Evidence from computer simulations for alterations in the membrane biophysical properties and dendritic processing of synaptic inputs in mutant superoxide dismutase-1 motoneurons

Abstract

A critical step in improving our understanding of the development of amyotrophic lateral sclerosis (ALS) is to identify the factors contributing to the alterations in the excitability of motoneurons and assess their individual contributions. Here we investigated the early alterations in the passive electrical and morphological properties of neonatal spinal motoneurons that occur by 10 d after birth, long before disease onset. We identified some of the factors contributing to these alterations, and estimated their individual contributions. To achieve this goal, we undertook a computer simulation analysis using realistic morphologies of reconstructed wild-type (WT) and mutant superoxide dismutase-1 (mSOD1) motoneurons. Ion channel parameters of these models were then tuned to match the experimental data on electrical properties obtained from these same motoneurons. We found that the reduced excitability of mSOD1 models was accompanied with decreased specific membrane resistance by approximately 25% and efficacy of synaptic inputs (slow and fast) by 12-22%. Linearity of summation of synaptic currents was similar to WT. We also assessed the contribution of the alteration in dendritic morphology alone to this decreased excitability and found that it reduced the input resistance by 10% and the efficacy of synaptic inputs by 7-15%. Our results were also confirmed in models with dendritic active conductances. Our simulations indicated that the alteration in passive electrical properties of mSOD1 models resulted from concurrent alterations in their morphology and membrane biophysical properties, and consequently altered the motoneuronal dendritic processing of synaptic inputs. These results clarify new aspects of spinal motoneurons malfunction in ALS.

Figure 1.

Summary of the alteration in electrical and morphological properties of mSOD1 motoneurons. A, Reconstructed morphologies of exemplar WT and mSOD1 lumbar motoneurons (P8–P10) illustrating the differences between the two groups (top). WT and mSOD1 computer models retain the detailed morphometrical and topological characteristics of the reconstructed motoneurons (i.e., the variation in dendritic branch diameter is not illustrated in the bottom). B, Summary of experimental data illustrating the percentage change in electrical and morphological properties of mSOD1 lumbar motoneurons. Experimental data were normalized to the mean values of WT motoneurons to illustrate the percentage change in mSOD1 motoneuron properties relative to WT. Experimental data on morphological properties were obtained from Amendola and Durand (2008), whereas electrical properties data were obtained from whole sample recordings (Table 1). Number of stars indicates the level of statistical significance (*p < 0.05; **p < 0.01; ***p < 0.001). Error bars express SD.

Figure 2.

Measurements of R_in and time constants. A, Simulation of R_in measurement in which model behavior (gray trace) was matched to the experimental recording (black trace) of that individual motoneuron. B, Simulation of membrane time constants (τ₀ and τ₁) measurement using the graphical peeling method. The values of τ₀ and τ₁ are measured from the reciprocal of the slopes of the linear ranges indicated between the small ticks.

Figure 3.

Simulations of reconstructed WT and mSOD1 motoneuron models. Comparison of R_in measurements of WT and mSOD1 models to experimental recordings of reconstructed motoneurons. Statistical significance in R_in measurements between the WT and mSOD1 models was found similar to experimental data of those reconstructed motoneurons (p = 0.044). Error bars represent SD n = 8 for WT motoneurons and n = 6 for mSOD1 motoneurons.

Figure 4.

Simulations of efficacy and summation of synaptic inputs. A, The measurement of synaptic efficacy of slow synaptic inputs in a simulation of WT motoneuron. A steady synaptic input was applied (bottom) when the somatic membrane was ramped during voltage clamp from −70 mV to −10 mV at a slow rate of 4 mV/s. Both ΣI_syn and I_N were measured simultaneously during the simulation of a passive and an active model. Assessment was done at subthreshold (−60 mV), suprathreshold (−45 mV), and peak potential (−30 mV). B, The measurement of synaptic efficacy of fast inputs in simulation of a WT motoneuron. Synaptic efficacy was computed as the ratio between the maximum amplitude of effective synaptic current (I_{N max}) reaching the soma when the soma is clamped at −60 mV to the maximum amplitude of the total synaptic current injected through individual synapses (ΣI_{syn max}). The summation of synaptic current was assessed by measuring the ratio between ΣI_{syn max} and the total synaptic current injected through individual synapses if they would behave as perfect current sources (I_ideal).

Figure 5.

Efficacy of synaptic currents (A) and linearity index (B) in passive models. In the mSOD1-like (morph) models, only morphology increase was included in the model, whereas in the mSOD1-like (morph + R_m) models morphology increase and R_m reduction were included. For WT, mSOD1-like (morph), and mSOD1-like (morph + R_m) models, n = 8. For mSOD1 models, n = 6. Even though paired Student's t test gave highly statistical p-values (p < 0.001) for comparisons between WT and mSOD1-like (morph), and mSOD1-like (morph + R_m) models, we only reported the p-values obtained from the nonparametric Wilcoxon Sign Rank test. *p < 0.05.

Figure 6.

Transformation of WT to mSOD1-like models. A, Transformation of WT MN 3 model to its comparable mSOD1-like (morph) model. B–E, Morphometrical properties of mSOD1-like (morph) models. Data of reconstructed WT (blue traces) and mSOD1 (red traces) motoneurons are plotted versus that of the MN 3 mSOD1-like (morph) model (black traces). All error bars represent SD n = 8 for WT data and n = 6 for mSOD1 data.

Figure 7.

Simulations of mSOD1-like (morph) models. A, R_in measurement in WT and mSOD1-like (morph) models. The mSOD1-like (morph) morphology merely resulted in 10% reduction in R_in; however, the experimentally observed reduction in R_in was obtained when R_m was simultaneously reduced by 30%. B, Summary of mSOD1-like (morph) and mSOD1-like (morph + R_m) simulation results. For each mSOD1-like (morph + R_m) model, R_in was reduced on average by 10% (second bar) due to morphology increase alone, and by 30% (third bar) when R_m was concurrently reduced in the model, which matched mSOD1 experimental data (fourth bar). Accordingly, the morphology increase contributed one third of the decrease in R_in, whereas R_m reduction contributed the other two thirds (see vertical arrows). R_m was reduced on average by 25% in mSOD1-like (morph + R_m) models to match R_in experimental data (last bar). n = 8 for WT, mSOD1-like (morph), and mSOD1-like (morph+ R_m) models. Error bars represent SD.

Figure 8.

Staircase currents and plateau potentials in active models. A, Generation of staircase currents (top) during voltage clamp of the somatic potential (bottom). The arrows denote the multiple steps during the activation of the Ca²⁺ PIC in a mSOD1-like (morph) model. B, Partial (black trace) and full (blue) deactivation of plateau potentials (top) by hyperpolarizing pulses (bottom) in the same mSOD1-like (morph) model as in A. In A and B, the model had dendritic L-type Ca²⁺ channels only, equivalent to the blockade of Na⁺ and K⁺ channels in the experiments of Carlin et al. (2009).

Figure 9.

Efficacy of slow (A) and fast (B) synaptic currents, and linearity index of slow (C) and fast (D) synaptic currents in active models. For WT, mSOD1-like (morph), and mSOD1-like (morph + R_m) models, n = 8. For mSOD1 models, n = 6. p-values were obtained from the nonparametric Wilcoxon Sign Rank test. *p < 0.05.

Figure 10.

Simulations of mSOD1-like (morph) and (morph + R_m) models for MN 3 with I_h current included in the model. R_in was measured as the ratio of the change in somatic membrane potential (difference between the steady-state membrane potential and the resting membrane potential, V_ss) to the amplitude of the current pulse. Note that the resting membrane potential was affected by I_h. When morphology increase was included in the mSOD1-like (morph) model, R_in was reduced by 15%. To further reduce R_in by nearly 30% similar to experimental data, R_m needed to be reduced in mSOD1-like (morph + R_m) model by 40%. The inset shows how the sag ratio was measured in the simulations.