Two questions

- Can one design an experiment to tell if IP3 has to oscillate in order to get an observed calcium oscillation?

- How do spatially distributed coupled oscillators behave?

For wetheads

For nerds

James Sneyd, Krasimira Tsaneva-AtanasovaUniversity of Auckland, NZ

David Yule, Trevor ShuttleworthUniversity of Rochester, USA

Michael SandersonUniversity of Massachusetts Medical Center, USA

Question 1: Dynamic Probing of Calcium Oscillations

wetheads

Calcium pressure

ER

Mitochondria

Ca2+ (mM)

Ca2+ (50 nM)

Ca2+-B(buffering)serca

IPR

RyR

PM pumps

ICa

leak

Why? So cells can raise their internal Ca2+ quickly, and then decrease it quickly.

This is absolutely not a leak. Very naughty to call it a leak. It is a carefully controlled and modulated calcium influx.

A: Hepatocytes

B: Rat parotid gland

C: Gonadotropes

D: Hamster eggs (post-fertilisation)

E, F: Insulinoma cells

Typical Calcium Oscillations

It is believed that the signal is carried by the frequency of the oscillation.

Really mean nM, not nm

Summary of calcium homeostasis

_

J pm

J in

J IPR

J RyR

J serca

mitochondriaJ uni

J mito

bufferedCa2+

Ca2+J on

J off

Ca2+

Ca2+

SOC, Icrac, AAOC

bufferedCa2+

J on,e

J off,e

Oscillations mediated by the IPR

We know that the kinetics of Ca2+ activation and inactivation of the IPR is sufficient (theoretically) to cause Ca2+ oscillations.

Result from sequential positive and negative feedback.

But.......

IP3 and Ca2+ interactions

_

Ca2+

Ca2+

G R

_

So, what causes the oscillations?Two basic hypotheses

Constant IP3 sets sensitivity

Oscillations caused byCa2+ modulation of the IPR.IP3 is NOT oscillating, ordoesn’t have to.

Oscillations caused by Ca2+ modulation of IP3 production and/or degradation

IP3 and Ca2+ MUST oscillate together.

1

IP3Agonist PLC IPR Ca2+

1 2

Does IP3 even oscillate?

Hirose et al, Science, 1999.

Measured flourescence of a GFP -labeled PH domain of PLC1. This binds both membrane-bound PIP2 and diffusible IP3, but IP3 displaces PIP2. Hence, higher [IP3] causes translocation of the GFP to the cytoplasm, and an increase in cytoplasmic flourescence.

So, yes. IP3 oscillates in Madin-Darby canine kidney epithelial cells.But this doesn’t mean it must.

Are IP3 oscillations necessary? I.

Wakui et al, Nature, 1989. Tried to clamp [IP3] by using a whole-cell patch pipette filled with a nonhydrolysable analogue of IP3, IP3S3 (inositol trisphosphorothioate). Oscillations continued as normal. Concluded that IP3 oscillations are not necessary. (Oscillations were detected by measurement of the whole-cell Ca2+-sensitive Cl- current).

This was in ACh-stimulated pancreatic acinar cells. We shall see these again in a minute.

Are IP3 oscillations necessary? II.

Dupont et al, FEBS Letts., 2003. Tried to remove Ca2+ modulation of IP3 production by increasing the rate of the pathway that doesn’t depend on Ca2+. (In hepatocytes.)

PLC IP3

IP4

IP2

3-kinase

5-phosphatase

Ca2+-dependent

Not Ca2+-dependentAddition of exogeneous 5-phosphataseincreases the rate of the red pathway. Add more agonist, oscillations come backand look the same.

control

Difficulties.

• How do you tell if [IP3] is clamped?

• How do you tell if most of the IP3 metabolism is via a Ca2+-independent pathway?

• How can you tell what the situation is in vivo?

• Basically, how can you tell if you’ve done what you think you’ve done, or if the cell does what you think it’s doing (if you haven’t done what you thought you did)?

• Tricky. Hmmmmm...... Call in the math nerds and sound the trumpets.

Constructing models

€

Jserca =Vsc

Ks + c⋅

1

ce, Jpm =

Vmc2

Km2 + c 2

JIPR = k f (0.1O+ 0.9A)4 + constant

Jleak =α 1 +α 2p

JIPRJserca

Jpm

Jleak

cell membrane

€

dc

dt= JIPR (ce − c) − Jserca + δ(Jleak − Jpm )

dcedt

= γ(Jserca − JIPR (ce − c))

dR

dt=L ,

dO

dt=L

+ other receptor equations

€

p = [IP3]

c = [Ca2+]

€

ce = [Ca2+]ER

This is a really crappy modelwhich has since been changed.

One really neat thing about our resultsis that it doesn’t seem to matter what expressions you use here.

Different flavoursEach model can be constructed in two different

flavours:

1. Where Ca2+ oscillations occur for constant [IP3].

2. Where Ca2+ oscillations occur only when [IP3] oscillates also.

So we can investigate the differences caused only by the different dynamic assumptions, not the other model details. But I won’t show the equations for each flavour. We’ve done this with a pile of different models and they all say the same thing.

Dynamic behaviour

[IP3]

osc

illa

tion

per

iod

An increase in IP3 decreasesthe oscillation period.

1constant IP3

time (s)

Add a pulse of IP3 here,then let it decay away.Get a transient increasein frequency.

Typical behaviourof such models

Dynamic behaviour 2oscillating IP3

time (s)

Add a pulse of IP3 here,then let it decay away.Get a phase shift.

[Ca2+]

[IP3]

limit cycle oscillation

IP3 p

ulse

phase delay

Typical behaviourof these other models

Thus, we predict....

Constant IP3 sets sensitivity

Start oscillations by agonist application.

Photorelease pulse of IP3

Oscillations should speed up.

Oscillations caused by Ca2+ modulation of IP3 production and/or degradation

Start oscillations by agonist application

Photorelease pulse of IP3

Get an initial response to the pulse and then a phase delay, with the oscillations appearing with the same period as before.

1 2

Pancreatic acinar cells

Typical secretory epithelial cells are pancreatic acinar cells, parotid acinar cells, avian nasal gland cells, etc.

Mouse pancreatic acinar cells

The methods slide

• Blend mouse• Add a pinch of salt• Get pancreatic cells• Add photoreleasable IP3

• Measure whole-cell Ca2+-sensitive Cl- current by patch pipette.• This detects (essentially) the apical concentration of Ca2+.

Pancreatic acinar cell responsesQuickTime™ and aMicrosoft Video 1 decompressorare needed to see this picture.

ResultsIP3 pulse gives a clear phase delay

These oscillations rely on IP3 oscillations together with the Ca2+ oscillations

Note how the period is long. This is consistent with the kinetics of IP3 metabolism.

This is in conflict with current dogma on the mechanism of Ca2+ oscillations in pancreatic acinar cells.

IP3 pulses

Side IssueNote this funny initial behaviourupon agonist application.

Oscillations on a decreasingbaseline. Neato. Math nerdslove this kind of thing.

We also believe we know why this happens. That was going tobe the topic of my talk.

Basically, the cell is hosing out Ca2+ during this initial period, andthus slowly modulating the oscillation properties. Analysis involvesa two time-scale bifurcation analysis.

Mouse pulmonary vascular smooth muscle

Mouse

• Cut mouse up.

• Needle in trachea, blow up lungs.

• Needle in pulmonary artery thingy from the heart. Fill pulmonary arteries up with jello.

• Pump the airways full of agar.

• Blow gently to get the agar out of the major pulmonary arteries, but leave it in all the alveoli.

• Take out lung. Freeze and slice.

• Melt away the jello.

• Hey presto. A lung slice. Garnish with parsley and serve.

To a math nerd, mice are the same as rats anyway

Calcium oscillations in smooth muscle: I

QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.

3.0

2.5

2.0

1.5

1.0

Flourescence ratio

300250200150100500

time (s)5HT

(From Mike Sanderson’s lab.)

Calcium oscillations in smooth muscle: II

3.0

2.5

2.0

1.5

1.0

Flourescence ratio

300250200150100500

time (s)5HT

(From Mike Sanderson’s lab.)

QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.

ResultsIP3 pulse gives a clear increase in frequency

These oscillations occur at constant [IP3]. Or, at least, oscillations in [IP3] are unimportant and not necessary.

Note how the period is short. This is consistent with the kinetics of Ca2+ modulation of the IP3 receptor.

IP3 pulse here

Conclusions

• A relatively simple experiment can be used to determine the dynamic properties of Ca2+ oscillations in vivo.

• This experiment doesn’t actually tell us that the specific mechanism is, it just tells us which class of oscillations we are looking at.

• An easy way to resolve one of the current major questions in the field.

• Couldn’t be done without mathematics. Even better.

Well, they’re easy for me because I don’tdo them. The wetheads say they aren’t all that easy, but I don’t believe them.

More work needed

• Have to do that GFP experiment thing in pancreatic acinar cells. We predict that IP3 has to be oscillating. This isn’t known. But that dye is bloody expensive and I ain’t paying for it. Well, actually, I am now because we just got an NIH grant. So a big thank you to George W. We love you. (Just kidding, we don’t really.)

• Mike has some of that dye but we can’t load into his lung slices. It’s also difficult to get into pancreatic acinar cells. Not sure what to do, actually. Maybe a cultured cell line?

• Do the full dose responses and controls with Ca2+ release. (Already done most of this.)

• Does the oscillatory mechanism change with time? A fascinating possibility.

• Most importantly, do the experiment in other cell types, especially hepatocytes.

Future directions

• Interaction of cAMP and Ca2+ pathways. Effects of phosphorylation of the IPR.

• Control of smooth muscle contraction by Ca2+ oscillations.

• Control of saliva secretion in parotid acinar cells by Ca2+ oscillations.

• How important are stochastic effects?

• How important is the detailed model of the IPR? Or the RyR?

And all of these questions will need detailed modeling (in conjunction with experimental work) to understand the answers. Many years of fun ahead.

Question 2: coupledcalcium oscillators

a

bc

Real imageApical Region

Mitochondrial bufferBasal Region

• Two dimensional model; no flux boundary conditions are applied on the external borders of each cell and the cells are connected by flux BC applied on the internal borders.

• Question: How important is intercellular diffusion of Ca2+ and IP3 for the coordination (or lack thereof) of the intercellular waves?

FEM mesh

Three spatially distributedcoupled oscillators

A point model

1

2 3

A B

ce

c

JIPR

JRyR

Jserca

Jpm

Jin

Bifurcations of the point model

Typical solutions of the point model

But so what?

The point model seems to be a crappy guide to the behaviour of the distributed model.

So, what do we do now?

The End

Identical cells

QuickTime™ and aVideo decompressor

are needed to see this picture.

Falls into the 2/1 pattern, where two go together with the third slightly out of phase. This seems to be a lot more stable.

Simulations of an 8-cell acinus

QuickTime™ and aNone decompressor

are needed to see this picture.

QuickTime™ and aNone decompressor

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uncoupled cells coupled cells

Quite different behaviour. We now need to go back and inspect thedata more thoroughly, at higher time resolution, to see which kindof behaviour is seen. Will we ever do this.......? I’m not sure.