Block 2 Equations Cheat Sheet

Pharmacodynamics

Equilibrium dissociation constant (Kd)

$K_d = \frac{[D] \times [R]}{[DR]}$

[D] = drug concentration
[R] = receptor concentration
[DR] = bound drug/receptor complex

Fractional Occupancy (FR)

$FR = \frac{[DR]}{[R] + [DR]} = \frac{[D]}{K_d + [D]}$

[D] = drug concentration
[R] = receptor concentration
[DR] = bound drug/receptor complex
Kd = Equilibrium dissociation constant

$FR = \frac{e}{E_{max}}$

e = observed effect size
Emax = maximum response

Pharmacokinetics

Molecule protonation

$\frac{\text{unprotonated}}{\text{protonated}} = 10^{pH - pKa}$

$log(\frac{\text{unprotonated}}{\text{protonated}}) = pH - pKa$

pKa = the point at which half the molecules are protonated
pKa = -log(Ka)

Half-life

$t_{\frac{1}{2}} = \frac{0.69}{K_e}$

Ke = rate constant of elimination

Drug concentration

$C = e^{-k_et}(C_0)$

C = concentration at time t
e = 2.7 (constant)
Ke = rate constant of elimination
C0 = initial concentration

$ln(C) = -kt + ln(C_0)$

k = rate constant of elimination
t = time
C0 = initial concentration

Volume of distribution

$V_d = \frac{D}{C_o}$

D = dosage (drug quantity)
C0 = initial concentration

Dosage

$D = C_0 \times V_d$

Vd = compartment volume
C0 = initial concentration

Clearance rate

$CR = K_e \times V_d$

Ke = rate constant of elimination
Vd = compartment volume

90% clearance < $4 \times t_{\frac{1}{2}}$

t1/2 = half-life

Bioavailability

$F = \frac{\text{quantity in circulation}}{\text{quantity administered}}$

Steady-state concentration

$C_{SS} = \frac{F \times \text{dose}}{CR \times \text{time}}$

F = bioavailability
dose (mg) = quantity administered
CR (mg/time) = clearance rate

Dosing rate

$DR = \frac{CR \times C_{SS}}{F}$