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Calcium Oscillation in the Pollen Tube Growth Presented by: XIA,Fan03050130.
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Transcript of Calcium Oscillation in the Pollen Tube Growth Presented by: XIA,Fan03050130.
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Calcium Oscillation in Calcium Oscillation in the Pollen Tube Growththe Pollen Tube Growth
Presented by:Presented by:
XIA,FanXIA,Fan
0305013003050130
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OutlineOutline
IntroductionIntroduction SystemSystem Main Players and processMain Players and process
ModelingModeling AssumptionAssumption ModelingModeling Result and discussionResult and discussion
Further workFurther work
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IntroductionIntroduction
SystemSystem Pollen tubePollen tube
• Essential for plant Essential for plant reproductionreproduction
• Paradigm for the study Paradigm for the study of polar and of polar and oscillatoryoscillatory growthgrowth
OscillationOscillation• UniversalUniversal• Unclear mechanismUnclear mechanism
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IntroductionIntroduction Oscillations of other quantitiesOscillations of other quantities
[Ca[Ca2+2+]c at the tip]c at the tip extracellular Caextracellular Ca2+2+ influx influx F-actin at the tipF-actin at the tip
• NotesNotes• Same periodSame period• Different phaseDifferent phase
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CaCa2+2+
o Tip-focused gradientTip-focused gradient• A localized gradient of A localized gradient of
cytosolic free cacytosolic free ca2+2+ at their at their apex. There exist pumps apex. There exist pumps along the shank of the pollen along the shank of the pollen tube.tube.
o Tip-focused extracellular Tip-focused extracellular CaCa2+2+ influx influx• directed inward specifically directed inward specifically
at the tipat the tip• This influx is measured This influx is measured
outside the cell wall. The outside the cell wall. The influx that really entering the influx that really entering the membrane is approximately membrane is approximately 10% of the influx measured.10% of the influx measured.
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F-actinF-actino Ring in the subapical regionRing in the subapical region
• In the subapical region, an cortical In the subapical region, an cortical actin collar or ring is observed.actin collar or ring is observed.
o A highly dynamic form of F-A highly dynamic form of F-actin in the extreme apexactin in the extreme apex
• It rapidly appear in and disappear It rapidly appear in and disappear from the cortex of the extreme from the cortex of the extreme apex of pollen tubes, the expected apex of pollen tubes, the expected site of excytosis.site of excytosis.
• The F-actin at the tip refer to this The F-actin at the tip refer to this kind of actin.kind of actin.
o The actin collar in the subapical The actin collar in the subapical region alternates with the highly region alternates with the highly dynamic form in the apex. 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°0°F-actin F-actin
at the tipat the tip
180° growth rate
[Ca2+ ]c at the tip
270°270°extracellular extracellular CaCa2+2+ influx influx
There might exists small phase difference between these two.
Holdaway-Clarke et al. 1997
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ComplexityComplexity Many playersMany players Many processesMany processes
Gu et al. 2004
Monteiro et al. 2005
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Basic ProcessesBasic Processeso ExocytosisExocytosis
• Vesicle docking Vesicle docking and fusionand fusion
o Wall constructionWall constructiono EndocytosisEndocytosis
• Retrieval of the Retrieval of the membrane and membrane and recyclingrecycling
Samaj et al. 2004
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Calcium /calcium channelCalcium /calcium channel• [Ca[Ca2+2+]]cc plays an important plays an important
role inrole in dockingdocking and and secretionsecretion of wall materials.of wall materials.
• It helps to release the It helps to release the vesicles from the vesicles from the cytoskeleton by cytoskeleton by depolymerization of F-actindepolymerization of F-actin..
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ModelingModeling IdeaIdea
o There exists a microscopic loop.There exists a microscopic loop.o The macroscopic oscillation is the The macroscopic oscillation is the synchronizedsynchronized
behavior of the microscopic events.behavior of the microscopic events.• OscillationOscillation Synchronization Global signal Synchronization Global signal
calcium tip concentrationcalcium tip concentration• Tip concentration can be a good candidates due to fast Tip concentration can be a good candidates due to fast
diffusion.diffusion.
2 2
~
~ / ~ 3 / 0.01 ~ 1
x Dt
t x D ms s
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Microscopic storyMicroscopic story
Channel open
[Ca2+]c
increase
F-actin depolymerization
Vesicle docking and fusion
Channel close
[Ca2+]c decrease
Membrane
retrieval Wall
construction growth
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AssumptionAssumption
o The open of the channel is a The open of the channel is a stochastic processstochastic process, , the probability of which is negatively correlated the probability of which is negatively correlated to the concentration at the position.to the concentration at the position.• The dependence is not necessarily direct.The dependence is not necessarily direct.• The function form depends on the property of the
channel.• Two possible mechanism: voltage-gated and stretch-
activated.o After open, the channel has to After open, the channel has to restrest for some time for some time
before the next open.before the next open.• The resting time relates to the time for membrane The resting time relates to the time for membrane
retrieval.retrieval.
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TargetTarget
o Check the synchronized behavior of the Check the synchronized behavior of the ion channel.ion channel.• Oscillation of tip [Ca2+]c
• Oscillation of tip F-actin
o Other oscillations are not included:Other oscillations are not included:• Oscillation of growth rate• Oscillation of extracellular influx
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ParametersParameters
o Physical dimension of the tube Physical dimension of the tube 33μμm,3m,3μμm,40 m,40 μμmmo Diffusion constant Diffusion constant 0.01 0.01 μμmm2 2 msms-1-1
o Influx of one channel Influx of one channel 5*10-9 pmole ms-1(which corresponding to 500 ions each ms)
o Channel density 100μμmm-2-2
• This data is the channel density in the neuron.This data is the channel density in the neuron.• The extracellular Ca2+ influx is around 2*10The extracellular Ca2+ influx is around 2*10-11-11pmolepmoleμμmm-2-2 ms ms-1-1
• The influx of each channel is around 5*10The influx of each channel is around 5*10-9-9pmole mspmole ms-1-1
• Assume the open of the channel behaves like the firing of neuron cells, Assume the open of the channel behaves like the firing of neuron cells, i.e. open for 1ms and then close.i.e. open for 1ms and then close.
• From the above assumptions, we can calculate the resting time.From the above assumptions, we can calculate the resting time.o Resting time Resting time 25,000ms25,000ms 9
11
5*10 *10025000
2*10ms
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ModelingModeling
Probability FunctionProbability Functiono We use the tanh
function for voltage-gated channel.
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ModelingModeling
Sink: Corresponding to the pump in the shank
and the X sink in the cytosol.
diffusioninflux
periodic boundary condition
channels
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ModelingModeling
Modeling of the whole pollen tubeModeling of the whole pollen tubeo Too heavy computation loado Modification: considering the channel area
only
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ModelingModeling
Lattice model of the Lattice model of the channel area onlychannel area onlyo ParameterParameter
• Physical dimension: 3Physical dimension: 3μμm,3m,3μμm m • The others remain the sameThe others remain the same
o Free space approximationFree space approximation
2
3
( )2exp( )
44j i
ji ii
r rmC
DtDt
i3i3
i2i2jj
i1i1
channels
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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ModelingModeling
o How good is the free space approximationHow good is the free space approximation
3um x 3um
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.
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ModelingModeling
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ModelingModeling
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ModelingModeling
Conclusion:The free space approximation is not bad.
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ModelingModeling
o To reduce the To reduce the computation loadcomputation load• Remove the Remove the
channels’ effect channels’ effect after 300ms from its after 300ms from its open time.open time.
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ResultResult
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DiscussionDiscussion
DiscussionDiscussiono Synchronized behavior and oscillation of Synchronized behavior and oscillation of
[Ca[Ca2+2+]]tiptip
o The period of oscillation is determined by The period of oscillation is determined by channel density/ resting time.channel density/ resting time.
o The synchronized behavior results from the The synchronized behavior results from the same/little spread resting time.same/little spread resting time.
o Biological support is needed.Biological support is needed.
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DiscussionDiscussion
Shortcomings:Shortcomings:• Parameters and Parameters and
mechanisms are mechanisms are borrowed from other borrowed from other system.system.
• Steady stateSteady state
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Mathematical AnalysisMathematical Analysis
Equation:Equation:
Steady StateSteady State
1( ) ( )
1( ) ( )
BB B
R
BD
dnn N n P C
dt
dCC m N n P C
dt
nB: number of channels in blocked stateC: concentration in the tip region
N: total number of channelsTR: resting timeTD: diffuse time m: concentration increase due to one channel
* * *
* * *
1( ) ( ) 0
1( ) ( ) 0
B BR
BD
n N n P C
C m N n P C
* * *
* * *
1( ) ( ) 0
1( ) ( ) 0
B BR
BD
n N n P C
C m N n P C
(C* ,nB*) :steady state solution
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Stability AnalysisStability Analysis
Small Perturbation:Small Perturbation:*
* * * ' *
* * ' *
( ) 1( ) ( )( ( ) ( ) )
( ) 1( ) ( )( ( ) ( ) )
BB B
R
BD
d n nn n N n n P C P C C
dt
d C CC C m N n n P C P C C
dt
* * ' *
* * ' *
( ) 1( ( )) ( ) ( )
( ) 1( ) ( ( ) ( ))
BR
BD
d nP C n N n P C C
dt
d CmP C n m N n P C C
dt
* * ' *
'
'* * ' *
1( ( )) ( ) ( )
1( ) ( ) ( )
BR
BD
P C N n P Cn n
CC mP C m N n P C
simplification
Matrix form
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Stability AnalysisStability Analysis
* * ' * * ' * *1 1( ( ))( ( ) ( )) ( ) ( ) ( ) 0B B
R D
P C m N n P C N n P C mP C
Eigenfunction
2
* * ' *
* ' * *
0
1 1( ( )) ( ( ) ( ))
1 1 1 1( ( ) ( )) ( )
BR D
BR D R D
b c
b P C m N n P C
c m N n P C P C
b>0 & c>0
stable
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Phase DiagramPhase Diagram
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Further WorkFurther Work
More reliable parametersMore reliable parameters More biological informationMore biological information New variablesNew variables
Resting time (function of concentration)Resting time (function of concentration) Stretch (stretch-activated)Stretch (stretch-activated)
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AcknowledgementAcknowledgement
Supervisor: Supervisor: Prof. L.H. TangProf. L.H. Tang Observer: Observer: Prof. N.H. CheungProf. N.H. Cheung Group Members: Group Members: Tony,Tony, Chunhui CaiChunhui Cai, ,
Chao WangChao Wang, , Zhu YangZhu Yang..