Harvey J. Motulsky

Fitting curves to data using nonlinear regression: a practical and nonmathematical review.

Many types of data are best analyzed by fitting a curve using nonlinear regression, and computer programs that perform these calculations are readily available. Like every scientific technique, however, a nonlinear regression program can produce misleading results when used inappropriately. This article reviews the use of nonlinear regression in a practical and nonmathematical manner to answer the following questions: Why is nonlinear regression superior to linear regression of transformed data? How does nonlinear regression differ from polynomial regression and cubic spline? How do nonlinear regression programs work? What choices must an investigator make before performing nonlinear regression? What do the final results mean? How can two sets of data or two fits to one set of data be compared? What problems can cause the results to be wrong? This review is designed to demystify nonlinear regression so that both its power and its limitations will be appreciated.— Motulsky, H. J.; Ransnas, L. A. Fitting curves to data using nonlinear regression: a practical and nonmathematical review. FASEB J. 1: 365‐374; 1987.

Adrenergic receptors in man

THE catecholamines norepinephrine and epinephrine are key regulators of many physiologic events in human beings; norepinephrine acts primarily as a neurotransmitter released from sympathetic-nerve ...

Calculating receptor number from binding experiments using same compound as radioligand and competitor

Saturation experiments using increasing concentrations of radioligand are commonly used to determine receptor number and affinity, but this protocol is not feasible in all situations. Alternatively, competitive binding experiments are often performed in which binding of a single concentration of radioligand is completed for by multiple concentrations of the same unlabelled ligand, but the analysis of such data has been difficult. Antonio DeBlasi and colleagues present here a simple method for calculating receptor number and affinity from competitive binding data. This experimental protocol is useful when a single class of binding site is present, but is often not able to detect the presence of two classes of site.

Interaction of verapamil and other calcium channel blockers with alpha 1- and alpha 2-adrenergic receptors.

To determine the specificity of the previously demonstrated competition of verapamil with radioligand binding to alpha-adrenergic receptors, we examined the interaction of calcium channel blockers with alpha 1- and alpha 2-adrenergic receptors on several tissues. Verapamil competed for [3H] prazosin binding to alpha 1-adrenergic receptors and for [3H]yohimbine binding to alpha 2-adrenergic receptors in several tissues (human platelets, rat kidney and heart, and cultured muscle cells) with dissociation constants of 0.6-6 microM. The calcium channel blockers D600, D591, fendiline, and prenylamine--which are structural analogues of verapamil--also competed for [3H]yohimbine binding to human platelets. Two other calcium channel blockers, diltiazem and nifedipine, did not compete for [3H] yohimbine binding to human platelets or [3H]prazosin binding to membranes prepared from rat ventricles. We used [3H]nitrendipine binding to identify putative calcium channels on rat myocardial membranes. Nifedipine and verapamil blocked these [3H]nitrendipine-binding sites on ventricular membranes, but epinephrine and prazosin did not, indicating that the ventricular alpha 1 receptors and calcium channels are distinct. We found no specific [3H]nitrendipine binding to human platelets. We conclude that the interaction of verapamil with alpha-adrenergic receptors is not receptor subtype or tissue specific, that interaction with alpha-adrenergic receptors is not a property of all calcium channel blockers, and that the interaction of verapamil with alpha-adrenergic receptors and its interaction with calcium channels occur at at least two distinct sites.

Characterization of α2-adrenergic receptors on human platelets using [3H]yohimbine

Summary In order to investigate properties of alpha-adrenergic receptors of human platelets, we have examined the binding of [ 3 H]yohimbine, a potent α 2 -adrenergic 3 antagonist, to intact platelets and platelet membranes. There were 207±41 [ 3 H]yohimbine sites per platelet. These had an equilibrium dissociation constant (K D ) of 2.7 ± 0.7nM, a Hill coefficient of 1.02±0.11, and were competed for by adrenergic compounds stereoselectively and with a rank order expected at α 2 -adrenergic receptors. Addition of Na + and GTP synergistically decreased the affinity of epinephrine in competing for [ 3 H]yohimbine sites in platelet membranes and the resulting affinity of epinephrine in membranes was similar to that obtained with intact platelets. Substitution of sucrose for NaCl increased the affinity of epinephrine for intact platelets. [ 3 H]yohimbine thus appears to be a useful ligand for characterization of platelet α 2 -adrenergic receptors. Our results suggest that extracellular Na + and intracellular GTP and Mg ++ may be physiological determinants of epinephrine binding to these receptors.

Sympathetic and immune interactions during dynamic exercise. Mediation via a beta 2-adrenergic-dependent mechanism.

BackgroundThe relation between the sympathetic nervous system and the immune system has not been fully defined. Recent investigations have suggested an adrenergically driven efflux of specific β2-receptorrich lymphocyte subsets into the circulation with either exercise or infusion of exogenous catecholamines. Methods and ResultsTo determine whether acute sympathetic stimulation mediates immunoregulatory cell trafflic and function via a β2-receptor mechanism, we exercised 20 healthy volunteers before and after 1 week of treatment with either the nonselective β-antagonist propranolol or the β1-selective antagonist metoprolol. Before treatment, exhaustive exercise according to the Bruce protocol led to a marked lymphocytosis. Tsuppressor/cytotoxic (Ts/c) and natural killer cells, subtypes with the largest density of β-receptors, showed the most pronounced increases after exercise, with less impressive elevations in Thelper and B cells. With respect to function, exhaustive exercise led to a decrease in concanavalin A-stimulated IL-2 receptor expression and [3H]thymidine incorporation while enhancing natural killer cell activity. One week of propranolol therapy blunted the exercise-induced increases in circulating Ts/c and natural killer subpopulations as well as the previously observed alterations in cellular immune function. Treatment with the β1-selective antagonist metoprolol, however, did not impair the influence of exercise on any of the above parameters. ConclusionsAcute sympathetic stimulation by exhaustive exercise leads to selective release of immunoregulatory cells into the circulation with subsequent alterations in cellular immune function, either secondary to subset changes or as a result of direct catecholamine effects on function. These changes are attenuated by propranolol but not metoprolol, suggesting a β2-mediated mechanism.

Stoichiometry of receptor-Gs-adenylate cyclase interactions.

Little is known about the relative stoichiometry of guanine nucleotide‐binding (G) proteins relative to the effector systems to which they link. We addressed this question for the stimulatory G protein (Gs) linked to adenylate cyclase. Forskolin stimulates the catalytic subunit of adenylate cyclase (C), but it has a higher efficacy and potency when C also interacts with the G protein Gg. Accordingly, we measured high‐affinity [3H]forskolin binding to intact cells to assay α,‐C complexes. No high‐affinity specific binding occurred with unstimulated cells. The β‐adrenergic agonist isoproterenol promoted the binding of [3H]forskolin to about 3000 sites per cell, suggesting that each receptor on average activates at least several Gg molecules. Activating Gg directly with cholera toxin maximally promoted [3H]forskolin binding to a similar number of sites, suggesting that this is the maximal number of αg‐C complexes formed per cell. We conclude that each cell likely contains only a few thousand functional copies of C, and that the availability of C (rather than Gg, which exists in more than 100,000 copies per cell) is likely to be limiting for agonist stimulation of adenylate cyclase activity.—Alousi, A.; Jasper, J. R.; Insel, P. A.; Motulsky, H. J. Stoichiometry of receptor‐Gg‐adenylate cyclase interactions. FASEB J. 5: 2300–2303; 1991.

Verapamil competitively inhibits alpha 1-adrenergic and muscarinic but not beta-adrenergic receptors in rat myocardium.

Recent studies indicate that antagonism of calcium channels may not be the only mechanism whereby drugs such as verapamil alter myocardial function. We have examined the effect of verapamil on the binding of [3H]prazosin (alpha 1-adrenergic), [3H]quinuclidinyl benzilate (QNB, muscarinic) and [3H]dihydroalprenolol (DHA, beta-adrenergic) to membranes prepared from rat heart. Verapamil competed for the binding of these radioligands in the following rank order: [3H]prazosin greater than [3H]QNB greater than [3H]DHA (Ki for verapamil = 0.6 microM, 7 microM, and 72 microM, respectively). Verapamil (10 microM) competitively inhibited [3H]prazosin binding to rat ventricular membranes; the apparent dissociation constant (KD) of [3H]prazosin increased from 0.13 +/- 0.02 to 1.5 +/- 0.6 nM (SD) without change in maximal binding capacity (Bmax). The effect of verapamil on the affinity of [3H]prazosin was completely reversed by washing the membranes. The verapamil derivative D-600 also inhibited [3H]prazosin binding (Ki = 1.1 microM). Verapamil (30 microM) competitively inhibited [3H]QNB binding in both atria and ventricles and increased the apparent KD of [3H]QNB fivefold (from 0.07 nM to 0.32 nM) without decreasing Bmax. Verapamil was a less potent inhibitor of [3H]DHA binding and its effect was noncompetitive: the KD for DHA was unaltered by 100 microM verapamil while the Bmax decreased severalfold. We conclude that verapamil, at concentrations clinically achieved in the myocardium (approximately 1 microM), competitively inhibits binding to alpha 1-adrenergic and muscarinic receptors and that this inhibition may play a role in the effects of verapamil on the heart.

Adrenergic control of circulating lymphocyte subpopulations. Effects of congestive heart failure, dynamic exercise, and terbutaline treatment.

The current studies were undertaken to explore the relationship between enhanced sympathetic nervous activity and lymphocyte subset distribution in three settings: congestive heart failure, dynamic exercise, and beta-adrenergic agonist treatment. We compared the number and subset distribution of circulating lymphocytes in 36 patients with congestive heart failure and 31 age-matched control subjects. The number of circulating lymphocytes was lower in heart failure than in control. This was due to a reduction in Tsuppressor/cytotoxic and natural killer cells without significant alteration of Thelper cells. The extent of the alteration was similar in patients with idiopathic and ischemic heart failure, but the reduction was more pronounced in patients with New York Heart Association class III-IV than in class I-II. The plasma catecholamine elevation in heart failure was also independent of etiology but more pronounced in the more severely ill patients. We also assessed lymphocyte subsets after acute stimulation of sympathetic activity by dynamic exercise and after treatment with the beta-adrenergic agonist terbutaline. Dynamic exercise until exhaustion increased the number of circulating lymphocytes in healthy controls and heart failure patients in a subset-selective manner. By contrast, a 7-d treatment with terbutaline caused a reduction in the circulating number of lymphocytes in some subsets that was identical to that seen in heart failure patients. We conclude that prolonged sympathetic activity reduces the number of circulating lymphocytes by a beta-adrenergic mechanism. Such alterations might be involved in the pathophysiology of heart failure and other disease states involving increased activity of the sympathetic nervous system.

[3H]dihydroergocryptine binding to alpha-adrenergic receptors of human platelets: A reassessment using the selective radioligands [3H]prazosin, [3H]yohimbine, and [3H]rauwolscine

Which subtype(s) of the alpha-adrenergic receptor occurs on human platelets? Studies of platelet responsiveness to adrenergic compounds and indirect radioligand binding studies addressing this question have yielded contradictory conclusions. These bindings studies employed the ligand [3H]dihydroergocryptine ( [3H]DHE), an alpha-adrenergic antagonist that does not select between alpha 1- and alpha 2-adrenergic receptors and that also binds to other receptor types in some tissues. To determine the subtype of the platelet alpha-adrenergic receptor, we have examined the binding to intact human platelets of [3H]prazosin (alpha 1-selective), [3H]yohimbine (alpha 2-selective), and [3H]rauwolscine (alpha 2-selective), and we have compared the binding of these selective radioligands with that of [3H]DHE. [3H]Yohimbine and [3H]rauwolscine both bound with high affinity (Kd = 2.7 and 4.6 nM, respectively) to an equal number and a single class (Hill coefficient approximately 1.0) of sites ( approximately 300 per platelet), but [3H]yohimbine yielded lower nonspecific binding than did [3H]rauwolscine. In paired experiments, [3H]DHE bound to 1.5 times as many (phentolamine-displaceable) sites as did [3H]yohimbine or [3H]rauwolscine. Unlabeled yohimbine and epinephrine competed for fewer [3H]DHE binding sites than did phentolamine. Thus, in addition to binding to the alpha 2-adrenergic receptors identified by [3H]yohimbine and [3H]rauwolscine, [3H]DHE seems to bind to other sites on human platelets. The nature of these sites is not clear. We found that [3H]prazosin did not identify alpha 1-adrenergic receptors on platelets, and that phenoxybenzamine only inhibited [3H]yohimbine and [3H]DHE binding at higher concentrations than usually observed for alpha 1-adrenergic receptors. We conclude that (1) all alpha-adrenergic sites on human platelets are of the alpha 2 subtype, (2) [3H]DHE may bind to additional, as yet ill-defined, sites in addition to those sites identified by [3H]yohimbine and [3H]rauwolscine, and (3) [3H]yohimbine is the preferred antagonist radioligand for studying the alpha 2-adrenergic receptors on human platelets.