Initiation of differential gene expression in sporulating Bacillus subtilis a sceptical biochemist l

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Initiation of differential gene expression in
sporulating Bacillus subtilis a sceptical
biochemist looks at mathematical modelling

• Michael Yudkin
• Kellogg College
• Oxford

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• Part I. The biological system

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Sporulation in Bacillus subtilis
Sporulation cycle
Vegetative cycle
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Establishing differential gene expression
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Three proteins act to regulate sF

• SpoIIAB (AB), a homodimer of 33 kDa
• SpoIIAA (AA), a monomer of 13 kDa
• SpoIIE (IIE), a multidomain protein of 91 kDa.

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• AB can engage in three interactions
• It can make a complex with sF in the presence of
  ATP
• It can make a complex with AA in the presence of
  ADP
• It can use ATP to phosphorylate AA on
• Ser-58, yielding AA-P.
• AA is the substrate of the AB kinase.
• IIE hydrolyses AA-P back to AA.

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Default situation pre-divisional cell and
mother cell

• sF is in a sFABATP complex, with one molecule
  of sF bound to an AB dimer
• AA is phosphorylated to AA-P, which cannot
  interact with AB
• IIE is absent or almost absent.

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Release of sF in the prespore

• IIE is made and hydrolyses AA-P to AA.
• The AA attacks the sFABATP complex.
• sF is liberated (induced release).
• AA is phosphorylated to AA-P ABATP is
  converted to ABADP.

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Cartoon of induced release
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Induced release and its consequences

• AA sFABATP ? sF AAABATP
• AAABATP ? AA-P ABADP
• ABADP ATP ? ABATP ADP
• sF ABATP ? sFABATP

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• How is the activation of sF maintained?

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Cycling of SpoIIAA
Summary ATP H2O ? AA
Pi A wasteful cycle?
Can the prespore slow down the cycle
to diminish the waste of ATP?
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Time course of phosphorylation of SpoIIAA
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• The time course shows that, after one round of
  phosphorylation, the enzyme has to return from an
  inactive to an active form.
• This return clearly includes a slow step.
• Our experiments have identified the slow step as
  the loss of ADP from ABADP.
• But we know from previous work that the loss of
  ADP from ABADP is usually extremely rapid.
• Why is this case different?

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Effect of adding ADP on the phosphorylation of AA
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• We can account for the results by suggesting that
  an interaction with AA changes the conformation
  of AB to AB.
• AB binds exceptionally tightly to ADP.
• ABADP loses its ADP into the solution extremely
  slowly, and so is long-lived.
• Unlike ABADP, ABADP can interact with AA to
  make AAABADP.
• The formation of AAABADP dramatically slows
  the phosphorylation of AA.

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Conclusions so far

• While phosphorylating AA, AB accumulates in the
  form AAABADP.
• The formation of this complex greatly slows the
  phosphorylation reaction.
• So long as AB is phosphorylating AA, it cannot
  interact with sF.
• Prolonging the phosphorylation reaction therefore
  serves to maintain the activity of sF.

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Phosphorylation reaction scheme
ATP
ABATP
AB
AA
ADP
ABADP
AAABATP
1 sec-1
ABADP
AA-PABADP
AAABADP
AA-P
AA
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Structure of SpoIIAB
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Conformational change in AB
ABATP
AAABADP
We suggest that the conformational change is a
closing of the ATP-lid when AA binds
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(No Transcript)
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Source of dephosphorylated AA

• Induced release of sF from the sFABATP complex
  depends on dephosphorylation of AA-P by IIE.
• Maintenance of free sF over the necessary period
  also depends on IIE activity.
• Where is the IIE activity located?

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IIE is a membrane-bound enzyme, found at the
asymmetric septum.
IIE
Is IIE activity confined to the prespore? If
so, how?
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• Part II. The mathematical model

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Mathematical models(a sceptical biochemists
view)

• How do they work?
• What are they for?
• Why are biochemists sceptical of them?
• How do we know if our model is any good?

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How do models work?

• We translate on and off rates of individual
  interactions into a set of equations,
• e.g.
  
  

A
k1
k2
k-1
k-2
k-3
B
C
k3
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• The kinetic constants (k1, k2 etc.) and the
  concentrations of the components (A, B etc.)
  are the parameters.
• These parameters are used to produce a set of
  linked differential equations.
• These linked equations constitute the model.

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What are models for? I Qualitative aspects

• A mathematical model should include all the
  components of a system and all of their
  interactions.
• If the model fails to simulate the known
  behaviour of the system, it is likely that one
  (or more than one) of the interactions has been
  omitted.

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What are models for? II Quantitative aspects

• Genetics and biochemistry identify the components
  in a system and show how these components
  interact.
• But to get a quantitative view of the outcome of
  such interactions, a verbal description is not
  enough.

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The need for a quantitative view IIE activity
in the prespore

• As we saw earlier, IIE activity is located on the
  asymmetric septum.
• The prespore is 5-fold smaller in volume than
  the mother cell.
• So the effective concentration of IIE is 5-fold
  higher in the prespore.
• Does this difference account for the specificity
  of gene expression?

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The need for a quantitative view the sF/sA
paradox

• In the prespore sF has to displace sA from the
  core RNA polymerase.
• But the affinity of core polymerase for sF is
  25-fold less than for sA, and the concentration
  of sF is only 2-fold higher.
• So how can sF displace sA?

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Why are biochemists sceptical of mathematical
models?

• The number of interactions involved in a
  regulatory scheme is often large.
• If we want to make the mathematics come out
  right, we may be tempted
• to change the parameters without regard to
  whether they make physical sense
• to increase the number of interactions without
  regard to the principle of parsimony.

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How do we know if our model is any good?

• The values for all the parameters should be
  justifiable
• (because they have been measured explicitly, or
  because they are similar to those measured in
  analogous systems)
• The model should make predictions that we can
  test experimentally.

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The sF regulatory interactions

• AB ATP ? ABATP
• sF ABATP ? sFABATP
• AA sFABATP ? sF AAABATP
• AAABATP ? AA-P ABADP
• AA-P H2O ? AA Pi
• AA ABADP ? AAABADP
• ABADP ATP ? ABATP ADP
• sF core RNAP ? sFholoenzyme

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• We have previously measured the kinetic constants
  for these interactions.
• We have also measured the concentrations of the
  intermediates.
• We can make a plausible estimate of the kinetic
  constants for the conformational changes in AB.
• We thus have a set of parameters, with which we
  can construct a model Model 1.
• We now use Model 1 to make verifiable
  predictions, both qualitative and quantitative.

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Predicted formation of sF-holoenzyme (Model 1)
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• Evidently some factor is missing from our model.
  What could it be?
• AB is a dimer, and we know that it can undergo
  conformational changes so maybe AB is an
  allosteric protein.
• If AB is allosteric, it is possible that AA binds
  to it cooperatively.
• Cooperativity can now be included in the model,
  to give Model 2.

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Sporulation Model 2
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Predicted formation of sF-holoenzyme (Models 1
and 2)
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Binding of AA to AB experiment and simulation
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Other simulations from Model 2

• The model can successfully simulate results
  obtained in vitro from experiments on
• Binding of AA to ABADP
• Binding of sF to ABATP
• Disruption of sFABATP complexes by AA
• Rebinding of sF to ABATP as AA is phosphorylated
• Response of this rebinding to IIE
• Time course of phosphorylation of AA.

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Quantitative aspects of Model 2 IIE activity
in the prespore

• As we saw earlier, IIE activity is located on the
  asymmetric septum.
• The prespore is 5-fold smaller in volume than
  the mother cell.
• So the effective concentration of IIE is 5-fold
  higher in the prespore.
• Does this difference account for the specificity
  of gene expression?

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Predicted release of sF
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Predicted release of sF
IIEAA-P
IIE
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Quantitative aspects of Model 2 the sF/sA
paradox

• In the prespore sF has to displace sA from the
  core RNA polymerase.
• But the affinity of core polymerase for sF is
  25-fold less than for sA, and the concentration
  of sF is only 2-fold higher.
• So how can sF displace sA?

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Predicted formation of sA-holoenzyme and
sF-holoenzyme
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Conclusions of a convinced sceptic

• When used judiciously and critically,
  mathematical modelling is an extremely valuable
  technique.
• Mathematical modelling can supply insights that
  could not be reached by any other method now
  available.

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Acknowledgments

• The model was developed by Joanna Clarkson and
  Dagmar Iber, using data obtained in my lab by the
  following
• Kyung-Tai Min
• Mahmoud Najafi
• Thierry Magnin
• Matt Lord
• Daniela Barillà
• Brian Lee
• Isabelle Lucet
• Jwu-Ching Shu
• Joanna Clarkson