10.37 Chemical and Biological Reaction Engineering, Spring 2007
Prof. K. Dane Wittrup
Lecture 14: Kinetics of Non-Covalent Biomolecular Interactions
This lecture covers : Significance, typical values and diffusion limit, approach to
equilibriu, and multivalency
Noncovalent Interactions
Protein
Ligand
P
+
L
Complex
kon
U
C
koff
Figure 1. Protein-ligand binding.
Association rate =
konC p CL
Dissociation rate =
koff Cc
@ equilibrium,
konC p CL = koff Cc
1
s
C p CL
Cc
=
koff
kon
= Kd
L
mol s
In general, for protein-protein interactions,
half-time for complex dissociation
τ1 2 =
nM
pM
fM (femtomolar)
stronger
interactions
Fractional saturation Y =
ln 2
koff
τ1 2
types
milliseconds
milliseconds-seconds
non-specific stickiness
cell surface, multi valent
minutes-hours
hours-weeks
weeks-months
antibodies, enzymes
growth factors
hycholase inhibitors
Kd
mM
μM (micromolar)
kon ≈ 105 mol −1s −1
Cc
Cc
=
C p , o Cc + C p
Cite as: K. Dane Wittrup, course materials for 10.37 Chemical and Biological Reaction Engineering, Spring
2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on
[DD Month YYYY].
Kd =
C p CL
Cc
→Y =
CL
CL + K d
Y
Y
Kd
CL
log CL
Figure 2. Left: Graph of fractional saturation versus ligand concentration. Right:
Graph of fractional saturation versus the logarithm of ligand concentration.
If
C p ,o ≈ CL ,o , then at equilibrium, CL ≠ CL ,o
Y=
Y=
If instead
CL ,o − yC p ,o
CL ,o − yC p ,o + K d
K d + CL,o + C p ,o − ( K d + CL,o + C p ,o ) 2 − 4C p ,o CL,o
2C p ,o
CL ,o C p ,o , CL ≈ CL,o
Y=
CL ,o
CL ,o + K d
How quickly is equilibrium reached?
dCc
= konCLC p − koff Cc
dt
If
CL , o C p , o
“pseudo-1st order”
konCL = konCL ,o
C p ,o = C p + Cc
(complexed)
C p = C p ,o − Cc
10.37 Chemical and Biological Reaction Engineering, Spring 2007
Prof. K. Dane Wittrup
Lecture 14
Page 2 of 5
Cite as: K. Dane Wittrup, course materials for 10.37 Chemical and Biological Reaction Engineering, Spring
2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on
[DD Month YYYY].
dCc
= konCL,oC p − koff Cc = konCL ,o (C p,o − Cc ) − koff Cc
dt
= kon C p,oCL ,o − (konCL,o + koff )Cc
⇒ Cc (t ) = C p,o
CL ,o
CL ,o + K d
(1− e −kobs t )
kobs = konCL,o + koff
ln 2
= half-time for reaching equilibrium
kobs
Cc
equlibrium
ln 2
kobs
t
Figure 3. Concentration of complex versus time. Equilibrium is approached at long
times.
Biosensor
Surface plasmon resonance (label-free)
flow
thin gold film
hν
amount of reflected light is a
function of complex formation
Figure 4. Schematic of how surface plasmon resonance works.
10.37 Chemical and Biological Reaction Engineering, Spring 2007
Prof. K. Dane Wittrup
Lecture 14
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2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on
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Kd
signal
kon
koff
koff
t
flow
signal
association
stop
signal
equilibrium
dissociation
Figure 5. Signal of detector versus time.
redundant estimates:
koff in both association & dissociation, K d =
koff
kon
in equilibrium
phase
best approach: fit one set of parameters to three phases of experiment. (global least
squares)
Multivalency (Avidity)
cell
cell
cell
surface
cell
multivalent
label
Figure 6. Three examples of multiple protein-ligand binding.
How does multivalency effect apparent interaction strength?
10.37 Chemical and Biological Reaction Engineering, Spring 2007
Prof. K. Dane Wittrup
Lecture 14
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Cite as: K. Dane Wittrup, course materials for 10.37 Chemical and Biological Reaction Engineering, Spring
2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on
[DD Month YYYY].
U
K eff
U
free
(high effective local
concentration)
bound
detected same
Figure 7. Multivalent binding equilibrium.
10.37 Chemical and Biological Reaction Engineering, Spring 2007
Prof. K. Dane Wittrup
Lecture 14
Page 5 of 5
Cite as: K. Dane Wittrup, course materials for 10.37 Chemical and Biological Reaction Engineering, Spring
2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on
[DD Month YYYY].