The mathematical properties of the quasi-chemical model for microorganism growth-death kinetics in foods.

Knowledge of the mathematical properties of the quasi-chemical model [Taub, Feeherry, Ross, Kustin, Doona, 2003. A quasi-chemical kinetics model for the growth and death of Staphylococcus aureus in intermediate moisture bread. J. Food Sci. 68 (8), 2530-2537], which is used to characterize and predict microbial growth-death kinetics in foods, is important for its applications in predictive microbiology. The model consists of a system of four ordinary differential equations (ODEs), which govern the temporal dependence of the bacterial life cycle (the lag, exponential growth, stationary, and death phases, respectively). The ODE system derives from a hypothetical four-step reaction scheme that postulates the activity of a critical intermediate as an antagonist to growth (perhaps through a quorum sensing biomechanism). The general behavior of the solutions to the ODEs is illustrated by several examples. In instances when explicit mathematical solutions to these ODEs are not obtainable, mathematical approximations are used to find solutions that are helpful in evaluating growth in the early stages and again near the end of the process. Useful solutions for the ODE system are also obtained in the case where the rate of antagonist formation is small. The examples and the approximate solutions provide guidance in the parameter estimation that must be done when fitting the model to data. The general behavior of the solutions is illustrated by examples, and the MATLAB programs with worked examples are included in the appendices for use by predictive microbiologists for data collected independently.

Unprecedented forms of vanadium observed within the blood cells of Phallusia nigra using K-edge X-ray absorption spectroscopy.

Fits to the vanadium K-edge X-ray absorption spectra (XAS) of five whole blood cell samples from the tunicate Phallusia nigra revealed unprecedented forms of intracellular vanadium. Endogenous vanadium was divided between the V(III) ion (74.2+/-5.1% of total V) and the vanadyl ion [V(IV)=O](2+) (25.2+/-5.4% of total V). The V(III) fraction included both [V(H(2)O)(6)](3+) (36.7+/-5.5%) modeled as VCl(3) in 1 M HCl, and three previously unprecedented chelated V(III) forms (37.5+/-4.6%). Two of these could be represented by the model ligand environments V(acetylacetonate)(3) (17.9+/-3.2%) and K(3)V(catecholate)(3) (13.1+/-4.7%), implying DOPA-like complexation. The third chelated form was represented by the 7-coordinate N(2)O(5) complex Na[V(edta)(H(2)O)] (8.0+/-1.8%). This coordination array, suggestive of a novel mononuclear V(III) protein site, contributed only to fits to samples 1, 2, 3 and 5, which were prepared in the presence of DTT. Endogenous V(IV) (25.2+/-5.4%) was principally modeled as VOCl(2) in 1 M HCl. EPR spectra (averages: A(parallel)=(1.842+/-0.006)x10(-2) cm(-1); A( perpendicular)=(0.718+/-0.007)x10(-2) cm(-1); g(parallel)=1.936+/-0.002; g( perpendicular)=1.990+/-0.001) confirmed the predominance of the aquated vanadyl ion. Blood cell sample five uniquely required the XAS spectrum of VOSO(4) in 0.1 M H(2)SO(4) solution (13.0%) and of [OV(V)(pivalate)(3)] (3.1%) to successfully fit the XAS pre-edge energy region. This endogenous V(V) signal is also unprecedented. These results are compared with those of analogous fits to the blood cells of Ascidia ceratodes and may support assignment of P. nigra to a different genus.

Vanadium K-edge x-ray absorption spectroscopy reveals species differences within the same ascidian genera. A comparison of whole blood from Ascidia nigra and Ascidia ceratodes.

Vanadium K-edge x-ray absorption spectroscopy (XAS) was used to examine whole blood preparations from the tunicates Ascidia nigra and Ascidia ceratodes. Each XAS spectrum exhibits a rising edge inflection near 5480 eV characteristic of vanadium(III) and an intensity maximum at 5484.0 eV. In A. ceratodes blood cells, intrinsic aquo-VSO4+ complex ion is indicated by an inflection feature at 5476 eV in the first derivative of the vanadium K-edge XAS spectrum, but this feature is notably absent from the first derivative of the vanadium K-edge spectrum of blood cells from A. nigra. A strong pre-edge feature at 5468.6 eV also uniquely distinguishes the vanadium K-edge XAS spectrum of A. nigra blood cells, implying that vanadyl ion represents approximately 25% of the endogenous vanadium. However, the energy position of the rising edge inflection of the vanadium K-edge XAS spectrum of A. nigra (5479.5 eV) is 1 eV lower than that of A. ceratodes (5480.5 eV), the reverse of any expected shift arising from the endogenous vanadyl ion. Thus, in contrast to A. ceratodes, a significant fraction of the blood cell vanadium(III) in A. nigra is apparently in a ligation environment substantially different from that provided by water. These novel species-related differences may have taxonomic significance.

Magnetic properties of tunicate blood cells. II. Ascidia ceratodes.

The magnetic properties of intact blood cells of the tunicate Ascidia ceratodes have been measured up to 50 kOe with a SQUID susceptometer. Analysis of total metal contents by plasma emission spectroscopy and V(IV) content by epr indicates that approximately 5% of the accumulated vanadium is +4 vanadyl ion. Measured values of the magnetic moment Mp at different values of the applied magnetic field H over the temperature range T = 2-100 K depend on the magnitude of the field indicating magnetic anisotropy of the ground state. The slope of the Mp vs. H/T curve at high temperature is significantly higher than expected from electron spin S = 1 per vanadium(III) ion. The model that fits these data best is a dimer with one V(III) S = 1 ion ferromagnetically coupled to a second V(III) S = 1 ion, with spin-coupling constant J = 3.5 cm-1, and 5% of the total vanadium content in the form of a V(IV) S = 1/2 ion. Since vanadium in A. ceratodes is known to reside in at least three different types of blood cell, the excellent fit indicates that the metal is stored predominantly as a dimer regardless of blood cell type. Ferromagnetic coupling implies that the two vanadium ions in the dimer are connected by an unprotonated mu-oxo bridge.

Glycolytic pH oscillations in a flow reactor.

A new type of flow reactor (UCSTR) has been developed that uses anisotropic ultrafiltration membranes in a continuous flow stirred tank reactor (CSTR) to facilitate the study of nonlinear enzyme catalyzed reactions. The design allows the study of enzymes with subunit molecular weights > or = 9000 dalton and protein concentrations up to at least 2 mg/ml under flow conditions with a residence time of 3 min or more, in a reactor of volume 1.67 ml. The UCSTR allows continuous potentiometric or spectrophotometric measurement without design change. Calibration of reactor performance was carried out by reproducing pH oscillations in the ferrocyanide-hydrogen peroxide reaction. Experimental verification of oscillatory glycolysis in the UCSTR was carried out with extract of rat skeletal muscle. Input feeds were fructose-6-phosphate and ATP with low concentrations of phosphate as buffer. Oscillations in pH, sustained for over eight hours, were observed. A six-step mechanism, including product activation and substrate inhibition, seven concentration variables, and four enzymes sufficed simulate the pH oscillations observed in the UCSTR.

In vivo incorporation of 14C-phenylalanine into ascidian tunichrome.

Ascidia ceratodes exposed to 14C-phenylalanine in the surrounding seawater incorporates the radiolabel into newly biosynthesized tunichrome molecules. Radioactivity can be detected in tunichrome extracted from circulating blood cells within one day following initial exposure to the radiolabel; weak activity (less than or equal to 4 microCi/mol tunichrome = 22 nmol phenylalanine/mol tunichrome) is detected in 1 to 10 days; significantly higher amounts of radiolabel (57 microCi/mol tunichrome = 318 nmol phenylalanine/mol tunichrome) appear 20 days after seawater exposure. Therefore, phenylalanine can function as a precursor in the biosynthesis of tunichrome.

The intracellular pH of tunicate blood cells: Ascidia ceratodes whole blood, morula cells, vacuoles and cytoplasm.

The intracellular pH of blood cells of the tunicate Ascidia ceratodes has been measured by equilibration of radioactively labeled markers between intra- and extracellular media. Labeled acid, 5,5-dimethyloxazolidine-2,4-dione (DMO), and base, methylamine (MA), have been used in the range of extracellular pH (pHm) of 4.5-7. For unsorted blood cells MA is less sensitive to the transmembrane pH gradient (delta pH) than is DMO in the pHm of 6.3-7. The data measured by DMO yield an intracellular pH value of 6.98 +/- 0.15. Ficoll density gradients separated 86.4% pure morula cells. Other experiments show that morula cells contain significant amounts of vanadium and most of the free tunichrome. Using both MA and DMO with morula cells yields pH values of 5.0 +/- 0.2 for the vacuoles and 7.1 +/- 0.2 for the cytoplasm. If vanadium is accumulated in the intravacuolar solution space, then this mildly acidic pH indicates that the aquo V3+ ion, which is only stable below pH 3, is stabilized by some factor other than high hydrogen ion concentration. This factor may be chelation by tunichrome. It is also possible that accumulated vanadium(III) is sequestered in hydrophobic regions of the vacuolar or cellular membranes.

Distribution of tunichrome and vanadium in sea squirt blood cells sorted by flow cytometry.

Specialized blood cells of many tunicates accumulate high concentrations of vanadium and phenolic peptide pigments called tunichromes (TC). In order to determine whether V and TC reside in the same cells, Ascidia nigra and Ascidia ceratodes blood cell subpopulations were isolated by fluorescence-activated cell sorting (flow cytometry) and chemically analyzed. V was found in the spherical, green/grey signet ring cells, and to a lesser degree in the mulberry-shaped, yellow/green morula cells (MRs), whereas free TC was detected mainly in MRs.

Magnetic properties of tunicate blood cells. I. Ascidia nigra.

The magnetic properties of intact and freeze-dried blood cells of the tunicate Ascidia nigra and of model vanadium(III) and (IV) compounds as polycrystalline solids and in aqueous solution have been measured up to 50 kOe with a SQUID susceptometer. Corrections for the samples' diamagnetism were extracted from the temperature dependence of the data without any further assumptions. For vanadium(IV), measured values of the magnetic moment at different values of the applied magnetic field over the temperature range 2-100 K obey a Brillouin function with spin 1/2. For vanadium(III), the magnetic moment data did not obey a Brillouin function and were analyzed in terms of a spin Hamiltonian with S = 1. Measurements on both whole and freeze-dried blood samples give consistent results with vanadium(III) the predominant species. These results are discussed in terms of the mechanisms of vanadium accumulation and the use of vanadium oxidation states as criteria of ascidian taxonomy.

Relaxation spectra of gramicidin dimerization in a lipid bilayer membrane.

The kinetics of formation and dissociation of gramicidin dimers in a lipid bilayer membrane have been studied by pressure-jump and electric field-jump methods. The traditional AC-coupled pressure-jump apparatus has been modified so that a known DC-voltage drop is maintained across a Teflon cell divided by a septum with a hole for membrane formation. From the response of the amplified output voltage after the pressure release, information about the kinetics of channel (dimer) formation is obtained. In addition, using the same apparatus, electric field-jump measurements were performed on the gramicidin/membrane system. In asolectin/7-dehydrocholesterol (5:1) membranes at 25 +/- 0.1 degrees C, the best fit to the pressure-jump data gives a dimer dissociation rate constant of 0.5 +/- 0.3 s-1. The standard volume change for dimerization determined from the amplitude of the pressure-jump experiments is -66 +/- 35 cm3/mol. Rate data determined by the electric field-jump method are consistent with the pressure-jump values; results obtained with either technique are compatible with other determinations of the kinetics of dimerization on gramicidin/membrane systems.

Isolation of tunichrome B-1, a reducing blood pigment of the sea squirt, Ascidia nigra.

The tunicates, or sea squirts, are common marine organisms that selectively accumulate metals such as V, Fe, Mo, Nb, in their blood cells. Despite the more than 70 years of interest in the compounds responsible for this accumulation, their extreme lability has eluded attempts to isolate and characterize them. The isolation and structure of the first of these blood pigments tunichrome B-1 from the Ascidia nigra is reported.

The influence of tunichrome and other reducing compounds on tunic and fin formation in embryonic Ascidia callosa Stimpson.

Tunic in 46-hr-old Ascidia callosa larvae reared from dechorionated neurulae is either markedly reduced in thickness or absent altogether. The epidermis is fragile and cuticular fins fail to develop. Dechorionated neurulae treated with tunichrome and other reducing compounds (e.g., glutathione, ascorbate) show an enhancement in tunic formation and rudimentary fin development. UV absorbance spectra of extracts from unfertilized eggs, late tail-bud embryos, and tadpole larvae indicate that tunichrome may be present in all developmental stages. Experiments with neurulae in which the chorion was punctured with tungsten needles but not removed signify that the test cells are the most likely source of tunichrome. Results are consistent with the hypothesis that tunichrome is involved in the natural processes of tunic morphogenesis in ascidian embryos.

Do vanadate polyanions inhibit phosphotransferase enzymes?

Decavanadate inhibits hexokinase, adenylate kinase and phosphofructokinase; neither mono-, tri nor tetrameric vanadate anion is an inhibitor. Decavanadate inhibits phosphofructokinase obtained from bacterial and protistic sources. No form of vanadium(V) anion inhibits galacto-, glycero-, pyruvate and creatine kinase, or inorganic pyrophosphatase. Decavanadate appears to be a non-competitive inhibitor of both hexokinase substrates.

Tunichrome content in the blood cells of the tunicate, Ascidia callosa Stimpson, as an indicator of vanadium distribution.

Morula, compartment, signet ring, orange, lymphocyte and amoebocyte (granular and agranular) cells have been identified in the blood of A. callosa; in addition, nephrocytes have been described. Blood cell lysates contain a yellow chromogen with spectrophotometric and fluorimetric properties similar to tunichrome. The fluorescent characteristics of each of the seven blood cell types were determined using microspectrofluorimetry. Vanadium in A. callosa blood cells is primarily associated with tunichrome extracts, although lesser amounts are measurable in blood plasma and blood cell residues; both vanadium and tunichrome concentrations are in the order morula greater than compartment greater than signet ring cells.

Kinetics and mechanism of Zn(II) complexation with reduced glutathione.

The kinetics of formation and dissociation of mono and bis complexes of Zn(II) with reduced glutathione (H4L+ = fully protonated form) were studied in aqueous solution at 25.0 +/- 0.1 degrees C and ionic strength 0.30 M (NaNO3) in the pH range 4.58 to 4.98 by temperature-jump. The reaction was found to proceed via two different mechanisms depending on degree of ligand protonation. In both cases, complex formation is predominantly if not completely through the sulfur. Reaction with the form HL-2 (only the amino nitrogen protonated), the dominant form of this species, proceeds by the expected rat limiting water loss (dissociative or Eigen) mechanism with rate constants of 9.3 X 10(7) M-1 sec-1 (+/- 24%) for mono and 5.1 X 10(7) M-1 sec-1 (+/- 25%) for bis complex formation. Reaction with H2L--(sulfur protonated) yields rate constants of 3.9 X 10(3) M-1 sec-1 (+/- 43%) for mono and 1.95 X 10(3) M-1 sec-1 (+/- 43%) for bis complex formation. The decrease in rate constant is attributed to blockage of the complexing site on reduced glutathione by intramolecular hydrogen bonding, with proton removal being the rate determining step.

Vanadium-containing tunicate blood cells are not highly acidic.

The intracellular pH of intact blood cells of the tunicate Ascidia nigra was measured by transmembrane equilibration of [14C] methylamine. The pH of unfractionated blood cells is 7.39 +/- 1.10. The pH of vanadocytes, determined in a fractionation study, is 7.2. Previously used methods, in which pH values less than 3.0 are inferred from cell lysis or vital staining experiments, are shown to be unsuitable for intracellular pH determination due to the chemical composition of these vanadium-containing cells.

Glutathione reduces cytoplasmic vanadate. Mechanism and physiological implications.

The mechanism by which cells reduce cytoplasmic vanadium(V) (vanadate) to vanadium(IV) was investigated using the human red cell as a model system. Vanadate uptake by red cells occurs with a rapid phase involving chemical equilibration across the plasma membrane and a slower phase resulting in a high concentration of bound vanadium(IV). The slow phase was inhibited in glucose-starved cells and restored upon addition of glucose indicating an energy requirement for this process. The time course of vanadium(IV) appearance (monitored by EPR spectroscopy of intact cells) paralleled the slow phase of uptake indicating that this phase involves vanadium reduction. The reduction of intracellular vanadate to vanadium(IV) was nearly quantitative after 23 h. The intracellular reduction is not enzymatic, since a similar time course of vanadium reduction and binding to hemoglobin was observed when glutathione was added to a hemoglobin + vanadate solution in vitro. Vanadium(IV) binding to hemoglobin was reduced by addition of ATP, 2,3-diphosphoglycerate or EDTA, probably through chelation of the cation. The stability constant of the ATP-vanadium (IV) complex was determined to be 150 M-1 at pH 4.9. The time course of red cell vanadate uptake and reduction was followed in the concentration range in which approximately 60% inhibition of the (Na+ + K+)-ATPase is observed. It is concluded that vanadate is reduced by cytoplasmic glutathione in this concentration range and that the reduction explains the resistance of the (Na+ + K+)-ATPase to vanadium in intact cells.