The paradox of the clumps mathematically explained

The lumpy distribution of species along a continuous one-dimensional niche axis recently found by Scheffer and van Nes (Scheffer and van Ness 2006) is explained mathematically. We show that it emerges simply from the eigenvalue and eigenvectors of the community matrix. Both the transient patterns—lumps and gaps between them—as well as the asymptotic equilibrium are explained. If the species are evenly distributed along the niche axis, the emergence of these patterns can be demonstrated analytically. The more general case, of randomly distributed species, shows only slight deviations and is illustrated by numerical simulation. This is a robust result whenever the finiteness of the niche is taken into account: it can be extended to different analytic dependence of the interaction coefficients with the distance on the niche axis (i.e., different kernel interactions), different boundary conditions, etc. We also found that there is a critical value both for the width of the species distribution σ and the number of species n below which the clusterization disappears.

In-vitro heat exchange at the rete of the Boer goat under specified laboratory conditions

1. Each half rete from five Boer goats was perfused with water at 38 °C and flow rate of 2 ml min⁻¹ while simultaneously perfusing the cavernous sinus with water at different temperatures and flow combinations and recording temperatures across the rete.

2. The minimum temperature difference across the rete was recorded at a cavernous sinus perfusion temperature of 37.8 °C and flow rate of 2 ml min⁻¹.

3. Slopes of heat exchange increased threefold when the flow was increased four times.

4. These results support the idea that the rete is an obligate heat exchanger.

Extending the method of mathematically controlled comparison to include numerical comparisons

MOTIVATION: The method of mathematically controlled comparison has been used for some time to determine which of two alternative regulatory designs is better according to specific quantitative criteria for functional effectiveness. In some cases, the results obtained using this technique are general and independent of parameter values and the answers are clear-cut. In others, the result might be general, but the demonstration is difficult and numerical results with specific parameter values can help to clarify the situation. In either case, numerical results with specific parameter values can also provide an answer to the question of how much larger the values might be. In contrast, a more ambiguous result is obtained when either of the alternatives can have the larger value for a given systemic property, depending on the specific values of the parameters. In any case, introduction of specific values for the parameters reduces the generality of the results. Therefore, we have been motivated to develop and apply statistical methods that would permit the use of numerical values for the parameters and yet retain some of the generality that makes mathematically controlled comparison so attractive. RESULTS: We illustrate this new numerical method in a step-by-step application using a very simple didactic example. We also validate the results by comparison with the corresponding results obtained using the previously developed analytical method. The analytical approach is briefly present for reference purposes, since some of the same key concepts are needed to understand the numerical method and the results are needed for comparison. The numerical method confirms the qualitative differences between the systemic behavior of alternative designs obtained from the analytical method. In addition, the numerical method allows for quantification of the differences and it provides results that are general in a statistical sense. For example, the older analytical method showed that overall feedback inhibition in an unbranched pathway makes the system more robust whereas it decreases the stability margin of the steady state. The numerical method shows that the magnitudes of these differences are not comparable. The differences in stability margins (1-2% on average) are small when compared to the differences in robustness (50-100% on average). Furthermore, the numerical method shows that the system with overall feedback responds more quickly to change than the otherwise equivalent system without overall feedback. These results suggest reasons why overall feedback inhibition is such a prevalent regulatory pattern in unbranched biosynthetic pathways.     

Maximizing the use of the abdominoplasty incision

Candidates for abdominoplasty often request multiple procedures at the time of consultation. Some of these patients have the potential opportunity to have ancillary procedures performed through the abdominoplasty incision, such as breast augmentation or suction-assisted lipectomy. Access via the abdominoplasty incision can also limit the need for distant donor sites, for instance, when autologous fillers or rib graft are necessary. The techniques described are straightforward and are based on standard principles that should be considered when ancillary procedures are performed in conjunction with abdominal contouring procedures. In a review of 70 consecutive patients undergoing abdominoplasty, 91 ancillary procedures were performed in conjunction with the abdominoplasty. Of the total number of patients undergoing abdominoplasty, 29 patients underwent 30 procedures facilitated through their abdominoplasty incision, including 23 suction-assisted lipectomies of the flanks, six breast augmentations, and one rib cartilage harvesting for rhinoplasty. A review of the author's experience and discussion for potential options afforded by this exposure are presented.     

The effect of misonidazole as a hypoxic radiosensitizer at low dose

Using an automated low dose survival assay, the radiosensitizing effectiveness of misonidazole at low radiation dose (0-6 Gy) was measured in cultured mammalian cells. Also measured was its effectiveness at high doses of radiation (0-35 Gy) using the conventional survival assay. In both cases, several concentrations of the drug from 0 to 5 mM were used. The data at low doses were analyzed by a two-parameter mathematical equation with linear and quadratic dose terms, S = e-alpha D-beta D2, which proved to be a good fit to the experimental data at all misonidazole concentrations. It is shown that whereas the coefficient of the quadratic dose term, beta, increases significantly with increasing misonidazole concentration, the drug does not significantly affect the coefficient of the linear term, alpha. The enhancement ratio (ER) of misonidazole is shown to be decreased at lower doses. The clinical implications of this result are discussed.     

Long-term inhibition of ovulation by a GnRH-antagonist at low dose level

Ac-D-Trp1,3, D-Cpa2, D-Lys6, D-Ala10-GnRH has been prepared by solid phase synthesis. The peptide was found to completely inhibit ovulation when administered on proestrus day in a dose of 1.5 microgram/rat, s.c. The peptide completely inhibited ovulation for a period corresponding to three to four cycles when administered daily in a dose of 5 micrograms/rat, s.c. and caused 70% inhibition of ovulation in a dose of 3 micrograms/rat.     

Equilibrium calculations on systems of biochemical reactions at specified pH and pMg.

The use of G' in discussing the thermodynamics of biochemical reactions at a specified pH and pMg is justified by use of a Legendre transform of the Gibbs energy G. When several enzymatic reactions occur simultaneously in a system, the standard transformed Gibbs energies of reaction delta rG'0 can be used in a computer program to calculate the equilibrium composition that minimizes the transformed Gibbs energy at the specified pH and pMg. The calculation of standard transformed Gibbs energies of formation of reactants at pH 7 and pMg 3 is described. In addition a method for calculating the equilibrium concentrations of reactants is illustrated for a system with steady state concentrations of some reactants like ATP and NAD.     

Equilibrium concentrations for pyruvate dehydrogenase and the citric acid cycle at specified concentrations of certain coenzymes

It is of interest to calculate equilibrium compositions of systems of biochemical reactions at specified concentrations of coenzymes because these reactants tend to be in steady states. Thermodynamic calculations under these conditions require the definition of a further transformed Gibbs energy G" by use of a Legendre transform. These calculations are applied to the pyruvate dehydrogenase reaction plus the citric acid cycle, but steady-state concentrations of CoA, acetyl-CoA and succinyl-CoA cannot be specified because they are involved in the conservation of carbon atoms. These calculations require the use of linear algebra to obtain further transformed Gibbs energies of formation of reactants and computer programs to calculate equilibrium compositions. At specified temperature, pH, ionic strength and specified concentrations of several coenzymes, the equilibrium composition depends on the specified concentrations of the coenzymes and the initial amounts of reactants.     

The development of a radioimmunoassay for formoterol

The development of a radioimmunoassay (RIA) for the beta 2-stimulant formoterol is described. The sensitivity of the method is 0.1 ng/ml in plasma and urine, when a 1-ml sample is used. The cross-reactivity of the antiserum with formoterol glucuronide was 30%. Since formoterol is metabolized extensively to formoterol glucuronide in rats, dogs and humans, extraction with ethyl ether prior to the radioimmunoassay was carried out. Satisfactory agreement was obtained for levels of formoterol in plasma and urine when they were determined by RIA and gas chromatography-mass spectrometry. The concentration of formoterol was determined in dog plasma and human urine after oral administration of formoterol fumarate to dogs (61 mcg/kg) and humans (40 mcg).     

Development of a radioimmunoassay for the soybean phytoalexin glyceollin I

A radioimmunoassay for glyceollin I, the major phytoalexin produced by soybean (Glycine max [L.] Merr.), has been developed. Antibodies were raised in rabbits against a glyceollin I-bovine serum albumin conjugate. The antisera were used to establish a radioimmunoassay for glyceollin I using [¹²⁵I]glyceollin I as the tracer. A logit plot of a standard concentration series yielded a straight line in the range of 1 to 100 picomoles (0.34-34 nanograms) of glyceollin I. The structurally related pterocarpan phytoalexins, glyceollins II and III, glyceollidin II and glycinol, which also accumulate in infected soybean tissue, show a low cross-reactivity in the radioimmunoassay (0.5-5% at 50% displacement of the tracer). Two related isoflavones present constitutively in soybean tissue, daidzein and genistein, have cross-reactivities of less than 0.84% and 1.1%, respectively. The radioimmunoassay permitted the quantitative determination of glyceollin I in 15-micrometer microtome sections of soybean hypocotyl tissue infected with zoospores of Phytophthora megasperma f. sp. glycinea.     

Fine structure of changes produced in cultured cells sampled at specified intervals during a single growth cycle of polio virus

Primary suspended cultures of rhesus monkey kidney cells were infected with poliomyelitis virus, type 1 (Brunhilde strain). The release of virus from these cells over a one-step growth curve was correlated with their change in fine structure, as seen in the electron microscope. Most of the cells were infected nearly simultaneously, and morphological changes developed in the cells were sufficiently synchronous to be classified into three stages. The earliest change (stage I) became visible at a time when virus release into the culture fluid begins, some 3 hours after adsorption. Accentuation of the abnormal characteristics soon occurs, at 4 to 7 hours after adsorption, and results in stage II. Stage III represents the appearance of cells after their rate of virus release had passed its maximum, and probably the abnormal morphology of these cells reflects non-specific physiological damage. There seems to be consistency between the previously described cellular changes as seen under the light microscope and the finer scale changes reported here. Cytoplasmic bodies, called U bodies, were seen in large number at the time when the virus release was the most rapid (stage II). While these bodies are not of proper size to be considered polio virus, they seem to be specifically related to the infection. No evidence was found for the presence of particles that could even be presumptively identified with those of polio virus.     

Maximizing the functional lifetime of Protein A resins

Protein A chromatography is currently the industry gold‐standard for monoclonal antibody and Fc‐fusion protein purification. The high cost of Protein A, however, makes resin lifetime and resin reuse an important factor for process economics. Typical resin lifetime studies performed in the industry usually examine the effect of resin re‐use on binding capacity, yield, and product quality without answering the fundamental question of what is causing the decrease in performance. A two part mechanistic study was conducted in an attempt to decouple the effect of the two possible factors (resin hydrolysis and/or degradation vs. resin fouling) on column performance over lifetime of the most commonly used alkali‐stable Protein A resins (MabSelect SuRe and MabSelect SuRe LX). The change in binding capacity as a function of sodium hydroxide concentration (rate of hydrolysis), temperature, and stabilizing additives was examined. Additionally, resin extraction studies and product cycling studies were conducted to determine cleaning effectiveness (resin fouling) of various cleaning strategies. Sodium hydroxide‐based cleaning solutions were shown to be more effective at preventing resin fouling. Conversely, cold temperature and the use of stabilizing additives in conjunction with sodium hydroxide were found to be beneficial in minimizing the rate of Protein A ligand hydrolysis. An effective and robust cleaning strategy is presented here to maximize resin lifetime and thereby the number of column cycles for future manufacturing processes. © 2017 American Institute of Chemical Engineers Biotechnol. Prog., 33:708–715, 2017     

Quantification of creative kinase isoenzymes by a radioimmunoassay

Summary It is not known whether loss of enzyme activity from the circulation is due to denaturation, inactivation or removal of intact enzyme molecules. This is in part due to the lack of an assay to measure enzyme protein concentration since available assays measure only enzyme activity. Radioimmunoassays for plasma enzymes and isoenzymes have not been possible because of oxidation in radioactive labelling by conventional methods and the problem of subunit dissociation. In the present study, antibodies specific to the B and M subunits of creatine kinase isoenzymes were obtained by immunization of rabbits with canine BB and MM creatine kinase. Anitgens (MM and BB) were radioactively labelled with ¹²⁵I by acylation, avoiding the problem of oxidation and subunit stabilized by mercaptoethanol (0.020 m) and Trisbuffer (1.6 m). A radioimmunoassay capable of detecting picogram amounts of CK isoenzymes was developed which measures the concentration of enzyme protein rather than activity. The method was shown to provide a sensitive quantitative method for analysis of plasma CK isoenzymes in dogs after myocardial infarction produced by coronary occlusion. This technique may provide a prototype for the development of radioimmunoassays for other plasma isoenzymes and should help to elucidate the nature of the disappearance of isoenzymes from the circulation.Work from the authors' laboratory was supported in part by the National Institutes of Health Grant HL 17646, SCOR in Ischemic Heart Disease     

Lipids of neocortex after X-ray irradiation of the rat head at a dose of 200 Gy

X-ray irradiation at a dose of 200 Gy with local exposure of the rat head induced the change of the lipid content in the neocortex tissue. The amount of phosphatidylinositol was decreased, the amount of free fatty acids, diglycerols, sphingomyelin was increased, and the amount of cholesterol had a growth trend in 2 h after X-ray exposition. The results testify in favor of participation of phosphatidylinositol- and sphingomyelin-relating signal systems and cholesterol in early stages of the cerebral radiation syndrome. We suggest that the change of the lipid content in early periods after the effect of a super-high dose of X-ray irradiation indicates the lipid dependence in the elimination of motion damages and the restoration of the functions of nerve cells. Effects on the lipid metabolism in the nerve tissue are promising for correcting the cerebral radiation syndrome.