Unit conversions Stochastic versus ODE Stochastic Units With

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Unit conversions

Unit conversions

Stochastic versus ODE Stochastic

Stochastic versus ODE Stochastic

Units • With concentrations* (ODE simulations only): – concentrations (eg moles/liter) for species –

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

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

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

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

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

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 • ->

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

Review: Michaelis Menten

Special Feature • explicit enzyme: : S + E -> P + E Sat(kcat,

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

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

Enzymatic Conversions • kcat' = kcat • Vmax' = Vmax*NA*V • Km' = Km*NA*V

Also… explicit enzyme: S + E -> P + E kcat/(Km + Stot) implicit

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