1. Calcium Oscillation in the Pollen Tube Growth Presented by: XIA,Fan03050130

2. Outline  Introduction  System  Main Players and process  Modeling  Assumption  Modeling  Result and discussion  Further work

3. Introduction  System  Pollen tube Essential for plant reproduction Essential for plant reproduction Paradigm for the study of polar and oscillatory growth Paradigm for the study of polar and oscillatory growth  Oscillation Universal Universal Unclear mechanism Unclear mechanism

4. Introduction  Oscillations of other quantities  [Ca 2+ ]c at the tip  extracellular Ca 2+ influx  F-actin at the tip Notes Notes Same period Same period Different phase Different phase

5. Ca 2+ o Tip-focused gradient A localized gradient of cytosolic free ca 2+ at their apex. There exist pumps along the shank of the pollen tube. A localized gradient of cytosolic free ca 2+ at their apex. There exist pumps along the shank of the pollen tube. o Tip-focused extracellular Ca 2+ influx directed inward specifically at the tip 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. This influx is measured outside the cell wall. The influx that really entering the membrane is approximately 10% of the influx measured.

6. F-actin o Ring in the subapical region In the subapical region, an cortical actin collar or ring is observed. In the subapical region, an cortical actin collar or ring is observed. o 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. 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 F-actin at the tip refer to this kind of actin. o The actin collar in the subapical region alternates with the highly dynamic form in the apex. Monteiro et al. 2005

7. Oscillation of growth rate and tip F-actin Range: 0.1 ~ 0.4 μm sec-1

8. 0°F-actin at the tip 180° growth rate [Ca2+ ]c at the tip 270° extracellular Ca 2+ influx There might exists small phase difference between these two. Holdaway-Clarke et al. 1997

9.  Complexity  Many players  Many processes Gu et al. 2004 Monteiro et al. 2005

10.  Basic Processes o Exocytosis Vesicle docking and fusion Vesicle docking and fusion o Wall construction o Endocytosis Retrieval of the membrane and recycling Retrieval of the membrane and recycling Samaj et al. 2004

11.  Calcium /calcium channel [Ca 2+ ] c plays an important role in docking and secretion of wall materials. [Ca 2+ ] c 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. It helps to release the vesicles from the cytoskeleton by depolymerization of F-actin.

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

13. Microscopic story Channel open [Ca 2+ ] c increase F-actin depolymerization Vesicle docking and fusion Channel close [Ca2+]c decrease Membrane retrieval Wall construction growth

14. Assumption o 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 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 rest for some time before the next open. The resting time relates to the time for membrane retrieval. The resting time relates to the time for membrane retrieval.

15. Target o Check the synchronized behavior of the ion channel. Oscillation of tip [Ca 2+ ] c Oscillation of tip F-actin o Other oscillations are not included: Oscillation of growth rate Oscillation of extracellular influx

16. Parameters o Physical dimension of the tube 3μm,3μm,40 μm o Diffusion constant 0.01 μm 2 ms -1 o Influx of one channel o Influx of one channel 5*10 -9 pmole ms -1 (which corresponding to 500 ions each ms) o μm -2 o Channel density 100μm -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*10 -11 pmoleμm -2 ms -1 The extracellular Ca2+ influx is around 2*10 -11 pmoleμm -2 ms -1 The influx of each channel is around 5*10 -9 pmole ms -1 The influx of each channel is around 5*10 -9 pmole ms -1 Assume the open of the channel behaves like the firing of neuron cells, i.e. open for 1ms and then close. 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. From the above assumptions, we can calculate the resting time. o Resting time 25,000ms

17. Modeling  Probability Function o o We use the tanh function for voltage- gated channel.

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

19. Modeling  Modeling of the whole pollen tube o o Too heavy computation load o o Modification: considering the channel area only

20. Modeling  Lattice model of the channel area only o Parameter Physical dimension: 3μm,3μm Physical dimension: 3μm,3μm The others remain the same The others remain the same o Free space approximation i3 i2j i1 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

21. Modeling o How 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.

22. Modeling

23. Modeling

24. Modeling Conclusion: The free space approximation is not bad.

25. Modeling o To reduce the computation load Remove the channels’ effect after 300ms from its open time. Remove the channels’ effect after 300ms from its open time.

26. Result

32. Discussion  Discussion o Synchronized behavior and oscillation of [Ca 2+ ] tip o The period of oscillation is determined by channel density/ resting time. o The synchronized behavior results from the same/little spread resting time. o Biological support is needed.

33. Discussion  Shortcomings: Parameters and mechanisms are borrowed from other system. Parameters and mechanisms are borrowed from other system. Steady state Steady state

34. Mathematical Analysis  Equation:  Steady State n B : number of channels in blocked state C: concentration in the tip region N: total number of channels T R : resting time T D : diffuse time m: concentration increase due to one channel (C*,n B *) :steady state solution

35. Stability Analysis  Small Perturbation: simplification Matrix form

36. Stability Analysis Eigenfunction b>0 & c>0 stable

37. Phase Diagram

38. Further Work  More reliable parameters  More biological information  New variables  Resting time (function of concentration)  Stretch (stretch-activated)

39. Acknowledgement  Supervisor: Prof. L.H. Tang  Observer: Prof. N.H. Cheung  Group Members: Tony, Chunhui Cai, Chao Wang, Zhu Yang.