Simple Rules Determine Distinct Patterns of Branching Morphogenesis

Name: Work Video:
Duration: 3 min 30 s
Wei Yu; Wallace F. Marshall; Ross J. Metzger; Paul Brakeman; Leonardo Morsut; Wendell A. Lim; Keith E. Mostov
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4430, 4482, 4498, 4532, 4550, 4591, 4599, 4679, 4713, 4736, 4777, 4804, 4839, 4851, 4855, 4898, 4923, 5040, 5052, 5065, 5083, 5119, 5157, 5212, 5247, 5270, 5277, 5363], 'trees': [7, 16, 155, 164], 'epithelial': [9, 157, 344, 378, 731, 1451, 2799, 2974], 'tubes;': [10, 158], 'how': [11, 134, 159, 282, 302, 2540, 3158, 4639, 4747], 'patterning': [12, 160, 1200], 'occurs': [13, 161, 5084], 'in': [14, 35, 53, 86, 142, 162, 183, 201, 234, 290, 299, 330, 490, 536, 594, 610, 651, 659, 673, 742, 832, 1032, 1126, 1166, 1351, 1445, 1495, 1563, 1665, 1677, 1728, 1747, 1808, 1869, 1937, 1984, 2016, 2029, 2053, 2102, 2129, 2175, 2215, 2264, 2271, 2295, 2303, 2318, 2335, 2373, 2416, 2438, 2459, 2480, 2565, 2590, 2672, 2715, 2925, 3202, 3208, 3282, 3345, 3377, 3453, 3564, 3765, 3772, 3995, 4003, 4020, 4058, 4090, 4102, 4221, 4316, 4337, 4345, 4402, 4419, 4432, 4445, 4502, 4511, 4562, 4576, 4682, 4701, 4730, 4759, 4779, 4791, 4808, 4826, 4841, 4861, 4870, 4888, 4902, 5041, 5048, 5054, 5079, 5096, 5135, 5178, 5205, 5261, 5309, 5326, 5344, 5349, 5368, 5431, 5530], 'these': [15, 163, 1214, 1739, 3298, 3363, 4078, 4349, 4414, 4493, 5210, 5245, 5384], 'is': [17, 165, 301, 357, 418, 612, 830, 869, 955, 1044, 1100, 1130, 1184, 1355, 1612, 1727, 1800, 1850, 1957, 2213, 2293, 2310, 3077, 3162, 3490, 3531, 3617, 3648, 3663, 3670, 3816, 3891, 3938, 3945, 4064, 4070, 4081, 4124, 4235, 4261, 4303, 4341, 4417, 4469, 4476, 4720, 4755, 4784, 4806, 4834, 4884, 5036, 5046, 5219, 5324, 5332, 5347, 5429], 'a': [18, 83, 125, 166, 231, 273, 307, 337, 341, 414, 419, 470, 547, 616, 784, 824, 923, 1190, 1221, 1467, 1472, 1592, 1661, 1704, 1714, 2185, 2467, 2536, 2597, 2600, 2997, 3088, 3110, 3121, 3138, 3159, 3291, 3304, 3314, 3319, 3491, 3507, 3538, 3632, 3652, 3679, 3694, 3726, 3799, 3859, 3874, 3883, 3917, 3922, 3946, 3957, 3987, 4024, 4050, 4132, 4152, 4185, 4268, 4319, 4625, 4722, 4734, 4756, 4776, 4822, 4830, 4871, 4874, 4885, 4896, 5061, 5070, 5101, 5183, 5311, 5379, 5556], 'fundamental': [19, 167, 671], 'problem': [20, 168, 4724], 'development.': [22, 170, 4293, 4890], 'Commonly,': [23, 171], 'branch': [24, 39, 115, 172, 187, 263, 1609, 1671, 1718, 1735, 1742, 1752, 1769, 1773, 1781, 1794, 1980, 1998, 2005, 2012, 2036, 2083, 2233, 2468, 2495, 2511, 3107, 3131, 3177, 3182, 3188, 3195, 3232, 3241, 3280, 3365, 3406, 3854, 4302, 4449, 4570, 4783], 'tips': [25, 40, 59, 102, 116, 173, 188, 207, 250, 264, 622, 901, 989, 1480, 1750, 2276, 2337, 2530, 2542, 2607, 2938, 3069, 4840], 'fill': [26, 174, 480, 5293], 'the': [27, 30, 46, 49, 54, 58, 61, 69, 73, 78, 87, 93, 96, 104, 114, 120, 140, 143, 175, 178, 194, 197, 202, 206, 209, 217, 221, 226, 235, 241, 244, 252, 262, 268, 288, 291, 312, 315, 351, 365, 368, 376, 409, 428, 431, 475, 478, 481, 484, 491, 494, 497, 503, 506, 600, 607, 621, 624, 627, 635, 639, 644, 665, 688, 706, 716, 725, 728, 735, 738, 743, 750, 754, 757, 760, 764, 778, 820, 866, 874, 879, 883, 889, 894, 899, 926, 930, 936, 941, 944, 949, 952, 963, 968, 972, 983, 988, 991, 997, 1000, 1042, 1090, 1096, 1127, 1146, 1150, 1154, 1162, 1167, 1178, 1198, 1201, 1352, 1417, 1428, 1443, 1450, 1454, 1496, 1564, 1596, 1615, 1650, 1667, 1685, 1691, 1729, 1733, 1790, 1809, 1870, 1938, 1962, 1966, 1978, 1985, 1993, 2032, 2063, 2066, 2079, 2081, 2089, 2094, 2104, 2114, 2120, 2161, 2165, 2180, 2207, 2231, 2244, 2253, 2260, 2273, 2281, 2285, 2296, 2304, 2319, 2323, 2330, 2341, 2344, 2348, 2374, 2417, 2461, 2472, 2494, 2500, 2507, 2513, 2532, 2541, 2603, 2606, 2612, 2615, 2673, 2716, 2796, 2804, 2808, 2835, 2904, 2913, 2926, 2931, 2936, 2944, 2948, 2971, 2979, 2983, 3064, 3084, 3095, 3105, 3126, 3145, 3166, 3175, 3185, 3193, 3219, 3223, 3227, 3230, 3239, 3243, 3249, 3259, 3263, 3268, 3275, 3326, 3341, 3372, 3378, 3382, 3388, 3416, 3428, 3459, 3467, 3477, 3480, 3494, 3500, 3510, 3516, 3523, 3526, 3528, 3542, 3562, 3573, 3578, 3587, 3596, 3612, 3621, 3629, 3636, 3645, 3658, 3666, 3676, 3685, 3688, 3707, 3709, 3712, 3720, 3731, 3733, 3741, 3744, 3754, 3760, 3764, 3780, 3785, 3805, 3808, 3814, 3827, 3832, 3847, 3851, 3877, 3889, 3912, 3941, 3950, 3953, 3963, 3967, 4010, 4032, 4040, 4061, 4074, 4086, 4115, 4135, 4141, 4207, 4236, 4253, 4259, 4265, 4279, 4286, 4295, 4312, 4323, 4367, 4376, 4389, 4424, 4439, 4458, 4467, 4474, 4477, 4480, 4496, 4508, 4520, 4530, 4536, 4541, 4560, 4567, 4584, 4589, 4597, 4609, 4640, 4648, 4665, 4672, 4695, 4710, 4731, 4792, 4796, 4802, 4818, 4835, 4838, 4842, 4853, 4859, 4864, 4878, 4881, 4913, 4919, 4928, 5042, 5058, 5067, 5080, 5117, 5128, 5133, 5179, 5217, 5250, 5265, 5272, 5278, 5283, 5287, 5294, 5298, 5303, 5327, 5338, 5345, 5421, 5434, 5448, 5531], 'volume': [28, 47, 176, 195, 482, 504, 601, 645, 736, 791, 2298], 'organ': [31, 105, 179, 253, 304, 316, 432, 485, 640, 677, 729, 2208, 3438, 4742, 4749], 'approximately': [32, 180, 486], 'uniformly,': [33, 181], 'e.g.,': [34, 182], 'mammalian': [36, 184, 492, 744, 821, 2809, 2984], 'lung,': [37, 185, 493, 745, 1168, 2345, 5134, 5299], 'airway': [38, 186, 779], 'dispersed': [42, 118, 190, 266, 501], 'roughly': [43, 191, 878, 893, 1705], 'uniformly': [44, 192], 'throughout': [45, 119, 193, 267, 502, 734], 'lung.': [50, 198], 'In': [51, 199, 346, 406, 465, 605, 713, 818, 2078, 2097, 2243, 2301, 3362, 3862, 3903, 4030, 4083, 4514, 5243], 'contrast,': [52, 200, 606, 819, 2098, 2302], 'developing': [55, 203, 1001, 1128, 1353, 1565, 1939, 2418, 2717], 'metanephric': [56, 204, 608, 945], 'kidney,': [57, 205, 1155, 2080, 2245, 4797, 5097], 'ureteric': [62, 210, 628], 'bud': [63, 211, 629, 1604, 1693], 'tree': [64, 212, 471, 499, 625, 699, 717, 752, 780, 806, 1203, 1441, 1473, 2270, 3161], 'located': [66, 214, 633, 733, 3505], 'close': [67, 215, 4027], 'to': [68, 101, 113, 129, 216, 249, 261, 277, 430, 596, 661, 686, 719, 768, 790, 847, 907, 910, 947, 967, 1015, 1211, 1470, 1614, 1674, 1684, 1764, 1778, 1788, 1960, 2002, 2009, 2022, 2040, 2065, 2088, 2093, 2113, 2164, 2259, 2329, 2347, 2454, 2488, 2517, 2522, 2528, 2538, 2587, 3029, 3047, 3104, 3217, 3238, 3257, 3290, 3312, 3370, 3433, 3466, 3532, 3586, 3618, 3626, 3674, 3683, 3784, 3797, 3849, 3867, 3876, 3905, 3921, 3935, 3939, 4028, 4066, 4071, 4085, 4137, 4290, 4306, 4383, 4395, 4428, 4466, 4471, 4547, 4618, 4630, 4634, 4647, 4657, 4727, 4767, 4786, 4816, 4820, 4904, 5038, 5044, 5077, 5115, 5140, 5195, 5198, 5292, 5306, 5321, 5335, 5382], 'outer': [70, 218, 636, 880, 2945], 'surface': [71, 106, 219, 254, 637, 666, 788, 998, 2283, 2342, 2613, 2946, 3806, 3924, 3931, 4271], 'kidney': [74, 97, 222, 245, 609, 707, 822, 845, 868, 884, 946, 984, 1002, 1013, 1094, 1129, 1266, 1354, 1393, 1986, 2221, 2286, 2444, 2591, 2616, 2868, 2905, 2951, 3481, 3568, 3622, 3755, 3767, 3815, 3890, 4011, 4033, 4260, 4287, 4481, 4497, 4531, 4603, 4684, 4860, 4889, 4963, 4973, 5043], 'rather': [75, 223, 641], 'than': [76, 224, 642, 4068, 4126, 4330, 4363, 4633], 'filling': [77, 225, 643], 'kidney.': [79, 227, 3269, 3809, 4843], 'Here,': [80, 228, 683, 4762], 'we': [81, 229, 684, 1409, 1436, 1606, 2534, 2593, 3328, 3339, 3393, 3426, 3457, 3474, 3545, 3559, 3811, 3845, 3864, 3887, 3915, 4055, 4093, 4166, 4284, 4527, 4558, 4581, 4763, 4911, 5124, 5300, 5370], 'describe': [82, 230, 3313], 'simple': [84, 126, 232, 274, 1050, 1468, 1991, 2998], 'alteration': [85, 233], 'rules': [89, 237, 3075, 4920], 'that': [90, 99, 111, 238, 247, 259, 310, 425, 766, 829, 917, 954, 986, 1474, 1647, 1688, 1726, 1783, 2031, 2309, 2354, 2584, 3004, 3022, 3561, 3644, 3753, 3788, 3813, 3925, 4009, 4057, 4197, 4206, 4240, 4252, 4300, 4314, 4529, 4583, 4596, 4709, 4717, 4725, 4846, 4895, 5173, 5189, 5209, 5268, 5282, 5372], 'accounts': [91, 138, 239, 286], 'for': [92, 139, 240, 287, 957, 1213, 1964, 2099, 2312, 2560, 3001, 3303, 3336, 3400, 3422, 3551, 3595, 3610, 4038, 4201, 4230, 4263, 4343, 4408, 4479, 4540, 4588, 4660, 4677, 4975, 5424, 5452, 5559], 'difference': [94, 242, 672, 689, 1418, 1429], 'between': [95, 243, 690, 724, 753, 1419, 1430, 2184, 2463, 4107, 4172, 4275, 4325], 'pattern': [98, 246, 549, 619, 675, 1469, 2059, 2505, 3086, 3140, 3317, 3344, 3374, 3386, 3530, 3570, 3592, 3624, 3757, 3769, 3793, 4013, 4035, 4047, 4257, 4379, 4483, 4499, 4533, 4551, 4600, 4685, 4805, 4824, 4856, 4899, 5063, 5305], 'leads': [100, 248, 426], 'near': [103, 251, 634, 996], 'versus': [107, 255, 1972], 'previously': [108, 256], 'known': [109, 257, 914, 1185, 2586], 'patterns': [110, 258, 455, 1164, 2564, 3356, 3399, 3554, 3603, 3897, 4098, 4149, 4360, 4431, 4700, 5248, 5342], 'lead': [112, 260], 'being': [117, 265], 'organ.': [121, 269, 604, 669, 739], 'We': [122, 270, 589, 654, 2156, 2555, 2994, 3082, 3270, 3286, 3440, 3738, 3961, 4113, 4365, 4422, 4636, 4707, 4844, 5355, 5437], 'further': [123, 271], 'use': [124, 272], 'toy': [127, 275, 2999, 3019, 3061], 'model': [128, 276, 1391, 3000, 3020, 3062, 4296, 4974], 'deduce': [130, 278], 'from': [131, 279, 427, 1449, 1649, 2340, 2471, 2512, 3267, 3415, 3463, 3515, 3541, 3584, 3635, 3665, 3706, 3730, 3831, 4463, 4877, 4932, 5066], 'first': [132, 280, 1656, 3016, 3180, 3187, 3240, 3299, 4374], 'principles': [133, 281], 'this': [135, 283, 355, 591, 656, 938, 1700, 1842, 1849, 2047, 2158, 2246, 3487, 3547, 3789, 3937, 4159, 4768, 5174], 'rule': [136, 284, 5259], 'change': [137, 285, 2479, 4369, 4561, 4585, 4642], 'differences': [141, 289], 'two': [144, 292, 462, 872, 1994, 2579, 3181, 4280, 4494, 5055, 5087, 5211, 5246, 5360], 'types': [145, 293, 2580, 5361], 'trees.': [147, 295], 'An': [296, 803], 'age-old': [297], 'question': [298, 4758, 4769], 'biology': [300, 424], 'an': [303, 395, 603, 613, 647, 668, 702, 709, 919, 1681, 1801, 1988, 2268, 3155, 3840, 4620, 4741, 4748, 4906, 4968], 'develops': [305, 4750], 'into': [306, 459, 871, 929, 935, 940, 3651, 4456, 4751], 'particular': [308, 3111, 3315, 3909, 3930, 4355, 4598], 'form': [309, 911, 1471, 1779, 1784, 2448, 3910, 4754, 5138, 5192], 'reflects': [311], 'function': [313, 828, 978, 4739], '(Aristotle,': [317], '1961Aristotle': [318], 'Parts': [319], 'Animals.': [321], 'Harvard': [322], 'University': [323], 'Press,': [324], '1961:': [325], '251Google': [326], 'Scholar).': [327, 405, 453, 588, 817, 861, 1087, 1143, 1405, 1581, 1836, 2155, 2923, 2993, 5034], 'For': [328, 488, 740], 'example,': [329], 'metazoans,': [331], 'most': [332, 697, 714, 2446, 4865], 'internal': [333], 'consist': [335], 'tube': [338, 356, 370, 410, 927, 965, 3068], 'lined': [339], 'by': [340, 375, 1133, 1358, 1619, 2357, 2449, 2551, 2759, 3050, 3072, 3125, 3144, 3358, 3572, 3956, 4158, 4373, 4492, 4566, 4573, 4770, 4858, 5086, 5393, 5400, 5420, 5433], 'layer': [342, 4873], 'cells.': [345], 'some': [347, 1173, 2313, 2336, 3869, 4359, 5350], 'cases,': [348, 408, 715, 4060], 'such': [349, 3872, 5188], 'as': [350, 534, 542, 649, 885, 915, 1030, 1103, 1408, 1732, 1806, 2014, 2355, 2436, 3070, 3087, 3119, 3318, 3409, 3476, 3642, 3873, 4131, 4215, 4217, 4318, 4333, 4400, 4617, 4789, 4833, 5095, 5098, 5100], 'vertebrate': [352], 'small': [353], 'intestine,': [354], 'unbranched.': [358], 'Partially': [359], 'digested': [360], 'food': [361], 'passes': [362], 'unidirectionally': [363], 'through': [364, 749, 3330], 'length': [366, 4521, 4571, 4613], 'intestinal': [369, 393], 'while': [371, 705, 2235, 2569], 'nutrients': [372], 'absorbed': [374], 'lining': [377], 'cells': [379, 732, 906, 4934], '(Walton': [380], 'et': [381, 509, 551, 793, 836, 1004, 1063, 1106, 1226, 1249, 1292, 1331, 1370, 1482, 1510, 1535, 1557, 1623, 1812, 1856, 1884, 1909, 1931, 2131, 2360, 2388, 2410, 2620, 2659, 2687, 2709, 2735, 2778, 2820, 2851, 2890, 2953, 4936, 4958, 4993, 5146, 5535], 'al.,': [382, 510, 552, 794, 837, 1005, 1064, 1107, 1227, 1250, 1293, 1332, 1371, 1483, 1511, 1536, 1624, 1813, 1857, 1885, 1910, 2132, 2361, 2389, 2621, 2660, 2688, 2736, 2779, 2821, 2852, 2891, 2954, 4937, 4994, 5147, 5536], '2016Walton': [383], 'K.D.': [384], 'Freddo': [385], 'A.M.': [386], 'Wang': [387], 'S.': [388, 2750, 2752], 'Gumucio': [389], 'D.L.': [390], 'Generation': [391], 'surface:': [394], 'absorbing': [396], 'tale.Development.': [397], '2016;': [398, 854, 1022], '143:': [399], '2261-2272Crossref': [400], 'PubMed': [401, 449, 529, 584, 813, 857, 1025, 1083, 1243, 1282, 1325, 1401, 1504, 1529, 1577, 1642, 1832, 1878, 1903, 1951, 2151, 2382, 2430, 2653, 2681, 2729, 2772, 2814, 2845, 2884, 2919, 2989, 4987, 5030, 5166, 5572], 'Scopus': [402, 450, 530, 585, 814, 858, 1026, 1084, 1140, 1244, 1283, 1326, 1365, 1402, 1505, 1530, 1578, 1643, 1833, 1879, 1904, 1952, 2152, 2383, 2431, 2654, 2682, 2730, 2773, 2815, 2846, 2885, 2920, 2990, 3983, 4988, 5031, 5167, 5573], '(71)': [403], 'Google': [404, 452, 532, 587, 816, 860, 1028, 1086, 1142, 1246, 1285, 1328, 1367, 1404, 1507, 1532, 1580, 1645, 1835, 1881, 1906, 1954, 2154, 2385, 2433, 2656, 2684, 2732, 2775, 2817, 2848, 2887, 2922, 2992, 3985, 4990, 5033, 5169, 5575], 'other': [407, 1288, 3590, 3601, 3659, 4046, 4549, 5049, 5218], 'branches': [411, 479, 495, 762, 1767, 2106, 2163, 2256, 2326, 2447, 2465, 2478, 3024, 3045, 3213, 4109, 4171, 4196, 4327, 4381, 4393, 5137, 5190], 'and': [412, 435, 545, 676, 692, 730, 759, 781, 888, 932, 979, 1035, 1047, 1059, 1180, 1274, 1421, 1432, 1520, 1611, 1633, 1659, 1711, 1722, 1792, 1894, 1956, 2025, 2034, 2044, 2056, 2091, 2189, 2209, 2218, 2240, 2289, 2435, 2520, 2576, 2802, 2833, 2876, 2906, 2977, 3008, 3011, 3032, 3129, 3192, 3200, 3214, 3254, 3278, 3335, 3599, 3669, 3751, 3777, 3880, 3894, 4340, 4386, 4436, 4451, 4473, 4489, 4522, 4569, 4579, 4614, 4798, 5009, 5196, 5231, 5240, 5252, 5275, 5315, 5389, 5408, 5447, 5523, 5562], 'forms': [413, 1149, 1713], 'tree.': [416, 2352], 'Branching': [417, 454, 574, 1088, 1124, 1144, 1237, 1315, 1349, 1493, 1867, 2371, 2643, 2670], 'foundational': [420, 4757], 'process': [421], 'developmental': [423, 1038, 1523, 1636, 1897, 4760], 'cellular': [429, 1181, 3009], 'scale': [433], '(Metzger': [434, 508, 1062, 1811, 5145], 'Krasnow,': [436], '1999Metzger': [437], 'R.J.': [438, 512, 1066, 1815, 2134, 5149], 'Krasnow': [439, 517, 1071, 1820, 2139, 5154], 'M.A.': [440, 518, 1072, 1821, 2140, 5155], 'Genetic': [441], 'control': [442], 'morphogenesis.Science.': [445], '1999;': [446], '284:': [447], '1635-1639Crossref': [448], '(412)': [451], 'can': [456, 2048, 2107, 2196, 3116, 3234, 3639, 3857, 4334, 5125, 5191], 'be': [457, 808, 2049, 2108, 2197, 2544, 3027, 3117, 3206, 3235, 3519, 3640, 3716, 3736, 3837, 4100, 4214, 4335, 4658, 4728], 'divided': [458, 870], 'at': [460, 1193, 1427, 1460, 1699, 1757, 1785, 2124, 2202, 2280, 2451, 2577, 2611, 2943, 3148, 3261, 3537, 3631, 3724, 4245, 4398, 4867, 5376], 'least': [461, 2578, 5377], 'broad': [463], 'classes.': [464], 'many': [466, 2572], 'composed': [468], 'tubes,': [474, 913], 'termini': [476, 4266], 'uniformly.': [487], 'instance,': [489, 741], 'respiratory': [498], 'lung': [507, 524, 1043, 1078, 1810, 1827, 2103, 2146, 2236, 2320, 2907, 5059, 5161, 5180, 5288, 5346], '2008Metzger': [511, 1065, 1814, 2133, 5148], 'Klein': [513, 1067, 1816, 2135, 5150], 'O.D.': [514, 1068, 1817, 2136, 5151], 'Martin': [515, 1069, 1818, 2137, 5152], 'G.R.': [516, 1070, 1819, 2138, 5153], 'The': [519, 862, 975, 1037, 1073, 1440, 1464, 1602, 1771, 1822, 2141, 3018, 3179, 3483, 3521, 3608, 4000, 4248, 4411, 4681, 4738, 5156, 5526], 'programme': [521, 1075, 1824, 2143, 5158], 'mouse': [523, 1077, 1093, 1447, 1566, 1826, 1940, 2145, 2419, 2574, 2718, 2950, 5160, 5566], 'development.Nature.': [525, 1079, 1828, 2147, 5162], '2008;': [526, 1080, 1829, 2148, 5163], '453:': [527, 1081, 1830, 2149, 5164], '745-750Crossref': [528, 1082, 1831, 2150, 5165], '(553)': [531, 1085, 1834, 2153, 5168], 'Scholar),': [533, 1029, 3986], 'shown': [535, 650, 1031, 2015, 2214], 'Figure': [537, 652, 1589, 2017, 2127, 2265, 3152, 3203, 3348, 4338, 4420], '1A.': [538], 'exocrine': [540], 'glands—such': [541], 'mammary,': [543], 'salivary,': [544], 'prostate—follow': [546], 'similar': [548], '(Hannezo': [550, 1291, 2619], '2017Hannezo': [553, 1294, 2622], 'E.': [554, 1295, 2623], 'Scheele': [555, 1296, 2624], 'C.L.G.J.': [556, 1297, 2625], 'Moad': [557, 1298, 2626], 'M.': [558, 798, 843, 1011, 1299, 1515, 1628, 1889, 2627, 2740, 4953], 'Drogo': [559, 1300, 2628], 'N.': [560, 1301, 2629], 'Heer': [561, 1302, 2630], 'R.': [562, 1303, 2631, 2748, 5544], 'Sampogna': [563, 1304, 2632, 2658], 'R.V.': [564, 1305, 1485, 1859, 2363, 2633, 2662], 'van': [565, 1306, 2634], 'Rheenen': [566, 1307, 2635], 'J.': [567, 1308, 1379, 1542, 1916, 2395, 2636, 2694, 2781, 2785, 2825, 2956, 2960, 4943, 4957], 'Simons': [568, 1309, 2637], 'B.D.': [569, 1310, 2638, 5006], 'A': [570, 1311, 1388, 2211, 2639, 2792, 2967], 'Unifying': [571, 1312, 2640], 'Theory': [572, 1313, 2641], 'Morphogenesis.Cell.': [575, 1316, 2644], '2017;': [576, 1317, 2645], '171:': [577, 1318, 2646], '242-255Abstract': [578, 1319, 2647], 'Full': [579, 581, 1320, 1322, 1572, 1574, 1946, 1948, 2425, 2427, 2648, 2650, 2724, 2726, 2767, 2769, 4982, 4984, 5025, 5027], 'Text': [580, 582, 1321, 1323, 1573, 1575, 1947, 1949, 2426, 2428, 2649, 2651, 2725, 2727, 2768, 2770, 4983, 4985, 5026, 5028], 'PDF': [583, 1324, 1576, 1950, 2429, 2652, 2728, 2771, 4986, 5029], '(91)': [586, 1327, 2655], 'call': [590], '"R3"': [592], 'reference': [595, 660, 5528], '3-dimensional': [597], 'Euclidian': [598, 663], 'space—specifically,': [599, 664], 'mammals': [611], 'example': [614, 1802, 3156], 'less-common': [617], 'where': [620, 770, 922, 2602, 2930], '(UB)': [630], 'all': [632, 994, 1838, 2062, 2278, 2941, 3023, 3396, 3405, 3470, 3504, 3552, 3600, 3628, 3822, 3836, 4059, 4173, 4392, 4429, 4678, 4699, 4772, 4849, 5258], 'organ,': [648, 4882], '1B.': [653], 'term': [655, 1607, 1616, 2157], '"R2"': [657], '2-dimensional': [662], 'This': [670, 1799, 2058, 2177, 3169, 4309, 4593, 4891], 'organization': [678, 834], 'has': [679, 708, 823, 1680, 3245, 4535, 5375], 'received': [680], 'little': [681], 'attention.': [682], 'attempt': [685, 3866], 'understand': [687], 'R2': [691, 710, 1098, 1420, 1431, 1971, 2269], 'R3': [693, 703, 1039, 1422, 1433, 1973, 2350], 'branching.': [694, 1439, 1974], 'Why': [695], 'do': [696, 2556, 3272, 3936, 4017], 'have': [701, 918, 1208, 2486, 2558, 2588, 3702, 3795, 4606, 5171, 5356], 'pattern,': [704, 1099, 3425, 4233], 'pattern?': [712], 'serves': [718, 3256], 'conduct': [720], 'liquid': [721], 'or': [722, 1136, 1287, 1361, 1414, 1456, 2111, 2169, 2200, 3101, 3190, 4110, 4145, 5120, 5216], 'gas': [723, 771], 'exterior': [726], 'air': [746], 'moves': [747], 'bidirectionally': [748], 'outside': [755], 'organism': [758], 'terminal': [761, 1479, 1749], 'airways': [765], 'connect': [767], 'alveoli': [769, 782], 'exchange': [772], 'occurs.': [773], 'Efficient': [774], 'respiration': [775], 'depends': [776], 'on': [777, 1220, 2071, 2206, 2531, 3014, 3248, 3387, 3412, 3506, 3692, 3826, 4267, 4671, 4829, 4962], 'having': [783], 'near-maximal': [785], 'ratio': [786], 'area': [789], '(Mauroy': [792], '2004Mauroy': [795], 'B.': [796, 802], 'Filoche': [797], 'Weibel': [799], 'E.R.': [800], 'Sapoval': [801], 'optimal': [804, 3771, 4101, 4501, 5348], 'bronchial': [805], 'may': [807, 2485, 3794, 4605, 4715, 4924], 'dangerous.Nature.': [809], '2004;': [810], '427:': [811], '633-636Crossref': [812], '(210)': [815], 'more': [825, 2050, 4361], 'complex': [826, 976, 5062], 'physiological': [827, 977], 'reflected': [831], 'its': [833, 2187, 2190, 2518, 2523, 3534, 4127, 4307, 4745, 4752, 4787], '(Little': [835, 1003], '2016Little': [838, 1006], 'M.H.': [839, 1007, 1119, 1344, 1385], 'Combes': [840, 1008, 1110, 1335, 1374, 1539, 1913, 2392, 2691], 'A.N.': [841, 1009, 1111, 1336, 1375, 1540, 1914, 2393, 2692], 'Takasato': [842, 1010], 'Understanding': [844, 1012], 'morphogenesis': [846, 1014, 1125, 1268, 1350, 2870, 3003], 'guide': [848, 1016, 4927], 'renal': [849, 1017], 'tissue': [850, 1018, 1561, 1935, 2414, 2713], 'regeneration.Nat.': [851, 1019], 'Rev.': [852, 1020, 3978], 'Nephrol.': [853, 1021, 1500, 1874, 2378, 2677], '12:': [855, 1023], '624-635Crossref': [856, 1024], '(31)': [859, 1027], 'gross': [863], 'structure': [864, 921, 1664, 2836], 'adult': [867], 'portions:': [873], 'cortex,': [875], 'which': [876, 891, 970, 1148, 1666, 1748, 1969, 2272, 3262, 3473, 3638, 3850, 3944, 4138, 4200, 4234, 4277, 4780, 4821, 4883, 5082, 5136, 5428], 'occupies': [877, 892], 'third': [881, 1741, 1791, 3231, 3279], 'measured': [886, 4396], 'radially;': [887], 'medulla,': [890], 'inner': [895], 'two-thirds.': [896], 'During': [897], 'development,': [898, 1095, 2445, 2460, 2592, 4317], 'UB': [900, 992, 1091, 1438, 1444, 1465, 1585, 1839, 2069, 2275, 2609, 2937, 4922], 'interact': [902], 'with': [903, 1852, 1977, 2227, 3091, 3174, 3450, 4272, 4354, 4380, 4608, 4624, 4837, 5017, 5229, 5319, 5516], 'cap': [904], 'mesenchymal': [905], 'induce': [908], 'them': [909], 'secondary': [912, 1668], 'nephrons,': [916], 'elaborate': [920], 'portion': [924], 'loops': [928], 'medulla': [931, 942, 2932], 'back': [933], 'out': [934, 3325, 4037, 4847], 'cortex;': [937], 'looping': [939], 'enables': [943], 'raise': [948], 'osmolarity': [950], 'urine': [953], 'important': [956], 'terrestrial': [958], 'vertebrates.': [959], 'One': [960, 3589, 3933], 'end': [961, 3431, 3471, 3498, 3501, 3535, 3700, 3823, 3855, 4111, 4118, 4129, 4464, 4544], 'nephron': [964, 1134, 1359], 'connects': [966], 'UB,': [969, 1147], 'becomes': [971, 1660], 'collecting': [973, 1151], 'duct.': [974], 'corresponding': [980], 'architecture': [981], 'dictate': [985], 'during': [987, 1092, 1587, 2442, 4292, 4602], 'arranged': [995, 2279], 'Figures': [1033, 1582, 2054, 2216], '1K1': [1034], '1L1.': [1036], 'largely': [1045, 1101], 'stereotyped': [1046], 'uses': [1048, 1466, 1844, 2222, 2237], 'three': [1049, 1163, 3300, 3346], 'local': [1051], 'modes': [1052], 'branching:': [1054], 'domain': [1055, 5073, 5118], 'branching,': [1056, 4182], 'planar': [1057, 5104, 5121], 'bifurcation,': [1058, 1171, 1805, 5091], 'orthogonal': [1060, 1170, 1804, 1845, 1982, 2100, 2316, 4244, 4305, 4382, 4785, 5093, 5129, 5139, 5175, 5194, 5314, 5328], 'bifurcation': [1061, 1658, 1745, 1983, 2101, 2317, 2450, 5094, 5122, 5130, 5176, 5329], 'best-known': [1097], 'stereotyped,': [1102], 'well': [1104, 4019, 5099], '(Short': [1105, 1509], '2018Short': [1108, 1333], 'K.M.': [1109, 1334, 1377, 1538, 1546, 1912, 1920, 2391, 2399, 2690, 2698, 2827, 2897], 'Lisnyak': [1112, 1337], 'V.': [1113, 1338], 'Lefevre': [1114, 1339, 1378, 1541, 1915, 2394, 2693, 2824], 'J.G.': [1115, 1340], 'Jones': [1116, 1341], 'L.K.': [1117, 1342], 'Little': [1118, 1343, 1384], 'Hamilton': [1120, 1345, 1380, 1555, 1929, 2408, 2707, 2830], 'N.A.': [1121, 1346, 1381, 1556, 1930, 2409, 2708, 2831], 'Smyth': [1122, 1347, 1382, 1516, 1629, 1890, 2828, 2898], 'I.M.': [1123, 1348, 1383, 2829, 2899], 'not': [1131, 1356, 2076, 2557, 2595, 2934, 3273, 3817, 3835, 3892, 3927, 4016, 4688, 4721, 5112], 'impacted': [1132, 1357], 'formation': [1135, 1360], 'integration.eLife.': [1137, 1362], '2018;': [1138, 1240, 1363, 4979, 5022], '7https://doi.org/10.7554/eLife.38992Crossref': [1139, 1364], '(18)': [1141, 1366], 'system': [1152], 'consists': [1156, 1476, 5181], 'almost': [1157], 'entirely': [1158, 4243], 'one': [1160, 3672, 4045, 4765, 5215], 'used': [1165, 1618, 2311, 3994, 4857, 5220, 5343], 'namely': [1169], 'though': [1172], 'steps': [1174, 3296], 'trifurcations.': [1176], 'At': [1177], 'molecular': [1179, 3007], 'levels,': [1182, 3309, 3403], 'much': [1183], 'about': [1186, 3079], 'mechanisms': [1187, 1199], 'forming': [1189], 'branch,': [1191, 2186, 2333], 'but': [1192, 1990, 2007, 3076, 5308], 'higher': [1194], 'levels': [1195, 4180, 4204, 4662], 'organization,': [1197], 'remain': [1204], 'unclear.': [1205, 4082], 'Several': [1206], 'models': [1207, 1218], 'been': [1209], 'proposed': [1210], 'account': [1212], 'patterns,': [1216, 1435, 4357, 4852, 5213], 'including': [1217], 'based': [1219, 1271, 2873, 3411], 'Turing': [1222], 'reaction-diffusion': [1223], 'mechanism': [1224, 1273, 2875], '(Lang': [1225], '2018Lang': [1228], 'C.': [1229, 1256, 2742, 2858, 4939], 'Conrad': [1230, 1257, 2859], 'L.': [1231, 1258, 1487, 1861, 2365, 2664, 2744, 2860, 4947], 'Michos': [1232, 1253, 2855], 'O.': [1233, 1254, 1550, 1924, 2403, 2702, 2856], 'Mathematical': [1234], 'Approaches': [1235], 'Morphogenesis.Front.': [1238], 'Genet.': [1239], '9:': [1241], '673Crossref': [1242], '(10)': [1245], 'Scholar)': [1247, 1286, 1508, 1955, 2434, 5170], '(Menshykau': [1248], '2019Menshykau': [1251, 2853], 'D.': [1252, 1262, 2854, 2864], 'Lang': [1255, 2857], 'McMahon': [1259, 1553, 1927, 2406, 2705, 2790, 2861, 2900, 2965], 'A.P.': [1260, 1554, 1928, 2407, 2706, 2791, 2862, 2901, 2966], 'Iber': [1261, 2863], 'Image-based': [1263, 2865], 'modeling': [1264, 2866, 5109], 'reveals': [1269, 2871], 'GDNF-RET': [1270, 2872], 'Turing-type': [1272, 2874], 'pattern-modulating': [1275, 2877], 'WNT11': [1276, 2878], 'feedback.Nat.': [1277, 2879], 'Commun.': [1278, 2880], '2019;': [1279, 2764, 2881, 2917], '10:': [1280, 2882], '239Crossref': [1281, 2883], '(45)': [1284, 2886], 'physical': [1289], 'processes': [1290], 'Scholar,': [1329, 1368, 1533, 1882, 1907, 2386, 2657, 2685, 2733, 2776, 2818, 2849, 2888, 4991], 'Short': [1330, 1376, 1534, 1883, 1908, 2387, 2686, 2826, 2896], 'Zubkov': [1369], '2015Zubkov': [1372], 'V.S.': [1373], 'Byrne': [1386], 'H.M.': [1387], 'spatially-averaged': [1389], 'mathematical': [1390], 'morphogenesis.J.': [1395], 'Theor.': [1396, 2840], 'Biol.': [1397, 2841, 2916], '2015;': [1398, 1501, 1875, 2379, 2678, 2842], '379:': [1399], '24-37Crossref': [1400], '(17)': [1403], 'As': [1406, 3839, 4219, 4910], 'far': [1407, 4298], 'know,': [1410], 'no': [1411, 3246, 4226], 'publication': [1412], 'considers': [1413], 'even': [1415, 3820], 'notes': [1416], 'patterns.': [1424, 2554, 4680, 5364, 5386], 'To': [1425, 2497, 3323, 3380], 'get': [1426], 're-examined': [1437], 'fetal': [1446], 'derives': [1448], 'outgrowth': [1452], 'Wolffian': [1455, 1651], 'mesonephric': [1457], 'duct': [1458, 1652], 'starting': [1459, 1976, 3173], 'embryonic': [1461, 2949], 'day': [1462, 2073], 'E10.': [1463], 'eventually': [1475, 1712], '>1,000': [1478], '(Sampogna': [1481, 1855, 2359], '2015Sampogna': [1484, 1858, 2362, 2661], 'Schneider': [1486, 1860, 2364, 2663], 'Al-Awqati': [1488, 1862, 2366, 2665], 'Q.': [1489, 1863, 2367, 2666, 2789, 2964], 'Developmental': [1490, 1864, 2368, 2667], 'Programming': [1491, 1865, 2369, 2668], 'Morphogenesis': [1494, 1868, 2372, 2671, 2902], 'Kidney.J.': [1497, 1871, 2375, 2674], 'Am.': [1498, 1872, 2376, 2675], 'Soc.': [1499, 1873, 2377, 2676], '26:': [1502, 1876, 2380, 2679], '2414-2422Crossref': [1503, 1877, 2381, 2680], '(32)': [1506, 1880, 2384, 2683], '2013Short': [1512, 1625, 1886], 'K.': [1513, 1626, 1887, 4998, 5550], 'Hodson': [1514, 1627, 1888], 'I.': [1517, 1630, 1891], 'Spatial': [1518, 1631, 1892], 'mapping': [1519, 1632, 1893], 'quantification': [1521, 1559, 1634, 1895, 1933, 2412, 2711], 'morphogenesis.Development.': [1525, 1638, 1899], '2013;': [1526, 1639, 1900], '140:': [1527, 1640, 1901], '471-478Crossref': [1528, 1641, 1902], '(68)': [1531, 1644, 1905], '2014Short': [1537, 1911, 2390, 2689], 'Ju': [1543, 1917, 2396, 2695], 'A.L.': [1544, 1918, 2397, 2696], 'Georgas': [1545, 1919, 2398, 2697], 'Lamberton': [1547, 1921, 2400, 2699, 2819], 'T.': [1548, 1922, 2401, 2700, 5546], 'Cairncross': [1549, 1923, 2402, 2701], 'Rumballe': [1551, 1925, 2404, 2703], 'B.A.': [1552, 1926, 2405, 2704], 'al.Global': [1558, 1932, 2411, 2710], 'dynamics': [1562, 1936, 2415, 2714], 'kidney.Dev.': [1567, 1941, 2420, 2719], 'Cell.': [1568, 1942, 2421, 2720, 2763, 5021], '2014;': [1569, 1943, 2422, 2721], '29:': [1570, 1944, 2423, 2722], '188-202Abstract': [1571, 1945, 2424, 2723], '(183)': [1579, 1953, 2432, 2731], '1D–1L2': [1583], 'shows': [1584, 3154, 3350], 'development;': [1588], '1C': [1590], 'provides': [1591], 'color': [1593, 3197], 'code': [1594], 'number': [1597, 4208, 4650, 4666], 'each': [1599, 2203, 3056, 3092, 3149, 3337, 3423, 3464, 4246, 4301, 4781], 'step.': [1601], 'initial': [1603, 1692, 2121, 2473, 3186, 3301], '(which': [1605], '"1st': [1608], 'generation"': [1610], 'equivalent': [1613], '"root"': [1617], "Smyth's": [1620, 1678], 'group': [1621], '[Short': [1622], 'Scholar])': [1646], 'arises': [1648], '(Figure': [1653, 1694, 1708, 1760, 1796, 2299, 2321, 3419], '1E,': [1654, 1695, 1709], 'yellow)': [1655], 'undergoes': [1657, 1744], 'nearly': [1662], 'T-shaped': [1663], 'tip': [1669, 1698, 1716, 2292], '(second': [1670], 'generation,': [1672, 1981, 2013, 3196, 3242], 'relates': [1673], 'generation': [1675, 2006, 3108, 3189, 3233, 4966], '1': [1676, 4339, 4631], 'nomenclature)': [1679], '∼90°': [1682, 1758, 1786], 'angle': [1683, 1759, 1787, 2182, 3123, 3260, 4350, 4368, 4415, 4426, 4452, 4523, 4568, 4641], 'parent': [1686, 1766, 2004, 2043, 2090, 2519], 'segment': [1687], 'originally': [1689], 'was': [1690, 2617, 3593, 3770, 4586, 4670, 4693, 4863, 4900, 5398, 5418], 'pink).': [1696], 'Each': [1697, 1737, 3133], 'stage': [1701, 1963, 3418], 'gradually': [1702], 'assumes': [1703, 3021], 'triangular': [1706], 'shape': [1707], 'pink)': [1710], 'triple': [1715], '(third': [1717, 1768], 'generation)': [1719, 1753], '(Figures': [1720, 2287], '1F': [1721], '1G,': [1723, 1761], 'light': [1724], 'blue)': [1725], 'same': [1730, 4425], 'plane': [1731], 'second': [1734, 1793, 3194, 4470], 'generation.': [1736, 2096, 2192, 3178], 'six': [1740, 3294], 'generations': [1743, 1774, 1782, 1795, 1999, 2037, 2084, 3183, 3281], '(fourth': [1751], 'orthogonal,': [1755], 'i.e.,': [1756], 'dark': [1762], 'blue),': [1763], 'their': [1765, 2003, 2010, 2042, 2455, 3030, 3048, 3829, 4384, 5141, 5199], 'generation).': [1770], 'fourth': [1772, 2026, 2033, 3176], 'then': [1775, 3033, 3881, 4387, 4437, 4799], 'bifurcate': [1776], 'again': [1777], 'fifth': [1780, 2023, 2035, 2232], 'both': [1789, 2041, 2238, 5092, 5193], '1I,': [1797], 'green).': [1798], 'described': [1807, 3207, 3448], 'Almost': [1837], 'beyond': [1841, 3297, 5352], 'step': [1843], 'bifurcation.': [1846, 5105], 'All': [1847, 4147], 'compatible': [1851], 'previous': [1853], 'reports': [1854], 'provided': [1958, 5378], 'here': [1959, 5358], 'set': [1961, 3852, 3958, 4542], 'understanding': [1965, 4918], 'next': [1967], 'step,': [1968, 2204], 'involves': [1970], 'Importantly,': [1975], 'sixth': [1979, 2020, 2514], 'follows': [1987, 5060], 'altered': [1989, 2562], 'pattern:': [1992], 'newly': [1995], 'formed': [1996, 2183], 'child': [1997], 'perpendicular': [2001, 2039, 2087, 2112, 2201, 2241, 2305, 2328, 2516, 3028], 'parallel': [2008, 2092, 2110, 2199, 2228, 2239, 2248, 2258, 2521, 5197, 5316], 'grandparent': [2011, 2045, 2095, 2115, 2162, 2191, 2262, 2332, 2524, 3106, 5322], '1J': [2018], '(compare': [2019], 'orange': [2021, 2254, 2324], 'green': [2024], 'blue).': [2027], 'Note': [2028, 2353], 'contrast': [2030], 'generations;': [2046], 'easily': [2051, 3375], 'appreciated': [2052], '1I': [2055], '1H.': [2057], 'continues': [2060], 'repeatedly': [2061], 'way': [2064, 2537, 3673, 3682, 3934], 'completion': [2067], 'postnatal': [2072], 'P3': [2074], '(data': [2075], 'shown).': [2077], 'grandchild': [2082, 2105, 2166, 2255, 2325], 'always': [2086, 3026], 'either': [2109, 2198], 'branch;': [2116], 'often,': [2117], 'especially': [2118], 'after': [2119], 'round,': [2122], 'apparently': [2123], 'random': [2125], '(see': [2126, 4405], 'S1': [2128, 5522, 5525], 'Metzger': [2130], 'relationship': [2159, 2178], '"Zu': [2167, 3566], 'Sun"': [2168, 3567], '祖孙': [2170], 'orientation,': [2171], 'meaning': [2172], '"grandparent-grandchild"': [2173], 'orientation': [2174, 2195, 2226, 2229, 2251, 2308, 2504, 2797, 2972, 3228, 3244], 'Chinese.': [2176], 'describes': [2179, 3171], 'dihedral': [2181, 3039, 3122, 3146, 5186, 5317], 'parent,': [2188, 3128, 4788], 'Zu': [2193, 2224, 2249, 2306, 2502, 3096, 3791, 4254], 'Sun': [2194, 2225, 2250, 2307, 2503, 3042, 3097, 3792, 4255], 'depending': [2205], 'situation.': [2210], 'schematic': [2212], '1M': [2217, 2266], '1N.': [2219], 'Mouse': [2220], 'only': [2223, 3255, 3671, 3725, 5359], '(after': [2230], 'generation),': [2234], 'orientations.': [2242], 'repeated': [2247], '(i.e.,': [2252, 3184], 'blue': [2261, 2331], 'branch)': [2263], 'generates': [2267], 'final': [2274, 2491], 'peripheral': [2282], '1K': [2288], '1L1).': [2290, 2300], 'No': [2291], 'observed': [2294, 2501, 4528, 5325], 'interior': [2297, 5296], 'rounds': [2314], '1N),': [2322], 'resulting': [2334], 'pointing': [2338], 'away': [2339, 3006], 'contributing': [2346], "lung's": [2349], 'reported': [2356], 'others': [2358, 5366], 'detailed': [2437], 'Table': [2439, 3454, 4004, 4222, 4346, 4403, 4446, 5206, 5262, 5524], 'S1C:': [2440], '(i)': [2441], 'early': [2443, 4793], 'right': [2452], 'angles': [2453, 2462, 3040, 3147, 4324, 4390], 'parent;': [2456], '(ii)': [2457], 'later': [2458, 4315], 'sibling': [2464], 'undergo': [2466], 'generation-specific': [2469], 'reduction': [2470], 'value': [2474], '180°;': [2476], '(iii)': [2477], 'length.': [2481], 'These': [2482, 3113], 'geometric': [2483, 3074], 'features': [2484], 'evolved': [2487, 3796], 'ensure': [2489], 'proper': [2490], 'positioning': [2492], 'termini.': [2496], 'test': [2498], 'whether': [2499, 3620, 4096, 4801, 5337], 'kidney—with': [2508], 'every': [2509, 3035, 3331], 'new': [2510], 'onward': [2515], 'branch—is': [2525], 'somehow': [2526], 'favorable': [2527, 4362], 'distributing': [2529, 3533], 'surface,': [2533, 3509, 3828, 3871, 3914, 4832], 'need': [2535], 'predict': [2539], 'will': [2543, 3025], 'spatially': [2545], 'distributed': [2546, 3723, 4828], 'if': [2547, 3719, 3821, 5214], 'development': [2548, 4604, 4794], 'were': [2549, 3367, 3503, 3825, 4278, 4525, 5391], 'guided': [2550], 'alternative': [2552, 3841, 5385], 'methods': [2559], 'creating': [2561], 'live': [2566], 'animals.': [2567], 'Indeed,': [2568], 'there': [2570, 4183], 'mutant': [2573], 'strains': [2575], 'nutritional': [2582], 'deficiencies': [2583], 'defects': [2589], 'did': [2594, 4687], 'find': [2596], 'report': [2598], 'condition': [2601], 'location': [2604], 'strictly': [2610, 3013, 4304], 'perturbed': [2618], 'Zhang': [2734], '2019Zhang': [2737], 'H.': [2738, 2754, 4945, 4996, 5538, 5540, 5542, 5548], 'Bagherie-Lachidan': [2739], 'Badouel': [2741], 'Enderle': [2743], 'Peidis': [2745], 'P.': [2746], 'Bremner': [2747], 'Kuure': [2749], 'Jain': [2751], 'McNeill': [2753], 'FAT4': [2755], 'Fine-Tunes': [2756], 'Kidney': [2757, 5014, 5415], 'Development': [2758], 'Regulating': [2760], 'RET': [2761], 'Signaling.Dev.': [2762], '48:': [2765], '780-792Abstract': [2766], '(23)': [2774], 'Yu': [2777], '2009Yu': [2780, 2955], 'Carroll': [2782, 2957], 'T.J.': [2783, 2958], 'Rajagopal': [2784, 2959], 'Kobayashi': [2786, 2961], 'A.': [2787, 2962, 4941, 4949, 4951, 4955, 5552, 5554], 'Ren': [2788, 2963], 'Wnt7b-dependent': [2793, 2968], 'pathway': [2794, 2969], 'regulates': [2795, 2970], 'cell': [2800, 2975], 'division': [2801, 2976], 'establishes': [2803, 2978], 'cortico-medullary': [2805, 2980], 'axis': [2806, 2981], 'kidney.Development.': [2810, 2985], '2009;': [2811, 2986], '136:': [2812, 2987], '161-171Crossref': [2813, 2988], '(182)': [2816, 2991], '2015Lamberton': [2822], 'T.O.': [2823], 'Comparing': [2832], 'distinguishing': [2834], 'biological': [2838, 4075], 'branching.J.': [2839], '365:': [2843], '226-237Crossref': [2844], '(8)': [2847], 'Menshykau': [2850], 'Rutledge': [2889], '2019Rutledge': [2892], 'E.A.': [2893], 'Parvez': [2894], 'R.K.': [2895], 'requires': [2908, 5289], 'branch-tip': [2909], 'directed': [2910], 'activity': [2911], 'Adamts18': [2914], 'metalloprotease.Dev.': [2915], 'https://doi.org/10.1016/j.ydbio.2019.06.012Crossref': [2918], '(20)': [2921], 'Even': [2924], 'absence': [2927], 'Wnt7b,': [2929], 'does': [2933, 3926, 4015, 5111], 'form,': [2935], 'still': [2940], 'arrayed': [2942], '(Yu': [2952], 'therefore': [2995, 3271, 3739], 'implemented': [2996], 'abstracts': [3005], 'details': [3010], 'focuses': [3012], 'geometrical': [3015, 4610], 'principles.': [3017], 'parents,': [3031, 4385], 'explores': [3034], 'possible': [3036, 3057, 3332, 3397, 4174, 4773, 4850], 'combination': [3037], '(Zu': [3041], 'orientation)': [3043], 'relative': [3046, 3103, 3237], 'grandparents': [3049], 'computationally': [3051], 'generating': [3052, 4375, 5233], 'virtual': [3053], 'kidneys,': [3054], 'following': [3055, 5527], 'pattern.': [3059, 4592, 4737, 5330], 'Our': [3060, 5201], 'illustrates': [3063], 'spatial': [3065, 3250, 3389, 4622, 4908, 5225], 'distribution': [3066, 3251, 3390, 3429, 3443, 3460, 3489, 3496, 3647, 3668, 3714, 3746, 3781, 4087, 4441, 4506, 4623, 5235], 'dictated': [3071], 'explicit': [3073], 'silent': [3078], 'biologic': [3080], 'processes.': [3081], 'specify': [3083], 'binary': [3089, 3134, 3321, 3333, 3360, 3574], 'number,': [3090, 3338], 'bit': [3093], 'determining': [3094], 'direction': [3099], '("perpendicular"': [3100], '"parallel")': [3102], 'branch.': [3112], 'directions': [3115], 'considered': [3118, 4095, 4167, 5357], 'defining': [3120], 'defined': [3124, 3143, 3236], 'grandparent,': [3127], 'daughter': [3130, 4782], 'generations.': [3132], 'sequence': [3135, 3167, 3170], 'thus': [3136, 4297, 5333], 'encodes': [3137], 'distinct': [3139, 3359, 3728], 'branches,': [3142, 3302, 5323], 'level.': [3151], '2A': [3153], 'built': [3163], 'up': [3164], 'using': [3165, 3444, 3966], '001111.': [3168], 'events': [3172], 'root': [3191, 3264], 'coded': [3198], 'yellow': [3199], 'pink': [3201], '2A)': [3204], 'cannot': [3205], 'terms': [3209, 3773, 4021, 4103, 4503, 4515, 4702, 4809], 'any': [3211, 3908, 3929, 4231, 4548], 'earlier': [3212], 'instead': [3215], 'serve': [3216], 'fix': [3218], 'coordinate': [3220], 'frame': [3221], 'model.': [3224], 'Likewise,': [3225], 'although': [3226, 4691], 'effect': [3247, 3383, 4412], 'endpoints': [3253, 3585, 3630, 3721, 3803, 4089, 4827, 4869, 5290], 'define': [3258], 'would': [3265, 3518, 3715, 3735, 3834, 4288, 5301], 'emerge': [3266], 'include': [3274], 'first,': [3276], 'second,': [3277], 'our': [3283, 3288, 4371, 4433, 5107, 5373], 'description': [3284], 'string.': [3285], 'limited': [3287], 'search': [3289], 'depth': [3292], 'total': [3305, 4186], 'nine': [3307, 3401, 4202, 4661], 'allowing': [3310], 'us': [3311, 4926, 5114], 'six-digit': [3320], 'number.': [3322], 'carry': [3324], 'enumeration,': [3327], 'loop': [3329], 'number;': [3334], 'render': [3340], 'predicted': [3342], 'dimensions.': [3347], '2B': [3349], 'several': [3351, 3445, 4675, 4811], 'examples': [3352], 'different': [3354, 3699, 3895, 3900, 4097, 5088, 5224], 'produced': [3357], 'sequences.': [3361], 'simulations,': [3364], 'lengths': [3366, 3407, 4450], 'deliberately': [3368], 'chosen': [3369], 'make': [3371, 4358], 'visualized': [3376], 'plots.': [3379], 'analyze': [3381], 'tips,': [3392], 'iteratively': [3394], 'generated': [3395, 4565], 'setting': [3404], 'equal': [3408], 'determined': [3410], 'quantitative': [3413], 'measurements': [3414], 'E15': [3417, 4344, 4399], '3A).': [3420], 'Then,': [3421], 'analyzed': [3427], 'points': [3432, 3502, 3536, 3701, 3824, 3856, 4119, 4465, 4545], 'obtain': [3434], 'numerical': [3435, 3446, 3947], 'indicators': [3436], 'morphology.': [3439], 'evaluated': [3441, 3546], 'endpoint': [3442, 3465, 4123, 4156, 4440, 4505, 4621, 5234], 'metrics': [3447], 'below,': [3449], 'results': [3451, 4250, 4575, 4825], 'summarized': [3452], 'S1B.': [3455], 'First,': [3456], 'calculated': [3458, 3740, 4114, 4559], 'distances': [3462, 3514, 3583, 3616, 3705, 3729, 3783, 3830, 4462], 'centroid': [3468, 3517, 3786, 3833, 4468], 'points,': [3472], 'take': [3475, 3882], '"center"': [3478], 'mass.': [3482], 'standard': [3484, 3511, 3524, 3580, 3606, 3613, 3661, 3775, 4459], 'deviation': [3485, 3512, 3581, 3614, 3662, 3776, 4460], 'distance': [3488, 3540, 3634, 3646, 3689, 3713, 3745, 4876], 'measure': [3492, 3684, 3918, 4133], 'radial': [3495], 'points—if': [3499], 'spherical': [3508], 'zero.': [3520], 'smaller': [3522], 'deviation,': [3525], 'closer': [3527, 4065, 4125, 4629], 'fixed': [3539], 'center.': [3543], 'When': [3544, 4448], 'figure': [3548, 3842], 'merit': [3550, 4814], '(Table': [3555, 3747, 4161, 4485, 4552], 'S1B,': [3556, 3748, 4005, 4162, 5263], 'column': [3557, 3749, 4006, 4163, 4224, 4554], '3),': [3558], 'found': [3560, 3752, 4582, 4845, 5172], 'actual': [3563, 4668, 4803, 4854], 'vivo': [3565, 3766, 4683, 4862], '(defined': [3571], 'string': [3575], '001111)': [3576], 'gave': [3577, 3604, 3759, 4049], 'lowest': [3579, 3597, 3761, 4537, 5279], 'centroid.': [3588], 'tied': [3594], 'value,': [3598], 'larger': [3605], 'deviations.': [3607], 'motivation': [3609], 'measuring': [3611], 'ask': [3619, 3846], 'tends': [3625], 'place': [3627], 'uniform': [3633, 3800, 4875], 'centroid,': [3637], 'interpreted': [3641], 'saying': [3643], 'highly': [3649], 'concentrated': [3650], 'narrow': [3653], 'range': [3654], 'distances.': [3656], 'On': [3657], 'hand,': [3660], 'derived': [3664], 'Gaussian': [3667], 'quantify': [3675], 'narrowness': [3677], 'distribution.': [3680], 'Another': [3681], 'broadness': [3686], 'distribution—without': [3690], 'relying': [3691], 'assuming': [3693, 3907], 'normal': [3695], 'distribution—is': [3696], 'entropy.': [3697, 3762], 'If': [3698], 'broadly': [3703], 'varying': [3704], 'center,': [3708, 3732], 'entropy': [3710, 3734, 3742, 3778, 4475], 'high,': [3717], 'whereas': [3718], 'few': [3727, 5380], 'low.': [3737], '5)': [3750], 'also': [3758, 4094, 4637, 5075], 'That': [3763], 'suggests': [3787, 4595, 4894], 'specific': [3790, 3870, 4735, 4753, 4897, 5339], 'produce': [3798, 5249], 'placement': [3801], 'onto': [3804], 'However,': [3810, 4054, 4294], 'note': [3812, 4056], 'spherical,': [3818, 3893], 'hence': [3819], 'identical.': [3838], 'merit,': [3844], 'degree': [3848, 4136, 4819], 'approximate': [3858], 'two-dimensional': [3860, 4831], 'surface.': [3861], 'principle,': [3863], 'could': [3865, 4198, 4213], 'fit': [3868], 'sphere,': [3875], 'point': [3878], 'cloud': [3879], 'residual': [3884], 'distance.': [3885], 'Again,': [3886], 'know': [3888], 'might': [3898, 4099, 4143], 'give': [3899, 5222], 'best-fit': [3901], 'shapes.': [3902], 'order': [3904, 4673], 'avoid': [3906], 'curved': [3913], 'want': [3916], 'closeness': [3920], '2D': [3923], 'require': [3928], 'shape.': [3932], 'calculate': [3940], 'fractal': [3942, 3964, 3991, 4025, 4042, 4052, 4062, 4517, 4538, 4563, 4627, 5236, 5254], 'dimension,': [3943, 4518, 4628], 'estimate': [3948, 3962, 3970], 'dimensionality': [3951, 4079, 5274], 'space': [3954], 'spanned': [3955], 'points.': [3960, 4112], 'dimension': [3965, 3969, 3992, 4026, 4063, 4539, 4564, 4632], 'correlation': [3968], '(Procaccia,': [3971], '1983Procaccia': [3972], 'P.G.I.': [3973], 'Characterization': [3974], 'Strange': [3976], 'Attractors.Phys.': [3977], 'Lett.': [3979], '1983;': [3980], '50:': [3981], '346-349Crossref': [3982], '(3998)': [3984], 'robust': [3988], 'estimator': [3989], 'commonly': [3993], 'analysis': [3996, 4310], 'dynamical': [3998], 'systems.': [3999], 'results,': [4001], 'given': [4002, 4239, 4823], '6,': [4007], 'show': [4008, 5208], '[001111]': [4014], 'particularly': [4018], 'producing': [4023], '2.': [4029, 4635], 'fact,': [4031, 5244], 'stands': [4036], 'giving': [4039], 'smallest': [4041], 'dimension.': [4043, 4053], 'Only': [4044], '[111111]': [4048, 5232], 'lower': [4051, 4696], '2': [4067], 'it': [4069, 4692], '1,': [4072], 'so': [4073, 4616], 'significance': [4076], 'estimates': [4080], 'addition': [4084], '3D': [4091], 'space,': [4092], 'avoiding': [4105], 'collisions': [4106], 'neighboring': [4108], 'fraction': [4116, 4154], 'whose': [4120], 'nearest': [4121], 'neighbor': [4122], 'sister': [4128, 4326], 'point,': [4130], 'subtrees': [4139], 'network': [4142, 4512, 4778], 'clash': [4144, 4157, 4169, 4719], 'overlap.': [4146], 'tested': [4150], 'showed': [4151], 'high': [4153, 4216], 'criterion': [4160], '7).': [4164], 'Finally,': [4165], 'steric': [4168, 4211, 4227, 4644, 4653, 4718], 'pairs': [4175, 4194], 'branches.': [4177], 'Given': [4178, 5281], 'n': [4179], '(2n': [4188], '−': [4189, 4191], '1)(2n': [4190], '2)/2': [4192], 'unique': [4193], 'clash,': [4199], 'means': [4205], 'potential': [4210, 4652], 'clashes': [4212, 4228, 4654, 4669], '130,305.': [4218], 'seen': [4220, 4336, 4601, 4790, 5047, 5256], 'S1C,': [4223, 4486, 4553, 4580], '8,': [4225], 'occurred': [4229], 'expected': [4237], 'result': [4238, 4320, 4594, 4892], 'remains': [4242, 4500], 'stage.': [4247], 'preceding': [4249], 'indicate': [4251], 'optimized': [4262], 'placing': [4264, 4868], 'single': [4269, 4872], 'smooth': [4270], 'minimal': [4273], 'overlap': [4274], 'endpoints,': [4276, 5228], 'main': [4281], 'design': [4282, 5285], 'goals': [4283], 'imagined': [4285], 'seek': [4289], 'satisfy': [4291], 'assumed': [4299], 'parent.': [4308, 5142], 'ignored': [4311], 'observation': [4313], 'growth,': [4322], 'less': [4329], '180': [4331], 'degrees,': [4332], 'tabulated': [4342], 'S1A.': [4347, 4404], 'Might': [4348], 'changes,': [4351, 4572], 'when': [4352, 4519, 4557], 'combined': [4353], 'others?': [4364], 'modeled': [4366], 'within': [4370], 'simulation': [4372], 'original': [4377], 'changing': [4388], 'according': [4394], 'values': [4397], 'listed': [4401, 4444], 'Supplemental': [4406, 5532], 'Information': [4407], 'methodological': [4409], 'details).': [4410], 'changes': [4416, 4427, 4453, 4510, 4524, 4611], 'illustrated': [4418], '2B.': [4421], 'applied': [4423], 'enumeration': [4434, 5203], 'scheme,': [4435], 're-analyzed': [4438], '(results': [4442], 'S1C).': [4447], 'taken': [4455], 'account,': [4457], 'lowest,': [4472, 4478], '001111': [4484, 4534, 4590, 4686], 'columns': [4487], '3': [4488], '5).': [4490], 'Thus,': [4491], 'criteria,': [4495], 'despite': [4507], 'dramatic': [4509], 'geometry.': [4513], 'applied,': [4526], 'compared': [4546], '6).': [4555], 'Interestingly,': [4556], 'comparing': [4574], 'Tables': [4577], 'S1B': [4578, 5207], 'greatest': [4587], 'co-evolved': [4607], '(branch': [4612], 'angle)': [4615], 'create': [4619], 'low': [4626], 'asked': [4638], 'affected': [4643], 'clash.': [4645], 'Compared': [4646], 'maximum': [4649, 5251], '(calculated': [4655], 'above': [4656], '130,305': [4659], 'branching),': [4664], 'thousand': [4676], 'stand': [4689], 'out,': [4690], 'among': [4694, 5257], 'half': [4697], 'numbers': [4704], 'clashes.': [4706], 'speculate': [4708], 'flexibility': [4711], 'tissues': [4714], 'mean': [4716], 'serious': [4723], 'needed': [4726], 'avoided': [4729], 'evolution': [4732, 4903], 'usually': [4743], 'dictates': [4744], 'form;': [4746], 'biology.': [4761], 'illustrate': [4764], 'approach': [4766, 5383, 5558], 'enumerating': [4771], 'configurations': [4774], 'asking': [4800], 'favored': [4807], 'figures': [4812], 'designed': [4815], 'evaluate': [4817], 'case': [4836], 'effective': [4866], 'center': [4879], 'key': [4886], 'goal': [4887], 'strongly': [4893], 'selected': [4901], 'achieve': [4905], 'organ-specific': [4907], 'arrangement.': [4909], 'enter': [4912], 'age': [4914], 'regeneration': [4916, 4929], 'medicine,': [4917], 'help': [4925], 'kidneys': [4931], 'stem': [4933, 4971], '(Boreström': [4935], '2018Boreström': [4938], 'Jonebring': [4940], 'Guo': [4942], 'Palmgren': [4944], 'Cederblad': [4946], 'Forslöw': [4948], 'Svensson': [4950], 'Söderberg': [4952], 'Reznichenko': [4954], 'Nyström': [4956], 'al.A': [4959], 'CRISP(e)R': [4960], 'view': [4961], 'organoids': [4964], 'allows': [4965], 'induced': [4969], 'pluripotent': [4970], 'cell-derived': [4972], 'drug': [4976], 'discovery.Kidney': [4977], 'Int.': [4978], '94:': [4980], '1099-1110Abstract': [4981], '(46)': [4989], 'Wu': [4992], '2018Wu': [4995], 'Uchimura': [4997], 'Donnelly': [4999], 'E.L.': [5000], 'Kirita': [5001], 'Y.': [5002], 'Morris': [5003], 'S.A.': [5004], 'Humphreys': [5005], 'Comparative': [5007], 'Analysis': [5008], 'Refinement': [5010], 'Human': [5012], 'PSC-Derived': [5013], 'Organoid': [5015], 'Differentiation': [5016], 'Single-Cell': [5018], 'Transcriptomics.Cell': [5019], 'Stem': [5020], '23:': [5023], '869-881Abstract': [5024], '(278)': [5032], 'It': [5035, 5331], 'instructive': [5037], 'compare': [5039], 'what': [5045], 'organs.': [5050], 'Lung': [5051], 'proceeds': [5053], 'phases.': [5056], 'Initially,': [5057], 'sides': [5068], 'tube,': [5071], 'termed': [5072, 5103], 'branching—which': [5074], 'contributes': [5076], 'space-filling': [5078], 'lung—after': [5081], 'primarily': [5085], 'sequences': [5089, 5260], 'variant': [5102], 'Although': [5106], 'current': [5108], 'framework': [5110], 'allow': [5113], 'represent': [5116, 5127], 'programs,': [5123], 'directly': [5126], 'program': [5131, 5177], 'Previous': [5143], 'studies': [5144, 5204], 'mixture': [5184, 5312], 'angles,': [5187, 5318], 'grandparents.': [5200], 'computational': [5202], 'exclusively,': [5221], 'dramatically': [5223], 'distributions': [5226], '[000000]': [5230], 'dimensions': [5237, 5255], '2.23': [5239], '1.76,': [5241], 'respectively.': [5242], 'minimum': [5253], 'confirming': [5264], 'intuitive': [5266], 'idea': [5267], 'all-perpendicular': [5269], 'gives': [5271], 'highest': [5273], 'all-parallel': [5276], 'dimensionality.': [5280], 'functional': [5284], '(bronchi)': [5291], 'three-dimensional': [5295], 'expect': [5302], 'all-orthogonal': [5304], 'predominate,': [5307], 'fact': [5310], 'respect': [5320], 'interesting': [5334], 'consider': [5336], 'balance': [5340], 'sense': [5351], 'just': [5353], 'space-filling.': [5354], 'Undoubtedly': [5365], 'exist': [5367], 'nature;': [5369], 'hope': [5371], 'discussion': [5374], 'tools': [5381], 'WAL,': [5387], 'KEM': [5388, 5397], 'WFM': [5390], 'supported': [5392, 5399, 5419], 'NSF': [5394], 'grant': [5395], 'DBI-1548297.': [5396], 'NIH': [5401], 'NIDDK': [5402], 'grants': [5403], 'R01': [5404, 5406], 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