1. What happens when you mix enzyme and substrate…

2. Velocity = DP/Dt or -DS/Dt
Product
Time

3. Rate constants are defined for reactions
V = DP/Dt = -DS/Dt = k1[S]
k1 is called the rate constant and has units of s-1
If k1 is small, the reaction rate is slow, if large the reaction is fast
A k of 0.03 s-1 indicates that 3% of the available S will be converted to P in 1 sec

4. The “order” of reactions
A zero order reaction is when the reaction is independent of substrate concentration ([S] >> [E]). System is saturated, V = k1
A first order reaction is what we have looked at, the rate depends on the first pwer of the concentration of S
A second order reaction occurs when two substrate molecules are necessary to form product

5. Rate is related to activation energy
k = (kT/h) e-DG|/RT
Lower activation energy means a higher reaction rate and vice versa

6. Molecular parameters from reaction ratesk1 k2
E + S ES E + P
k-1
Assume the conversion of ES to E + P is non-reversible, then the rate of
product formation or reaction velocity is dependent solely on [ES] and k2
v = d[P]/dt = k2[ES] (1)
If we could measure v and [ES] then we could determine k2, however
[ES] is not usually measurable. We can measure substrate (or product)
concentrations and the total concentration of enzyme [E]t.
[E]t = [E] + [ES] = free enzyme + enzyme in complex with substrate (2)
Thus, we want to express the rate, v, in terms of substrate concentration
[S], and total enzyme concentration [E]t.

7. From this equation: k1 k2
E + S ES E + P
k-1
Under certain circumstances (if k-1 >>k2), E and S are in
equilibrium with ES, with an equilibrium dissociation
constant Ks.
Ks = k-1/k1 = [E][S]/[ES]
However, this assumption is not always valid, thus it is
of more general use to introduce the concept of the steady
state.

8. In steady state, the rates of formation and breakdown of [ES]
are equal:
k1[E][S] = k-1[[ES] k2 [ES]
Rearrange to give [ES] = (k1/k-1+k2)[E][S]
Define a constant Km = (k-1+k2/ k1)
Km[ES] = [E][S] (3)
Recall we want to get a formula with measurable quantities
[S] and [E]t
Rearrange equation 2 (solve for [E]) and plug into 3 to get:
Km[ES] = [E]t[S] – [ES][S]

9. Transfer second term on right side to left side to get:
[ES](Km + [S]) = [E]t[S]
Rearrange to
[ES] = [E]t[S]/(Km + [S])
Using equation 1 we can finally solve for v, velocity
v = k2[E]t[S]/(Km + [S]) (4)
This formula is referred to as the Michaelis-Menten equation

10. Consider a graph that we can construct from the
measurable quantities v and [S]
v = change in product
change in time
[S] = Km
Increasing [substrate]
At high substrate concentrations, the reaction reaches a
Maximum velocity Vmax, because the enzyme molecules are
saturated; every enzyme is occupied by substrate and carrying
out the catalytic step

11. From these relationships, consider the following:
What is Km and what does it mean?
Km is a ratio of rate constants:
Km = (k-1+k2/ k1)
Thus in our catalyzed reaction, if k2 is much smaller than k-1,
Km= k-1/k1 = Ks, the equilibrium constant for [ES] formation.
In this case, a large Km means k-1 >>k1, thus the enzyme binds
the substrate very weakly. However, in a separate instance
a large k2 can have a similar effect on Km.
Thus, what is the utility of Km?

12. The most useful way to think of Km is reflected in the plot
of a reaction that follows the Michaelis-Menten equation

13. In this plot, Km is numerically equal to the substrate
Concentration at which the reaction velocity equals half of its maximum value.
Where [S] = Km, the Michaelis-Menton equation simplifies to
v = Vmax/2
Thus, an enzyme with a high Km requires a higher substrate concentration to achieve a given reaction velocity than an enzyme with a low Km.

14. What are some enzyme’s Km’s

15. In considering Vmax mathematically, by making [S] much
larger than Km the Michaelis-Menten equation simplifies to:
Vmax = k2[E]t
Thus, another way of writing the Michaelis-Menten rate
Equation is:
v = Vmax[S] / (Km + [S])
Typically, all of this is an oversimplification, and enzyme-
Mediated catalysis looks more like: k1 k2 k3
E + S ES EP E + P
k-1

16. In this more complex system, k2 must be replaced with a more general constant, called kcat
v = kcat [E]t [S]/ (Km + [S])
In the two step reaction we considered first, kcat = k2. For more complex reactions, kcat is a combination of rate constants for all reactions between ES and E + P.

17. kcat is a rate constant that reflects the maximum number of molecules of substrate that could be converted to product each second per active site. Because the maximum rate is obtained at high [S], when all the active sites are occupied with substrate, kcat (the turnover number) is a measure of how rapidly an enzyme can operate once the active site is filled.
kcat = Vmax/[E]t

18. What are some kcat values?

19. Under physiological conditions, enzymes usually do not
operate under saturating substrate conditions. Typically, the
ratio of [S] to Km is in the range of
When Km >> [S], the Michaelis-Menten equation simplifies to:
v = kcat/Km ([E]t[S])
The ratio kcat/Km is referred to as the specificity constant
which indicates how well an enzyme can work at low [S].
The upper limit of kcat/Km is in the range of 108 to 109 due
to limits of diffusion theory.

20. Both kinetic parameters contribute to enzyme efficiency

21. Lineweaver-Burk plots are convenient for
determination of Km and kcat

22. Lineweaver-Burk plots result from taking a double reciprocal
of the Michaelis-Menten equation.
v = Vmax[S] / (Km + [S])
1/v = Km/(Vmax[S]) + 1/Vmax
Plotting 1/v on the y-axis and 1/[S] on the x-axis (both
known quantities)
The slope is equal to Km/Vmax, the y-intercept is 1/Vmax
And the x-intercept is –1/Km

23. Kinetics of enzymes with multiple substrates
Ordered
Ping-Pong

24. Enzyme Inhibition – distinct from Lehninger
Non-competitive
Competitive

25. An uncompetitive inhibitor binds to ES

26. Irreversible inhibition destroy enzyme function
Suicide inactivators

27. Substrate binding influences rates of activity
Hysteresis
Cooperativity

28. Enzyme modification can alter their activity
Types of modification
Reversible, non-covalent binding of regulatory compounds or proteins
Enzymes modified in this manner are called Allosteric – threonine dehydratase is an example
Reversible, covalent modification such as phosphorylation (LHCII in chloroplasts)
Activation via proteolytic cleavage

29. Regulation of an enzyme’s activity via post-translational mechanisms
Allostery
Phosphofructokinase
Aspartate carbamoyl transferase
Glycogen phosphorylase
Calmodulin

30. Modulators can be stimulatory or inhibitory
A stimulator or activator is often the substrate itself (homotropic)
When the modulator is a molecule other than the substrate the enzyme is said to be heterotropic
Note that allosteric enzymes don’t necessarily have just active sites, but include other sites for modulator binding
Only in homotropic enzymes are active sites also regulatory sites

31. Allosteric enzymes exist in different “states”

32. Properties of allosteric enzymes
Sigmoidal instead of hyperbolic Michaelis-Menten plots
Reflects cooperative interactions between multiple subunits (allosteric enzymes often contain multiple subunits)

33. Substrate-activity curves for allosteric enzymes

34. Enzymes can be covalently modified with a wide assortment of groups
Phosphoryl, adenylyl, methyl, etc.
One third to one half of all proteins in a eukaryotic cell are phosphorylated
Tyrosine, serine, threonine, and histidine are known amino acids to accept phosphate groups from enzymes known as protein kinases

35. Phosphorylation regulates glycogen phosphorylase
Catalyzes the
removal of a glucose
from the polymer
glycogen in the form
of G1P
Although covalent –
reversible

36. Some enzymes are made as inactive precursors
These inactive precursors are called zymogens or proproteins
For instance, the serine proteases involved in insect immunity (Kanost) are synthesized as zymogens and are active only following cleavage
In addition, these enzymes are also regulated by interactions with other cellular proteins

37. Activation by subtraction

38. Naturally, biology is more complicated than one enzyme exhibiting one mode of regulation.
Enzymes can be regulated by multiple mechanisms!

39. Enzymes have optimal pH’s
Given what you know about the ionizable states of various amino acids, this is not surprising.
Amino acids with ionizable side chains can have important catalytic and structural roles, by changing their protonation state you are likely interfering with their function.

40. Remember …
In closely packed protein environments, the pKa of amino acid side chains can be significantly altered.
For example, a nearby positive charge can lower the pKa of a lysine residue, and a nearby negative charge can increase it (bacteriorhodopsin)
Such effects can shift the pKa by 2 or more pH units.
Check out Thematics

41. Enzymes also have optimal temperatures
Rate constants ~double
every ten degrees or so
(Arrehenius plot)
Eventually too high temp
disrupts molecular interactions
and denatures protein
Proteins built to work at
different temperatures,
thermophilic, mesophilic,
and psychrophilic

42. What is enzyme catalysis?
A catalyst is a substance
that accelerates a chemical
reaction without itself
undergoing any net change

43. How do enzymes work?
Free energy

44. Thermodynamics of catalysis DG0 = DH0 – TDS0 -RTlnKeq
DG = Gibbs Free energy
DH = Change in heat (energy)
of formation
DS = Degree of randomness

46. How do enzymes work? Transition state vs. Ground State theory
Do enzymes accelerate catalysis by putting substrates
in close proximity? OR
As Pauling among others suggested is catalysis a
result of an enzyme having a higher affinity for the
transition state
Still to this day a topic of debate, but presently it seems to be
a little of both

47. Affinity for the Transition state
knon
E + S E + (S)*
E + S ES (ES)*
KTS Ks
kcat
KTS
= [E][S]*/[ES]* = [(kcat/Km)/knon]-1
For Triosephosphate isomerase KTS = 10-12, and Km = 10-4
Thus, this enzyme binds the transition state eight orders of magnitude
more strongly than the substrate.

48. Recognition of transition state effects have led to
developments in analogs and catalytic antibodies

50. Specific catalytic mechanisms
General acid-base catalysis
Covalent catalysis
Metal Ion catalysis (nucleophile, electrophile)
Carbonic Anhydrase
Serine proteases
Phosphoryl transfer

51. Most Enzymes use combinations of these mechanisms

53. Chymotrypsin is a serine protease

54. Domain duplication and evolution

55. Substrate binding and catalysis

56. Establishing a relationship between catalytic
mechanism and substrate specificity

57. Crystal structures of proteins with inhibitors can be insightful

58. Convergent evolution in proteins

59. Structural maintenance of active sites

60. Investigating the structure-function relationship of proteins
Chemical Modification
Site-directed mutagenesis
Fluorescent labeling
Protein structure determination
One is not enough! Need to use combinations of these methods!

61. Certain chemicals can react with specific amino
acids to form covalent complexes
N-ethylmaleimide (NEM) reacts with free cysteines
reagent which modifies H, Y or K residues = DEPC, diethyl pyrocarbonate
reagent which modifies H, Y or W residues = NBS, N-Bromosuccinimide
reagent which modifies H or carboxyl = Woodward's K; N-ethyl-5-phenylisoxazolium 3'sulfonate
reagents which modify lysine or primary amino acid residues = Succinic anhydride; TNBS,
2,4,6-trinitrobenzenesulfonic acid)
reagent which modifies Y residues = N-acetylimidazole
reagent which modifies SER residues = PMSF, Phenylmethyl sulfonamide
reagent which modifies R residues = phenylglyoxal

63. Amino acids that are close together have been
observed to be similar in properties in proteins
Dayhoff matrix

64. Variant not mutant

65. Defining roles of amino acids in catalysis through kinetics

66. Assisted catalysis
Substrate
Buffer

67. Scanning mutagenesis
Alanine scanning mutagenesis - considered semi-conservative
at most positions important for structure, but non-conservative
at most positions important for catalysis
Cysteine scanning mutagenesis – puts a functional group at
positions throughout the protein sequence

68. Example of scanning mutagenesis (lactose permease)
417 amino acid
residues
FASEB J 1998 Oct;12(13): Cys-scanning mutagenesis: a novel approach to structure function relationships in polytopic membrane proteins. Frillingos S, Sahin-Toth M, Wu J, Kaback HR

69. Fluorescent labeling allows you to examine the
conformation of the protein
N-(1-pyrene)maleimide

70. Fluorescence resonance energy transfer (FRET) is a
way of measuring intra and intermolecular distances