#davidsonx

Clearance

Total clearance = hepatic clearance + renal clearance

Also clearance depends on blood flow (Q) and extraction ratio (E)

Therefore total clearance = Qh*Eh + Qr*Er

Volume of Distribution (Vd)

Apparent volume of plasma required to contain drug in plasma

An average 70kg man has 2.7L of plasma but Vd is often much larger than 2.7L (plasma volume is 0.039L/kg) because in reality drugs redistribute to peripheral compartment

Since concentration = amount/volume and the amount and Vd of a drug is known, the concentration can be determined. Then that concentration can be used with plasma volume to determine how much of the drug is actually in the central compartment

E.g. 25mg of ranitidine is given, Vd = 1.4L/kg = 98L in a 70kg man

C = 25mg/98L = 0.255mg/L

Since plasma volume is 2.7L:

0.255mg/L = amount of drug in plasma / 2.7L

Amount of drug in plasma = 2.7L * 0.255mg/L = 0.69mg

Therefore, only 0.69mg of 25mg ranitidine given is in plasma

Protein Bound

A higher % of protein binding decreases clearance and decreases Vd

However, half life and kel (elimination constant) remain the same

Phases

Drug concentration decreases sharply during the distribution phase, then more slowly during the elimination phase (though both happen together)

The end of the distribution phase is when concentration in tissues (Ct) reaches maximum and Vss (steady state volume) is reached

The equation for the blue line is represented by the equations (A and alpha representing distribution phase and B and beta representing elimination phase, in which alpha is usually larger than beta)

Oral absorption

Clearance and Vd

kel = clearance / Vd = ln(2)/half-life

Therefore clearance = Vd * ln(2) / half-life -> linear line

Generally aim for 8 hour half-life

To increase half-life,

Increase Vd by increasing lipophilicity (logP)

Decrease hepatic clearance by making the molecule more stable

Acidic Molecules

Contain a carboxylic acid group (pKa 4-5) that is deprotonated, thus negative

Because it is charged, it is less lipophilic

Because it is negative, it is prone to being bound to albumin

Therefore acidity decreases Vd

Basic Molecules

Contain an amine group (pKa 10) that is protonated, thus positive (ammonium, NH4+)

Cell membranes contain phospholipids which have negative phosphate groups and thus attracted to NH4+

Thus phosphilipids draw molecules out of plasma

Therefore basic increases Vd

E.g. nifedipine is neutral and amlodipine is similar structurally other than a short basic chain, increasing half-life from 1.9 hours to 34 hours

Blood

Blood volume 71ml/kg

In a 70kg person:

Whole blood 5L

Plasma 2.7L

Interstitial fluid 10L

Intracellular fluid 25L

Total body water 38L

Body volume 70L

Albumin

5% of blood by weight

Binds to acidic drugs well (e.g. warfarin, ibuprofen)

Globulin

2.5% of blood by weight

Alpha-1 acid glycoprotein binds basic drugs (e.g. disopyramid, lidocaine)

Lipinski’s rules

Set of rules created by Chris Lipinski in 1997 to predict whether a molecule is likely able to diffuse across membranes

Molecular weight, max value 500

Lipophilicity (log P), max value 5

Hydrogen bond acceptors, max value 10

Hydrogen bond donors, max value 5

Lipophilicity is measured as the logP for the partitioning of a drug in a biphasic system of 1-octanol (non-polar) and water (polar)

logP > 5 means too strongly favors octanol = too non-polar

Hydrogen bond acceptors = number of oxygen and nitrogen atoms

Lone pairs of nitrogen and oxygen can accept hydrogen bond

Exceptions if lone pair is involved extensively in resonance

Clark’s occupancy theory

States that binding = response

If there is 50% binding there is 50% response

If there is 80% binding there is 80% response etc etc

Exceptions

Receptors with constituent activity, because even in 0% binding there is “response“ or activity

Spare receptors: not all receptors need to be bound for maximal response

Downregulation and desensitization

Upregulation and sensitization

Clark’s equation, in which E/Emax is 0 to 1

Alternative theory: drug residence time

koff = rate of dissociation, kon = rate of binding, tau = residence time

The greater the rate of dissociation, the shorter the residence time = less effect

For example with EGFR:

Lapatinib has greater Ki (lower potency) than gefitinib and erlotinib but has greatest activity, going against Clark’s occupancy theory

Receptor Superfamilies

Ligand gated

Membrane bound

Control ion flow across the membrane

Associated with synapses

Called “fast neurotransmitters“

G protein coupled

Membrane bound

Pass signal across membrane

Signal proteins released into cell – complex pathways

Called “slow neurotransmitters“

Tyrosine kinase linked

Membrane bound

Ligand binding causes receptor dimers

Dimers act as enzymes

Associated with cancer

Nuclear receptors

Not membrane bound

Found in nucleus; ligand must enter the cell in order to bind

Control gene expression

Ligand types

Full agonist: upgoing sigmoidal curve, reaches Emax = full effect

Partial agonist: upgoing sigmoidal curve, reaches only a fraction of Emax, tend to bind to same position on receptor as full agonist = compete with full agonist

Antagonist: downgoing sigmoidal curve, binds to same receptor as agonist but causes no response; there are competitive and non-competitive antagonists

Inverse agonist: receptor has inherent activity called constituent activity; inverse agonist causes the activity to drop to zero ; downgoing sigmoidal curve with intercept > 0

IC50 and Ki

Both used to measure how much drug is required to inhibit an enzyme

In both cases, the higher the better

IC50 = inhibitor concentration 50 = the concentration of inhibitor required to inhibit rate of conversion by 50%

In linear equation format:

Cheng-Prussoff equation:

I didn’t expect this at all, but learning the next section allowed me to explore math like the good days in high school.

Equation for a plateau: y = ax+b / cx + d

As x approaches infinity, the constants b and d become irrelevant and the limit of this equation is a/c.

To simplify, if the equation is y = ax/(x+b), then the limit is a.

If x = b, y = 1/2 * a (half of limit)

If x = b/2, y = 1/3 * a (third of limit)

if x = b/3, y = 1/4 * a (fourth of limit)

If x = b/(k-1), y = 1/k * a (kth of limit)

Michaelis-Menten Kinetics

enzyme + substrate -> enzyme-substrate complex -> enzyme + product

V = rate of reaction (y-axis), S is substrate concentration (x-axis)

Vmax is the maximum rate, when S is infinite

1/2 Vmax is reached when S=Km aka Michaelis constant

If we put values into the equation y = ax/ (x+b):

y = V, x = S

a = limit = Vmax

1/2 Vmax is reached when x= b, and b is Km

Therefore, V = Vmax * [S] / ( [S] + Km) (the Michaelis-Menten equation)

This equation can be put into a linear form to the Lineweaver-Burk equation

Inhibition

Reversible

Competitive

Vmax not changed, still reached if substrate concentration high enough

Km increases (affinity dropped)

Non-competitive

Binds to allosteric site not the active site

Binds to both enzyme and enzyme-substrate complex

Lower Vmax

Km not changed (affinity not changed)

Uncompetitive

Binds only to enzyme-substrate complex

Vmax and Km decreases