Unit conversions Stochastic versus ODE Stochastic Units With
- Slides: 14
Unit conversions
Stochastic versus ODE Stochastic
Units • With concentrations* (ODE simulations only): – concentrations (eg moles/liter) for species – Unit concentration / unit time for reactions • With particles (ODE or stochastic): – Number of molecules for species – Reaction firings per unit time * Usual way that measurements are reported in the literature.
Concentrations <-> Particles • NA = Avogadro’s Number, V=volume • Concentration C -> C*NA*V particles • Particles P -> P/(NA*V) concentration (eg moles/liter)
Mass Action • A->C, rate k 1: – [C] = k 1[A]: Units of k 1 must be /time • A+B->C, rate k 2: – [C] = k 2[A][B]: Units of k 2 must be /conc/time • ->C, rate k 0: – [C] = k 0: Units of k 0 must be conc/time
Unimolecular reactions A -> B Concentrations Particles • A->B k 1 • Units: /time Conversion: k 1’ = k 1’
Avogadro’s constant • The Avogadro constant (NA) is defined as the ratio of the number of constituent particles N (usually atoms or molecules) in a sample to the amount of substance n (unit mole) through the relationship – NA = N/n • Wikipedia • NA = 6. 02214129× 1023 mol− 1
Bimolecular reactions Concentrations Particles • A+B -> C k 2 • Units: /conc/time k 2’ • Units: /time Conversion: k 2’ = k 2/(NA*V)
Constant Reaction Concentrations • -> C k 0 • Units: conc/time Particles • -> C k 0’ • Units: /time Conversion: k 0’ = k 0*(NA*V)
Review: Michaelis Menten
Special Feature • explicit enzyme: : S + E -> P + E Sat(kcat, Km) • Implicit enzyme(!): S -> P Sat(Vmax, Km)
Use the second method if… a) the enzyme is unknown b) the enzyme concentration is large and constant, and the user intends to run networkfree simulations with NFsim.
Enzymatic Conversions • kcat' = kcat • Vmax' = Vmax*NA*V • Km' = Km*NA*V
Also… explicit enzyme: S + E -> P + E kcat/(Km + Stot) implicit enzyme: S -> P Vmax/(Km + Stot) Stot is an observable, giving the amount (concentration or #particles) of S Multiply reactant quantities times the formula
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