Determinants of voltage attenuation in neocortical pyramidal neuron dendrites

Abstract

How effectively synaptic and regenerative potentials propagate within neurons depends critically on the membrane properties and intracellular resistivity of the dendritic tree. These properties therefore are important determinants of neuronal function. Here we use simultaneous whole-cell patch-pipette recordings from the soma and apical dendrite of neocortical layer 5 pyramidal neurons to directly measure voltage attenuation in cortical neurons. When combined with morphologically realistic compartmental models of the same cells, the data suggest that the intracellular resistivity of neocortical pyramidal neurons is relatively low ( approximately 70 to 100 Omegacm), but that voltage attenuation is substantial because of nonuniformly distributed resting conductances present at a higher density in the distal apical dendrites. These conductances, which were largely blocked by bath application of CsCl (5 mM), significantly increased steady-state voltage attenuation and decreased EPSP integral and peak in a manner that depended on the location of the synapse. Together these findings suggest that nonuniformly distributed Cs-sensitive and -insensitive resting conductances generate a "leaky" apical dendrite, which differentially influences the integration of spatially segregated synaptic inputs.

Fig. 1.

Experimental measurements of steady-state voltage attenuation in neocortical layer V pyramidal neurons.A–C, Representation of the dendritic morphology of three fully reconstructed cells, with the site of the dendritic recording indicated (arrow). The images shown were generated by NEURON using the measured coordinates and diameters for each cell (1099, 1112, and 610 compartments). D–E, Average somatic and dendritic responses obtained from the cell shown inA during somatic 200 msec, −50 pA current pulses in control (D) and in the presence of 5 mm CsCl (E). F, Steady-state voltage attenuation in control conditions (○) and in 5 mm CsCl (•) during dendritic recordings at different distances from the somata of 13 neurons. The smooth line is the best fit to the control (bottom line) and CsCl (top line) data arbitrarily fitted with a Gaussian function. Thedotted lines indicate 50% steady-state attenuation, and the arrows indicate the distance from the soma where this occurred for recordings in control and CsCl.

Fig. 2.

Estimates of R_i models based on steady-state voltage attenuation. A, Plot of steady-state attenuation (V_dendrite/V_soma; •) and mean squared error (MSE) between the simulated and recorded data (○) during long somatic current pulses for the model shown in Figure 1A for values of internal resistivity (R_i) ranging from 50 to 400 Ωcm. The horizontal line indicates the experimentally recorded steady-state attenuation, showing that this coincides with an R_i value of 151 Ωcm. This R_i value also coincides with the lowest mean squared error. B, Recorded (solid lines) and simulated (broken lines) responses to somatic long current pulses (−50 pA, 200 msec). The simulated data were generated using parameters based on an analysis as shown in Figure2A, for the cell shown in Figure1A. Note that simulated responses decay too slowly in the dendrite and too quickly in the soma. C, Recorded (solid lines) and simulated (broken lines) responses to somatic short current pulses (−2 nA for 1 msec). Same model as in B. Note that the simulated dendritic response peaks too late, and as with the simulated responses to long current pulses (B), the simulated dendritic response decays too slowly, whereas the somatic response decays too quickly. The values of R_i,C_m, and R_min the model shown in B and C were 151 Ωcm, 1.3 μF/cm², and 17,981 Ωcm², respectively.

Fig. 3.

Models with nonuniformR_m provide the best fits to short and long current pulse responses. A, Recorded (solid lines) and simulated (broken lines) responses to somatic short (left, −2 nA for 1 msec) and long (right, −50 pA, 200 msec) current pulses using a model derived from a direct fit to the somatic short-pulse data. Same cell as shown in Figure 1A. The values ofR_i,C_m, and R_min this model were 104 Ωcm, 1.46 μF/cm², and 18,591 Ωcm², respectively. Note that the fit to the dendritic short-pulse data are poor. B, The same recorded data as in A with superimposed simulations using parameters derived from a direct fit to the dendritic data. Note that the fits to the somatic short-pulse data are poor, and that simulations of the long-pulse response using the same model parameters generated too little steady-state attenuation. The values ofR_i,C_m, and R_min this model were 76 Ωcm, 1.35 μF/cm², and 15,315 Ωcm², respectively. C, The same recorded data as in A with superimposed simulations derived from a direct fit to both the somatic and dendritic long- and short-pulse data in a model in which R_m was made nonuniform as a function of distance from the soma as described by Equation 1 (see Materials and Methods). The final values ofR_i,R_m(soma),R_m(end),d_half, steep, andC_m were 68 Ωcm, 34,963 Ωcm², 5,357 Ωcm², 406 μm, 50 μm, and 1.54 μF/cm², respectively. Similar models with low R_i and nonuniformR_m also provided the best fits of the data from the other two neurons modeled (Figs.1B,C).

Fig. 4.

Comparison of the average (±SEM) combined mean squared error (MSE) for fits to the somatic and dendritic long- and short-pulse responses in various models for the three cells analyzed. The text under the histogram indicates (1) whether the long or short current pulses, or both, were used to optimize the fit, (2) whether the somatic or dendritic response, or both, was fit, and (3) whether the model used to generate the fit incorporated uniform or nonuniform R_m.

Fig. 5.

A nonuniform distribution of Cs-sensitive conductances is required to fit the steady-state attenuation observed in control conditions. A, Recorded (solid lines; in the presence of CsCl) and simulated (broken lines) long-pulse responses. Data from the cell shown in Figure1A, modeled with nonuniformR_m as in Figure 3C.B, Addition of a uniform density ofI_h to the model shown in Asimulates the sag in the somatic control response but predicts too little steady-state voltage attenuation. The values ofg_h and R in this model were 0.0282 mS/cm²and 7.83 respectively.C, Addition of a nonuniform distribution ofI_h to the model shown in A, with a higher density in the distal apical dendrites, adequately simulates the experimentally observed control steady-state attenuation. The density of I_h in different compartments (g_h) ranged from low to high as a function of distance from the soma as described by Equation 2 (see Materials and Methods), with final values ofg_h(soma),g_h(end),d_half, steep, and R of 0.020 mS/cm², 20 mS/cm², 439 μm, 50 μm, and 1.27, respectively. Similar models with nonuniformI_h also provided the best fits of the data from the other two neurons modeled (Figs.1B,C).

Fig. 6.

Effects of resting conductances on EPSP attenuation and decay. A, Left, simulated dendritic (larger response, 403 μm from the soma) and somatic (smaller response) EPSPs using nonuniform R_mand I_h in the model shown in Figure5C. Simulated EPSPs were generated with a transient, 5 nS conductance increase distributed at five sites between 350 and 450 μm from the soma. Right, experimental data of EPSPs evoked by extracellular synaptic stimulation close to the dendritic recording pipette (400 μm from the soma) under control conditions (not the same cell as simulated). B,Left, simulations of EPSPs with nonuniformR_m and no I_h.Right, experimental EPSPs recorded in the presence of 5 mm CsCl (same cell as in A). Note the crossover of the somatic and dendritic EPSPs in both Aand B. Calibration same as in A.C, Comparison of simulated (left) and experimentally recorded (right) somatic EPSPs under the same conditions as in A and B. Note the additional attenuation and accelerated decay produced by resting Cs-sensitive conductances such as I_h.

Fig. 7.

Attenuation of distally generated EPSPs in different models. A, Representation of the dendritic morphology of the neuron modeled (same cell as in Fig.1A). The distance to the middle recording location in this simulation is 596 μm from the soma. The sites of simulated synaptic inputs are indicated by the black dots. B–E, Simulated EPSPs recorded in four different models at three separate locations: a distal apical tuft branch near the site of one synaptic input (∼1000 μm from the soma), a more proximal apical dendritic location just on the somatic side of the first major apical branch point (596 μm from the soma), and at the soma. The somatic EPSPs are also shown amplified 10 times (broken lines). EPSPs were simulated by a transient, 5 nS conductance increase in the distal apical dendritic tuft (>1000 μm from the soma), which was distributed over the five sites indicated in A (i.e., each individual synapse had a conductance of 1 nS). The different models used were eitherB, a high R_i, uniformR_m model (as in Fig. 2); C, a lower R_i, nonuniformR_m model (as in Fig. 3C);D, a lower R_i, nonuniform R_m, uniformI_h model (as in Fig. 5B); orE, a lower R_i, nonuniform R_m, nonuniformI_h model (as in Fig.5C).