Analysis of a mathematical model of the effect of inhibitors on the growth of tumors

In this paper, we study a model of tumor growth in the presence of inhibitors. The tumor is assumed to be spherically symmetric and its boundary is an unknown function r=R(t). Within the tumor the concentration of nutrient and the concentration of inhibitor (drug) satisfy a system of reaction-diffusion equations. The important parameters are Lambda(0) (which depends on the tumor's parameters when no inhibitors are present), gamma which depends only on the specific properties of the inhibitor, and beta; which is the (normalized) external concentration of the inhibitor. In this paper, we give precise conditions under which there exist one dormant tumor, two dormant tumors, or none. We then prove that in the first case, the dormant tumor is globally asymptotically stable, and in the second case, if the radii of the dormant tumors are denoted by R(s)(-),R(s)(+) with R(s)(-)infinity)R(t)=R(s)(-), provided the initial radius R(0) is smaller than R(s)(+); if however R(0)R(s)(+) then the initial tumor in general grows unboundedly in time. The above analysis suggests an effective strategy for treatment of tumors.     

Mechanism of reaction of melatonin with human myeloperoxidase

Recently, it was suggested that melatonin (N-acetyl-5-methoxytryptamine) is oxidized by activated neutrophils in a reaction most probably involving myeloperoxidase (Biochem. Biophys. Res. Commun. (2000) 279, 657-662). Myeloperoxidase (MPO) is the most abundant protein of neutrophils and is involved in killing invading pathogens. To clarify if melatonin is a substrate of MPO, we investigated the oxidation of melatonin by its redox intermediates compounds I and II using transient-state spectral and kinetic measurements at 25 degrees C. Spectral and kinetic analysis revealed that both compound I and compound II oxidize melatonin via one-electron processes. The second-order rate constant measured for compound I reduction at pH 7 and pH 5 are (6.1 +/- 0.2) x 10(6) M(-1) s(-1) and (1.0 +/- 0.08) x 10(7) M(-1) s(-1), respectively. The rates for the one-electron reduction of compound II back to the ferric enzyme are (9.6 +/- 0.3) x 10(2) M(-1) s(-1) (pH 7) and (2.2 +/- 0.1) x 10(3) M(-1) s(-1) (pH 5). Thus, melatonin is a much better electron donor for compound I than for compound II. Steady-state experiments showed that the rate of oxidation of melatonin is dependent on the H(2)O(2) concentration, is not affected by superoxide dismutase, and is quickly terminated by sodium cyanide. Melatonin can markedly inhibit the chlorinating activity of MPO at both pH 7 and pH 5. The implication of these findings in the activated neutrophil is discussed.     

Characterization of Suppressor of Fused, a Complete Suppressor of the Fused Segment Polarity Gene of Drosophila Melanogaster

fused (fu) is a maternal effect segment polarity gene of Drosophila melanogaster. In addition, fu females have tumorous ovaries. Two ethyl methanesulfonate mutageneses were carried out in order to isolate suppressors of the fu phenotype. A new gene, Suppressor of fused (Su(fu)), was identified. It is located in the 87C8 region of the third chromosome. Su(fu) displays a maternal effect and is also expressed later in development. Although Su(fu)LP is a complete loss-of-function mutation, it is homozygous viable and has no phenotype by itself. Su(fu) fully suppresses the embryonic and adult phenotypes of fu mutants. Su(fu) mutations are semidominant and a Su(fu)+ duplication has an opposite effect, enhancing the fused phenotype. It is proposed therefore that the Su(fu)+ product is involved in the same developmental step as the Fu+ kinase. Thus, a new gene interacting with the segment polarity pathway was identified using an indirect approach.     

Analytic computation of the expectation of the linkage disequilibrium coefficient r2

The squared correlation coefficient r(2) (sometimes denoted Delta(2)) is a measure of linkage disequilibrium that is widely used, but computing its expectation E[r(2)] in the population has remained an intriguing open problem. The expectation E[r(2)] is often approximated by the standard linkage deviation sigma(d)(2), which is a ratio of two expectations amenable to analytic computation. In this paper, a method of computing the population-wide E[r(2)] is introduced for a model with recurrent mutation, genetic drift and recombination. The approach is algebraic and is based on the diffusion process approximation. In the limit as the population-scaled recombination rate rho approaches infinity, it is shown rigorously that the asymptotic behavior of E[r(2)] is given by 1/rho+O(rho(-2)), which, incidentally, is the same as that of sigma(d)(2). A computer software that computes E[r(2)] numerically is available upon request.     

Patterns of investment of the reproductive strategy of two stream-dwelling Characidae.

The reproductive strategy of two congeneric species (Astyanax janeiroensis--AJ and Astyanax hastatus--AH) was assessed, in order to address the costs imposed by different investment patterns, on four major life history characters: migratory behaviour, breeding time, fecundity and egg size. Altitudinal segregation of young and adult individuals plus data from the literature indicated that AJ is a migratory species, whereas AH is non migratory. Breeding season (BS) analysis revealed that AH was reproductively active year-round (12 months), whereas AJ breeds during 9 months. Brood costs (Ovarian Investment) were almost the same for both species (AJ--364 oocytes/g and egg volume = 0.52 mm(3); AH--702 oocytes/g and egg volume = 0.27 mm(3)). Reproductive costs (RC), considered as product of gamete production (OI) and gamete output (BS), were 1,703.7 for AJ and 2,274.0 for AH; thus RC is 25% higher in AH. It is concluded that the costs with OI (egg size and egg numbers) are equal for both species but as breeding season is larger for AH the overall strategy is 25% more expensive in AH. Thus, it is hypothesized that this 25% should be considered as the extra costs that AJ uses during migration and is compensated by its shorter breeding time (9 months versus 12 months of AH).     

Cybernetic formulation of the definition of life

A definition of life (a living individual) in cybernetic terms is proposed. In this formulation, life (a living individual) is defined as a network of inferior negative feedbacks (regulatory mechanisms) subordinated to (being at service of) a superior positive feedback (potential of expansion). It is suggested that this definition is the minimal definition, necessary and sufficient, for life to be distinguished from inanimate phenomena and, as such, it describes the essence of life. Subsequently, a quantitative expression for the amount of the biologically relevant ("purposeful") information (as opposed to the amount of information in the thermodynamic sense) is proposed. This is followed by the application of the formulated approach to different phenomena of a dubious status existing presently on the Earth as well as to the process of origination of life on our planet.     

The role of respiration in the activation of photosynthesis upon illumination of dark adapted Chlamydomonas reinhardtii

It is reported that O(2) is required for the activation of photosynthesis in dark adapted Chlamydomonas reinhardtii in State 1, under low light intensity. The concentration of dissolved O(2) of ca. 9 microM is sufficient to saturate the requirement. When the concentration of O(2) is 3 muM or below, the activation of photosynthesis is strongly inhibited by myxothiazol, a specific inhibitor of the mitochondrial cytochrome bc(1). The effect of this inhibitor decreases as the O(2) concentration is raised, to disappear completely above 50 muM. Low concentrations of uncouplers delay the activation of photosynthesis, but do not inhibit it when steady state is reached. It is concluded that in State 1 C. reinhardtii mitochondrial respiration is required for the activation of photosynthesis upon illumination of dark adapted cells only when the concentration of O(2) is too low (less than 5 muM) to allow an appreciable activity of the Mehler reaction. The role of respiration does not seem to be due to the synthesis of ATP by oxidative phosphorylation, because photosynthesis activation is not sensitive to oligomycin.     

Structure and function of RNA replicase of bacteriophage Qbeta.

(1) The RNA replicase induced by bacteriophage Qbeta consists of four non-identical subunits designated as alpha (mol. wt. 74000), beta (mol. wt. 64000), gamma (mol. wt. 47000) and delta (mol. wt. 33000), only one (subunit beta) of which is specified by the phage genome. (2) Subunit alpha (30 S ribosomal protein "S1" as well as translational interference factor "i") is required only for (+) strand-directed RNA synthesis in the presence of the host factor. (3) Qbeta replicase lacking subunit alpha (R-alpha) is capable of replicating templates other than (+) strand, such as (--), "6S" RNA, poly(C) etc., in the absence of the host factor. (4) Subunit beta is suggested to be the nucleotide-polymerizing enzyme, but is unable to initiate RNA synthesis by itself. (5) Subunits gamma and delta are identical to the protein synthesis elongation factors, EF-Tu and EF-Ts, respectively, and are required only for initiation of RNA synthesis, but not for elongation. (6) A model of Qbeta replicase is presented in order to discuss observed template-enzyme interactions.     

Kinetic analysis and mechanistic aspects of autoxidation of catechins

A peroxidase-based bioelectrochemical sensor of hydrogen peroxide (H(2)O(2)) and a Clark-type oxygen electrode were applied to continuous monitoring and kinetic analysis of the autoxidation of catechins. Four major catechins in green tea, (-)-epicatechin, (-)-epicatechin gallate, (-)-epigallocatechin, and (-)-epigallocatechin gallate, were used as model compounds. It was found that dioxygen (O(2)) is quantitatively reduced to H(2)O(2). The initial rate of autoxidation is suppressed by superoxide dismutase and H(+), but is independent of buffer capacity. Based on these results, a mechanism of autoxidation is proposed; the initial step is the one-electron oxidation of the B ring of catechins by O(2) to generate a superoxide anion (O(2)(*-)) and a semiquinone radical, as supported in part by electron spin resonance measurements. O(2)(*-) works as a stronger one-electron oxidant than O(2) against catechins and is reduced to H(2)O(2). The semiquinone radical is more susceptible to oxidation with O(2) than fully reduced catechins. The autoxidation rate increases with pH. This behavior can be interpreted in terms of the increase in the stability of O(2)(*-) and the semiquinone radical with increasing pH, rather than the acid dissociation of phenolic groups. Cupric ion enhances autoxidation; most probably it functions as a catalyst of the initial oxidation step of catechins. The product cuprous ion can trigger a Fenton reaction to generate hydroxyl radical. On the other hand, borate ion suppresses autoxidation drastically, due to the strong complex formation with catechins. The biological significance of autoxidation and its effectors are also discussed.     

Rate of Decrease of Genetic Variability in a Two-Dimensional Continuous Population of Finite Size

The rate of decay of genetic variability was investigated for two-dimensional continuous populations of finite size. The exact value of the rate involves a rather complicated expression (formula (4-1)). However, numerical examples indicate that in a population habitat size LxL and density D, the rate is approximately equal to (see PDF) where sigma(2) is the variance of dispersion distance assuming isotropical migration. The value given in (2) is equal to that of a panmictic population of size DL(2). It is remarkable that whether the rate assumes the value given by (1) or by (2) depends only on Dsigma(2) (a local property), which is independent of the habitat size. Since, in a one-dimensional population, this depends on both Dsigma(2) and the habitat size, there is an essential difference between the two types of population structure.-The function giving the probability of two homologous genes separated by a given distance being different alleles was also obtained, (formula (5-1)).     

Identification of regulatory sites of phosphorylation of the bovine endothelial nitric-oxide synthase at serine 617 and serine 635

Endothelial nitric-oxide synthase (eNOS) is regulated by signaling pathways involving multiple sites of phosphorylation. The coordinated phosphorylation of eNOS at Ser(1179) and dephosphorylation at Thr(497) activates the enzyme, whereas inhibition results when Thr(497) is phosphorylated and Ser(1179) is dephosphorylated. We have identified two further phosphorylation sites, at Ser(617) and Ser(635), by phosphopeptide mapping and matrix-assisted laser desorption ionization time of flight mass spectrometry. Purified protein kinase A (PKA) phosphorylates both sites in purified eNOS, whereas purified Akt phosphorylates only Ser(617). In bovine aortic endothelial cells, bradykinin (BK), ATP, and vascular endothelial growth factor stimulate phosphorylation of both sites. BK-stimulated phosphorylation of Ser(617) is Ca(2+)-dependent and is partially inhibited by LY294002 and wortmannin, phosphatidylinositol 3-kinase inhibitors, suggesting signaling via Akt. BK-stimulated phosphorylation of Ser(635) is Ca(2+)-independent and is completely abolished by the PKA inhibitor, KT5720, suggesting signaling via PKA. Activation of PKA with isobutylmethylxanthine also causes Ser(635), but not Ser(617), phosphorylation. Mimicking phosphorylation at Ser(635) by Ser to Asp mutation results in a greater than 2-fold increase in activity of the purified protein, whereas mimicking phosphorylation at Ser(617) does not alter maximal activity but significantly increases Ca(2+)-calmodulin sensitivity. These data show that phosphorylation of both Ser(617) and Ser(635) regulates eNOS activity and contributes to the agonist-stimulated eNOS activation process.     

Properties of the C-terminal domain of enzyme I of the Escherichia coli phosphotransferase system

The bacterial phosphoenolpyruvate (PEP):glycose phosphotransferase system (PTS) mediates uptake/phosphorylation of sugars. The transport of all PTS sugars requires Enzyme I (EI) and a phosphocarrier histidine protein of the PTS (HPr). The PTS is stringently regulated, and a potential mechanism is the monomer/dimer transition of EI, because only the dimer accepts the phosphoryl group from PEP. EI monomer consists of two major domains, at the N and C termini (EI-N and EI-C, respectively). EI-N accepts the phosphoryl group from phospho-HPr but not PEP. However, it is phosphorylated by PEP(Mg(2+)) when complemented with EI-C. Here we report that the phosphotransfer rate increases approximately 25-fold when HPr is added to a mixture of EI-N, EI-C, and PEP(Mg(2+)). A model to explain this effect is offered. Sedimentation equilibrium results show that the association constant for dimerization of EI-C monomers is 260-fold greater than the K(a) for native EI. The ligands have no detectable effect on the secondary structure of the dimer (far UV CD) but have profound effects on the tertiary structure as determined by near UV CD spectroscopy, thermal denaturation, sedimentation equilibrium and velocity, and intrinsic fluorescence of the 2 Trp residues. The binding of PEP requires Mg(2+). For example, there is no effect of PEP on the T(m), an increase of 7 degrees C in the presence of Mg(2+), and approximately 14 degrees C when both are present. Interestingly, the dissociation constants for each of the ligands from EI-C are approximately the same as the kinetic (K(m)) constants for the ligands in the complete PTS sugar phosphorylation assays.     

Microsome-stimulated activation of ferrous bleomycin in the presence of DNA

The inhibition of Fe(II)-bleomycin activation, by a large excess of DNA, is overcome by rat liver microsomes in the presence of NADPH. This release of inhibition, as indicated by increased yields of base propenal from DNA scission, is enhanced by menadione, is inhibited by superoxide dismutase, and is therefore dependent on superoxide anion. Microsomal activation of Fe(II)-bleomycin doubles the stoichiometry of base propenal yield compared to that obtained upon self-activation of the drug; 0.5 mol of base propenal is formed and 0.5 mol of NADPH is oxidized per mol of Fe(II)-bleomycin. In the presence of a large excess of DNA, Cu(II)-bleomycin is not reduced and Fe(III)-bleomycin is neither reduced nor activated by microsomes in cases where activation of Fe(II)-bleomycin is maximal. We suggest that in vivo, electron transport enzymes at or near the nucleus can stimulate the activation of Fe(II)-bleomycin under conditions where self-activation does not readily occur.     

Redox characteristics of the tungsten DMSO reductase of Rhodobacter capsulatus

The dimethylsulfoxide reductase (DMSOR) from Rhodobacter capsulatus is known to retain its three-dimensional structure and enzymatic activity upon substitution of molybdenum, the metal that occurs naturally at the active site, by tungsten. The redox properties of tungsten-substituted DMSOR (W-DMSOR) have been investigated by a dye-mediated reductive titration with the concentration of the W(V) state monitored by EPR spectroscopy. At pH 7.0, E(m)(W(VI)/W(V)) is -194 mV and E(m)(W(V)/W(IV)) is -134 mV. Each E(m) value of W-DMSOR is significantly lower (220 and 334 mV, respectively) than that of the corresponding couple of Mo-DMSOR. These redox potentials are consistent with the ability of Mo-DMSOR to catalyze both the reduction of DMSO to DMS and the back reaction, whereas W-DMSOR is very effective in catalyzing the forward reaction, but shows no ability to catalyze the oxidation of DMS to DMSO.     

The origin of the genetical diversity of Microtus mandarinus chromosomes

Here we describe our comparative studies on two types of X chromosomes, namely X(M) and X(SM,) of the mandarin vole (Microtus mandarinus). By chromosome G- and C-banding analysis, we have found that two different types of X chromosomes exist in mandarin voles. The two types of X chromosomes present two different G- and C-banding patterns: the X(M) chromosome is a longer metacentric X chromosome which is C-band negative; and the X(SM) is a shorter submetacentric X chromosome which has one C-band at the centromere and another one at the middle part of the short arm. The X(SM) has 6 G-bands including one on the kinetochore, one in the middle of the short arm, and four on the long arm. The X(M) has 7 G-bands including one on the kinetochore, two on the short arm, and four on the long arm. We have further found that female voles can be grouped into three types based on the composition of the X chromosome but the male voles have only one type. The three female groups are: (1) female voles (X(M)X(SM)), in which the two X chromosomes are different, the longer one is metacentric and the shorter is submetacentric; (2) female vole (X(SM)X(SM)), in which the two X chromosomes are both submetacentric; (3) female vole (X(M)O), in which there is only one X chromosome that is metacentric. Surprisingly, we have never found female voles with X(M)X(M), females with X(SM)O or males with X(M)Y. We hypothesize that the X(SM) chromosome is derived from the X(M) through its breakage and re-joining. The paper also discusses the formation of X(M)O females.     

Review of the Eustrophinae (Coleoptera, Tetratomidae) of America north of Mexico

The Nearctic fauna (north of Mexico) of Eustrophinae is reviewed, and consists of the following five genera and 12 species: Pseudoholostrophus (Pseudoholostrophus) impressicollis (LeConte), Pseudoholostrophus (Holostrophinus) discolor (Horn), Holostrophus bifasciatus (Say), Eustrophus tomentosus Say, Eustrophopsis confinis (LeConte), Eustrophopsis bicolor (Fabricius), Eustrophopsis brunneimarginatus (Dury), Eustrophopsis indistinctus (LeConte), Eustrophopsis arizonensis (Horn), Eustrophopsis ornatus (Van Dyke), Eustrophopsis crowdyisp. n., and Synstrophus repandus (Horn). A lectotype is designated for Eustrophus brunneimarginatus Dury. A key is given to separate genera and species, supplemented with illustrations of relevant features, including aedeagi of all Nearctic species of Eustrophopsis. Detailed distribution (including Mexican records) and natural history data are provided.     

Roles of protein kinase C and actin-binding protein 280 in the regulation of intracellular trafficking of dopamine D3 receptor

D(3) dopamine receptor (D(3)R) is expressed mainly in parts of the brain that control the emotional behaviors. It is believed that the improper regulation of D(3)R is involved in the etiology of schizophrenia. Desensitization of D(3)R is weakly associated with G protein-coupled receptor kinase (GRK)/beta-arrestin-directed internalization. This suggests that there might be an alternative pathway that regulates D(3)R signaling. This report shows that D(3)R undergoes robust protein kinase C (PKC)-dependent sequestration that is accompanied by receptor phosphorylation and the desensitization of signaling. PKC-dependent D(3)R sequestration, which was enhanced by PKC-beta or -delta, was dynamin dependent but independent of GRK, beta-arrestin, or caveolin 1. Site-directed mutagenesis of all possible phosphorylation sites within the intracellular loops of D(3)R identified serine residues at positions 229 and 257 as the critical amino acids responsible for phorbol-12-myristate-13-acetate (PMA)-induced D(3)R phosphorylation, sequestration, and desensitization. In addition, the LxxY endocytosis motif, which is located between residues 252 and 255, was found to play accommodating roles for PMA-induced D(3)R sequestration. A continuous interaction with the actin-binding protein 280 (filamin A), which was previously known to interact with D(3)R, is required for PMA-induced D(3)R sequestration. In conclusion, the PKC-dependent but GRK-/beta-arrestin-independent phosphorylation of D(3)R is the main pathway responsible for the sequestration and desensitization of D(3)R. Filamin A is essential for both the efficient signaling and sequestration of D(3)R.