Enzyme kinetics and inhibition

what is enzyme rate? + give equation

the number of moles of product produced per unit time

rate (v) = d[P]/dt = k₂ [ES]

give the equation describing how an enzyme-controlled reaction proceeds, and explain what it shows

E + S <=> ES —> E + P

enzyme and substrate must combine to form ES complex, then enzyme must be recycled after the reaction is finished

k₁ = forward reaction of E + S to ES

k₂ = ES —> E + P - catalytic rate, rate limiting step

k_-1 = reverse reaction ES to E + S

what is the rate limiting step of an enzyme driven reaction?

the production of the product (driven by k₂ rate)

describe what zero, first and second order enzyme-driven reactions are

zero - no relationship between V and [S]

first - rate dependent on [S]

second - relationship between V and [S] not proportional to [S], but rather multiple substrates

what order kinetics must be present to study enzymes and why?

first order

allows easy measure of enzyme’s catalytic efficiency, as describes the phase of a reaction where the rate is directly proportional to the substrate concentration

describe how an enzyme-controlled reaction changes from first to zero order kinetics as the reaction proceeds

velocity increases as [S] increases up to a point where the enzyme is ‘saturated’ with substrate (V_max)

at V_max the rate of reaction is unaffected by increase in [S] as all enzyme active sites are in use

what assumptions must be met for Michaelis-Menten equation?

equilibrium - the association and dissociation of the substrate and enzyme is assumed to be a rapid equilibrium (e + s to es is fast)

steady state - ES immediately comes to a steady state and is a constant (ie ES is formed as fast as enzyme releases the product)

what is the ratio of rate constants from the Michaelis-Menten equation defined as?

the Michaelis constant (K_M)

K_M = k_-1 + k₂ / k₁

give the Michaelis-Menten equation

V₀ = V_max [S]/ K_M + [S]

what does the Michaelis-Menten constant K_M represent?

[S] at which the rate of reaction is half its maximum (1/2 V_max)

dissociation constant of ES (substrate affinity) - low values indicate ES complex is held together tightly and rarely dissociates without S first reacting to form P

what is the enzyme catalytic constant?

K_cat

turnover number = the maximum number of S converted to P per second by each active site, when the enzyme is fully saturated with substrate

measures how fast a given enzyme can catalyse a specific reaction

units = s^-1

larger k_cat = more rapid catalytic events at the enzymes active site

what is the Lineweaver-Burke plot?

a graphical representation of the Michaelis-Menten equation

used to calculate V_max and K_M

describe 4 factors that influence enzyme kinetics

concentration of substrate molecules - more substrate available = increased frequency of enzyme binding

temperature - higher temperatures = increased molecular motion (limited by protein denaturation limits)

pH - protein conformation and molecular changes of active sites

presence of inhibitors

what is an enzyme unit?

the conversion of one micromole of a substrate to product per minute, under specific conditions of pH and temperature

1 enzyme unit = micromole/min

what are some real-world limitations of Michaelis-Menten kinetics?

relies on law of mass action - assumes free diffusion and thermodynamically-driven random collision

many biochemical or cellular processes deviate from these conditions

eg,

• cytoplasm behaves more like a gel than a freely flowable aqueous solution, severely limiting molecular movements

• heterogenous (different phases) enzymatic reactions - molecular mobility of E or S can be restricted, due to immobilisation or phase-separation of reactants

• homogenous (same phase) enzymatic reactions - mobility of of E or S ma be limited

describe the concept of random substrate binding

assumes independent binding of substrates and products

two independent binding sites - substrate binding independent of other substrate

describe the concept of ordered substrate binding

one substrate must bind before second substrate can bind effectively

describe the concept of the ping-pong mechanism of multisubstrate reactions

likely theoretical - not seen in reality

enzyme binds substrate A and then releases P

intermediate form of enzyme (E*) often carries A fragment and then binds B

product Q released and enzyme returns to original state (E)

outline where competitive, non-competitive and uncompetitive inhibitors behind

comp - to enzyme’s active site

non - at separate site (not AS)

un - at separate site, but only bind enzyme-substrate complex

outline how competitive inhibitors work

reversible

has a structure similar to the substrate

competes with S for active site

effect is reversed by increasing [S]

V_max unchanged, K_m increase by (1 + [I]/k_i)

outline how non-competitive inhibitors work

have a structure different to S

bind to allosteric site

distorts the shape of E and active site, preventing S from binding

not reversed by increasing [S]

V_max decreases by (1 + [I]/k_i)

K_m no change

outline how uncompetitive inhibitors work

only exist in theory, not in practice

inhibitor binds only to ES complex, not free E