FIG. 1. Response of the full model to a total constant current of 0.4 nA to the glomerulus, divided evenly among the compartments ( 4.3 pA per compartment). (A) Somatic membrane potential trace and (B) Membrane potential trace at base of glomerular tuft, for varying _K in the tuft. These figures show the double somatic spike and extended dendritic calcium spike seen with low _K, that are removed by increasing the value of the parameter. Increasing _Kfurther delays the somatic spike and abolishes the dendritic calcium spike.

FIG. 2. Schematic of the four-compartment model showing ion channels and points of stimulation. Currents are sodium (I_Na), slow potassium delayed rectifier (I_K), fast potassium delayed rectifier (I_Kfast), potassium anomalous rectifier (I_KA), calcium-dependent potassium (I_KCa) and L-type calcium (I_LCa). The conductances between soma and secondary dendrite, soma and primary dendrite, and primary dendrite and glomerulus are g_sd, g_sp and g_pg, respectively.

FIG. 3. Somatic membrane potential trace for full and reduced models with I_full = 0.4 μA cm⁻² after fitting to spike shape. Both three- and four-compartment models give good fits to the full model. The two-compartment model has a markedly raised reset potential.

FIG. 4. Somatic membrane potential trace for full and reduced models with I_full = 0.8 μA cm⁻² after fitting to spike shape with I_full = 0.4 μA cm⁻². The miniature spike on the down-slope of the action potential in the three-compartment model is due to the delay between spiking in the soma and in the secondary dendrite.

FIG. 5. Comparing fit-to-shape to fit-to-time for the four-compartment model. (A) Firing frequency, (B) latency of first spike. Current was injected in the soma compartment. The four compartment model with fit-to-shape parameters shows almost zero deviation from the full model with current injection 0.4 μA cm⁻², the level at which it was fitted, but large differences with higher or lower inputs. In contrast, the four-compartment model with fit-to-time parameters fits reasonably well over a wide range of input levels.

FIG. 6. Somatic membrane potential trace for full and four-compartment models with I_full = 0.2 μA cm⁻² and 1.6 μA cm⁻² after fitting to spike timing. (A) Current injection to soma. (B) Current injection to glomerulus. The models fit well in terms of first spike latency and firing frequency, but there are discrepancies in the detailed shape of the membrane potential traces. This illustrates one of the problems with very-reduced compartmental models.

FIG. 7. Comparing reduced models with two, three and four compartments, with fit-to-time parameters: (A) Firing frequency as a function of current for stimulation of soma; (B) as A for stimulation of glomerulus; (C) Latency of first spike as a function of current for stimulation of soma; (D) as C for stimulation of glomerulus. The three- and four-compartment models fit the full model closely for a wide range of input levels and for both somatic and glomerular inputs. The two-compartment model gives a tolerable fit for somatic input and for low glomerular input, but deviates considerably for high glomerular input.

Table 1. Best fit parameter values