sebkopf/Isotope labeling and growth.ipynb

## isolabel.html
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},
{
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},
{
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},
{
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},
{
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},
{
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"value": 0.18848,
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},
{
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"value": 0.1891,
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},
{
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"value": 0.18971,
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},
{
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"value": 0.19032,
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},
{
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"value": 0.19093,
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},
{
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"value": 0.19154,
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},
{
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"value": 0.19214,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.4349,
"value": 0.19273,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.4429,
"value": 0.19333,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.4509,
"value": 0.19392,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.4589,
"value": 0.19451,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.4669,
"value": 0.19509,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.4749,
"value": 0.19567,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
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"value": 0.19625,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time":  1.491,
"value": 0.19683,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time":  1.499,
"value": 0.1974,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time":  1.507,
"value": 0.19797,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time":  1.515,
"value": 0.19853,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time":  1.523,
"value": 0.19909,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.5311,
"value": 0.19965,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.5391,
"value": 0.20021,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.5471,
"value": 0.20076,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.5551,
"value": 0.20131,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.5631,
"value": 0.20186,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.5711,
"value": 0.2024,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.5792,
"value": 0.20294,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.5872,
"value": 0.20348,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.5952,
"value": 0.20402,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.6032,
"value": 0.20455,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.6112,
"value": 0.20508,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.6192,
"value": 0.2056,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.6273,
"value": 0.20613,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.6353,
"value": 0.20665,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.6433,
"value": 0.20716,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.6513,
"value": 0.20768,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.6593,
"value": 0.20819,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.6673,
"value": 0.2087,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.6754,
"value": 0.2092,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.6834,
"value": 0.20971,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.6914,
"value": 0.21021,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.6994,
"value": 0.2107,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.7074,
"value": 0.2112,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.7154,
"value": 0.21169,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.7234,
"value": 0.21218,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.7315,
"value": 0.21267,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.7395,
"value": 0.21315,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.7475,
"value": 0.21363,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.7555,
"value": 0.21411,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.7635,
"value": 0.21459,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.7715,
"value": 0.21506,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.7796,
"value": 0.21553,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.7876,
"value":  0.216,
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"FNlong": "FN = 30%"
},
{
 "time": 1.7956,
"value": 0.21646,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.8036,
"value": 0.21693,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.8116,
"value": 0.21739,
"FN": "30%",
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},
{
 "time": 1.8196,
"value": 0.21785,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.8277,
"value": 0.2183,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.8357,
"value": 0.21875,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.8437,
"value": 0.2192,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.8517,
"value": 0.21965,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.8597,
"value": 0.2201,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.8677,
"value": 0.22054,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.8758,
"value": 0.22098,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.8838,
"value": 0.22142,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.8918,
"value": 0.22185,
"FN": "30%",
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},
{
 "time": 1.8998,
"value": 0.22229,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 1.9078,
"value": 0.22272,
"FN": "30%",
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},
{
 "time": 1.9158,
"value": 0.22314,
"FN": "30%",
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},
{
 "time": 1.9238,
"value": 0.22357,
"FN": "30%",
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},
{
 "time": 1.9319,
"value": 0.22399,
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},
{
 "time": 1.9399,
"value": 0.22441,
"FN": "30%",
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},
{
 "time": 1.9479,
"value": 0.22483,
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},
{
 "time": 1.9559,
"value": 0.22525,
"FN": "30%",
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},
{
 "time": 1.9639,
"value": 0.22566,
"FN": "30%",
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},
{
 "time": 1.9719,
"value": 0.22608,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time":   1.98,
"value": 0.22649,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time":  1.988,
"value": 0.22689,
"FN": "30%",
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},
{
 "time":  1.996,
"value": 0.2273,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time":  2.004,
"value": 0.2277,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time":  2.012,
"value": 0.2281,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time":   2.02,
"value": 0.2285,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.0281,
"value": 0.2289,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.0361,
"value": 0.22929,
"FN": "30%",
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},
{
 "time": 2.0441,
"value": 0.22968,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.0521,
"value": 0.23007,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.0601,
"value": 0.23046,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.0681,
"value": 0.23084,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.0762,
"value": 0.23123,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.0842,
"value": 0.23161,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.0922,
"value": 0.23199,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.1002,
"value": 0.23236,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.1082,
"value": 0.23274,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.1162,
"value": 0.23311,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.1242,
"value": 0.23348,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.1323,
"value": 0.23385,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.1403,
"value": 0.23422,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.1483,
"value": 0.23458,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.1563,
"value": 0.23494,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.1643,
"value": 0.23531,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.1723,
"value": 0.23566,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.1804,
"value": 0.23602,
"FN": "30%",
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},
{
 "time": 2.1884,
"value": 0.23637,
"FN": "30%",
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},
{
 "time": 2.1964,
"value": 0.23673,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.2044,
"value": 0.23708,
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},
{
 "time": 2.2124,
"value": 0.23743,
"FN": "30%",
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},
{
 "time": 2.2204,
"value": 0.23777,
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},
{
 "time": 2.2285,
"value": 0.23812,
"FN": "30%",
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},
{
 "time": 2.2365,
"value": 0.23846,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.2445,
"value": 0.2388,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.2525,
"value": 0.23914,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.2605,
"value": 0.23948,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.2685,
"value": 0.23981,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.2766,
"value": 0.24015,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.2846,
"value": 0.24048,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.2926,
"value": 0.24081,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.3006,
"value": 0.24114,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.3086,
"value": 0.24146,
"FN": "30%",
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},
{
 "time": 2.3166,
"value": 0.24179,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.3246,
"value": 0.24211,
"FN": "30%",
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},
{
 "time": 2.3327,
"value": 0.24243,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.3407,
"value": 0.24275,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.3487,
"value": 0.24307,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.3567,
"value": 0.24338,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.3647,
"value": 0.2437,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.3727,
"value": 0.24401,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.3808,
"value": 0.24432,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.3888,
"value": 0.24463,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.3968,
"value": 0.24493,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.4048,
"value": 0.24524,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.4128,
"value": 0.24554,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.4208,
"value": 0.24584,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.4289,
"value": 0.24614,
"FN": "30%",
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},
{
 "time": 2.4369,
"value": 0.24644,
"FN": "30%",
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},
{
 "time": 2.4449,
"value": 0.24674,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.4529,
"value": 0.24703,
"FN": "30%",
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},
{
 "time": 2.4609,
"value": 0.24733,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.4689,
"value": 0.24762,
"FN": "30%",
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},
{
 "time":  2.477,
"value": 0.24791,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time":  2.485,
"value": 0.2482,
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},
{
 "time":  2.493,
"value": 0.24848,
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},
{
 "time":  2.501,
"value": 0.24877,
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},
{
 "time":  2.509,
"value": 0.24905,
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},
{
 "time":  2.517,
"value": 0.24934,
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},
{
 "time": 2.5251,
"value": 0.24962,
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},
{
 "time": 2.5331,
"value": 0.2499,
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},
{
 "time": 2.5411,
"value": 0.25017,
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},
{
 "time": 2.5491,
"value": 0.25045,
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},
{
 "time": 2.5571,
"value": 0.25072,
"FN": "30%",
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},
{
 "time": 2.5651,
"value":  0.251,
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},
{
 "time": 2.5731,
"value": 0.25127,
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},
{
 "time": 2.5812,
"value": 0.25154,
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},
{
 "time": 2.5892,
"value": 0.25181,
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},
{
 "time": 2.5972,
"value": 0.25207,
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},
{
 "time": 2.6052,
"value": 0.25234,
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},
{
 "time": 2.6132,
"value": 0.2526,
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},
{
 "time": 2.6212,
"value": 0.25287,
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},
{
 "time": 2.6293,
"value": 0.25313,
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},
{
 "time": 2.6373,
"value": 0.25339,
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},
{
 "time": 2.6453,
"value": 0.25365,
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},
{
 "time": 2.6533,
"value": 0.2539,
"FN": "30%",
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},
{
 "time": 2.6613,
"value": 0.25416,
"FN": "30%",
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},
{
 "time": 2.6693,
"value": 0.25441,
"FN": "30%",
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},
{
 "time": 2.6774,
"value": 0.25466,
"FN": "30%",
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},
{
 "time": 2.6854,
"value": 0.25492,
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},
{
 "time": 2.6934,
"value": 0.25517,
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},
{
 "time": 2.7014,
"value": 0.25541,
"FN": "30%",
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},
{
 "time": 2.7094,
"value": 0.25566,
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},
{
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"value": 0.25591,
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},
{
 "time": 2.7255,
"value": 0.25615,
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},
{
 "time": 2.7335,
"value": 0.25639,
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},
{
 "time": 2.7415,
"value": 0.25664,
"FN": "30%",
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},
{
 "time": 2.7495,
"value": 0.25688,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
 "time": 2.7575,
"value": 0.25712,
"FN": "30%",
"FNlong": "FN = 30%"
},
{
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{
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{
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{
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{
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{
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{
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{
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{
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{
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{
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{
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{
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{
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{
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{
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{
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{
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{
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{
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{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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{
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{
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{
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{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
 "time": 3.7675,
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},
{
 "time": 3.7756,
"value": 0.27882,
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},
{
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},
{
 "time": 3.7916,
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},
{
 "time": 3.7996,
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},
{
 "time": 3.8076,
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},
{
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},
{
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"value": 0.27952,
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},
{
 "time": 3.8317,
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},
{
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},
{
 "time": 3.8477,
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},
{
 "time": 3.8557,
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},
{
 "time": 3.8637,
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},
{
 "time": 3.8717,
"value": 0.28019,
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},
{
 "time": 3.8798,
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},
{
 "time": 3.8878,
"value": 0.28041,
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
 "time": 3.9519,
"value": 0.28126,
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},
{
 "time": 3.9599,
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},
{
 "time": 3.9679,
"value": 0.28147,
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},
{
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},
{
 "time":  3.984,
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},
{
 "time":  3.992,
"value": 0.28177,
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},
{
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"value": 0.28187,
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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},
{
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## Isotope labeling and growth.ipynb
{
 "metadata": {
  "name": ""
 },
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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Load all prerequisite python libraries."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from IPython.display import display\n",
      "import sympy as sym\n",
      "import numpy as np\n",
      "from sympy import *\n",
      "from numpy import *\n",
      "from sympy.interactive import printing\n",
      "printing.init_printing()\n",
      "%load_ext rmagic"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "On the R side, make sure to install ggplot2 (should include scales and grid packages as dependencies) and pull rCharts from GitHub (requires devtools to pull and RJSONIO to run).\n",
      "```\n",
      "install.packages(\"ggplot2\", depen=T)\n",
      "install.packages(\"devtools\", depen=T)\n",
      "install.packages(\"RJSONIO\", depen=T)\n",
      "require(devtools)\n",
      "install_github('rCharts', 'ramnathv')\n",
      "```"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Isotope labeling calculations\n",
      "This is to calculate how the the isotopic composition of an exponentially growing population changes after pulse labeling.\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The following rules define the variables in the system:\n",
      "\n",
      "- $B$ is the total biomass in the system, $O$ is the old (unlabeled) material that was produced before the pulse, $N$ is the new (labeled) material produced since the pulse. \n",
      "- $\\mu$ is the specific growth rate of the population, $k_{dil}$ is the dilution rate (think of this as dilution or death depending on the system)\n",
      "- dilution/death affects all material (old and new) in proportion to the size of the pool\n",
      "- at the time of the pulse, all material is old/unlabeld $(O_0 = B_0)$ and there is no new/labeled material ($N_0 = 0$)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Equation derivations\n",
      "#### $B, O, N$ equations defining the system"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "B, O, N = map(Function, 'BON')\n",
      "mu, k, t = symbols(\"mu k_dil t\", positive=True)\n",
      "deqB = Eq(Derivative(B(t), t), (mu - k) * B(t)); display(deqB)\n",
      "deqO = Eq(Derivative(O(t), t), - k * O(t)); display(deqO)\n",
      "eqT = Eq(B(t), O(t) + N(t)); display(eqT)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{d}{d t} B{\\left (t \\right )} = \\left(- k_{dil} + \\mu\\right) B{\\left (t \\right )}$$"
       ],
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAOgAAAArBAMAAACA+9lRAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nP9FYobEvKjuZf6JG/uTNB7KT+Sb6By5hGJWWrjIfAAAAAElFTkSuQmCC\n",
       "text": [
        "d                           \n",
        "\u2500\u2500(B(t)) = (-k_dil + \u03bc)\u22c5B(t)\n",
        "dt                          "
       ]
      },
      {
       "latex": [
        "$$\\frac{d}{d t} O{\\left (t \\right )} = - k_{dil} O{\\left (t \\right )}$$"
       ],
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAK4AAAArBAMAAAATX662AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMARLvvmVQQid3NIqt2\nMmaorGxOAAADIElEQVRIDbVWS2gTURQ9k8+b/FsoiOAiAVcV0YAKIlQiFopUaJbdSIcK0q4SoWiL\nSLuzfqBRFKqgDC50UVARoQjVjqiIqDjg0k+z6MZdqrRiMNb73jTMpzPYxZsDk3fvu/ecefPmzc0F\nOJSdJTFK/+koS5cUgnktHN3xcGRxPQzd1PyH1TB0u/TIWgi67DBitRB0Y2tIVEPQjRZQ6QxBt1LF\nEDT5wpUyuuO6fN2kkbusypcFWzg/98Kt+427OdM9uSXPn5kaO/uc6KmC0HgWqDR80Bu633euTnMB\nzAkTaTrKSQ0Y0ZH0km3f+92rt4GnFPZnjhYotB94Q8MQkAk+1Z7vnl0jRrQUxJylKBaBQzQcA1iR\n+35QPN99coqy0o0AprrCNSZNhWddoOsGXb5QabOcmOwkT23Bn/lQZA90qiUoj38sAGNOrtNOVnNH\nTXsi9ZvbsRX4MycNHp7RI3Ug3iDzO/fVmwIlbrdR2Xami5YYayFTYns19Q8PJJpwM9vZM3wJ7CcS\nZaLUyB5sR7zj0BcxwxrI6tiORIu7lWIAc12jaOYXorQUUeGWeLoDbHaacNHEwFUxG+c3p93qEK/x\nY9XJXG+jgRmedbIooqLCeXV5XODKnFCk7STcQaJBA9tHR41WtJm5qFF40RRPkwcDPSFB5Wucnn7E\n7Q2wFltNgR1/W1beAU2k+XrTtBl8B21mOz1fJxU6a3z3J3Bi4721o44x12ArKkbMJU2taNkilL8U\n5GfNn5npAevWSZvW1s8MoJfS/ZAuoKVS9BPuDSJTAF6aGL5FmQHMz329dFMoU8Dd92RYb4cMD2hZ\nywYOgDZhNyIGkH0ydoTn/Id5ydJJFa3R/5c1secUWzOjXx1xF3NT17dsZaqGg7HZ7Mm26vFatSPj\nCLmZ1PVRWbQRsZxRe8bP2vH6VZ3N67HTjqCbmdd4WbSxUZ132TNbtdzMcVEWHdwH3M7pjpmtmi4m\nVX9eFuWCd31WWZSrK7o+URal6lpdn/zGz+r65Dd+VtcnipvUfbC6PlHc5OqKrk+URam6VtfXzwyp\nqvT3Ibo+URZlKv8Dr6ffSHivLyUAAAAASUVORK5CYII=\n",
       "text": [
        "d                     \n",
        "\u2500\u2500(O(t)) = -k_dil\u22c5O(t)\n",
        "dt                    "
       ]
      },
      {
       "latex": [
        "$$B{\\left (t \\right )} = N{\\left (t \\right )} + O{\\left (t \\right )}$$"
       ],
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAK0AAAAVBAMAAADGGHNoAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\ndxgAAAAASUVORK5CYII=\n",
       "text": [
        "B(t) = N(t) + O(t)"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Solving the differential equations"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "C1, B0, O0 = symbols(\"C1 B0 O0\")\n",
      "eqB = dsolve(deqB, B(t)).subs(C1, B0); display(simplify(eqB))\n",
      "eqO = dsolve(deqO, O(t)).subs(C1, B0); display(Eq(Eq(eqO.lhs, eqO.rhs.subs(B0, O0)), eqO.rhs)) \n",
      "eqN = Eq(N(t), solve(eqT, N(t))[0].subs(eqO.lhs, eqO.rhs.subs(O0, B0)).subs(eqB.lhs, eqB.rhs)); display(simplify(eqN))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$B{\\left (t \\right )} = B_{0} e^{t \\left(- k_{dil} + \\mu\\right)}$$"
       ],
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAALkAAAAaBAMAAAAZC+AvAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nKaQAAAAASUVORK5CYII=\n",
       "text": [
        "           t\u22c5(-k_dil + \u03bc)\n",
        "B(t) = B\u2080\u22c5\u212f              "
       ]
      },
      {
       "latex": [
        "$$O{\\left (t \\right )} = \\frac{O_{0}}{e^{k_{dil} t}} = \\frac{B_{0}}{e^{k_{dil} t}}$$"
       ],
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAMEAAAAqBAMAAAD47yLuAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "text": [
        "           -k_dil\u22c5t       -k_dil\u22c5t\n",
        "O(t) = O\u2080\u22c5\u212f         = B\u2080\u22c5\u212f        "
       ]
      },
      {
       "latex": [
        "$$N{\\left (t \\right )} = \\frac{B_{0}}{e^{k_{dil} t}} \\left(e^{\\mu t} - 1\\right)$$"
       ],
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAMsAAAAqBAMAAADvzbInAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "text": [
        "          \u239b \u03bc\u22c5t    \u239e  -k_dil\u22c5t\n",
        "N(t) = B\u2080\u22c5\u239d\u212f    - 1\u23a0\u22c5\u212f        "
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Ratios of old and new material"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "eqNR = Eq(N(t)/B(t), eqN.rhs/eqB.rhs); display(simplify(eqNR))\n",
      "eqOR = Eq(O(t)/B(t), eqO.rhs/eqB.rhs); display(simplify(eqOR))\n",
      "eqNO = Eq(N(t)/O(t), eqN.rhs/eqO.rhs); display(simplify(eqNO))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{N{\\left (t \\right )}}{B{\\left (t \\right )}} = 1 - e^{- \\mu t}$$"
       ],
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAJMAAAAyBAMAAACqi/RtAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nIoU6DxjwUBXyD4pcvATSL4RtAAAAAElFTkSuQmCC\n",
       "text": [
        "N(t)        -\u03bc\u22c5t\n",
        "\u2500\u2500\u2500\u2500 = 1 - \u212f    \n",
        "B(t)            "
       ]
      },
      {
       "latex": [
        "$$\\frac{O{\\left (t \\right )}}{B{\\left (t \\right )}} = e^{- \\mu t}$$"
       ],
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAG0AAAAyBAMAAACkDkhHAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "text": [
        "O(t)    -\u03bc\u22c5t\n",
        "\u2500\u2500\u2500\u2500 = \u212f    \n",
        "B(t)        "
       ]
      },
      {
       "latex": [
        "$$\\frac{N{\\left (t \\right )}}{O{\\left (t \\right )}} = e^{\\mu t} - 1$$"
       ],
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAIYAAAAyBAMAAABrDL7BAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nxfnASzcmcAsAAAAASUVORK5CYII=\n",
       "text": [
        "N(t)    \u03bc\u22c5t    \n",
        "\u2500\u2500\u2500\u2500 = \u212f    - 1\n",
        "O(t)           "
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**Noteworthy**: \n",
      "\n",
      "- In this model, the dilution/death rate $k_{dil}$ only affects how biomass $B(t)$ changes with time\n",
      "- $k_{dil}$ does **NOT** affect the extent of label incorporation (%$N$ or %$O$) because it takes away proportionally from both pools."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Application in chemostat\n",
      "In a chemostat, the dilution rate $k_{kil}$ is artifically imposed by the medium flowrate $q$ and the reactor vessel volume $V$: ($k_{dil}=\\frac{q}{V}$). Once the system reaches steady-state $\\frac{d}{d t} B = 0$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "display(Eq(deqB, 0))\n",
      "Eq(mu, solve(Eq(deqB.rhs, 0), mu)[0])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{d}{d t} B{\\left (t \\right )} = \\left(- k_{dil} + \\mu\\right) B{\\left (t \\right )} = 0$$"
       ],
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAARAAAAArBAMAAABC7sr8AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nQrLN/Iwpu35/hRiNs1e+lV2/r0LuAxCnNhX4ejzOAAAAAElFTkSuQmCC\n",
       "text": [
        "d                               \n",
        "\u2500\u2500(B(t)) = (-k_dil + \u03bc)\u22c5B(t) = 0\n",
        "dt                              "
       ]
      },
      {
       "latex": [
        "$$\\mu = k_{dil}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAEcAAAASBAMAAAD73d5oAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAMu92q4ndmc0QVCK7\nRGaiMfZFAAABLUlEQVQoFW2QMUjDQBiFX5qe6SVtjbq5WBcHpwyK0qlL94KDOAiC6OQQFNTN23RR\nMgmCkE6u7eDiZKG7iojgls21WZQmCP6XoSbnPbjce9//7g4C6HS7pKMqO1eBLic6qLDaWAG6yIRC\njQbMlsIqnfqhm2dsB1M+AXaRSVqEH1uvL4AVw/T5cwBUfIRdOcmpN5cFPoLRxzt5avSoW9DZZRZt\nIbdNWtQ4lT6v3XshI/Pl94rWMbDnSLKfqUWWxzxxwI/Wu7UVICVyACdhtOdUH/Efhmt3IWBhYDTo\n1BesdD7XIFseIGY4wSwe7mAOAPt7w1v1iqVqhE8Py6C3hqjSsCyKhUniKZ5u+NgtzQAl5ZZJCYtG\nHNmiM20Cj+4fLrq35lrE231rG9n/LA7/p199xUQAbJ8eywAAAABJRU5ErkJggg==\n",
       "prompt_number": 5,
       "text": [
        "\u03bc = k_dil"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Additionally, in the chemostat, the concentration of the limiting substrate $S(t)$ can be described by the following differential equation where\n",
      "\n",
      "- $S_0$ is the starting concentration of the limiting nutrient in the medium\n",
      "- $\\gamma$ is the yield coefficient for the substrate $\\gamma=\\frac{m_B}{m_S}$ (assumed to be independent of $B$ and $\\mu$ - for a discussion of alternative models, check *e.g.* Chapter 8 of *The Theory of the Chemostat: Dynamics of Microbial Competition* by Smith and Waltman, 1995)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "S = Function('S')\n",
      "S0, gamma = symbols('S0 gamma')\n",
      "deqS = Eq(Derivative(S(t)), k*(S0 - S(t)) - mu * B(t)/gamma); display(deqS)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{d}{d t} S{\\left (t \\right )} = k_{dil} \\left(S_{0} - S{\\left (t \\right )}\\right) - \\frac{\\mu}{\\gamma} B{\\left (t \\right )}$$"
       ],
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAS8AAAAvBAMAAABAh1FfAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n+acc3gAAAABJRU5ErkJggg==\n",
       "text": [
        "d                              \u03bc\u22c5B(t)\n",
        "\u2500\u2500(S(t)) = k_dil\u22c5(S\u2080 - S(t)) - \u2500\u2500\u2500\u2500\u2500\u2500\n",
        "dt                               \u03b3   "
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "At steady state, $\\frac{d}{dt}S(t)=0$ and $\\mu = k_{dil}$ (see section above) and this simplifies to yield an equation for steady-state $B_{steady}$:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "SC, BC = symbols('S_steady B_steady') #at steady state\n",
      "display(Eq(deqS, 0))\n",
      "eqBC = Eq(BC, solve(Eq(deqS.rhs.subs(mu, k), 0), B(t))[0].subs(S(t), SC)); display(eqBC)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{d}{d t} S{\\left (t \\right )} = k_{dil} \\left(S_{0} - S{\\left (t \\right )}\\right) - \\frac{\\mu}{\\gamma} B{\\left (t \\right )} = 0$$"
       ],
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAVcAAAAvBAMAAAClGZQzAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nAABJRU5ErkJggg==\n",
       "text": [
        "d                              \u03bc\u22c5B(t)    \n",
        "\u2500\u2500(S(t)) = k_dil\u22c5(S\u2080 - S(t)) - \u2500\u2500\u2500\u2500\u2500\u2500 = 0\n",
        "dt                               \u03b3       "
       ]
      },
      {
       "latex": [
        "$$B_{steady} = \\gamma \\left(S_{0} - S_{steady}\\right)$$"
       ],
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAOgAAAAWBAMAAAA4H80iAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "text": [
        "B_steady = \u03b3\u22c5(S\u2080 - S_steady)"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Lastly, the Monod equation (same as Michalis-Menten kinetics) links the specific growth rate $\\mu$ to the substrate concentration $S$ with\n",
      "\n",
      "- $\\mu_{max}$ the maximum specific growth rate of the bug\n",
      "- $K_s$ the half saturation/growth constant $\\left(K_s = S \\middle|\\frac{\\mu}{\\mu_{max}}=0.5 \\right)$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mumax, Ks = symbols('mu_max K_s')\n",
      "monoeq = Eq(mu(t), mumax * (S(t)) / (Ks + S(t))); display(monoeq)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\mu{\\left (t \\right )} = \\frac{\\mu_{max} S{\\left (t \\right )}}{K_{s} + S{\\left (t \\right )}}$$"
       ],
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAJwAAAAyBAMAAABbgK/gAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nTkSuQmCC\n",
       "text": [
        "       mu_max\u22c5S(t)\n",
        "\u03bc(t) = \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "        K_s + S(t)"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "At steady state again, $\\mu = k_{dil}$ so this comes down to"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "eqSC = Eq(SC, solve(monoeq, S(t))[0].subs(mu(t), k)); display(eqSC)\n",
      "Eq(BC, eqBC.rhs.subs(SC, eqSC.rhs))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$S_{steady} = \\frac{K_{s} k_{dil}}{- k_{dil} + \\mu_{max}}$$"
       ],
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAANQAAAAvBAMAAABppfnxAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nj45cGv2wBRPQoNvfCP8AIwRRAE8aI4gAAAAASUVORK5CYII=\n",
       "text": [
        "              K_s\u22c5k_dil   \n",
        "S_steady = \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "           -k_dil + mu_max"
       ]
      },
      {
       "latex": [
        "$$B_{steady} = \\gamma \\left(- \\frac{K_{s} k_{dil}}{- k_{dil} + \\mu_{max}} + S_{0}\\right)$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAUMAAAAyBAMAAAA0FKTkAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nSUVORK5CYII=\n",
       "prompt_number": 9,
       "text": [
        "             \u239b     K_s\u22c5k_dil        \u239e\n",
        "B_steady = \u03b3\u22c5\u239c- \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + S\u2080\u239f\n",
        "             \u239d  -k_dil + mu_max     \u23a0"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This can further be simplified by introducing the maximal dilution rate $k_{max}$ at $B_{steady}=0$ (commonly referred to as the **washout** dilution rate) and scaling $k_{dil}$ to $k_{max}$ with the proportionality factor $f \\in [0;1]$ and scaling $S_0$ (the initial substrate concentration) to $K_s$ (the half saturation constant) with $r$. Commonly in laboratory cultures we provide enough substrate $S_0$ such that $r >> 1$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "kmax, Smax, Bmax, f, r = symbols('k_max S_max B_max f r')\n",
      "eqkmax = Eq(kmax, solve(eqBC.rhs.subs(SC, eqSC.rhs), k)[0]); display(eqkmax)\n",
      "eqk = Eq(k, f*kmax); display(eqk)\n",
      "eqKs = Eq(Ks, S0/r); display(eqKs)\n",
      "eqSCred = simplify(eqSC.subs(eqk.lhs, eqk.rhs).subs(eqkmax.lhs, eqkmax.rhs).subs(eqKs.lhs, eqKs.rhs)); display(eqSCred)\n",
      "eqBCred = Eq(BC, eqBC.rhs.subs(SC, eqSCred.rhs)); display(Eq(eqBCred, simplify(eqBCred.rhs)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$k_{max} = \\frac{S_{0} \\mu_{max}}{K_{s} + S_{0}}$$"
       ],
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAJQAAAAtBAMAAAC6119aAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\ngrmq62bGmCZr6CuzMPBmyiFhBWLfKfwFgrIWOOQ20NUAAAAASUVORK5CYII=\n",
       "text": [
        "        S\u2080\u22c5mu_max\n",
        "k_max = \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "         K_s + S\u2080"
       ]
      },
      {
       "latex": [
        "$$k_{dil} = f k_{max}$$"
       ],
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAHMAAAASBAMAAACaxfwqAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n3no6SgvWpAAAAABJRU5ErkJggg==\n",
       "text": [
        "k_dil = f\u22c5k_max"
       ]
      },
      {
       "latex": [
        "$$K_{s} = \\frac{S_{0}}{r}$$"
       ],
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAFAAAAAqBAMAAADWhsE5AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nYJ/ReHVaAAAAAElFTkSuQmCC\n",
       "text": [
        "      S\u2080\n",
        "K_s = \u2500\u2500\n",
        "      r "
       ]
      },
      {
       "latex": [
        "$$S_{steady} = \\frac{S_{0} f}{- f r + r + 1}$$"
       ],
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAMoAAAAvBAMAAABQwkiqAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nSUVORK5CYII=\n",
       "text": [
        "               S\u2080\u22c5f    \n",
        "S_steady = \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "           -f\u22c5r + r + 1"
       ]
      },
      {
       "latex": [
        "$$B_{steady} = \\gamma \\left(- \\frac{S_{0} f}{- f r + r + 1} + S_{0}\\right) = \\frac{S_{0} \\gamma \\left(f r + f - r - 1\\right)}{f r - r - 1}$$"
       ],
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAhQAAAAyBAMAAAD2Pl/UAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nfodl3egMy3OwY1ie8/1+Bvku6rJR5k1lAAAAAElFTkSuQmCC\n",
       "text": [
        "             \u239b      S\u2080\u22c5f         \u239e   S\u2080\u22c5\u03b3\u22c5(f\u22c5r + f - r - 1)\n",
        "B_steady = \u03b3\u22c5\u239c- \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + S\u2080\u239f = \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "             \u239d  -f\u22c5r + r + 1     \u23a0        f\u22c5r - r - 1      "
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In practice, this is what these curves look like:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R -r 100 -w 1000 \n",
      "library(ggplot2)\n",
      "library(reshape2)\n",
      "# custom function for easy plotting DF generation\n",
      "df.fun <- function(SAF = FALSE, ...){\n",
      "  ns <- sapply(list(...), function(x) length(x)) # lengths of each vector\n",
      "  each <- c(1, cumprod(ns)[-length(ns)]) # each multipliers\n",
      "  times <- c(rev(cumprod(rev(ns)))[-1], 1) # times multipliers\n",
      "  data.frame(mapply(function(var, each, times) list(rep(var, each = each, times = times)),list(...), each, times), stringsAsFactors = SAF)\n",
      "}\n",
      "                    \n",
      "# model framework\n",
      "df <- df.fun(\n",
      "    f = seq(from=0, to=1, length.out=101), # fraction k_max \n",
      "    r = c(100, 20, 5), # the ratio of S0 to Ks\n",
      "    gamma = 0.8 # the yield coefficient for substrate to biomass conversion\n",
      ")\n",
      "\n",
      "S0 <- 1 # this is just a scaling factor for the y axis                    \n",
      "df$S <- S0 * df$f / (-df$f * df$r + df$r + 1) # S at steady state\n",
      "df$B <- df$gamma * (S0 - df$S) # B at steady state\n",
      "              \n",
      "p<-ggplot(melt(df, id=c('f', 'r', 'gamma')), \n",
      "          aes(x=f, y=value, colour=variable)) + \n",
      "    geom_line(size=1.5) +\n",
      "    labs(y=\"\", x=bquote(k[dil]~('='~mu))) +\n",
      "    scale_x_continuous(expand=c(0,0), lim=c(0, 1.2), breaks=c(0,1), labels=expression(0, k[max]~\"=\"~frac(S[0]*mu[max],K[s] + S[0]))) +\n",
      "    scale_y_continuous(expand=c(0,0), lim=c(0, S0), breaks=c(0, S0*df$gamma[1], S0), labels=expression(0, gamma*S[0], S[0])) +\n",
      "    scale_colour_manual(\"\", values=c(\"orange\", \"dark green\"), label = expression(B[steady], S[steady])) +\n",
      "    facet_grid(~r, labeller = label_bquote(frac(S[0],K[s])~'='~.(x))) + \n",
      "    annotate(\"text\", label = \"washout\", x = 1.1, y = 0.5, size = 6, colour = \"black\", angle=90) +\n",
      "    theme_bw() + theme(panel.grid.minor = element_blank(), panel.grid.major = element_line(colour=\"black\"))\n",
      "print(p) "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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pHnvsMXr66afF9m116tShadOm0RNPPEG8PzsH3nf9+++/pxEjRog4/gEBEPBNAosXL6ZZ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\nCEAAAhCAAAQgAAEIQAACwQj8H1zEPcR2hzhDAAAAAElFTkSuQmCC\n"
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "####Noteworthy\n",
      "\n",
      "- Changing the dilution rate (= growth rate) will only affect the equilibrium amounts $S_{steady}$ and $B_{steady}$ significantely if you're operating at an initial substrate concentration $S_0$ close to the $K_s$ *(which is unlikely in most systems because $K_s$ tend to be in the $\\mu M$ range I think)*. Otherwise, the total biomass $B_{steady}$ as well as the $S_0$ will stay pretty close to 0 no matter how much you vary the growth rate until you get very close to $k_{max}$."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### *Alternative models for growth* -- work in progress\n",
      "Given indications from proteomic data that protein pools might be turning over faster than expected from growth rates, there are several different models which could be considered. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "####Model 1: dilution/death only affects old material\n",
      "\n",
      "This model is not really that likely in a chemostat system where new cells would have to physically avoid dilution out of the bioreactor but is conceivable in an environmental system where you assume that only old cells actually are physically removed from the system (by death and complete dissolution). "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "deqO2 = Eq(Derivative(O(t), t), - k * eqB.rhs); display(simplify(deqO2))\n",
      "eqO2 = dsolve(deqO2, O(t)); display(simplify(eqO2))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{d}{d t} O{\\left (t \\right )} = - B_{0} k_{dil} e^{- t \\left(k_{dil} - \\mu\\right)}$$"
       ],
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAP0AAAArBAMAAABBfJP9AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMARLvvmVQQid3NIqt2\nMmaorGxOAAAEhElEQVRYCcVXXWgcVRT+Znfnzv7M7C5GSiFg1hYKxdQGsViElgWLVaxk8UEE0Q5t\n1VSErFA0kdRuQVFaNSv2QQVlUPClYJc+GCTBjCFFpWk72BfFagapin+4UbKFhBDPuTOb7Lo7CbEN\n88He83vPuXPn3rNzAIayOS9paEOmEFpqmbjLDDf/QLjpcSrM/MmRC7Nh5u+wIrUQ84vdiJVDzB+r\nIV5cv/xJKzC2Ki3RHPqzgT7XbXgK+l0BQQyXDf1F7IfJ3I3He8AW4HhQ4KNs6C9gq2oxd8MhalBs\n0BiAA6xP2OmTWoDDdarVEiIWlFJQmIhDFjF29PTnzR4/SPHPZuXapeR9p5w4oOWvVFom9yFVgG43\n65NHnv+MNMmcVKd4de2RHp8fPXurZzuws70PaRMFfEvjTxvoDcRKSMB4o+77KzIO1P+sa9BBqkwT\nTNqVEwCxQcjkgF5/fcHFO2PhJiDzIEdR8hDAtnrAEZwhXa4uSnqYxTuBL4ioVY9KQ+swbQNdeU/f\npnirmwhb0AF0ApcnCuSouTSgBw+xyaQ78SNgND/h2+wxDtxNhEviQZbb45IF/GVLmxJ4vHFeWF8D\nE0aPgz++tNSp+pul7a1h5Gkolcbo2gxLxxx5Xrkk0usLwmYKsdOUVo1WGoB9GvqAbqNUVItRqDcj\nTVEl1Fpy9uFlUerOyEC9WS1P27b9NpsOrtS3G+aBbz7xDIli+h6nwUcMTVq+2HkBcRPvYsxJOLQR\n25DK+pbYS1O/u8ui1B6zmQxbEZfIfvql5YIG32E0HzJjfmriZUAfKlL92vBcB4WNLUDPi+0mNlpJ\n0tahu5KLm0MFUcrGn/D18QIzCV/yyLBDVPwDabufeLXkGVpHfY5ORwW/4FFa6RVpF1UYFjYiuQOH\nOFAdOckoL066GDO1F3x1v8nM477kkUWTqH4N0SzRV+hnVGloxOFXGVTUIz3kOYvXkTHR+6Z0UctM\njiC1e+rnxjm3NApLPJUFetYKsFhHFcOsO9gj8ws+iy352UEiQzP1a2IO0QJeOy0ze4flfbCpEarT\nKDXxutkkjrM47sj9V6ow/cI9IB/6ZJPrtAukZgz6cnDFgphNQuz7qqCcB+aQKTZ5rkHooqB8B/n8\naWVad1o+WLsIfP2nc5zfTlfFDF0zZ9rU+k2Ddo/y2+3mrKrTd0FspcBahU5z5Rka8kFz3qLaeYdp\n0P7bqRwWNOzBZXz0CPQc9DIOUZD/g+/27snSPKVEf0HdNl0Pltrh08XR0U0FiAVksrRbV23sAG1+\nNyI2MHnRbTdnDboTvu+Hq805zuefQSfx9idFzYl+L8W1DS3d51V//tBqcSb5/kvsMhZctVzM6KtN\naWen7rPPajDQNwtDlCVZYdD23utbO89NumLEij27gnegqcuU5XbJnsxJ1l/GknrdmAGAy+0yPpbs\nb8uK9eXov4XLbTjg7lM5+/dYONkB2X2q1bDSe90nf22FA6/75K+tcOB1n+vZgK78XF732cXf5qHA\n6z4H8Vgo2ek/TnafDwg7pPxe9/nBVEjp/wVQoScTmaOc5AAAAABJRU5ErkJggg==\n",
       "text": [
        "d                     -t\u22c5(k_dil - \u03bc)\n",
        "\u2500\u2500(O(t)) = -B\u2080\u22c5k_dil\u22c5\u212f              \n",
        "dt                                  "
       ]
      },
      {
       "latex": [
        "$$O{\\left (t \\right )} = \\begin{cases} - B_{0} k_{dil} t + C_{1} & \\text{for}\\: \\mu = k_{dil} \\\\\\frac{B_{0} k_{dil}}{k_{dil} - \\mu} e^{t \\left(- k_{dil} + \\mu\\right)} + C_{1} & \\text{otherwise} \\end{cases}$$"
       ],
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAZUAAAA/BAMAAADahUg0AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIomZq2bNMhC7791E\ndlRWeDEkAAAKn0lEQVRoBdVaDXBUVxX+9ve97F+2UmekjpNXsJHRMt0pYC0Rs6WhmrExK6BWHez2\nLzrFadYp6kCn5gGdVkrppjNpTajITlvE0YKBtjRKITttdSrYYQtFpU7IDo5tLcWE8pNQIPGc+97b\n7Ht5m92NdCZ7Zrj3nO+ec9799t533703AKXJ5ZnS/CrAy3NWrYBeltbF/khpfhXgJZ2rgE6W2EX/\nyRIdK8DtQHsFdLLELtbHSnSsALfNWVMnl442NHSlBSRv7DY12RgbOhpiH7PBi0CBps4iHlj3u2Ie\nNu2taTNIS4FrSIO8lhVufdjsiuAW4F/0r1xZ9ciFoiF3FPUY79CaMGHSRSBwSoOqs6YmDOjmar2W\nn1SJ+CTWjuvNeW2tEVt0YtDCJUhd8xAflgOqqHLF53XthF57h0kJpHSrjKqhuG+Ac5crFi5VKeDh\nHi1JrSXXTt02uNRnCZAsE9ESY2uWwMUZt42cGLRwqY5Cel7VQm7Hkq1jwYHGc02apXNxnGdTNs/R\nMf/C2orfNmBN39X487Zjt7GXlEIwanH3Kp75ZWe2cGlr6nsyq+WVL6x55Nm8R4QGdUPn4tSnYp5L\niWojpB2oyuDpd89whLMb/gjXLUJYRfK1WfvSrJQjFi79YcjPAAcPAqGhjEhUn8AhrBuGKy5MQOfi\n15c7rNTxkqtG+BVIQ1iuRdB6mcxaggfuFwAtqcGIvFm1tBYwBRd5+W6SXQlgI7n1Zz1KKArX2bSI\nSQI/QoB+O0WYOS6+QbZl3PtVHS+5akRbFvgAd2oRRGRAtQTX/1AA8iCkMPZbGguZlnE5TX79ij+B\nYfjfuEkEvc2lk367NCu1LS1/bGnh1d8vuLwDHGe8HGnEQBo4B/0bQkSMJTKXZc/lcdZDopzJagli\n5iLxBG5OJ8PYjmQimQ2TKTJ5YzhAYyBEn2PalyUyKS48LqcMLnXATgdldvLk2L07Sqo8JI8IiNID\nd3FRgpi58OeFTgFtKl7ArTQSCtb23YPXo6gOoxY0Biw6F8cHpDvVSXHxRRC4YHD5AxwjTk48Jp5B\n+YIT8oK/ZQNvAqV+js1cvClgXydz2YNGVCcU+UVpGLOGsQqYK2e0h+lcMBBD6AsElT3HuiBthVfB\ncyKffJ42Dz/TUhulux1DTqxPtKnOpEprdmli4uJuPd3Q+CugLYxteByeBXBFpJTj0W4cAab36RkN\nLvL1DV9kqFwuK0Y3YdqMm/GXUXoUvROnZmcO6j8T2yxVMSzJYA79hJ84jmC7BmqlFOP6W/mQoZu4\nGGAyAX3358vSZ4w+BZuMJqoNLgZULhcjTq/dcQuQM7eDJtgmfjyJY+aMRVxP5wLuhKjMhS0Xf5rW\nMSHJcNUtavIhbM2L/ZM5Q9njYgn3ia5aQDblk3j85/JwwvdTtmoTEKx/QA07gDhjFunN62SuKRih\n74sQX6Ltx3jbicFCDySv9zTXyZY1dj0QybZKQ7FQXKkOkvVgOxVPA0GFZuUgfc2Fh7n4vdnUrZkz\nVU0LNJ2YhweuxLVpvWV8Na23aTxYBrK/oO+rRw/F5IVh19XksZy9mgFfmM4ZcdoAk2kRWkQqQpzi\n/b0mIfYAvAPxZsf128MfiQqQmjh3sj7NX+5XN3dkeCNiFX/KikxN+5oM96s3TF8KiAOuJ84A7ahI\n7mCVmGZFNeULsUTJHwJ7qau8ewt1W/vsEQcIKzoF7VGVOhWkF+JZqnfSP2mQCpPMT5vMqWv0ctce\nTgkuMq8D47k8xS6VIM0q9bI5IeZYYBAqH6hIPid21s+zik92ioqKwOYb5z4mjLcUA7PUl1nscWZo\nHHLJgAMx2pPzeNC774yHEtDe/fz88u6c9R3gs8KgDYytyIoOBwuNprbtsw3+f8HgVshPhCnLp+lT\nGd1ARWRcypqoAc2ltU5lIylK1vLEm0CVatgvGYpWB3LmZ3LaJVdWXDsnzUn30y5zU4a+lWkyzOLi\ncROyR1vrhLeBjdVE8HXDkvV9p2FXGQrW5bSPTPHz4JBcoVX5Ze5PSTLdeNAWlGSmRDttqxwHtLeJ\nGrTXbsxjjEtVYgz9iDSPPrdm2+Qf1bHAxb4OYM1iFXe9z7OsjrfV98X01mm7rkO3Ee2M3B81dK4F\nl/VwZxHM5OOsy0caFjkU1mxk5e02IKRtdmgO035SOZ4DxpTWsKY74/D0oFNux6kEI6+AFr6x3/ke\nSHHNkabq916jWebqhhfSCwQKLt+kEzVCUcPHqN+ic/T8mGHl1/SWydpimo+SLk28RdTOYlV6t02x\nraLn1KEI5BEM4jfSNnFyvYq9fDnXkwi0G0b1dawFKAD4BWmCy0LUEKb7yMaT1vVQe71hcVhO1pJG\nM6FsccQ45Ot2cQaX6ixCJx0pvBhsXyXB07cDJzL6eZTCAikEogh1kXRi1ZEsQU6RM4WbWu5uaYnh\nJXybftI4NZCEMlqNVpWUfbphrpaQORku5iwmy+DSpuIKhblUZe5z4hhSeD+CxYZrMLpaajeMI1Iq\ngWX/DIf64GCQx4XWtoWrma8Qg4trhM17NdBchviPPLZcHOJIbPYuzdK5OHvnzP0leI55w+6/4/vU\nc3pZbuYc8uxDYVdGkbuNhJukbiWk+BB6BR6FQOYSGnaMvKuZbOnjUiNiHiLEJHzJv/R8QxYdn3qT\nPKctviFw99Haj/fu/e7ZdPOW6achHe2LM2yKKm4Y46J58rvP0uM8ivUB9GRJ3x92KIGmBHjqC7kN\nTQlvYiW/LO40IczF9Vzf0phmkmVw0U4dNPe0rNTCol3y8+VYV8xBL2IP9qm+LyVjyQztGuml7uDv\nVLeAhX/JhZnL2sVhEfnysnlw/wMzyHJsx9oEg4fzc/rV2Vm5O+1/lEDm4s9yq5cLEoOLfjEize3W\ncK2kIy5d8jOXjcAZ+BT4Ml7yoGuWZ+DkmbdPhSLg/LDiupmLjb97S98tAuYu5yRw1aEYmlTnlYS4\n6F9S5aZ/c0FicNEuRlTLwakty5f8zOUJ4CLa5n1jacwbpaiToX78lbn4z72hweRThmhcRgsKqqN6\ntkBsgrQ/4TY5yiX9SWj5r1taIqT2sk2b2pBpXAbSfMkv5hhzuTVLTl52f8rpyyrMRa4djQiYwDKk\n6LhUK0a2dwylUB1U9RZjXMSXhYbNzIXH5RRxyaBLjEuGogSXug3OToW5XAbPhTaGyxOdS8FDC09n\nemp5YnCpoVjMsnLxiUv+O6FoXPxxyBnBpe0G6WKYuRwDFgm4vMfqXPzpQmHBONbSA8oSg0voDP1n\nBtXKRbvkrzO40N98XKo/Qg+g7u+iqgvvqXhMwGU9FToX7d21DT10OGaLTwAaXLC248Y0+ZnnmLjk\nh3theMXol//zYRQPLJgV2HwuS3cTMV4sV4x+5eVli9MMT/AIuyady367tkljOS56BguXSectEqhz\nsTu00Jf+a0WiCzRbl7xQqoDjpYV1LnaHFroeGLokD3PUnc5ckkRFkuhc7A4tbsUxWCR6ajU3Z7k/\n5kOLvrf3pz3tU6uzRXqj/TdY20NLUnXPChcJn1LNyRR3x/bQMqDW/Ffl1koR7X/ojDu0cPfrFhxe\nVCk0tH7qLz8Z+YcWbturOVRQ+WDuti/v0ML9t17pVQKn/ph9L42LCPvWqYk6KmCt+h8O8+i5VBMz\nRwAAAABJRU5ErkJggg==\n",
       "text": [
        "       \u23a7      -B\u2080\u22c5k_dil\u22c5t + C\u2081         for \u03bc = k_dil\n",
        "       \u23aa                                            \n",
        "       \u23aa          t\u22c5(-k_dil + \u03bc)                    \n",
        "O(t) = \u23a8B\u2080\u22c5k_dil\u22c5\u212f                                  \n",
        "       \u23aa\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + C\u2081    otherwise  \n",
        "       \u23aa       k_dil - \u03bc                            \n",
        "       \u23a9                                            "
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In this scenario, the ratio equations become more complicated if $\\mu \\neq k_{dil}$ but in a chemostat or in an environment at steady state $\\mu = k_{dil}$ and it simplifies to:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "eqO2 = dsolve(deqO2.subs(k,mu), O(t)).subs(C1, B0); display(simplify(eqO2))\n",
      "eqN2 = Eq(N(t), solve(eqT, N(t))[0].subs(eqO.lhs, eqO2.rhs).subs(eqB.lhs, eqB.rhs)).subs(k, mu); display(simplify(eqN2))\n",
      "eqNR2 = Eq(N(t)/B(t), eqN2.rhs/eqB.rhs.subs(k, mu)); display(simplify(eqNR2))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$O{\\left (t \\right )} = B_{0} \\left(- \\mu t + 1\\right)$$"
       ],
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAALQAAAAVBAMAAAAdo9lKAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nAABJRU5ErkJggg==\n",
       "text": [
        "O(t) = B\u2080\u22c5(-\u03bc\u22c5t + 1)"
       ]
      },
      {
       "latex": [
        "$$N{\\left (t \\right )} = B_{0} \\mu t$$"
       ],
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAHMAAAAVBAMAAACHwMySAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nAAAAAElFTkSuQmCC\n",
       "text": [
        "N(t) = B\u2080\u22c5\u03bc\u22c5t"
       ]
      },
      {
       "latex": [
        "$$\\frac{N{\\left (t \\right )}}{B{\\left (t \\right )}} = \\mu t$$"
       ],
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAFwAAAAyBAMAAAAjP6FBAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\ns4yoLEpFxSMT+A8hNKnNDNj64QAAAABJRU5ErkJggg==\n",
       "text": [
        "N(t)      \n",
        "\u2500\u2500\u2500\u2500 = \u03bc\u22c5t\n",
        "B(t)      "
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**Noteworthy**: \n",
      "\n",
      "- For $t \\ll \\mu$, $\\mu t$ is a reasonable approximation for the original model ($\\frac{N(t)}{B(t)} = 1 - e^{-\\mu t}$) but deviates for longer incubations with the isotope label (longer relative to the growth rate).\n",
      "- This **CANNOT** explain the significantely higher incorporation rates observed for proteomics labeling. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Model 2: doubling decoupled from protein synthesis\n",
      "This model assumes that total protein $P_t(t)$ is produced at a specific protein production rate $\\lambda$ and actively degraded (or falls apart) at a rate $d$ (the degradation or repair rate) that removes it from the total protein pool in addition to dilution/death of the system $k_{dil}$. The usual assumptions:\n",
      " \n",
      " - Old protein $PO(t)$ from before an isotopic spike is completely unlabeled and is only degraded. \n",
      " - The system is in equilibrium w.r.t growth (e.g. in chemostat at steady state), so $k_{dil} = \\mu$. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "P = Function('P'); PO = symbols('PO')\n",
      "P0, C1, lam, d = symbols(\"P0 C1 lambda d\")\n",
      "deqP = Eq(Derivative(P(t), t), (lam - d - k) * P(t)); display(deqP)\n",
      "deqPO = Eq(Derivative(PO(t), t), (- d - k) * PO(t)); display(deqPO)\n",
      "eqP = dsolve(deqP, P(t)).subs(C1, P0)\n",
      "eqPO = dsolve(deqPO, PO(t)).subs(C1, P0)\n",
      "display(Eq(N(t)/B(t), simplify((eqP.rhs - eqPO.rhs)/eqP.rhs)))\n",
      "display(Eq(N(t)/O(t), simplify((eqP.rhs - eqPO.rhs)/eqPO.rhs)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{d}{d t} P{\\left (t \\right )} = \\left(- d - k_{dil} + \\lambda\\right) P{\\left (t \\right )}$$"
       ],
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAQsAAAArBAMAAACdoLDjAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nDMXwAAAAAElFTkSuQmCC\n",
       "text": [
        "d                               \n",
        "\u2500\u2500(P(t)) = (-d - k_dil + \u03bb)\u22c5P(t)\n",
        "dt                              "
       ]
      },
      {
       "latex": [
        "$$\\frac{d}{d t} \\operatorname{PO}{\\left (t \\right )} = \\left(- d - k_{dil}\\right) \\operatorname{PO}{\\left (t \\right )}$$"
       ],
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAQwAAAArBAMAAAB/fKuaAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nUZGLtLTbOGGoi7S02zhhqIu0tNsYYfwHsUVFG/ZahuUAAAAASUVORK5CYII=\n",
       "text": [
        "d                             \n",
        "\u2500\u2500(PO(t)) = (-d - k_dil)\u22c5PO(t)\n",
        "dt                            "
       ]
      },
      {
       "latex": [
        "$$\\frac{N{\\left (t \\right )}}{B{\\left (t \\right )}} = 1 - e^{- \\lambda t}$$"
       ],
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAJMAAAAyBAMAAACqi/RtAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n0OIGA+7oQv4CFsS/14j69rQAAAAASUVORK5CYII=\n",
       "text": [
        "N(t)        -\u03bb\u22c5t\n",
        "\u2500\u2500\u2500\u2500 = 1 - \u212f    \n",
        "B(t)            "
       ]
      },
      {
       "latex": [
        "$$\\frac{N{\\left (t \\right )}}{O{\\left (t \\right )}} = e^{\\lambda t} - 1$$"
       ],
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAIYAAAAyBAMAAABrDL7BAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nL/eBu+ruUtEEAAAAAElFTkSuQmCC\n",
       "text": [
        "N(t)    \u03bb\u22c5t    \n",
        "\u2500\u2500\u2500\u2500 = \u212f    - 1\n",
        "O(t)           "
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**Notes**\n",
      "Assuming that the protein production is in steady state in this system:\n",
      "\n",
      "- $\\lambda = k_{dil} + d = \\mu + d$\n",
      "- $\\to d = \\lambda - \\mu$ \n",
      "\n",
      "The difference $d$ between $\\lambda$ and $\\mu$ can be thought of as a *degradation* or *repair* rate and appears to be $\\ne 0$ for proteins at fast growth in chemostat (as of what we know now) as well as lipids in Gram-negative bacteria during slow growth."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Isotopic Mass Balance\n",
      "Given the isotopic composition of biomass generated before the spike ($F_O$) and new biomass generated after the spike ($F_N$), the isotopic composition of the total biomass $F(t)$ evolves as follows. This makes the following assumptions\n",
      "\n",
      "- all biomass *generated* before the spike has a uniform isotopic composition $F_O$ that is time-invariant\n",
      "- all biomass *generated* after the spike has a uniform isotopic composition $F_N$ that is time-invariant (i.e. the spike takes *immediate* effect on biosynthesis, there is no delay due to diffusion of the label, speed of biosynthesis or biological storage of old precursor material for biosynthesis such as carbon storage or amino acid pools)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "FB = Function('F')\n",
      "FO, FN = symbols(\"F_O F_N\")\n",
      "eqMB = Eq(FB(t) * eqB.rhs, eqO.rhs * FO + eqN.rhs * FN); display(eqMB)\n",
      "eqMB = Eq(FB(t), collect(expand(solve(eqMB, FB(t))[0]), FN)); display(eqMB)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$B_{0} F{\\left (t \\right )} e^{- k_{dil} t + \\mu t} = \\frac{B_{0} F_{O}}{e^{k_{dil} t}} + F_{N} \\left(B_{0} e^{- k_{dil} t + \\mu t} - \\frac{B_{0}}{e^{k_{dil} t}}\\right)$$"
       ],
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAf0AAAAyBAMAAACkKx9uAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nrkJggg==\n",
       "text": [
        "         -k_dil\u22c5t + \u03bc\u22c5t           -k_dil\u22c5t       \u239b    -k_dil\u22c5t + \u03bc\u22c5t       -k_\n",
        "B\u2080\u22c5F(t)\u22c5\u212f               = B\u2080\u22c5F_O\u22c5\u212f         + F_N\u22c5\u239dB\u2080\u22c5\u212f               - B\u2080\u22c5\u212f   \n",
        "\n",
        "dil\u22c5t\u239e\n",
        "     \u23a0"
       ]
      },
      {
       "latex": [
        "$$F{\\left (t \\right )} = F_{N} \\left(1 - e^{- \\mu t}\\right) + \\frac{F_{O}}{e^{\\mu t}}$$"
       ],
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAPsAAAAqBAMAAACHPjAfAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "text": [
        "           \u239b     -\u03bc\u22c5t\u239e        -\u03bc\u22c5t\n",
        "F(t) = F_N\u22c5\u239d1 - \u212f    \u23a0 + F_O\u22c5\u212f    "
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Sample calculations\n",
      "Let's see how this looks in practice for the evolution of the isotopic composition of a population that starts with isotopic composition $F_O = 1\\%$ (*e.g.* carbon natural abundance) and is spiked with $F_N=50\\%$ (and other isotopic compositions) at $t=0$. In addition to the assumptions outlined in the equation derivations above, we assume that\n",
      "\n",
      "- There is no isotopic fractionation in the biosynthetic pathways.\n",
      "- The spiked material is the only source of the element for the population.\n",
      "\n",
      "    *i.e.* everything the bugs make is of isotopic composition $F_N$\n",
      "    \n",
      "Note: I'm generating the labeling curve in python because I can convert the symbolically derived mass balanced equation `eqMB`  into a numeric function. Because I'm more used to plotting in R and don't feel like opening that can of worms in python, I'm using R magic to push everything over and plot there using `ggplot` (http://ggplot2.org/)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n = 500\n",
      "FOval = 0.01\n",
      "FNvals = [0.3, 0.5, 0.8]\n",
      "\n",
      "# easier to express time in multiples of doubling time #\n",
      "muval = 1 \n",
      "DBLT = ln(2)/muval; \n",
      "tmax = 4*DBLT\n",
      "\n",
      "# generate curve\n",
      "ts = np.linspace(float(0), float(tmax), n)\n",
      "fn = sym.lambdify((FO, FN, mu, t), eqMB.rhs, modules=['numpy'])\n",
      "res = []\n",
      "for FNval in FNvals:\n",
      "    res = np.concatenate([res, fn(FOval, FNval, muval, ts)], axis=0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%Rpush ts res n muval FNvals"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R -r 100 -w 1000 \n",
      "library(ggplot2)\n",
      "library(scales)\n",
      "library(grid)\n",
      "\n",
      "# data frame\n",
      "df <- data.frame(time=rep(ts*muval/log(2), times=length(FNvals)), value=res, FN=rep(paste0(100*FNvals, \"%\"), each=n))\n",
      "\n",
      "# base plot and variants\n",
      "p <- ggplot() + \n",
      "    geom_hline(data = data.frame(FN=FNvals, label=paste0(100*FNvals, \"%\")), aes(yintercept=FN, colour=label)) + # FN markers\n",
      "    geom_line(data=df, aes(x=time, y=value, colour=FN), size=2) + # modelled functions\n",
      "    scale_y_continuous(label=percent) +  # scale parameters y\n",
      "    labs(title=\"Isotopic composition as a function of time.\", y=expression(F(t)), x='number of doublings', color=expression(F[N])) + # axis labels\n",
      "    theme_bw() # theme\n",
      "p1 <- p + scale_x_continuous(expand=c(0,0)) \n",
      "p2 <- p + scale_x_continuous(expand=c(0,0), lim=c(0,1)) + labs(title=\"Closeup\")\n",
      "\n",
      "# grid\n",
      "grid.newpage()\n",
      "pushViewport(viewport(layout = grid.layout(1, 2)))\n",
      "print(p1, vp = viewport(layout.pos.row = 1, layout.pos.col = 1))\n",
      "print(p2, vp = viewport(layout.pos.row = 1, layout.pos.col = 2))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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1df80yNdgTQO4ylK460diol/s9cu4acLsM7XkPlMT6jO1w/ZHCu0gzPyS63v88cd9pgbZ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aX8trHAqB6eepb6QBHgLEILSSFfdHY51udsgc1Fqt/K47G1W4+C3iu+G8YksUI+EkNoHnmEReYn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\nRK5CYII=\n"
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Interactive visualization\n",
      "This is an interactive representation of the sample calculations using an `NVD3` chart (http://nvd3.org/). I quite like these charts for looking at data although admittedly in this case it's more for the fun of it than by necessity. I use `rCharts` (http://rcharts.io/) to generate the `d3.js` code because the package works great with R data frames and makes life easy by supporting several interactive javascript visualization tools (not just `NVD3`)."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**Load `rCharts` library**"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%R library(rCharts);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "*Overwrite `nPlot` with a modified `Nvd3` class to implement `y2Axis` parameters for `lineWithFocusChart` (not natively supported in `rCharts` at the moment.). NOTE: this code block is not necessary if using just `lineChart` instead of `lineWithFocusChart`. To look at the fragements, go to the gists at*\n",
      "\n",
      "- nPlot with y2Axis.R: https://gist.github.com/sebkopf/6955798\n",
      "- NVD3 template.html: https://gist.github.com/sebkopf/6955612"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Important: rawgithub.com downloads only work if the file name has no special characters!!!\n",
      "!curl 'http://rawgithub.com/sebkopf/6955612/raw/NVD3.template.html' > NVD3.html\n",
      "!curl 'http://rawgithub.com/sebkopf/6955798/raw/nPlot_with_y2Axis.R' > nPlot.R\n",
      "%R source('nPlot.R');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "  % Total    % Received % Xferd  Average Speed   Time    Time     Time  Current\r\n",
        "                                 Dload  Upload   Total   Spent    Left  Speed\r\n",
        "\r",
        "  0     0    0     0    0     0      0      0 --:--:-- --:--:-- --:--:--     0"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "100   966    0   966    0     0   1515      0 --:--:-- --:--:-- --:--:--  1697\r",
        "100   966    0   966    0     0   1515      0 --:--:-- --:--:-- --:--:--  1697\r\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "  % Total    % Received % Xferd  Average Speed   Time    Time     Time  Current\r\n",
        "                                 Dload  Upload   Total   Spent    Left  Speed\r\n",
        "\r",
        "  0     0    0     0    0     0      0      0 --:--:-- --:--:-- --:--:--     0"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "100  1463    0  1463    0     0   2969      0 --:--:-- --:--:-- --:--:--  2973\r",
        "100  1463    0  1463    0     0   2968      0 --:--:-- --:--:-- --:--:--  2973\r\n"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**Put together the `Nvd3` chart**"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "# define width and height of graph (will be pulled later by python to adjust size of iFrame)\n",
      "width <- 600\n",
      "height <- 400\n",
      "\n",
      "# make FN categories label more complete\n",
      "df$FNlong <- paste(\"FN =\", df$FN)\n",
      "\n",
      "# generate plot object\n",
      "n1 <- nPlot(value ~ time, group = \"FNlong\", data = df, type = 'lineWithFocusChart') # use lineChart instead for simpler plotting\n",
      "\n",
      "# width and height of chart\n",
      "n1$params$width <- width\n",
      "n1$params$height <- height\n",
      "\n",
      "# tick formats - simple utility function that generates js code for formatting axis ticks\n",
      "tickFormatter <- function(format) paste0(\"#!  function(y) { return d3.format('\", format, \"')(y) } !#\")\n",
      "\n",
      "# set axis labels and tick formats\n",
      "n1$yAxis(axisLabel=\"F(t)\", tickFormat = tickFormatter(\"01%\")) \n",
      "n1$xAxis(tickFormat = tickFormatter(\".2f\"))\n",
      "n1$y2Axis(axisLabel = \"F(t)\", tickFormat = tickFormatter(\"01%\"))\n",
      "n1$x2Axis(axisLabel=\"number of doublings\", tickFormat = tickFormatter(\"01f\"))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 24
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      " **Save chart to `filename` locally and to the gist with ID `gistID` on GitHub.**"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "# file name and gist ID\n",
      "filename <- \"isolabel.html\"\n",
      "gistID <- 6942741 # gistID = NULL # if NULL, will not save plot as a gist\n",
      "\n",
      "# save graph to file\n",
      "n1$save(destfile = filename, cdn = TRUE) # change to 'cdn = FALSE' if you want to run completely offline\n",
      "filepath <- file.path(getwd(), filename)\n",
      "message(paste(\"The graph was saved locally as\", filename))\n",
      "    \n",
      "# save file on GitHub in gist with gistID\n",
      "if (!is.null(gistID)) {\n",
      "    get_credentials() # ask for git username and password (only necessary once) / rChart function\n",
      "    token = get_token(getOption('github.username'), getOption('github.password')) # generate authentication token / rChart function\n",
      "    response = postForm(\n",
      "        uri = sprintf('https://api.github.com/gists/%s', gistID),\n",
      "        .opts = list(postFields = create_gist(filename, \"Isotope Labeling Computation\"), \n",
      "                     httpheader = c('Authorization' = paste('token', token)))) \n",
      "    #html_url = fromJSON(response[1])$html_url #FIXME: helps to get new gistID but doesn't work if updating to an existing gist\n",
      "    filepath <- file.path(\"http://rawgithub.com\", getOption('github.username'), gistID, \"raw\", filename)\n",
      "    message(paste(\"The graph was saved as a gist and can be viewed at\", filepath))\n",
      "}"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "The graph was saved locally as isolabel.html\n",
        "The graph was saved as a gist and can be viewed at http://rawgithub.com/sebkopf/6942741/raw/isolabel.html\n"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**Display interactive plot inline using an `iframe`.**\n",
      "\n",
      "This displays the graph either from local source or, if it was saved as a gist, from GitHub. The graph has the following features:\n",
      "\n",
      "- Hide/show different lines by clicking on the legend labels\n",
      "- Show point values by hovering at a point over a plot line for a second\n",
      "- Zoom in on specific parts of the graph by selecting the an xrange in the lower plot"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from IPython.display import HTML\n",
      "import time #used as a timestamp to avoid caching\n",
      "%Rpull width height filepath\n",
      "HTML(\"<iframe width=\" + str(width[0]+50) + \" height=\" + str(height[0]+50) + \" src='\" + filepath[0] + \"?v=\" + str(time.time()) + \"'></iframe>\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<iframe width=650.0 height=450.0 src='http://rawgithub.com/sebkopf/6942741/raw/isolabel.html?v=1382205371.48'></iframe>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 26,
       "text": [
        "<IPython.core.display.HTML at 0x10ab1be10>"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "EOF"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}