It does seem strange that the time constant for the activation variable m is so much longer than the time constant for theI am sending evidence that the models of R-type Ca2+ channels (CaR) in soma and dendrites of at least 2 ModelDB entries (Poirazi 2003 https://senselab.med.yale.edu/modeldb/s ... odel=20212 and Bianchi 2012 https://senselab.med.yale.edu/modeldb/s ... del=143719) are dysfunctional due to errors in the time constants . . . following 100 ms depolarization to -20 mV from holding -70 mV . . . there is no Ca2+ current (ica) produced nor raise in internal Ca2+ (cai). I noticed that the activation time constant is 20 times larger (100 ms) than inactivation time constants (5 ms) . . . I have checked the original publication, and I have found that the Supplement [to Poirazi et al.] contains also wrongly reversed time constants
inactivation variable h. But is this actually an error?
According to the supplement to Poirazi et al., the calcium currents in that model were based on
Magee, J.C., and Johnston, D.
Synaptic activation of voltage-gated channels in the dendrites of hippocampal pyramidal neurons.
Science 268:301–304, 1995.
That in turn cited
Fisher et al.
Properties and distribution of single voltage-gated calcium channels in adult hippocampal neurons.
J Neurophysiol. 64:91-104, 1990
Fisher et al. identified three different single channel calcium currents, of which one (the "25pS channel") was a high-voltage activated current that comes closest to having the properties of an R current (although Fisher et al. regarded it as an N or L type current). On page 98 they wrote
And that is essentially what happened when a single compartment model with the car mechanism was voltage clamped and subjected to a depolarizing step command--soma.ica appeared* to be 0 during the depolarizing step, but it became very obviously nonzero after v returned to -70 mV.The 25pS channel, which normally opened only at depolarized potentials, often opened during the hyperpolarizing step, even if the channel was in the closed state at the beginning of the step (Fig. 11A). This is different from a tail channel, which refers to a channel that opens during a voltage step and remains open for a finite period of time after repolarization. Furthermore, the channel openings were frequently prolonged (~20-100 ms) . . .
*Expanding the Y axis revealed that there was actually a small inward calcium current during the depolarizing step, exactly as one would expect given the values of eca and v.
Plotting the gating variables m and h, and m^3 (car's conductance is proportional to h*m^3) revealed that a depolarizing step made h drop toward zero much faster than m^3 could increase. And when v returned to -70 mV, the recovery of h was much faster than the deactivation of m, so the product h*m^3 grew large enough to allow a noticeable inward current to appear _after_ the end of the depolarizing pulse. This is similar to what Fisher et al. observed in their single channel recordings.
So the bottom line is this: Poirazi et al. did not reverse the time constants--the values in their ModelDB entry are what they intended, and were "correct" in the sense that the resulting current did what they wanted it to do. Of course, one has to read the paper that describes the model in order to discover the modelers' intent, and in this case that was difficult because the paper was not freely available and the ModelDB user's institution did not have online access to the paper.
Comments (and apologies to readers who already know this)
Many (most? all?) voltage-gated calcium channels have very slow activation/deactivation kinetics (m time constants)--so slow that most calcium influx happens well after the depolarization that triggered channel opening. This is an "old" observation--dates back to the 1980s if not earlier. Indeed, most of the sodium (potassium) current that flows during a squid axon's spike potential enters (leaves) the axon after the peak of the spike. For ina and ica, the reason is that driving force for ina and ica decreases during the rapid upstroke of the spike, but increases with time during the spike's falling phase; for the delayed rectifier's ik, the reason is that the activation gate n has very slow kinetics.