4. Drug Calculations

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(Units of Measurement) 10^-3

Back 1

Milli (m)

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(Units of Measurement) 10^-6

Back 2

Micro (μ)

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(Units of Measurement) 10^-9

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Nano (n)

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(Units of Measurement) 10^-12

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Pico (p)

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(Units of Measurement) 10^-15

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Femto (f)

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1 x 10^0 g = ...#g, mg

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1 g = 1,000 milligrams (mg)

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1 x 10^-3 g = ...#mg, μg

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1 milligram (mg) = 1,000 micrograms (μg)

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1 x 10^-6 g = ...#μg, ng

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1 microgram (μg) = 1,000 nanograms (ng)

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1 x 10^-9 g = ...#ng, pg

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1 nanogram (ng) = 1,000 picograms (pg)

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1 x 10^-12 g = ...#pg, fg

Back 10

1 picogram (pg) = 1,000 femtograms (fg)

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Drug doses, Common Units

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Grams / per unit of weight

Examp: 10 mg / Kg

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Drug concentrations, Common Units

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Units of Molar (M)

Examp; Plasma concentration

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Logarithm

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The logarithm of a number is the exponent to which another fixed value (the base) must be raised to produce that number.

For example, the logarithm of 1000 to base 10 is 3
(1000 = 10^3)

If x = b^y, then y is the logarithm of x to base b
––> y = logb(x), so log10(1000) = 3.

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Common Logarithm

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The logarithm to base b = 10 is called the common logarithm.

Routinely used when plotting CONCENTRATION RESPONSE CURVES.

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Common Logarithms:

1x10^0 M = ...(M, and Log Scale)

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1 M = 0 (log scale)

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Common Logarithms:

1x10^-3 M = ...(M, and Log Scale)

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1 millimolar (μM) = –3 (log scale)

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Common Logarithms:

1x10^-6 M = ...(M, and Log Scale)

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1 micromolar (μM) = –6 (log scale)

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Common Logarithms:

1x10^-9 M = ...(M, and Log Scale)

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1 nanomolar (nM) = –9 (log scale)

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Common Logarithms:

1x10^-12 M = ...(M, and Log Scale)

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1 picomolar (pM) = –12 (log scale)

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Percentage of weight per volume (%w/v)

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Expressing the weight of a drug relative to the volume it is dissolved in

1 mL weighs 1g (1L weighs 1 kg)

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%w/v Examples:

1% w/v = (g in 1L, and mg/ml)

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1% w/v = 10g in 1L or 10 mg/ml

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%w/v Examples:
(If 1% w/v = 10g in 1L or 10 mg/ml)...

3% w/v = (g in 1L, and mg/ml)

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3% w/v = 30g in 1L or 10 mg/ml

(*If you first calculate 1% w/v, to calculate 3% (or others), just work from 1% up...)

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%w/v Examples:
(If 1% w/v = 10g in 1L or 10 mg/ml)...

10% w/v = (g in 1L, and mg/ml)

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10% w/v = 100g in 1L or 100 mg/ml

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Concentration Response Curve

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In an experimental study, you can generate a curve of the biological response (contractile response of muscle) to varying doses of a particular drug given (carbachol = cholinergic agonist; activates acetylcholine receptor)

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How to generate Agonist Concentration-Response Curves (aka Dose-Response Curves)

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In the experiment you have values for amount of drug added (mL), Molarity of the drug (M).

(1) Those values can be used to calculate the Moles of drug added (mol), and drug concentration in the organ bath (M).

In the experiment you measure muscle response (mm of contraction).

(2) To plot a (sigmoidal) agonist conc.-response curve, work out the Log of each drug concentration added.

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Working out Log values...

Drug concentration (M)
(1) 1.64 x 10^-7
(2) 1.66 x 10^-8
(3) 2.11 x 10^-6

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Log of each concentration added:

(1) -6.79 (*Key; since 1.64x10^-7 is close to 1x10^-7, you know that the answer should be close to -7)

(2) -7.78

(3) -5.68

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Benefits of sigmoidal/log scale concentration-response curve

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You more easily determine EC50, because the values are more spread out/ easier to read the curve.

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Concentration-response curve;

Max Response & EC50

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MAX RESPONSE: is the largest biological response possible from a given drug, where further increases in drug concentration cannot generate any larger of a response. *This value tells about the EFFICACY of a drug (capacity to produce an effect).

EC50: is the HALF MAXIMAL CONCENTRATION, which refers to the concentration of a drug inducing a response halfway between the baseline and maximum. *This value tells about a drug's POTENCY (measure of drug activity, expressed in terms of the amount required to produce an effect of given intensity)

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Drug concentrations (M) used in tissue bath;

Significance of "half log increments"

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When comparing "actual drug concentration in tissue bath" to "Log of drug concentration" values...

The midway point between Log10(–10) and Log10(–9) (aka the difference b/w 1x10^-10 and 1x10^-9) IS NOT 5x10^-10 --> BECAUSE LOGS AREN'T LINEAR.

The actual midway point b/w Log10(–10) and Log10(–9) is... 3x10^–10.

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Calculating MAXIMUM RESPONSE values for each drug.

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Circle: 2.3 g

Square: 2.3 g

Triangle: 0.8 g

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Calculating Log EC50 for each drug.

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Circle: -7.6 M

Triangle: -7.2 M

Square: -5.9 M

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RANK drugs in order of potency...

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Looking at drug concentration for 50% max response (EC50 values)... (circle = -7.6M < triangle = -7.2 M < square = -5.9 M)

POTENCY: Circle > Triangle > Square

(*Note: This assumes all the drugs are agonists)

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RANK drugs in order of efficacy...

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Looking at maximum response levels... (circle & square = 2.3 g response > triangle = 0.8 g response)

EFFICACY: Circle & Square (same max response) > Triangle.

(*Note: This assumes all the drugs are agonists)

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What if Square and Triangle are responses to the SAME AGONIST but in the presence of DIFFERENT ANTAGONISTS?

(Circle = agonist alone w/ no antagonist present)

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REMINDER: agonist = triggers response, & antagonist = blocks agonist. (2 types of competitive antagonists = reversible & irreversible)

Square: Agonist + REVERSIBLE COMPETITIVE ANTAGONIST (although antagonist binds, it dissociates; shifting the curve to the right––higher drug concentration needed for same response)

Triangle: Agonist + IRREVERSIBLE ANTAGONIST (competitive binding of antagonist, once it binds it stays there/doesn't dissociate --> decreasing maximum response)

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Calculate max response, Log EC50, and EC50 for both curves.

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Use the graph to calculate:
Max response–
Black Square = 1.0 g/mg
White Square = 0.45 g/mg

Log EC50–
Black Square = -7 M
White Square = -6.9 M

EC50–
Black Square = 1x10^-7
White Square = (1x10^-6.9) = 1.26 x 10^-7

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SCENARIO 1:

Both curves are the response to agonists which are acting on different receptors.

COMPARE POTENCY & EFFICACY.

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If both curves are response to agonists, then White Square must be a PARTIAL AGONIST. (No conclusions can be said about if Black Square is full/ or partial agonist b/c a third drug could have even higher max response).

So...
Comparing EFFICACY (capacity to produce effect, -->see max response):
Black Square > White Square

Comparing POTENCY (drug activity, amount to produce effect of given intensity, -->see EC50):
Very close potency (Black Square slightly > White Square, but biologically not likely to be significant)

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SCENARIO 2:

Both curves are the response to agonists which are acting on the same receptor.

COMPARE POTENCY & EFFICACY.

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If both agonists are fighting for the same receptor...

Comparing EFFICACY (capacity to produce effect, -->see max response):
These agonists have a DIFFERENT Efficacy, Black Square > White Square.

Comparing POTENCY (drug activity, amount to produce effect of given intensity, -->see EC50):
These drugs have SIMILAR POTENCY.

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SCENARIO 3.

Both curves are the response to a single agonist, but WHITE SQUARE was observed in the presence of an antagonist.

What can be determined?

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The antagonist is a IRREVERSIBLE COMPETITIVE ANTAGONIST.

(There is competitive binding, once the antagonist binds it doesn't dissociate, resulting in a decrease in max response of the agonist.)