PMC:2654804 / 1771-4908 JSONTXT

{"project":"2_test","denotations":[{"id":"19176548-16605367-5601999","span":{"begin":579,"end":583},"obj":"16605367"},{"id":"19176548-16605367-5602000","span":{"begin":653,"end":657},"obj":"16605367"},{"id":"19176548-17350997-5602001","span":{"begin":706,"end":710},"obj":"17350997"},{"id":"19176548-17350997-5602002","span":{"begin":746,"end":750},"obj":"17350997"},{"id":"19176548-17441553-5602003","span":{"begin":792,"end":796},"obj":"17441553"},{"id":"19176548-17441553-5602004","span":{"begin":883,"end":887},"obj":"17441553"},{"id":"19176548-17441553-5602005","span":{"begin":931,"end":935},"obj":"17441553"},{"id":"19176548-14559783-5602006","span":{"begin":991,"end":995},"obj":"14559783"},{"id":"19176548-15513993-5602007","span":{"begin":1035,"end":1039},"obj":"15513993"},{"id":"19176548-14988125-5602008","span":{"begin":1150,"end":1154},"obj":"14988125"},{"id":"19176548-16960969-5602009","span":{"begin":1226,"end":1230},"obj":"16960969"},{"id":"19176548-17591176-5602010","span":{"begin":1312,"end":1316},"obj":"17591176"},{"id":"19176548-17591176-5602011","span":{"begin":1353,"end":1357},"obj":"17591176"},{"id":"19176548-17038344-5602012","span":{"begin":1397,"end":1401},"obj":"17038344"},{"id":"19176548-12651723-5602013","span":{"begin":1438,"end":1442},"obj":"12651723"},{"id":"19176548-8568860-5602014","span":{"begin":1486,"end":1490},"obj":"8568860"},{"id":"19176548-17441553-5602015","span":{"begin":1537,"end":1541},"obj":"17441553"},{"id":"19176548-17441553-5602016","span":{"begin":1586,"end":1590},"obj":"17441553"},{"id":"19176548-15514004-5602017","span":{"begin":1626,"end":1630},"obj":"15514004"},{"id":"19176548-16819798-5602018","span":{"begin":1672,"end":1676},"obj":"16819798"},{"id":"19176548-16585066-5602019","span":{"begin":1710,"end":1714},"obj":"16585066"},{"id":"19176548-15513993-5602020","span":{"begin":1796,"end":1800},"obj":"15513993"},{"id":"19176548-18321886-5602021","span":{"begin":1824,"end":1828},"obj":"18321886"},{"id":"19176548-11262963-5602022","span":{"begin":1874,"end":1878},"obj":"11262963"},{"id":"19176548-11262963-5602023","span":{"begin":1956,"end":1960},"obj":"11262963"},{"id":"19176548-15514004-5602024","span":{"begin":2001,"end":2005},"obj":"15514004"},{"id":"19176548-18321886-5602025","span":{"begin":2043,"end":2047},"obj":"18321886"},{"id":"19176548-16605367-5602026","span":{"begin":2084,"end":2088},"obj":"16605367"},{"id":"19176548-18321886-5602027","span":{"begin":2186,"end":2190},"obj":"18321886"},{"id":"19176548-16585066-5602028","span":{"begin":2304,"end":2308},"obj":"16585066"},{"id":"19176548-12145321-5602029","span":{"begin":2360,"end":2364},"obj":"12145321"},{"id":"19176548-17038344-5602030","span":{"begin":2428,"end":2432},"obj":"17038344"},{"id":"19176548-16491024-5602031","span":{"begin":2476,"end":2480},"obj":"16491024"},{"id":"19176548-16819798-5602032","span":{"begin":2545,"end":2549},"obj":"16819798"},{"id":"19176548-15608262-5602033","span":{"begin":2584,"end":2588},"obj":"15608262"}],"text":"We consider the problem of identifying both the structure and the parameters of an ordinary differential equation (ODE) system from time series data. In recent years, there has been a significant increase in the number of reported methods approaching this problem in the biological literature (see Table 1 and the references).\nTable 1. Benchmark problems for ODE system identification\nProblem name Original problem reference Source system/Model #var #exp #pts Noise (%)\nsimpleLin1 Simple linear system 3 3 13 0\nsimpleLin2 8 13 10\nsimpleFb1 Simple feedback loop (McKinney et al., 2006) 3 4 7 0\nsimpleFb2 4 7 5\nsimpleFb3 1 7 0\nsimpleFb4 (McKinney et al., 2006) 1 7 ≈5a\nosc1 An oscillator (Karnaukhov et al., 2007) 3 1 41 0\nosc2 (Karnaukhov et al., 2007) 1 41 3\nmetabol1 (Gennemark and Wedelin, 2007) A metabolic pathway (Arkin and Ross, 1995) 5 12 7 0\nmetabol2 (Gennemark and Wedelin, 2007) 12 21 10\nmetabol3 (Gennemark and Wedelin, 2007) 12 21 20\n3genes1 A 3-step gene network (Moles et al., 2003) 8 16 21 0\nss_cascade1 (Tsai and Wang, 2005) A cascaded pathway (Voit, 2000) 3 8 41 0\nss_cascade2 4 41 0\nss_cascade3 8 41 5\nss_branch1 (Voit and Almeida, 2004) A branched pathway (Voit, 2000) 4 3 21 0\nss_branch2 (Marino and Voit, 2006) 6 51 0\nss_branch3 (Tucker and Moulton, 2006) 5 20 0\nss_branch4 (Kutalik et al., 2007) 4 20 0\nss_branch5 (Kutalik et al., 2007) 4 20 2.5\nss_branch6 (Gonzalez et al., 2007) 5 31 0\nss_5genes1 (Kikuchi et al., 2003) A genetic network (Hlavacek and Savageau, 1996) 5 10 11 0\nss_5genes2 (Gennemark and Wedelin, 2007) 10 9 20\nss_5genes3 (Gennemark and Wedelin, 2007) 10 3 0\nss_5genes4 (Kimura et al., 2005) 15 11 0\nss_5genes5 (Daisuke and Horton, 2006) 10 11 0\nss_5genes6 (Cho et al., 2006) 1 16 0\nss_5genes7 (Tucker and Moulton, 2006) 10 20 0\nss_5genes8 (Tsai and Wang, 2005) 8 41 0\n(Liu and Wang, 2008)\nss_15genes1 A genetic network (Maki et al., 2001) 15 10 11 0\nss_15genes2 20 11 10\nss_30genes1 A genetic network (Maki et al., 2001) 30 15 11 0\nss_30genes2 (Kimura et al., 2005) 20 11 10\nss_30genes3 (Liu and Wang, 2008) 8 41 0\ncytokine1 (McKinney et al., 2006) Immunologic data (Rock et al., 2004) 4 1 7 10a\ncytokine2 1 7 10a\nss_ethanolferm1 (Liu and Wang, 2008) Ethanol fermentation (Wang et al., 2001) 4 2 11–15 ≈30a\nss_ethanolferm2 3 11–19 ≈30a\nss_sosrepair1 (Cho et al., 2006) SOS repair system Escherichia coli (Ronen et al., 2002) 6 1 50 10a\nss_sosrepair2 1 50 10a\nss_cadBA1 (Gonzalez et al., 2007) cadBA network in E. coli (Kuper and Jung, 2005) 5 1 25 \u003c20a\nss_cadBA2 1 25 \u003c20a\nss_clock1 (Daisuke and Horton, 2006) Mice cell cycle (Barrett et al., 2005) 7 1 12 ≈10a\nss_clock2 1 12 ≈10a\naEstimate from or assumption about data. See web site for further information.\n#var, number of dependent variables; #exp, number of experimental conditions with different initial conditions and/or input functions; #pts, number of data-points per time series.\nNoise is added from a Gaussian distribution with SD given as a certain percentage (denoted Noise) of each experimental value. Problem names starting with ‘ss_’ correspond to S-systems. The last section lists problems with real data from biological systems."}