Kinetic manifestations of allosteric interactions in models of regulatory enzymes with "indirect" co-operativity

Modeling the Effects of Chemotherapy and Immunotherapy on Tumor Growth

Mathematical modeling has been used to simulate the interaction of chemotherapy and immunotherapy drugs intervention with the dynamics of tumor cells growth. This work studies the interaction of cells in the immune system, such as the natural killer, dendritic, and cytotoxic CD8+ T cells, with chemotherapy. Four different cases were considered in the simulation: no drug intervention, independent interventions (either chemotherapy or immunotherapy), and combined interventions of chemotherapy and immunotherapy. The system of ordinary differential equations was initially solved using the Runge-Kutta method and compared with two additional methods: the Explicit Euler and Heun's methods. Results showed that the combined intervention is more effective compared to the other cases. In addition, when compared with Runge-Kutta, the Heun's method presented a better accuracy than the Explicit Euler technique. The proposed mathematical model can be used as a tool to improve cancer treatments and targeted therapy.

The binding of a ligand to an acceptor undergoing indefinite self-association

Explicit expressions are derived which describe the binding of a univalent ligand to equivalent and independent sites on each state of an acceptor undergoing indefinite self-association that is governed by an isodesmic equilibrium constant KI. From considerations of systems in which the same site-binding constant kA applies to all acceptor-ligand interactions, the general forms of binding curves and Scatchard plots are deduced for situations in which binding sites are either created or lost at each monomer-monomer interface. Greater generality is then introduced into the model by allowing ligand interactions with polymeric acceptor states to be governed by a site-binding constant kp that differs in magnitude from that for monomeric acceptor kA. Finally, experimental results with the glutamate dehydrogenase-GTP and lysozyme-saccharide systems are used to illustrate ways in which the present quantitative expressions may be applied to the characterization of inteactions between a ligand and an indefinitely self-associating acceptor.

Dependency on serine concentration of the activity of tryptophan synthase. Cooperative properties

The activity of the enzyme tryptophan synthase from Escherichia coli was tested as a function of the concentration of L-serine which serves as a substrate in the indole to tryptophan reaction as well as for the L-serine deaminase activity. L-Serine binding was found to follow the pattern of negative cooperativity both by kinetic and by equilibrium methods. The enzyme kinetic data support the view that a rapid equilibration model for the enzyme . substrates complex formation is not strictly obeyed.

The evaluation of non-hyperbolic ligand binding and substrate saturation data using variable Hill coefficients

A fitting method for saturation curves is described that may be applied to any kind of ligand binding process, regardless of whether positive, negative or mixed cooperativity is involved. The procedure yields 'best values' of maximal saturation (or maximal velocity with enzymes); in addition, an empirical function is calculated that represents the concentration dependence of the Hill slope (i.e. the slope of the corresponding Hill plot). Since the method does not require the maximal saturation to be known in advance, it can be successfully applied to systems which, due to experimental limitations, may not be saturated with ligand. It is shown that in these cases values of maximal saturation are obtained that are considerably more reliable than those estimated by customary methods. Moreover, it is demonstrated that the concentration dependence of the Hill slope, the other main result of the proposed procedure, may offer useful evidence as to the molecular events leading to non-hyperbolicity and thus provide a rational basis for selecting more specific models to describe the properties of the system studied.

Kinetic cooperativity in the concerted model for allosteric enzymes

The cooperativity of enzyme-substrate interactions is investigated in the concerted allosteric model of Monod, Wyman and Changeux. The general case of K-V systems is considered, in which the two protomer conformational states R and T postulated in the theory differ in catalytic and binding properties. An expression for the Hill coefficient nH defined with respect to the asymptotic velocity V infinity to is analyzed in conditions which exclude substrate inhibition. Kinetic cooperativity is always positive (nH greater than 1) in the case of a dimer enzyme, and in the case of an inactive T state. Slight kinetic negative cooperativity (nH less than 1) occurs under restrictive conditions for larger numbers of protomers when the substrate binds significantly to the less active state of the enzyme, but the phenomenon remains negligible for trimers and tetramers. These conclusions differ from those obtained [A. Goldbeter, J. Mol.Biol.90 (1974) 185] with the Hill coefficient based on the absolute maximum velocity, which may exceed the experimental value V infinity to in K-V systems. The results extend those of Paulus and DeRiel [J. Mol. Biol. 97 (1975) 667] and support the view that in most cases, negative cooperativity is not compatible with a mechanism based on a concerted and conservative allosteric transition. The Hill coefficients for binding and catalysis are compared in K-V systems.

Studies of homogeneous "biosynthetic" L-threonine dehydratase from Escherichia coli K-12. Some kinetic properties and molecular multiplicity

"Biosynthetic" L-threonine dehydratase (EC 4.2.1.16) was purified to a homogeneous state with 29% yield of total activity from Escherichia coli K-12. The homogeneity of the enzyme was shown by polyacrylamide gel disc electrophoresis in the presence of dodecyl sulphate. The enzyme consisted of equal subunits having a molecular weight of about 57 000. The polyacrylamide gel disc electrophoresis has shown that the native enzyme consisted of a set of oligomeric forms. The multiplicity of molecular organization of the enzyme was reflected in complicated kinetic behaviour: at pH greater than 9 on the plots of initial reaction rate (v) versus initial substrate concentration ([S]o) there were four inflexion points (two intermediate plateaux), the position and deepness of which depended on enzyme concentration. At pH 8.3 on the v versus [S]o plots appeared two inflexion points (one intermediate plateu), the position of which practically did not depend on enzyme concentration in the reaction mixture, but strongly depended on the enzyme concentration in the stock solution. Repeated polyacrylamide gel disc electrophoresis of several oligomeric forms, isolated by the first electrophoresis, has shown that the oligomeric forms underwent a slow polymerization. It was suggested that "biosynthetic" L-threonine dehydratase from E. coli K-12 is a set of multiple oligomeric forms, having different kinetic parameters. Probably, each form of the enzyme has a "simple" kinetics characterized by hyperbolic or sigmoidal shape of v versus [S]o plots. The rate of equilibrium installation between the oligomeric forms was small in comparison with the enzyme reaction velocity, that lead to the complex kinetic curves, appearing as a result of summing up of the kinetics inherent to theindividual forms.