An introduction to enzyme kinetics
Rate at which a reaction proceeds is dependent on the constant ‘k’ and the concentration of
the enzyme and substrate
Rate is equal to the rate of change of the concentration of our product with respect to time
If we assume that k is constant, then the only way to increase the rate is to increase either [E]
or [S]
Generally in the cell, total [E] is constant
Ex: 4 enzymes, each of which can catalyze 10 reactions per second
Vmax is the maximum rate, the total number of reactions that can be catalyzed per
second by the cumulative effort of the enzymes
o When Vmax is reached, even increasing [S] won’t increase the number of reactions
catalyzed per second, since the enzymes are working at full capacity
Note: not all enzymes are proteins. Non-protein enzymes include inorganic metals (ex. Mg 2+),
small organic molecules (ex. flavin), and ribozymes (ex. RNase P)
Steady states and the Michaelis Menton equation
Steady-state assumption – [ES] is constant, and therefore formation of ES = loss of ES
Michaelis-Menten equation:
V0 = initial velocity of the reaction
Vmax = maximum rate of the reaction
[S] = concentration of substrate
Km = Michaelis constant
o An inverse measure of affinity (so a higher Km means a lower affinity)
The lower the Km, the better the enzyme is at working when substrate
levels are small (enzyme has more affinity for the substrate)
o Km = [S] when Vo = ½Vmax
o Km is the concentration of substrate which permits the enzyme to achieve half
Vmax.
Kcat = Vmax / [E]T
Kcat = enzyme turnover number
o How many substrates (S) an enzyme (E) can turn into product (P) per one second
at its maximum speed.
o Units: sec-1
Vmax = maximum speed of the reaction
[E]T = total concentration of available enzyme
Catalytic efficiency = Kcat / Km
Enzymatic inhibition and Lineweaver Burk plots
Lineweaver Burk plot
Comes from an inverse and rearrangement of the MM equation:
Inhibition (non-covalent)
Competitive Inhibition – inhibitor resembles the substrate and will bind to the enzyme’s active
site, preventing the substrate from occupying the active site
Km is increased, since the affinity of the substrates has decreased because of the
competition with the inhibitor
Vmax stays the same, because a high concentration of substrate can overcome inhibition
(through probability).
Uncompetitive Inhibition – binding of substrate to the active site of the enzyme causes a
conformational change, opening up a new site (allosteric site) for the uncompetitive inhibitor to
bind.
Inhibitor can now bind to form the ESI
Km is decreased, because the substrate gets ‘locked in’ to the enzyme, and so in a
sense, the enzyme has ‘increased affinity’ with the substrate, leading to.
Vmax is decreased, since this form of inhibition cannot be overcome by increasing
susbtrate concentration.
Noncompetitive Inhibition – allosteric site is available to be bound by the inhibitor even before
the substrate binds. Inhibitor can either bind to the enzyme or the enzyme-substrate complex.
Km stays the same
Vmax is decreased
Kcat (turnover number) is decreased
Mixed inhibition – very similar to noncompetitive inhibition. The inhibitor can bind to either
the allosteric site of the enzyme or the allosteric site of enzyme-substrate complex, but now has
a different affinity for each of these states.
If the mixed inhibitor ends up binding more readily to the enzyme, Km is higher
If the mixed inhibitor binds more readily to the enzyme-substrate complex, Km is lower
Vmax decreases because increasing substrate concentration would not lead to more
enzymes being available.
Summary:
Type MoA Effect
Competitive Inhibitor binds in place of substrate in enzyme’s active ↑ Km
site
Uncompetitive Inhibitor can only bind after substrate has bound and ↓ Km
opened up the allosteric site ↓ Vmax
Non-competitive Inhibitor can bind to allosteric site either before or
after the substrate has bound ↓ Vmax
Mixed Inhibitor can bind to allosteric site either before or ↑/↓ Km
after the substrate has bound, but has a higher affinity ↓ Vmax
for one state over the other.
If the mixed inhibitor ends up binding more
readily to the enzyme, Km is higher
If the mixed inhibitor binds more readily to the
enzyme-substrate complex, Km is lower
.
Cooperativity
Some enzymes or proteins can house more than one substrate at the same time.
However, sometimes substrate binding changes substrate affinity (cooperativity):
Positive cooperative binding – substrate binding increases affinity for subsequent
substrates
o Ex. Hemoglobin (Hb) Hb(O2)4
o Sigmoidal graph shape
Negative cooperative binding – substrate binding decreases affinity for subsequent
substrates
o Hyperbolic graph shape
Non-cooperative binding – substrate binding does not affect affinity for subsequent
substrates
o Ex. Myoglobin (Mb) MbO2
o Hyperbolic graph shape
Allosteric regulation and feedback loops
Allosteric regulators bind to allosteric sites (which exist anywhere on the enzyme) to regulate
the activity of the enzyme
Allosteric activators increase enzymatic activity
o Either by increasing Vmax or decreasing Km
Allosteric inhibitors decrease enzymatic activity
o Either by decreasing Vmax or increasing Km
Feedback loop – downstream products regulate reactions upstream
Positive feedback loop – a change that causes an even further change in the same
direction
Negative feedback loop – a change that causes a change in the opposite direction
Example:
Consider this step in glycolysis
Glycolysis is the process by which cells use to make ATP. Thus, ATP is a product of the pathway.
ATP is also an allosteric inhibitor of phosphofructokinase as part of a negative feedback loop to
ensure that glycolysis is downregulated when ATP levels are adequate.
However, this is an interesting case, because while ATP is the product that feeds back to
inhibit the enzyme, it is also a substrate for the enzyme (see in the pathway above how
it is a substrate too)
o Homotropic regulator – a molecule that is both a substrate and a regulator
AMP is an allosteric activator of phosphofructokinase that turns on glycolysis when ATP levels
are low.
AMP is a regulator but not a substrate for the enzyme
o Heterotrophic regulator
This reaction in particular has a ΔG° = –4.5 kcal/mol, meaning that a lot of energy is released
from the reaction. This makes the reaction more or less a one way reaction, making it an
excellent control point for all 10 steps of glycolysis
Covalent modifications to enzymes
Methylation – addition of a methyl group
Acetylation – addition of an acetyl group ––––––––––––
Ex. acetylation of a lysine on its R group NH3+ can change acidic/basicity and electrostatic
interactions of this AA.
Glycosolation – addition of a sugar molecule
Zymogen – inactive form of an enzyme that requires covalent modification to become active
Ex. Trypsinogen –––enterokinase––> Trypsin
Zymogen form of an enzyme has the suffix -ogen
Suicide inhibition – covalently bind to an enzyme and prevent it from catalyzing reactions.
Models of substrate binding – Lock & Key vs. Induced fit
Similarities
Both require an enzyme and a substrate.
Both state that only one substrate will work when it meets the active site of the enzyme.
Differences
Lock and Key – states that there is no change needed and that only a certain type will fit.
o Induced fit – states that the active site will change to help to substrate fit.
Lock and Key – states that the active site has one single entry
o Induced fit – states that the active site is made of two components.
