Department of Anatomy, Histology and Embryology, Faculty of Medicine, Medical and Health Science Center, University of Debrecen, Nagyerdei krt 98, Debrecen, H-4032, Hungary

Abstract

Background

The location specific motor pattern generation properties of the spinal cord along its rostro-caudal axis have been demonstrated. However, it is still unclear that these differences are due to the different spinal interneuronal networks underlying locomotions or there are also segmental differences in motoneurons innervating different limbs. Frogs use their fore- and hindlimbs differently during jumping and swimming. Therefore we hypothesized that limb innervating motoneurons, located in the cervical and lumbar spinal cord, are different in their morphology and dendritic signal transfer properties. The test of this hypothesis what we report here.

Results

Discriminant analysis classified segmental origin of the intracellularly labeled and three-dimensionally reconstructed motoneurons 100% correctly based on twelve morphological variables. Somata of lumbar motoneurons were rounder; the dendrites had bigger total length, more branches with higher branching orders and different spatial distributions of branch points. The ventro-medial extent of cervical dendrites was bigger than in lumbar motoneurons. Computational models of the motoneurons showed that dendritic signal transfer properties were also different in the two groups of motoneurons. Whether log attenuations were higher or lower in cervical than in lumbar motoneurons depended on the proximity of dendritic input to the soma. To investigate dendritic voltage and current transfer properties imposed by dendritic architecture rather than by neuronal size we used standardized distributions of transfer variables. We introduced a novel combination of cluster analysis and homogeneity indexes to quantify segmental segregation tendencies of motoneurons based on their dendritic transfer properties. A segregation tendency of cervical and lumbar motoneurons was detected by the rates of steady-state and transient voltage-amplitude transfers from dendrites to soma at all levels of synaptic background activities, modeled by varying the specific dendritic membrane resistance. On the other hand no segregation was observed by the steady-state current transfer except under high background activity.

Conclusions

We found size-dependent and size-independent differences in morphology and electrical structure of the limb moving motoneurons based on their spinal segmental location in frogs. Location specificity of locomotor networks is therefore partly due to segmental differences in motoneurons driving fore-, and hindlimbs.

Background

Investigation and comparison of morphological and electrical properties of

The location specific motor pattern generation properties of the spinal cord along its rostro-caudal axis were clearly demonstrated in experiments with newt embryos. In these experiments, when grafts of limb innervating cervical and lumbo-sacral spinal cord segments were replaced by each other, the rhythm, coordination, and general characters of limb movements were determined by the innervating spinal segments irrespective of their heterotopic nature to the innervated limb

Methods

The sample of motoneurons

In this study a sample of eight cervical and eight lumbar limb innervating alpha MNs of adult frogs (

Details about the labeling procedures, tissue preparations, shrinkage and optical corrections of morphological data were described in the original papers

Morphometry

To characterize the MNs quantitatively, twelve morphological variables were used. These morphological variables may be divided into three groups describing the soma, the stem dendrites and the rest of the dendritic trees (Table

**Group**

**Morphological variable**

**Description**

Descriptors were divided into three groups describing the somata, stem dendrites and dendritic arborization.

**Soma**

Roundness

The ratio between the maximum and minimum diameters of the soma.

Soma surface

The average surface area of the prolate and oblate ellipsoids fitted to the soma.

**Stem dendrites**

Number of stem dendrites

Number of dendrites connected to the soma.

Sum of diameters of stem dendrites

The mean stem diameter multiplied by the number of stem dendrites.

**Dendritic tree**

Number of dendritic branches

A branch is defined as part of the dendritic tree between two branch points, a branch point and an end point or between the soma and the first branch point.

Maximum order of dendritic branches

The highest number of branch points along dendritic paths from the soma to end points.

Combined (total) dendritic length

Sum of the length of all dendritic branches.

Surface

Sum of the surface of all dendritic branches.

Mean parent length

Mean length of branches connecting two branch points in the dendritic tree of the neuron.

Mean distance to BRP

Mean distance of branch points from the soma measured along the dendritic branches (path distance).

Mean distance to ENDP

Mean distance of end points from the soma measured along the dendritic branches (path distance).

Max distance of ENDP

Path distance of the farthest end point from the soma.

Perikarya of MNs innervating limb muscles have ellipsoid or fusiform shapes both in the lumbar and cervical spinal cord. Calculation of surface area of somata was based on the major and minor diameters of somata measured on photographs of the perikarya at 500X magnification, which were corrected for tissue shrinkage

Computer modeling and descriptors of signal transfer properties

Discretization of the model

We used the simulation environment of NEURON
^{2}). In this case the 0.2 λ criterion yielded 38 μm as the maximum geometrical length of compartments, what we used in all simulations. The number of compartments ranged between 880 and 6209 per neuron depending on neuronal size and complexity.

Membrane properties

We assumed passive membrane with biophysical properties measured for similar MNs. The mean input resistance at the soma and the axial resistivity of the cytoplasm of spinal MNs in frogs were measured to be 1.4 ± 0.7 MΩ
_{ms} = R_{md}) and this common value was determined by the compartmental model so that the input resistance at the soma had 1.4 MΩ or 5 MΩ values. In the inhomogeneous model we assumed a step increase in membrane resistance towards the dendrites at the soma-dendritic junction (R_{ms} < R_{md}) but the membrane was uniform over the dendrites and the soma
_{ms} < R_{md}) the specific dendritic membrane resistance was fixed and the resistance of the soma was determined by using the computer model to reproduce the physiologically realistic input resistance of the MN. In simulations when the effects of changes in the general level of synaptic activity received by dendrites (background synaptic activity of dendrites) were investigated, the specific membrane resistance of dendrites was varied and the somatic specific membrane resistance was kept constant
^{2} specific resistances for dendrites to mimic high, middle (control) and low levels of background synaptic activities and the somatic resitance was 500 Ω·cm^{2}. With these R_{md}-R_{ms} pairs the somatic input resitance remained within its physiological range
^{2}.

Initiation of PSPs and measures of dendritic signal transfer

To analyze MNs electrotonically, different measures of signal transfers were computed between dendritic points and the soma in the various membrane models of MNs by using the NEURON software

In our investigations current and voltage transfers as well as somatic to dendritic ratios of shape parameters of transient EPSPs were weighted by the surface of the dendritic compartment whose mid-point was used to generate the signal (see Figure
^{th}, 25^{th}, 50^{th}, 75^{th} and 90^{th} percentiles; the values in the distributions, below which the corresponding percents of all observations fall. Since the frequency of dendrites with very low and high transfer values to soma is limited, the errors associated with increasingly lower and higher percentiles are disproportionally bigger than the error associated with the 50^{th} percentile
^{th} percentile (or median value, whose weight was 1). Weighting process was performed by two different sets of weighting factors to check if our results are independent on the particular weighting strategy. First, the 10^{th}, 90^{th} and 25^{th}, 75^{th} percentiles had 0.2 and 0.8 weights respectively, while in the second case, the weights were 0.33 and 0.67. The two sets of these weighted percentiles were then used as descriptors in hierarchical cluster analysis to classify MNs based on their dendritic signal transfer properties and the percentiles are shown as box plots in figures.

Steps of data processing to create standardized area weighted distributions of signal transfer values.

**Steps of data processing to create standardized area weighted distributions of signal transfer values.** Example is based on current transfers of MN C-IC82 but steps are similar for other measures of signal transfers we used. (**A**) Frequency distribution of somatopetal current transfers measured from mid-points of each compartment. These raw values were area weighted (**B**) to give proportionally bigger weight to transfers from compartments with bigger surface area. Then the area weighted distribution was standardized (**C**) to eliminate variable size effects of MNs on signal transfers. Shape of standardized and area weighted distribution of transfers was quantified by the 10^{th}, 25^{th}, 50^{th}, 75^{th} and 90^{th} percentiles of the distribution (see lower horizontal axis in part **C**).

Statistical analysis

For statistical analysis and plotting the figures the Microsoft Office (Microsoft Corp.), PAST

**MET descriptor**

**Cervical MNs**

**Lumbar MNs**

**R**_{N} **= 1.4 MΩ**

**R**_{N} **= 5 MΩ**

**R**_{N} **= 1.4 MΩ**

**R**_{N} **= 5 MΩ**

MET descriptors were measured in cervical and lumbar limb moving MNs with homogeneous (R_{ms} = R_{md}) and inhomogeneous (R_{ms} < R_{md}) soma-dendritic membranes and with different neuron resistances. Measures of length of dendrites in METs are in units of generalized space constant (λ). Variables with statistically significant differences in pair-wise comparisons of METs of MNs from different spinal segments were marked by asterisks (Mann–Whitney test, p < 0.05). BRP and ENDP abbreviate branch points and end points, R_{N} is the neuron resistance.

**Homogeneous membrane**

Combined MET length (λ)

439.9 ± 66.2 *

260.7 ± 25.6*

819.8 ± 130.4 *

434.7 ± 32.5 *

Mean length (λ)

3.6 ± 0.6

2.1 ± 0.2

3.7 ± 0.5

2.0 ± 0.1

Mean parent length (λ)

2.2 ± 0.3

1.1 ± 0.1

2.2 ± 0.3

1.3 ± 0.1

Mean distance to BRP (λ)

5.7 ± 0.8

3.4 ± 0.2

7.1 ± 1.1

4.3 ± 0.4

Mean distance to ENDP (λ)

12.9 ± 1.9

7.3 ± 0.5

14.2 ± 2.0

8.1 ± 0.6

Max. distance of ENDP (λ)

24.8 ± 3.7

12.9 ± 1.2

28.7 ± 4.1

14.5 ± 1.3

**Inhomogeneous membrane**

Combined MET length (λ)

181.8 ± 26.8 *

169.4 ± 16.6 *

302.5 ± 18.7*

288.0 ± 17.9 *

Mean length (λ)

1.4 ± 0.2

1.3 ± 0.1

1.4 ± 0.1

1.3 ± 0.1

Mean parent length (λ)

1.2 ± 0.1

0.9 ± 0.1

1.1 ± 0.1

1.1 ± 0.2

Mean distance to BRP (λ)

4.1 ± 0.5

2.9 ± 0.1 *

4.8 ± 0.3

3.6 ± 0.2 *

Mean distance to ENDP (λ)

6.7 ± 0.8

5.4 ± 0.2

7.4 ± 0.4

6.0 ± 0.3

Max. distance of ENDP (λ)

9.3 ± 1.2

7.8 ± 0.4

10.5 ± 0.7

9.2 ± 0.6

In analysis of dendritic orientation, the full circle around the soma in the transverse plane of the spinal cord was divided into equal bins of 40 degree angles and the total lengths of projected dendritic arbors of the two groups of MNs within each bin was compared by Mann–Whitney tests.

Cluster analysis was applied when MNs were characterized by percentiles of standardized and area weighted voltage-, and current transfer distributions to describe dendritic signal propagation. These descriptors have no easy direct interpretation, and therefore identification of those descriptors that discriminate cervical and lumbar MNs significantly by discriminant analysis gives no further information. However, by using these standardized descriptors we could avoid the confounding effects of size-related variability among neurons and could focus on structural rather than size-dependent electrotonic properties of dendrites.

The cluster analysis was used with Euclidean distance metric and with two different agglomerative algorithms, the Ward’s and the Pair group methods. In the beginning of the agglomerative analysis all MNs were separated and later they were united step by step to form clusters with increasing numbers of MNs. In each consecutive agglomerative step, when further MNs or clusters of MNs were fused, the fusion occurs at increasing distances (at decreasing similarity levels). The hierarchy of agglomerative steps may be represented by a tree-like structure called dendrogram (see Figure

Sample cluster formations represented by dendrogram and similarity level (dashed line) at last order clusters

**Sample cluster formations represented by dendrogram and similarity level (dashed line) at last order clusters.** In calculation of homogeneity indexes measuring segmental homogeneities of MNs in the biggest two clusters (last order clustering and Peterson’s indexes), the ratios of MNs from the lumbar (L) and cervical (C) segments were considered in each cluster. See Methods for more details.

To check if MNs have a tendency to form last order clusters where cervical and lumbar MNs are segregated, homogeneity (or similarity) indexes were used to measure segmental homogeneity within clusters. Measuring segmental homogeneities is feasible since increasing segmental differences among MNs are reflected in their increasing segregation tendency to different clusters shown by the cluster analysis, and as a consequence of segregation, the clusters become more and more homogeneous in terms of segmental origins of MNs they contain. This way, increasing segmental segregation of MNs between clusters may be measured by segmental homogeneities (homogeneity indexes) within clusters. Two different homogeneity indexes were used. In addition to the Peterson’s index
_{*} (2/5) + 9 _{*} (3/6)]/16 = 0.46 being the total number of neurons is 16. Another index used to measure last order cluster formations was the Peterson’s index
_{i} | a_{i} – b_{i} | where a_{i} and b_{i} are the segmental portions of MNs in cluster A and B; i = lumbar or cervical. With the clusters of the above example the calculation yields: 1 – 0.5 * [| (2/7) – (6/9) | + | (5/7) – (3/9) |] = 0.62. Both indexes may have values between 0 and 1. The indexes are closer to 1 if cervical and lumbar MNs are more similar and they are getting smaller with increasing differences between MNs of the two spinal segments. The significance of segmental cluster formation tendencies (when cervical and lumbar MNs get segregated in different last order clusters) was tested by comparing these homogeneity indexes with those of artificially generated cluster formations, where segmental origins of MNs were assigned randomly prior to the cluster analysis. For each actual dendrogram 100 other artificial dendrograms were generated reflecting grouping tendencies of the real set of MNs with their segmental origins artificially randomized. The mean value of indexes was calculated for the 100 artificial dendrograms and the mean was then compared with the actually found index by one sample t-test. If this test showed a significant difference between the real and artificial indexes, then we concluded that MNs tended to form homogeneous groups determined by their segmental location in the spinal cord.

Results

Morphology of motoneurons

The purpose of this study was to investigate differences between alpha motoneurons (MNs) located in the cervical and lumbar enlargements of the frog that innervate the muscles of forelimbs and hindlimbs. These MNs had ellipsoid or fusiform perikarya in the lateral area of the ventral horn. The dendritic arborization of these MNs could be divided into a dorsomedial, dorsal and lateral dendritic arrays with many dendrites extending to the lateral funiculus of the white matter. The lateral dendrites extended to the border of spinal cord where they formed a subpial meshwork (Figure

Camera lucida drawings of dendritic trees of fore- and hindlimb moving motoneurons (MNs) of frogs.

**Camera lucida drawings of dendritic trees of fore- and hindlimb moving motoneurons (MNs) of frogs.** Neurons are from the 3^{rd} cervical and the 8^{th} or 9^{th} lumbar segments as seen in the transverse plane of the spinal cord. Drawings of MNs were superimposed with the contours of spinal cord to show locations of somata and direction and extent of dendrites. Dashed lines mark the border of white and gray matters. Scale bars are 100 μm. Part of this Figure was reprinted from

Metric morphological description of cervical and lumbar motoneurons

The mean surface area of somata for cervical MNs was about 35% bigger than that of the lumbar MNs but the difference did not reach the significant level because of the high variances in both spinal segments (Table

**Group**

**Variables**

**Cervical MNs**

**Lumbar MNs**

Variables with statistically significant differences between limb moving motoneurons of the two parts of the spinal cord are marked by asterisks (Mann–Whitney-test, p < 0.05). BRP and ENDP are branch point and end point of the dendritic trees. Values are means ± S.E.M.s, medians are in brackets.

**Soma**

* Roundness

3.9 ± 0.3 (3.9)

2.6 ± 0.3 (2.8)

Surface (μm^{2})

9212 ± 1347 (7642)

6776 ± 652 (6885)

**Stem dendrite**

Number

4.8 ± 0.6 (4)

5.7 ± 0.6 (5)

Sum of diameters (μm)

26.4 ± 1.9 (27.8)

32.7 ± 3.9 (32.1)

**Dendritic tree**

* Total number of branches

127 ± 3.7 (127)

216 ± 5.3 (226)

* Max. order

9.9 ± 0.6 (9)

11.3 ± 0.4 (11)

* Combined (total) dendritic length (μm)

32908 ± 3087 (32818)

54522 ± 7083 (60783)

Surface (μm^{2})

141975 ± 6717 (141491)

193239 ± 18270 (163233)

Mean parent length (μm)

145.4 ± 2.8 (138.6)

163.7 ± 6 (154.7)

Mean distance to BRP (μm)

390.7 ± 8.8 (380.3)

495.3 ± 24.2 (448.6)

Mean distance to ENDP (μm)

881.8 ± 40.1 (831.9)

973.5 ± 114.4 (881.4)

Max distance of ENDP (μm)

1615.1 ± 100 (1596.3)

2034.5 ± 257.2 (1925.8)

Distribution of branch points

The total number of branch points was more numerous in lumbar MNs than in MNs of the cervical part of the spinal cord (101 ± 18.9 and 59 ± 4.8 in lumbar and cervical MNs respectively, Mann–Whitney test, p < 0.005). The distributions of branch points over different path distance domains were also different (Wilcoxon test, p < 0.0005, Figure

Spatial distributions of branch points in dendritic trees of limb moving MNs.

**Spatial distributions of branch points in dendritic trees of limb moving MNs.** Distances of branch points were measured along dendritic paths from the soma. Closed and open circles stand for the cervical and lumbar MNs respectively. Both the mean total numbers and the distributions of branch points are significantly different (Mann–Whitney test, p < 0.005; Wilcoxon test, p < 0.0005) in MNs of the cervical and lumbar parts of the frog spinal cord.

We did not find any significant difference in the average lengths of dendritic branches in the proximal region (154 ± 6 μm and 131 ± 3.9 μm in cervical and lumbar MNs respectively, Mann–Whitney-test, p = 0.83). This indicates that difference in branch point frequencies was due to longer total length of dendrites with the same average tendency of branching in the lumbar MNs close to somata as also found by Dityatev et al.

Orientation of dendritic trees of motoneurons

Early analyses of dendritic orientation of limb moving MNs in frog spinal cord described three dendritic arrays that extended in the dorso-medial, dorsal and lateral directions

Here we compared orientation of MN dendrites in the lumbar and cervical levels of the cord. Polar histograms were created (Figure

Polar histograms showing angular distributions of dendritic lengths projected to the transverse plane.

**Polar histograms showing angular distributions of dendritic lengths projected to the transverse plane.** Full circle around somata (S) was divided into 40 degree angle intervals starting with the dorsal direction (0°), the total lengths of dendritic branches were measured within these intervals and averaged over MNs within the same part of the cord. Mean dendritic lengths were represented on a relative scale by the length of a line drawn from the soma in the given direction and finally end points of these lines were interconnected (gray line for the cervical MNs and black line for lumbar MNs). The direction with the longest dendritic length was taken as 100% for the lumbar and cervical MNs separately. Ventromedial (VM) direction (120–160°), where significant segmental difference in angular distributions of dendrites was detected (Mann–Whitney-test, p < 0.05) is shaded in gray.

Morphoelectrotonic transformation of motoneurons

Qualitative analysis

Since it is difficult to infer how MNs’ dendritic architecture affects electrical signal propagation, we used the graphical approach of the morphoelectrotonic transformation (MET,
_{ms} = R_{md}) and inhomogeneous (R_{ms} < R_{md}) soma-dendritic membranes (see Methods) at different neuron resistances.

Dendritic morphology and morphoelectrotonic transforms of a cervical motoneuron.

**Dendritic morphology and morphoelectrotonic transforms of a cervical motoneuron.** Morphology (**A**) and METs (**B**) and (**C**) of the same MN (C-167) with homogeneous (R_{ms} = R_{md}) and inhomogeneous (R_{ms} < R_{md}) soma-dendrite membranes constrained by the physiological 5 MΩ somatic input resistance of the MN for both METs. Arrows 1 and 2 point to homologous proximal (red) and distal (green) dendritic branches where changes during METs are visibly non-proportional to their geometrical sizes (for quantitative analysis see body text). Arrows labeled by S point to the center of the soma (its entire shape is not shown in the figures). D-dorsal, V-ventral, M-medial, L-lateral directions. Note the different size of the MET with our choice of the physiologically constrained pair of Rms-Rmd values in the inhomogeneous soma-dendritic membrane (**C**) relative to the MET of the same MN with homogeneous membrane (**B**) drawn to a common scale of space constants. Both METs show attenuations of somatopetal PSP propagation (‘V_{in} mode’ in NEURON) at DC input (frequency = 0 Hz), recording electrode was at mid-soma, stimulating electrode was at mid-points of dendritic compartments. Dendritic and somatic specific membrane resistances (R_{md} and R_{ms}) were equally 8348 Ωcm^{2} for the homogeneous soma-dendritic membrane, while for the MET with inhomogeneous membrane R_{md} and R_{ms} were 20000 and 1046 Ωcm^{2} respectively. With these R_{ms} and R_{md} values the somatic input resistance was 5 MΩ in both membrane models of the MN.

If the METs of the same MN with homogeneous and inhomogeneous soma-dendrite membranes but with identical somatic neuron resistances are compared the size (compactness) of the MET may be different (Figure
_{md}) and the soma (R_{ms}). Note that both R_{md} and R_{ms} are different in these two METs; R_{md} is bigger, while R_{ms} is smaller in Figure
_{md} makes the MET more compact, while the decreasing R_{ms} has the opposite effect on compactness. When the geometry and the METs of dendritic arbors were compared, careful inspection found non-proportional changes in the MET size of dendritic branches relative to their morphological appearance (see branches 1 and 2 in Figure

Quantitative analysis of morphoelectrotonic transforms

Comparison of different morphoelectrotonic transforms

To compare different METs of dendrites (representing electrotonic architectures in different membrane models) of the same MN, a set of MET descriptors (Table
_{ms} < R_{md}), cervical and lumbar MNs also differed in their mean MET distances measured to branch points.

Discriminant analysis using MET descriptors classified cervical and lumbar MNs 100% and 95% correctly in all membrane models (Wilks’ lambda <0.02, p < 0.005). Similar results were obtained when the number of descriptors was reduced. With just four descriptors (combined MET length, mean MET distance to branch points, mean MET distance to end points and the maximum MET distance to end points) MNs were still classified 87% segmentally correctly. These results were cross validated by the 16-fold and the repeated random subsampling techniques

Comparison of morphoelectrotonic transforms of dendrites with their original morphology

In case of the two previously selected dendritic branches we calculated their geometrical and MET size ratios. The lengths of the proximal and distal branches were 84 and 533 μm respectively (branch 1 and 2 in Figure
_{ms} < R_{md}) membrane. These values yield 84/533 = 0.16 proximal to distal ratio for the geometrical size of branches, and 1.97/2.50 = 0.79 and 1.94/1.68 = 1.15 ratios in the METs with homogeneous and inhomogeneous membranes respectively. This observation suggests non-proportional changes in the size of dendrites during the MET, which depend on the distance of dendritic branch from the soma.

To investigate these changes further, log attenuations of PSPs to soma were determined from different regions of the dendrites located within 100 μm path distance domains from the perikaryon. Then, the computed attenuations were divided by the mean attenuation of PSPs measured from dendritic sites within 0–100 μm from the perikaryon. These relative attenuations were not linearly related to the path distances of locations where PSPs were generated indicating again a non-proportional change in size of dendrites during the METs (Figure
_{ms} < R_{md}) membrane model with 1.4 MΩ neuron input resistance was assumed.

Comparison of morphoelectrotonic transformations with their original geometry in (A) cervical and (B) lumbar MNs.

**Comparison of morphoelectrotonic transformations with their original geometry in (A) cervical and (B) lumbar MNs.** Somatopetal log attenuations of PSPs were computed from thousands of dendritic locations per neuron and divided by the mean attenuation calculated from locations within 100 μm from the soma. Finally, these ratios (relative log attenuations) were averaged and graphed over 100 μm path distance ranges from the soma. Attenuation ratios were computed in four different models of MNs by using 1.4 MΩ neuron resistance with homogeneous (R_{ms} = R_{md}) and inhomogeneous (R_{ms} < R_{md}) soma-dendritic membranes (closed and open rectangles) and by 5 MΩ neuron resistance with homogeneous and inhomogeneous membranes (closed and open circles). In homogeneous membrane models R_{md} was equal to R_{ms}, in inhomogeneous models R_{md} = 20000 Ωcm^{2} was assumed. The common specific membrane resistance for the soma and dendrites in homogeneous models and the R_{ms} values in inhomogeneous models were defined to have neurons with 1.4 or 5 MΩ input resistance measured at the soma. Continuous linear thick line is a reference where data points would be positioned if METs cause proportional changes in size of dendrites relative to their morphological appearance. Note that many error bars, representing S.E.M.s, are too small to be visible because of the high numbers of sampling sites.

Rates of log attenuations are different in cervical and lumbar motoneurons

The mean somatopetal log attenuations of PSPs were determined as a function of path distance from the soma in different membrane models of the cervical and lumbar MNs (Figure
^{−6}) from the same geometrical distance in lumbar and in cervical MNs both in the homogeneous (R_{ms} = R_{md}), Figure
_{ms} < R_{md}, Figure

Comparison of somatopetal log attenuations of postsynaptic potentials.

**Comparison of somatopetal log attenuations of postsynaptic potentials.** Attenuations of PSPs were computed from dendritic locations and averaged within 100 μm path distance ranges from the soma. Homogeneous (R_{ms} = R_{md}, part **A** and **B**) and inhomogeneous (R_{ms} < R_{md}, part **C** and **D**) soma-dendrite membrane models were used with 1.4 MΩ (**A** and **C**) and 5.0 MΩ (**B** and **D**) neuron resistances, where R_{ms} and R_{md} values were defined as described in the legend of Figure

Structural comparison of signal transfer properties

Nerve cells with significantly different sizes are likely to be different electrotonically too. However, it remains an important question if neurons with different sizes keep their electrotonic difference if their comparison is based only on their topological structure and size-dependency is ignored. Here we studied this issue by using size-independent comparisons of dendritic signal transfer properties in cervical and lumbar MNs. This type of electrotonic comparison is feasible since electrotonic structure - in analogy to the geometrical structure - is not only defined by metric-related properties, but also by the branching structure (topology) of dendritic trees affecting the shape of distributions of voltage and current transfer properties over the length of dendrites.

To focus on such structural rather than size-related features of dendrites, we used distributions of standardized and area weighted voltage and current transfer values
^{th}, 25^{th}, 50^{th}, 75^{th} and 90^{th} percentiles (these were graphed as box plots in Figures

Voltage and current transfers in steady-state.

**Voltage and current transfers in steady-state.** Box plots show 10^{th}, 25^{th}, 50^{th}, 75^{th} and 90^{th} percentiles of standardized and area weighted voltage- (**A**) and current transfers (**D**) in steady-state measured from dendritic points to the soma in limb moving MNs in the cervical (shaded boxes) and lumbar (open boxes) segments. Higher and lower percentiles were weighted relative to the median (50^{th} percentile) and used as descriptors for cluster analysis of MNs. The 10^{th} and 90^{th} as well as the 25^{th} and 75^{th} percentiles are shown by the wings and by the borders of boxes respectively, the median is marked by the line within the box (see insert). Dendrograms show segmental segregation tendencies between the cervical and lumbar MNs based on voltage and current transfer properties under high (voltage: part **B**, current: part **E**) and low (voltage: part **C**, current: part **F**) background synaptic activities. Different levels of synaptic background activities were modeled by varying the specific dendritic membrane resistance (R_{md}). High activity: R_{md} = 5000 Ωcm^{2} and low activity: R_{md} = 50000 Ωcm^{2}. In cluster analyses shown, the Ward’s method was used and the weighting factors for percentiles were: 0.2 for the 10^{th} and 90^{th} percentiles and 0.8 for the 25^{th} and 75^{th} percentiles. MN labels starting with letters C and L stand for the cervical and lumbar neurons respectively.

Propagation of voltage transients.

**Propagation of voltage transients.** Somatic to dendritic ratios of PSP amplitudes, half-widths and rise times were computed for each dendritic compartment, ratios were then weighted by the area of the compartments and distributions were standardized. Percentiles are shown as box plots (see insert) for amplitudes (**A**), half-widths (**B**) and rise times (**C**) respectively (boxes for cervical MNs are shaded). These percentiles were then weighted relative to the median and used as descriptors in cluster analysis. Dendrograms of cluster formations (using Pair group method) were based on ratios of amplitudes (**D**), half-widths (**E**) and rise times (**F**). A control, or middle level of synaptic background activity (R_{md} = 20000 Ωcm^{2}) was assumed in all cases shown. Labels starting with letters L and C stand for cervical and lumbar MNs respectively. The weighting factors for percentiles were: 0.33 for the 10^{th} and 90^{th} percentiles and 0.67 for the 25^{th} and 75^{th} percentiles.

Segmental segregation was measured by homogeneity indexes of the last order clusters. The significance of segmental segregation was tested by comparing these homogeneity indexes with those calculated for clusters formed when segmental origin of MNs was randomized (see Methods for more details).

Steady-state signal transfer

In this set of analysis a constant current was injected to generate steady depolarizations in the midpoints of all cylindrical compartments of the cable model and voltage and current transfers to soma were measured. These transfer values were then processed as summarized above.

Voltage transfer

By using somatopetal voltage transfers, our first observation was the higher variabilities for all, except the 90^{th} percentiles of distributions for the lumbar MNs (F-test, p < 0.02) and the generally shifted nature of percentiles relative to those of the cervical MN group (Figure
^{−18}) in their steady-state voltage transfer properties. These segmental differences between MNs were detected at all levels of background synaptic activities with some tendency of MNs to get more similar with the decrease of background activity.

Grouping tendencies of MNs based on steady-state voltage- and current transfers (open and closed triangles).

**Grouping tendencies of MNs based on steady-state voltage- and current transfers (open and closed triangles).** ‘High’, ‘Medium’, and ‘Low’ levels of synaptic background activities on dendrites were modeled by 5000, 20000 and 50000 Ωcm^{2} specific dendritic membrane resistivities respectively. To reveal grouping tendencies cluster analysis was used with the Pair group and Ward’s methods (see horizontal labels starting with ‘pg’ and ‘wm’) with differently weighted (‘fact1’ and ‘fact2’) descriptors. The five descriptors were the 10^{th}, 25^{th}, 50^{th}, 75^{th}, and 90^{th} percentiles of standardized and area weighted distributions of voltage and current transfers between dendritic points and the soma. The two sets of weighting factors of percentiles (‘fact1’ and ‘fact2’) were as follows: In factor set 1, the 10^{th} and 90^{th} percentiles were weighted by 0.2 and the 25^{th} and 75^{th} percentiles by 0.8. In factor set 2, the weighting factors were 0.33 for the 10^{th} and 90^{th} percentiles and 0.67 for the 25^{th} and 75^{th} percentiles. In both sets of weighting factors the weight was 1 for the 50^{th} percentile. In cluster analyses the Euclidian distances were used. Homogeneity indexes, last order clustering index (**A**) and Peterson’s index (**B**), were used to measure segmental homogeneities of MNs within last order clusters, which reflect segregation of cervical and lumbar MNs between the clusters. Homogeneity indexes with values closer to one indicate higher similarity (poorer segregation) of cervical and lumbar MNs. Continuous horizontal lines mark the levels of homogeneity indexes below which segmental separation of MNs by their voltage and current transfer properties is significant.

Current transfer

When signal transfer properties of MNs were characterized by current transfers we found, similarly to the voltage transfer, that lumbar MNs showed higher variabilities in their medians (F-test, p < 0.03) with a less obvious general shift in the standardized distributions (Figure

Transient signal transfer

While steady-state approach measures transfer properties when the generation of PSPs can be approximated by a constant current injection, many synaptic events are short in time and are better approximated by transient conductance changes. Propagation properties of these transient voltage signals are different than those under steady-state circumstances. Therefore, we extended our analysis and investigated transfers of voltage transients. In these simulations PSPs were generated by brief conductance changes in dendritic points. The changes in shape parameters (amplitude, half-width and rise time) of transient PSPs were computed during their propagation to the soma and descriptors of these changes were created as described earlier. Box plots of these descriptors, once again, showed that lumbar MNs were more variable than the cervical ones in the way the amplitudes of voltage transients were reduced during their propagation to the soma (Figure

Cluster formations based on attenuation of peak potentials

The two last order clusters showed significant segmental homogeneity in the origin of MNs they contained (Figure

Segregation of cervical and lumbar limb moving motoneurons based on somatopetal propagation of voltage transients.

**Segregation of cervical and lumbar limb moving motoneurons based on somatopetal propagation of voltage transients.** Cluster analysis was used with the Pair group and Ward’s methods (see horizontal labels starting with ‘pg’ and ‘wm’) with differently weighted (‘fact1’ and ‘fact2’) descriptors. These descriptors were the standardized and area weighted percentiles of somatic to dendritic ratios of peak potentials (open triangles), half-widths (closed circles) and rise times (open circles) of PSPs to quantify the changes in shape of voltage transients generated by conductance changes according to an α-function (g_{max} = 2 nS, t_{max} = 1.5 ms). Last order clustering index (**A**) and Peterson’s homogeneity index (**B**) were used to measure homogeneities within last order clusters, which reflect segregation of cervical and lumbar MNs between these clusters. Homogeneity indexes with values closer to one indicate higher similarity (poorer segregation) of cervical and lumbar MNs. Continuous horizontal lines mark levels of homogeneities below which separation of MNs is significant. ‘High’, ‘Medium’, and ‘Low’ levels of synaptic background activities on dendrites were modeled by 5000, 20000 and 50000 Ωcm^{2} specific dendritic membrane resistivities respectively.

Cluster formations based on somatic to dendritic ratios of half-widths and rise times

Neither the box plots (Figure

The results obtained on propagation of voltage transients may be summarized in the following way: 1) Cervical and lumbar limb-moving MNs of frogs have structurally different dendrites imposing different attenuations of voltage amplitudes during their propagation to the soma. 2) On the other hand, these structural differences in dendrites do not distinguish the two classes of MNs in the way how half-widths and rise times of transient potentials are changing during their dendritic propagation.

Discussion

We investigated morphological and electrical differences between cervical and lumbar spinal motoneurons (MNs) that innervate fore- and hindlimb muscles in adult frogs. We deliberately did not want to compare MNs according to the specific muscles they innervate

MNs undergo substantial developmental changes during embryological and postnatal life that affect the size of cell bodies, size and branching structure of dendrites and these changes are accompanied by physiological maturation of membrane properties like specific membrane resistance, neuron resistance, resting membrane potential, spike shapes and excitability

Overall, these findings suggest that MN maturation is highly dependent on rostro-caudal position of neurons and therefore intrinsic differences in morphology and electrical properties of MNs may be expected to occur along the rostro-caudal axis. These differences have been investigated in the present study.

Methodology

Choice of statistical methods

To investigate segmental differences between MNs, we used pair-wise comparisons of morophological and electrotonic properties, multivariate discriminant analysis and cluster analysis. These methods have been successfully applied in classifying spinal MNs in the turtle

Choice of neuron models

We used high-fidelity compartmental cable models with a set of different membrane properties to account for the variability in neuron resistances measured experimentally, to analyze the effects of the varying size of inhomogeneity in the soma-dendritic membrane and to mimic synaptic background activity. However, in our models we considered a passive membrane. This restriction is validated by a number of factors. Although there is an ever growing list of evidence that voltage-dependent ion channels are present in the dendritic membranes of different nerve cells (see

Subsequent physiological studies suggested involvement of persistent inward currents mediated by voltage-dependent L-type calcium channels of MNs
_{v1.3} channel, a subtype of L-type calcium channels, was studied immunohistochemically in MNs of the mouse, cat and turtle, but not in the frog
_{v1.3} channel

The presence of non-linear processes on limb moving MNs in the frog does not rule out the importance of the proper description of passive signal transfer properties of these neurons as a necessary step to be able to elucidate the functional relevance of active channels better. The view that it is much more difficult to understand the influence of voltage-dependent channels in the absence of detailed knowledge on current and voltage transfers imposed by the passive membrane is shared by many neurobiologists

Morphology

In the present study we characterized forelimb and hindlimb moving MNs of the frog with the aid of quantitative morphological parameters that describe the somata, stem dendrites and the rest of dendritic trees. Pair-wise comparisons of the individual variables indicated that lumbar MNs had rounder somata and bigger dendritic trees comprising more dendritic branches than the cervical MNs. Multivariate discriminant analysis could separate cervical and lumbar MNs into two distinct groups according to their somato-dendritic morphology.

Accuracy of the reconstructed dendritic diameters

We used state of the art neuron reconstruction systems to digitize the 3D geometry of dendrites. However, the morphological data, as in case of any measurement, cannot be free of errors. One critical parameter is the accuracy of dendritic diameters since they affect dendritic impulse propagation

Based on the small contribution of the thinnest (<0.5 μm) dendrites to total surface area and the low sensitivity of dendritic impulse propagation to the thickness of these dendrites we conclude, that the impact of 0.1–0.2 μm overestimation of diameters for the thinnest dendrites is unlikely to be significant in our study.

Branching structure

We found segmental differences both in the numbers and distributions of branch points in dendrites of limb moving MNs of the cervical and lumbar segments. The bigger number of branch points in lumbar MNs does not merely mean more dendritic branches but also a topologically and electrotonically more complex dendritic architecture. Based on various morphological measures of dendritic complexity Dityatev et al.

Locations of branch points are related to signal propagation in the dendrites both in the presence and absence of voltage–dependent ion channels. In dendrites with passive membrane, the current transfer effectiveness generally changes abruptly at branch points altering the ‘cost’ of moving a synapse to a geometrically different location in terms of the change in the soma potential during synaptic activity

Projections of dendrites

Comparison of the orientation of dendritic arborization also demonstrated differences between cervical and lumbar MNs. We found that the ventromedial extension of dendritic trees is more powerful in the cervical MNs. Experiments using retrograde cell degeneration technique showed that the ventromedial area in the gray matter of the cervical segments corresponds to the terminal fields of contralateral tectospinal pathways that do not extend to lumbar segments in frogs

Comparison with other species

The morphology of MNs located in cervical, lumbar and sacral spinal segments have been investigated in several studies

Comparison of our data on the morphology of lumbar MNs of frogs with MNs of cats showed several differences between the two species. The MNs in the frog presented smaller, elongated cell bodies emitting fewer stem dendrites. The size of the dendritic trees was about the half of that found in hindlimb innervating MNs of mammals

The organization of dendritic arbor seemed to be also different in lumbar MNs of frogs and cats. While the dendritic trees of cat MNs emerge in almost all directions without any obvious preference, the dendritic trees of frog MNs are organized into dorsal, lateral and dorsomedial groups. The lateral dendrites dendrites form a dense subpial meshwork running parallel with the border of the spinal cord. This subpial dendritic plexus is well developed in lower vertebrates including anurans but it is reduced in mammals.

Electrical properties of limb moving motoneurons

Our major aim was to test if limb moving MNs are different electrically in the cervical and lumbar segments of the spinal cord. Factors shaping the electrical properties of neurons include the specific membrane resistance of the soma (R_{ms}) and dedndrites (R_{md}). However, the detailed membrane properties (R_{ms} and R_{md}) of these large neurons are still not well known. In addition, the effective membrane resistance may be dependent on the activation state of synapses received by MNs in the functioning spinal networks. Therefore we used two approaches. First, we compared the METs of MNs by assigning different physiologically realistic somatic input resistances (1.4 or 5 MΩ)
_{ms} = R_{md}) and inhomogeneous (R_{ms} < R_{md}) soma-dendritic membrane with a canonical R_{md} = 20000 Ωcm^{2} value for the dendrites (see Figures
_{ms}-R_{md} pairs) of the same neuron (see Figure
_{md} = 20000 Ωcm^{2} as a control value. Higher and lower levels of synaptic activities were modelled by decreasing the R_{md} to 5000 Ωcm^{2} and increasing it to 50000 Ωcm^{2}, while the R_{ms} was kept constant at 500 Ωcm^{2}

Quantitative analysis of morphoelectrotonically transformed motoneurons

We started the investigation of electrotonic properties by performing morphoelectrotonic transformation (MET,

Comparison of the METs with the original geometry of dendrites showed increasingly disproportionate changes in MET sizes in the more distant locations. This was observed independently of the size of soma-dendritic membrane inhomogeneity and the resistance of the neurons. According to the cable theory, in an infinite cylinder with passive membrane the voltage is decaying exponentially with distance if a steady current is injected (see

Next, we investigated: 1) Which distance domains of the dendrites do differentiate between cervical and lumbar MNs and 2) How these distance domains do change when properties of the soma-dendrite membrane are altered?

Two distance domains, whose separation was at ~1500 μm distance, could be identified from where voltage attenuations to soma were characteristically related to the segmental origin of MNs. In this context we found the followings: i) PSPs propagating along the passive dendrites of cervical MNs attenuated less to soma than PSPs in lumbar MNs if the synapses were closer than ~1500 μm. The relationship is the opposite if PSPs were generated farther than ~1500 μm from the soma. ii) These findings are independent of the size of neuron resistivity and the inhomogeneity of the soma-dendritic membrane surface.

The observation that these relationships are independent of the size of neuron resistance suggests implications for the control of PSP attenuations by the uniform decrease or increase of background synaptic activity that changes the effective membrane resistance over the soma-dendritic membrane
_{ms} < R_{md}) nature of the soma-dendritic membrane would be kept, while the neuron input resistance becomes lower with the overall increase in synaptic activity. However, the impact of background synaptic activity on membrane resistance is presumably bigger in dendrites than in the soma since ~95–98% of the membrane surface is given by the dendrites and the majority of synapses are received there in frog spinal MNs

Rates of voltage and current transfers differentiate limb moving motoneurons

Global comparison of log attenuations (MET) of cervical and lumbar MNs resulted in a nearly 100% segmentally correct classification by discriminant analysis. Electrical structures of MNs were further investigated by the voltage and current transfers in dendrites at different intensities of synaptic background activity. In these analyses we used standardized distributions of the transfer values to isolate structure-related electrical differences from those related purely to size. Such structural differences were suggested by the different numbers and distributions of branch points in MNs of the two spinal segments and by the different distance-dependence of log attenuations in the two groups of MNs.

This way, it was relevant to ask directly whether the electrotonic differences between fore- and hindlimb moving MNs are entirely due to their different metric (size-related) morphological properties or they are (also) consequences of the different dendritic structures.

Voltage transfer properties showed differences in the two groups of neurons both in steady-state and in case of transient signals. This suggests that identical inputs propagate differently in the dendrites of cervical and lumbar MNs and the level of depolarization reaching the soma or the nearby axon hillock may be different. Threshold potentials were investigated experimentally in putative MNs along the spinal cord in young frogs and no significant tendency of changes was detected according to the rostro-caudal positions of neurons

However, it is disputed if the major determinant of firing is to exceed a certain voltage threshold or to deliver enough current (charge) to the soma since experimental evidence exists to support each view depending on the conditions of action potential initiation (see

The current transfer from a dendritic point to soma is equal to the rate of voltage transfer in the reverse (somatofugal) direction

Under steady-state conditions we detected a general tendency of increasing segregation (differences) between the limb moving MNs as the background synaptic activity was increased. This tendency was more pronounced if current rather than voltage transfers were considered. A similar tendency of increasing differences in electrotonic properties during higher synaptic activities was reported in a comparative study on different classes of spinal neurons, including MNs, in the cat

Our findings on segmental segregation tendencies of limb moving MNs based on their morphological and dendritic signal transfer properties are strengthened by the consistency of the results obtained with the many different and validated statistical approaches, independently of the type of homogeneity index used, the choice of hierarchical cluster analysis and the weighting factors of descriptors.

Conclusions

We showed location specificity of morphological and electrical transfer properties of the limb moving class of motoneurons in the frog spinal cord. Many of the location-specific differences were size-independent emphasizing the importance of

The results present the first detailed systematic analysis of the location-dependent properties of spinal motoneurons and suggest that specificity of locomotor networks, which control fore- and hind limb movements, is partly due to differences in their motoneurons.

These differences might reflect a basic initial segmental developmental pattern of MNs, which may then be refined according to the needs of specific muscles they innervate. This concept may obtain support from the experimental findings that the targets of these MNs are specified before the outgrowth of axon

Abbreviations

ANOVA: Analysis of variance; BRP: Branch point of a dendrite; CNS: Central nervous system; ENDP: End point of a dendrite; EPSP: Excitatory postsynaptic potential; Hox: Homeobox; MET: Morphoelectrotonic transformation; MN: Motoneuron; PAST: Palaeontological statistics; PSP: Postsynaptic potential; SEM: Standard error of means; SPSS: Statistical package for the social sciences; λ: Space constant; g_{max}: Peak synaptic conductance; t_{max}: Time to peak of the synaptic conductance; R_{md}: Specific dendritic membrane resistance; R_{ms}: Specific somatic membrane resistance; R_{N}: Neuron resistance.

Competing interests

The authors declare that they have no competing interests.

Authors’ contributions

AS wrote the program codes, run simulations, carried out statistical tests and contributed to drafting the paper. JS participated in running simulations and in data analysis. IW and AB reconstructed the neurons. AB also contributed to the body text. EW designed the study, participated in analysis and interpretation of data, and finalized the text. All authors read and approved the final manuscript.

Acknowledgements

The authors are grateful to Dr. Dityatev for allowing the use of some of the neurons, he dye-filled in earlier experiments and for the grants ETT 025/2006 and OTKA K67747 for financial support.

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