Formula sheet toxicology
Isoboles: V = expected ED50 (A+B)/observed ED50 (A+B)
Reversable reaction equation: R+T > RT with R + T RT = k1 and RT R + T = k2
[ R ] [T ] k 2
With = = KT KT = dissociation constant complex
[ RT ] k1
Total receptor concentration = [Rt} = [R] + [RT]
[ RT ] [T ]
And = = fraction of receptors occupied by toxic compound
[Rt ] K T +[T ]
Response of effect: e = k 3[RT]
Maximum response: Emax = k 3[Rt]
[ RT ]
Effect as a function of fraction of occupied receptors: e = Emax
[Rt ]
Emax [T ]
Effect as function of tox comp conc.: e =
K T +[T ]
If e = ½ Emax [T] = KT
TD 50 LD 50
Therapeutic index: TI = or
ED 50 ED 50
TD 1 LD 1
Margin of safety = or
ED 99 ED 99
Rule of thumb: t(steady state) = 4 or 5 x t1/2 so you reach Css after 4 or 5 times half life
FxD
Steady state concentration: Css =
∆ t x CL
KA(C 2−C 1)
Fick’s law: rate of diffusion =
d
[ lipid phase ]
Partition coefficient: p = (usually expressed as log(p)
[aqueous phase ]
For HA <-> H+ + A- (acid)-: pH = pKa + log ¿ ¿
For H+ + A <-> HA+ (base): pH = pKa +
log [ A ]
¿¿
[ A]
Antilog(pH-pKa) = = 10pH – pKa
[ HA ]
kel x t
10th log plasma conc. At time t: Log10(C(t)) = Log10(C0) -
2.303
kel
Slope = -
2.303
ln ( 2 ) x V D
half-life time plasma conc. : t1/2 =
CL
Isoboles: V = expected ED50 (A+B)/observed ED50 (A+B)
Reversable reaction equation: R+T > RT with R + T RT = k1 and RT R + T = k2
[ R ] [T ] k 2
With = = KT KT = dissociation constant complex
[ RT ] k1
Total receptor concentration = [Rt} = [R] + [RT]
[ RT ] [T ]
And = = fraction of receptors occupied by toxic compound
[Rt ] K T +[T ]
Response of effect: e = k 3[RT]
Maximum response: Emax = k 3[Rt]
[ RT ]
Effect as a function of fraction of occupied receptors: e = Emax
[Rt ]
Emax [T ]
Effect as function of tox comp conc.: e =
K T +[T ]
If e = ½ Emax [T] = KT
TD 50 LD 50
Therapeutic index: TI = or
ED 50 ED 50
TD 1 LD 1
Margin of safety = or
ED 99 ED 99
Rule of thumb: t(steady state) = 4 or 5 x t1/2 so you reach Css after 4 or 5 times half life
FxD
Steady state concentration: Css =
∆ t x CL
KA(C 2−C 1)
Fick’s law: rate of diffusion =
d
[ lipid phase ]
Partition coefficient: p = (usually expressed as log(p)
[aqueous phase ]
For HA <-> H+ + A- (acid)-: pH = pKa + log ¿ ¿
For H+ + A <-> HA+ (base): pH = pKa +
log [ A ]
¿¿
[ A]
Antilog(pH-pKa) = = 10pH – pKa
[ HA ]
kel x t
10th log plasma conc. At time t: Log10(C(t)) = Log10(C0) -
2.303
kel
Slope = -
2.303
ln ( 2 ) x V D
half-life time plasma conc. : t1/2 =
CL
