**4. Effect of anatomical alterations on motoneuron electrical properties**

The enlarged anatomy of mutant motoneurons has consequences for their electrical properties and firing behaviour. Computer simulations have been used to assess the effect of enlargement in motoneuron anatomy and its contribution to the changes in electrical properties (ElBasiouny et al., 2010). Realistic computer models were developed from the reconstructed morphologies of WT and mutant motoneurons of the G85R model and were optimized to replicate the electrophysiological recordings obtained from individual cells. For the 30% reduction in input resistance of mutant motoneurons relative to WT, computer simulations showed that one third of this reduction (i.e., input resistance decrease by 10%) is due to the enlargement of motoneuron anatomy, whereas two thirds of this reduction (i.e., input resistance decrease by additional 20%) is due to a decrease in the specific membrane resistance of the motoneuron membrane. The specific membrane resistance represents the number of leak channels available in a patch of cell membrane and its decrease means that there are more ion channels inserted into the membrane (i.e., the cell has higher conductance). Comparison of WT and mutant motoneuron models

Electrophysiological Abnormalities in SOD1 Transgenic

stage of ALS (Jiang et al., 2009).

**neuroprotective mechanisms?** 

Models in Amyotrophic Lateral Sclerosis: The Commonalities and Differences 169

excitability of interneurons, through NMDA receptors, that starts in the presymptomatic

Computer simulations of mutant motoneuron models predicted a reduction in the efficacy of dendritic processing of synaptic inputs early in ALS (ElBasiouny et al., 2010). The amplitude of somatic excitatory postsynaptic potentials (EPSPs) was reduced in mutant motoneurons by 15%, relative to WT. This reduction was comparable to experimental measurements of EPSP amplitudes in the G85R transgenic model (Bories et al., 2007). The computer simulations showed that the reduction in EPSP amplitude resulted from the alteration in various motoneuron properties such as: the increase in motoneuron morphology, the decrease in specific membrane resistance, and the increase in dendritic active conductance activation. The changes in these properties counteract each other and produce the net reduction in EPSP amplitude. These changes were consistent in synaptic

inputs with different dynamics (i.e., slow and fast inputs) (ElBasiouny et al., 2010).

represent disease or protective mechanisms (see next section for discussion).

**7. Anatomical alterations versus excitability changes: Disease versus** 

The individual changes seen in properties of mutant motoneurons could be a disease mechanism, which produces a physiological malfunction, or a neuroprotective (i.e., compensatory) mechanism of the nervous system, which mitigates the physiological malfunction caused by the disease. These mechanisms develop sequentially and act antagonistically. Given that ALS pathogenesis is still poorly understood (i.e., disease mechanisms are not identified yet), it is unfeasible to categorize the changes in mutant motoneurons to disease or compensatory mechanisms with assertion; however, some hypotheses could be formulated from available data regarding the nature of these changes. For instance, the relationship between the alterations in anatomy and excitability of mutant motoneurons is paradoxical. In the G93A (high expressor line) model, the enlargement in motoneuron anatomy and concomitant increase in persistent inward current have opposite

**6. The functional ramifications of the alteration in motoneuron properties** 

The combined changes in motoneuron properties (anatomical, electrical, biophysical) and synaptic inputs converging on them in ALS alter the input-output function of mutant motoneurons and affect their recruitment. For instance, the reduction in input resistance of mutant motoneurons makes them harder to recruit. Similarly, the enlargement in motoneuron anatomy and development of dendritic overbranching increase the attenuation of excitatory and inhibitory post synaptic potentials as they flow to the soma along the dendrites and reduce their efficacy. Computer simulations of reconstructed morphologies of WT and mutant motoneurons indicated a reduction in the efficacy of slow and fast synaptic inputs (by ≈20%) in mutant motoneurons (ElBasiouny et al., 2010). Half of this efficacy reduction was due to the dendritic overbranching, whereas the second half was due to the decrease in specific membrane resistance, leading to increased signal loss through leak conductances. The simulations demonstrated that reduction in synaptic efficacy was still present despite the upregulation in the dendritic active conductances mediating persistent inward current. These combined reductions in cell input resistance and synaptic input efficacy push toward reduced excitability of the cell. It is unclear whether these changes

indicated a 25% decrease in the somatic and dendritic specific membrane resistance of the mutant models. Therefore, the simulation results indicate that the enlargement in motoneuron anatomy does not fully account for the reduction in input resistance as previously suggested by Bories et al. (2007). This is because the additional dendritic branches causing the increased surface area are electrotonically distant from the soma, the site of input resistance measurement. This electrotonic separation reduces the influence of the additional dendritic area at the soma. Thus, a 60% increase in total surface area of mutant motoneurons causes only a 10% decrease in cell input resistance (not 40% as would be predicted from the reciprocal of surface area increase of an electrotonically compact sphere). Secondly, the simulation results indicate that the reduction in input resistance of mutant motoneurons is a function of two factors: the enlargement in motoneuron anatomy and the decrease in specific membrane resistance; the weights of these factors determine the magnitude of input resistance reduction. This could explain why the enlargement of motoneuron anatomy was not always associated with reduction in input resistance as in the case of the G93A (low expressor line) model (see Table 2), suggesting an insignificant change in the membrane specific membrane resistance in this transgenic model. In contrast, the significant reduction in input resistance of mutant motoneurons of the G93A (high expressor line) model despite the truncation in motoneuron dendrites in the slice preparation in Quinlan et al. (2011) might indicate a substantial change in the specific membrane resistance in that transgenic model.

The effects of enlargement in mutant motoneuron anatomy are not only limited to cell input resistance, but also extend to cell firing properties. For instance, the enlargement in mutant motoneuron anatomy would be expected to cause reductions in the motoneuron F-I gain and initial and maximum firing rates and increases in rheobase current and total cell capacitance. Given that no change was seen in some of these properties of mutant motoneurons indicate that compensatory mechanisms have masked those effects (e.g., upregulation in motoneuron transient and persistent inward currents). Estimating the contribution of anatomy enlargement to the changes in mutant motoneurons firing activity and identifying potential ionic mechanisms for masking these changes using computer simulations would be an important step in revealing hidden alterations in motoneuron properties and improving our understanding of ALS pathogenesis.

### **5. The changes in synaptic inputs to motoneurons**

In ALS patients and transgenic models, synaptic inputs converging onto motoneurons experience changes during disease progression. These changes involve loss of specific types of synaptic inputs, rearrangement of the synaptic contacts, and alteration in the size of synaptic boutons. For instance, it has been shown that cholinergic synapses on lumbar motoneurons are lost in ALS patients (Nagao et al., 1998). This loss starts before motoneuron degeneration. Given that cholinergic synapses provide inhibitory input to motoneurons (Nagy et al., 1993), their loss could alter the balance toward more excitatory inputs, leading to motoneurons overactivation. This prediction has been confirmed in G93A (high expressor line) transgenic mice in which the ratio of inhibitory to excitatory synapses was reduced due to the loss of inhibitory boutons (loss was mediated by nitric oxide) and increase in excitatory boutons (Sunico et al., 2011). Furthermore, residual inhibitory boutons exhibit shorter active zone length and smaller synaptic vesicle density (Sunico et al., 2011). Along the same line, there was a progressive increase in the

indicated a 25% decrease in the somatic and dendritic specific membrane resistance of the mutant models. Therefore, the simulation results indicate that the enlargement in motoneuron anatomy does not fully account for the reduction in input resistance as previously suggested by Bories et al. (2007). This is because the additional dendritic branches causing the increased surface area are electrotonically distant from the soma, the site of input resistance measurement. This electrotonic separation reduces the influence of the additional dendritic area at the soma. Thus, a 60% increase in total surface area of mutant motoneurons causes only a 10% decrease in cell input resistance (not 40% as would be predicted from the reciprocal of surface area increase of an electrotonically compact sphere). Secondly, the simulation results indicate that the reduction in input resistance of mutant motoneurons is a function of two factors: the enlargement in motoneuron anatomy and the decrease in specific membrane resistance; the weights of these factors determine the magnitude of input resistance reduction. This could explain why the enlargement of motoneuron anatomy was not always associated with reduction in input resistance as in the case of the G93A (low expressor line) model (see Table 2), suggesting an insignificant change in the membrane specific membrane resistance in this transgenic model. In contrast, the significant reduction in input resistance of mutant motoneurons of the G93A (high expressor line) model despite the truncation in motoneuron dendrites in the slice preparation in Quinlan et al. (2011) might indicate a

substantial change in the specific membrane resistance in that transgenic model.

properties and improving our understanding of ALS pathogenesis.

**5. The changes in synaptic inputs to motoneurons** 

The effects of enlargement in mutant motoneuron anatomy are not only limited to cell input resistance, but also extend to cell firing properties. For instance, the enlargement in mutant motoneuron anatomy would be expected to cause reductions in the motoneuron F-I gain and initial and maximum firing rates and increases in rheobase current and total cell capacitance. Given that no change was seen in some of these properties of mutant motoneurons indicate that compensatory mechanisms have masked those effects (e.g., upregulation in motoneuron transient and persistent inward currents). Estimating the contribution of anatomy enlargement to the changes in mutant motoneurons firing activity and identifying potential ionic mechanisms for masking these changes using computer simulations would be an important step in revealing hidden alterations in motoneuron

In ALS patients and transgenic models, synaptic inputs converging onto motoneurons experience changes during disease progression. These changes involve loss of specific types of synaptic inputs, rearrangement of the synaptic contacts, and alteration in the size of synaptic boutons. For instance, it has been shown that cholinergic synapses on lumbar motoneurons are lost in ALS patients (Nagao et al., 1998). This loss starts before motoneuron degeneration. Given that cholinergic synapses provide inhibitory input to motoneurons (Nagy et al., 1993), their loss could alter the balance toward more excitatory inputs, leading to motoneurons overactivation. This prediction has been confirmed in G93A (high expressor line) transgenic mice in which the ratio of inhibitory to excitatory synapses was reduced due to the loss of inhibitory boutons (loss was mediated by nitric oxide) and increase in excitatory boutons (Sunico et al., 2011). Furthermore, residual inhibitory boutons exhibit shorter active zone length and smaller synaptic vesicle density (Sunico et al., 2011). Along the same line, there was a progressive increase in the excitability of interneurons, through NMDA receptors, that starts in the presymptomatic stage of ALS (Jiang et al., 2009).

Computer simulations of mutant motoneuron models predicted a reduction in the efficacy of dendritic processing of synaptic inputs early in ALS (ElBasiouny et al., 2010). The amplitude of somatic excitatory postsynaptic potentials (EPSPs) was reduced in mutant motoneurons by 15%, relative to WT. This reduction was comparable to experimental measurements of EPSP amplitudes in the G85R transgenic model (Bories et al., 2007). The computer simulations showed that the reduction in EPSP amplitude resulted from the alteration in various motoneuron properties such as: the increase in motoneuron morphology, the decrease in specific membrane resistance, and the increase in dendritic active conductance activation. The changes in these properties counteract each other and produce the net reduction in EPSP amplitude. These changes were consistent in synaptic inputs with different dynamics (i.e., slow and fast inputs) (ElBasiouny et al., 2010).
