Histamine dose-response curves in guinea pigs

Histamine dose-response curves were performed on anesthetized tracheostomized guinea pigs that were paralyzed and mechanically ventilated at a constant tidal volume and breathing frequency. The dose was calculated by generating an aerosol of known concentration and measuring the volume delivered to the lung. Increasing the dose was accomplished by increasing the number of breaths of aerosol delivered. The response to each dose was determined by measuring the change in airway resistance (RL) and dynamic compliance (Cdyn) using the method of Von Neergaard and Wirz (Z. Klin. Med. 105: 51-82, 1927). With increasing doses of histamine, RL increased and reached a plateau at approximately five times the base-line value and Cdyn fell to approximately 20% of its initial value. The variability in the base-line and maximum response as well as the calculated sensitivity and reactivity was less than that previously reported. Propranolol pretreatment increased resting RL and shifted the dose-response curve for RL to the left of the controls, increasing reactivity but not sensitivity. Atropine shifted the dose-response curve to the right of the control, decreasing sensitivity but without changing reactivity. The data for Cdyn showed that atropine pretreatment caused a higher resting value and propranolol pretreatment a lower value at the highest histamine dose but no differences in either sensitivity or reactivity.     

Mathematical interpretation of dose-response curves

The dose-response of an individual organism can be described by a step functions if the organism survives when the dose is below a certain lethal level and dies when this level is exceeded. If, in a population of organism, the lethal dose for an individual has a unimodal distribution, the latter's properties will determine the shape of the population's response in the following manner. If the distribution is symmetric the dose-response curve has a symmetric sigmoid shape when plotted on linear coordinates. The location of the inflection point and the curve's slope around it are determined by the distribution's mode and variance. When the distribution is skewed, the dose-response curve has an asymmetric sigmoid shape which becomes reminiscent of an exponential decay when the distribution is strongly skewed to the right. The population's dose-response curve can be constructed by integration of the step changes over the distribution range. The step function representing the dose-response of an individual organism can be approximate by a Fermi function, and the distribution of an lethal doses can be represented by the Weibull distribution function. When the two functions are combined, the resulting dose-response of the populationS(X)), which is the fraction of survivors after exposure to a doseX, is given by:S(X)=∫ ₀ ¹ [1/{+exp{(X-X _c (φ))/a _i ]}]dω whereX _c (ω)={(1/b)[-ln(1-ω)]}^(1/n),n andb being the constants of the Weibull distribution anda _i an arbitrarily small number, i.e.a _i ≪[X−X _c (ϕ)], whose actual magnitude is of little significance. This model can be used to determine the underlying distributions of experimental dose-response relationship. It was applied to published survival data of microorganisms exposed to pulsed electric field, X-ray radiation and ozone to show that the different observed shapes of the dose-response curve, and shifts between them, can be expressed in terms of the correponding distribution parameters, namely the mode, variance and skewness.     

Maximum likelihood estimation for cytogenetic dose-response curves

In vitro dose-response curves are used to describe the relation between chromosome aberrations and radiation dose for human lymphocytes. The lymphocytes are exposed to low-LET radiation, and the resulting dicentric chromosome aberrations follow the Poisson distribution. The expected yield depends on both the magnitude and the temporal distribution of the dose. A general dose-response model that describes this relation has been presented by Kellerer and Rossi (1972, Current Topics on Radiation Research Quarterly 8, 85-158; 1978, Radiation Research 75, 471-488) using the theory of dual radiation action. Two special cases of practical interest are split-dose and continuous exposure experiments, and the resulting dose-time-response models are intrinsically nonlinear in the parameters. A general-purpose maximum likelihood estimation procedure is described, and estimation for the nonlinear models is illustrated with numerical examples from both experimental designs. Poisson regression analysis is used for estimation, hypothesis testing, and regression diagnostics. Results are discussed in the context of exposure assessment procedures for both acute and chronic human radiation exposure.     

Graphical aids to interpretation of Scatchard plots and dose-response curves

General expressions are derived for the limiting slopes and intercepts of graphical representations of experimental binding data in either the Scatchard or the “dose-response” co-ordinate systems. We apply a previously formulated general model that includes heterogeneity and/or cooperativity of receptor affinity. One must establish or assume a physical chemical mechanism in order to fully interpret these limiting slopes and intercepts. However, they do provide satisfactory initial estimates for the binding parameters, for use in a non-linear least squares curve fitting approach using an exact model.     

A dose-response model for teratological experiments involving quantal responses

This paper introduces a dose-response model for teratological quantal response data where the probability of response for an offspring from a female at a given dose varies with the litter size. The maximum likelihood estimators for the parameters of the model are given as the solution of a nonlinear iterative algorithm. Two methods of low-dose extrapolation are presented, one based on the litter size distribution and the other a conservative method. The resulting procedures are then applied to a teratological data set from the literature.     

Difference in dose-response curves for glucose-induced insulin and somatostatin release in rat pancreas

We studied the glucose dependence of insulin and somatostatin release from rat pancreata, which were perfused in vitro in the presence of 3-isobutyl-1-methylxanthine (IBMX; 0.5 mM). Half-maximal insulin release occurred at approx. 12 mM glucose, and half-maximal somatostatin release at approx. 7 mM glucose.     

Evaluation of the Fermi equation as a model of dose-response curves

 When plotted in linear coordinates, the dose-response curves of microorganisms exposed to a lethal agent, such as radiation or a toxic substance, often have a characteristic sigmoid shape. Irrespective of whether they are very narrow or broad they can be described by the Fermi function, which is a mirror image of the logistic function, i.e. S(X)=1/{1+ exp [(X−X _c)/a]} where S(X) is the fraction of the surviving organisms, X the dose of the lethal agent, X _c a characteristic dose marking the inflection point of S(X), which corresponds to 50% mortality, and a a measure of the steepness of the survival curve around X _c. It is demonstrated that, if the susceptibilities of the individual organisms, expressed in terms of a characteristic lethal dose, have a symmetric unimodal distribution, the dose-response curve of the population has a Fermian sigmoid shape. It is also shown that the mode and variance of the distribution can be estimated from the shape parameters of the Fermian survival curve, X _c and a. Received: 7 November 1995 / Received last revision: 11 April 1996 / Accepted: 29 April 1996     

Efficient design for estimation of median lethal dose and quantal dose-response curves

The results of quantal dose-response experiments are often summarized by an estimate of the "median lethal dose," denoted LD50, and many sequential designs have been proposed for efficient estimation of LD50. These designs strive to produce a sequence of trials at dose levels that get closer and closer to LD50. Consequently, they may not provide very good estimates of the overall shape of the dose-response curve. In this paper we propose guidelines for the design of experiments that estimate LD50 fairly efficiently and that also allow for efficient global estimation of the curve.     

Interaction between prostaglandins and calcium: The importance of bell-shaped dose-response curves

Biological response to PGs show two basic forms of dose/response relationship, plateau and bell-types. although bell-shaped dose/response curves are well documented their possible occurrence is almost always ignored on the design and interpretation of experiments on PGs and related substances. This may lead to serious errors, several types of which are described. The ignoring of a well-documented phenomenon may take place because there is no accepted hypothesis which attempts to explain the bell-type curves. A hypothesis is proposed which accounts for both plateau and bell type responses. It is developed primarily with respect to PG-calcium interactions but may be applicable to some PG-cyclic nucleotide interactions as well. The model leads to precise predictions which can be experimentally tested in many systems.     

Monotone smoothing with application to dose-response curves and the assessment of synergism

A spline-based procedure for monotone curve smoothing is proposed and is illustrated by application to dose-response curves. It is then shown how such smoothing can be applied to assess possible synergism or antagonism of two drugs.     

Interactions between prostaglandins and calcium: the importance of bell-shaped dose-response curves

Biological responses to PGs show two basic forms of dose/response relationship, plateau and bell-types. Although bell-shaped dose/response curves are well documented their possible occurrence is almost always ignored in the design and interpretation of experiments on PGs and related substances. This may lead to serious errors, several types of which are described. The ignoring of a well-documented phenomenon may take place because there is no accepted hypothesis which attempts to explain the bell-type curves. A hypothesis is proposed which accounts for both plateau and bell type responses. It is developed primarily with respect to PG-calcium interactions but may be applicable to some PG-cyclic nucleotide interactions as well. The model leads to precise predictions which can be experimentally tested in many systems.     

Eosinophils in the bronchial mucosa in relation to methacholine dose-response curves in atopic asthma.

Asthma is characterized by both local infiltration of eosinophils in the bronchial mucosa and bronchial hyperreactivity (BHR). A detailed characterization of BHR implies analysis of a histamine or methacholine dose-response curve yielding not only the dose at 20% fall of baseline forced expiratory volume in 1 s (FEV1), but also a plateau (P) representing the maximal narrowing response in terms of percent change in FEV1 and reactivity as the steepest slope at 50% of P (%FEV1/doubling dose). In the baseline condition, the specific airway conductance (sGaw) may be considered closely related to airway lumen diameter. In 20 nonsmoking asthmatic patients, methacholine dose-response curves were obtained, and a sigmoid model fit yielded the BHR indexes. Immunohistochemistry with the monoclonal antibodies (EG1 and EG2) was used to recognize the total number of eosinophils and activated eosinophils, respectively. The number of activated eosinophils was significantly correlated to both P (r = 0.62; P < 0.05) and sGaw (r = -0.52; P < 0.05), whereas weaker and nonsignificant correlations were found for dose at 20% fall of baseline FEV1 and the total number of eosinophils. We conclude that the number of activated eosinophils can be considered a marker of the inflammation-induced decrease of airway lumen diameter as represented by the plateau index and sGaw.     

Phase shifting by novelty-induced running: activity dose-response curves at different circadian times

This study compared phase shifting after novelty-induced running at different circadian times (CTs). In Experiment 1, hamsters were confined to novel wheels for 3 h, starting at CTs 2, 4, 6, 8, 10 or 22. The largest shifts were found at CTs 2, 4 and 6. At each CT there was a relationship between the number of revolutions during the pulse and the size of phase shift. Maximum shifts were usually observed at each CT when animals ran 5000–9000 revolutions during the pulse. In Experiment 2, hamsters were confined to novel wheels for 1 h, also starting at CTs 2, 4, 6, 8, 10 or 22. Unlike with 3-h pulses, the largest shifts with 1-h pulses occurred at CT 8. In Experiment 3, hamsters were shut into a small nest box after a 1-h pulse at CT 8; phase shifting was unaffected, showing that movement about the home cage after a 1-h pulse had ended was not required for shifting. At CTs 2, 4 and 22, 3-h pulses produced shifts but 1-h pulses did not. Possibly, there are two different mechanisms of nonphotic phase shifting that can be activated by being placed in a novel wheel, but the results can also be explained in terms of a single mechanism. Accepted: 8 August 1997