Principles of branch dynamics governing shape characteristics of cerebellar Purkinje cell dendrites

Dendrite morphologies of CNS neurons are highly diverse, depending on cell type and function (Gao, 2007). The architecture of dendritic arbors crucially affects the integration of inputs and propagation of signals, and, hence, determines the connectivity of neurons (London and Häusser, 2005; Branco and Häusser, 2010). The question of how neurons acquire their appropriate morphology is a major issue in the study of neuronal development (Whitford et al., 2002; Gao, 2007; Parrish et al., 2007; Jan and Jan, 2010).

Time-lapse visualization of growing dendrites in live preparations has shown that establishment of a dendritic tree is governed by a combination of local branch dynamics, including elongation, branching and retraction (Dailey and Smith, 1996; Portera-Cailliau et al., 2003; Wu and Cline, 2003; Emoto et al., 2004; Williams and Truman, 2004; Mumm et al., 2006). In spite of individual differences in branch patterns, the apparent homogeneity of dendrite shape of the same neuronal class suggests that there are cell type-specific rules for local branch dynamics, which might be affected by both genetic and environmental factors. Various molecular signals have been identified as regulators of dendritic arborization patterns (Jan and Jan, 2010). However, how the series of local branch dynamics build up cell class-specific dendrite shapes, and which specific steps of branch dynamics are regulated by each molecule, remain largely elusive.

Attempts have been made to reconstitute dendrite growth processes using mathematical models. Among these are growth models aimed at finding elementary rules of dendrite development that inform branch pattern variation. Stochastic growth models assume that dendritic growth is an outcome of serial stochastic processes (van Pelt and Uylings, 2002). Alternatively, mechanistic growth models reconstitute dendrite differentiation based on cellular mechanisms, including protein reaction dynamics (Luczak, 2006; Sugimura et al., 2007; Shimono et al., 2010). Most of these models employ hypothetical parameter sets, and thus lack a strong connection with actual dynamics in live cells.

The cerebellar Purkinje cell forms space-filling dendrites that extensively ramify non-overlapping branchlets in a single parasagittal plane (Ramon y Cajal, 1911). The non-overlapping dendrites of a Purkinje cell enable it to make hundreds of thousands of non-redundant synapses with parallel fibers (Napper and Harvey, 1988), which pass perpendicularly through the planes formed by Purkinje cell dendrites. Considerable efforts have been made to define anatomical characteristics of Purkinje cell dendrites (Berry et al., 1972; Berry and Bradley, 1976a; Mori and Matsushima, 2002; McKay and Turner, 2005) and underlying molecular mechanisms (Metzger and Kapfhammer, 2003; Kapfhammer, 2004; Shima et al., 2004; Ohkawa et al., 2007; Sotelo and Dusart, 2009; Tanaka, 2009; Li et al., 2010). Recent studies have focused on time-lapse observation of Purkinje dendrite arborization in vivo and in culture (Lordkipanidze and Dunaevsky, 2005; Tanaka et al., 2006; Tanabe et al., 2010). However, long-term observation over days to weeks of the gradual progression of Purkinje cell development has been challenging owing to the concurrent dynamic morphogenetic changes, including cell migration and deepening of the lobules in the cerebellum. It has also been difficult to distinguish specific dynamic parameters affected by genetic and pharmacological manipulations deforming dendrites. The mechanisms and rules of dendrite formation in the Purkinje cell are, thus, still largely unknown.

In this study, we conducted long-term time-lapse observation of dendrite formation of Purkinje cells in culture, for up to several days with short time intervals. Using quantitative analyses and computer-aided simulation, we identified the fundamental rules of growth dynamics that govern the construction of the characteristic dendrite patterns in Purkinje cells.

Mice were handled in accordance with the Animal Experiment Committee of the RIKEN Brain Science Institute and Kyoto University.

The PKD1 K618N mutant was created by the QuickChange Site-Directed Mutagenesis Kit (Agilent), which was fused with mCherry-tag and cloned into pAAV-CAG vector. AAV-CAG-EGFP and AAV-CAG-TdTomato (adeno-associated virus vector carrying EGFP/TdTomato under the CMV enhancer and chicken β-actin promoter) were constructed and injected as previously described (Kaneko et al., 2011). Detailed methods for immunostaining and confocal analyses of labeled Purkinje cells were described previously (Kaneko et al., 2011). Antibodies used for immunostaining were as follows: mouse anti-calbindin D28K (Swant); rabbit anti-Pax6 (Covance); rabbit anti-DsRed (Clontech); chick anti-GFP (Invitrogen); rabbit anti-PKD1 (SantaCruz); rabbit anti-PKD2 (Calbiochem); rabbit anti-PKD3 (Calbiochem); rat anti-Thy1 (CD90.2, BioLegend); Alexa488- or Alexa568-conjugated anti-rabbit, anti-mouse or anti-chick IgG (Invitrogen).

Purkinje cells from postnatal day (P) 0 mouse cerebella were dissociated and plated on a glass-based dish coated with poly-d-lysine in DMEM/F12 supplemented by 10% FBS. Two hours after plating, media were replaced by maintenance medium containing DMEM/F12, 0.1 mg/ml bovine serum albumin, 2.1 mg/ml glucose, 3.9 mM glutamine, a modified N3 supplement (8 μM progesterone, 20 μg/ml insulin, 100 μM putresine, 30 nM selenium dioxide) and 1% penicillin-streptomycin. Plasmids containing PKD1-K618N and TdTomato were transfected by nucleofection of dissociated cells from one and a half cerebella using 10 μg of each plasmid with nucleofector protocol O-03 (Wagner et al., 2011). Transfected cells were observed using a confocal microscope (FV1000, Olympus) with 40× air UPlan SApo objective. For time-lapse imaging, Purkinje cells were GFP-labeled by adding 1 μl of AAV-CAG-EGFP [10⁹-10¹⁰ plaque-forming units (pfu)/ml] to the medium. Labeled cells were observed every 3 hours with an incubation microscope (LCV100, Olympus) using a 20× objective (numerical aperture 0.7, Olympus). Dendrites were traced and reconstructed with the aid of Neurolucida software (MBF Bioscience) for quantitative analysis using Neurolucida Explore and ImageJ (NIH). Branch angle was defined as the angle between the lines produced by a branch point and the branch points or dendritic tips terminating each of the daughter segments. All data are expressed as mean ± s.e.m. unless otherwise indicated. Comparisons of variables between two groups were made by Student’s t-test. A probability value of P<0.05 was considered to be significant.

Mice were injected in the cerebellum with AAV-CAG-TdTomato at P0. Cerebella were dissected and embedded in 3.5% agarose at P7. Vibratome sections (370 μm) were plated on a Millicell-CM plate (Millipore), settled in a culture medium at 37°C in a CO₂ incubator for 2-5 hours, and then observed with a confocal microscope (FV1000, Olympus) with 20× air UPlan SApo objective (numerical aperture=0.75) at 8-hour intervals.

Pharmacological agents used for primary dissociation culture and organotypic culture were as follows: Gö6976 (Calbiochem), Gö6983 (Calbiochem), CGP41251 (Alexis Biochemicals), LY333531 (Alexis Biochemicals), Ro-31-8220 (Calbiochem), CID755673 (Sigma-Aldrich), phorbol-12-myristate-13-acetate (phorbol ester, Calbiochem). These agents were bath-applied one or two hours before recording.

Numerical simulations and quantitative analysis were carried out in Matlab (Mathworks).

Dendrite growth dynamics was modeled on two-dimensional space following previous mathematical models (van Pelt et al., 2003) as repeats of operations of unit fragments at the terminals of dendrites. The ‘elongation’ and ‘branching’ were alternative processes that occurred at each terminal every 3 hours, and were represented by the addition of one and two unit fragment(s), respectively (supplementary material Fig. S3). After the ‘elongation’ or ‘branching’, one choice of operations in the ‘contact treatment’ was carried out depending on the condition number.

The algorithm carried out the following sequence: (1) One of the growing terminals is selected. (N.B. All terminals are growing terminals at the initial time point); (2) ‘Elongation’ or ‘branching’ process is selected and carried out (determined by the branching probability); (3) The new fragments are tested to determine whether they are contacted by other branches. Each of the contacted terminals is processed for a ‘contact treatment’; (4) Steps 1-3 are repeated until the calculation time (step number)^*(terminal number)^* Δt reaches the given maximum time.

The soma was approximated by a circle with a radius of 8.65 μm, which was determined from somal area measured in real cultured Purkinje cells using the equation r=√(area/π) (somal area; 236±6.1 μm², n=16). Primary dendrites were initiated at 0 hour with a single unit without a branch. The position and the direction of the primary dendrites were determined by distributions of two classes of angles: the ‘divergence angle of primary dendrites’ and the ‘direction angle of primary dendrites’ (supplementary material Fig. S3A).

A unit fragment is added at each terminal of a dendrite with the elongation probability p_e=r_eΔt=0.74, where the Δt is 3 hours, corresponding to the observation interval in experiments. The ‘deviation angle’, the angle between mother fragment and newly added daughter fragment, is assumed to follow a homogeneous distribution from –5° to +5°.

Two unit segments are added at each terminal with the branching probability 1 – p_e=1 – r_eΔt=0.26. Directions of two daughter segments are determined by distributions of two angles: the ‘divergence angle of branching’ and the ‘direction angle of branching’ (supplementary material Fig. S3C). The distribution of the divergence angle was approximated by a log-normal distribution with an average value of 65°, whereas that of the direction angle was assumed to be a normal distribution with average 3.39°. Values were determined from measurement of real cells as shown in Fig. 3.

If a new added fragment contacts other branches, either of the following operations is carried out:

Condition 1 (contact-dependent retraction): the branch including the added fragment is stopped from growing and then eliminated 7 steps later. The entire dendritic segment is removed from the branching root (supplementary material Fig. S3D).

Condition 3 (contact-dependent stalling): the terminal of the branch with the added fragment becomes a ‘non-growing’ terminal, which will never be selected as a growing terminal (supplementary material Fig. S3D).

Condition 2: either of ‘retraction’ or ‘stalling’ processes is selected with the probability shown in Fig. 4D. The probability is approximated by a quadratic 0.058T² – 0.0072T + 0.0054, where T is calculation step (1≤T≤31).

Purkinje cell soma extend multiple dendrites in random orientations during the first postnatal week in mice. A single or a few primary dendrites are determined during the second postnatal week, which extend and branch in a single parasagittal plane until the sixth week (McKay and Turner, 2005; Sotelo and Dusart, 2009). Figure 1A shows a typical Purkinje cell in the 10-day-old (P10) mouse labeled with enhanced green fluorescent protein (EGFP) by AAV-mediated gene transfer (Hirai, 2008; Kaneko et al., 2011). We monitored dendrite morphometry using three-dimensional confocal reconstruction of labeled cells. Consistent with previous studies (Berry and Bradley, 1976b; Berry and Flinn, 1984), the segment length between two branching nodes was longer for proximal segments, whereas it decreased and plateaued in distal segments at about 5.72±0.099 μm (n=1771 segments of 10th order and above from 21 cells; Fig. 1C, left and middle).

The morphometric characteristics of Purkinje cell dendrites can be partly reconstructed in a dissociation culture (Fig. 1B)(Calvet et al., 1985; Hirai and Launey, 2000; Tanaka et al., 2006; Kawaguchi et al., 2010). Overall arboreal size and complexity was smaller in the dissociation culture that is deficient in trophic and structural support from neighboring cells within the tissue. However, the spatial distribution of dendrites showed striking parallels with those in vivo; dendrites formed non-overlapping arbors with longer proximal segments and constant distal segments of 5.41± 0.37 μm (n=112 segments of 10th order and above from 20 cells; Fig. 1C, right). The frequency distributions of branch angles were also comparable in vivo and in vitro (Fig. 1D). Thus, the mechanisms of branch formation in Purkinje cells are at least partly conserved in culture.

We next performed long-term time-lapse observation of the dynamics of dendrite outgrowth in Purkinje cells in dissociation cultures. Purkinje cells were visualized by infecting with AAV-CAG-EGFP at 0 days in vitro (DIV) (Niwa et al., 1991; Kaneko et al., 2011). Infection with AAV induced little or no morphological changes in Purkinje cells (Hirai, 2008) (supplementary material Fig. S1A). Multiple thick dendrites emerged and initiated extension at ∼8 DIV, concomitant with the timing of initiation of dendrite outgrowth in vivo. We monitored dendrite outgrowth of Purkinje cells from 8 to 12 DIV (Fig. 2A; supplementary material Movie 1). About six to ten stem dendrites were initiated around the soma at 8 DIV, half of which were degraded within 48 hours (Fig. 2A, asterisks; see also Fig. 6I). Persistent dendrites grew radially from the soma by repeated elongation and branching. The growth of dendrites appeared to be rather constant without drastic changes in overall arrangement. Retraction of growing branches was also observed (Fig. 2A, arrowheads). Thus, the basic three dynamics seen in other cell classes – elongation, branching and retraction – were observed in Purkinje cells. We next conducted quantitative evaluation of each dynamic.

First, we focused on the elongation process. We monitored the growing speed by tracing the displacement of individual dendritic tips in image sequences from 8 DIV to 12 DIV (Fig. 2B). Dendritic tips displaced distally from the soma at constant speeds with relatively small individual variations at an average of 0.66±0.02 μm/hour (n=33 dendrites from 11 cells). To investigate whether dendrites elongated at the tip (terminal elongation) or by each segment throughout the entire dendrite (segment elongation), image sequences were compared to measure time-dependent changes in the segment length and translocation of distal tips. As depicted in Fig. 2C, the distal-most region extended linearly, whereas proximal segments were rather static. These results indicate that Purkinje dendrites elongate at a constant speed by terminal elongation.

Branches can be formed either by extension of collaterals from the dendritic shafts (lateral branching) or by division of growing tips (terminal branching) (Berry and Flinn, 1984; Sugimura et al., 2003). Time-lapse images revealed that most of the branching processes in Purkinje cells took place at or near the growing terminals (Fig. 3A; supplementary material Movie 2); nearly 90% of branching events occurred within the distal-most segments (Fig. 3B). The other 10% were lateral branching, but most of these events took place at distal regions near the terminal segment of the dendrite. By contrast, sprouting of collaterals in the proximal dendritic shafts was scarcely observed. Together with the results described above, Purkinje dendrites predominantly undergo elongation and branching at active zones in the growing terminals. Branching of growing terminals occurred stochastically, so that the frequency distribution of branching events was approximated by a Poisson distribution for 90 hours (Fig. 3C; average frequency 0.087±0.003 times/hour; n=57 dendritic terminals from 19 cells). Inter-branch intervals with respect to time distributed exponentially as predicted from a Poisson process (Fig. 3D). Angles formed between emerged sister branches were distributed with a mean ± s.d. of 65±21.2° (n=143 branches from four cells in time-lapse movies; Fig. 3E).

Serial images indicated retraction (elimination) of branches, which was triggered by contacts (or tight apposition) between growing dendrites. Dendritic tips immediately stopped growing after encountering a neighboring dendrite or the soma, and were then retracted to the proximal branching node by one or two segments in ∼20 hours (Fig. 4A; supplementary material Movie 3). By contrast, the dendritic shafts that were hit by growing tips from the side largely remained intact. Contacts between growing tips induced retraction of either (84%) or both (16%) tips to the proximal node(s) (Fig. 4B). The contact-dependent dendritic retraction was more evident in earlier stages of observation (from 8 DIV) and, thus, many of the initial stem dendrites were eliminated by dendro-dendritic contacts. Some of the initial stem dendrites were eliminated without experiencing obvious contact with other dendrites (e.g. yellow asterisks in Fig. 2A). Growing dendrites were gradually stabilized, so that dendro-dendritic contacts induced stalling of the terminals but not the subsequent branch retraction in later stages (Fig. 4C). The ratio of ‘stalled’ terminals among contacted dendrites increased non-linearly and reached close to 100% at the end of observation at 12 DIV (Fig. 4D). Interaction between dendrite branches was often mediated by filopodia-like motile protrusions. These protrusions disappeared in the stalled dendrites after contact, so that the tips of dendrites were dissociated from each other and stabilized in a non-overlapping arrangement (Fig. 4E).

Contact-dependent dendritic repulsion (retraction and stalling) seen in the present study, has been implicated in the self-avoidance mechanism that ensures a space-filling dendrites in invertebrate sensory neurons (Gan and Macagno, 1995; Grueber et al., 2003; Emoto et al., 2006; Han et al., 2012; Kim et al., 2012). Homotypic repulsive interactions have been shown to act not only between branches of the same cell but also between neighboring cells of the same type. Similarly, dendro-dendritic contacts between neighboring Purkinje cells induced retraction and stalling of branches (Fig. 4F, Fig. 5A). By contrast, dendrites of granule cells frequently overlapped with Purkinje cell dendrites in culture (Fig. 5B). In addition, contacts with the axon did not change the behavior of growing dendrites, indicating that contact-dependent repulsion is specific for homotypic dendro-dendritic interactions in Purkinje cells (Fig. 4G).

We next searched for conditions that specifically altered certain parameters of dendrite dynamics. Previous studies have implicated protein kinase C (PKC) as a regulator of dendritic outgrowth in Purkinje cells (Metzger and Kapfhammer, 2003; Kapfhammer, 2004): pharmacological inhibition of PKC induces excess branch formation, which led to the assumption that PKC signaling negatively regulates branching. We first confirmed that Purkinje cells grown in the presence of a PKC inhibitor Gö6976 exhibited complicated dendritic arbors with higher spatial density (Fig. 6A). Next, time-lapse observation was performed in the presence of Gö6976 (Fig. 6B; supplementary material Movie 4). Dendritic terminals were constantly extended at a slightly but significantly lower speed in Gö6976-treated cells (Fig. 6C; control: 0.66±0.02 μm/hour, n=33; Gö6976: 0.47±0.02 μm/hour, n=36; P<0.01). Unexpectedly, the branching frequency was significantly lower in Gö6976-treated cells compared with untreated control cells, despite the crowded appearance of dendrites (Fig. 6D; control: 0.087±0.003 times/hour, n=57 dendritic terminals; Gö6976: 0.054±0.003 times/hour, n=40; P<0.01). As a result, the branching probability per unit length of dendrites was almost comparable in control and Gö6976-treated cells (control: 0.137±0.004; Gö6976: 0.119±0.008; P>0.05). What causes the crowded appearance of Gö6976-treated cells? A notable feature of Gö6976 treatment was a drastic suppression of branch retraction after dendro-dendritic contacts (Fig. 6E,F; supplementary material Movie 5). In most cases, branches stalled after collision with other branches, but never retracted or crossed over the contacted branches thereafter.

Next, we investigated how changes in dynamics induced by Gö6976 affected the entire structure of dendrites. There were no significant changes in the total dendritic length and the number of branch terminals by Gö6976 treatment (Fig. 6G,H). By contrast, the number of primary dendrites was significantly increased in the presence of Gö6976 (control: 3.85±0.31, n=14; Gö6976: 6.42±0.58, n=12 at 90 hours; Fig. 6I). Time-lapse images revealed that the loss of primary stem dendrites in early stages was suppressed in Gö6976-treated cells (supplementary material Movie 4).

We evaluated time-dependent changes in the geometrical patterns of Purkinje cell dendrites by Sholl analysis (Sholl, 1953). In control cells, peaks of branch distribution were shifted distally as development proceeded, in concert with elongation and branching of dendritic terminals (Fig. 6J, top). Notably, the number of proximal branches around the soma gradually decreased during dendrite outgrowth. This could be accounted for either by elimination of proximal branches or by elongation of proximal segments. As elongation occurred exclusively at active growing terminals (Fig. 2), the clearance of proximal dendrites was likely to be due to branch retraction. Consistent with this prediction, reduction of the proximal intersections was not observed in Gö6976-treated neurons defective in branch retraction: new branches were added distally without changes in proximal branches (Fig. 6J, bottom). In addition, the distal shift of peak branch density was retarded in Gö6976-treated cells owing to slower elongation and branching.

We measured next the segment length by order of branches to compare further the arborization patterns of dendrites in the presence and absence of the inhibitor. Dendritic segments interconnected by branching nodes were numbered in centrifugal order (Fig. 1C, left). In control cells, the length of the first and second order segments progressively increased, whereas that of higher order segments were rather constant during development (Fig. 6K, top). Time-lapse imaging indicated that the apparent extension of proximal segments in control cells was due to contact-dependent retraction of proximal branches, leading to disappearance of the branching nodes and ligation of two sequential segments into a single long segment. By contrast, the length of proximal segments in inhibitor-treated cells remained constant and was comparable to higher order branches (Fig. 6K, bottom). Thus, contact-dependent elimination appears to preferentially reduce proximal branches and to contribute to the characteristic shape of Purkinje dendrite arbors, with long primary and secondary segments and short distal segments.

To confirm PKC involvement in dendrite dynamics, we examined the effect of PKC activation with phorbol ester. Purkinje cells treated with 10 nM phorbol ester immediately withdrew growing dendrites proximally (supplementary material Movie 6). These results point to a role of PKC signaling in dendrite retraction.

In an attempt to identify the PKC subtype(s) involved in the dendrite retraction, we tested the effects of several PKC inhibitors with differential subtype specificities on the dendrite morphology. Among the five inhibitors examined, only Gö6976 treatment induced dendrites with crowded proximal segments (supplementary material Table S1). Comparison of subtype specificities highlighted PKCμ as a potential candidate molecule involved in dendrite retraction. PKCμ has recently been renamed protein kinase D1 (PKD1; Prkd1 – Mouse Genome Informatics) and is one of three isoforms: PKD1, PKD2 (Prkd2 – Mouse Genome Informatics) and PKCν (PKD3; Pkrd3 – Mouse Genome Informatics) (Rykx et al., 2003). We first confirmed by immunocytochemistry that all PKD isoforms were expressed in Purkinje cells as previously reported (Azoitei et al., 2011) (Allen Brain Atlas: http://mouse.brain-map.org). PKD1-3 exhibited overlapping but not identical subcellular localization (supplementary material Fig. S2): PKD1 and PKD2 localized at the Golgi apparatus in perinuclear regions and proximal dendrites, whereas PKD3 was enriched in the nucleus. Diffuse signals of PKD1 and PKD3 were also seen along dendrites. Transfected PKD1 preferentially localized to the cell periphery, including filopodia, and to cytoplasmic vesicles in Purkinje dendrites (supplementary material Fig. S2E).

To confirm the involvement of PKDs, we utilized CID755673, a potent and selective inhibitor of kinase activity of PKDs with minimal effect on classical PKCs (Sharlow et al., 2008). CID755673 induced complicated dendritic arbors with higher spatial density and with shorter proximal segments similar to those treated with Gö6976 (Fig. 7A,B). Neither total dendritic length (control: 1326±76 μm, n=25; CID755673: 1337±81 μm, n=22) nor the number of dendritic terminals (control: 79.4±5.6, n=25; CID755673: 86.4±5.7, n=22) was significantly affected in CID755673-treated cells. By contrast, CID755673 significantly suppressed dendrite retraction in time-lapse images (Fig. 7C). However, inhibition of dendritic retraction by CID755673 was less efficient than that induced by Gö6976 (number of eliminated dendrites: control: 29.2±1.8, n=26 versus CID755673: 15.6±1.5, n=21, P<10^–5; compared with control: 33.6±2.14, n=12 versus Gö6976: 6.1±1.5, n=12, P<10^–9). Incomplete suppression of branch retraction could imply that other PKC subtypes or kinases blocked by Gö6976 might regulate dendrite retraction in parallel with the PKD pathway. The contribution of PKD in dendrite retraction was validated further by genetic inhibition using a dominant-negative form of PKD1 (Fig. 7D). Overexpression of kinase-dead mutant PKD1 K618N is thought to block activities of all PKD isoforms to varying degrees (Rémillard-Labrosse et al., 2009). PKD1 K618N was transfected by nucleofection as it exceeded the limited insert size of the AAV vector. Similarly to CID755673, Purkinje cells expressing PKD1 K618N exhibited crowded dendrites with significantly shorter proximal segments compared with control cells expressing TdTomato (Fig. 7E,F). In time-lapse movies, retraction of growing dendrites was significantly inhibited in PKD1 K618N-expressing cells (Fig. 7G; supplementary material Movies 7, 8). Consistent with Gö6976 treatment, PKD1 K618N did not alter branching probability per unit length (control: 0.160±0.008 times/μm, n=25 dendrites from 12 cells; PKD1 K618N: 0.151±0.007 times /μm, n=49 dendrites from 26 cells; P=0.45), as it simultaneously lowered elongation speed (control: 0.53±0.02 μm/hour, n=25 dendrites from 12 cells; PKD1 K618N: 0.38±0.01 μm/hour, n=49 dendrites from 26 cells; P<10^–5) and branching frequency (control: 0.082±0.003 times/hour, n=25 dendrites from 12 cells; PKD1 K618N: 0.057±0.003, n=49 dendrites from 26 cells; P<10^–5). Taking these data together, we conclude that dendritic retraction in growing Purkinje cells is at least partly mediated by PKD activity.

The results described above suggest the important contribution of contact-dependent retraction to Purkinje cell morphogenesis. In order to support this view, we performed a computer-assisted simulation of dendrite growth using experimental values of a parameter set obtained from time-lapse images of live Purkinje cells. The initial dendrites emerged from random positions on the perimeter of a soma. The constant elongation of dendritic terminals was recapitulated by the addition of one unit fragment per 3 hours (=1 step in simulation) at the terminal of the dendrites (supplementary material Fig. S3). Dichotomous branching was reproduced by the addition of two unit fragments to the dendritic terminal at a mean bifurcation angle of 65°. The branching was set to take place stochastically at an average rate of 0.26 times/3 hours. In the model of control cells (condition 1), a branch segment was eliminated at 21 hours after the growing tip contacted other branches. In the model of retraction-deficient cells (condition 3), branch growth was arrested by contacts between branches. Other parameters, including elongation and branching, were the same in control and retraction-deficient cells. Figure 8A shows representative images of growing cells in the models. The apparent shapes of the control and retraction-deficient cells were strikingly reminiscent of the live control and Gö6976-treated Purkinje cells, respectively. Early loss of primary dendrites took place only in control cells with contact-dependent retraction (condition 1 in Fig. 8A,B; supplementary material Movie 9). By contrast, excess branches increasingly accumulated in retraction-deficient cells (condition 3 in Fig. 8A; supplementary material Movie 11). Notably, the early contact-independent retraction of stem dendrites was not included in the parameter sets, indicating that its contribution is dispensable for the reduction of the primary dendrite number. Sholl analyses indicated that developmental changes in dendrite configuration in the model cells remarkably paralleled those in live cells (Fig. 8C). Furthermore, time-dependent elongation of the proximal segments was seen in the model control cell, whereas it was abrogated in the retraction-deficient cell (Fig. 8D, compare conditions 1 and 3). By contrast, other changes seen in Gö6976-treated cells, including elongation speed and branching probability, had little effect on spatial distribution of dendrites except for an overall reduction in the arbor size (supplementary material Fig. S4). Specifically, the gradual elongation of the first-order segment was hardly affected by the perturbations in the elongation speed and/or branching probability in the model, unlike in the retraction-deficient conditions. These results indicate that contact-dependent retraction of branches is the major cause for the apparent extension of proximal segments and reduced complexity in the perisomal region.

By contrast, the segment length was progressively shortened from the proximal to distal segments in condition 1, whereas it plateaued in the higher order segments in real cells (Fig. 6K, Fig. 8D). We attributed this incompatibility to the oversimplified conditions of retraction in the model, and subsequently accounted for the time-dependent mode transition of the contact-induced response from branch retraction to branch stalling, as was observed in real cells (Fig. 4D). Under these conditions, the distribution of segment length in the modified model of control cells was much more similar to the live control cells (condition 2 in Fig. 8A,D; supplementary material Movie 10).

Together, these results support the notion that the simple set of parameters of dynamics that include elongation, branching and elimination extracted from real cells are sufficient for modeling some morphometric characteristics of growing Purkinje dendrites in culture. Moreover, contact-dependent repulsion of dendritic branches was found to be crucial for the spatial distribution of dendrite branches, with long proximal segments and short higher-ordered segments, in addition to their non-overlapping arrangement.

During postnatal development, the first dendritic segments in Purkinje cells are gradually elongated to a greater degree than higher order segments (Fig. 1, Fig. 9A,B). To confirm the contribution of branch elimination to dendrite configuration in vivo, we performed time-lapse observation using an organotypic culture in which the cortical cytoarchitecture of the cerebellum was at least partly retained. Extensive elongation and branching of dendrite tips were observed in slice culture (Fig. 9C, arrows). Retraction of growing branches was also evident and appeared to follow contacts with other branches of the same or adjacent cells (Fig. 9C, arrowheads and asterisks). Retraction of proximal branches caused elimination of the branching nodes and increased the length of the proximal segments. Such contact-dependent retraction was repressed by the application of Gö6976 in slice culture, consistent with the data using dissociation cultures (Fig. 9D, arrows). These data support the notion that the contact-dependent retraction plays a pivotal role in spatial arrangement of Purkinje cell dendrites.

Quantitative assessment of dendrite outgrowth in cultured Purkinje cells by long-term time-lapse imaging revealed that the essential rules of dendrite arborization are a combination of relatively simple dynamics despite of their intricate appearance: Our experimental observations agreed with earlier predictions using fixed Golgi-stained cells (Hollingworth and Berry, 1975; Sadler and Berry, 1989). The former study generated possible topological patterns of dendrites by computer simulations assembling several putative branching rules. Of those, the dendrite pattern formed by stochastic addition of branches to dendritic terminals was similar to the morphology of real Purkinje cell dendrites. Consistently, direct observation of growing dendrites in the present study indicate that the basic frameworks of dendrites are constructed by constant elongation and random dichotomous branching at active sites near the termini of dendrites. This is in contrast to hippocampal pyramidal cells, which are known to sprout collateral branches from the shaft of dendrites (Dailey and Smith, 1996). Thus, dendrite dynamics vary by neuronal species with distinct morphology (Hattori et al., 2007; Jinushi-Nakao et al., 2007).

Time-lapse imaging also revealed dendrite repulsion, including retraction and stalling, which were induced by contacts or tight apposition with neighboring dendrites. Dendritic repulsion was a two-step process seen in early phases of dendrite growth: the dendritic tips immediately stalled upon collision with nearby dendrite(s), and they were retracted by one or two segments in the 20 hours after collision. Responsiveness to the retraction-inducing signal might decay during dendrite differentiation, as increasing numbers of branches were stalled and stabilized rather than retracted after dendro-dendritic collision in the late phase of dendrite outgrowth. We demonstrated that the contact-induced retraction is regulated by PKD kinase activity. Contact-independent retraction of emerging primary dendritic processes in earlier stages were also suppressed by inhibition of PKD, suggesting that branch retraction mechanisms converge at the level of PKD regardless of initiation cues.

The PKD family controls a variety of cellular functions, including remodeling of actin filaments (Eiseler et al., 2010; Spratley et al., 2011), receptor recycling (Woods et al., 2004; di Blasio et al., 2010), vesicle transport at the trans-Golgi network (Hausser et al., 2005) and neuronal polarization (Bisbal et al., 2008; Yin et al., 2008). In hippocampal neurons, suppression of PKD activity has been shown to cause a significant decrease in dendritic size and complexity, presumably owing to a deficit in secretory transport in dendrites (Horton et al., 2005; Czöndör et al., 2009). We observed overlapping but distinct subcellular localization of PKD isoforms in the Golgi apparatus, nucleus, dendritic periphery and cytoplasm in Purkinje cells. It is thus plausible that PKD activity affects multiple branch dynamics, including dendrite retraction and elongation, via regulation of different cellular contexts. Candidate upstream mediators of PKD during contact-dependent dendrite retractions would be homophilic adhesion molecules, such as Dscam, Turtle and Cadherin superfamily molecules Flamingo/Celsr 1,2,3, that are responsible for the recognition of homotypic interaction of dendrites (Kimura et al., 2006; Fuerst et al., 2008; Fuerst et al., 2009; Long et al., 2009). Precise molecular mechanisms underlying the contact-dependent repulsion and other branch dynamics are an important direction for future studies.

In contrast to previous simulation studies aiming to define the elementary rules for dendrite growth using hypothetical parameter sets (Hollingworth and Berry, 1975; van Pelt, 1997; van Pelt and Uylings, 2002; Luczak, 2006; Sugimura et al., 2007; Shimono et al., 2010), we adopted the actual values of dynamic parameters obtained by live imaging, and reproduced the deployment of dendritic arbors of real Purkinje cells. Our time-lapse images proved that proximal segments gradually increased in length, whereas higher ordered segments remained constant. Consistent with the prediction of earlier anatomical studies (Berry and Bradley, 1976b), the present live imaging demonstrates that retraction of proximal branches is induced by dendro-dendritic contacts in Purkinje cells. Here, the computer simulation provides a powerful approach to dissect the relative impact of each aspect of dynamics in appropriate dendrite morphogenesis: the contact-induced branch repulsion was confirmed to be crucial for the spatial disposition of dendrites, whereas elongation speed, branching probability of growing terminals and contact-independent retraction had only minor effects. Thus, time-lapse observation combined with numerical simulations enabled us to extract the important dynamic parameters for dendrite morphogenesis by means of a recursive method.

Purkinje cells elaborate numerous dendritic branches in flat parasagittal planes that cover their receptive fields with minimal overlaps. Self-repulsive properties ensure the dendritic tiling for complete and non-redundant coverage of the receptive field in invertebrate sensory neurons and mammalian retinal ganglion cells (Wässle et al., 1981; Perry and Linden, 1982; Grueber and Truman, 1999; Grueber et al., 2002; Sugimura et al., 2003). We assume that, among repulsive reactions in the Purkinje cell, the contact-dependent retraction in earlier stages contributes to the segment distribution in the proximal dendrites, whereas the contact-dependent stalling ensures the non-overlapping arrays of distal branches in the same cell (self-avoidance) and between neighboring Purkinje cells (regular alignment or tiling).

Despite many morphological similarities between Purkinje cell dendrites in dissociation culture and in vivo, there are a number of significant differences, including the small arboreal size and the number of the primary dendrites. Small arboreal size and complexity are probably due to lack or shortage of trophic and structural support from neighboring cells, including granule cells and inhibitory interneurons (Baptista et al., 1994; Altman and Bayer, 1997; Kawaguchi et al., 2010). Purkinje cells in vivo retain a single primary dendrite from numerous immature primary dendrites in the second postnatal week. The reduction of primary dendrites was recapitulated in dissociation culture, but most Purkinje cells retained three or four primary dendrites at fully developed stages in culture. As Purkinje cells are sparsely distributed in dissociated culture, retraction of primary dendrites was induced mostly by dendro-dendritic contacts in the same cell. By contrast, Purkinje cell dendrites in vivo are densely filled in the molecular layer, and most of the original primary dendrites are likely to be eliminated by frequent contacts with dendrites of the same and adjacent cells. Three-dimensional computer simulation following detailed in vivo analyses of developing Purkinje cells would be the next step for a better understanding of Purkinje cell development.

The present combinatorial approach using time-lapse imaging and computer simulations will be of use in searching for fundamentals of various dendrite patterns. It will also help to clarify the specific actions of functional molecules in dendrite dynamics and how they orchestrate dendrite shape.

We thank Drs J. Hejna and C. Yokoyama for invaluable advice for the manuscript.