Setting the basal level for Intracellular Calcium Concentrat

[auatai]

Sir,

I wanted your opinion on the following. If I want to calculate the depletion of ca in a fixed extracellular volume and i have inserted a L type Ca channel and the cdp mechanism in the section, then, can i proceed in a way similar to that outlined in the thread on Extracellular K accumulation?

[Darshan]

Hi,

But if one wants to leave the rate constants unchanged and use the membrane's ion channels plus a "constant ca source" to force resting cai to a desired value, the question is how to find the required intensity of the "constant ca source."

I'm going to have to think about this some more.

I have a similar doubt of setting the basal cai concentration without changing the pump parameters and setting using a value constant ca source. I have pumps, buffers and intracellular mechanisms influx and efflux mechanisms in the model. I found one initialization strategy for pump here: https://senselab.med.yale.edu/ModelDB/S ... 00/cdp.mod . But the model of pump is different here: ca[0] <-> sump . This strategy makes a threshold for pump activity. But, I cannot get a desired slow ca transient behavior from this model and hence not using it. Or is it possible to get transients decaying in seconds using this model (only the 'gamma' and 'cath' can be changed here).

Can a threshold be set for the model of the kind:
cai+ pump <-> capump
capump <-> cao + pump

?
I have been trying for a while to fit the Kf and kb parameters for the above model. Can you suggest me a method to look for these parameters.

Thanks,
Darshan

[ted]

Models that involve ion accumulation can pose difficult challenges for initialization and ensuring balance in the resting state. Special implementation-specific strategies are often required.

The ion accumulation mechanism you mention is quite complex. There is no way to just look at the code and answer the question

is it possible to get transients decaying in seconds using this model

--computational experiments would be necessary to develop some intuition about what the model can do. Either that, or one would have to try to use nonlinear dynamical analysis to predict the behavior of the model.

Can a threshold be set for the model of the kind:
cai+ pump <-> capump
capump <-> cao + pump

Yes, although it seems like a hack. Fink et al. did it by using the Heaviside function (unit step function) to control whether the forward and backward rates were 0 or nonzero. The same thing could be done to control the forward and/or backward rate of either or both of the reactions in a two-stage scheme. My intuition doesn't tell me that this would produce the effect you want.

I have been trying for a while to fit the Kf and kb parameters for the above model. Can you suggest me a method to look for these parameters.

You could try using NEURON's MultipleRunFitter. For links to tutorials, see the thread
MRF to explore parameter space viewtopic.php?f=23&t=3480
in the NEURON Forum.

[Darshan]

Thank you Ted.

I will do some computational analysis of the model to understand the model better. Will also try the MultipleRunFitter to get a good parameter fit.

Regards,
Darshan

[ted]

If all you need is slow decay of cai, even a simple first-order ODE representation of calcium transport, with the proper time constant, should be enough. If you're using MSWin, look in ca:\nrn\examples\nrniv\nmodl for some off-the-shelf examples like capmp (omits buffering) and cabpmp (radial diffusion of free internal ca, two-stage pump, buffering). If you're using OS X or Linux, you'll want to get the gzipped tar source code, expand it, then look for the examples/nrniv/nmodl subdirectory. I'd suggest using cabpmp.mod; equilibration rate will depend on section surface/volume ratio, pump0 (pump density), and the c2 and c3 rate constants. I'd vary pump0 and leave c2 and c3 alone. Make sure that beta (ratio of bound to free intracellular ca) is appropriate for your cell type.

[Darshan]

Hi Ted,

As you suggested, I am using the cabpump.mod file. Needed one clarification on the factor (1+beta) in the COMPARTMENT statement. Is this factor used to take into account the rapid buffer approximation? I read about the theory in the book "Principles of Computational Modelling in Neuroscience" by Steratt et al. in which there is an equation: d[Ca]/dt = JCa/(1+beta) where JCa is the flux of the calcium coming into the cell.

I also wanted to introduce LONGITUDINAL_DIFFUSION into the model for which I added the following line to the mod file:

Code: Select all

LONGITUDINAL_DIFFUSION j, (1+beta)*DCa*diam*diam*vol[j] {ca}

But on checking the units with modlunit, it gives me an error:

Code: Select all

1-18 m3: With LONGITUDINAL_DIFFUSION the compartment volume must be measured in micron3/micron (1-12 m2)

Here, diam is in um, DCa is in um2/ms. So the units of the flux_expression is um4/ms. Even tried dividing and multiplying 1(um) to the expression but was not able to resolve the unit inconsistency. Any suggestions on this?

Thanks,
Darshan

[hines]

Yes. "With LONGDITUDINAL_DIFFUSION the compartment volume
must be measured in micron3/micron" means the COMPARTMENT statements must be changed so that their units are volume/length instead of volume.
(ie remove the *1(um) from those statements. However that starts a long fall of dominoes. The diff of the final result is (however, you should verify that the
result in the absence of longitudinal diffusion gives the same result as before the transformation)

Code: Select all

@@ -51,16 +51,16 @@
 	vol[NANN]	(1)	: gets extra cm2 when multiplied by diam^2
         ica_pmp (mA/cm2)
         last_ica_pmp (mA/cm2)
-        area1    (um2)
-        c1      (1+8 um5/ms)
-        c2      (1-10 um2/ms)
-        c3      (1-10 um2/ms)
-        c4      (1+8 um5/ms)
+        area1    (um)
+        c1      (1+8 um4/ms)
+        c2      (1-10 um/ms)
+        c3      (1-10 um/ms)
+        c4      (1+8 um4/ms)
 
 }
 
 CONSTANT {
-	volo = 1 (liter)
+	volo = 1 (liter/um)
 }
 
 STATE {
@@ -115,15 +115,17 @@
 }
 
 KINETIC state {
-	COMPARTMENT i, (1+beta)*diam*diam*vol[i]*1(um) {ca}
+	COMPARTMENT i, (1+beta)*diam*diam*vol[i] {ca}
 	COMPARTMENT (1e10)*area1 {pump pumpca}
 	COMPARTMENT volo*(1e15) {cao}
 
+LONGITUDINAL_DIFFUSION j, (1+beta)*DFree*diam*diam*vol[j] {ca}
+
 	: all currents except pump
-	~ ca[0] << (-(ica-last_ica_pmp)*PI*diam*1(um)*(1e4)*frat[0]/(2*FARADAY))
+	~ ca[0] << (-(ica-last_ica_pmp)*PI*diam*(1e4)*frat[0]/(2*FARADAY))
 	:diffusion
 	FROM i=0 TO NANN-2 {
-		~ ca[i] <-> ca[i+1] (DFree*frat[i+1]*1(um), DFree*frat[i+1]*1(um))
+		~ ca[i] <-> ca[i+1] (DFree*frat[i+1], DFree*frat[i+1])
 	}
 	:pump
 	~ ca[0] + pump <-> pumpca	(c1, c2)
@@ -135,7 +137,7 @@
 	
 PROCEDURE parms() {
 	coord()
-	area1 = 2*PI*(diam/2) * 1(um)
+	area1 = 2*PI*(diam/2)
         c1 = (1e7)*area1 * k1
         c2 = (1e7)*area1 * k2
         c3 = (1e7)*area1 * k3

[Darshan]

Thank you, Michael!

I did the changes in units and compared the results using the original and the transformed files (without LONGITUDINAL_DIFFUSION). The results were similar. The longitudinal diffusion also worked well when added to the model.

Regards,
Darshan