Dictyostelium Aggregation How can pattern-formation inform cell biology

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Dictyostelium AggregationHow can
pattern-formation inform cell biology

• Herbert Levine and Wouter-Jan Rappel
• (PF) Center for Theoretical Biological Physics -
  UCSD
• (in collaboration with
• E. Bodenschatz, Cornell/MPI W. Loomis
  UCSD)
• Introduction to Dicty
• The gradient detection problem
• Survey of existing paradigms
• A new module - activator annihilation
• Where do we go from here?
• supported by NSF PFC/ITR/Biocomplexi
  ty programs

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Dictyostelium amoebaea pattern-dominated
lifecycle
After starvation, cells aggregate,
differentiate, sort and cooperate to create a
functional multicellular organism
24 hour life-cycle of Dictyostelium courtesy of
L. Blanton
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• Aggregation stage is fairly
• well-understood
• cAMP excitable signaling
• Chemotactic response
• Streaming instability
• -gt mound formation
• Research focus has shifted
• to trying to understand the
• cell biology of chemotaxis
• to spatio-temporal signals

Courtesy P. Newell
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Genetic Feedback Model

• We need wave-breaking to get spirals where does
  the large inhomogeniety come form?
• Key insight excitability is varying in time,
  controlled by the expression of genes controlling
  the signaling which in turn are coupled to cAMP
  signals
• This accounts for observed history of the
  wavefield abortive waves -gt fully developed
  spirals
• This naturally gives wave-breaking during weakly
  excitable epoch
• Specific predictions mutant non-spiraling
  strains, spiral coarsening, wavefield-resetting

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Wave-resetting simulation
M. Falcke H. Levine, PRL 80, 3875 (1998)
agrees with resetting experiment of Lee,
Goldstein and Cox, PRL (2001)
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Formation of streaming pattern
Collapse to the mound is not radially symmetric
Courtesy R. Kessin
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Streaming Instability

• Due to feedback between the signaling field
  guiding the cell motion and the cell density
• Requires that wave velocity increases with
  density confirmed experimentally!
• Cell-cell adhesion matters quantitatively, but
  not for getting the basic instability (verified
  by gene knockout experiments)
• Ongoing comparison of theory with mutant strain
  experiments (Parent et al)

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Experiments on 2d aggregates

• Development done
• with agar overlay
• 2d aggregates with
• several hundred cells
• form in 8-12 hours
• can freeze the system
• in this state

n.b. no long-range interaction
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Self-organized motion - a new schema!
rotation period 10 minutes
Bodenschatz lab
Loomis Lab Cornell Univ
UCSD-Biology 2d rotating mound of
Dicty annulus Dicty amoebae

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Formation of the vortex stateactive walker model
With soft core and no velocity averaging,
particles can rotate in opposite directions With
either effect, final state consists of unique
rotation Preliminary data indicate maximal
vortex size
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Liquid crystal analog
Kudrolli et al, 2003 Copper cylinders 6.2mm x .5
mm
Shaken up and down - tilt gives rise to a
horizontal velocity
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Close-up view of chemotaxis
Dictybase Website http//dictybase.org/index.html
Currently, we are pursuing a experimental/computat
ional approach to understanding how the cell
decides which way to move and now it implements
that decision mechanically.
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Neutrophil chasing a bacterium (Staphylococcus
aureus) Movie made by David Rogers, taken from
the website of Tom Stossel (expmed.bwh.harvard.edu
)
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What is the problem?

• How does a cell utilize the information available
  to it (binding of external chemical to 50,000
  receptors uniformly located on its membrane) to
  decide which way to move?
• Without gradients, cells send out multiple
  pseudopods, but eventually pick one direction to
  move - spontaneous (transient) polarization
• Cells can detect small gradients (few ), in a
  few seconds
• Cells are able to re-orient if the gradients
  change they remain flexible as they respond
• A conceptual model should address all these
  aspects
• Spatial information must be represented within
  the cell - this is a pattern formation problem!

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Some of the ideas

• LEGI (local-activation, global inhibition)
• Iglesias and Levchenko
• Temporal sensing (first hit model)
• Rappel, Loomis and HL
• Autocatalytic Turing pattern
• Meinhardt Narang, Subramanian and Lauffenburger
• Claim none of these models is sufficient

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LEGI

• Local activation and global inhibition
• explains adaptation to global stimulus
• versus steady gradient response
• Successes
• Reasonable match to data (esp. in Latrunculin
  treated cells)
• Can be extended to model more biological detail
• Shortcomings
• Gives linear amplification (x3 in Lat)- no
  polarity formation!
• Inconsistent with data (Postma et al) on
  spontaneous structures

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Parent/Devreotes - PH Activation Marker
Dicty lt---- Neutrophil ---gt

• PH domain localization occurs near the front (but
  not the back)
• of the cell after a few seconds first part of
  signal response

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Latrunculin-treated cells
Decision dynamics can be decoupled from actual
motility
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LEGI

• Local activation and global inhibition
• explains adaptation to global stimulus
• versus steady gradient response
• Successes
• Reasonable match to data (esp. in Latrunculin
  treated cells)
• Can be extended to model PTEN effects
• Shortcomings
• Gives linear amplification (x3 in Lat)- no
  polarity formation!
• Inconsistent with data (Postma et al) on
  post-adaptation structures

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LEGI - simplest version
Since A and I are both proportional to S in
steady-state, uniform S results in a transient
activation of E but eventual perfect adaptation.
With a non-uniform S, I gives average value and A
remains local - pattern in the effector E
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Phase Field Approach
Diffusion equation becomes
For stationary shapes second equation drops
out We can show that boundary conditions are
implemented correctly (in the limit of vanishing
interface thickness)
Kockelkorn, Rappel HL PRE (2003)
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Example of 3D code prolate spheriod in cube.
cAMP stimulus from one face of computational
boundary. Implemented on cubic regular grid
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LEGI

• Local activation and global inhibition
• explains adaptation to global stimulus
• versus steady gradient response
• Successes
• Reasonable match to data (esp. in Latrunculin
  treated cells)
• Can be extended to model more biological detail
• Shortcomings
• Gives linear amplification (x3 in Lat)- no
  polarity formation!
• Inconsistent with data (Postma et al) on
  spontaneous structures

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Why cant we post-amplify?

• To amplify the internal gradient, we need to set
  a threshold for some process
• Small gap between front and back at a variable
  PIP3 level
• Impossible to hit this target in a robust manner
  (N.B. y-axis)

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Temporal Sensing

• Cell responds in the short time period (lt 1sec ?)
  when concentration on back has not yet reached
  threshold
• Based on initial reports that PH-domain response
  is immediately asymmetric - these results have
  not held up in recent experiments
• Clear response to suddenly applied small
  gradients clear evidence that the back remains
  responsive
• This model made the starkest predictions and
  hence it was easiest to disprove - this is how
  conceptual modeling is supposed to operate!

Janetoupolis et al PNAS 2004
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Membrane dynamics
Quiescent
Inhibited
Activated
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Temporal Sensing

• Cell responds in the short time period (lt 1sec ?)
  when concentration on back has not yet reached
  threshold
• Based on initial reports that PH-domain response
  is immediately asymmetric - these results have
  not held up in recent experiments
• Clear response to suddenly applied small
  gradients clear evidence that the back remains
  responsive
• This model made the starkest predictions and
  hence it was easiest to disprove - this is how
  conceptual modeling is supposed to operate!

Janetoupolis et al PNAS 2004
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Microfluidics set-up (Bodenschatz lab)
Mixer
Output streams
0 200
500
microns
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Steady-state response
Cells chemotax in small gradients, even without
temporal information Thus, timing information
may be used, but cannot be the whole story L.
Song, Cornell
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Cell migration in a gradient
cAMP gradient flow rate 640 ?m/s 1h real time
8 sec movie
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Gradient Detection Data
Cornell group preprint (2005)
NB Detection of constant gradients if highly
inefficient, and so system may in fact be tuned
for temporal response
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Temporal Sensing

• Cell responds in the short time period (lt 1sec)
  when concentration on back has not yet reached
  threshold
• Based on initial reports that PH-domain response
  is immediately asymmetric - these results have
  not held up in recent experiments
• Clear response to suddenly applied small
  gradients clear evidence that the back remains
  responsive
• Doesnt explain spontaneous patterning
• This model made the starkest predictions and
  hence it was easiest to disprove - this is how
  conceptual modeling is supposed to operate!

Janetoupolis et al PNAS 2004
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Spontaneous PH-domain localization (Van Haastert
et al)

• Recent work has pointed out that there is not
  perfect adaptation to uniform stimulation
• Localized PH-domain patterns from in second phase
  of excitation

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Turing pattern

• Strong autocatalytic activation leads to a
  spontaneous pattern
• which is then oriented by the external gradient
• Successes
• Natural explanation for polarity formation
• Turing structures seen experimentally in
• (Postma, et al) spot-size is the same
• Shortcomings
• Cannot explain why polarization (e.g. in response
  to external gradients) is always uniaxial!
• Cells becomes inflexible to further stimuli (no
  evidence of self-poisoning postulated by
  Meinhardt, spots stable 1 min at least in the
  case with cAMP stimulation)
• It appears to us that the Turing instability is
  part of the story, but cannot operate directly
  from shallow gradient input

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A new module

• We have been investigating a new model in which
  the inhibitor acts via removing the activator. We
  balance the system (via negative feedback) such
  that the amount of (diffusing) inhibitor created
  by the signal roughly equals the amount of
  (local) activator.
• Large response followed by adaptation (not
  perfect) to global stimulus (like LEGI)
• With gradient surplus activator in front
  (follows external signal), surplus inhibitor in
  back (no response at all!)
• In principle, a single-pool global depletion
  model might work the same way (n.b. actin-based
  transport model for yeast)

Membrane-bound activator Diffusing inhibitor
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AAM model - simple version
But, this requires non-robust equality of the two
production rates for activator a and inhibitor b
- More complex version implements this balance
via feedback
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Robust version
Feedback loop (negative) ensures an approximate
balance of activation and inhibition. There is a
need to guard against extensive oscillations but
this seems manageable by choosing y lt1
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Activator Annihilation Module (AAM)

• Initial Response at both front and back - as seen
• Adaptation drives both down
• Steady response at the back is zero
  post-amplification is easy!
• Cell remains flexible to shifts

Levine and Rappel, in preparation
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Experiment
Levine and Rappel, unpublished
Janetopoulos et al 2004
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AAM output

• The activator then acts as input to a Turing
  system
• If A is very high, global response. If A is
• intermediate, Turing pattern if A is small,
• the Turing pattern is suppressed. In some
• cell lines, basal level may be already unstable
• Gives uni-axial polarization much more
  generically
• Explains connection between spontaneous pattern
  and gradient-determined pattern (Postma et al)
• Explains biphasic response of Ph-domain makers
• Cell retains flexibility because activator
  pattern can continue to follow external gradient.
  

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AAM output-gt Turing input
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Turing pattern without stimulation
Firtel lab (2005)
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SUMMARY

• Dictyostelium provides a wealth of
  pattern-formation challenges - progress can be
  made despite the overall complexity
• Current efforts focused on the intracellular
  signaling system underlying chemotaxis
• This problem will not be solved by biologists
  acting alone - they have a hard enough time
  dealing with purely temporal dynamics
• This problem will not be solved by physicists
  alone as it depends on some (but not all!) of the
  cell biology details