9 - Ligand Binding and Equilibria I Flashcards
What does ligand binding allow for?
Molecular recognition in biology
What are some examples of molecular recognition?
Antibodies, DNA and transcription factor, receptors, etc.
What is the general equation for ligand binding?
P + L –> PL
What type of interaction is ligand binding?
A noncovalent interaction
What is the formula for Ka (association constant)?
Ka = [PL]/[P][L]
What is the formula for Kd (dissociation constant)?
Kd = [P][L]/[PL]
What is the relationship between Kd and Ka?
Kd = 1/Ka
What are the units of Kd?
M
If a Kd is small, is this a strong or weak association?
Strong association (weak disassociation)
If a Kd is large, is this a strong or weak association?
Weak association (strong dissasociation)
In a cell, what does Kd reflect?
The concentrations in a cell
If DNA concentration is on the order of 1 nM, what is the estimated Kd?
~ 1 nM (same order of magnitude)
What is the Kd of enzyme-ATP?
Millimolar to Micromolar
What is the Kd of signaling protein to a target?
Micromolar
What is the Kd of a sequence-specific recognition of DNA by a transcription factor?
Nanomolar
What is the Kd of an inhibitor drug to a protein?
Nanomolar to picomolar
What is the Kd of biotin binding to aviding?
Femtomolar (one of the strongest noncovalent interactions)
What is specific binding limited by?
The number of available sites
What is a hallmark of specific binding interactions?
Saturable binding
What does a binding isotherm look like in a linear scale?
Exponential saturation
What does a binding isotherm look like in a log scale?
Sigmoidal
How can Kd be determined from L concentration?
When [P] = [PL], Kd = [L]
What is [L]?
Concentration of FREE ligand
What is [P]?
Concentration of FREE protein
What is [PL]?
Concentration of PL complex
What is [L]T?
Total ligand concentration ([L]T = [L] + [PL])
What is [P]T?
Total protein concentration ([P]T = [P] + [PL])
In an experiment, what quantities in Kd are usually known?
[P]T and [L]T (NOT [L] and [P])
What happens if [P]T < Kd?
There is very little [PL], so [L] = [L]T
What happens if [P]T > Kd?
A lot of complex [PL] is formed, so [L] < [L]T
What is f?
Fractional occupancy
What is the equation for f?
f = [PL]/([PL}+[P])
What happens at f = 0.5?
Kd = [L]
If a binding isotherm plots f vs. [L], how can Kd be determined?
The [L] where f = 0.5
If a binding isotherm plots f and [L]T, how can you determine Kd?
Need more complicated math (Kd does not equal [L])
What is the challenge with plotting f with [L]?
[L] is usually very hard to determine, while [L]T is very easy to determine
How can f be experimentally calculated?
By plotting [PL] vs [L], and seeing where the curve saturates
In a [PL] vs. [L] isotherm, how can Kd be determined?
By finding the half maximal point (f = 0.5), and Kd = [L] at this point
What thermodynamic quantity changes upon ligand binding?
Delta G
What is delta G bind?
The energy released when binding (P + L –> PL)
What is the formula for delta G bind?
Delta G bind = RT ln(Kd)
If a Kd is small, what can you say about delta G bind?
It is more negative (higher magnitude)
If a Kd is large, what can you say about the delta G bind?
It is less negative (lower magnitude)
What is the formula for delta G?
Delta G = delta H - T delta S
What does delta H come from in ligand binding?
Hydrogen bonds (distance dependent, geometric constraint), electrostatic bonds (Coulomb’s law), salt bridges
How does ligand binding decrease entropy?
There is less degrees of freedom, hydrophobic effect
How does ligand binding increase entropy?
When ligand binds, water is released, which increases entropy (same if ligand is solvated)
In delta G, what is easy to predict and why?
H, because you can estimate based on the bonds and energetics
In delta G, what is hard to predict and why?
S, because there are compensating effects
How does the filter binding assay work?
Two test tubes with [P] and [L] are mixed, and the [L] is separated from the [PL] and [P] using the filter
How is Kd determined from a filter binding assay?
Plot f and L to find Kd
How does fluorescence polarization / anisotropy work?
A fluorophore is used to measure tumbling. There is less tumbling when bound, so changes in tumbling can be plotted
How is Kd determined from fluorescence polarization / anisotropy?
Can plot tumbling changes, and fit to a Kd
How does FRET work?
Direct observation of two probes (see changes in concentration)
How does the bead halo assay work?
A halo can be detected through microscopy, so small changes in fluorescence can be measured
What are some methods to measure Kd?
- Filter binding assay
- Fluorescence polarization / anisotropy
- FRET
- Bead halo assay
- Isothermal titration calorimetry
- Surface plasma resonance
- Biolayer interferometry
- Gel shift
- Co-sedimentation (SEC, AUC)
What is the general method for ligand binding assays?
Detect changes of the system due to ligand binding (shape changes, etc.)
What concentration ranges are needed for a Kd assay?
A concentration range where Kd is in the middle
What is the purpose of saturation measurements?
Bound fraction remains small
Why is radioactivity used in ligand binding?
Only way to not change chemistry of ligand
How is retinoic acid used in ligand binding?
Radioactive retinoic acid is combined with the receptor, and charcoal is used to separate free ligand
What is the purpose of radioactivity with retinoic acid?
Calculate radioactivity to measure free ligand
What assumption is used in the retinoic acid test?
Equilibrium time is longer than separation time (experiment is very specific to retinoic acid)
What is retinoic acid?
Metabolite of vitamin A
When is the Scatchard analysis done?
Estimate Kd when receptor concentration is unknown
How does the Scratchard analysis work?
Plot [Lbound]/[L] vs. [Lbound] to find Kd and [P]T
What is the formula for Scatchard analysis?
[Lbound]/[L] = (-1/Kd)[Lbound] + [P]T/Kd
What is the slope of Scatchard analysis?
-1/Kd
What is the x intercept of a Scatchard analysis?
[P]T / Kd
What does the Hill equation describe?
The binding isotherm
What is the Hill equation?
f^n = L^n / (L^n + Kd)
What is n?
Hill coefficient
What happens when n = 1?
No cooperativity
What happens when n < 1?
Negative cooperativity
What happens when n > 1?
Positive cooperativity
Where does the biggest change of f occur?
Between 0.1 and 10 of L/Kd
What is the chemical equation for competition?
PA + L P + L + A PL + A (two Kd)
What does the Cheng-Prusoff equation describe?
Relate IC50% to Ki (more standardized value)
What does ITC stand for?
Isothermal titration calorimetry
What is ITC used for?
Measuring thermodynamics of binding?
How does ITC work?
Drops of ligand are added, and the heat released is measured, as well as the binding isotherm
How does ITC measure delta G?
It uses the binding isotherm to find Kd, which can be used to calculate delta G
What is the formula for ITC Kd?
f = (L/Kd) / (1 + L/Kd)
How does ITC measure delta H?
It uses the heat released
How doe ITC measure delta S?
It uses delta G and delta H to calculate delta S
What is lock and key binding?
No change in conformation
What is induced fit binding?
There is a conformational change in the protein
What is the consequence of a protein interconverting between many states?
Binding of a ligand can select one state over another
What is ligand induced folding?
Binding of a ligand changes the protein shape
What is conformational selection?
A ligand binds in only one state, so it selects the particular state
True or false: the timescale of protein conformational dynamics affects binding
True: this determines how often a state is available to be selected for by the ligand
What is the Cheng Prusoff equation?
Ki = IC50% / (1 + ([A]/Kd2))
