The median-effect equation derived from the mass-action law principle at equilibrium-steady state via mathematical induction and deduction for different reaction sequences and mechanisms and different types of inhibition has been shown to be the unified theory for the Michaelis-Menten equation, Hill equation, Henderson-Hasselbalch equation, and Scatchard equation. It is shown that dose and effect are interchangeable via defined parameters. This general equation for the single drug effect has been extended to the multiple drug effect equation for n drugs. These equations provide the theoretical basis for the combination index (CI)-isobologram equation that allows quantitative determination of drug interactions, where CI 1 indicate synergism, additive effect, and antagonism, respectively. Based on these algorithms, computer software has been developed to allow automated simulation of synergism and antagonism at all dose or effect levels. It displays the dose-effect curve, median-effect plot, combination index plot, isobologram, dose-reduction index plot, and polygonogram for in vitro or in vivo studies. This theoretical development, experimental design, and computerized data analysis have facilitated dose-effect analysis for single drug evaluation or carcinogen and radiation risk assessment, as well as for drug or other entity combinations in a vast field of disciplines of biomedical sciences. In this review, selected examples of applications are given, and step-by-step examples of experimental designs and real data analysis are also illustrated. The merging of the mass-action law principle with mathematical induction-deduction has been proven to be a unique and effective scientific method for general theory development. The median-effect principle and its mass-action law based computer software are gaining increased applications in biomedical sciences, from how to effectively evaluate a single compound or entity to how to beneficially use multiple drugs or modalities in combination therapies.

http://www.protocol-online.org/forums/uploads/monthly_09_2010/post-8165-008503000%201284677034.ipb

Theoretical Basis, Experimental Design, and Computerized Simulation of Synergism and Antagonism in Drug Combination Studies

The ionotropic glutamate receptors are ligand-gated ion channels that mediate the vast majority of excitatory neurotransmission in the brain. The cloning of cDNAs encoding glutamate receptor subunits, which occurred mainly between 1989 and 1992 ([Hollmann and Heinemann, 1994][1]), stimulated this

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The glutamate receptor ion channels

The mammalian ionotropic glutamate receptor family encodes 18 gene products that coassemble to form ligand-gated ion channels containing an agonist recognition site, a transmembrane ion permeation pathway, and gating elements that couple agonist-induced conformational changes to the opening or closing of the permeation pore. Glutamate receptors mediate fast excitatory synaptic transmission in the central nervous system and are localized on neuronal and non-neuronal cells. These receptors regulate a broad spectrum of processes in the brain, spinal cord, retina, and peripheral nervous system. Glutamate receptors are postulated to play important roles in numerous neurological diseases and have attracted intense scrutiny. The description of glutamate receptor structure, including its transmembrane elements, reveals a complex assembly of multiple semiautonomous extracellular domains linked to a pore-forming element with striking resemblance to an inverted potassium channel. In this review we discuss International Union of Basic and Clinical Pharmacology glutamate receptor nomenclature, structure, assembly, accessory subunits, interacting proteins, gene expression and translation, post-translational modifications, agonist and antagonist pharmacology, allosteric modulation, mechanisms of gating and permeation, roles in normal physiological function, as well as the potential therapeutic use of pharmacological agents acting at glutamate receptors.

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Glutamate Receptor Ion Channels: Structure, Regulation, and Function

The locus coeruleus-noradrenergic system: modulation of behavioral state and state-dependent cognitive processes.

[3H]CP 55,940, a radiolabeled synthetic cannabinoid, which is 10-100 times more potent in vivo than delta 9-tetrahydrocannabinol, was used to characterize and localize a specific cannabinoid receptor in brain sections. The potencies of a series of natural and synthetic cannabinoids as competitors of [3H]CP 55,940 binding correlated closely with their relative potencies in several biological assays, suggesting that the receptor characterized in our in vitro assay is the same receptor that mediates behavioral and pharmacological effects of cannabinoids, including human subjective experience. Autoradiography of cannabinoid receptors in brain sections from several mammalian species, including human, reveals a unique and conserved distribution; binding is most dense in outflow nuclei of the basal ganglia--the substantia nigra pars reticulata and globus pallidus--and in the hippocampus and cerebellum. Generally high densities in forebrain and cerebellum implicate roles for cannabinoids in cognition and movement. Sparse densities in lower brainstem areas controlling cardiovascular and respiratory functions may explain why high doses of delta 9-tetrahydrocannabinol are not lethal.

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Cannabinoid receptor localization in brain

Quantitative analysis of drug-receptor interactions: I. Determination of kinetic and equilibrium properties.

A sensitive and convenient procedure for the determination of dopamine-β-hydroxylase (DBH) activity in homogenates of sympathetically innervated organs is described. The assay uses either phenylethylamine or tyramine as substrate and is based on the sequential conversion of the product of the DBH reaction to a radioactively labeled N-methyl derivative by reaction with partially purified bovine adrenal phenylethanolamine-N-methyltransferase in the presence of S-adenosyl-l-methionine methyl- 14 C. The N-methyl derivatives are separated by solvent extraction and their radioactivity is determined. The identity of the reaction products has been determined chromatographically, and the characteristics of the two enzymatic steps in the assay procedure are defined. Endogenous tissue inhibitors of DBH must be inactivated by cupric ions prior to determination of the enzyme activity. DBE activity in sympathetically innervated tissues of the rat has been measured.

A sensitive enzymatic assay for dopamine- -hydroxylase.

Treatment with desmethylimipramine (DMI), a tricyclic antidepressant, for 7 to 21 days resulted in a 35 to 45% decrease in the accumulation of adenosine cyclic 3':5'-monophosphate (cAMP) in response to a maximally effective concentration of (-)-isoproterenol (ISO) in rat cerebral cortical slices. The EC50 for ISO-stimulated cAMP accumulation was not affected by DMI administration. The diminution in responsiveness to catecholamines was accompanied by a 35 to 40% decrease in the density of beta adrenergic receptors as measured by the binding of [125I]iodohydroxybenzylpindolol. Decreases in ISO-sensitive cAMP accumulation and in beta adrenergic receptor density were temporally correlated, maximal decreases being observed within 5 to 7 days. Within 7 days after cessation of chronic DMI treatment ISO-stimulated cAMP accumulation and beta adrenergic receptor density returned to normal. The role of presynaptic nerve terminals in mediating these phenomena was also investigated. Treatment of newborn rats with 6--hydroxydopamine inhibited the development of noradrenergic nerve terminals in the cerebral cortex and blocked the effects of DMI on cortical cAMP accumulation and on beta adrenergic receptor density. The administration of the beta adrenergic receptor antagonist propranolol led to increases in maximal ISO-stimulated cAMP accumulations and beta adrenergic receptor density in the rat cerebral cortex. This increase was not affected by the simultaneous administration of propranolol and DMI. Thus, the effect of DMI appears to be mediated through an action of norepinephrine at beta adrenergic receptors. Chronic treatment with two other clinically effective antidepressants, pargyline and iprindole, led to effects similar to those observed with DMI administration. Pretreatment of neonates with 6-hydroxydopamine blocked the effect of iprindole on beta adrenergic receptors. Preincubation of cortical membranes with guanosinetriphosphate before determination of the density of beta adrenergic receptors had no effect on the decreased number of receptors had no effect on the decreased number of receptors seen in DMI-treated animals. These experiments suggest that antidepressants, acting presynaptically, increase the concentration of transmitter at noradrenergic synapses and induce a compensatory decrease in the density of beta adrenergic receptors.

Presynaptic modulation of beta adrenergic receptors in rat cerebral cortex after treatment with antidepressants.

Developmental switch in the expression of NMDA receptors occurs in vivo and in vitro

A method for determining the relative concentrations and properties of β-1 and β-2-adrenergic receptors in tissues containing both receptor subtypes has been developed. Since (125I)-iodohydroxybenzylpindolol has similar affinities for β-1 and β-2-adrenergic receptors, it is possible to determine the total concentration of β-adrenergic receptors in a tissue by Scatchard analysis of specific (125I)-iodohydroxybenzylpindolol binding. In the presence of GTP, inhibition of specific (125I)-iodohydroxybenzylpindolol binding in rat heart, lung and five regions of rat brain by agonists and antagonists that are not specific for β-1 or β-2-adrenergic receptors yields linear Hofstee plots with Hill coefficients of approximately 1.0. On the other hand, the inhibition of specific (125I)-iodohydroxybenzylpindolol binding by drugs which have been shown to have different affinities for heart (β-1) and lung (β-2) receptors in vitro results in nonlinear Hofstee plots in each of these tissues. Two of these drugs (practolol and metoprolol) are more potent on β-1 than β-2 receptors and two of these drugs (zinterol and salmefamol) are more potent on β-2 than on β-1 receptors. The nonlinear Hofstee plots are consistent with there being two types of binding sites in each of the tissues with different affinities for the drugs. The relative number of each type of binding site and the affinity of each drug for each of the two types of site has been calculated using a computer based iterative procedure. Using this method, the relative percentages of the two receptor subtypes in rat heart, lung, cerebral cortex, caudate, cerebellum, hippocampus and diencephalon were determined. In each tissue, the use of four different drugs with different in vitro selectivity (two β-1 selective and two β-2 selective) resulted in approximately the same calculated β-1/β-2 ratio. This suggests that the assumption that the nonlinear Hofstee plots are composed of only two components is correct. In addition, the calculated affinity of each drug for β-1 and β-2 receptors was quantitatively similar in each of the seven tissues examined. The calculated ratios of β-l:β-2-adrenergic receptors are: heart 83:17; lung 15:85; cortex 81:19; caudate 76:24; cerebellum 15:85; hippocampus 81:19; and diencephalon 71:29. The absolute concentrations of β-1-adrenergic receptors in the brain regions examined varied by almost 20-fold. However, the absolute concentration of β-2-adrenergic receptors varied less than 3-fold. This suggests that β-2-adrenergic receptors in rat brain are associated with a more homogeneously distributed cellular element than are β-1-adrenergic receptors.

Perry B. Molinoff

Papers

Quantitative analysis of drug-receptor interactions: I. Determination of kinetic and equilibrium properties.

A sensitive enzymatic assay for dopamine- -hydroxylase.

Presynaptic modulation of beta adrenergic receptors in rat cerebral cortex after treatment with antidepressants.

Developmental switch in the expression of NMDA receptors occurs in vivo and in vitro

Simultaneous Determination of Beta-1 and Beta-2-Adrenergic Receptors in Tissues Containing Both Receptor Subtypes