Mathematical modelling of dynamics and control in metabolic networks. I. On Michaelis-Menten kinetics

As a starting point for modeling of metabolic networks this paper considers the simple Michaelis-Menten reaction mechanism. After the elimination of diffusional effects a mathematically intractable mass action kinetic model is obtained. The properties of this model are explored via scaling and linearization. The scaling is carried out such that kinetic properties, concentration parameters and external influences are clearly separated. We then try to obtain reasonable estimates for values of the dimensionless groups and examine the dynamic properties of the model over this part of the parameter space. Linear analysis is found to give excellent insight into reaction dynamics and it also gives a forum for understanding and justifying the two commonly used quasi-stationary and quasi-equilibrium analyses. The first finding is that there are two separate time scales inherent in the model existing over most of the parameter space, and in particular over the regions of importance here. Full modal analysis gives a new interpretation of quasi-stationary analysis, and its extension via singular perturbation theory, and a rationalization of the quasi-equilibrium approximation. The new interpretation of the quasi-steady state assumption is that the applicability is intimately related to dynamic interactions between the concentration variables rather than the traditional notion that a quasi-stationary state is reached, after a short transient period, where the rates of formation and decomposition of the enzyme intermediate are approximately equal. The modal analysis reveals that the generally used criterion for the applicability of quasi-stationary analysis that total enzyme concentration must be much less than total substrate concentration, et much less than St, is incomplete and that the criterion et much less than Km much less than St (Km is the well known Michaelis constant) is the appropriate one. The first inequality (et much less than Km) guarantees agreement over the longer time scale leading to quasi-stationary behavior or the applicability of the zeroth order outer singular perturbation solution but the second half of the criterion (Km much less than St) justifies zeroth order inner singular perturbation solution where the substrate concentration is assumed to be invariant. Furthermore linear analysis shows that when a fast mode representing the binding of substrate to the enzyme is fast it can be relaxed leading to the quasi-equilibrium assumption. The influence of the dimensionless groups is ascertained by integrating the equations numerically, and the predictions made by the linear analysis are found to be accurate.(ABSTRACT TRUNCATED AT 400 WORDS)     

Effects of cyclic adenosine 3': 5'-monophosphate on phosphoprotein kinase and phosphatase fractions prepared from rat liver nuclei.

A soluble rat liver nuclear extract containing total RNA polymerase activities also exhibits appreciable amounts of protein kinase activity. This unfractionated protein kinase catalyzes the phosphorylation of both endogenous proteins and exogenous lysine-rich histone in the presence of [γ-³²P]ATP and Mg²⁺. The optimal concentration of Mg²⁺ is 5 mm for histone phosphorylation and 25 mm for the phosphorylation of endogenous proteins. Cyclic AMP has no effect on the phosphorylation of lysine-rich histone by this unfractionated nuclear protein kinase. However, addition of cyclic AMP causes a reduction in the ³²P-labeling of an endogenous protein (CAI) which can be characterized by its mobility during SDS-acrylamide gel electrophoresis and elution in the unbound fraction of a DEAESephadex column. If CAI is first labeled with ³²P and then incubated with 10^?6m cyclic AMP under conditions where protein kinase activity is inhibited, the presence of the cyclic nucleotide causes a loss of the ³²P-labeling of this protein, implying the activation of a substrate-specific protein phosphatase. When rat liver RNA polymerases are purified by DEAE-Sephadex chromatography, protein kinase activity is found in the unbound fraction and in those column fractions containing RNA polymerase I and II. The fractionated protein kinases exhibit different responses to cyclic AMP, the unbound protein kinase being stimulated and the RNA polymerase-associated protein kinases being dramatically inhibited. A second protein (CAII) whose phosphorylated state is modified by cyclic AMP is found within the DEAE-Sephadex column fractions containing RNA polymerase II. The cyclic nucleotide in this case appears to reduce labeling of CAII by inhibition of the protein kinase activity which co-chromatographs with both CAII and RNA polymerase II. Based on molecular weight estimates, neither CAI nor CAII appears to be an RNA polymerase subunit. The identity of CAI as a protein factor whose phosphorylated state influences nuclear RNA synthesis is suggested by the fact that addition of fractions containing CAI to purified RNA polymerase II inhibits the activity of this enzyme, but only if CAI has been previously incubated in the presence of cyclic AMP.     

Stereospecific binding of 3H-phencyclidine in brain membranes

Phencyclidine (PCP) displaceable binding of ³H-PCP to glass-fiber filters was eliminated and total binding markedly reduced by initial treatment of the discs with 0.05% polyethyleneimine. Assessed with treated filters, unlabeled PCP displaced ³H-PCP in both rat and pigeon brain membranes with an EC50 of 1 μM. Of similar high inhibitory potency were dextrorphan, levorphanol, SKF 10047 and ketamine, while morphine, naloxone and etorphine had EC50 values higher then 1 mM. Using the dissociative anesthetic dexoxadrol and its inactive isomer levoxadrol as displacing agents, stereospecific binding of ³H-PCP was obtained in rat and pigeon brain membranes. The markedly higher potency of dexoxadrol, relative to levoxadrol, in displacing bound ³H-PCP is compatible with behavioral data for these enantiomers. However, they were equipotent in displacing ³H-PCP bound to glass-fiber filters in the absence of tissue. Heat denaturation, but not freezing, abolished stereospecific binding of ³H-PCP, which was also absent in rat liver membranes. The stereospecific binding component in brain displayed biphasic saturability at 60–70 nM and 300–400 nM, respectively.     

Mathematical modelling of dynamics and control in metabolic networks. II. Simple dimeric enzymes

The dynamics of enzyme cooperativity are examined by studying a homotropic dimeric enzyme with identical reaction sites, both of which follow irreversible Michaelis-Menten kinetics. The problem is approached via scaling and linearization of the governing mass action kinetic equations. Homotropic interaction between the two sites are found to depend on three dimensionless groups, two for the substrate binding step and one for the chemical transformation. The interaction between the two reaction sites is shown capable of producing dynamic behavior qualitatively different from that of a simple Michaelis-Menten system; when the two sites interact to increase enzymatic activity over that of two independent monomeric enzymes (positive cooperativity) damped oscillatory behavior is possible, and for negative cooperativity in the chemical transformation step a multiplicity of steady states can occur, with one state unstable and leading to runaway behavior. Linear analysis gives significant insight into system dynamics, and their parametric sensitivity, and a way to identify regions of the parameter space where the approximate quasi-stationary and quasi-equilibrium analyses are appropriate.     

Synthesis and structural investigation of biologically active complexes of 4-acetyl-2-(acetylamino)-5-dimethyl-Δ2-1,3,4-thiadiazole with Zn(II), Hg(II), Cd(II) and Cu(II)

4-Acetyl-2-(acetylamino)-5-dimethyl-Δ2-1,3,4-thiadiazole (AAT) has been used to obtain the complexes of the general formula [M(AAT)X₂]·H₂O where M(II) = Zn, Hg, Cd and Cu, and X  Cl or $\text{1}\text{2}$ SO₄. The complexes have been characterized on the basis of their elemental analysis, molar conductance, magnetic susceptibility and spectral data. Probable structures for the complexes have been proposed on the basis of their physico-chemical properties. The fungitoxicity of AAT and the isolated complexes has been tested on pathogenic fungi.     

Frog lysozyme. II. Isozymes of lysozyme during the larval development of the leopard frog, Rana pipiens.

Eight isozymes of lysozyme were found differentially distributed among six developmental stages of Rana pipiens. Qualitative changes during early development involved a progressive loss of the more basic isozymes which then reappeared between metamorphosis and maturity. Though the egg contained five isozymes, only two were present by early metamorphosis including one not found in the egg. By metamorphic climax, the four isozymes in the egg were regained and one additional form appeared. By maturity, two less basic forms appeared giving a total of eight isozymes.From hatching to early metamorphosis, lysozyme units per animal increased, but lysozyme units/mg dry weight remained unchanged. Both lysozyme units per animal and units/mg dry weight increased sharply towards the end of metamorphosis.     

The role of glycosidically bound mannose in the assimilation of β-galactosidase by generalized gangliosidosis fibroblasts

Bovine testicular β-galactosidase is rapidly assimilated by generalized gangliosidosis skin fibroblasts. The enzyme contains equimolar amounts of mannose and glucosamine and strongly binds to concanavalin A-Sepharose. Pretreatment of β-galactosidase with a mannosidase preparation from $\text{Aspergillus}\text{niger}$ reduced the rate of assimilation of the enzyme 97%. These data indicate that mannosyl residues play a role in assimilation of the enzyme. This conclusion is supported by observed inhibition of β-galactosidase assimilation by mannose, methyl α- and β-mannopyranosides, and mannose-containing testicular glycoproteins.     

Rapid and efficient preparation of free amino acids from strong acid salts on columns of crosslinked poly-4-vinylpyridine

Acidic and neutral amino acids were recovered from their strong acid salts or from large excesses of strong acids by passage through columns of crosslinked poly-4-vinylpyridine. Basic amino acids eluted as the monoacid salts. High recoveries were possible with submicromolar samples.     

Suppression of natural killer (NK) cell activity of spleen cells by thymocytes

The in vitro influence of thymus cells on natural killer cell activity of spleen cells against prelabeled target cells (YAC-I and RL♂I) has been studied in syngeneic as well as in allogeneic murine models. In mixing experiments to demonstrate suppression, total thymocytes have been found to have no effect on NK activity of syngeneic or allogeneic spleen cells. Among several thymocyte fractions separated by velocity sedimentation, a relatively faster sedimenting fraction showed remarkable suppression of NK activity by spleen cells against two target cells. The suppressive effect of this particular fraction on NK activity was demonstrated to be proportional to the cell dose. The suppressive function was resistant to irradiation at 1000 or 2000 rad administered in vitro and was not restricted by the major histocompatibility complex. Moreover, the thymocyte fraction which induced suppression was not sensitive to NK-mediated cytolysi? by syngeneic spleen cells. The suppression of NK cytolysis in vitro by certain subpopulations of thymocytes as observed in the present studies may be consistent with a role for the thymus in regulating NK activity in vivo.     

Insulin-like growth factors, IGF-1, IGF-2 and somatomedin C trigger cell proliferation in mammalian epithelial cells cultured in a serum-free medium

A single insulin-like growth factor which constitutes part of a defined serum-free medium is sufficient to stimulate DNA synthesis and mitosis in mammalian lens epithelial cells. Rabbit lenses were cultured in KEI-4, a medium which mimics rabbit aqueous humor, or in KEI-4 containing insulin growth factor I (IGF I), insulin growth factor II (IGF II) or somatomedin C. The magnitude of DNA synthesis and mitosis was evaluated on whole mount preparations of the epithelium at various times of culture. IGF I and II, the most highly purified of the insulin-like growth factors, and somatomedin C were equipotent lens mitogens, were active at the ng level, were more mitogenic toward lens epithelial cells than insulin, and initiated cell proliferation throughout the normally amitotic central region of the lens epithelium. The time course of the mitotic response elicited by the insulin-like growth factors was identical to that noted in lenses cultured in medium supplemented with serum or insulin. The present results, coupled with those of other investigators, suggest that insulin-like factors may regulate cell division in the mammalian lens in vivo.     

Quantitation of oligosaccharides released by the β-elimination reaction

A quantitative micromethod has been described for monitoring the rate and extent of the β-elimination reaction as applied to O-glycosyl-glycoproteins utilizing alkaline tritiated borohydride. The procedure simultaneously labels the released oligosaccharides by their reduction to the corresponding tritiated alditols. The alkaline tritiated borohydride treatment also results in the labeling of the protein moiety of the glycoprotein and this can be quantitatively separated from the carbohydrate moiety on a cation exchange resin; the carbohydrate moiety is not adsorbed, while the protein moiety is adsorbed and then eluted with HCl. The radioactivity in the aqueous eluate of the resin is therefore a direct measure of the amount of oligosaccharides released by the β-elimination reaction. The sensitivity of the method is dependent on the specific activity of the tritiated sodium borohydride used. The stoichiometry of the reaction has been established by the use of N-acetylgalactosaminyl-O-glycoproteins, demonstrating that at the completion of the β-elimination reaction: (a) none of the radioactivity attributable to the protein moiety contaminates the carbohydrate moiety, (b) all the carbohydrate components of the glycoprotein are found in the aqueous eluate from the cationic exchange resin, (c) all the radioactivity in this aqueous eluate is associated with the sugar known to be at the reducing end of the oligosaccharide chain bound to serine or threonine of the glycoprotein (in the examples discussed, N-acetylgalactosamine), and (d) there is no additional hydrolysis of the oligosaccharide chains during the processing.     

Enzyme-linked lectin assay (ELLA). II. Detection of carbohydrate groups on the surface of unfixed cells

An enzyme-linked lectin assay (ELLA) has been developed to detect specific carbohydrate units on the surface of unfixed cells. The assay may be read in standard ELISA plate readers, since the cell-bound enzyme-lectin conjugate is specifically eluted from the cells prior to development of the conjugate. ELLA, when read in an enzyme-linked immunosorbent assay (ELISA) plate reader, allows better detection and relative quantitation of specific surface carbohydrate units than is possible by standard immunofluorescence with fluorescein-conjugated lectins.     

Red cell ouabain binding sites, Na+K+-ATPase, and intracellular Na+ as individual characteristics

Healthy male volunteers were infused for three hours with either a dopamine hydrochloride solution at a rate of 4 ug/kg/min or with normal saline. Plasma amine oxidase and platelet MAO activity towards benzylamine both increased in response to intravenous dopamine. There was no increase in enzyme activity when dopamine was added to the platelet and plasma enzymes in vitro. This heretofore unreported increase in the oxidative deaminating capacity of the human organism may represent an adaptive physiologic response to the high circulating levels of dopamine and provides further evidence for a possible functional significance of these enzymes in man.     

Effect of histamine and histamine antagonists on natural and antibody-dependent cellular cytotoxicity of human lymphocytes in vitro

The in vitro effect of histamine and its antagonists, cimetidine and clemastine fumarate, on natural killer (NK) and antibody-dependent cellular Cytotoxicity (ADCC) activities of human lymphocytes was investigated. The histamine 1 (H1) antagonist, clemastine fumarate, and the histamine 2 (H2) antagonist, cimetidine, but not histamine alone, inhibited the NK and ADCC activities of lymphocytes when added directly to the mixture of effector and target cells in a ⁵¹Cr-release assay. This inhibition was proportional to the concentration of drugs added and was observed at various effector to target ratios against several targets. H1 and H2 antagonists also inhibited NK activities of T cells as well as Percoll-separated, NK-enriched effector cells. The inhibition was significantly reversed by histamine. In target binding assays, clemastine fumarate and cimetidine also decreased the target binding capacity of effector lymphocytes. Further, PBL precultured with histamine (10^?3–10^?4M) for 24 hr showed a significant decrease in their NK and ADCC activities. In coculture experiments, PBL precultured with histamine suppressed the NK activity of normal autologous effector lymphocytes. PBL precultured with histamine showed an increased number of OKT8⁺ cells, as estimated using monoclonal antibodies. The suppression of Cytotoxicity was not due to either direct toxicity, steric hindrance, crowding, or cell death, but by functionally viable suppressor cells. An immunoregulatory role for histamine in NK and ADCC reactions is proposed.     

Interaction of alpha 2-macroglobulin with trypsin, chymotrypsin, plasmin, and papain

The interaction alpha 2-macroglobulin with four proteinases has been investigated by binding assays and by gel electrophoresis. At pH 7.65 the binding ratios of the proteinase-alpha 2-macroglobulin complexes were found to be 2:1 (trypsin and papain), 1.4:1 (chymotrypsin), and 1:1 (plasmin). The progressive decrease in the stoichiometry of the three seryl proteinase complexes was paralleled by a concomitant decrease in the proteinase-dependent specific cleavage of the alpha 2-macroglobulin peptide chains. Rate studies have shown that the relative rates of reaction of the proteinases with alpha 2-macroglobulin also varied greatly: papain greater than trypsin greater than chymotrypsin greater than plasmin. The data suggest that the ability of a proteinase to saturate the second proteinase binding site is a reflection of its ability to bind to alpha 2-macroglobulin and cleave the second pair of scissile alpha 2-macroglobulin peptide bonds before the alpha 2-macroglobulin has undergone the conformational change initiated by the formation of the 1:1 proteinase alpha 2-macroglobulin complex.     

Solvent interactions with the active site of the pig heart cytosolic aspartate aminotransferase.

Aqueous solvent interactions with the chromophoric pyridoxal phosphate prosthetic group of aspartate aminotransferase (EC 2.6.1.1) were analyzed quantitatively with ethylene glycol, glycerol, dimethylsulfoxide (DMSO), sucrose, and xylitol as cosolvents. The smaller cosolvents perturb the visible absorption and visible dichroic spectra of the free enzyme, but this solvent perturbation is not observed with the acidic enzymeglutarate complex. Addition of cosolvents caused an increase in the enzyme's affinity for glutarate. This increase in affinity resulted from an increase in the acidic dissociation constant (pK₂) of the enzyme-glutarate complex. The changes in the acidic dissociation constant of the enzyme-glutarate complex, upon addition of cosolvents, correlate well with the changes observed in the pK_a's of carboxylic acids in comparable solvents. Since these solvents have little effect on the pK_a of the enzyme itself, it is concluded that the increase in affinity is due to a specific solvation effect on a carboxyl group of the enzymebound glutarate, rather than resulting from a conformational change in the protein.     

A possible molecular mechanism for beta-receptor desensitization: experiments and hypotheses

β-Receptor desensitization in intact NRK-S cells and in a crude membrane preparation derived from these cells was found not to involve methylation, cAMP dependent phosphorylation, Ca⁺⁺ dependent phosphorylation or ADP ribosylation, but is absolutely dependent on ATP in cell-free systems. Also, the desensitized state could not be relieved by protein phosphatases or alkaline phosphatases. Depletion of intact cells from ATP by prolonged incubation with 2-deoxy-glucose and NaN₃ did not inhibit the rapid onset of desensitization by incubating the cells with β-agonists. In order to rationalize the two seemingly contradictory findings, namely, the absolute requirement of ATP in the cell-free desensitization system and the inability to reverse the desensitized state by a variety of phosphatases, we propose that the uncoupling reaction responsible involve for establishing the desensitized state does not Our working hypothesis suggests instead, that the uncoupling reaction involves a covalent modification of the receptor protein and is catalyzed by a receptor modulator protein which is under the control of the ATP dependent phosphorylation.     

Potential tumor or organ-imaging agents, 24. Radioiodinated pregnenolone esters

A series of radioiodinated pregnenolone esters was prepared in an effort to find an agent that would be rapidly and selectively taken up by adrenal cortical tissue. Achievement of such a goal would provide the basis for the development of an adrenal imaging agent having several advantages over those agents currently available for clinical use. The radioiodinated esters for this study were readily prepared by treating pregnenolone with the appropriate iodobenzoic acid in the presence of dicyclohexylcarbodiimide (DCC) and 4-dimethylamino-pyridine (DMAP). The resulting esters were readily labeled with radioiodine by isotope exchange with sodium iodide-125 in pivalic acid. Subsequent tissue distribution studies in rats revealed that those esters displaying the most stability towards hydrolysis achieved the highest concentration in adrenal cortical tissue. For example, the 2,3,5-triiodobenzoate (6) showed an adrenal uptake of 23% of administered dose per gram of tissue at 0.5 hours. The achievement of high levels of radioactivity in the adrenal with this agent at early time periods warrants further evaluation of this agent in other animals.     

A new theory on the origin and the nature of viruses

The hypothetical model presented herein concerns the origin and nature of viruses. It advances the possibility of the appearance and existence of an organism lacking a cohesive morphological structure, that is: its subsystems are not in structural continuity. An attempt to delimit the concepts of life and organism and to integrate the viruses into this framework is made. Viruses are presented as organisms which pass in their ontogenetic cycle through two distinctive phenotypic phases: (1) the vegetative phase and (2) the phase of viral particle or nucleic acid. In the vegetative phase, considered herein to be the ontogenetically mature phase of viruses, their component molecules are dispersed within the host cell. In this phase the virus shows the major physiological properties of other organisms: metabolism, growth, and reproduction. Therefore, life is an effective presence. It is shown also, that in this phase so called "DNA viruses" have both nucleic acids: RNA as well as DNA. The virions are considered to be "spores" or reproductive forms of the virus, possessing life only as a potential property.