Modeling Biochemical Networks Cheat Sheet1
Stoichiometric Amount
The stoichiometric amount is the number of molecules of
a particular reactant or product taking part in a reaction.
e.g.
2A+ 4B−→ 3C
Stoichiometric amount of A= 2; B= 4 and C= 3.
Stoichiometric Coefficient
The stoichiometric coefficient, c, of a species Xis the
difference between the stoichiometric amount of species
on the product side minus the stoichiometric amount of
the same species on the reactant side.
e.g.
A−→ B
cA= 0 −1 = −1
cB= 1 −0 = 1
2A+B−→ C
cA= 0 −2 = −2
cB= 0 −1 = −1
cC= 1 −0 = 1
Reaction Rate
A
v
−→ B
Units: mol per time per volume, defined as:
v=1
cX
dX
dt
Rate of Change
The rate of change of a substance Xis
dX
dt =cXv
where cXis the stoichiometric coefficient for X.
αis usually +
for products.
αis usually −
for reactants.
e.g.
2A−→ B
dA
dt =−2vdB
dt =v
Mass Conservation
X
v1
v2
v3
v3
dX
dt = (v1+v2)−(v3+v4)
In general:
dX
dt = Flows In −Flows Out
Rate Laws
Mass-action: v=kAm1Bm2. . .
Mass-action reversible:
v=k1Am1Bm2. . . −k2Pn1Qn2. . .
e.g.
A−→ B v =k1A[−k2B]
2A−→ B v =k1A2[−k2B]
2A+B−→ C v =k1A2B[−k2C]
2A+B−→ C+D v =k1AB [−k2CD]
Equilibrium Constant
Keq =Pn1Qn2. . .
Am1Bn2. . .
e.g.
A−→ B Keq =B
A
A+B−→ C Keq =C
AB
A+A−→ B Keq =B
A2
Mass-Action Ratio
For a reaction such as A−→ B, the mass-action ration, Γ
is given by:
Γ = B
A
where Aand Bare at their in vivo concentrations.
Dissequilibrium Ratio
ρ=Γ
Keq
At equilibrium, ρ= 1, if out of equilibrium then ρ < 1.
Rates of Change and Rates Laws
A−→ BdA
dt =−vdB
dt =v
A+B−→ CdA
dt =−vdB
dt =−vdC
dt =v
A+A−→ BdA
dt =−2vdB
dt =v
Modified Mass-Action Rate Law
v=k1A1 + Γ
Keq
Enzyme Rate Laws
Briggs-Haldane Rate Law:
v=VmA
A+Km
0 5 10 15
0
0.2
0.4
0.6
0.8
1Vm
Km
Substrate
Rate, v
Reversible Enzymatic Rate Law
v=Vm
Km1
A−B/Keq
1 + A/Km1+B/Km2
Sigmoid Responses
v=VmAh
K+AhActivation
v=Vm
K+AhRepression
1Version 0.5
