Calcium Oscillation in the Pollen Tube Growth

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Calcium Oscillation in the Pollen Tube Growth

• Presented by
• XIA,Fan
• 03050130

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Outline

• Introduction
• System
• Main Players and process
• Modeling
• Assumption
• Modeling
• Result and discussion
• Further work

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Introduction

• System
• Pollen tube
• Essential for plant reproduction
• Paradigm for the study of polar and oscillatory
  growth
• Oscillation
• Universal
• Unclear mechanism

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Introduction

• Oscillations of other quantities
• Ca2c at the tip
• extracellular Ca2 influx
• F-actin at the tip
• Notes
• Same period
• Different phase

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Ca2

• Tip-focused gradient
• A localized gradient of cytosolic free ca2 at
  their apex. There exist pumps along the shank of
  the pollen tube.
• Tip-focused extracellular Ca2 influx
• directed inward specifically at the tip
• This influx is measured outside the cell wall.
  The influx that really entering the membrane is
  approximately 10 of the influx measured.

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F-actin

• Ring in the subapical region
• In the subapical region, an cortical actin collar
  or ring is observed.
• A highly dynamic form of F-actin in the extreme
  apex
• It rapidly appear in and disappear from the
  cortex of the extreme apex of pollen tubes, the
  expected site of excytosis.
• The F-actin at the tip refer to this kind of
  actin.
• The actin collar in the subapical region
  alternates with the highly dynamic form in the
  apex.

Monteiro et al. 2005
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Oscillation of growth rate and tip F-actin
Range 0.1 0.4 µm sec-1
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0 F-actin at the tip
270 extracellular Ca2 influx
180 growth rate Ca2 c at the tip
There might exists small phase difference between
these two.
Holdaway-Clarke et al. 1997
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• Complexity
• Many players
• Many processes

Gu et al. 2004
Monteiro et al. 2005
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• Basic Processes
• Exocytosis
• Vesicle docking and fusion
• Wall construction
• Endocytosis
• Retrieval of the membrane and recycling

Samaj et al. 2004
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• Calcium /calcium channel
• Ca2c plays an important role in docking and
  secretion of wall materials.
• It helps to release the vesicles from the
  cytoskeleton by depolymerization of F-actin.

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Modeling

• Idea
• There exists a microscopic loop.
• The macroscopic oscillation is the synchronized
  behavior of the microscopic events.
• Oscillation Synchronization Global signal
  calcium tip concentration
• Tip concentration can be a good candidates due to
  fast diffusion.

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Microscopic story
Channel open Ca2c increase F-actin depolymerization Vesicle docking and fusion Channel close Ca2c decrease
Membrane retrieval Wall construction growth Membrane retrieval Wall construction growth Membrane retrieval Wall construction growth
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Assumption

• The open of the channel is a stochastic process,
  the probability of which is negatively correlated
  to the concentration at the position.
• The dependence is not necessarily direct.
• The function form depends on the property of the
  channel.
• Two possible mechanism voltage-gated and
  stretch-activated.
• After open, the channel has to rest for some time
  before the next open.
• The resting time relates to the time for membrane
  retrieval.

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Target

• Check the synchronized behavior of the ion
  channel.
• Oscillation of tip Ca2c
• Oscillation of tip F-actin
• Other oscillations are not included
• Oscillation of growth rate
• Oscillation of extracellular influx

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Parameters

• Physical dimension of the tube 3µm,3µm,40 µm
• Diffusion constant 0.01 µm2 ms-1
• Influx of one channel 510-9 pmole ms-1(which
  corresponding to 500 ions each ms)
• Channel density 100µm-2
• This data is the channel density in the neuron.
• The extracellular Ca2 influx is around
  210-11pmoleµm-2 ms-1
• The influx of each channel is around 510-9pmole
  ms-1
• Assume the open of the channel behaves like the
  firing of neuron cells, i.e. open for 1ms and
  then close.
• From the above assumptions, we can calculate the
  resting time.
• Resting time 25,000ms

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Modeling

• Probability Function
• We use the tanh function for voltage-gated
  channel.

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Modeling
periodic boundary condition
channels
influx
diffusion
Sink Corresponding to the pump in the shank and
the X sink in the cytosol.
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Modeling

• Modeling of the whole pollen tube
• Too heavy computation load
• Modification considering the channel area only

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Modeling
channels

• Lattice model of the channel area only
• Parameter
• Physical dimension 3µm,3µm
• The others remain the same
• Free space approximation

i1
i2
j
i3
m amount of Ca deposit by one firing D
diffusion constant r position of the channel t
duration after the open of the channel
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Modeling

• How good is the free space approximation

Open one channel and examine the concentration
changes of the three channels in different
models pollen tube with sink, pollen tube
without sink and free space.
3um x 3um
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Modeling
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Modeling
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Modeling
Conclusion The free space approximation is not
bad.
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Modeling

• To reduce the computation load
• Remove the channels effect after 300ms from its
  open time.

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Result
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Discussion

• Discussion
• Synchronized behavior and oscillation of
  Ca2tip
• The period of oscillation is determined by
  channel density/ resting time.
• The synchronized behavior results from the
  same/little spread resting time.
• Biological support is needed.

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Discussion

• Shortcomings
• Parameters and mechanisms are borrowed from other
  system.
• Steady state

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Mathematical Analysis

• Equation
• Steady State

nB number of channels in blocked state C
concentration in the tip region
N total number of channels TR resting time TD
diffuse time m concentration increase due to
one channel
(C ,nB) steady state solution
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Stability Analysis

• Small Perturbation

simplification
Matrix form
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Stability Analysis
Eigenfunction
bgt0 cgt0 stable
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Phase Diagram
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Further Work

• More reliable parameters
• More biological information
• New variables
• Resting time (function of concentration)
• Stretch (stretch-activated)

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Acknowledgement

• Supervisor Prof. L.H. Tang
• Observer Prof. N.H. Cheung
• Group Members Tony, Chunhui Cai, Chao Wang, Zhu
  Yang.