A self-avoidance mechanism in patterning of the urinary collecting duct tree
© Davies et al.; licensee BioMed Central Ltd. 2014
Received: 17 March 2014
Accepted: 24 July 2014
Published: 10 September 2014
Glandular organs require the development of a correctly patterned epithelial tree. These arise by iterative branching: early branches have a stereotyped anatomy, while subsequent branching is more flexible, branches spacing out to avoid entanglement. Previous studies have suggested different genetic programs are responsible for these two classes of branches.
Here, working with the urinary collecting duct tree of mouse kidneys, we show that the transition from the initial, stereotyped, wide branching to narrower later branching is independent from previous branching events but depends instead on the proximity of other branch tips. A simple computer model suggests that a repelling molecule secreted by branches can in principle generate a well-spaced tree that switches automatically from wide initial branch angles to narrower subsequent ones, and that co-cultured trees would distort their normal shapes rather than colliding. We confirm this collision-avoidance experimentally using organ cultures, and identify BMP7 as the repelling molecule.
We propose that self-avoidance, an intrinsically error-correcting mechanism, may be an important patterning mechanism in collecting duct branching, operating along with already-known mesenchyme-derived paracrine factors.
Pattern formation in branching morphogenesis has been the subject of biological speculation since the beginning of embryology . On the one hand, theoreticians have stressed that branched trees have a self-similar (fractal) nature that suggests a simple, repetitive mechanism of generation ,. On the other, anatomists have stressed that branching systems of different organs are easily distinguishable even in silhouette and that, even within the same organ, different generations of branching are distinct. In particular, the first branch events of an organ follow a stereotyped pattern different from subsequent branch events, a fact that has prompted the suggestion that the early branching events might be under the control of a special genetic program . The competition between the general repetitive and the particular, sequential models has prompted much research into the molecular cell biology of branching morphogenesis .
First branch divergence is significantly greater than that of subsequent branches
In the branched epithelia of developing glandular organs such as kidney and lung, the first branch shows a divergence angle markedly different from divergence angles of subsequent branching events, at least once the branches have had time to elongate . Throughout this report, we use `divergence angle' to refer to the relative directions at which branches lie after they have elongated and responded to any guidance cue present in the system. No claim is made or implied about the shape of a branch tip at the moment of bifurcation.
Branch divergence is controlled by presence of other branches
The difference between first and subsequent divergence angles  might be explained by arguing that the first branch is made a special `early branch' mechanism, before control is handed to a routine branching programme . An alternative hypothesis would be that the branching mechanism is the same for all branching events but the angles are controlled by the environment, specifically the presence of other bud tips. To test these two models, branch tips (epithelia and their associated mesenchyme) isolated from unbranched, or from already once-branched, ureteric buds were cultured and the divergence angles of their next-formed branches were measured. Isolated tips from unbranched ureteric buds (Figure 2b) branched first with a wide divergence angle (mean = 149°, σ = 20°) then diverged more acutely (mean = 93°, σ = 19°, p = 0.018). Tips from buds that had already branched once and were placed in isolation made another open initial divergence angle (128° σ = 11°) characteristic of a normal first branch (Figure 2c). Subsequent branch events were more acute, as expected for second branch events (82°, σ = 22°, p = 1.8 × 10-6). These data (summarized quantitatively in Figure 2d) show that the change in divergence angle between first and later branching events is controlled by the presence or absence of another nearby tip.
A simple, qualitative computer model for self-avoidance
The direction taken by new branches in all of the cases described above have one thing in common: the branches seem to maximize their separation from other nearby branches. We used computer modelling to test if a secreted repulsive factor could achieve such patterning. The word `model' is sometimes misunderstood: we emphasize that what we present here is not intended to be a formal description of a real kidney (far too little is known about real rate constants, diffusion constants etc. for such a thing to be possible), but is a simplified system in which ideas can be explored in principle and used to direct experimental confirmation. The model is intended just as an abstract thinking tool to identify promising lines of wet-lab experimentation, and the conclusions of this manuscript rest on the wet lab data, not the details of the model.
The model is of the cellular Potts type, in which the tissue is represented by a two-dimensional grid of locations, each of which has a few associated parameters such as concentration of a particular molecule, or occupation by part of a ureteric bud tree. The `tip' and `stalk' components of the tree are represented with distinct identities. Tree tubules are considered to be sources of a factor, horrid, that diffuses away from them. The concentration of horrid arising from any particular point of the tubule, measured at another location in the tissue, decreases exponentially with distance, as would happen for first order decay/loss of a molecule that is either short-lived or is lost to the bulk medium above or below the plane of the tissue. The total concentration at any one point in the tissue is taken as the sum of the contributions to that place from each part of the bud, with some random noise added. The model makes the simplifying assumption that he diffusion of horrid is rapid compared to the speed of growth of the tubules: this is justified by the observation that treating real cultured kidneys with even large proteins such as growth factors or antibodies can produce an immediate effect on subsequent development of their ureteric bud trees, demonstrating that protein diffusion in the system is rapid compared with tree growth. Making this assumption allows the concentration gradients to be calculated at each stage from current tree anatomy, with no need for history to be taken into account. The model begins with one or more unbranched stalks. The tip(s) of the stalk(s) and subsequent tree(s) bifurcate only when the local concentration of horrid is below a threshold, and the new tips are regarded as instantly making their own contribution to the horrid field (we make no claim that control of branch timing by an inhibitor is true of real ureteric buds: the model has to have some mechanism to create branch points every so often, and the choice to use the concentration of horrid was made to avoid cluttering the model with any extra arbitrary features such as time intervals). Each tip advances at a rate determined inversely by its local concentration of horrid, in the direction of lowest local horrid as measured in the immediate vicinity of the tip. Stalks are left behind by advancing tips, as a slime trail may be left behind by an advancing snail. Further details of the model, source code and movies of its output, can be found in the Supplementary Data (Additional file 1: Code S1, Additional file 2: Movie S1, Additional file 3: Movie S2a, Additional file 4: Movie S2b, Additional file 5: Movie S3, Additional file 6: Movie S4, Additional file 7: Spreadsheet S1, Additional file 8: Text S1 and Additional file 9: Text S2).
Control of branch divergence by a secreted repulsive factor would be predicted to function also between buds from different trees. We tested this in the computer model. Beginning with two closely-spaced buds, either pointing at one another directly (Figure 3c) or offset (Figure 3d) the simulation produces trees that become distorted as mutual inhibition operates between branches belonging to different trees. This makes a prediction, testable in organ culture, that ureteric bud systems set up on collision courses will avoid contact even at the expense of making very distorted branch patterns.
Ureteric bud trees of cultured kidneys avoid collision
Implication of signalling by the TGFβ-superfamily, specifically BMP7, in collision avoidance
The ability of branching ureteric buds to avoid collisions even when cultured in close apposition was used as an assay to identify the signalling system involved. An obvious candidate signalling system for inhibiting epithelial advance is the TGFβ-superfamily: cells from other branching systems such as mammary gland show a reduced motility from shaped wells in the presence of autocrine-secreted, accumulating TGFβ ,. Furthermore, treatment of ureteric bud/collecting duct-derived cell lines with TGFβ itself inhibits advance and branching of tubules in 3-dimensional collagen gel culture  and intact kidney rudiments .
Discussion and conclusion
The results presented above have shown that the ureteric bud system of kidney rudiments cultured flat show the wide first divergence angle and narrower subsequent angles that are typical of 3-dimensional organs in vivo . Culture of tips from unbranched and once-branched buds showed that divergence angle is not controlled by different, sequential genetic programs but by proximity of other branches. A simple computer model suggested that this behaviour could be accounted for by a self-avoidance system, in which growing branches are repelled by something they themselves secrete. The implication of the model, that deliberate attempts to cause collisions between bud trees would be thwarted by self-avoidance, was confirmed by culture of real kidneys. Use of attempted collisions as an assay identified BMP signalling through Alk receptors as being critical to self-avoidance, with BMP7 being at least one of the molecules involved. Blocking BMP7 signalling produces a significant incidence of collisions, but many branches still appear to avoid contact, so there may in addition be parallel systems to keep them apart.
What does self-avoidance add to the existing repertoire of guidance systems, such as the biophysics of tube tips  and paracrine signalling from stroma , believed to control pattern formation in tubule trees? First, self-avoidance can explain how branch divergence angles can change automatically from very open to more closed without any need for special, sequential systems. Instead, the changing anatomy may result from an unchanging mechanism of control. The system may therefore be simpler than it first appears. Second, self-avoidance might also provide a means of automatic error correction. A striking feature of organ culture, observed for many years although attention is not normally drawn to it, is that a ureteric bud tree that would normally grow and spread out three-dimensionally will, when cultured in a two-dimensional system, produce a tree that still spreads out without collisions. Simple reduction of the three-dimensional anatomy of a normal tree to two dimensions, for example in a projection, would produce an image in which many shadows of branches would cross. This is not what happens in culture: instead, buds adapt and produce a properly-spaced two-dimensional tree. This demonstrates both the flexibility of bud patterning and its ability to compensate for even large-scale departures from normal anatomy. Such compensation would be expected in a system using self-avoidance; proper spreading out of the branches of the two-dimensional trees in the computer model was driven by self-avoidance alone.
Self-avoidance is probably not critical to the formation of a tree in the first place. The BMP7-/- mouse has severe renal dysgenesis with too few nephrons but it does have a small and cystic collecting duct system . The presence of any kind of collecting duct system underlines the fact that an epithelial tree, albeit a morphologically-abnormal one, can be constructed even without BMP7-mediated self-avoidance. It is possible that other self-avoidance systems were still active; our data implicate BMP7 in self-avoidance but do not prove that it is solely responsible. It is also possible that other, cell-level mechanisms , are enough to make a basic tree, and that self-avoidance is used only to mitigate the effects of occasional errors of positioning.
BMP7 is already known to be an inhibitor of the first emergence of the ureteric bud from the nephric duct  and, at high concentrations, an inhibitor of collecting duct cell line proliferation in culture . Supporting this is the observation that the BMP receptor Alk3 is needed to prevent excessive ureteric bud branching . BMP7 is not expressed in every organ that involves epithelial branching morphogenesis but organs may use different members of the TGFβ-superfamily for the same purpose. The autocrine production of motility-inhibiting TGFβ itself by mammary gland cells  suggests that mammary ducts may use a similar self-avoidance system, but based on TGFβ. It may be that, just as different organs use different activators of branching (FGF7, FGF10, GDNF) that feed into similar intracellular pathways , so they use different members of the TGFβ-superfamily as autocrine inhibitors. They may also use more than one molecule, just as many organs use more than one activator of branching. The main point of this report is not to argue for any particular molecule being generally important in self-avoidance, but is rather to illustrate that self-avoidance seems to exist, at least in kidney, and that it offers an explanation for branch angles changing during development and for branches not tangling even when the system is perturbed.
Inhibitory influences on the migrations of cells and cell processes are important in patterning other parts of the embryo, such as segmentation of the the peripheral nervous system , mapping of optic nerve to the colliculus in the brain , positioning of aortae each side of the midline , segmentation of intersomitic vessels , positioning the foregut and controlling the position at which the ureteric bud emerges from the Wolffian duct . These systems use a variety of molecules, such as Ephs/Ephrins, Semaphorins, Robo/Slit and BMP4, sometimes balanced by their antagonists -. There is evidence for repulsion being involved in the patterning of branching systems of bacterial colonies , dendritic trees  and fungal hyphae . Some simple culture studies have suggested that epithelia derived from the branched tubes of mammary and salivary glands can show repulsion ,: here we have shown this repulsion at work in the context of a complete organ rudiment.
Kidney dissection and culture
Kidneys were dissected manually from E10.5 (unbranched UB for first-branch-angle experiments) and E11.5 (T-branched; used for all other experiments) CD-1 mouse embryos. For time-lapse images kidneys from intercrosses between Tg(Hoxb7-cre)13Amc/J  and Gt(ROSA)26Sortm1(EYFP)Cos were used. For tip angle experiments, ureteric bud tips were isolated manually, with the mesenchyme that stuck to them, using fine hypodermic needles. The bud tips were cultured on filters marked with a notch, to keep track of the orientation of the bud tip. For collision avoidance experiments, extraneous mesenchyme was removed from the rudiments, leaving only the bud and the dense mesenchyme surrounding it. This prevented cultured organs from becoming so thick that tubules could cross over/under one another without contact, giving a false impression of collision. The ureter itself was trimmed close to the kidney so that it did not interfere with potential tree-tree collisions. For collision avoidance experiments, two or more kidney rudiments were placed in direct contact: it was not possible to control their relative orientations so this was allowed to be random. Beads soaked in BMP7 or control proteins were placed at the periphery of kidney rudiments using pulled pasteur pipettes. The deep blue colour of the beads allowed them to be observed. Kidney rudiments grown for the time-lapse imaging were cultured on 0.4 μm PET Transwell membranes (Corning), while all other rudiments were grown on fragments (about 5 mm 5mm) of Millipore 0.4 μm polycarbonate filters (Sigma P9449) supported at the air-medium interface on a stainless steel Trowell grid. In all cases, culture medium was Minimum Essential Eagle's with Earle's Salts (Sigma M5650) with 10% newborn calf serum and with penicillin and streptomycin (Sigma P5333 diluted 1/100 to the working concentration. When reagents were added, the appropriate equal volume of vehicle control was added to control cultures.
Growth factors and inhibitors
Alk inhibitor II [2-(3-(6-Methylpyridin-2-yl)-1H-pyrazol-4-yl)1,5-naphthyrine] was obtained from Calbiochem (616452) and dissolved at 5 μmg/ml in DMSO. Gremlin was from R&D systems (956-GR), reconstituted to 250 μg/ml in 4 mM HCl with 0.1% bovine serum albumin, as recommended by the manufacturer. BMP7 was from R&D systems (5666-BP) and reconstituted to 100 μg/ml in 4 mM HCl with 0.1% bovine serum albumin, again as recommended by the manufacturer: polyclonal anti-BMP7 was Aviva (ARP32329).
Immunostaining, imaging and quantification
Cultured kidney rudiments were fixed in −20°C methanol, which was allowed to warm towards room temperature over 15 minutes and then replaced by phosphate buffered saline (PBS). Still attached to their filters, they were stained overnight in 1/100 mouse anti-calbindinD28k (abcam 82812) and, in some cases, 1/200 rabbit anti-Six2 (LSBio LS-C10189), washed for 6-8 h in PBS, incubated overnight in FITC anti-mouse (Sigma F2012) for most experiments, and TRITC anti-mouse (Sigma T5393) and FITC anti-rabbit (Sigma F0382) for the Six2 staining experiments, and washed for 2-4 h in PBS. After staining, samples were mounted in 50% PBS: 50% glycerol, between 22 × 64mm coverslips, themselves separated by 22 × 22mm coverslips at their ends to maintain a space for the samples. The coverslip sandwich was then placed on a microscope slide for observation using a Zeiss epifluorescence microscope (the coverslip sandwich technique was used so that it could be turned over if the filter happened to be mounted kidney side-down).
Branch angles were measured manually, by electronically drawing skeleton lines along the centre of ureteric bud trunk and branches then measuring the divergence angles with a protractor on a printout of each image. For collision avoidance experiments, collisions were defined as approaches so close that no gap could be discerned by light microscopy: cultures were scored categorically, as having collisions or not having them. For bead experiments, measurements of closest approach were made by measuring the distance between the nearest edges of the bead and the branch that were the closest in each culture. Measurements of tip growth velocities in time-lapse movies were made by examining successive frames. For measuring the speed of free tips (for Figure 5b), the x and y pixel coordinates in frame n and frame n + 1, taken 1 h apart, were recorded, and the distance travelled was calculated as [(xn+1-xn)2 + (yn+1-yn)2]: this was done every 5 frames. Speed was calculated as difference in location divided by elapsed time. For approaching tips (for Figure 5c), the x and y pixel coordinates of each of two nearby tips were recorded in frame n and frame n + 1, the distance between the two tips was calculated (Pythagoras) in frame n and frame n + 1, and approach velocity was recorded as the difference between the distance at frame n + 1 and at frame n, divided by elapsed time. Between four and ten tip pairs were recorded in this way per frame (early frames include few nearby tips, later frames include more because there are more tips in all by then). This analysis was performed using LibreOffice Calc.
For the angle experiments in Figure 2, all samples were included. For collision avoidance experiments, only cultures that had no gap between the kidneys were included in the analysis.
Modelling was done using the Processing language: a description of the model, and its source code, appear separately in the Supplementary Data (Additional file 1: Code S1, Additional file 2: Movie S1, Additional file 3: Movie S2a, Additional file 4: Movie S2b, Additional file 5: Movie S3, Additional file 6: Movie S4, Additional file 7: Spreadsheet S1, Additional file 8: Text S1 and Additional file 9: Text S2). For simulations of collision experiments, a variety of anatomical starting conditions was used to correspond with what was done in real culture. A selection of these conditions is available in the program (see program notes in Supplementary Material (Additional file 1: Code S1, Additional file 2: Movie S1, Additional file 3: Movie S2a, Additional file 4: Movie S2b, Additional file 5: Movie S3, Additional file 6: Movie S4, Additional file 7: Spreadsheet S1, Additional file 8: Text S1 and Additional file 9: Text S2)).
For cell line-based chemotaxis assays, 6TA2 ureteric bud cells  were seeded on the top surface of BD Falcon™ FluoroBlok™ Cell Culture Inserts for 24-well plates, 8.0 μm (cat. 351152, BD Biosciences) and pre-incubated for 24 h with medium both above and below the inserts. The culture medium medium consisted of DMEM-F12 (Sigma D8437) with 10% FCS (Invitrogen 10108165), 1x ITS (insulin, transferrin, selenium) supplement (Sigma. I3146), 1x antioxidant supplement (Sigma A1345), and 1x penicillin-streptomycin-glutamine mix (Invitrogen 10378016). BMP7 (0, 140 or 290 μg/ml) was then added to the lower solution, the cells were incubated for a further 4 h, then the filters were removed, fixed in 4%PFA for 20 min, washed in 0.1% Triton X-100 (cat. H0934, Sigma) in 1X PBS (cat. P4417, Sigma) for 5 min, stained with propidium iodide (cat. P3566, Molecular Probes) and FITC Phalloidin (cat. P5282, Sigma) washed in 0.1% Triton X-100 in 1X PBS for 10 min mounted inverted and the number of cells spreading out from filter pores per microscope field was counted (images being blind-coded). Only fields in which the filter edge did not encroach were counted. For preliminary diffusion experiments using ink, a drop of Parker Quink fountain pen ink was placed in the centre of either a 3 cm petri dish containing 3mls PBS, of in the contained space of a Fluoroblok cell culture insert in a similar 3 cm petri dish containing 3mls PBS: the fluoroblok cell culture insert was filled with PBS to the same level as the surrounding dish. Photographs were taken using a hand-help camera at intervals from 0-4 h.
For continuously-variable quantitative data, standard deviations and standard errors of the mean were used to indicate variation and t-tests were used for testing significance. For scoring proportions of cultures showing collisions (each individual culture yielding a `categorical' yes/no state rather than a continuously-variable quantity), 95% confidence intervals were calculated as ±1.96√(p(1-p)/n) + 1/2n . Hypothesis testing for these data was performed using two sample z tests . For analysis of the relationship between velocity and log of proximity in time-lapse movies (Figure 5c), linear regression was applied, using the `LINEST' function built into the LibreOffice Calc spreadsheet software.
This work involved no human material or data, and involved no experiments on living animals. Tissues were obtained from animals killed by a method approved by Schedule 1 of the UK Animals (Scientific Procedures) Act, by licenced technical staff in Home-Office licenced premises.
JAD designed the experiments, performed all of the renal cultures except the time-lapse imaging, analysed all organ culture results including that of the movie and wrote the simulation software. PH and RB produced the time-lapse images. C-HC performed the cell line-based taxis assays. All authors read and approved the final manuscript.
We would like to thank Weijia Liu for blind-coding samples and for general help in running the laboratory. Work in this paper was funded by the Biology and Biotechnology Research Council and the Medical Research Council.
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