The regulatory capacity of Turing's model for morphogenesis, with application to slime moulds

For a one-dimensional system (elongated organism), regulation of a pattern of alternating regions of two cell types against disturbance by growth or or by cutting is discussed. Turing's linear two-morphogen model requires the number of regions to be that which maximizes the exponential growth rate of morphogen concentrations. On this basis, a diagram is constructed to show ranges of system length for patterns with various numbers of regions. Experimental features of pattern in the Dictyostelium slug, especiially the wide size range having regulatory capacity and the inequality of numbers of the two cell types, are compared with the simple model and with extensions of it to include dependence of diffusivity on cell type and morphogen transport by movement of whole cells.     

Shift of the high-performance liquid chromatographic retention times of metabolites in relation to the original drug on an RP8 column with acidic mobile phase

The effect of the structural change in the metabolization of drugs on the HPLC retention time with an RP8 column with an acetonitrile–phosphate buffer (pH 2.3) as the mobile phase was investigated at model compound pairs of 29 functionalization reactions. A more or less typical region for T_M=log(k′_M/k′_D) was found for each of these reactions (with k′_M and k′_D being the capacity factors of the metabolite and the drug, respectively), which can be explained by an increase or a decrease of the hydrophilic properties caused by the structural change. This effect is superimposed by an essential influence of the unchanged part of the molecule and in some cases by special intramolecular interactions like the hydrogen bond. Despite the more complicated structure of real drugs the results obtained at the model compound pairs were confirmed for most of the 55 metabolite/drug pairs. The practical use of the T_M values as a support to distinguish between different metabolites in the HPLC-DAD analysis of intoxications is demonstrated with cases of poisoning with diphenhydramine, propafenone and methaqualone.     

Reversible linkage isomerization of pentaamminecobalt(III) complexes of urea and its N-methyl derivatives

The (NH₃)₅CoOC(NH₂)₂³⁺ ion is consumed in water according to the rate law k(obs.) = k₁ + k₂[OH⁻], where k₁ = 4.0 × 10⁻⁵ s⁻¹ and k₂ = 14.2 M⁻¹ s⁻¹ (0–0.1 M [OH⁻];μ = 1.1 M, NaClO₄, 25 °C). A hitherto unrecognized intramolecular O- to N- linkage isomerization reaction has been detected. In strongly acid solution only aquation to (NH₃)₅CoOH₂³⁺ is observed, but in 0.1–1.0 M [OH⁻], 7% of the directly formed products is the urea-N complex (NH₃)₅CoNHCONH₂²⁺ which has been isolated. In the neutral pH region a much greater proportion (25%) of the products is the urea-N species. These results are interpreted in terms of an urea-O to urea-N linkage isomerization reaction competing with hydrolysis for both spontaneous (k₁) and base-catalyzed (k₂) pathways; the rearrangement is not observed in strongly acidic solution (pH ⩽ 1) because the protonated N-bonded isomer (pK′_a ≈ 3) is unstable with respect to the O-bonded form. The appearance of the isomerization pathway as the pH is raised in the 0–6 region is commensurate with a rate increase which cannot be attributed to a contribution from the base catalysis term k₂[OH⁻]. It is argued that this observation establishes, for the spontaneous pathway, that hydrolysis and linkage isomerization are separate reaction pathways — there is no common intermediate. The product distribution and rate data lead to the complete rate law, k(obs.) = k₁ + k₂[OH⁻] = (k_s + k_ON) + (k_OH + k′_ON) [OH⁻] for the reactions of the O-bonded isomers, where k_s, k_OH are the specific rates for hydrolysis, and k_ON, k′_ON are the specific rates for O- to N-linkage isomerization, by spontaneous and base-catalyzed pathways respectively; k_ON = 1.3 × 10⁻⁵ s⁻¹ and k′_ON = 1.1 M⁻¹ s⁻¹ (μ = 1.0 M, NaClO₄, 25 °C). The O- to N- linkage isomerization has been observed also for complexes of N-methylurea, N,N-dimethylurea and N-phenylurea, but not for the N,N′-dimethylurea species. There is an approximately statistical relationship among the data for −NH₂ capture (versus H₂O), while −NHR and −NR₂ do not compete with water as nucleophiles for Co(III) in either the spontaneous or base-catalyzed hydrolysis processes. For each urea-O complex, O- to N-isomerization is a more significant parallel reaction in the spontaneous as opposed to the base-catalyzed pathway. This is interpreted as being indicative of more associative character in the spontaneous route to products, a conclusion supported by other evidence. Some activation parameter data have been recorded and the effect of the N-substitution on the rates of solvolysis (H₂O, Me₂SO) is discussed. The urea-N complexes have been isolated as their deprotonated forms, [(NH₃)₅CoNHCONRR′](ClO₄)₂·xH₂O (R,R′ = H, CH₃). They are kinetically inert in neutral to basic solution but in acid they protonate (H₂O, pK′_a 2–3; μ = 1.0 M, 25 °C) and then isomerize rapidly back to their O-bonded forms. Some solvolysis accompanies this N- to O-rearrangement in H₂O and Me₂SO. Specific rates and activation parameters are reported. The kinetic data follow a rate law of the form k_NO(obs.) = (k + k_NO)[H⁺]/(K′_a + [H⁺]) and the active species in the reaction is the protonated form; k, k_NO are the specific rates for hydrolysis and isomerization, respectively. Proton NMR data establish that the site of protonation (in Me₂SO) is the cobalt-bound nitrogen atom. For the unsubstituted urea species (NH₃)₅CoNH₂CONH₂³⁺, diastereotopic exo-NH₂ protons arising from restricted rotation about the CN bond are observed. The relevance to the mechanism of the linkage isomerization process is considered. ¹³C and ¹H NMR and electronic absorption spectral data are presented, and distinctions between linkage isomers and the solution structures (electronic and conformational) are discussed. The urea-N/urea-O complex equilibrium is governed by the relation K′_NO(obs.) = K′_NO[H⁺]/[H⁺](K′_a), where K′_NO is the equilibrium constant = [(NH₃₅Co(urea-O)³⁺]/[(NH₃)₅Co(urea-N)³⁺]. Values for K′_NO(=k_NO/k_ON = 260 and pK′_a ≈ 3 for the NH₂CONH₂ system are consistent with the stability of the N-isomer in feebly acidic to basic solution (e.g. pH 6, K′_NO(obs.) = 2.6 × 10⁻²) and instability in acid solution (e.g. pH 1, K′_NO(obs.) = 240). The equilibrium data for this and other urea complexes of (NH₃)₅Co(III) are contrasted with the result for the analogous Rh(III)NH₂CONH₂ system K′_NO ≈ 1).     

Molecular packing and intermolecular contacts of sickling deer type III hemoglobin

The X-ray structure of sickling deer type III hemoglobin, solved by the molecular replacement method and refined to an R value of ~25%, has been used to determine the mode of molecular packing and the residues involved in the intermolecular contacts between the hemoglobin tetramers in the crystalline state. The molecules pack in linear arrays (“fibrils”), with adjacent fibrils displaced ~27 Å from one another along the long axis of the arrays. A view down this axis shows an hexagonal network of six fibrils surrounding a central solvent cavity (each hexameric unit is termed a fiber) with adjacent fibers sharing a common wall of fibrils. Contacts less than 5 Å are observed between the following subunits of different molecules: α₁α′₁, α₁α′₂, α₁β′₁, α₁β′₂, α₂β′₁, α₂β′₂, β₂β′₂, in which the primes refer to adjacent molecules.     

The interaction of nucleotides and yeast hexokinase

The kinetics of ethenoadenosine triphosphate (?ATP) as the phosphate donor in the phosphoryl transfer reaction of hexokinase were examined to obtain the K_m′s, V's, and K_α's for the nucleotide and sugar. Dissociation constants for eATP and ?ADP with hexokinase were obtained from fluorometric measurements and compared with similar constants obtained kinetically. Other selected nucleoside triphosphates were used as phosphate donors in the hexokinase reaction and their kinetic constants were obtained. Reactions were also performed using two nucleotides simultaneously as phosphorylating substrates for the hexokinase reaction in an attempt to find the individual dissociation constants, K_m′s and K_i′s. These were compared with the K_m′s obtained from using the nucleotides separately in the hexokinase reaction. From these kinetic and fluorescence binding studies, evidence is presented supporting the postulate that the K_m′s are primarily dissociation constants in a random bi-bi mechanism. Analysis of the K_m values provides additional evidence to support the importance of the amino group in position 6 on the purine ring as a hydrogen-bond acceptor during binding. It was found that ?CTP was a much better hexokinase substrate than CTP. These observations suggest that the V for this reaction is highly dependent upon the size of the nucleotide.     

Flow injection chemiluminescence study of acridinium ester stability and kinetics of decomposition

Decomposition of phenyl acridinium-9-carboxylate is monitored using electrogenerated chemiluminescence in a flow system. The formation of the pseudobase from the acridinium ester [AE] is described by rate = k′₁[AE] + k″₁[AE][OH^?]^0.5, where k′₁ = 0.020 ± 0.006 s^?1 and k″₁ = 2.1 ± 0.8 (L/mol)^?0.5 s^?1. Irreversible decomposition of the pseudobase is described by rate = k′₂[AE][OH^?], where k′₂ = 20.1 ± 3.8 (L/mol s). These kinetic equations, plus measurement of variation in emission intensity for constant acridinium ester concentration, are used to predict the resulting emission intensity v. pH behaviour given various contact times (in the 0.25 to 25 s range) for the acridinium ester to be in an alkaline solution prior to initiation of the chemiluminescence reaction.     

Non-reductive iron release from horse spleen ferritin using desferoxamine chelation

The rate of Fe³⁺ release from horse spleen ferritin (HoSF) was measured using the Fe³⁺-specific chelator desferoxamine (DES). The reaction consists of two kinetic phases. The first is a rapid non-linear reaction followed by a slower linear reaction. The overall two-phase reaction was resolved into three kinetic events: 1) a rapid first-order reaction in HoSF (k₁); 2) a second slower first-order reaction in HoSF (k₂); and 3) a zero-order slow reaction in HoSF (k₃). The zero-order reaction was independent of DES concentration. The two first-order reactions had a near zero-order dependence on DES concentration and were independent of pH from 6.8 to 8.2. The two first-order reactions accounted for 6-9 rapidly reacting Fe³⁺ ions. Activation energies of 10.5 ± 0.8, 13.5 ± 2.0 and 62.4 ± 2.1 kJ/mol were calculated for the kinetic events associated with k₁, k₂, and k₃, respectively. Iron release occurs by: 1) a slow zero-order rate-limiting reaction governed by k₃ and corresponding to the dissociation of Fe³⁺ ions from the FeOOH core that bind to an Fe³⁺ binding site designated as site 1 (proposed to be within the 3-fold channel); 2) transfer of Fe³⁺ from site 1 to site 2 (a second binding site in the 3-fold channel) (k₂); and 3) rapid iron loss from site 2 to DES (k₁).     

Reduction of dimensionality in Bayesian nonlinear regression with a pharmacokinetic application

Application of Bayes's theorem to the analysis of nonlinear regression models is limited by numerical problems associated with calculation of integrals of functions of several variables. For k-parameter models that are linear in l of the parameters, a dimension-reduction procedure is described for factoring the posterior distribution into the product of a multivariate normal density and a function of k-l nonlinear parameters. Integrals can then be calculated with (k-l)-dimensional numerical integration. A four-parameter, two-compartment pharmacokinetic model of lidocaine disposition is analyzed using a change of variables in order to obtain a model that is linear in two parameters. It is shown that a Bayesian analysis, with reduction of dimensionality, applied to this model produces appropriate results with reasonable CPU-time requirements.     

Light dependence of the decay of the proton gradient in broken chloroplasts

The initial rates and steady-state values of proton uptake by broken chloroplasts have been measured as functions of light intensity at various concentrations of chlorophyll, pyocyanine, supporting electrolyte, buffer, as well as pH and temperature. Kinetic analysis of the data shows that the rate of decay of proton gradient due to backward leakage depends on light intensity. Under steady illumination, the decay constant k_L is equal to k_D + mR₀, where R₀ is the initial rate of proton uptake which is a function of light intensity, k_D is the decay constant in the dark and m is a parameter which is independent of light intensity. Treatment of chloroplasts with lysolecithin, neutral detergent, 2,4-dinitrophenol, or valinomycin in the presence of K⁺ increases k_D without affecting m. Treatment with N,N′-dicyclohexylcarbodiimide or adenylyl imidodiphosphate under appropriate conditions decreases m without affecting k_D. Treatment with glutaraldehyde makes k_L independent of light intensity and hence m = 0. These results suggest that the light-dependent part (mR₀) of k_L is due to leakage of protons through the coupling factor (CF₁-CF₀) complex which can open or close depending on light intensity and that the light-independent part (k_D) of the decay constant k_L is due to proton leakage elsewhere.     

Extraction of hemoglobin with calixarenes and biocatalysis in organic media of the complex with pseudoactivity of peroxidase

The present work involves the use of p-tert-butylcalix[4,6,8]arene carboxylic acid derivatives (^tButyl[4,6,8]CH₂COOH) for selective extraction of hemoglobin. All three calixarenes extracted hemoglobin into the organic phase, exhibiting extraction parameters higher than 0.90. Evaluation of the solvent accessible positively charged amino acid side chains of hemoglobin (PDB entry 1XZ2) revealed that there are 8 arginine, 44 lysine and 30 histidine residues on the protein surface which may be involved in the interactions with the calixarene molecules. The hemoglobin–^tButyl[6]CH₂COOH complex had pseudoperoxidase activity which catalysed the oxidation of syringaldazine in the presence of hydrogen peroxide in organic medium containing chloroform. The effect of pH, protein and substrate concentrations on biocatalysis was investigated using the hemoglobin–^tButyl[6]CH₂COOH complex. This complex exhibited the highest specific activity of 9.92 × 10^?2 U mg protein^?1 at an initial pH of 7.5 in organic medium. Apparent kinetic parameters (V′_max, K′_m, k′_cat and k′_cat/K′_m) for the pseudoperoxidase activity were determined in organic media for different pH values from a Michaelis–Menten plot. Furthermore, the stability of the protein–calixarene complex was investigated for different initial pH values and half-life (t_1/2) values were obtained in the range of 1.96 and 2.64 days. Hemoglobin–calixarene complex present in organic medium was recovered in fresh aqueous solutions at alkaline pH, with a recovery of pseudoperoxidase activity of over 100%. These results strongly suggest that the use of calixarene derivatives is an alternative technique for protein extraction and solubilisation in organic media for biocatalysis.     

Complexes of vitamin B6. XVI. Kinetics and reaction mechanism of iron(III) complexes with pyridoxal-5′-phosphate

The stopped flow technique has been used to study the kinetics of complex formation of iron(III) with pyridoxal-5-phosphate (PLP) in the pH range 1.00–2.50, and in the temperature range 18 °C– 30 °C, at an ionic strength of. 0.50 M (NaCl). From the initial concentration dependence of PLP (T_PLP,) of the reaction rate it can be shown that two kinetic steps can be represented as: k_obs′ = m_i + m_i′_PLP where m_i and m_i′ are pH-dependent parameters. The calculated activation data are δE* = 23.2 ± 1.8 kcal mol^?1 and 10.98 ± 0.53 kcal mol^?1 for the first and second kinetic steps, respectively and δS* are ?20.50 ± 5.96 e.u. and 24.62 ± 1.81 e.u., respeetively.     

Antibody binding of cartilage-specific proteoglycans

The spectroscopically observable acid dissociation constant of aspartate aminotransferase (EC 2.6.1.1) varies to different degrees upon the addition of different monovalent anions. These interactions may be described by the minimal scheme

where XEH and XE represent anion complexes with the acidic (EH) and basic (E) forms of the enzyme, respectively. Both graphical and computer procedures were used to determine the three equilibrium constants which describe such a system. The analysis was based upon the effects of salt concentration (X) upon the apparent pK′_a of the enzyme determined spectrophotometrically. The affinities for anions of the basic enyzme are less than those of the acidic form of the enzyme so that the apparent pK′_a rises with anion concentration to a limiting value; pK₄ of the enzyme anion complex. That different anion-enzyme complexes have different pK₄'s reflects the fact that the interaction specificities of the basic and acidic enzymes differ. Cacodylate did not appear either to cause significant effects on the chromophoric pK's or to compete with the binding of halide or carboxylate anions which cause a perturbation of the pK_a.     

Distribution of substituents in O-(2-hydroxyethyl)cellulose: A 13C-N.M.R. approach

O-(2-Hydroxyethyl)cellulose was converted into a mixture of the corresponding d-glucitol derivatives by hydrolysis followed by reduction of the sugars with NaBH₄. On the basis of the spectra of individual O-(2-hydroxyethyl)-d-glucitols, the ¹³C-n.m.r. spectrum of this mixture was assigned to the extent that permitted quantitative analysis in terms of monomer composition of the polymer. The monomer mole-fractions conform to a statistical, kinetic model that assumes that the reactivity of the 3-hydroxyl group of the d-glucosyl residues of cellulose depends on the state of substitution at O-2. The relative rate-constants of the hydroxyl groups in the (hydroxyethyl)ation reaction are k₂:k₃:k₃′:k₆:k_x = 6.0:1.0:4.0:11.1:34.6, indicating that the reactivity of OH-3 increases fourfold upon (hydroxyethyl)ation of OH-2.     

Some chemical aspects of dose-response relationships in alkylation mutagenesis

Alkylation of DNA can lead to induction of potentially miscoding groups (promutagenic) or potentially template-inactivating groups (lethal). The proportions of these are found to vary with the chemical nature of the alkylating agent. Agents of low Swain and Scott s factor (or those tending to Ingold's S_Ni type) react relatively more extensively at O-atom sites in DNA, and yield relatively more of the miscoding O₆-alkylguanine residues. Phosphotriester formation is also relatively more extensive with S_Ni agents.Inactivation of DNA can result from depurinations, strand breakage, and cross-linkage.Both promutagenic and lethal lesions are subject to repair; 3 principal enzymatic systems appear to exist; one for excision and repair of cross-links or aralkyl groups resembles the uvr system; others for repair of single-strand breaks parallel repair of X-ray-induced breaks (exr, rec systems); another, less well defined at present, recognizes certain methylated bases, and depurinated sites (probably Goldthwait's endonuclease II).These factors can be shown to influence dose-response in alkylation mutagenesis. This, broadly, can be classified as linear with the promutagenic group-inducing or directly miscoding agents, and is independent of cytotoxicity; whereas with other agents non-linear response parallels the occurrence of “shouldered” survival curves, and reflects mutation induction by “repairs errors”.Additionally, alkylation of cellular constituents other than DNA, e.g. repair enzymes, may influence dose response, and will again depend on chemical reactivity of the agent.     

Residue Phe42 is critical for the catalytic activity of Escherichia coli major nitroreductase NfsA

The major O₂-insensitive nitroreductase (NfsA) of Escherichia coli shares low sequence homology but similar biochemical and structural features with NfsB, the E. coli minor O₂-insensitive nitroreductase. A structural comparison revealed Phe42 was present in the active site of NfsA but not NfsB. F42Y, F42N and F42A were generated and had decreased activity toward nitrofurazone by 52, 96, and 99 %, respectively. The kinetic parameters for other nitroaromatic substrates were also determined. Compared to wild type, the mutants did not have significantly altered K _ms, but had dramatically decreased k _cat and k _cat/K _m values. Far-UV CD spectral analysis of the mutants suggested that there were no significant conformational changes however F42A and F42N had changes from 208 to 222 nm, which was attributed to loss of helix content. These findings revealed that Phe42 is important for maintaining NfsA activity and structure.     

Robustness in Escherichia coli Glutamate and Glutamine Synthesis Studied by a Kinetic Model

Metabolic control of glutamine and glutamate synthesis from ammonia and oxoglutarate in Escherichia coli is tight and complex. In this work, the role of glutamine synthetase (GS) and glutamate dehydrogenase (GDH) regulation in this control was studied. Both enzymes form a linear pathway, which can also have a cyclic topology if glutamate–oxoglutarate amino transferase (GOGAT) activity is included. We modelled the metabolic pathways in the linear or cyclic topologies using a coupled nonlinear differential equations system. To simulate GS regulation by covalent modification, we introduced a relationship that took into account the levels of oxoglutarate and glutamine as signal inputs, as well as the ultrasensitive response of enzyme adenylylation. Thus, by including this relationship or not, we were able to model the system with or without GS regulation. In addition, GS and GDH activities were changed manually. The response of the model in different stationary states, or under the influence of N-input exhaustion or oscillation, was analyzed in both pathway topologies. Our results indicate a metabolic control coefficient for GDH ranging from 0.94 in the linear pathway with GS regulation to 0.24 in the cyclic pathway without regulation, employing a default GDH concentration of 8 μM. Thus, in these conditions, GDH seemed to have a high degree of control in the linear pathway while having limited influence in the cyclic one. When GS was regulated, system responses to N-input perturbations were more sensitive, especially in the cyclic pathway. Furthermore, we found that effects of regulation against perturbations depended on the relative values of the glutamine and glutamate output first-order kinetic constants, which we named k ₆ and k ₇, respectively. Effects of regulation grew exponentially with a factor around 2, with linear increases of (k ₇???k ₆). These trends were sustained but with lower differences at higher GS concentration. Hence, GS regulation seemed important for metabolic stability in a changing environment, depending on the cell’s metabolic status.     

Persistence of Viruses in Desert Soils Amended with Anaerobically Digested Sewage Sludge

Pima County, Ariz., is currently investigating the potential benefits of land application of sewage sludge. To assess risks associated with the presence of pathogenic enteric viruses present in the sludge, laboratory studies were conducted to measure the inactivation rate (k = log₁₀ reduction per day) of poliovirus type 1 and bacteriophages MS2 and PRD-1 in two sludge-amended desert agricultural soils (Brazito Sandy Loam and Pima Clay Loam). Under constant moisture (approximately -0.05 × 10⁵ Pa for both soils) and temperatures of 15, 27, and 40°C, the main factors controlling the inactivation of these viruses were soil temperature and texture. As the temperature increased from 15 to 40°C, the inactivation rate increased significantly for poliovirus and MS2, whereas, for PRD-1, a significant increase in the inactivation rate was observed only at 40°C. Clay loam soils afforded more protection to all three viruses than sandy soils. At 15°C, the inactivation rate for MS2 ranged from 0.366 to 0.394 log₁₀ reduction per day in clay loam and sandy loam soils, respectively. At 27°C, this rate increased to 0.629 log₁₀ reduction per day in clay loam soil and to 0.652 in sandy loam soil. A similar trend was observed for poliovirus at 15°C (k = 0.064 log₁₀ reduction per day, clay loam; k = 0.095 log₁₀ reduction per day, sandy loam) and 27°C (k = 0.133 log₁₀ reduction per day, clay loam; k = 0.154 log₁₀ reduction per day, sandy loam). Neither MS2 nor poliovirus was recovered after 24 h at 40°C. No reduction of PRD-1 was observed after 28 days at 15°C and after 16 days at 27°C. At 40°C, the inactivation rates were 0.208 log₁₀ reduction per day in amended clay loam soil and 0.282 log₁₀ reduction per day in sandy loam soil. Evaporation to less than 5% soil moisture completely inactivated all three viruses within 7 days at 15°C, within 3 days at 27°C, and within 2 days at 40°C regardless of soil type. This suggests that a combination of high soil temperature and rapid loss of soil moisture will significantly reduce risks caused by viruses in sludge.     

Diversity indices: Which ones are admissible?

Many indices have been proposed for measuring diversity. If we demand that any index satisfy a few basic properties, including that it contain hierarchical components, then only the subset, {N_a for a > 0} of Hill's family need be considered. (This subset includes indices related to the Shannon-Wiener index, H′ = log N₁, and Simpson's index of concentration, λ = 1/N₂.) Ecological components can also be defined for any of these indices. Only N₂, however, can be used consistently to define local diversity and segregation components. These observations suggest that N₂ is the best, single measure of diversity, and that the only other index worth considering is N₁ .     

The dynamics of a discrete population model with threshold

The dynamics of the discrete, scalar population model x_{k + 1} = ax²_k(1 – x_k) are investigated. In addition to density dependence, which has been studied previously by many, this equation models the threshold phenomenon. Some similarities to and differences from previous models are observed. In particular, for large a values this model exhibits chaos which is restricted to a nowhere dense Cantor set of measure 0. In order to explain this, a piecewise linear simplification of the model is considered. Other models exhibiting similar dynamics are also mentioned.