Given an amino acid string Peptide, we will begin by assuming that it represents a linear peptide. Our approach to generating its theoretical spectrum is based on the assumption that the mass of any subpeptide is equal to the difference between the masses of two prefixes of Peptide. We can compute an array PrefixMass storing the masses of each prefix of Peptide in increasing order, e.g., for Peptide = "NQEL", PrefixMass = (0, 114, 242, 371, 484).
Then, the mass of the subpeptide of Peptide beginning at position i + 1 and ending at position j can be computed as PrefixMass(j) − PrefixMass(i). For example, when Peptide = "NQEL",
Mass(QE) = PrefixMass(3) − PrefixMass(1) = 371 − 114 = 257.
Write a Python function linearspectrum that generates the ideal linear spectrum of a peptide. It takes as parameter an amino acid string and returns a list of masses in the linear spectrum, in increasing order.
>>> linearspectrum("NQEL")
[0, 113, 114, 128, 129, 242, 242, 257, 370, 371, 484]
>>> linearspectrum("MPYENCCCWMFNIRKGQPDFFRKGAVPYVVPMNCIRWS")
[0, 57, 57, 71, 87, 97, 97, 97, 97, 99, 99, 99, 103, 103, 103, 103, 113, 113, 114, 114, 114, 115, 128, 128, 128, 128, 129, 131, 131, 131, 147, 147, 147, 156, 156, 156, 163, 163, 170, 185, 185, 185, 186, 186, 196, 196, 198, 206, 206, 212, 216, 217, 217, 225, 227, 227, 228, 228, 243, 245, 256, 260, 260, 261, 262, 262, 267, 269, 269, 273, 278, 282, 284, 284, 289, 292, 294, 295, 303, 309, 313, 317, 320, 324, 327, 330, 340, 341, 341, 342, 342, 346, 348, 355, 359, 359, 359, 361, 372, 374, 383, 389, 391, 392, 392, 397, 397, 406, 409, 410, 412, 420, 423, 426, 429, 430, 431, 441, 445, 449, 450, 452, 454, 455, 458, 458, 458, 461, 464, 469, 486, 487, 487, 488, 495, 503, 505, 506, 509, 511, 511, 520, 523, 525, 529, 530, 540, 542, 544, 544, 552, 555, 557, 558, 558, 559, 565, 566, 567, 568, 578, 578, 582, 586, 589, 606, 608, 609, 612, 615, 617, 626, 628, 634, 634, 635, 643, 645, 654, 657, 658, 658, 661, 662, 670, 672, 672, 679, 681, 681, 685, 686, 691, 691, 693, 696, 703, 706, 709, 714, 714, 715, 715, 725, 737, 738, 740, 750, 755, 756, 759, 771, 773, 782, 784, 785, 789, 790, 790, 793, 794, 794, 800, 803, 805, 806, 812, 813, 813, 819, 821, 828, 840, 843, 846, 847, 847, 847, 856, 869, 870, 887, 887, 890, 897, 899, 900, 901, 902, 903, 908, 910, 912, 913, 918, 918, 918, 919, 920, 940, 941, 943, 950, 969, 970, 974, 975, 975, 975, 975, 975, 987, 998, 999, 1000, 1001, 1002, 1016, 1016, 1017, 1017, 1017, 1027, 1032, 1032, 1032, 1041, 1046, 1053, 1055, 1055, 1065, 1066, 1071, 1073, 1075, 1078, 1086, 1088, 1098, 1103, 1103, 1114, 1114, 1115, 1116, 1129, 1129, 1130, 1130, 1131, 1135, 1145, 1155, 1156, 1160, 1160, 1164, 1172, 1179, 1180, 1181, 1185, 1186, 1186, 1197, 1202, 1202, 1202, 1213, 1231, 1238, 1242, 1243, 1243, 1244, 1257, 1258, 1259, 1260, 1261, 1263, 1263, 1270, 1271, 1276, 1277, 1279, 1284, 1293, 1299, 1311, 1316, 1330, 1333, 1341, 1342, 1344, 1348, 1349, 1358, 1358, 1360, 1360, 1366, 1371, 1372, 1372, 1376, 1378, 1387, 1390, 1398, 1399, 1399, 1405, 1406, 1407, 1414, 1427, 1429, 1445, 1455, 1457, 1458, 1462, 1463, 1469, 1475, 1475, 1475, 1480, 1486, 1486, 1491, 1500, 1503, 1504, 1505, 1519, 1521, 1527, 1527, 1527, 1528, 1543, 1544, 1561, 1561, 1562, 1566, 1572, 1578, 1583, 1583, 1584, 1585, 1590, 1599, 1603, 1605, 1606, 1614, 1615, 1622, 1633, 1634, 1636, 1659, 1660, 1666, 1672, 1674, 1680, 1681, 1683, 1689, 1690, 1690, 1696, 1700, 1703, 1708, 1712, 1713, 1713, 1720, 1725, 1746, 1747, 1757, 1761, 1764, 1769, 1787, 1788, 1790, 1795, 1800, 1809, 1810, 1817, 1821, 1821, 1822, 1823, 1828, 1830, 1831, 1844, 1845, 1859, 1860, 1869, 1872, 1875, 1885, 1888, 1892, 1918, 1920, 1924, 1925, 1936, 1942, 1944, 1945, 1950, 1956, 1957, 1958, 1972, 1972, 1973, 1975, 1975, 1977, 1991, 2002, 2007, 2016, 2016, 2028, 2033, 2041, 2048, 2053, 2057, 2069, 2071, 2072, 2078, 2087, 2088, 2089, 2092, 2103, 2103, 2105, 2110, 2120, 2130, 2131, 2154, 2156, 2161, 2163, 2171, 2172, 2177, 2181, 2184, 2189, 2200, 2213, 2218, 2218, 2219, 2233, 2234, 2245, 2250, 2251, 2259, 2268, 2274, 2278, 2280, 2284, 2285, 2286, 2315, 2316, 2317, 2318, 2331, 2346, 2350, 2365, 2373, 2374, 2374, 2375, 2377, 2381, 2383, 2387, 2389, 2399, 2399, 2415, 2430, 2437, 2449, 2462, 2462, 2478, 2480, 2486, 2501, 2502, 2502, 2502, 2502, 2503, 2513, 2536, 2537, 2540, 2546, 2546, 2559, 2560, 2583, 2590, 2600, 2609, 2615, 2616, 2630, 2634, 2635, 2639, 2643, 2647, 2658, 2660, 2665, 2677, 2688, 2697, 2722, 2729, 2729, 2732, 2738, 2742, 2746, 2762, 2763, 2765, 2771, 2775, 2791, 2793, 2819, 2826, 2835, 2841, 2844, 2845, 2860, 2863, 2876, 2885, 2890, 2892, 2893, 2894, 2931, 2938, 2944, 2950, 2957, 2959, 2966, 2977, 2989, 2989, 2989, 3007, 3021, 3032, 3041, 3044, 3058, 3069, 3071, 3080, 3080, 3086, 3088, 3120, 3152, 3155, 3158, 3163, 3172, 3183, 3183, 3187, 3193, 3217, 3218, 3249, 3251, 3284, 3286, 3286, 3286, 3296, 3305, 3348, 3349, 3349, 3350, 3380, 3389, 3399, 3400, 3415, 3436, 3447, 3447, 3452, 3479, 3502, 3503, 3529, 3535, 3544, 3555, 3578, 3578, 3616, 3622, 3632, 3638, 3658, 3675, 3675, 3692, 3725, 3741, 3745, 3772, 3789, 3795, 3806, 3828, 3844, 3892, 3901, 3908, 3920, 3931, 3958, 4005, 4023, 4045, 4064, 4087, 4136, 4161, 4174, 4250, 4292, 4337, 4347, 4434, 4478, 4565]