Modelling the Interaction of Rho GTPases in Moving Cells

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Modelling the Interaction of Rho GTPases in
Moving Cells

• Alexandra Jilkine

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How Cells Move
From Molecular Biology of the Cell, Alberts et
al. (2002)
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Rho Family GTPases

• Key players in cell motility
• Link receptor signaling to assembly of the
  cytoskeleton
• Molecular switches cycle between inactive
  (GDP-bound) and active (GTP-bound) forms
• Transduce upstream signal to downstream effectors
  in their active state

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Some members of the Rho family

• Rac activates formation of lamellipodia and is
  necessary for cellular protrusion.
• Cdc42 activates formation of filopodia and
  regulates polarization.
• Rho is necessary for contraction of the cell body.

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Cdc42, Rac and Rho in migrating cells

• High concentration of active Rac is found at the
  front of the migrating cell concentration
  decreases towards rear of the cell
• The Rho concentration is the inverse of Rac
  highest at the rear and decreasing towards the
  front
• Cdc42 tends to have same distribution as Rac

Rac, Cdc42
Rho
Rac, Cdc42
Rho
BACK
FRONT
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Interactions of the Rho GTPases

• Multiple (often contradictory) interaction
  schemes have been proposed

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Model Formulation

• Idealize pathways as direct effects (positive or
  negative feedback)
• Assume a vast pool of inactive forms and only
  keep track of the active forms
• Determine which interaction schemes give rise to
  a local (ODE) model that has bistability
• High CDC42/Rac, low Rho
• Low CDC42/Rac, high Rho
• Add diffusion of proteins to get a reaction
  diffusion system

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Questions to Address

• Which proposed interaction schemes are not
  consistent with biological observations?
• What features are necessary to achieve bistable
  behavior?
• What kind of reaction kinetics predict the
  distribution of Cdc42, Rac, and Rho found in
  migrating cells?
• What distinguishes these different kinetics
  biologically?

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Possible Interaction Schemes

• From the 5 pathways listed, only pathway 2)
• has feedback to Cdc42 from the other proteins
• In other cases the level of Cdc42 would be
  independent of Rac and Rho levels, so feedback to
  Cdc42 is necessary.
• Mutual inhibition between Cdc42 and Rho is
  necessary to achieve a high Cdc42/Rac, low Rho
  and low Cdc42/Rac high Rho system

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What are the corresponding kinetics?

• One protein can exert a positive effect on
  another via two different processes
• Increase conversion of GDP-bound to GTP-bound
  (active) form
• Decrease conversion of GTP-bound to GDP-bound
  form
• We look at the consequences of these different
  assumptions

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Different Inhibitory Kinetics

• 1) Increasing the GTP-hydrolysis rate will not
  work.
• 2) Slowing down GDP/GTP exchange can give us
  desired behavior.

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Activation Inhibition Model
This is the minimal model that is plausible with
the biology
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Spatial Variant
Want to develop spatial segregation in response
to signal
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Polarization due to Amplification of a Gradient
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Polarization due to Injection of Active Protein