Chapter 8: Kinetics and Regulation

kinetics

study of dynamics of enzyme activity

first order reactions

rate proportional to reactant concentration

second order rxn

• bimolecular

• rate depends on 2 reactants

calc for rate of reaction: second order

V = k[A][B] or [A]²

• A is the substrate

• k is the rate constant

pseudo first order reaction

bimolecular rxns where [ ] of one reactant greatly exceeds [ ] of the second reactant, making the rxn seem first order with respect to lesser reactant

zero order rxn

rate is independent of reactant concentrations

V₀

intial rate of catalysis → initial slope of rxn rate vs time

michaelis menten eqn: what does it describe and what are the variables

describes initial rate as a function of substrate concentration

• Km → michaelis constants

• Vmax → maximal velocity. attained when enzyme is fully saturated

• S → substrate

• V₀ → inital velocity

Vmax relationship to enzyme concentration

directly related. more enzyme → faster rate

K_m

• michaelis constant

• describes enzyme substrate affinity → higher Km means lower affinity

• equals [s] at ½ V_max

when would enzymes display 0 order rxn mechanism

enzyme is fully saturated → increasing [s] has no effect on the reaction rate

what causes alchohol flushing in some individuals

• alchohol is processed in 2 steps: ethanol → acetaldehyde→ acetate

• acetalaldehyde causes flushing and tachycardia

• 2 enzymes break acetaldehyde: a high Km (cytoplasm) and a low Km (mictochondria). lacking low Km enzyme means acetaldehyde is only processed at high [ ]

elasticity

since [s] is usually ~ K_m in organisms, enzymes are highly responsive to changes in [s] while still having significant activity

turnover number

number of substrate molecules enzyme can convert into product per unit time at full saturation → k₂ kinetic constant

Km and Vmax relation to enzyme

Km → characteristic of the enzyme. doesn’t change by changing [enzyme]

Vmax → dependant on the [enzyme]; not characteristic of the enzyme

isoenzymes

diffent enzymes that catalyze the same rxn → different tissues kinetics, tissues and regulations

isoenzymes glucokinase and hexokinase: glucokinase

glucose senser → in liver, higher Km (low affinity), higher V_max, not inhibited by G6P

liver glucose is quickly broken down only at high [ ] to regulate. ensures the tissues that really need it have access first

isoenzymes glucokinase and hexokinase: hexokinase

in glucose oxidizing tissue, low Km (high affinity), lower V_max, inhibited by G6P (caps itself after getting what it needs)

2 types of bisubstrate enzyme rxns

• sequential rxns

• double displacment (ping pong) rxns

2 types of bisubstrate enzyme rxns: sequential

• all substrates in together, all products out together

• forms ternary complex → complex with enzyme and all substrates

• can be ordered (substrates bind in specific sequence) or random

2 types of bisubstrate enzyme rxns: ping pong (double displacement)

• one of more products released before all substrates bind

• forms substitued enzyme intermediate → enzyme modified breifly

• substrates and products appear to bounce on and off e

michaelis menten enzymes

• display michaelis-menten kinetics → if substrate is present, they catalyze

• produces hyperbolic saturation curve

allosteric enzymes

regulate flux of biochemicals through metabolism

features of allosteric enzymes

• regulate catalysis based on environment

• complex kinetics

• quaternary structure w mutiple active sites

• sensitive and responsive

commited step

• step in a metabolic pathway that “commits” to producing the end product, usually rate limiting step

• catalyszed by an allosteric enzymes → feedback inhibited by end product binding to allosteric site

allosteric enzymes in complex pathways

inhibited or activated by molecules in the pathway to ensure coordination and no intermediates are wasted

• F stimulates e10 but inhibits e1; I stimulates e1 but inhibits e10

how do michaelis menten enzyme kinetics differ from allosteric enzyme kineticss

on velocity-[s] graph:

• allosteric: sharp increase of V in the middle of the curve → sigmoidal shape (s)

• michaelis menten: begins with sharp increase then levels off → hyperbolic shape

affinity constant for allosteric enzymes

K_0.5 → still shows [ ] yeilding 0.5V_max

why do allosteric enzymes have a signmoidal curve

bcz they have multiple active sites and regulatory (allosteric) binding sites

2 models for allosteric enzymes

concerted model and sequential model

T and R state of allosteric enzymes

• T → tense, less active, more stable → common

• R → relaxed, active, less stable → less common

2 models for allosteric enzymes: assumtions of concerted model

• mutiple active sites on different polypeptide chains

• 2 distict states: R or T

• all active sites on an enzyme must be in the same state → symmetry rule

• s binds better to R than T

2 models for allosteric enzymes: mechanism of concerted model

• displays cooperativity

• as [s] increases, more likely for s to catch an R state, bind, and turn all active sites of that enzyme into R

• substrate binding R shifts T ⇌ R in favour of R → rmore R produced → rapid V increase (sigmoidal shape)

why is cooperativity of allosteric enzymes important

causes them to be way more senstive to changes in [s] → more elastic near Km than MM enzymes with the same Vmax

threshold effect

below certain [s], little enzyme activity (mostly T). but after threshold reached, enzyme activity increases rapidly (mostly R) → cooperativity causing on/off switch between T and R

concerted model: regulatory molecules

alter T ⇌ R equilibrium

• positive effectors: bind R at allosteric site and stabilizes it → more R → more chance of R binding s

• negative effectors: bind T at allosteric site and stabilizes it → more T → s binding R

concerted model: effect of regulatory molecules on threshold concentration

• positive effectors → lower threshold and shift sigmoidal curve left

• negative effectors → increase threshold and shift signmoidal curve right

heterotropic allosteric effectors

• effector molecule (regulatory molecule) is distict from substrate→ binds to allosteric site

• usually upstream or downstream of metabolic process

• shifts the entire curve to the right or left

homotropic allosteric effectors

substrate acts as an effector, for example, cooperative binding → causes the sigmoidal shape of allosteric kinetics

sequential model of allosteric enzymes

• T and R can exist as hybrids

• binding at one site influces binding affinity of surrounding sites without necessary changing the entire enzyme