Detailed Biophysical Model of Layer 5 Pyramidal Cells

We included ten key active ionic currents known to play a role in L5 PCs or generally in neocortical neurons [39] (link), with kinetics taken strictly from the experimental literature. Kinetics of ion conductances that were characterized in room temperature (21°C) were adjusted to the simulation temperature of 34°C using Q₁₀ of 2.3, and those taken from experiments where the junction potential was not corrected for were shifted by −10 mV. The reversal potentials for Na⁺ and K⁺ were E_Na = 50 mV and E_K = −85 mV, respectively, and a −45 mV reversal potential was used for the I_h current [13] (link).
Ion currents were modeled using Hodgkin-Huxley formalism, so that for each ion current:
Where is the maximal conductance (or density); x and y are the number of gate activation and inactivation variables, respectively; E is the reversal potential of the ion involved; and V is the membrane potential.
The kinetics of the conductance mechanisms used in this study is detailed below (see also Figures S4, S5). Time constants are given in milliseconds (ms), voltage in millivolts (mV), and ion concentration in millimolar (mM). F is Faraday's constant; d is the depth of sub-membrane shell for concentration calculations in µm; γ is the inverse of the Ca²⁺ buffer's binding ratio; and τ_decay is the time constant of Ca²⁺ diffusion. 1e-4 mM refers to the steady state intracellular free Ca²⁺ concentration. The activation time constant of SK is estimated to be instantaneous (1 ms), since we could find no definite characterization of it in the literature due to the difficulty in measuring it experimentally.
Fast inactivating Na⁺ current, I_Nat[57] (link):




Persistent Na⁺ current, I_Nap[71] (link):




Non-specific cation current, I_h[13] (link):


Muscarinic K⁺ current, I_m[72] (link):


Slow inactivating K⁺ current, I_Kp[73] (link):




Fast inactivating K⁺ current, I_Kt[73] (link):


Fast, non inactivating K⁺ current, I_Kv3.1[74] (link):

Intracellular [Ca²⁺] dynamics[35] (link), [75] (link):
High voltage activated Ca²⁺ current, I_{Ca_HVA}[76] (link):




Low voltage activated Ca²⁺ current, I_{Ca_LVA}[77] (link)–[78] (link) :


Small-conductance, Ca²⁺ activated K⁺ current, I_SK[79] (link):

Temperature adjustment factor:
The optimization algorithm aimed at searching the densities for the ion channels (except for I_h which we fixed, see below) and the parameters of the Ca²⁺ buffer mechanism that best fit the target experimental features (see also [36] (link)). The list of the free parameters and their limits used by the search algorithm is given in Table 2. The lower limits for density were 0, and upper limits were as high as biologically plausible.