## How to implement temperature dependent rates

NMODL and the Channel Builder.
ted
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Joined: Wed May 18, 2005 4:50 pm
Location: Yale University School of Medicine
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### How to implement temperature dependent rates

On Wednesday, March 15, 2006, GTR asked
Is there any code or tutorial for temperature alignment using a Q10...?
First decide what value to use for Q10. If you don't have an experimentally-determined value, try to make a reasonable guess. As a very rough rule of thumb, Q10 is often assumed to be 3. However, this is truly only a crude guess. Chapter 7 in the book Kinetics for the Life Sciences, by H. Gutfreund (Cambridge University Press, 1995), has an eye-opening discussion of temperature effects on reaction rates. Table 7.1 on p.234 of this book (may still be available in paperback for ~\$30 and well worth it) lists the Q10s at ~20 deg C that correspond to various activation energies. Quoting from the bottom of that page, "in biological systems, the majority of reactions has a Q10 near 2. Those with lower Q10 are likely to be diffusion controlled and those with a larger Q10 involve entropy effects due to structural rearrangements."

For example, suppose Q10 really is 3, and that the experimentally observed rates were measured at 22 deg C. Add the following items to your code:

Code: Select all

``````PARAMETER {
Q10 = 3 (1)
Q10TEMP = 22 (degC)
. . .
ASSIGNED {
celsius (degC)
qt (1)
. . .
INITIAL
qt = Q10^((celsius-Q10TEMP)/10)
. . .
PROCEDURE rates(v (mV)) {
taum = temp_insensitive_expression_for_taum / qt
tauh = temp_insensitive_expression_for_tauh / qt
. . .
}``````
bosleyjr
Posts: 5
Joined: Mon Mar 11, 2013 6:11 pm

### Re: How to implement temperature dependent rates

This is a side topic, but given that the HH gating is dominated by Boltzmann-related forms, and the Boltzmann equation does depend upon temperature, should there be a temperature effect not only on the final tau values one gets, but also on the steady-state values (minf, hinf...).

Also, does the temperature of the cell affect it's equilibrium K, Na, and Ca concentrations, and thus the Nernstian voltages?

Perhaps there is a citation comparing gating and ePhys at 22° and 37°C, to see if there's a difference, but I couldn't find one. And perhaps this all lost in the noise/not relevant!?

Thanks!

Jim
ted
Posts: 5894
Joined: Wed May 18, 2005 4:50 pm
Location: Yale University School of Medicine
Contact:

### Re: How to implement temperature dependent rates

bosleyjr wrote:given that the HH gating is dominated by Boltzmann-related forms, and the Boltzmann equation does depend upon temperature, should there be a temperature effect not only on the final tau values one gets, but also on the steady-state values (minf, hinf...).
steady state value = alpha/(alpha+beta) where alpha and beta are the forward and backward rates for the gating state transitions. If alpha and beta have quite similar temperature sensitivity, steady state value is unaffected by temperature.
does the temperature of the cell affect it's equilibrium K, Na, and Ca concentrations, and thus the Nernstian voltages?
Temperature affects membrane transport processes so it could affect steady state concentrations. Temperature is an explicit term in the Nernst equation so it affects equilibrium potentials even if concentrations are unchanged. All this aside, most computational models do not include representations of ion accumulation or membrane transport because they are not relevant to the hypothesis that the model was designed to address.
Perhaps there is a citation comparing gating and ePhys at 22° and 37°C, to see if there's a difference, but I couldn't find one.
Try a PubMed search for
temperature channel gating
or
temperature change gating
Those hits barely scratch the surface. A Google search generates about 1e5 results; if even 1% of those are "real" you've got 1000 to look at.
bosleyjr
Posts: 5
Joined: Mon Mar 11, 2013 6:11 pm

### Re: How to implement temperature dependent rates

Thanks, Ted. Yes, there's a lot of literature to dig into. But your answer confirmed what I'm seeing in the literature: the temperature difference is mostly dealt with using Q10, if at all, probably for the reasons you mention.
Jim