Asymmetry in Signal Propagation between the Soma and Dendrites Plays a Key Role in Determining Dendritic Excitability in Motoneurons
Figure 2
Comparison of the anatomical (blue) and reduced (red) MN model.
(A). Reduction of anatomical dendrites. A dendrogram (upper panel) of a MN (i.e. vemoto6 in Methods) with path length (Dpath) from the soma and two compartments (bottom panel) of the reduced model representing the soma/initial segment/axonal hillock (indicated by left arrow) and all points in the narrow band (e.g. mean of 600 µm and standard deviation of 4 µm, right arrow) of dendrites of its original cell. Note that membrane potentials at individual points in the dendrites of the anatomical model were averaged for the purpose of comparison to the reduced model. (B) – (E). Passive dynamics. All five passive parameters (Gm,S = 0.143 mS/cm2, Gm,D = 0.131 mS/cm2, Cm,S = 1.058 µF/cm2, Cm,D = 0.915 µF/cm2, GC = 0.211 mS/cm2) of the reduced model were analytically determined to retain the five system properties measured from the anatomical model: input resistance (RN = 1.29 MΩ) and membrane time constant (τm = 7.2 ms) obtained by peeling analysis at the soma, and three voltage attenuation factors (VASDDC = 0.76, VADSDC = 0.75, VASDAC = 0.27) at Dpath = 600 µm. (B). Time course of membrane potential (Vm) in response to the step current (Isoma) injected to the soma for calculating RN. (C). The semilog plot (solid lines) of transient voltage response at the soma to brief current pulse with smaller amplitude for anatomical than reduced case for τm and τ1 (equalizing time constant) equivalent to the inverse of slope of linear regression (dotted) line fitting the tail of each curve. (D). Time courses of Vm for VASDDC from the soma (solid lines) to dendrites (dotted lines) and VADSDC in the opposite direction, in response to DC input (bottom panel) to the soma (solid line) and dendrites (dotted line). (E). Time course of Vm normalized with its amplitude for VASDAC from the soma (solid line) to dendrites (dotted line), in response to somatically injected AC current (Isoma) with the frequency of 250 Hz. (F), (G). PIC activation with the addition of ICa,L to the dendrites of both models. (F). Time course of effective PIC (IPIC, upper panel) obtained by subtracting leak (ILeak) from total current (ITotal) injected for following the triangular voltage-clamp (Vm, middle panel) at the soma, and ITotal-Vm relationship (bottom panel). (G). Time course of Vm (upper panel) at the soma (solid lines) and dendrites (dotted lines) in response to triangular current clamp at the soma (Isoma, middle panel), and Vm-Isoma relationship (bottom panel). Arrows indicate the ascending and descending phase of triangular voltage and current clamp. Maximum conductance (GCa,L) for ICa,L was 1.37 mS/cm2 for the anatomical and 0.124 mS/cm2 for the reduced case. (H), (I). Cellular excitability with the addition of INa,f, INa,p, IK,Dr, ICa,N and IK(Ca) to the soma of both models. (H). Instantaneous firing rates (F, upper panel), time course of Vm (blue & red for the soma, and gray for the dendrite) in response to triangular current stimulation (Isoma) to the soma, and F-Isoma curve (bottom panel). Maximum conductances for the active currents in the anatomical case were GNa,f = 0.71 [S/cm2], GK,Dr = 0.23 [S/cm2], GCa,N = 0.01 [S/cm2], GK(Ca) = 0.0258 [S/cm2] at the soma, GNa,f = 2.7 [S/cm2], GNa,p = 0.033*10−3 [S/cm2], GK,Dr = 0.17 [S/cm2] at the initial segment and axon hillock, and GCa,L = 1.37 [mS/cm2] in the dendrites. For the reduced model, GNa,f = 26.75 [mS/cm2], GNa,p = 0.00086 [mS/cm2], GK,Dr = 6.2 [mS/cm2], GCa,N = 0.008 [mS/cm2], GK(Ca) = 0.54 [mS/cm2] at the soma and GCa,L = 0.124 [mS/cm2] at the dendrite. (I). F, Vm (blue & red for the soma, and gray for the dendrite) in response to triangular variation of the maximum conductance (Gsyn) for the synaptic receptors positioned at all points at Dpath = 600 µm, and F-Gsyn curve. Arrows indicate the ascending and descending phase of Gsyn.
