We simulate reconstructed α-motoneurons (MNs) under physiological and morphological realistic parameters and compare the modeled reciprocal (REC) and recurrent (REN) inhibitory postsynaptic potentials (IPSPs) containing voltage-dependent channels on the dendrites with the IPSPs of a passive MN model. Three distribution functions of the voltage-dependent channels on the dendrites are applied: a step function (ST) with uniform spatial dispersion; an exponential decay (ED) function, with channels with high density located proximal to the soma; and an exponential rise (ER) with a higher density of channels located distally. The excitatory and REN inhibitory inputs are located as a gaussian function on the dendrites, while the REC inhibitory synapses are located proximal to the soma. Our simulations generate four key results. (1) The distribution pattern of the voltage-dependent channels does not affect the IPSP peak, its time integral (TI), or its rate of rise (RR). However, the IPSP peak decreased in the presence of the active dendrites, while the EPSP peak increased. (2) Proximally located IPSP conductance produces greater IPSP peak, RR, and TI. (3) Increased duration of the IPSP produces greater RR and moderately increased TI and has a small effect on the peak amplitude. (4) The IPSP of both REC and REN models is specific to each MN: its amplitude is proportional to the MNs' input resistance, RN; the increase of IPSP at the proximal location of the IPSP synapses is inversely related to RN; and the effect of the IPSP conductance duration is insensitive to RN.
The reciprocal (REC) and recurrent (REN) inhibitions in the mammalian spinal cord entail a major glycinergic component in their inhibitory postsynaptic potentials (IPSPs). A disynaptic pathway involving Ia REC interneuron (Stuart & Redman, 1990) mediates the feedforward REC inhibition. The REN inhibition is a feedback system: the α-motoneuron (MN) itself activates a polysynaptic interneuronal pathway of self-inhibition. The location of the REC inhibitory synapses has been assumed to be near the motoneuron soma (Curtis & Eccles, 1959). This was based on the fact that the decay time of the inhibitory postsynaptic potential (IPSP) matches the decay time of a voltage response to a current injection at the soma. In contrast, REN synapses are distributed on the dendrites distally to the soma (Fyffe, 1991), similar to the excitatory AMPA and NMDA inputs. The duration of the REC inhibitory conductance is shorter than the REN conductance, whereas the maximal conductance amplitude seems similar, as evident from their efficacy in inhibiting the spinal monosynaptic reflex (Schleifstein-Attias, Tarasiuk, & Grossman, 1994).
Various factors determine the efficiency of the synaptic input. Intrinsic properties of the synapses and the postsynaptic cell's membrane can modify the synaptic potential. Moreover, the interaction between dendritic voltage-dependent channels and the synapses may increase or decrease the synaptic potential (Bui, Grande, & Rose, 2008; Gradwohl & Grossman, 2008). The branching of the dendritic tree and its membrane properties are crucial in determining the efficacy of synaptic signal transmission and the electrical distance that it must travel (Cuntz, Borst, & Segev, 2007). Mutual changes in the conductance due to the interaction of the synaptic inputs and other postsynaptic conductances can influence the membrane conductance and thus the synaptic potential (Segev & Parnas, 1983; Gradwohl, Nitzan, & Grossman, 1999).
These dynamics raise the question of the significance of the location (distribution profile is described above) of the inhibitory synapses and the duration of their conductances. In a previous simulation study (Gradwohl & Grossman, 2008), we analyzed the influence of voltage-dependent channel location on MN excitatory postsynaptic potentials (EPSP). We found that the dendritic location of an active conductance was more efficient in amplifying the EPSP than similar channel densities located on the soma or axon alone. Furthermore, we were able to show that densely located voltage-dependent channels (hot spots) are more effective in increasing EPSP than sparsely located ones.
Bui et al. (2008) examined the interaction between different located synaptic inhibitory inputs and dendritic Ca2+ persistent inward currents (PICs) on the amplification of the IPSP. They concluded that in the absence of PIC channels, the proximal distribution of inhibitory synapses produced the largest IPSP. In contrast, in the presence of PICs, inhibitory synapses, when distributed similarly to the REN synaptic distribution, generated the greatest amplitude in comparison to the other distributions.
In our previous model, we had incorporated only basic voltage-dependent channels, including fast sodium and delay rectifier potassium conductances (Luscher & Larkum, 1998; Gradwohl & Grossman, 2008) despite the knowledge that sodium PIC (INaP) (Li & Bennett, 2003; Li, Murray, Harvey, Ballou, & Bennett, 2007) and dendritic Ca2+ currents also exist in the dendrites and may amplify the subthreshold potential (Manuel, Meunier, Donnet, & Zytnicki, 2007). We limited our study to be able to compare the results for the IPSPs to those of previous studies on EPSPs (Luscher & Larkum, 1998; Gradwohl & Grossman, 2008). Furthermore, PICs with persistent sodium and calcium conductances affect mainly the firing pattern of neurons (Lee & Heckman, 2001; Li & Bennett, 2003) rather than single subthreshold potentials like the IPSP. It is conceivable, however, that PICs could be incorporated in future models.
In this study, we modeled uniform, exponential rise and exponential decay of active channel dispersions (with respect to the soma) on the dendrite and addressed the following questions: (1) Do dendritic voltage-dependent channels modulate IPSPs in both pathways? (2) Do REN and REC conductance properties affect IPSPs' parameters differently in terms of peak amplitude, time integral, and rate of rise? (3) Is the IPSP modulation in the specific inhibitory pathway dependent on the location of the conductance, the duration, or both? Furthermore, is it also related to the membrane properties of the motoneuron?
Our simulations suggest that the addition of active dendritic conductances, relative to the passive state, does not change the IPSP. However, the REC inhibitory conductance, defined by proximal location and short conductance, alters the IPSP parameters significantly in comparison to the REN inhibition, characterized by distal location and long duration. In addition, the influence of the distinct location of these pathways is dependent on the cell's input resistance.
2.1. Morphological and Physiological Parameters.
The physiological and morphological data of the five α-motoneurons (MNs) of the muscle triceps surea were taken from previous publications on anesthetized cats (the data were provided by I. Segev). The input resistance (RN), membrane time constant (τo), and surface area (Am) were determined according to previous intracellular recordings (Cullheim, Fleshman, Glenn, & Burke, 1987b). Cullheim, Fleshman, Glenn, and Burke (1987a, 1987b) reconstructed the three-dimensional morphological structure of the α-MNs with the aid of a light microscope after a color reaction with injected horseradish peroxidase (HRP). The model simulated one slow (S), two fast fatigue (FF), and two fast fatigue resistance (FR) type α-MNs. The numbers of the synapses and their spatial distribution on the dendrites were taken from earlier studies (Burke & Glenn, 1996; Ornung, Ottersen, Cullheim, & Ulfhake, 1998) based on light microscopy after HRP injection.
2.2. Computer Model.
2.2.1. Simulation and Passive Membrane Properties.
2.2.2. Synaptic Input.
A number of 70 postsynaptic glycinergic REC and REN inhibitory synapses (see Figure 1) were incorporated in the model. The number of the synapses involved in the REC inhibition was based on the observation that an average of 69 Ia-interneurons are in contact with a single MN (Jankowska & Roberts, 1972). Indeed, every contact yields about two to three synaptic buttons (Brown & Fyffe, 1981; Fyffe, 1991), but if the probability of the glycinergic neurotransmitter release is smaller than one (Jack, Redman, & Wong, 1981), for example, 0.5, it will yield about 70 active synapses. A similar number was assumed for the synapses of the REN inhibition.
We fixed the REC inhibitory synapses on the proximal dendrite near the MN soma (Curtis & Eccles, 1959) and assumed an exponential behavior of the density distribution of the REC inhibition as a function of the distance from the soma. A Gauss function mimicked the REN inhibition similar to the EPSP density distribution (Segev et al., 1990; Gradwohl & Grossman, 2008) (see Figure 2A). The activation time of the inhibitory synaptic activation was distributed in a time window of 0 to 1.4 ms (Luscher, Ruenzel, & Henneman, 1979).
2.2.3. The Numerical Model.
2.2.4. Types of Simulation Models.
The simulations were based on a model containing voltage-dependent channels solely on the dendrites, distributed by three different functions. The simulations deal with subthreshold potentials based on the premise that even subthreshold depolarizing IPSPs may activate multiple voltage-dependent conductances (Stuart & Sakmann, 1995; Andreasen & Lambert, 1999; Gonzalez-Burgos & Barrionuevo, 2001), similar to what is observed in EPSP (Magee, 1998; Gradwohl & Grossman, 2008). The model had three types of voltage-dependent channels: a fast inactivating Na+ conductance (gNa) (Barrett, Barrett, & Crill, 1980) and both a fast (gKf) and a slow (gKs) potassium conductance (Barrett et al., 1980). Spike repolarization was caused mainly by the gKf, whereas the AHP is influenced by gKs (Schwindt & Crill, 1981). There are undoubtedly other currents on the MN's initial segment, soma, and dendrites, for example, persistent sodium (INap), calcium current producing a plateau potentials (Bui, Cushing, Dewey, Fyffe, & Rose, 2003), and multiple K+ channels, like IKCa, shaping firing properties (Viana, Bayliss, & Berger, 1993). However, in our present model, our goal was to analyze the IPSP and its modification due to basic voltage-dependent channels as gNa, gK, and gKs. We consequently did not include the Ca2+ currents INaP and IKCa (see Luscher & Larkum, 1998). Locating low-voltage-dependent conductances on the dendrites in the presence of a passive soma and axon diminished the potential relative to a full passive neuron. MNs' voltage-dependent channels, in contrast to the ones in the cortical pyramidal neurons (Stuart & Sakmann, 1995), are absent in certain dendrites, while their neighbors may include these channels (Larkum, Rioult, & Luscher, 1996). Even the density distributions of voltage-dependent conductances in the active dendrites are not known. We therefore simulated three types of channel distributions as detailed previously (Gradwohl & Grossman, 2008) at a distance of 0 to 400 μm from the soma: (1) a step function (ST), where the active conductance density was kept uniform over the dendritic tree, (2) an exponential decay (ED), where high-conductance density, located proximal to the soma, decays exponentially away from the soma; and (3) an exponential rise (ER), where proximal low-conductance density increases exponentially with distance. Densities of the sodium conductance (gNa) were varied relative to the type of conductance distribution between a minimum and a maximum value in order to attain equal total conductance, G (S, Siemens) for each MN. The densities of the delayed rectifier (gK) and slow (gKs) potassium conductances were one-third relative to gNa (Luscher & Larkum, 1998). For each density model, we ran simulations with two, four, six, and eight active dendrites. The total numbers of the dendrites of MN 36, MN 38, MN 41, MN 42, and MN43 were 10, 13, 12, 8, and 11, respectively. In each case, we executed 10 runs of randomly selected dendrites.
3.1. IPSPs Simulated in the Five -Motoneurons Using a Passive Model.
We simulated two types of IPSPs produced by the REC and the REN inhibitory pathways. REC synapses are located proximal to the soma, and REN synapses are distributed distally. In addition, the conductance rise time of REC and REN was 1 ms, while the decay times were 2 and 6 ms, respectively. In order to isolate the effect of the location versus the duration on the IPSP, a pseudo-REC inhibition (PREC) was also simulated with an input distribution similar to that of the REN distal input. In newborn rats, Ia EPSP is depressed by the REC and REN synapses due to shunt and depolarizing inhibition, as these synapses are mediated by chloride ions with a reversal potential more positive to the resting potential (see section 2).
REC, REN and PREC IPSPs dispersed (see Figure 1B) similar to the EPSPs (Segev et al., 1990; Gradwohl & Grossman, 2008) among the MN types but with smaller amplitudes. The passive IPSPs result from a single simulation containing 8 active dendrites with no statistical trials of 10 arbitrarily selected active dendrites. Like all other types of MNs, the IPSP generated by the REC inhibitory synapses has the largest amplitude relative to the REN and PREC synapses (see Table 1). The largest IPSP was obtained in the S-type MN 36 due to its relatively high RN of 1.93 MΩ. The relation between the depolarizing passive IPSP peak to the MN's RN is like an increasing monotonic function (except for MN 42). This is similar to the behavior of passive MNs EPSP peaks, which was investigated through experiments (Burke, 1968a, 1968b) and simulations (Segev et al., 1990). REC IPSPs' peak were 10.53% to 54.35% larger than REN IPSPs, but depended on the type of MN. It is noticeable that the passive amplitude of the PREC IPSPs was similar to that of the REN IPSPs in all MNs simulated, indicating the influence of the input location (see also section 3.4). All IPSP amplitudes are small; however, they may be effective in modulating Ia- EPSP response.
|.||MN .||RN .||MN .||REN IPSP .||REC IPSP .||(REC-REN)/ .||PREC IPSP .|
|MN .||Type .||(MΩ) .||Type .||Peak (mV) .||Peak (mV) .||REN (%) .||Peak (mV) .|
|.||MN .||RN .||MN .||REN IPSP .||REC IPSP .||(REC-REN)/ .||PREC IPSP .|
|MN .||Type .||(MΩ) .||Type .||Peak (mV) .||Peak (mV) .||REN (%) .||Peak (mV) .|
Notes: The REC inhibitory inputs generate greater IPSPs relative to the REN inhibitory inputs. Note that MN 36 produced the largest IPSP amplitude of all types of inhibitory synapses.
3.2. Active Dendrites Decrease IPSP's Peak, Time Integral, and Rate of Rise.
We compared the REN, REC, and PREC IPSPs in the presence of active dendritic ST, ER, and ED models at the same MN and between different MNs. In order to keep the affected active membrane equal, our approach (Gradwohl & Grossman, 2008) fixes the range of G to be equal for all MNs by using the precalculated minimal and maximal gNa. The range between these values was divided into five steps, and the resultant IPSPs were then simulated. Densities of the sodium conductance (gNa) were varied relative to the type of conductance distribution between a minimum and a maximum value in order to attain equal total conductance G (S, Siemens) for each MN. The densities of the delayed rectifier (gK) and slow (gKs) potassium conductances were one-third relative to gNa (Luscher & Larkum, 1998). This meant that in the ED model, gNa had to be set higher than in the ER model (due to the fact that branching distal dendrites contain more surface area than proximal dendrites), while at the ST model, the conductance density had to be the smallest one. The uncertainty about the population of active dendrites in each MN has also forced us to simulate 10 random dendrite combinations for 2, 4, 6, and 8 dendrites at the 5 gNa. This statistical approach yielded 200 values of IPSP peak as a function of G for each model (see Figure 3) for every MN. This procedure enabled us to compare the results of the ED, ER, and ST models at the same MN and between different MNs. This method enabled measurement of IPSP peak, time integral (TI), and rate of rise (RR), which are important parameters determining the efficacy of synaptic transmission.
3.2.1. IPSP Peak.
ED, ER, and ST distributions of the voltage-dependent channels had no significant difference among them and produced similar IPSP peaks for each inhibitory input (for an example of MN 41, see Figure 3). Nevertheless, REN, REC, and PREC inhibitory synapses generated different IPSP peaks. The proximally (relative to the soma) located REC synapses yielded the largest IPSP peak (∼0.5 mV), while the distally distributed REN and PREC synapses generated smaller IPSP peaks (∼0.25 mV). The IPSP amplitude was very small, but the result based on the 200 IPSP peaks of the random simulation model has a small standard deviation and is significant.
3.2.2. IPSP TI.
IPSP TI in MN41 (see Figure 4) are ∼5.5, ∼5.0, and ∼2.8 mV. ms in the REN, REC, and PREC models, respectively. Again, ED, ER, and ST distributions produced the same IPSP TI.
3.2.3. IPSP RR.
Similarly, the RR was affected by the type of the inhibitory synapses and was not altered by the type of dendritic voltage-dependent channels distribution. For example, IPSP RR in MN 41 (see Figure 5) in the REN, REC, and PREC models are 0.045, 0.125, and 0.06 mV/ms, respectively.
3.3. Comparison of the IPSP's Peak, TI, and RR at the Various MNs.
We have examined the effect of dendritic active conductance on IPSP amplitude and kinetics in a single MN41 using the three models of inhibitory input. We further compared under similar conditions all five MNs, which have different morphologies and consequently exhibit different input resistances (Segev et al., 1990; Gradwohl & Grossman, 2008). As our simulation did not reveal any significant difference among the three tested distribution models (see Figures 3 and 4), we present in Figures 6 to 8 only the ED model results of the IPSP peak amplitude, with its TI and its RR for each inhibitory input at various active conductance levels. The values are the means from 200 simulations.
3.3.1. IPSP Peak.
IPSP generated by the REN, REC, and PREC synapses at MN 42 had the largest peak, while MN 43's IPSP had the smallest (see Figure 6). In contrast to the passive IPSP peak, the relation between the RN and the active IPSP could not be defined by a monotonic function. REC IPSP peaks at all MNs were significantly larger than the appropriate REN and PREC IPSP amplitudes. For example, the REC IPSP peaks at MN 38 and MN 42 were 92% and 63% larger than the REN IPSP peak, whereas at MN 36, the difference was approximately 26%.
3.3.2. IPSP TI.
REN IPSP TI was the largest in all MNs (see Figure 7), as it also has the longest conductance duration. The REC TI was the second largest, and the PREC TI was the smallest in all MNs.
3.3.3. IPSP RR.
The IPSP RR (see Figure 8) exhibited the greatest difference between the IPSP REC and REN. Namely, the REC IPSP RR of MN 38 and MN 42 was about 173% and 137%, larger than REN IPSP RR, and in MN 36, this relation is “only” 82%. PREC values are slightly larger than those of REN in all MNs.
3.4. Analysis of the Importance of Input Location Versus Conductance in Determining the IPSP at the Various MNs.
In order to isolate the effect of dendritic location of the input on the IPSP, we compared the REC IPSP to the unrealistic PREC IPSP with identical conductance, but with a distal instead of a proximal distribution. Proximal location of the synapses increased IPSP parameters significantly relative to the distal dispersion at all MNs with their unique RN (see Figure 9A). Interestingly, the degree of enhancement depended inversely on the MN's RN: the lower the RN, the larger the increase. As mentioned earlier, the active IPSP was not correlated to the RN, but its enhancement related to RN by a monotonically decreasing function. Furthermore, there was no correlation between the MN's size (the surface) and the magnitude of IPSP attenuation. The mean values of the increase in the IPSP peak, TI and RR (see Figure 9B), were not significantly different due to the large standard deviations relative to the means (n = 5 MNs; SDs of the IPSP peak, TI, and RR were 15.438 mV, 9.500 mV. ms, and 15.713 mV/ms, respectively).
In order to analyze solely the effect of synaptic conductance duration on the IPSP, we compared the REN IPSP to the nonrealistic PREC IPSP synapses with identical dendritic location but shorter duration of the inhibitory conductance. At all MNs, an increase in the conductance duration amplified IPSP TI and RR, but had little effect on the IPSP peak (see Figure 10A). However, these modifications of the IPSP were insensitive to the MN's RN since the SDs of the IPSP peak, TI, and RR, were 1.285 mV, 1.366 mV. ms, and 0.109 mV/ms, respectively. The effect on IPSP RR was significantly the largest, while the mean IPSP peak was almost unaffected in all MNs (see Figure 10B).
This study enabled us to incorporate realistic synapses into the models and examine the effect of the synaptic dendritic location and their conductance duration on the IPSP's peak, time integral and rate of rise. Similar to our previous study of MNs' EPSP modification (Gradwohl & Grossman, 2008), we included various voltage-dependent channels in the dendritic tree and simulated them at three alternative channel distributions and diverse specific conductances. Because our previous study of the EPSPs and this simulation of IPSPs were examined under the same conditions, we can further simulate their interactions (or effective inhibition) in the spinal cord. Our preliminary results suggest that the inhibition may reduce EPSP's peak, its TI, and its RR.
Our results allow several key observations:
The distribution pattern of the voltage-dependent channels does not affect the IPSP peak, TI, and RR. However, the IPSP peak decreases in the presence of the active dendrites, while EPSP's peak increases (Gradwohl & Grossman, 2008).
Proximally located IPSP conductance produces greater IPSP peak, RR, and TI.
Slower initial decay of the inhibitory conductance produces greater RR and moderately increased TI and has a small effect on the peak amplitude.
The IPSPs of both REC and REN models are specific to each MN; their amplitudes are proportional to the MNs' input resistance, RN, yet the increases of IPSP at the proximal location (2) of the IPSP synapses are inversely related to RN, whereas the effect of the IPSP conductance duration (3) is insensitive to RN.
4.1. Modulation of Synaptic Potentials by Dendritic Voltage-Dependent Channels.
REC and REN IPSPs are decreased relative to the passive model by dendritic sodium and potassium voltage-dependent channels. The inhibitory effect is expressed mainly by the shunt inhibition and less by the depolarizing chloride conductance; the latter has a reversal potential close to the membrane's resting potential (not shown). However, recent model simulations indicate that depolarizing EPSPs (Gradwohl & Grossman, 2008) and Ia EPSP inhibition (Gradwohl & Grossman, 2001) are enhanced by a dendritic tree containing active channels (De Schutter & Bower, 1994; Gradwohl & Grossman, 2008). In order to understand the attenuation or the amplification of the membrane's voltage, we investigated the half maximal activations (A1/2) of the m and h sodium and n potassium gates as a function of the membrane voltage. A1/2 of the n and m activating gates are −53.5 mV and −40 mV, respectively, while h inactivating gate's A1/2 is −62.5 mV. Thus, small depolarizing IPSPs (0–0.7 mV) relative to the Vrest of −70 mV are influenced mainly by the hyperpolarizing potassium conductance and are therefore decreased. However, depolarizing EPSPs (5–24 mV) are dominated by the depolarizing sodium conductance and are therefore increased.
Recent reports suggest that other types of dendritic voltage-dependent channels amplify IPSP in spinal cords. Bui et al. (2008) and Hyngstrom, Johnson, and Heckman (2008) have simulated the interaction between persistent inward currents (PICs) and IPSPs in the dendrites of spinal MNs using a compartmental model. IPSPs were generated by REN synapses, dispersed on the dendrite at proximal, distal, uniform, and realistic-based locations. The largest IPSP peak was generated in the presence of the PIC and consisted of L-type Ca2+ channels and REN synapses distributed according to the realistic location.
In contrast to the spinal cord, it was shown that at cortical pyramidal neurons, the somatic IPSP duration, generated by proximal synapses, is increased by axo-somatic located sodium channels (Williams & Stuart, 2003). The increment was obtained only when the IPSP was activated at depolarized membrane potentials. However, IPSPs obtained at hyperpolarized potentials were similar to the “passive” IPSP. Furthermore, distally activated IPSPs measured at the soma were unchanged at all voltage potentials. Stuart (1999) claimed that the peak and TI of a hyperpolarizing IPSP initiated at depolarized potentials increased in neocortical pyramidal neurons. The cause of these amplifications is the hyperpolarization associated with those IPSPs, which decreases the voltage-dependent sodium conductance and thus its impact on the IPSP. Similar results were reported in Purkinje cells (Solinas, Maex, & De Schutter, 2006). The deactivation of the dendritic Ca2+- and Ca2+-dependent K+ currents increases the hyperpolarizing IPSP. As a result, the distal activation of inhibitory currents creates larger somatic IPSP amplitudes than the IPSP of a passive dendritic tree. However, the rise time was not affected by the active components of the dendrite.
The major reason our analysis generated different results is that we did not introduce PICs in our model. We explicitly excluded them based on the observation that INaP currents (Harvey, Li, Li, & Bennett, 2006) and L-type Ca2+ currents (Hounsgaard & Kiehn, 1993; Larkum et al., 1996), believed to be the dominant PICs (Elbasiouny, Bennett, & Mushahwar, 2005), are usually involved with generating plateau potentials and repetitive firing (Lee & Heckman, 2001; Bui et al., 2003). The objective of this study was to examine synaptic modifications rather than firing pattern of the neurons. Moreover, the distribution functions of the voltage-dependent channels on the cortical pyramidal dendrites and the spinal cord MNs are different. All proximal cortical dendrites contain active channels, and the conductance density decreases linearly as a function of the distance from the soma (Stuart & Sakmann, 1995).
4.2. Location-Dependent Variability of Inhibitory Synaptic Input.
The existence of L type Ca2+(Cav 1.3) PIC in MN dendrites was reported recently (Elbasiouny et al., 2005; Grande, Bui, & Rose, 2007; Heckman, Hyngstrom, & Johnson, 2008). In the presence of PIC, the current entering by the excitatory synapses of MNs was five times larger than the synaptic current entering a passive dendrite (Heckman et al., 2008). At hippocampal neurons, the PIC T-type Ca2+ and persistent Na+ channel minimized synaptic variability (Cook & Johnston, 1997). This is known as the boosting hypothesis of distal synaptic inputs by dendritic voltage-dependent channels that renders all synapses electronically equidistant from the soma (Cook & Johnston, 1997). In our study, since no PICs were introduced in the dendrites, the only active channel components were sodium and delayed rectifier potassium currents. These were not enough to produce an entire boosting effect. In fact, under the conditions of our model, the MNs' dendrites behaved almost like Rall's passive dendrite (Rall, 1959). According to this theory, the efficacy of a synapse, as measured at the soma, is dependent on its dendritic location. This means, for example, that the somatically measured IPSP peak of proximally located synapses is larger than a distal one, as was the case in our simulation of the IPSPs.
4.3. IPSP Dependence on MN Input Resistance.
Based on our simulations we can conclude that IPSP attenuation between the synaptic input location and the soma depends on the MNs' input resistance (RN) in α- MNs and that these results are adequately explained by passive membrane properties alone (Rall, 1967; Carnevale & Johnston, 1982; Nitzan, Segev, & Yarom, 1990; Larkum, Launey, Dityatev, & Luscher, 1998). RN variability seems to depend on the dendritic branch order (Larkum et al., 1998; Mouchet & Yelnik, 2004). Larkum et al. (1998) analyzed synaptic inputs of two separated dendritic locations by using patch electrodes in cultured MNs. They concluded that in a passive dendritic tree, signals of the same shape but different amplitude would decrease by the same proportion when traveling in the same direction over the same section of dendritic tree. Such a signal can be fitted by a regression line, where the attenuation ratio functions as the gradient.
We have shown in our simulations that the ratio of two different IPSPs, generated at the same location on the dendrites but with distinct inhibitory conductance durations, is insensitive to the MN's RN. In other words, the ratio of IPSPs is identical in all MNs when created from the same conductances. In contrast, the ratio of two IPSPs with the same conductance duration but located differently is a linear function of MN's RN.