Functional response for oxygen

[Philipp-Neubauer]

... could also be formulated with the same function as the uptake of carbon: f_O2 = V_O C_O/(V_O C_O + H_O), where V_O is the “search rate” for oxygen: gamma_O*w^n, C_O is the concentration of oxygen in the environment, and H_O = h_O w^n is the maximum uptake rate of oxygen.

[Philipp-Neubauer]

This is the part of the model that I am the most unsure about: I chose the current formulation to have a parameter analogous to the P50 of the oxygen–haemoglobin dissociation curve, i.e., a parameter that is the oxygen availability at which only 50% of the maximum/asymptotic O_2 can be delivered for aerobic metabolism in the various fish tissues.

The attached book chapter from fish physiology has a relatively good list of equations for the different steps involved in oxygen transport from 'inhaled' water all the way to the tissues. The f_{O_2} integrates these processes into a simple functional form that goes straight from ambient O_2 to O_2 available in the tissues.

One could mention that any of these steps could be modeled separately - but we probably won't be able to parametrise the whole pathway for any one species, so it's a bit pointless. Any other formulation is a bit arbitrary and hard to parametrise I think - happy to use any kind of model that makes sense and that we can parameterise in some way.

[Philipp-Neubauer]

After some more reading and some more thinking, I've come to the conclusion that the current f(O2) formulation is probably insufficient since it does not include any temperature effect on oxygen supply.

I seems that the heart-rate is strongly temperature dependant, such that supply increases with temp, until the point when the heart beats too fast to fill up correctly, such that the stroke volume decreases and oxygen delivery is compromised.

There are some good studies out there to parametrise such a curve, so I might just give that a go...

[Philipp-Neubauer]

E.g. experimental papers by Guy Claireaux et al

Lefrançois and Claireaux - 2003 - Influence of ambient oxygenation and temperature o.pdf Claireaux and Lagardère - 1999 - Influence of temperature, oxygen and salinity on t.pdf

[Kenhasteandersen]

Hi Phil,

You might be right, but I don’t quite understand what you mean. I imagine that the heart rate is determined by the tissue’s demand for oxygen. If we have the temperature effect on demand, then that should already be covered. Or is there something I miss in that?

Clearly, the demand can be so large that the heart cannot keep up, and if that demand is due to high temperature the failure of the heart is part of the story with the entire system failing when temperature exceeds the individuals temperature niche.

Ken

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Ken H. Andersen, http://ken.haste.dk, twitter: @69kno Professor in theoretical marine ecology, head of section, and deputy director of Centre for Ocean Life http://www.oceanlifecentre.dk

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On 15 Sep 2016, at 2:45 , Philipp Neubauer notifications@github.com<mailto:notifications@github.com> wrote:

After some more reading and some more thinking, I've come to the conclusion that the current f(O2) formulation is probably insufficient since it does not include any temperature effect on oxygen supply.

I seems that the heart-rate is strongly temperature dependant, such that supply increases with temp, until the point when the heart beats too fast to fill up correctly, such that the stroke volume decreases and oxygen delivery is compromised.

There are some good studies out there to parametrise such a curve, so I might just give that a go...

— You are receiving this because you are subscribed to this thread. Reply to this email directly, view it on GitHubhttps://github.com/Philipp-Neubauer/AdaptiveActivityModel/issues/5#issuecomment-247200866, or mute the threadhttps://github.com/notifications/unsubscribe-auth/AMp1gfXFoTH6YTgGAbTeXLga5cN_ehuwks5qqJUlgaJpZM4JvFLp.

[Philipp-Neubauer]

I imagine that the heart rate is determined by the tissue’s demand for oxygen. If we have the temperature effect on demand, then that should already be covered.

That's what I thought too, but I couldn't quite line up our formulation with the experimental work that I was looking at to parametrise the model - most experiments suggest a temperature effect on supply also (perhaps stronger so than the one for O2 demand).

For example, in Lefrançois and Claireaux 2003 (link above), fish were chased to exhaustion at different temperatures and O2 regimes. At constant O2 and increasing temperature, the O2 consumption at exhaustion (i.e., when the metabolic scope is exhausted) seems to increase to an optimum. This increase is faster than that of standard metabolism, thus leading to a bell-shaped (or sometimes, peaked) curve for metabolic scope with temperature. This seems to fairly universally accepted (at least from what I've read...).

However, in our model, the maximum O2 was so far determined by f(02), which was independent of temperature. In that scenario, the metabolic scope can only ever decrease if standard metabolism increases with temperature.

Not sure if the heart rate is the only explanation, but the paper above does measure heart rate, and seems to suggest that while the heart rate is essentially driven by demand, there is an upper limit to the heart rate that increases with temperature. At the upper end of the temperature axis, something else must limit the scope (because the heart rate keeps increasing), that may be a lower affinity by hemoglobin for oxygen or the lower efficiency of the heart at extreme tachycardia - but that's just speculation.

I hope this makes a bit more sense now...I'm just trying out a different formulation that induces the bell shaped curve with temperature (i.e, have a temperature optimum in O2 supply) to see what difference it makes over-all. It will probably lead to oxygen effects kicking in later, but more severely...I'll send you some results tomorrow.

[Philipp-Neubauer]

I have deployed an alternative version of the app, which includes a re-parameterization of the oxygen supply. I had some trouble getting to grips with the units, and am tentatively sure that I got there in the end...possibly. The resulting curves for the scope (dashed line on the P_O2 plot) and resulting oxygen limitation look more like the experimental curves I am used to seeing.

An alternative explanation for dome-shaped O2 availability that is not dependant on heart rate is given in Verberk et al. - 2011 - Oxygen supply in aquatic ectotherms partial press.pdf. They argue that O2 supply increases with temperature due to higher diffusivity at high temp - which more than compensates for lower solubility. As I've mentioned before, the problem I see with that explanation is that in fish, it seems the gill membrane is the rate limiting factor, not the water O2 diffusivity - and I am not sure if that changes much with temperature (although it might compensate to some degree, I just don't know..).

[Philipp-Neubauer]

PS essentially the new formulation just over-lays a temperature dependence on the initial saturating function...

[Kenhasteandersen]

Have you added the new formulation in the note? I need to see the equations to really understand what you have done.

Ken

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Ken H. Andersen, http://ken.haste.dk, twitter: @69kno Professor in theoretical marine ecology, head of section, and deputy director of Centre for Ocean Life http://www.oceanlifecentre.dk

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On 19 Sep 2016, at 5:41 , Philipp Neubauer notifications@github.com<mailto:notifications@github.com> wrote:

I have deployed an alternative version of the apphttps://dragonfly-science.shinyapps.io/Shiny_app_alt, which includes a re-parameterization of the oxygen supply. I had some trouble getting to grips with the units, and am tentatively sure that I got there in the end...possibly. The resulting curves for the scope (dashed line on the P_O2 plot) and resulting oxygen limitation look more like the experimental curves I am used to seeing.

An alternative explanation for dome-shaped O2 availability that is not dependant on heart rate is given in Verberk et al. - 2011 - Oxygen supply in aquatic ectotherms partial press.pdfhttps://github.com/Philipp-Neubauer/AdaptiveActivityModel/files/479195/Verberk.et.al.-.2011.-.Oxygen.supply.in.aquatic.ectotherms.partial.press.pdf. They argue that O2 supply increases with temperature due to higher diffusivity at high temp - which more than compensates for lower solubility. As I've mentioned before, the problem I see with that explanation is that in fish, it seems the gill membrane is the rate limiting factor, not the water O2 diffusivity - and I am not sure if that changes much with temperature (although it might compensate to some degree, I just don't know..).

— You are receiving this because you commented. Reply to this email directly, view it on GitHubhttps://github.com/Philipp-Neubauer/AdaptiveActivityModel/issues/5#issuecomment-247906593, or mute the threadhttps://github.com/notifications/unsubscribe-auth/AMp1gRtUkBM9DLT8rhdrOkiPOp1esdRgks5qrgR2gaJpZM4JvFLp.

[Philipp-Neubauer]

I just pushed the code and updates to draft.tex (now .rnw to generate figures in the code) to a new branch - latest changes are here: 2db50a80751b5718cd82975190fbcf4aa866ecce

Have a look at the figure and formula, hope that makes it easier to understand.