Log dose

Log-dose response curves, 17 Lowest positive Log(DR-l) value, 105 LTD4, 191 Luciferase, 83, 88... 

The concentration of the unknown is then read off the standard curve opposite its B/Bq value. This sigmoid shaped standard curve, because of its linear portion, simplifies data handling. A mathematical transform of the B/Bq vs log dose is shown in Figure 2. This logit of B/Bq vs log dose is a widely used method of standard curve presentation (5,6,7). Logit B/B is defined as follows ... 

This latter transform is used to linearize the usual sigmoid curve produced in plotting B/Bq vs log dose. This transform may be accomplished by using a computer, logit paper or a table of logit values. 

If the response of interest is death or lethality, the response versus log dose curve of Figure 2-7 is called a lethal dose curve. For comparison purposes the dose that results in 50%... 

Figure 2-8 The various types of response vs. log dose curves. ED, effective dose TD, toxic dose LD, lethal dose. For gases, LC (lethal concentration) is used.

If the response to the chemical or agent is minor and reversible (such as minor eye irritation), the response-log dose curve is called the effective dose (ED) curve. Values for ED50, ED10, and so forth are also used. 

Finally, if the response to the agent is toxic (an undesirable response that is not lethal but is irreversible, such as liver or lung damage), the response-log dose curve is called the toxic dose, or TD curve. 

The relationship between the various types of response-log dose curves is shown in Figure 2-8. 

Figure 2-10 The probit transformation converts the sigmoidal response vs. log dose curve into a straight line when plotted on a linear probit scale. Source D. J. Finney, Probit Analysis, 3d ed. (Cambridge Cambridge University Press, 1971), p. 24. Reprinted by permission.

Figure 4.6. Log dose-response relationships for the effects of synthetic neurotensin, synthetic brady-kinin, and various preparations of NRP on the release of histamine from isolated rat mast cells [73], Each point is the mean obtained for two separate incubations.

For a positive resist, the film thickness of the irradiated region after development decreases until eventually a critical dose Dp is reached which results in complete removal of the film 8,9). The sensitivity and contrast (7p) are evaluated in a manner similar to that for a negative resist. After they have been spin-coated and prebaked, a series of pads of known area are exposed to varying doses. The substrate is developed in a solvent that does not attack the unexposed film and the thickness of the film remaining in the exposed areas measured. The film thickness is normalized to the original thickness, and this value is plotted as function of log dose, as shown in Figure 5 where Dp represents the sensitivity of the positive resist. Contrast (7p) is determined from the extrapolated slope of the linear portion of the response curve as... 

In the case of dose additivity, the dose-response curve of A is determined on a linear- or log-dose scale, and an equi-effective dose of A (liA.equi) and B d resulting in the same effect is estimated. Using the fixed dose d of chemical B and adding various doses dp - i A.equi) of A, the dose-response curve should shift to the left and reach the same maximum as the maximum for the dose-response curve of A alone when the effect of B is smaller than Amax- However, in case of competitive agonism, the effect of B does not affect the effect of A -f B at higher dose of A. 

A log dose-response curve affords an investigator an easy method for assessing cooperativity. By comparing the concentration of the ligand that yields a 90% response (or 90% Emax) to the concentration that generates a 10% response, the ratio obtained (the value) will provide information on the degree of cooperativity (R < 81 is positive cooperativity and Rs > 81 for negative cooperativity). The Rs value and the Hill coefficient are mathematically related Rs = 81... 

Fig. 1.5.2 Log dose response curve showing competitive antagonism.

Fig. 1.5.3 Log dose response curve showing non- pjg. 5 4 Hyperbolic or exponential dose-response...

If the log dose of a drug is plotted against the percentage response, the relationship becomes linear, which is termed as log-dose response curve. 

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