Hello Forum members,
We have a model with BK/SK channels (KCa calcium-activated potassium channels) and if I understand correctly they are sensitive to the internal [Ca] in the section. However BK/SK are linked to different Ca channels e.g. https://www.jneurosci.org/content/24/40/8818.short or https://www.sciencedirect.com/science/a ... 7317309820. Is there a way to make nanodomains where we can simulate proximity of the KCa to specific Ca channel.
Thanks
Roy

This could be done in NMODL as a point process. Such an implementation might represent interactions within a "complex of elements" that consists of a cluster of P/Q channels, a nearby SER cistern, and a nearby cluster of BK channels. Done properly, this would allow any segment to have as many such complexes as you like. For example, within a single complex each element would be surrounded by its own local (cytoplasmic) volume that has its own local calcium concentration.

For the sake of illustration, let the three elements be called P, S, and B (for PQ cluster, SER, and BK cluster). Also define

volp == volume of cytoplasm adjacent to a PQ cluster, local concentration cap
vols == volume of cytoplasm adjacent to an SER cistern, local concentration cas
volb == volume of cytoplasm adjacent to a BK cluster, local concentration cab

Ignoring buffering for the moment, and assuming that equilbration among these compartments and between them and cytoplasm can be approximated by first order kinetics, we have

cap' = -icap / volp / (2*F) + (cas - cap)/taups + (cab - cap)/taubp + (cai - cap)/tauip
where F is Faraday's constant,
icap is the Ca current that enters the cell through this particular PQ cluster,
taups is the time constant for equilibration between volp and vols
taubp is the time constant for equilibration between volp and volb
tauip is the time constant for equilibration between volp and bulk cytoplasm

cas' = ca_efflux_from_SER / vols + (cap - cas)/taups + (cab - cas)/taubs + (cai - cas)/tauis
where taubs is the time constant for equilibration between volb and vols
tauis is the time constant for equilibration between vols and bulk cytoplasm

cab' = (cap - cab)/taubp + (cas - cab)/taubs + (cai - cab)/taubi
where
taubi is the time constant for equilibration between volb and bulk cytoplasm

You might be able to reduce the number of parameters by assuming that
volp = volb
taups = taubs
tauip = taubi

Instantaneous buffering could be implemented by changing the first term in cap's ODE to
-icap / (volp * k) / F
where k the total calcium/free calcium ratio i.e. if 90% of cai is buffered, then k would be 10.

Clearly an instance of this mechanism would have to
USEION ca READ cai
It should probably also contain an ODE description of the PQ channel so that it generates its own ip, and a description of CICR from the SER cistern. It should WRITE ica, and the numeric value that it writes should be calculated from the total flux from its three compartments to bulk cytoplasm
(volp*(cai - cap)/tauip + vols*(cai - cas)/tauis + volb*(cai - cab)/taubi)
(the current would be 2*F* the sum of the fluxes)
However, the second and third terms of this expression are "electrically silent", that is, they aren't produced by ca influx through the cell membrane, so the mechanism will have to generate a NONSPECIFIC_CURRENT i
to cancel out their effects on charge balance
i = -2*F*(vols*(cai - cas)/tauis + volb*(cai - cab)/taubi)

You'd also probably want the mechanism to calculate the BK current which means it must
USEION k READ ek WRITE ik

I may have left something out or made at least a typographical error, but maybe this is enough to get you started.

Hi Ted,
Thanks so much this will keep me busy for a while. Do you know of anyone who implemented something similar in the past? Would be nice to have a template to start from...

Can't say that I've seen anybody else do this, but it should work. Would start small--first just a cluster of P/Q channels with local ion accumulation that equilibrates with bulk cytoplasm, then add a cluster of BK channels with its own local volume that equilibrates with bulk cytoplasm, then couple the two local volumes. If that works add the cistern with its local volume, couple the cistern's local volume to the P/Q local volume, and finally couple the cistern's volume to the BK's volume.

You might first want to look at J Gen Physiol or J Physiol to see if someone has already published something that might be reimplementable with NMODL.

A couple of PubMed searches turned up many interesting papers; you might find this one to be helpful:

@Article{Montefusco2019,
author = {Montefusco, Francesco and Pedersen, Morten G},
title = {From local to global modeling for characterizing calcium dynamics and their effects on electrical activity and exocytosis in excitable cells},
journal = {International Journal of Molecular Sciences},
year = {2019},
volume = {20},
issue = {23},
doi = {10.3390/ijms20236057},
pmid = {31801305},
}

It cites other relevant papers e.g. (I knew Biophys J would have something about this):

Montefusco, F.; Tagliavini, A.; Ferrante, M.; Pedersen, M.G. Concise Whole-Cell Modeling of BK Ca-CaV Activity Controlled by Local Coupling and Stoichiometry. Biophys. J. 2017, 112, 2387–2396.

Williams, G.S.; Huertas, M.A.; Sobie, E.A.; Jafri, M.S.; Smith, G.D. A Probability Density Approach to
Modeling Local Control of Calcium-Induced Calcium Release in Cardiac Myocytes. Biophys. J. 2007,
92, 2311–2328.