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Effects of [beta]-catenin on dendritic morphology and simulated firing patterns in cultured hippocampal neurons.

Introduction

Neurons in the mammalian brain have morphologically complex and diverse dendritic trees (Purkinje, 1837; Golgi, 1874; Kolliker, 1891; Lorente del No, 1934; Sholl, 1953; Rall, 1964; Segev, 1992; Cajal, 1995). [beta]-catenin is an intracellular signaling molecule that plays a key role in regulating dendritic arborization (Yu and Malenka, 2003, 2004). It is present in neuronal processes early in development and is a critical component of the cadherin/catenin cell adhesion complex, which serves as a molecular bridge between the extracellular environment and the intracellular actin cytoskeleton (Gumbiner, 1996; Benson and Tanaka, 1998). [beta]-catenin is a component of the Wnt signaling pathway. Together, Wnt signaling and [beta]-catenin regulate the development and patterning of many brain regions (Cadigan and Nusse, 1997). The Wnt signaling pathway is required for normal brain development (McMahon and Bradley, 1990). However, overexpression of [beta]-catenin can increase cortical size abnormally (Chenn and Walsh, 2002).

Both experimental work and computer simulations have shown that dendritic morphology affects the firing behavior of neurons (Larkman and Mason, 1990; Mason and Lark-man, 1990; Migliore et al., 1995; Mainen and Sejnowski, 1996; Magee and Cook, 2000; Vetter et al., 2001; van Ooyen et al., 2002). In previous work, we combined CA3 pyramidal cell reconstructions with computational modeling to study how dendritic morphology influences neuronal electrophysiology (Washington et al., 2000; Krichmar et al., 2002). Specifically, we showed that cells with larger dendritic trees tended to be more excitable and are more likely to exhibit bursting behavior.

In the present study, we examine the effect of the cadherin/catenin complex on dendritic morphology and its potential effect on cell activity. Because we carried out three-dimensional reconstructions of the cultured hippocampal neurons, some of which were overexpressing [beta]-catenin, we were able to conduct a thorough morphometric analysis on the data (Ascoli, 1999; Ascoli et al., 2001a, b; Scorcioni et al., 2004). We found increases in dendritic branching and overall size, as well as topological differences due to [beta]-catenin expression. Moreover, the 3-D reconstructions of dendritic morphology allowed us to carry out computational simulations of electrophysiology that suggest the larger dendritic trees seen in neurons overexpressing [beta]-catenin may result in increased neuronal sensitivity and excitability.

Materials and Methods

Neuron reconstructions and morphometric analysis

Three-dimensional reconstructions of 29 cultured hippocampal neurons were generated, using Neuron_Morpho, ver. 1.1.5 (Brown et al., 2005), from confocal microscope images at various depths. Cells were divided into three groups based on the level of available cadherin/catenin complex (Fig. 1): green fluorescent protein (GFP) alone (control, n = 11), a stabilized form of [beta]-catenin (GFP-[beta]-cat*, n = 11), and the intracellular domain of N-cadherin which binds to [beta]-catenin and sequesters it away from functional cadherin/catenin complexes (Ncad(intra), n = 7). The experimental details of cadherin/catenin complex and GFP expression, cell culture conditions, and microscopic imaging are described in the study from which the confocal stacks were obtained (Yu and Malenka, 2003). For morphometric analysis, we used L-Measure, ver. 2.0, a tool that allows researchers to extract quantitative morphological measurements from cell reconstructions (Scorcioni and Ascoli. 2001).

Because cells of this type had not been reconstructed before, we carried out a thorough mophometric analysis of the size and topology of these cultured neurons. In this analysis, we measured the area and the length of the dendritic tree, as well as the number of dendritic branches and terminations. We calculated metrics describing tree topology, such as the symmetry of the dendritic tree (Asymmetry), the tapering of the branches (Branch Taper and Rall Ratio), and the straightness of the branches (Meander and Fractal). We also compared the dendritic arbors as a function of their branch order, which is defined as the number of branch points, or bifurcations, in the path from the soma to a given point in the dendritic tree.

Although many of these measurements have been defined elsewhere (Scorcioni and Ascoli, 2001), we briefly explain some of the less apparent metrics here. Asymmetry is the average topological partition over all bifurcations. The topological partition of a bifurcation giving rise to subtrees with N1 and N2 terminal tips is defined as |N1 - N2|/(N1 + N2 - 2), and measures the imbalance between the two subtrees. BranchTaper is the difference between the ending and the starting diameter of a branch, divided by the starting value. RallRatio is the sum of the diameters of the two daughter branches at a bifurcation, each elevated to the power of 1.5, divided by the diameter of the parent branch, also elevated to 1.5. Meander measures the average branch tortuousity as the ratio of the Euclidean distance between the branch starting and ending points, and the path distance between the same two points. Fractal is the Hausdorff dimension computed with the box-counting method. BrAngle measures the angle between the daughter branches, while TrmBrOrder is the average branch order of the dendritic terminations or tips.

All reconstruction files, as well as the reconstruction and analysis software, are publicly available from the internet or the authors (Ascoli, 2006).

Computational modeling

The cell reconstructions were in SWC format (Turner et al., 1995; Cannon et al., 1998), which consists of a list of lines each describing a small neuronal segment, or "compartment." These SWC files were converted into a format compatible with the GENESIS neural simulator system (Bower and Beeman, 1994), while preserving the three-dimensional morphology. Each line in a GENESIS cell descriptor file describes a compartment with its position, diameter, and inter-connectivity, and it includes the density of different active currents within the compartment.

Care was taken to ensure that simulation parameters not specific to dendritic morphology were the same in different cells. Therefore, the morphology of the soma was set to be spherical with a 15-[micro]m radius in all simulated cells, and the axon initial segment and axon compartments of all simulated cells were cylindrical with diameters of 2 [micro]m and 1 [micro]m, respectively, and a length of 75 [micro]m for both. Since the active conductances for the initial segment are identical to that of the axon, the axon can be regarded as 150 [micro]m long with a taper. In all of the simulated cells, the specific axial resistance ([R.sub.i]) was set to 200 [ohm] x cm for soma/dendrite and 100 [ohm] x cm for axon/axon initial segment, the membrane resistance ([R.sub.m]) was set to 50, 000 [ohm] x [cm.sub.2] for soma/dendrite and 1000 [ohm]. [cm.sup.2] for axon/axon initial segment, and the capacitance ([C.sub.m]) was set to 0.75 [micro]F/[cm.sup.2].

A previously developed modification of the CA3 pyramidal cell Traub model (Traub et al., 1991, 1994; Krichmar et al., 2002) was used for the neural simulations. The number of compartments, which was related to the neuron's size and branching complexity, ranged from 356 to 2823 per cell. Passive membrane properties and active channels were evenly and uniformly distributed across the dendrites. The active conductances were [Na.sup.+], high threshold [Ca.sup.2+] and four [K.sup.+]: delayed rectifier ([K.sub.DR]), slow after-hyperpolarization ([K.sub.AHP]), calcium-dependent ([K.sub.C]), and transient ([K.sub.A]). The kinetic equations for the conductances are given in previous modeling papers (Traub et al., 1991, 1994) and are provided with the GENESIS simulator package (Bower and Beeman, 1994). In Traub's 66-compartment model, a scaling constant [phi] was used to convert calcium current to calcium concentration in the submembrane shell for a given compartment (Traub et al., 1994). Since [phi] linearly depends on the surface area of the dendritic compartment, we scaled [phi] appropriately depending on the area of each compartment in the cell models. Specifically, we normalized the constant [phi] by multiplying the value taken from Traub's model by the ratio of Traub's compartment surface area to our dendritic compartment surface area (Table 1).

The model of the pyramidal cell physiology consisted of sets of differential equations that describe the active currents and calcium concentration within each compartment and the propagation of voltage potential between compartments. In our previous work with this model, we had different distributions of conductances for proximal and distal apical and basal dendritic compartments (Krichmar et al., 2002). Because the cultured hippocampal neurons reconstructed in this study lack dendritic lamination and not much is known regarding the distribution of conductances in these cells, a parsimonious and controlled strategy in the present study was to take the average of the four different sets of dendritic tree conductances from our previous work. The axon, soma, and dendrite conductance densities are given in Table 1.

In simulated current clamp experiments, somata were injected with a normalized current such that the observed electrophysiological differences in the neurons would be due only to morphological differences. In particular, the current injected in each neuron was scaled by the ratio of that cell's input resistance to the somatic input resistance of one of the control cells. Thus, the initial instantaneous depolarization was equivalent for all cells, eliminating the influence of the input resistance on the electrophysiological response to current injections. The somatic input resistance of each of the simulated neurons was calculated by measuring the steady-state voltage change in response to 200-ms hyperpolarizing current pulses (0.2, 0.5, and 1.0 nA), using the full cell model with its detailed morphology and active currents (Table 3 for input resistance statistics). Subsequent simulation protocols consisted of a range of somatic current clamp stimulations (corresponding to 0, 5, 10, 50, and 100 pA in the reference neuron) for 5 s, while recording the somatic membrane potential.

Results

Quantitative morphometry

Although it has been shown that dendritic trees are more complex and extensive in GFP-[beta]-cat* cells, and less in Ncad(intra) cells, than in control cells (Yu and Malenka, 2003), the digital reconstruction of dendritic morphology in this study allowed a more detailed morphometric analysis of the different cell groups than had been done previously (Fig. 1).

The distribution of bifurcations and terminations as a function of path distance from the soma illustrates differences in the three cell groups (Fig. 2). Path distance is defined by the distance in micrometers traveled from the soma through the dendritic tree to a particular branch point (i.e., bifurcation) or branch termination (i.e., termination tip). The number of bifurcations could be fitted for all three groups (GFP-[beta]-cat*, control, and Ncad(intra)) with a gamma distribution as a function of path distance (Fig. 2A). Interestingly, there was no difference in the position of the peak number of bifurcations per cell (i.e., the path distance of the peak in the two experimental groups were within 1[micro]m of the peak in the control cells), which was about 50 [micro]m from the soma. However, the peak of the number of bifurcations varied based on the neuronal groups; GFP-[beta]-cat* (14 bifurcations) > control (7 bifurcations) > Ncad(intra) (5 bifurcations), at ~50 [micro]m from the soma. Similar to the bifurcation measurements, the distribution of branch terminations had a peak at about the same path distance for all three groups (~100 [micro]m), but the peak number of terminations was greater for the GFP-[beta]-cat* cells than the control and Ncad(intra) cells (Fig. 2B). The spread of the number of terminations as a function of path distance, measured by the standard deviation of the normal distributions, was also similar among the three groups. The cumulative fraction (as opposed to absolute number) of bifurcations and terminations was plotted as a function of normalized path distance from the soma--that is, a percentage of distance relative to the maximum in each cell. The relative distributions of both bifurcations (Fig. 2C) and terminations (Fig. 2D) were shifted toward the left in GFP-[beta]-cat* cells and toward the right in Ncad(intra) cells. Specifically, the median fraction of bifurcations was located at 26%, 33%, and 36% of the maximum path distance in GFP-[beta]-cat*, control, and Ncad-(intra) neurons, respectively; and the median fraction of terminations per cell was located at 35%, 45%, and 50% of the maximum path distance in GFP-[beta]-cat*, control, and Ncad(intra) neurons, respectively.

Dendritic diameter and length were analyzed as a function of branch order. Internal branches, which end in a bifurcation, and termination branches, which end in a termination tip, were examined separately (Fig. 3A, B). Internal branch diameter (Fig. 3A) decreased in all three groups with branch order, and was well fitted by a power function. The differences in both constant and exponent were not significant between any pair of groups. Termination branch diameter (Fig. 3B) was essentially independent of branch order, as quantified by near-zero values of the fitting exponent. Ncad(intra) cells tended to have thinner termination tips (0.32 [+ or -] 0.12 [micro]m, mean [+ or -] standard deviation) than control (0.43 [+ or -] 0.08 [micro]m) and GFP-[beta]-cat* neurons (0.45 [+ or -] 0.03 [micro]m), although these numbers can only be considered rough estimates because of the large experimental error associated with values close to the limit of light diffraction.

GFP-[beta]-cat* neurons differed from the other cell groups in that the length of their internal branches did not decrease with branch order. Internal branch length decreased linearly with branch order for control and Ncad(intra) cells, but was essentially constant in GFP-[beta]-cat* neurons (Fig. 3C). A similar, but less extreme, situation was observed for terminal branch length (Fig. 3D). Specifically, the negative correlation of termination branch length with branch order in GFP-[beta]-cat* neurons was less pronounced than for the other groups, but not as constant as with the internal branches.

The number of trees in a cell and the number of terminations in a tree are often positively correlated with the somatic surface area and the dendritic stem section area, respectively (Cullheim et al., 1987; Li et al., 2005). In the three groups of cultured hippocampal cells, there were no significant correlations between the number of trees and the somatic surface area (Fig. 4A). However, the number of terminations was well described as a power function of the stem diameter (Fig. 4B), with the strongest dependence (and nonlinearity) observed in the GFP-[beta]-cat* group.

In general, the effect of [beta]-catenin overexpression was an increase in dendritic tree size (Table 2). In particular, GFP-[beta]-cat* cells had significantly more branches (+86% with respect to controls), significantly larger dendritic surface area (+72%), significantly longer dendrites (+65%), and significantly longer maximum path distances (+33%). Ncad(intra) cells typically followed the opposite trend, but the results did not reach statistical significance. Moreover, we found topological differences in the branching structure (Table 2). GFP-[beta]-cat* cells had a significantly higher Rall ratio (+8%), a significantly higher termination branch order (+42%), and a significantly lower meander (-1.3%) than control cells.

Taken together, the morphometric analyses show that neurons overexpressing [beta]-catenin are larger in surface area because of greater branching at all distances from the soma and longer branches with higher branch order. Topological morphometric differences, such as a higher Rall ratio, less branch meandering, and higher termination branch order, were also found when comparing GFP-[beta]-cat* to control neurons.

Simulated electrophysiology

When injected with simulated somatic current steps, all cells responded with a brief discharge transient and reached a steady-state firing pattern after about 1 s (Fig. 5). Cells in all three groups displayed a variety of firing behaviors, ranging from regular spiking (Fig. 5, top panel), to bursting with a plateau of action potential (Fig. 5, middle panel), to bursting with several action potentials in rapid succession followed by a period of quiescence (Fig. 5, bottom panel). Firing frequency always increased with the amount of somatic current injection, but firing mode (spiking vs. bursting) tended to remain consistent within each individual cell. Although the GFP-[beta]-cat* group had a slightly higher proportion of bursters than the control and Ncad(intra) groups, these differences were not significant.

The morphological differences between GFP-[beta]-cat* and control cells, and the range of electrophysiological behavior in response to somatic stimulation, prompted an analysis of the effects of dendritic morphology on the neuronal firing properties. Figure 6 illustrates two such relations for the normalized 50-pA somatic injection condition. Because the responses of these simulated neurons is either regular spiking or bursting, the spiking rate (i.e., firing frequency for regular spikers or intraburst spiking frequency for bursters) was used for comparison. The spiking rate was significantly positively correlated with the number of tree terminations, as well as with several other measures of dendritic size (Fig. 6A). However, there appear to be two regimes: cells with less than 100 terminal tips seem to fire at low rates, while cells with greater than 100 terminal tips tend to fire at high rates. In particular, GFP-[beta]-cat* neurons, characterized on average by a larger dendritic size, also typically displayed higher firing rates. This dichotomy may be a reflection of the bimodal firing properties of the set of simulated neurons.

A better measure of neuron excitability, which tends to capture all the data, is the spike amplitude. The spike amplitude is the difference in membrane potential between the peak and trough of an action potential (Krichmar et al., 2002). The average spike amplitude of a train of spikes displayed a significantly negative correlation with several measures of dendritic size, such as total surface area (Fig. 6B). On average, GFP-[beta]-cat* cells tended to fire lower-amplitude spikes in irregular bursts. The electrophysiological behavior of Ncad(intra) and control neurons tended to be regular spiking (Table 3).

The higher excitability of GFP-[beta]-cat* cells was reflected by an increase in neuronal sensitivity, or amount of current needed to cause a cell to tire. Measurements of neuronal excitability, such as sensitivity and gain, can be derived from the spike frequency/current injection (F/I) relationship of a neuron. The sensitivity corresponds to the intercept and the gain corresponds to the slope of the F/I relationship (Scorcioni et al., 2004). We computed sensitivity and gain for each of the 29 cells, recording the number of post-transient spikes within the first 5 s of the membrane voltage trace at five normalized stimulation currents (0, 5, 10, 50, and 100 pA). Figure 7 illustrates the results of this analysis. The input/output relationship between the number of spikes and current injection was highly linear (Fig. 7A). There was a significant positive correlation between the F/I intercept (or sensitivity) and dendritic size (Fig. 7B). Note that, in our simulations, some of the cells fired with no or slight hyper-polarizing currents and the intercept could be negative. However, no significant correlations were detected between the gain and morphometric parameters. Thus, GFP-[beta]-cat* cells owe their higher excitability to an increased average sensitivity (they need less excitation to start firing) rather than to gain.

In the simulated electrophysiological experiments, parameters characterizing neuronal firing excitability were higher in GFP-[beta]-cat* cells than in the other groups (Table 3). At both low (5 pA) and high (50 pA) stimulation, GFP-[beta]-cat* were consistently characterized by increased firing rate and decreased spike amplitude. Ncad(intra) cells generally displayed opposite trends, but none of these differences were statistically significant. GFP-[beta]-cat* cells, compared to controls, had a significantly lower input resistance. However, as stated in the Methods section, the injection current was normalized by the input resistance to eliminate the influence of this parameter in the simulated electrophysiological experiments.

An interesting question is to what extent the effect of dendritic morphology on neuronal electrophysiology depends on the specific active properties of the model. To investigate this aspect, we repeated all simulations with three variants of the biophysical model: (1) removing all "slow" active properties, including all Ca-dependent processes, but leaving Na and [K.sub.DR] currents; (2) removing Na and [K.sub.DR], and leaving all other conductances and calcium dynamics [complementary to (1)]; and (3) stripping all active properties, rendering the dendritic membranes completely passive. In all three cases, the active channels were left intact in the soma and axonal compartments, guaranteeing the maintenance of the basic spiking ability of the cells. Figure 8 illustrates representative traces from a control cell in each of these conditions. Under the control and removal of Na and [K.sub.DR] conditions, cells fired with irregular bursts (Fig. 8A, C). However, when the calcium-dependent conductances were removed or the dendritic tree was passive, the cell fired with regular spiking (Fig. 8B, D).

Of all significant correlations found between morphological and electrophysiological properties, only the interaction between dendritic surface area and spike amplitude was significant in all model alterations, including the passive model (Table 4). All other effects were drastically dampened and generally appeared to necessitate both "fast" and "slow" components of the dendritic active membrane properties.

Discussion

Neuronal function is closely coupled with neuronal structure and it is of great importance to characterize that relationship. To that end, we present here a computational study that investigates the possible effect of a specific structural change on neuronal response. We digitally reconstructed 29 cultured hippocampal neurons that had differences in the expression of the intracellular signaling protein [beta]-catenin, which allowed us to conduct a complete morphometric analysis and simulated electrophysiology. By utilizing morphometric analyses (Ascoli et al., 2001a, b; Scorcioni et al., 2004), we found further evidence that overexpression of [beta]-catenin caused cultured neurons to be significantly larger, in specific measurements of size, than control neurons. Computational modeling made it possible to examine the relationship between dendritic structure and neuron activity. The present results yield interesting predictions on the potential effect that regulators of dendritic morphogenesis could have on neuronal function. These cells had significantly smaller action potential amplitude than control neurons and were more sensitive to current injections. As a consequence, neurons overexpressing [beta]-catenin fired at a higher frequency and tended to burst more than the control neurons.

The morphometric analyses presented here not only documented that the dendritic trees of GFP-[beta]-cat* neurons were larger than normal, they also revealed subtle differences in the branching structure. For example, the numbers of branches and terminations and the maximum path length were significantly greater for GFP-[beta]-cat* neurons (Table 2; Fig. 2). Moreover, measurements of topology identified differences due to overexpression of [beta]-catenin. The termination branch order, the ration of the daughter diameters to the parent, and the relationship between branch length and branch order were significantly different when comparing GFP-[beta]-cat* neurons to control neurons (Table 2; Fig. 3). The result of these differences is a larger, bushier dendritic tree with more regions for synaptic contact (Fig. 1).

The morphological differences described above had a significant influence on neuronal firing behavior. As has been shown previously (Migliore et al., 1995; Mainen and Sejnowski, 1996; Washington et al., 2000; Krichmar et al., 2002), computational modeling can result in useful predictions about the effects of dendritic morphology on electro-physiology. The computational simulations of the neurons in this present study showed a variety of firing behaviors (Figs. 5 and 8). However, the activity of a given neuron when exposed to increased current injections did not show the transition from bursting to regular spiking that had been seen in electrophysiological experiments (Hablitz and Johnston, 1981; Bilkey and Schwartzkroin, 1990) and modeling studies (Traub et al., 1991, 1994; Krichmar et al., 2002). A reason for this discrepancy may be that the cultured hippocampal pyramidal cells are structurally different than the hippocampal pyramidal cells from slice preparations. The cultured hippocampal cells are an order of magnitude smaller in dendritic length and area than pyramidal cells from CA3 slice neurons (compare with Turner et al., 1995). Additionally, the cultured cells do not "look like" classic pyramidal cells; for example, there is no clear distinction between apical and basal dendritic trees.

Our simulation results suggest that the larger [beta]-catenin neurons have greater sensitivity than controls and need less input to be activated. As in previous studies (Mainen and Sejnowski, 1996; Krichmar et al., 2002), spike amplitude and surface area had negative correlation (Fig. 6B). We also found a positive correlation between size, as measured by the number of termination tips, and spike rate (Fig. 6A). These results suggest that neurons overexpressing [beta]-catenin are more excitable than normal neurons. It could be that the increases in spiking rate and excitability in larger cells were due to an overall increase in the number of active channels. But, because the conductances are proportional to membrane area, we would argue that this increase in channels is a function of the morphology.

To further discriminate how this excitability arises, we investigated the input/output relationship of all 29 cultured cells. By plotting the spike rate against the current injection, we were able to examine the sensitivity (i.e., the intercept of the F/I curve in Fig. 7A) and the gain (i.e., the slope of the F/I curve in Fig. 7A). Although there was no significant relationship between gain and morphometrics, the sensitivity had a strong positive correlation with dendritic tree size as measured by the number of terminations (Fig. 7B).

It was not obvious from these results that the inclusion of both active conductances and dendritic morphology were necessary to exhibit the variation in neuronal firing patterns. Recent models investigating the effects of morphology have used fairly simple active parameters (Mainen and Sejnowski, 1996; Vetter et al., 2001) or only passive parameters (London et al., 1999). Therefore, we tested versions of the computational model that had either subsets of active channels or a passive dendritic tree. With the exception of the relationship between surface area and spike amplitude, we found that simplified models did not reveal important relationships between structure and neuronal function (Table 4). For example, the relationship between sensitivity and dendritic tree size was observed only with the full model (Table 4; Fig. 8). Because we used the active parameters that are known to be present in this type of neuron, our results with the simplified model show that all of these parameters are necessary to get a full range of the responses seen in our control model. Moreover, it has been shown that active channels may be necessary for cells to exhibit bursting behavior and that these firing types depend on topological asymmetry and total dendritic length (van Ooyen et al., 2002). For these reasons, it may be important when testing hypotheses of morphology's effect on physiology to include as many as possible of the parameters that influence neuronal dynamics. The present results not only confirm that the interaction between morphology and active parameters is a complex one, they also quantitatively describe how that interaction shapes firing patterns given constant channel density. In the future, we will need to combine electrophysiological studies on the neurons with modeling to completely understand how the different active currents contribute to dendritic physiology.

Like previous work (Washington et al., 2000; Krichmar et al., 2002), this study shows that neuronal structure influences neuronal function. Specifically, these findings show that [beta]-catenin, which causes a particular enlargement of the dendritic arborization, could have implications for the electrophysiological behavior of neurons and therefore could affect the function of neuronal networks. Gene knockout studies have implicated the cadherin/catenin complex as having a functional role at the behavioral level in fear conditioning (Manabe et al., 2000; Park et al., 2002; Israely et al., 2004). These studies suggested that cadherin and catenin alterations cause deformation of the synapse and can affect long-term plasticity. The present work raises the additional possibility that neuronal responses, influenced by alterations in the cadherin/catenin complex, may compromise the signaling necessary for long-term plasticity and behavioral learning.

Acknowledgments

The authors thank Drs. Xiang Yu and Robert Malenka for providing the confocal stacks and for many useful discussions. JLK was supported by the Neuroscience Research Foundation which supports The Neurosciences Institute. GAA was supported by NIH R01 grants NS39600 jointly funded by NINDS, NIMH, and NSF under the Human Brain Project, and AG025633 as part of the NSF/NIH Collaborative Research in Computational Neuroscience program. The authors are also indebted to Mr. William Zettler for technical assistance in the initial phases of this project.

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JEFFREY L. KRICHMAR (1,*), DAVID VELASQUEZ (2,3), AND GIORGIO A. ASCOLI (2,3)

(1) The Neurosciences Institute, 10640 John Jay Hopkins Drive, San Diego, California 92121; (2) Department of Psychology, George Mason University, Fairfax, Virgina 22030; and (3) Krasnow Institute for Advanced Study, George Mason University, MS 2A1, Fairfax, Virginia 22030

Received 13 January 2006; accepted 11 May 2006.

* To whom correspondence should be addressed. krichmar@nsi.edu
Table 1 Active and passive biophysical parameters for the different
compartment types in the cell model

                                                      Axon & Axon
Property/Structure               Dendrites  Soma      segment

[R.sub.i] ([ohm] x cm)             200        200      100
[R.sub.m] ([ohm] x cm)           50000      50000     1000
[C.sub.m] ([micro]F/[cm.sup.2])      0.75       0.75     0.75
Na (mS/[cm.sup.2])                   2        100      500
Ca (mS/[cm.sup.2])                   2          1        0
[K.sub.DR] (mS/[cm.sup.2])          17.5      135      250
[K.sub.AHP] (mS/[cm.sup.2])          1.6        0.8      0
[K.sub.C] (mS/[cm.sup.2])           12         20        0
[K.sub.A] (mS/[cm.sup.2])            0.5        0.5      0
[phi]                               82.5       24     na

The constant [phi], which is scaled linearly with the size of the
compartment, is used to convert calcium current to calcium
concentration in the submembrane shell for a given compartment.

Table 2 Summary of morphometric measures

                                                    GFP-[beta]-cat*
Parameter                  Control (n = 11)         (n = 11)

Size
  [A.sub.soma]              898 [+ or -] 320         765 [+ or -] 321
    ([micro][m.sup.2])
  Trees                       5.6 [+ or -] 2.1         6.5 [+ or -] 2.3
  [summation][A.sub.stem]    73.0 [+ or -] 36.7       95.1 [+ or -] 67.4
    ([micro][m.sup.2])
  Branches                  152 [+ or -] 68.0        282 [+ or -] 98.9
  [summation][A.sub.dend]  4724 [+ or -] 2117       8124 [+ or -] 2150
    ([micro][m.sup.2])
  [summation][L.sub.dend]  2276 [+ or -] 652.5      3759 [+ or -] 926.7
    ([micro]m)
  MaxPath ([micro]m)        209 [+ or -] 41.6        278 [+ or -] 79.3

Topology
  Asymmetry                   0.595 [+ or -] 0.068     0.635 [+ or -]
                                                         0.051
  BranchTaper                 0.27 [+ or -] 0.05       0.24 [+ or -]
                                                         0.04
  RallRatio                   1.50 [+ or -] 0.11       1.62 [+ or -]
                                                         0.09
  Meander                     0.958 [+ or -] 0.006     0.946 [+ or -]
                                                         0.008
  Fractal                     1.14 [+ or -] 0.25       1.02 [+ or -]
                                                         0.04
  BrAngle (deg)              77.1 [+ or -] 5.93       79.1 [+ or -]
                                                         9.42
  TrmBrOrder                  6.37 [+ or -] 2.22       9.05 [+ or -]
                                                         2.88

Parameter                  P      Ncad(intra) (n = 7)      P

Size
  [A.sub.soma]             NS      700 [+ or -] 248        NS
    ([micro][m.sup.2])
  Trees                    NS        4.0 [+ or -] 1.0      NS
  [summation][A.sub.stem]  NS       79.3 [+ or -] 76.9     NS
    ([micro][m.sup.2])
  Branches                 0.015   119 [+ or -] 80.0       NS
  [summation][A.sub.dend]  0.017  3291 [+ or -] 1504       NS
    ([micro][m.sup.2])
  [summation][L.sub.dend]  0.008  1703 [+ or -] 665.7      NS
    ([micro]m)
  MaxPath ([micro]m)       0.03    188 [+ or -] 27.7       NS

Topology
  Asymmetry                NS        0.628 [+ or -] 0.115  NS
  BranchTaper              NS        0.286 [+ or -] 0.34   NS
  RallRatio                0.02      1.39 [+ or -] 0.12    NS
  Meander                  0.01      0.960 [+ or -] 0.008  NS
  Fractal                  NS        1.12 [+ or -] 0.12    NS
  BrAngle (deg)            NS       73.1 [+ or -] 7.97     NS
  TrmBrOrder               0.03      7.21 [+ or -] 3.46    NS

Morphometries used to describe size were the somatic area
([A.sub.soma]), the number of trees (Trees), the summed section area of
all the tree stems ([summation][A.sub.stem]), the number of branches
(Branches), the total surface area of the dendritic tree ([summation]
[A.sub.dend]), the total length of the dendritic tree ([summation]
[L.sub.dend]), and the maximum reached path distance from the soma (Max
Path), Morphometries used to describe topology were dendritic tree
symmetry (Asymmetry), the tapering of the dendritic branches (Branch
Taper), the ration of the daughter branch diameters to the parent branch
diameter (Rall Ratio), the straightness of the branches (Meander), its
fractal pattern (Fractal), the branch angle from the parent (BrAngle),
and the terminal tip branch order (Trm BrOrder). All P values are from
false-discovery-rate corrected Wilcoxon rank-sum tests comparing the
experimental groups [GFP-[beta]-cat* and Ncad(intra)] to controls.

Table 3 Summary of electrophysiological measures

                                                   GFP-[beta]-cat*
Parameter                   Control (n = 11)       (n = 11)

Input Resistance            122.44 [+ or -] 12.64  105.30 [+ or -] 12.80
  (M[OMEGA])
Spike/Current Intercept       0.42 [+ or -] 0.98     4.28 [+ or -] 7.32
Spike/Current Slope (pA-1)    0.74 [+ or -] 0.31     0.70 [+ or -] 0.33
Firing rate (Hz) @5 pA       11.16 [+ or -] 20.24   55.57 [+ or -] 64.76
Firing rate (Hz) @50 pA      14.12 [+ or -] 13.60   59.57 [+ or -] 59.77
Spike Amplitude (mV) @5 pA   87.13 [+ or -] 7.81    72.65 [+ or -] 25.73
Spike Amplitude (mV) @50     84.70 [+ or -] 7.24    71.59 [+ or -] 19.34
  pA

Parameter                   P      Ncad(intra) (n = 7)    P

Input Resistance            0.002  131.90 [+ or -] 11.61  NS
  (M[OMEGA])
Spike/Current Intercept     0.049    0.36 [+ or -] 1.89   NS
Spike/Current Slope (pA-1)  NS       1.00 [+ or -] 0.36   NS
Firing rate (Hz) @5 pA      0.021   18.07 [+ or -] 29.88  NS
Firing rate (Hz) @50 pA     0.012   24.83 [+ or -] 19.92  NS
Spike Amplitude (mV) @5 pA  0.045   92.03 [+ or -] 6.88   NS
Spike Amplitude (mV) @50    0.024   89.93 [+ or -] 7.63   NS
  pA

The spike/current intercept and slope were obtained from the F/I plots
(one example for each cell group shown in Figure 7A). The spike
amplitude is the difference in membrane potential between a peak and
trough of an action potential. The number reported in the table is the
average across a spike train. All P values are from false-discovery-rate
corrected Wilcoxon rank-sum tests comparing the experimental groups
[GFP-[beta]-cat* and Ncad(intra)] to controls.

Table 4 Relationships between electrophysiological measurements and
morphometrics

                                                        Na/[K.sub.DR]
Activity Metric                         Full Model      only

Spiking rate vs. #tips R (P)             0.711 (0.001)   0.654 (0.001)
Spike amplitude vs. surface area R (P)  -0.898 (0.001)  -0.911 (0.001)
Spike/Current Intercept vs. #tips R      0.629 (0.001)  -0.494 (NS)
  (P)
Firing rate @5 pA:                       4.979 (0.021)   2.135 (NS)
  GFP-[beta]-cat*/control (P)
Spike amplitude @5 pA:                   0.834 (0.045)   0.921 (NS)
  GFP-[beta]-cat*/control (P)

Activity Metric                         No_Na/[K.sub.DR]  Passive

Spiking rate vs. #tips R (P)             0.460 (NS)        0.399 (NS)
Spike amplitude vs. surface area R (P)  -0.828 (0.001)    -0.786 (0.001)
Spike/Current Intercept vs. #tips R      0.387 (NS)        0.081 (NS)
  (P)
Firing rate @5 pA:                       0.898 (NS)        2.970 (NS)
  GFP-[beta]-cat*/control (P)
Spike amplitude @5 pA:                   0.577 (0.001)     0.855 (NS)
  GFP-[beta]-cat*/control (P)

The Pearson correlation coefficients (R) and their respective P values
(NS denotes P > 0.05) for relationships between electrophysiological
measurements and morphometrics are reported in the first three rows of
the table. Ratio parameters, where a ratio is calculated of a
GFP-[beta]-cat* physiological measurement over the control measurement,
are reported in the last two rows of the table.
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Author:Krichmar, Jeffrey L.; Velasquez, David; Ascoli, Giorgio A.
Publication:The Biological Bulletin
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Date:Aug 1, 2006
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