Two questions - Can one design an experiment to tell if IP 3 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-Atanasova University of Auckland, NZ David Yule, Trevor Shuttleworth University of Rochester, USA Michael Sanderson University of Massachusetts Medical Center, USA Question 1: Dynamic Probing of Calcium Oscillations wetheads

Calcium pressure ER Mitochondria Ca 2+ (mM) Ca 2+ (50 nM) Ca 2+ -B (buffering) serca IPR RyR PM pumps I Ca leak Why? So cells can raise their internal Ca 2+ 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

Oscillations mediated by the IPR We know that the kinetics of Ca 2+ activation and inactivation of the IPR is sufficient (theoretically) to cause Ca 2+ oscillations. Result from sequential positive and negative feedback. But

IP 3 and Ca 2+ interactions

So, what causes the oscillations? Two basic hypotheses Constant IP 3 sets sensitivity Oscillations caused by Ca 2+ modulation of the IPR. IP 3 is NOT oscillating, or doesn’t have to. Oscillations caused by Ca 2+ modulation of IP 3 production and/or degradation IP 3 and Ca 2+ MUST oscillate together. 1 IP 3 AgonistPLCIPRCa 2+ 12

Does IP 3 even oscillate? Hirose et al, Science, Measured flourescence of a GFP -labeled PH domain of PLC  1. This binds both membrane-bound PIP 2 and diffusible IP 3, but IP 3 displaces PIP 2. Hence, higher [IP 3 ] causes translocation of the GFP to the cytoplasm, and an increase in cytoplasmic flourescence. So, yes. IP 3 oscillates in Madin-Darby canine kidney epithelial cells. But this doesn’t mean it must.

Are IP 3 oscillations necessary? I. Wakui et al, Nature, Tried to clamp [IP 3 ] by using a whole- cell patch pipette filled with a nonhydrolysable analogue of IP 3, IP 3 S 3 (inositol trisphosphorothioate). Oscillations continued as normal. Concluded that IP 3 oscillations are not necessary. (Oscillations were detected by measurement of the whole-cell Ca 2+ -sensitive Cl - current). This was in ACh-stimulated pancreatic acinar cells. We shall see these again in a minute.

Are IP 3 oscillations necessary? II. Dupont et al, FEBS Letts., Tried to remove Ca 2+ modulation of IP 3 production by increasing the rate of the pathway that doesn’t depend on Ca 2+. (In hepatocytes.) PLC IP 3 IP 4 IP 2 3-kinase 5-phosphatase Ca 2+ -dependent Not Ca 2+ -dependent Addition of exogeneous 5-phosphatase increases the rate of the red pathway. Add more agonist, oscillations come back and look the same. control

Difficulties. How do you tell if [IP 3 ] is clamped? How do you tell if most of the IP 3 metabolism is via a Ca 2+ - 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 J IPR J serca J pm J leak cell membrane This is a really crappy model which has since been changed. One really neat thing about our results is that it doesn’t seem to matter what expressions you use here.

Different flavours Each model can be constructed in two different flavours: 1.Where Ca 2+ oscillations occur for constant [IP 3 ]. 2. Where Ca 2+ oscillations occur only when [IP 3 ] 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 [IP 3 ] oscillation period An increase in IP 3 decreases the oscillation period. 1 constant IP 3 time (s) Add a pulse of IP 3 here, then let it decay away. Get a transient increase in frequency. Typical behaviour of such models

Dynamic behaviour 2 oscillating IP 3 time (s) Add a pulse of IP 3 here, then let it decay away. Get a phase shift. [Ca 2+ ] [IP 3 ] limit cycle oscillation IP 3 pulse phase delay Typical behaviour of these other models

Thus, we predict.... Constant IP 3 sets sensitivity Start oscillations by agonist application. Photorelease pulse of IP 3 Oscillations should speed up. Oscillations caused by Ca 2+ modulation of IP 3 production and/or degradation Start oscillations by agonist application Photorelease pulse of IP 3 Get an initial response to the pulse and then a phase delay, with the oscillations appearing with the same period as before. 12

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 IP 3 Measure whole-cell Ca 2+ -sensitive Cl - current by patch pipette. This detects (essentially) the apical concentration of Ca 2+.

Pancreatic acinar cell responses

Results IP 3 pulse gives a clear phase delay These oscillations rely on IP 3 oscillations together with the Ca 2+ oscillations Note how the period is long. This is consistent with the kinetics of IP 3 metabolism. This is in conflict with current dogma on the mechanism of Ca 2+ oscillations in pancreatic acinar cells. IP 3 pulses

Side Issue Note this funny initial behaviour upon agonist application. Oscillations on a decreasing baseline. Neato. Math nerds love this kind of thing. We also believe we know why this happens. That was going to be the topic of my talk. Basically, the cell is hosing out Ca 2+ during this initial period, and thus slowly modulating the oscillation properties. Analysis involves a 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 (From Mike Sanderson’s lab.)

Calcium oscillations in smooth muscle: II (From Mike Sanderson’s lab.)

Results IP 3 pulse gives a clear increase in frequency These oscillations occur at constant [IP 3 ]. Or, at least, oscillations in [IP 3 ] are unimportant and not necessary. Note how the period is short. This is consistent with the kinetics of Ca 2+ modulation of the IP 3 receptor. IP 3 pulse here

Conclusions A relatively simple experiment can be used to determine the dynamic properties of Ca 2+ 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’t do 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 IP 3 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 Ca 2+ 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 Ca 2+ pathways. Effects of phosphorylation of the IPR. Control of smooth muscle contraction by Ca 2+ oscillations. Control of saliva secretion in parotid acinar cells by Ca 2+ 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: coupled calcium oscillators a b c Real image Apical Region Mitochondrial buffer Basal 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 Ca 2+ and IP 3 for the coordination (or lack thereof) of the intercellular waves? FEM mesh Three spatially distributed coupled oscillators

A point model

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 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 uncoupled cells coupled cells Quite different behaviour. We now need to go back and inspect the data more thoroughly, at higher time resolution, to see which kind of behaviour is seen. Will we ever do this ? I’m not sure.