Interactions with ligands
C6215 - Lecture 8
Igor Kučera
C
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Lecture
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IgorKučera
[R], [L], and [RL] are the concentrations of free R, free L and the complex at equilibrium.
Mass balance equations for the total concentration of R and L (cR and cL) can be written as
R (receptor) could be enzyme, transporter, carrier protein, receptor, etc.
L (ligand) could be substrate, cofactor, inhibitor, hormone, DNA/RNA, another protein, etc.
Receptor-ligand equilibrium
cR = [R] + [RL] (2)
cL = [L] + [RL] (3)
(1)
By elimination of [R] from equations (1) and (2) we obtain
𝐑𝐋 = 𝐜 𝐑
𝐊 𝐚[𝐋]
𝐊 𝐚 𝐋 + 𝟏
= 𝐜 𝐑
[𝐋]
𝐋 + 𝐊 𝐝
(4)
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[L]
[RL]
cR
free ligand concentration
required to achieve half maximal
saturation
a rectangular hyperbola
The graphical representation of equation (4) is:
The problem is that we often do not know [L] but only the total ligand concentration cL.
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Elimination of both [R] and [L] from equations (1) - (3) leads to a quadratic equation in [RL]
[RL]2 – (cL + cR + Kd) [RL] + cL cR = 0
The only acceptable root is
𝐑𝐋 =
𝐜 𝐋 + 𝐜 𝐑 + 𝐊 𝐝 − (𝐜 𝐋 + 𝐜 𝐑 + 𝐊 𝐝) 𝟐−𝟒𝐜 𝐋 𝐜 𝐑
𝟐
Using the well-known identity (a-b)(a+b)=a2-b2, Eq. (5) can be put in the form
𝐑𝐋 =
𝟐𝐜 𝐑
𝟏 +
𝐜 𝐑
𝐜 𝐋
+
𝐊 𝐝
𝐜 𝐋
+ 𝟏 +
𝐜 𝐑
𝐜 𝐋
+
𝐊 𝐝
𝐜 𝐋
𝟐
− 𝟒
𝐜 𝐑
𝐜 𝐋
from which it follows that [RL] → cR, and hence also [RL]/cR → 1, when cL → ∞ . Contrary to
the dependence of [RL] on [L] (Eq. (4)), the [RL] vs. cL dependence (Eq. (5)) is generally not
hyperbolic, although it displays a saturation behavior.
(5)
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In the limiting case where ligand binding is extremely tight (Ka → ∞, Kd → 0), Eq. (5)
simplifies to
𝐑𝐋 =
𝐜 𝐋 + 𝐜 𝐑 − 𝐜 𝐋 − 𝐜 𝐑
𝟐
[RL]
cR
cL
cR
The amount of receptor-ligand complex increases equimolarly with the amount of ligand
added and the receptor becomes saturated at cL = cR.
equivalence point
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Since for small x it holds 𝟏 − 𝐱 ≈ 𝟏 −
𝒙
𝟐
after dividing both numerator and denominator of Eq. (5) by cL+ cR+ Kd we obtain
𝐑𝐋 =
𝟏− 𝟏−
𝟒𝐜 𝐋 𝐜 𝐑
𝐜 𝐋+𝐜 𝐑+𝐊 𝐝
𝟐
𝟐
𝐜 𝐋+𝐜 𝐑+𝐊 𝐝
≈
𝟏− 𝟏−
𝟐𝐜 𝐋 𝐜 𝐑
𝐜 𝐋+𝐜 𝐑+𝐊 𝐝
𝟐
𝟐
𝐜 𝐋+𝐜 𝐑+𝐊 𝐝
=
𝐜 𝐋 𝐜 𝐑
𝐜 𝐋+𝐜 𝐑+𝐊 𝐝
𝐑𝐋 =
𝐜 𝐋 𝐜 𝐑
𝐜 𝐋+𝐜 𝐑+𝐊 𝐝
≈ 𝐜 𝐑
𝐜 𝐋
𝐜 𝐋+𝐊 𝐝
In case of cR << Kd, it simplifies further
Thus, when the condition cR << Kd is fulfilled, the dependence of [RL] on cL is hyperbolic
and half maximal saturation of the receptor occurs at the total ligand concentration equal
to Kd.
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Scatchard plot
George Scatchard
(1892-1973)
ν =
𝐋 𝐛𝐨𝐮𝐧𝐝
𝐜 𝐑
= 𝐧 ∙
𝐋
𝐋 + 𝐊 𝐝
Assume that R has n independent binding sites for L. The number
of occupied sites (ν) can be expressed as
ν
𝐋
= −
𝟏
𝐊 𝐝
∙ ν +
𝐧
𝐊 𝐝
ν
𝐋
ν
n
𝐧
𝐊 𝐝
𝐬𝐥𝐨𝐩𝐞 = −
𝟏
𝐊 𝐝
= −𝐊 𝐚
𝐋 → ∞
𝛎 → 𝐧
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Techniques to measure binding constants
SEPARATION-BASED
 heterogeneous
• dialysis
• chromatography
• surface plasmon resonance
 homogeneous
• affinity capillary electrophoresis
• centrifugation
• electrospray ionization mass spectrometry
NON-SEPARATION-BASED
• spectroscopy (UV-Vis, IR)
• fluorescence
• isothermal titration calorimetry
• nuclear magnetic resonance
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cR = 6
cL = 7
[L] = 5
[RL] = 7-5 = 2
[R] = 6-2 = 4
cL = [L] = 5
𝐊 𝐝 =
𝟒×𝟓
𝟐
= 10
Equilibrium dialysis uses a two-chambered device with
the chambers separated by a semipermeable membrane.
The protein solution containing ligand is placed in one
chamber while buffer is placed in the opposing chamber.
When equilibrium is reached, the unbound ligand will be
at equal concentrations on both sides of the membrane
while the bound ligand will remain in the protein
chamber. The total ligand concentration is sampled from
the protein side while the free ligand concentration is
sampled from the buffer side. The bound ligand is then
calculated from these measurements.
Howard et al. Comb Chem High Throughput
Screen. 2010, 13, 170
A schematic illustration of
the calculation of the
dissociation constant from
the equilibrium dialysis
data
Equilibrium dialysis
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A known quantity of receptor is injected on a size exclusion chromatography column and
eluted with a buffer containing a constant concentration of ligand. An amount of ligand,
determined by the dissociation constant(s) of the equilibrium and the free ligand
concentration, binds to the receptor and migrates with it, while a trough in the ligand
concentration, corresponding to the quantity withdrawn from the solvent, migrates at its
proper rate.
Hummel-Dreyer elution profile (trace B)
from the injection of 50 µl of 54 µM
HSA into a mobile phase of 81.1 µM
warfarin in 0.067 M phosphate buffer
(pH = 7.4) flowing at 2.0 ml/min
through a 5 cm × 4.6 mm ISRP column.
Mobile phase response monitored at
310 nm with response zeroed at the
beginning of the run. Trace A is from
the injection of 50 µl of 0.067 M buffer
blank.
The bound ligand concentration is calculated as ligand concentration in the buffer times
(As – Ab)/Ab where As is area of the sample peak and Ab area of the buffer peak.
Hummel and Dryer, Biochim. Biophys. Acta 1962, 63, 530
Pinkerton and Koeplinger, Anal. Chem. 1990, 62, 2114
Berger and Girault, J. Chromatogr. B 2003, 797, 51
Hummel – Dryer method
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The electrophoretic mobility (μ) of a receptor protein (R) changes upon binding to the
charged ligand (L) present in the electrophoresis buffer, due to changes in its chargeto-mass
ratio. If the protein binds a charged ligand of relatively small mass, the change
in mobility due to the change in mass is negligible relative to the change in mobility
due to the change in charge.
Affinity capillary electrophoresis
ΔμR+L
ΔμRL
S R R+L RL
Weak-to-moderate binding systems
𝑹𝑳
𝒄 𝑹
=
∆𝝁 𝑹+𝑳
∆𝝁 𝑹𝑳
=
∆𝒕
∆𝒕𝒍𝒊𝒎
S R RL
Tight binding systems
𝑹
𝑹𝑳
Chu and Cheng, Cell. Mol. Life Sci. 1998, 54, 663
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Affinity capillary electrophoresis of
bovine carbonic anhydrase B (CAB) in
0.192 M glycine-0.025 M Tris
buffer (pH 8.4) containing various
concentrations of L. The total analysis
time in each experiment was ~5.5 min
at 30 kV using a 70-cm (inlet to
detector), 50-μm open quartz capillary.
Horse heart myoglobin (HHM) and
mesityl oxide (MO) were used as
internal standards.
Chu et al., J. Med. Chem. 1992, 35, 2915
 Kd = 2.1 μM
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Sucrose gradient centrifugation after Draper and Hippel
𝐑𝐋 𝟏 = 𝐜 𝐋𝟏
𝐜 𝐑
𝐜 𝐑 + 𝐊 𝐝
R is applied in a large surplus (> 10-fold) over L, so that [R] ≈ cR. When the R band migrates
due to the centrifugation, it takes the bound ligand along, while free ligand is left at the
starting position. Then the new distributions between free and bound ligand are repeatedly
established.
𝐑𝐋 𝟐 = 𝐑𝐋 𝟏
𝐜 𝐑
𝐜 𝐑 + 𝐊 𝐝
𝐑𝐋 𝐢 = 𝐜 𝐋𝟏
𝐜 𝐑
𝐜 𝐑 + 𝐊 𝐝
𝐢
Bisswanger, Enzyme Kinetics. Principles and Methods 2002
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Electrospray ionization mass spectrometry
Concepts Guide, Agilent Technologies 2015
ToF mass analyzer
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1) native chicken muscle adenylate kinase (AK)
2) chicken muscle adenylate kinase covalently
modified with 8-N3-ATP (AK´)
+
Spectrum of the reaction mixture (10 μM
total protein) of AK and AK´ with 10 μM
of Ap5A in 50 mM (HNEt3)HCO3. Almost
no binding to AK’ is observed, suggesting
that the inhibitor binds in the binding
pocket of the protein.
𝐫 =
𝐑𝐋
𝐑
𝐊 𝐝 =
𝐜 𝐋
𝐫
−
𝐜 𝐑
𝐫 + 𝟏
Daniel et al., J. Am. Soc. Mass Spectrom. 2003, 14, 442
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Fluorescence quenching titration
Vuilleumier et al., Biochemistry 1999, 38, 16816
The viral nucleocapsid protein NCp7
contains two Trp residues that constitute
sensitive intrinsic fluorescent probes.
Binding of oligonucleotides to NCp7 is
accompanied by fluorescence quenching.
The fluorescence that is measured (I) is a sum of the fluorescence of the free and complexed
receptor. Denoting the fluorescence intensities measured when the receptor is completely
free and when is complexed as IR and IRL (IR > IRL), we get I as a function of [RL] as follows:
𝐈 = 𝐈 𝐑
𝐑
𝐜 𝐑
+ 𝐈 𝐑𝐋
𝐑𝐋
𝐜 𝐑
= 𝐈 𝐑
𝐜 𝐑 − 𝐑𝐋
𝐜 𝐑
+ 𝐈 𝐑𝐋
𝐑𝐋
𝐜 𝐑
= 𝐈 𝐑 −
𝐈 𝐑 − 𝐈 𝐑𝐋
𝐜 𝐑
𝐑𝐋
𝐈
𝐈 𝐑
= 𝟏 − 𝟏 −
𝐈 𝐑𝐋
𝐈 𝐑
𝐑𝐋
𝐜 𝐑
The functional dependence of [RL] on cL is given by Eq. (5).
When cL changes from zero to infinity, [RL] increases from
zero to cR and I decreases from IR to IRL.
Kd = 5.9 × 10-7 M-1
Kd = 9.1 × 10-6 M-1
I/IR
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Titration with a fluorescent ligand
Suppose that the measured fluorescence intensity I depends linearly on the concentrations
[L] and [RL] with the coefficients of proportionality εL and εRL. The intensity then can be
expressed as
I = εL [L] + εRL [RL] = εL (cL – [RL]) + εRL [RL] = εL cL + (εRL – εL ) [RL]
[RL] changes with cL according to Eq. (5) from zero to cR. After the receptor becomes
saturated, adding more ligand cause only a linear increase in I with a slope of εL .
FAD
FMN
van den Heuvel et al., J. Biol. Chem. 2004, 279, 12860
The bound FAD fluoresces more than a free FAD
molecule.
FMN either does not bind at all or does not change
fluorescence upon binding. Measurement of
fluorescence anisotropy might be informative here.
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Additivity law of anisotropy:
In cases where the emission of a fluorescent ligand does not change upon binding to
receptors, IL/I = [L]/cL, IRL/I = [RL]/cL and
𝐫 = 𝐫𝐋
𝐋
𝐜 𝐋
+ 𝐫 𝐑𝐋
𝐑𝐋
𝐜 𝐋
= 𝐫𝐋
𝐜 𝐋 − 𝐑𝐋
𝐜 𝐋
+ 𝐫 𝐑𝐋
𝐑𝐋
𝐜 𝐋
= 𝐫𝐋 +
𝐫 𝐑𝐋 − 𝐫𝐋
𝐜 𝐋
𝐑𝐋
Interaction of fluorescein-labeled moenomycin with a
penicillin-binding protein (PBP). The anisotropy of F-Moe
increases during incubation with various concentrations of
E. coli PBP1b, because of the formation of an F-Moe–PBP1b
complex with a reduced rotational freedom.
Chang et al., Proc. Natl. Acad. Sci. 2008, 433
[RL] rises from
zero to cL and r
from rL to rRL with
increasing cR
Fluorescence anisotropy binding assays
The anisotropy r reflects the rotational diffusion
of a fluorescent species.
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Binding of two different ligands
R RA
RB RABA
A
BB
KA
KB KAB
+ +
+
+
KBA
𝐊 𝐀 =
𝐑 𝐀
𝐑𝐀
𝐊 𝐀𝐁 =
𝐑𝐀 𝐁
𝐑𝐀𝐁
𝐊 𝐁 =
𝐑 𝐁
𝐑𝐁
𝐊 𝐁𝐀 =
𝐑𝐁 𝐀
𝐑𝐀𝐁
𝐊 𝐀 𝐊 𝐀𝐁 = 𝐊 𝐁 𝐊 𝐁𝐀 𝜶 =
𝐊 𝐁𝐀
𝐊 𝐀
=
𝐊 𝐀𝐁
𝐊 𝐁
𝜶 < 1 … positive cooperativity
𝜶 > 1 … negative cooperativity
𝐜 𝐑 = 𝐑 +
𝐑 𝐀
𝐊 𝐀
+
𝐑 𝐁
𝐊 𝐁
+
𝐑 𝐀 𝐁
𝛂𝐊 𝐀 𝐊 𝐁
𝐜 𝐑 = 𝐑 + 𝐑𝐀 + 𝐑𝐁 + 𝐑𝐀𝐁
𝐑 =
𝐜 𝐑
𝟏 +
𝐀
𝐊 𝐀
+
𝐁
𝐊 𝐁
+
𝐀 𝐁
𝛂𝐊 𝐀 𝐊 𝐁
𝐑𝐀 =
𝐀
𝐊 𝐀
𝐑 =
𝐜 𝐑
𝐀
𝐊 𝐀
𝟏 +
𝐀
𝐊 𝐀
+
𝐁
𝐊 𝐁
+
𝐀 𝐁
𝛂𝐊 𝐀 𝐊 𝐁
𝐑𝐀𝐁 =
𝐀 𝐁
𝛂𝐊 𝐀 𝐊 𝐁
𝐑 =
𝐜 𝐑
𝐀 𝐁
𝛂𝐊 𝐀 𝐊 𝐁
𝟏 +
𝐀
𝐊 𝐀
+
𝐁
𝐊 𝐁
+
𝐀 𝐁
𝛂𝐊 𝐀 𝐊 𝐁
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Competitive binding
R RA
RB
A
B
KA
KB
+
+ Competitive binding can be viewed as an extreme case
of negative cooperativity (α → ∞, 1/α → 0).
Discarding the term containing α from the denominator
of the expression for [RA] gives:
𝐑𝐀 =
𝐜 𝐑
𝐀
𝐊 𝐀
𝟏 +
𝐀
𝐊 𝐀
+
𝐁
𝐊 𝐁
= 𝐜 𝐑
𝐀
𝐀 +𝐊 𝐀 𝟏 +
𝐁
𝐊 𝐁
From this, it is apparent that the value of KA, the dissociation constant of ligand A,
is increased by a factor of 1 + [B]/KB, so that KA is increased in direct proportion to
the concentration of the competing ligand B.
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Competitive binding (solution for total concentrations)
𝐊 𝐀 =
𝐑 𝐀
𝐑𝐀
𝐊 𝐁 =
𝐑 𝐁
𝐑𝐁
cR = [R] + [RA] + [RB]
cA = [A] + [RA] cB = [B] + [RB]
𝐑𝐀 =
𝐑 𝐜 𝐀
𝐊 𝐀 + 𝐑
𝐑𝐁 =
𝐑 𝐜 𝐁
𝐊 𝐁 + 𝐑
𝐑 𝟑 + 𝐊 𝐀 + 𝐊 𝐁 + 𝐜 𝐀 + 𝐜 𝐁 − 𝐜 𝐑 𝐑 𝟐
− 𝐊 𝐁 𝐜 𝐀 − 𝐜 𝐑 + 𝐊 𝐀 𝐜 𝐁 − 𝐜 𝐑 + 𝐊 𝐀 𝐊 𝐁 𝐑 −𝐊 𝐀 𝐊 𝐁 𝐜 𝐑 = 𝟎
Wang, FEBS Lett. 1995, 360, 111
[R] obtained by solving this cubic equation is then used to calculate [RA] and [RB].
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Fluorescence anisotropy-based competitive assays
Rinken et al., Trends Pharmacol. Sci. 2018, 39, 187
Allikalt et al., Eur. J. Pharmacol. 2018, 839, 40
Kd (nM)
Dopamine D1 receptor
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The calorimetric thermogram is
plotted as ITC compensating
power (dQ/dt) versus time.
The amount of heat at each
injection of ligand is
represented by the area under
the corresponding peak.
Isothermal titration calorimetry
Freyer and Lewis, Methods in Cell Biology 2008, 84, 79
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Wiseman et al., Anal. Biochem. 1989,
179, 131
To find an expression for the heat per mole of ligand added, we first differentiate [RL],
described by Eq. (5), with respect to cL.
𝐝 𝐑𝐋
𝐝𝐜 𝐋
=
𝟏
𝟐
𝟏 +
𝐜 𝐑 − 𝐜 𝐋 − 𝐊 𝐝
𝐜 𝐋 + 𝐜 𝐑 + 𝐊 𝐝
𝟐 − 𝟒𝐜 𝐋 𝐜 𝐑
=
𝟏
𝟐
𝟏 +
𝟏 −
𝐜 𝐋
𝐜 𝐑
−
𝐊 𝐝
𝐜 𝐑
𝟏 +
𝐜 𝐋
𝐜 𝐑
+
𝐊 𝐝
𝐜 𝐑
𝟐
− 𝟒
𝐜 𝐋
𝐜 𝐑
cL/cR
Kd/cR
dcL
d[RL]
The change in [RL] can be related to the
heat change as
dQ = d[RL] ΔH0 V
where ΔH0 is the molar enthalpy change
of the ligand binding reaction and V the
reaction volume.
In the limit Kd/cR approaching zero, this
equation reduces to
𝐝 𝐑𝐋
𝐝𝐜 𝐋
=
𝟏
𝟐
𝟏 +
𝟏 −
𝐜 𝐋
𝐜 𝐑
𝟏 −
𝐜 𝐋
𝐜 𝐑
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Titration of a protein with three different ligands. Each ligand binds to the protein with
either A) a high affinity, B) a medium affinity or C) a low affinity. Top panels: experimental
trace. The baseline is indicated in red. Bottom panels: the integrated heats upon injection
(black squares) and the data fit (red line) after subtraction of the control data.
Harris and Scott, Biochemist 2019, 41, 4
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k1
k-1
Pseudo-first order transient kinetics
𝐝 𝐑
𝐝𝐭
= −𝐤 𝟏 𝐜 𝐋 𝐑 + 𝐤−𝟏 𝐜 𝐑 − 𝐑
𝐝 𝐑
𝐝𝐭
= 𝐤−𝟏 𝐜 𝐑 − 𝐤 𝟏 𝐜 𝐋 + 𝐤−𝟏 𝐑
cR = [R] + [RL] [L] ≈ cL >> cR
kobs
Tepper et al., J. Biol. Chem. 2004, 279, 13425
Fluoride binding to
2.5 µM tyrosinase
λex = 285 nm
λem = 320 nm
Linear fit:
k1 = 11.7 mM-1s-1
k-1 = 13.9 s-1
F-(mM)
𝐑 = 𝐑 ∞ + 𝐑 𝟎 − 𝐑 ∞ 𝐞−𝐤 𝐨𝐛𝐬 𝐭
𝐑𝐋 = 𝐑 𝟎 − 𝐑 ∞ 𝟏 − 𝐞−𝐤 𝐨𝐛𝐬 𝐭
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ASSOCIATION
DISSOCIATION
REGENERATION
Patching, Biochim. Biophys. Acta 2014, 1838, 43
kSP ksp
kx kx
k k
SP
Critical angle
glass
gold
Surface plasmon resonance (SPR)
~ 𝟏 − 𝒆− 𝒌 𝟏 𝒄 𝑳+𝒌−𝟏 ∙𝒕
~𝒆−𝒌−𝟏∙𝒕
Response is
for ASSOCIATION and
for DISSOCIATION.
The measurement of the SPR is done using monochromatic and
polarized light. Although incident light is totally reflected at the
interface glass-gold, the electromagnetic field component does
penetrate a short (tens of nanometers) distance into the metal
creating an exponentially attenuated ‘evanescent wave’, which can
excite surface plasmons. Due to resonance energy transfer between
the evanescent wave and surface plasmons (SP), the intensity of the
reflected light is reduced at a specific incident angle. The resonance
angle at which the intensity minimum occurs is a function of the
refractive index of the solution close to the gold layer.
k = wave vectors
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Lecture
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IgorKučera
Enzyme reaction (equilibrium approximation)
enzyme substrate complex enzyme + product
kcat
kcat (s-1) = catalytic rate constant, molecular activity, „turnover number“
By applying previous considerations to a case with R = E (enzyme) and L = S (substrate),
the rate of enzyme reaction v = kcat [ES] can be expressed in three ways as
𝐯 = 𝐤 𝐜𝐚𝐭 𝐜 𝐄
[𝐒]
𝐒 + 𝐊 𝐝
𝐯 = 𝐤 𝐜𝐚𝐭
𝐜 𝐒 + 𝐜 𝐄 + 𝐊 𝐝 − (𝐜 𝐒 + 𝐜 𝐄 + 𝐊 𝐝) 𝟐−𝟒𝐜 𝐒 𝐜 𝐄
𝟐
𝐯 = 𝐤 𝐜𝐚𝐭 𝐜 𝐄
𝐜 𝐒
𝐜 𝐒 + 𝐊 𝐝
In all three cases, v tends to kcat cE (= limiting or “maximum“ rate) as substrate
concentration tends to infinity.
Holds only if cE << Kd; then [ES] is small and cS ≈ [S].
Requires [S] to be known, which is rarely the case in
in vivo conditions.
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Lecture
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IgorKučera
When working with isolated enzymes, the substrate concentrations are usually held at
least 1000 times higher than that of the enzyme (i.e., cS >> cE). Under in vivo conditions,
however, the actual cS/cE ratio may be significantly lower. For various enzymes of glycolysis
in mammalian skeletal muscle it ranges from 0.057 (for glyceraldehyde 3-phosphate
dehydrogenase) to 62 (for phosphofructokinase).
In-vivo concentrations of substrates and enzymes
Punekar, Enzymes: Catalysis, Kinetics and Mechanisms 2018
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Lecture
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IgorKučera
When substrates A and B react with a single enzyme E without formation of any ternary
complex containing A and B, then in mixtures of A and B each substrate acts as a
competitive inhibitor of the other:
E
EAA
B
KA
+
+
𝐤 𝐜𝐚𝐭
𝐀
EB
KB 𝐤 𝐜𝐚𝐭
𝐁
Competition of two substrates for a single enzyme
𝐯 𝐀 = 𝐤 𝐜𝐚𝐭
𝐀
𝐄𝐀 = 𝐤 𝐜𝐚𝐭
𝐀
𝐜 𝐄
𝐀
𝐊 𝐀
𝟏 +
𝐀
𝐊 𝐀
+
𝐁
𝐊 𝐁
= 𝐤 𝐜𝐚𝐭
𝐀
𝐜 𝐄
𝐀
𝐀 +𝐊 𝐀 𝟏 +
𝐁
𝐊 𝐁
𝐯 𝐁 = 𝐤 𝐜𝐚𝐭
𝐁
𝐄𝐁 = 𝐤 𝐜𝐚𝐭
𝐁
𝐜 𝐄
𝐁
𝐊 𝐁
𝟏 +
𝐀
𝐊 𝐀
+
𝐁
𝐊 𝐁
= 𝐤 𝐜𝐚𝐭
𝐁
𝐜 𝐄
𝐁
𝐁 +𝐊 𝐁 𝟏 +
𝐀
𝐊 𝐀
𝐯 𝐀
𝐯 𝐁
=
𝐤 𝐜𝐚𝐭
𝐀
𝐊 𝐀
𝐤 𝐜𝐚𝐭
𝐁
𝐊 𝐁
𝐀
𝐁
=> The relative rate of turnover of two competing substrates is
defined by their relative concentrations and kcat/K values. The kcat/K
ratio is called specificity constant (or kinetic efficiency) and is used
as a measure of the substrate preference of an enzyme .
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Lecture
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IgorKučera
Kraut, Kurtz, Clin. J. Am. Soc. Nephrol. 2008, 3, 208
Management of toxic alcohol ingestions
General principles in the treatment
of alcohol intoxications
Gastric lavage, induced emesis, or
use of activated charcoal to remove
alcohol from gastrointestinal tract
needs to be initiated within 30 to 60
min after ingestion of alcohol.
Administration of ethanol or
fomepizole to delay or prevent
generation of toxic metabolites
needs to be initiated while sufficient
alcohol remains unmetabolized.
Dialysis helpful in removing
unmetabolized alcohol and possibly
toxic metabolites and delivering
base to patient to ameliorate
metabolic acidosis.
Ethanol has 10 to 20 times greater affinity for alcohol
dehydrogenase (ADH) than the other alcohols. At a
serum concentration of 1 g ethanol/L, the conversion
of other alcohols by ADH is completely inhibited.
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Lecture
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IgorKučera
Clopidogrel is a prodrug of the thienopyridine
family, which has little, if any, platelet
inhibitory effect in its original state. Its active
form is produced by metabolism of the
prodrug through the cytochrome P450
system of the liver, most particularly by the
enzyme CYP2C19.
Comin, Kallmes, Am. J. Neuroradiol. 2011, 32, 2002
=> There is reduced inhibition of platelet
aggregation by clopidogrel when PPIs are
coadministered.
Proton pump inhibitors (PPIs) irreversibly block
the gastric proton pump responsible for the
acidification of the stomach. Elimination of
these drugs occurs almost entirely by cytochrome
P450 metabolism to inactive or less active
metabolites.
Meyer, Yale J. Biol. Med. 1996, 69,203
CLOPIDOGREL
PPIs are often coadministered to patients receiving
clopidogrel to reduce the risk of gastrointestinal
bleeding.
An example of drug interactions
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Lecture
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IgorKučera
𝐯 =
𝐯𝐥𝐢𝐦 𝐒
𝐒 + 𝐊 𝐒
𝐯 ≈
𝐯𝐥𝐢𝐦
𝐊 𝐒
𝐒 =
𝐤 𝐜𝐚𝐭 𝐜 𝐄
𝐊 𝐒
𝐒
𝐯 ≈ 𝐯𝐥𝐢𝐦 = 𝐤 𝐜𝐚𝐭 𝐜 𝐄
[S] << KS :
[S] >> KS :
=> An enzyme reaction can be appropriately characterized by the
parameters specificity constant (kcat/KS) and catalytic rate constant (kcat).
Johnson, Beilstein J. Org. Chem. 2019, 15, 16
𝐤 𝐜𝐚𝐭
𝐬𝐥𝐨𝐩𝐞 =
𝐤 𝐜𝐚𝐭
𝐊 𝐒
An enzyme reaction at low and high concentrations of substrate
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6215
Lecture
8
IgorKučera