whereas lycopene was the predominant carotenoid in testes.     

Cell-free phosphorylation of the murine small heat-shock protein hsp25 by an endogenous kinase from Ehrlich ascites tumor cells.

The small heat-shock protein hsp25 of the Ehrlich ascites tumor exists in one non-phosphorylated (hsp25/1) and two phosphorylated (hsp25/2, hsp25/3) isoforms. In stationary phase tumor cells, a protein kinase activity was detected which phosphorylates hsp25/1, resulting in the formation of several phosphorylated hsp25 isoforms, including those occurring naturally in the tumor. Cell-free phosphorylation of hsp25 required Mg2+ and ATP and was independent of Ca2+, phosphatidylserine, cAMP and cGMP. Polymyxin B inhibited, specifically, hsp25 phosphorylation, whereas trifluoperazine, staurosporine and the protein inhibitor of protein kinase A had no effect. In its properties, the hsp25 phosphorylating kinase differs from other common kinases such as protein kinases A and C, calcium/calmodulin-dependent kinases, and the ribosomal protein S6 kinase.