kinetics of complex reactions Flashcards
how are rate laws for elementary reactions written?
in differential form
in terms of rate of loss of reagents (-ve) or gain of products (+ve)
assumptions for sequential (multi-step) reactions
if one rate constant is much greater than another, the slowest step is the rate determining step
the reaction can be simplified to depending only on the step w the smallest k
(only for first order - 2nd order is also concentration dependent)
what is the pre-equilibrium hypothesis?
for mechanisms where the species involved in the RDS are in equilibrium w reagents
assumes species remain in equilibrium, ie. species –> products is slow enough to not disturb equilibrium and is therefore rate determining
often used for intermediates involving simple protonation/de-protonation, fast compared to making/breaking bonds
k(eq) for pre-equilibrium hypothesis
k(eq) = k(1) / k(-1) = [eq prod]/[eq reac]
what is the steady state assumption?
for sequential reactions A–>B–>C where process 2 much greater than process 1, conc intermediate B changes very little, assume constant
d[B]/dt(SS) = 0
greatly simplifies
in what cases might the steady state assumption be appropriate?
generally appropriate for reactive intermediates (high in energy) which are slow to form but consumed at once
NOT appropriate for species that accumulate / decay during the reaction
NOTE: rate laws derived from SSA only valid when reaction is at SS (not initial/completion)
describe saturation kinetics
for a fixed quantity of enzyme, the rate of the catalysed reaction first increases linearly then levels of to a maximum value as the amount of substrate increases
overall kinetic scheme of the Michaelis-Menten equation
E + S <=> ES –> E + P
how is the Michaelis-menten equation derived?
d[ES]/dt = 0 (SSA) (construct eqn from elementary steps)
sub [E]0 = [ES] + [E] to find expression for [ES]
expression for velocity of reaction
V = k(cat) [ES]
essentially rate of catalysed reaction
Michaelis-Menten equation
V = k(cat) [E]0 [S] / [S] + K(M)
Michelis constant, K(M) expression
K(M) = (k(cat) + k(-1)) / k(1)
in terms of rate constants from the elementary steps of the Michaelis-Menten equation
expression for max velocity from Michaelis-Menten eqn
V(max) = k(cat) [E]0
what does the graph of velocity vs substrate concentration look like? (for Michaelis-Menten saturation kinetics)
from 0, very steep initial increase (approximately linear), then slowing down to flatten out (“saturation”)
Michaelis-Menten eqn for LOW substrate concentrations
[S] «_space;K(M)
hence denominator of MM eqn approximates to K(M)
resulting in expression for V(low[S]) linear in terms of [S] and [E}0
corresponds to LINEAR region of saturation kinetics graph (rate vs [substrate])
