DRUG-RECEPTOR INTERACTION AND DATA ANALYSIS OF DOSE RESPONSE CURVES

About Authors:
Emanual Michael Patelia*, Rakesh Thakur, Jayesh Patel
Department of Pharmaceutical analysis and chemistry (Gujarat technical university)
Department of Pharmacology (University of Bedfordshire)
*ricky.emanual@gmail.com

Abstract:
Drug receptor interaction can generally be defined as specific, dose-related and saturable. These characteristics of a drug at a receptor are described by K_D and ED₅₀ and can be obtained from ligand binding and dose–response curves. The dose–response relationship, or exposure–response relationship, describes the change in effect on an organism caused by differing levels of exposure (or doses) to a stressor (usually a chemical) after a certain exposure time.

REFERENCE ID: PHARMATUTOR-ART-1923

Introduction:
The equilibrium dissociation constant K_D is loosely defined as the concentration of a radioligand that occupies half of a particular receptor population.¹ The concentration used here is the in vitro concentration; clinically the mass (dose) of drug given to a patient is more commonly used (see below). K_D is determined experimentally and is a measure of the affinity of a drug for a receptor. More simply, the strength of the ligand–receptor interaction. To determine K_D, a fixed mass of membranes (with receptor) are incubated with increasing concentrations of a radioligand until saturation occurs. High affinity binding occurs at low drug concentrations; conversely, low affinity binding occurs at high drug concentration. If a ligand has affinity it does not necessarily mean that it will produce a response. For example, an antagonist that displays high affinity does not produce a response in its own right.²

A dose–response curve is a simple X–Y graph relating the magnitude of a stressor (e.g. concentration of a pollutant, amount of a drug, temperature, intensity of radiation) to the response of the receptor (e.g. organism under study). The response may be a physiological or biochemical response, or even death (mortality), and thus can be counts (or proportion, e.g., mortality rate), ordered descriptive categories (e.g., severity of a lesion), or continuous measurements (e.g., blood pressure).^[3] A number of effects (or endpoints) can be studied, often at different organizational levels (e.g., population, whole animal, tissue, cell).

The measured dose (usually in milligrams, micrograms, or grams per kilogram of body-weight for oral exposures or milligrams per cubic meter of ambient air for inhalation exposures) is generally plotted on the X axis and the response is plotted on the Y axis. Other dose units include moles per body-weight, moles per animal, and for dermal exposure, moles per square centimeter. In some cases, it is the logarithm of the dose that is plotted on the X axis, and in such cases the curve is typically sigmoidal, with the steepest portion in the middle. Biologically based models using dose are preferred over the use of log(dose) because the latter can visually imply a threshold dose when in fact there is none.

The first point along the graph where a response above zero (or above the control response) is reached is usually referred to as a threshold-dose. For most beneficial or recreational drugs, the desired effects are found at doses slightly greater than the threshold dose. At higher doses, undesired side effects appear and grow stronger as the dose increases. The more potent a particular substance is, the steeper this curve will be. In quantitative situations, the Y-axis often is designated by percentages, which refer to the percentage of exposed individuals registering a standard response (which may be death, as in LD₅₀). Such a curve is referred to as a quantal dose-response curve, distinguishing it from a graded dose-response curve, where response is continuous (either measured, or by judgment).

A commonly used dose-response curve is the EC₅₀ curve, the half maximal effective concentration, where the EC₅₀ point is defined as the inflection point of the curve.

Statistical analysis of dose-response curves may be performed by regression methods such as the probit model or logit model, or other methods such as the Spearman-Karber method. Empirical models based on nonlinear regression are usually preferred over the use of some transformation of the data that linearizes the dose-response relationship.^[4]

Dose–response curves can be fit to the Hill equation (biochemistry) to determine cooperativity

Report :

Calculation

3. ED50 Values for Mepyramine
Following ED50 values for Mepyramine are determined from graph.1 concentration –effect curve.
ED50 (1 x 10^-9) = 1 x 10^-8 M
ED50 (1 x 10^-8) = 5 x 10^-8 M
ED50 (1 x 10^-7) = 1 x 10^-6 M

ED50 control = 5 x 10^-9M

Equipotent concentration ratios (ECR):

ECR (1 x 10^-9) =    ED50 (1 x 10^-9 )     =    1 x 10^-8    =   2
                               ED50 control            5 x 10^-9

ECR (1 x 10^-8) =    ED50 (1 x 10^-8 )     =    5 x 10^-8    =   10
                              ED50 control              5 x 10^-9

ECR (1 x 10^-7 ) =  ED50 (1 x 10^-7 )   =    1 x 10^-6     =   200
                              ED50 control              5 x 10^-9

4. Log of ECR-1 and negative log of the antagonist concentration:

4.1. Log of ECR-1;
ECR (1 x 10^-9) – 1 = 2 – 1 = 1
Log ECR-1 (1 x 10^-9) = 0

ECR (1 x 10^-8) – 1 = 10-1= 9
Log ECR-1 (1 x 10^-8) = 1.0

ECR (1 x 10^-7) – 1 = 200-1=199
Log ECR-1 (1 x 10^-7) = 2.3

4.2. Negative log of the antagonist concentration;
Log 1 x 10^-9 = 9
Log 1 x 10^-8 = 8
Log 1 x 10^-7 = 7

DRAW GRAPH – LOG OF ANTAGONIST ON X-AXIS AND ON Y-AXIS THEN TAKE THEIR SLOPE AND INTERCEPT FOR PA2 VALUE.

6) The x-axis intercept should give you a pA₂ value.
The intercept of line is estimated to at 9  on x –axis so pA₂ value is 9.

7) Measurement of slope of the regression.

y = y₂-y₁
= 0.5-1
= -0.5

x = x₂-x₁
= 9-8
= 1

m = y/x
= -0.5/1
= -0.5

y =  -0.5 x +9

y = 8.5

So, slop of regression is 8.5

References:
1. Crump, KS; Hoel DG, Langley CH, Peto R. (1976). "Fundamental Carcinogenic Processes and Their Implications for Low Dose Risk Assessment". Cancer Research 36 ((9_Part1)): 2973–2979.
2. U.S. EPA (2009). Benchmark Dose Software (BMDS) Version 2.1 User's Manual Version 2.0, DRAFT. Doc No.: 53-BMDS-RPT-0028. Washington, DC: Office of Environmental Information.
3. Altshuler, B (1981). "Modeling of Dose-Response Relationships". Environ Health Perspect 42: 23–27.
4. Bates, D. and D. Watts (1988). Nonlinear regression analysis. New York: John Wiley and Sons. p. 365.

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