Pre-lecture version
The lecture recording pauses at
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that you should think about.
Providing the answers beforehand
would defeat that purpose.
Therefore, if you look at the slides
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A complete version will also be
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koala.
By Sheba Also 43,000 photos [CC BY-SA
2.0 (https://creativecommons.org/
licenses/by-sa/2.0)], via Wikimedia
Commons
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Cooperativity and allostery
协调和变构效应
ICMB 1, Lecture 3.2
Melanie I Stefan - melanie.stefan@ed.ac.uk
Semester 2, 2019/20
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What’s this?
Julian Voss-Andreae. Heart of Steel.
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Structure and function: Cooperativity (e.g. Hemoglobin)
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Structure and function: Cooperativity (e.g. Hemoglobin)
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Learning Objectives
Week 3 Learning Objectives covered in this lecture:
1
Explain the terms reaction energy, activation energy, catalysis
2
(Functionally) define the term cooperativity
3
Explain allostery and the role of allosteric activators and inhibitors
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Outline
1
What is cooperative binding?
2
Looking at binding systems
3
By what mechanism is cooperative binding achieved?
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Let’s look at haemoglobin again
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Basic definitions
When we look at a protein binding to more than one ligand molecule,
what could the following concepts mean?
Cooperative binding
Positive cooperativity
Negative cooperativity
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Basic definitions
When we look at a protein binding to more than one ligand molecule,
what could the following concepts mean?
Cooperative binding:
Binding of ligand molecule(s) to a protein molecule changes the
probability of more ligand molecules binding
Positive cooperativity:
Ligand binding increases the probability of more ligand binding
Negative cooperativity:
Ligand binding decreases the probability of more ligand binding
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Outline
1
What is cooperative binding?
2
Looking at binding systems
3
By what mechanism is cooperative binding achieved?
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Binding curve
Average number of occupied binding sites as a function of initial ligand
concentration.
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Binding curve
Check axes carefully! Sometimes, binding curves are drawn with a log
scale for the x axis. E.g. calmodulin binding to Calcium:
钙调素[⽣] ; 钙调蛋⽩[医]
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Saturation curve
Same as binding curve, but y axis is normalised to total number of binding
sites
(Ȳ - “Y bar” or θ - “theta”)
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Can we see cooperativity from the binding curve?
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Another way of looking at binding: The Hill plot
log
Ȳ
1−Ȳ
as a function of log X (X is the ligand concentration).
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The Hill plot
Let’s maths around a bit . . .
Where is Ȳ = 21 ?
What does that have to do with Kd ? (Assume for this that binding is
non-cooperative)
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The Hill plot
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What is so great about the Hill plot?
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What is so great about the Hill plot?
This plot will often (but not always) be linear. Easy to read key
parameters off the plot. Leads to an easy way of assessing cooperativity.
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“Traditional” definition of cooperativity
Frequently used definition
Slope of the Hill plot at
Ȳ = 12
If slope > 1: positive
If slope < 1: negative
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“Traditional” definition of cooperativity
Frequently used definition
Slope of the Hill plot at
Ȳ = 12
If slope > 1: positive
If slope < 1: negative
Problems
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“Traditional” definition of cooperativity
Frequently used definition
Slope of the Hill plot at
Ȳ = 12
If slope > 1: positive
If slope < 1: negative
Problems
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It’s complicated . . .
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It’s complicated . . .
Different definitions of cooperativity and of other biochemical
concepts (such as binding curve, association constants etc.) exist.
The different definitions often come from different underlying
theoretical approaches.
The extent to which definitions are equivalent is an active area of
research (see, for instance this paper by Martini et al., 2016)
Cooperativity can depend on cellular context.
When reading or writing about cooperativity and related concepts,
make sure you clarify exact definitions.
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Outline
1
What is cooperative binding?
2
Looking at binding systems
3
By what mechanism is cooperative binding achieved?
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How does cooperative binding happen?
Allosteric regulation
Activity at one site of a protein can be regulated by events at another
site (or other sites).
Originally defined for enzymes, but can also relate to other types of
activity, e.g. binding activity.
Often involves conformational change.
Several models exist.
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The two conformational states of haemoglobin
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The two conformational states of haemoglobin
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MWC model of allostery through concerted transition
协调过渡的变构MWC模型
(Jacques) Monod - (Jeffries) Wyman - (Jean-Pierre) Changeux.
Main idea: Protein exists in two states:
T (“tense”) and R (“relaxed”).
The R state has a higher ligand affinity than the T state.
The entire protein (with all subunits) transitions at the same time
between T and R.
More ligand binding means the protein is more likely to exist in the R
state.
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MWC model: Reaction scheme
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MWC model: Reaction scheme
What state has the lowest free energy?
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MWC model: Free energy diagram
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So, what is happening here?
In the absence of ligand, the T state is favoured
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So, what is happening here?
In the absence of ligand, the T state is favoured
Ligand binding shifts the energy balance from T to R, so R becomes
the more favoured state
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So, what is happening here?
In the absence of ligand, the T state is favoured
Ligand binding shifts the energy balance from T to R, so R becomes
the more favoured state
R has a higher ligand affinity
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So, what is happening here?
In the absence of ligand, the T state is favoured
Ligand binding shifts the energy balance from T to R, so R becomes
the more favoured state
R has a higher ligand affinity
Therefore, ligand binding increases the probability of more ligand
binding.
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So, what is happening here?
In the absence of ligand, the T state is favoured
Ligand binding shifts the energy balance from T to R, so R becomes
the more favoured state
R has a higher ligand affinity
Therefore, ligand binding increases the probability of more ligand
binding.
This is exactly the definition of cooperativity.
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So, what is happening here?
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So, what is happening here?
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So, what is happening here?
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So, what is happening here?
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Allosteric modulators
An allosteric activator
binds to (and thereby
stabilises) the R state.
This increases the overall
ligand affinity.
Why?
What does an allosteric
inhibitor do?
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Allosteric modulators: Hemoglobin
Carbon dioxide is an
allosteric inhibitor of
haemoglobin
What does this mean for
oxygen affinity in the
presence of CO2 ?
What is the physiological
function of this?
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Review - Learning Objectives for today
Week 3 Learning Objectives covered in this lecture:
1
Explain the terms reaction energy, activation energy, catalysis
2
(Functionally) define the term cooperativity
3
Explain allostery and the role of allosteric activators and inhibitors
What questions do you have?
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Optional further reading
The Wikipedia page on Cooperative Binding lists some of the definitions
of cooperativity and is a good starting point if you want to learn more. A
lot of the figures I used in this presentation are from there. We usually tell
you that Wikipedia can be unreliable, and that it is not good to rely on it
too much. In this case though, I wrote (most of) the Wikipedia entry, so I
guess it’s fine.
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Optional Copasi files
To illustrate cooperative and non-cooperative system, we have provided a number of Copasi files. You can play around with the
models by changing rate constants, cooperativity coefficients, concentrations etc. The files are in the zip archive
Lecture3.2 Copasi files.zip with the following content:
single binding site.cps
non cooperative binding.cps
positive cooperative binding.cps
negative cooperative binding.cps
*.txt
ligand binding.R
receptor with a single ligand binding site
receptor with 4 ligand binding sites, non-cooperative binding
receptor with 4 ligand binding sites, positive cooperativity
receptor with 4 ligand binding sites, negative cooperativity
simulation data from each model (after running “Parameter Scan” task)
R file used to read data and produce plots
In models with more than one binding site, a bit of thought needs to go into defining reaction rate constants. Let’s say the
system is non-cooperative and all binding sites are equal with some intrinsic kf and kb. For the first binding event, there are
four sites that the ligand can bind to, so the overall forward rate constant is 4 ∗ kf . For the reverse reaction, the rate constant is
just kb, because there is only one site to dissociate from. In the models here, this has been taken care of. For the cooperative
systems, rate constants are additionally multiplied with a cooperativity constant coop, which is positive for positively
cooperative systems and negative for negatively cooperative systems.
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Image credits
Binding curve for R state, T state and whole protein for an allosteric protein. My own work.
Binding curve of Calcium binding to calmodulin. My own work.
Binding curve of Oxygen binding to haemoglobin. By Hazmat2 - This file was derived from: Hb saturation curve.png,
Public Domain, viaWikimedia Commons
Heart of Steel (Hemoglobin sculpture). By Photographer: Julian Voss-Andreae [GFDL
(http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0
(http://creativecommons.org/licenses/by-sa/3.0/)], via Wikimedia Commons
Hemoglobin T and R state. My own work (2020), using UCSF Chimera and PDB structures 1HGB and 1RVW. CC
BY-SA 4.0
Hill Plot. By Lenov - Own work, CC BY 3.0, via Wikimedia Commons
Hill Plot of the MWC binding function. By Lenov - Own work, CC BY 3.0, via Wikimedia Commons
Ligand binding to an allosteric protein (reaction scheme and free energy diagram). From: Stefan and Le Novere (2013).
Cooperative binding. PLoS Comput Biol 9(6):e1003106
Various binding curves for non-cooperative, positively cooperative and negatively cooperative binding systems. My own
work from Copasi models, visualised using R. CC BY-SA, 3.0, 2019.
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