Lecture 10: Time Course of Immediate drug effects Flashcards
Pharmacokinetics vs Pharmacodynamics
Pharmacokinetics: time course of concentration (conc)
- the science linking dose and concentration
Pharmacodynamics: how effects change with concentration (effects)
- the science linking concentration and effect
What are the 3x ways to think of the time course of drug effects?
- effects are immediately related to observed drug concentration (e.g. in plasma)
- effects are delayed in relation to observed drug concentration
- effects determined by accumulative action of the drug
What should a concentration and effect curve look like based on the law of mass action principle
binding of a drug to a receptor should follow a hyperbolic curve (rectangular hyperbole)
- C50 and Kd will be the same if the effect is directly proportional to the binding
Kd
equilibrium binding constant
- concentration of unbound drug at which 50% of the binding sites are occupied
When can you achieve Emax
You cant directly observe Emax, it is an acitotic/abstract quantity
- it the asymptomatic effect of the drug at an infinite concentration
- can only approach Emax/guess/estimate it
Log Transformation curve
S shaped sigmoidal curve
X axis allows a wide range of concentrations to be plotted –> can see at very high concentrations the effect approaches E max
curve b/w 20-80% of Emax = approximately straight line/almost linear. used to be helpful to calculate slope via simple equations
Used to be called “log-dose response curves”- but there is no underlying biological or physical reason to think that drugs effects are related more closely to the log of concentration than untransformed concentrations
What are the positives of the Log Transformation curve?
can “see more”
- expands concentration scale so can see lower concentrations and can get to higher concentrations
What are the negatives of the Log Transformation curve?
- Slope isnt reflective of rate
- log of concentration when concentration is zero
- zero concentration should have zero effect
- but on a log scale the log of zero is mathematically undefined therefore the effect is undefined - Doesnt recognise that the effects will approach a maximum (as does every biological system)
Emax model
The fundamental description of the concentration effect relationship.
Strong theoretical support from the physicochemical principles governing bind of a drug to a receptor (law of mass action)
All biological responses must reach a max
Emax model when concentrations are low in relation to C50
When concentrations are low in relationship to C50 –> concentration effect relationship approx. a straight line
Linear pharmacodynamic model
E = slope x concentration
Emax model equation
E = (Emax . Conc) / ( C50 + Conc) E= drug effect Conc= concentration at the receptor Emax= max drug effect C50= conc at 50% of Emax
Emax model predictions
C20 (when the concentration is 20% of maximum effect) = 1/4 of C50
C80 (when concentration is 80% of maximum effect) = 4x C50
Note: 20% is essentially minimum considered value as is barely distinguishable from baseline noise and you dont tend to increase higher than 80% max response, therefore this is the range most considered
–>
Therefore there is a 16x fold change in concentration b/w 20%-80% of Emax
Steep Emax model predictions
Many drugs have a steep relationship b/w concentration and effect –> therefore a smaller change is required
- steeper Emax models are described by the sigmoid Emax model
What is the change in effect when you double the concentration?
17% increase in effect (even though the concentration has doubled)
Sigmoid Emax model
Hill investigates Oxygen-Hb saturation relationship (sigmoidal oxygen saturation curve)
- steeper than simple binding predictions of Emax model
Added an exponential parameter to the Concentration (Hill coefficient)
Illustrates co-operative binding –> (the binding of each oxygen affects the other binding sites on the Hb –> steep O2-Hb binding curve)
Sigmoidal Emax model equation
E = (Emax . Conc^Hill) / (C50^Hill + Conc^Hill)
Sigmoid Emax model when Hill co-efficient = 1
Same curve as Emax model (rectangular hyperbole)
Sigmoid Emax model when Hill co-efficient = 2
Only takes a 4x concentration change to go from C20 –> C80 (of Emax)
- steeper around C50 and approaches Emax faster
- this is due to the co-operative binding/allosteric interaction (first binding changes structure of Hb so second molecule can bind more easily)
Note: Steeper curve when Hill= greater than 1
Sigmoid Emax model when Hill co-efficient = >10
Very large Hill co-efficient, leads ot the Concentration-Effect relationship being similar to an On/Off switch
Threshold Concentration close to C50 –> Effect “turns on”
Examples of Steep concentration effect relationships:
1. arrhythmic drugs
2. Local anasthetics
Sigmoid Emax model when Hill co-efficient = <1
Steep start but slow approach to Emax
e.g. Olympic EPO doping. Excessively high doses of EPO can lead to excess RBC in circulation –> coagulation –> thrombosis in brain and hearts –> death
- the synthesis rate of Hb is rapid when O2 concentration is low
- But natural adaptive mechanism to slow RBC production after reach EC50 to avoid dangerous excessive RBC (this natural protective mechanism is overridden by dosing)
Note: Curve is shallower than Emax model when less than 1
What are some Examples of Steep concentration effect relationships:
- Arrhythmic drugs: Travel b/w elements of the conduction system, therefore are determines by the circuit mechanism of electrical activity going into the heart to create Tachycardia.
- Dependant on the time delays of the conduction system
“switch”: the drug needs to reach a critical conduction velocity, which slows conduction and breaks the circuit –> so that the arrythmia’s stop - Local Anaesthetics: effect Na Channels and effect the rate of depolarisation of nervous tissue/muscle
Theophylline in relation to Emax model
Theophylline is a bronchodilator used to treat severe asthma
- Peak flow change reflects airway constriction/degree of bronchodilation
- C50 achieved at 10mg/L
- Emax is increased peak flow 100% above baseline peak flow
- above 20mg/L adverse effects
What are 3x questions related to the time course effect of a drug?
- How long does the drug effect last
- Is there a half life for effect
- What is the relevance of C50
What is the time course of immediate drug effect dependant on?
- Initial concentration
2. Pharmacokinetics of the drug
Concentration Peak = 10 x C50
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