Kinetic & Affinity Analysis
An introduction
What are kinetics and affinity?
Kinetics
• How fast do things happen? – Time-dependent
• Association – how fast molecules bind
• Dissociation – how fast complexes fall apart
• Kinetics determine whether a complex forms or dissociates within a
given time span
Affinity
• How strong is a complex? – Time-independent
• Affinity determines how much complex is formed at equilibrium
(steady state where association balances dissociation)
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What is the relevance of binding kinetics?
The cell is a dynamic system – rarely in equilibrium
The same affinity can be resolved into different on and off rates for
different interactions
• Kinetic data reveal more information
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Same affinity but different kinetics
All 4 compounds have the same affinity KD = 10 nM = 10-8 M
The binding kinetic constants vary by 4 orders of magnitude
Concentration = 1000 nM
Concentration = 100 nM
kon
koff
106
10-2
105
10-3
104
10-4
103
10-5
(M-1s-1) (s-1)
Response
All target
sites
occupied
30
min
30
min
60
min
60
min
Time
Time
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Three ways to obtain kinetic and affinity data
in Biacore
Monitor association and dissociation rates
• Affinity
Kinetics
Monitor steady state levels
• Affinity
Kinetics
Measure free analyte in solution
• Affinity
Kinetics
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Rate equations for 1:1 kinetics
A
Association:
Dissociation:
d [AB]
dt
-d [AB]
dt
ka
kd
B
AB
B
A
ka
[A]
[B]
kd
[AB]
ka
[A]
[B]
kd
[AB]
M-1s-1
M
M
s-1
M
B
A
Net rate equation:
d [AB]
dt
M/s
where
k a association rate constant [M-1s-1]
k d dissociation rate constant [s-1]
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Equilibrium constants
At equilibrium:
Dissociation
Association
ka
[A]
[B]
kd
[AB]
M-1s-1
M
M
s-1
M
The equilibrium constants:
KA
ka
kd
[AB]
[A] [B]
the equilibrium association constant [M-1]
KD
kd
ka
[A] [B]
[AB]
the equilibrium dissociation constant [M]
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Equilibrium and kinetics in Biacore
ka
A + B ⇔ AB
kd
A is the analyte in solution
• Free concentration maintained constant by flow system
AB is the complex
• Concentration of complex measured directly as R in RU
B is the ligand on the surface
• Total concentration can be expressed in RU, as maximum binding
capacity Rmax
• Free concentration is Rmax-R
We do not need to know the “real” concentration
of ligand or complex
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Rate and affinity in Biacore terms
A
d [AB]
dt
dR
dt
RU/s
ka
kd
B
ka
AB
kd
[A]
[B]
ka
C
[R max R]
M-1s-1
M
RU
[AB]
kd
R
s-1 RU
A has one binding site and reacts with immobilized ligand
B has n identical and independent binding sites
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The net rate equation terms in a
sensorgram
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Information in a Sensorgram
The relationship between Rmax, Req and KD
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Mass transport
A phenomenon with relevance to kinetics measurements in
Biacore
• Describes the movement of molecules from solution to a
surface
• Is independent of biomolecular interaction processes
Rates measured in Biacore depend on both mass transport and
biomolecular binding
• The relative importance of mass transport effects can be
largely controlled by the assay conditions used
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What is mass transport?
Diffusive mass transport
• Simple example in a static system
analyte
gradient
Over time, analyte concentration at the surface will be depleted
and a gradient will be generated through the liquid layer
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Analyte consumption & supply
flow cell height
1
diffusion
distance
2
3
1. Analyte supplied by convection (continuous flow)
2. Diffusion becomes increasingly important as the flow rate
reduces closer to the surface
3. Biomolecular interaction processes at the ligand/analyte
interface
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Dealing with mass transport limitations
Low Rmax (ligand density)
High flow rates
• High flow rates reduce diffusion distance
Mass transport correction included in all kinetic models
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Experimental Design
Experimental design
Affinity determination by steady-state analysis
Determine steady state binding levels over a range of analyte
concentrations
High immobilization level
Concentration range should cover at least
20-80% saturation of the surface
Use reference surface
Include at least one concentration in duplicate
Include zero concentration sample
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Important experimental parameters
Kinetic analysis
The purity of the reagents
Immobilization procedure
Immobilization level
Ligand activity
Flow rate
Analyte concentration range
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Analyte concentrations
Kinetic analysis
Concentrations should cover a full range of binding curves
Include at least one concentration in duplicate
Include zero-concentration samples
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1- What am I looking for?
1.
Specificity?
2.
Ranking?
3.
Kinetics?
4.
Concentration?
5.
Thermodynamics?
6.
Other?
Collect
information
about interacting
partners
• MW
• pI
• stability
• solubility
• purity
• activity
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1- What am I looking for?
1.
Specificity?
2.
Ranking?
3.
Kinetics?
4.
Concentration?
5.
Thermodynamics?
6.
Other?
Choose suitable
immobilization
chemistry and
ligand density
Wait for a stable
baseline
Check for drifts
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1- What am I looking for?
1.
Specificity?
2.
Ranking?
3.
Kinetics?
4.
Concentration?
5.
Thermodynamics?
6.
Other?
Scout for buffer
composition
• pH
• ionic strength
• DMSO
• metals
• metal chelators
• BSA
• cofactors
Keep it as simple as possible
and match running buffer
and sample buffer
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1- What am I looking for?
1.
Specificity?
2.
Ranking?
3.
Kinetics?
4.
Concentration?
5.
Thermodynamics?
6.
Other?
Check for a
positive control
• reproducibility
• dose dependency
• saturation
• stoichiometry
Check for a
reference control
• non specific binding
• always check not subtracted
signals
• run zero concentrations and
negative controls
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1- What am I looking for?
1.
Specificity?
2.
Ranking?
3.
Kinetics?
4.
Concentration?
5.
Thermodynamics?
6.
Other?
Scout for
regeneration
• from mildest to harsh, never
the reverse
• try with regeneration
cocktails
• always check for ligand
activity and stability after
regeneration
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1- What am I looking for?
Adjust flow rate
1.
Specificity?
2.
Ranking?
3.
Kinetics?
4.
Concentration?
5.
Thermodynamics?
6.
Other?
• mass transport
limitation
• rebinding
Adjust injection
parameters
• association phase
• dissociation phase
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Sensorgrams appearance
•Take time to look at the shapes of the sensorgrams
• Check for low quality data, such as drifts, air bubbles, spikes, aggregations
• Always have a look at what happens on the reference flow cell and on the
active, not just at the subtracted
• Look at the curvatures of the sensorgrams if you are performing a kinetic
analysis
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Have a look...
A, B, C: Same kon but different koff
D: Equilibrium reached
within seconds
E:Ligand saturation
F: partial mass transport
limitation
Rich R and Myszka D, J. Mol. Recognit. 2008; 21: 355-400
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More complexity...
Is it a biphasic interaction?
Maybe... But it is virtually impossible to resolve what actual event is leading to
complex response
SO
Take a step back and riconsider experimental design and conditions
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Bad data sets
Drifting baseline
Substandard responses
• ligand stability
• perform start up
• regeneration issues
• aggregation
• precipitation
• instrument maintenance
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Data evaluation
Yes/No data
Specificity studies
What is the purpose of the
evaluation?
Ranking
Early selection
of binders
Equilibrium analysis
KD
Determination of
binding strength
Kinetic rate analysis
ka, kd
Modelling binding reactions
to determine the dynamic
behaviour of a system
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Include zero-concentration samples
“Double referencing”
• Compensates for system disturbances
• Important for high-quality work
Sample
Reference-subtracted
Zero-conc
Double-referenced
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Control experiments
Non-specific binding
Surface performance test
Regeneration optimization
Mass transport limitations
Linked reactions
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Control experiments
Vary contact time at equilibrium to check for linked reactions
No linked reactions
Linked reactions
Dissociation rates are not affected by contact time if reactions
are independent
Two-state reactions and competition are examples of linked
reactions
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Summary
B
Affinity analysis
A
• Derives the affinity constants
• For analysis of interactions with very fast on and off rates
Kinetic analysis
• Derives the rate constants and the affinity constants
• For detailed characterization of a molecular interaction
• Interactions with the same affinity may have entirely different
association and dissociation rate constants
• Rate constants may be more significant than affinity in
understanding biological processes
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