[en] Abrupt shifts between alternative regimes occur in complex systems, from cell regulation to brain functions to ecosystems. Several model-free early warning signals (EWS) have been proposed to detect impending transitions, but failure or poor performance in some systems have called for better investigation of their generic applicability. Notably, there are still ongoing debates whether such signals can be successfully extracted from data in particular from biological experiments. In this work, we systematically investigate properties and performance of dynamical EWS in different deteriorating conditions, and we propose an optimized combination to trigger warnings as early as possible, eventually verified on experimental data from microbiological populations. Our results explain discrepancies observed in the literature between warning signs extracted from simulated models and from real data, provide guidance for EWS selection based on desired systems and suggest an optimized composite indicator to alert for impending critical transitions using distribution data.
Disciplines :
Sciences du vivant: Multidisciplinaire, généralités & autres
Auteur, co-auteur :
PROVERBIO, Daniele ; University of Luxembourg > Luxembourg Centre for Systems Biomedicine > Imaging AI > Team Andreas HUSCH ; College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QL, UK
SKUPIN, Alexander ; University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB) > Integrative Cell Signalling ; National Center for Microscopy and Imaging Research, University of California San Diego, Gilman Drive, La Jolla, CA 9500, USA
GONCALVES, Jorge ; University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB) > Systems Control ; Department of Plant Sciences, University of Cambridge, Cambridge CB2 3EA, UK
Co-auteurs externes :
no
Langue du document :
Anglais
Titre :
Systematic analysis and optimization of early warning signals for critical transitions using distribution data.
The authors would thank their colleagues for valuable discussions. D.P.’s work is supported by the FNR PRIDE DTU CriTiCS , ref. 10907093 , and A.S. by the FNR ( C14/BM/7975668/CaSCAD ) and by the NIH NBCR ( NIH P41 GM103426 ).
Scheffer, M., Bascompte, J., Brock, W.A., Brovkin, V., Carpenter, S.R., Dakos, V., Held, H., Van Nes, E.H., Rietkerk, M., Sugihara, G., Early-warning signals for critical transitions. Nature 461 (2009), 53–59, 10.1038/nature08227.
Ashwin, P., Zaikin, A., Pattern selection: The importance of ”how you get there”. Biophys. J. 108 (2015), 1307–1308, 10.1016/j.bpj.2015.01.036.
Hirota, M., Holmgren, M., Van Nes, E.H., Scheffer, M., Global Resilience of Tropical Forest. Science 334 (2011), 232–235, 10.1126/science.1210657.
Wang, R., Dearing, J.A., Langdon, P.G., Zhang, E., Yang, X., Dakos, V., Scheffer, M., Flickering gives early warning signals of a critical transition to a eutrophic lake state. Nature 492 (2012), 419–422, 10.1038/nature11655.
Lenton, T.M., Livina, V.N., Dakos, V., Van Nes, E.H., Scheffer, M., Early warning of climate tipping points from critical slowing down: comparing methods to improve robustness. Philos. T. R. Soc. A 370 (2012), 1185–1204, 10.1098/rsta.2011.0304.
Drijfhout, S., Bathiany, S., Beaulieu, C., Brovkin, V., Claussen, M., Huntingford, C., Scheffer, M., Sgubin, G., Swingedouw, D., Catalogue of abrupt shifts in Intergovernmental Panel on Climate Change climate models. P. Natl. Acad. Sci. USA 112 (2015), E5777–E5786, 10.1073/pnas.1511451112.
Dmitriev, A., Dmitriev, V., Sagaydak, O., Tsukanova, O., The Application of Stochastic Bifurcation Theory to the Early Detection of Economic Bubbles. Procedia Comput. Sci. 122 (2017), 354–361, 10.1016/j.procs.2017.11.380.
Diks, C., Hommes, C., Wang, J., Critical slowing down as an early warning signal for financial crises?. Empir. Econ. 57 (2019), 1201–1228, 10.1007/s00181-018-1527-3.
Korolev, K.S., Xavier, J.B., Gore, J., Turning ecology and evolution against cancer. Nat. Rev. Cancer 14 (2014), 371–380, 10.1038/nrc3712.
Trefois, C., Antony, P.M.A., Goncalves, J., Skupin, A., Balling, R., Critical transitions in chronic disease: Transferring concepts from ecology to systems medicine. Curr. Opin. Biotechnol. 34 (2015), 48–55, 10.1016/j.copbio.2014.11.020.
Aihara, K., Liu, R., Koizumi, K., Liu, X., Chen, L., Dynamical network biomarkers: Theory and applications. Gene, 808, 2022, 145997, 10.1016/j.gene.2021.145997.
Quail, T., Shrier, A., Glass, L., Predicting the onset of period-doubling bifurcations in noisy cardiac systems. P. Natl. Acad. Sci. USA 112 (2015), 9358–9363, 10.1073/pnas.1424320112.
Meisel, C., Kuehn, C., Scaling effects and spatio-temporal multilevel dynamics in epileptic seizures. PLoS One, 7, 2012, e30371, 10.1371/journal.pone.0030371.
Angeli, D., Ferrell, J.E., Sontag, E.D., Detection of multistability, bifurcations, and hysteresis in a large class of biological positive-feedback systems. P. Nat. Acad. Sci. USA 101 (2004), 1822–1827, 10.1016/j.sysconle.2003.08.003.
Sharma, Y., Dutta, P.S., Gupta, A.K., Anticipating regime shifts in gene expression: The case of an autoactivating positive feedback loop. Phys. Rev. E 93 (2016), 032404–032413, 10.1103/PhysRevE.93.032404.
Ghaffarizadeh, A., Flann, N.S., Podgorski, G.J., Multistable switches and their role in cellular differentiation networks. BMC Bioinf. 15 (2014), S7–S13, 10.1186/1471-2105-15-S7-S7.
Mojtahedi, M., Skupin, A., Zhou, J., Castaño, I.G., Leong-Quong, R.Y.Y., Chang, H., Trachana, K., Giuliani, A., Huang, S., Cell Fate Decision as High-Dimensional Critical State Transition. PLoS Biol. 14 (2016), 20006400–e2000728, 10.1371/journal.pbio.2000640.
Lang, J., Nie, Q., Li, C., Landscape and kinetic path quantify critical transitions in epithelial-mesenchymal transition. Biophys. J. 120 (2021), 4484–4500, 10.1016/j.bpj.2021.08.043.
Kuehn, C., A mathematical framework for critical transitions: Bifurcations, fast–slow systems and stochastic dynamics. Physica D 240 (2011), 1020–1035, 10.1016/j.physd.2011.02.012.
Drake, J.M., Griffen, B.D., Early warning signals of extinction in deteriorating environments. Nature 467 (2010), 456–459, 10.1038/nature09389.
Lade, S.J., Gross, T., Early warning signals for critical transitions: a generalized modeling approach. PLoS Comput. Biol., 8, 2012, e1002360, 10.1371/journal.pcbi.1002360.
Chen, L., Liu, R., Liu, Z.P., Li, M., Aihara, K., Detecting early-warning signals for sudden deterioration of complex diseases by dynamical network biomarkers. Sci. Rep. 2 (2012), 342–420, 10.1038/srep00342.
Navid Moghadam, N., Nazarimehr, F., Jafari, S., Sprott, J.C., Studying the performance of critical slowing down indicators in a biological system with a period-doubling route to chaos. Physica A, 544, 2020, 123396, 10.1016/j.physa.2019.123396.
Matsumori, T., Sakai, H., Aihara, K., Early-warning signals using dynamical network markers selected by covariance. Phys. Rev. E 100 (2019), 052303–052309, 10.1103/PhysRevE.100.052303.
Carpenter, S.R., Cole, J.J., Pace, M.L., Batt, R., Brock, W.A., Cline, T., Coloso, J., Hodgson, J.R., Kitchell, J.F., Seekell, D.A., et al. Early warnings of regime shifts: A whole-ecosystem experiment. Science 332 (2011), 1079–1082, 10.1126/science.1203672.
Dai, L., Vorselen, D., Korolev, K.S., Gore, J., Generic indicators for loss of resilience before a tipping point leading to population collapse. Science 336 (2012), 1175–1177, 10.1126/science.1219805.
Wilkat, T., Rings, T., Lehnertz, K., No evidence for critical slowing down prior to human epileptic seizures. Chaos 29 (2019), 091104–091107, 10.1063/1.5122759.
Proverbio, D., Kemp, F., Magni, S., Gonçalves, J., Performance of early warning signals for disease re-emergence: A case study on COVID-19 data. PLoS Comput. Biol., 18, 2022, e1009958, 10.1371/journal.pcbi.1009958.
Boettiger, C., Hastings, A., Quantifying limits to detection of early warning for critical transitions. J. R. Soc. Interface 9 (2012), 2527–2539, 10.1098/rsif.2012.0125.
Clements, C.F., Ozgul, A., Indicators of transitions in biological systems. Ecol. Lett. 21 (2018), 905–919, 10.1111/ele.12948.
Dudney, J., Suding, K.N., The elusive search for tipping points. Nat. Ecol. Evol. 4 (2020), 1449–1450, 10.1038/s41559-020-1273-8.
Kuehn, C., Lux, K., Neamtu, A., Warning Signs for Non-Markovian Bifurcations: Color Blindness and Scaling Laws. P. Roy. Soc. A, 478, 2022, 20210740, 10.1098/rspa.2021.0740.
Cohen, A.A., Leung, D.L., Legault, V., Gravel, D., Blanchet, F.G., Côté, A.M., Fülöp, T., Lee, J., Dufour, F., Liu, M., Nakazato, Y., Synchrony of biomarker variability indicates a critical transition: Application to mortality prediction in hemodialysis. iScience, 25, 2022, 104385, 10.1016/j.isci.2022.104385.
Mazzocchi, F., Complexity and the reductionism–holism debate in systems biology. Wires Syst. Biol. Med. 4 (2012), 413–427, 10.1002/wsbm.1181.
Stumpf, P.S., Smith, R.C.G., Lenz, M., Schuppert, A., Müller, F.J., Babtie, A., Chan, T.E., Stumpf, M.P.H., Please, C.P., Howison, S.D., et al. Stem cell differentiation as a non-markov stochastic process. Cell Syst. 5 (2017), 268–282.e7, 10.1016/j.cels.2017.08.009.
Ferrell, J.E. Jr., Pomerening, J.R., Kim, S.Y., Trunnell, N.B., Xiong, W., Huang, C.-Y.F., Machleder, E.M., Simple, realistic models of complex biological processes: positive feedback and bistability in a cell fate switch and a cell cycle oscillator. FEBS Lett. 583 (2009), 3999–4005, 10.1016/j.febslet.2009.10.068.
Moris, N., Pina, C., Arias, A.M., Transition states and cell fate decisions in epigenetic landscapes. Nat. Rev. Genet. 17 (2016), 693–703, 10.1038/nrg.2016.98.
Maini, P.K., Myerscough, M.R., Winters, K.H., Murray, J.D., Bifurcating spatially heterogeneous solutions in a chemotaxis model for biological pattern generation. Bull. Math. Biol. 53 (1991), 701–719, 10.1007/BF02461550.
Yasemi, M., Jolicoeur, M., Modelling cell metabolism: a review on constraint-based steady-state and kinetic approaches. Processes, 9, 2021, 322, 10.3390/pr9020322.
Del Vecchio, D., Dy, A.J., Qian, Y., Control theory meets synthetic biology. J. R. Soc. Interface, 13, 2016, 20160380, 10.1098/rsif.2016.0380.
MacArthur, B.D., Ma'ayan, A., Lemischka, I.R., Systems biology of stem cell fate and cellular reprogramming. Nat. Rev. Mol. Cell Biol. 10 (2009), 672–681, 10.1038/nrm2766.
Kuznetsov, Y.A., Elements of Applied Bifurcation Theory, 112, 2013, Springer Science and Business Media, 10.1007/b98848.
Kuehn, C., Bick, C., A universal route to explosive phenomena. Sci. Adv., 7, 2021, 10.1126/sciadv.abe3824 eabe3824–7.
Su, Y., Bintz, M., Yang, Y., Robert, L., Ng, A.H.C., Liu, V., Ribas, A., Heath, J.R., Wei, W., Phenotypic heterogeneity and evolution of melanoma cells associated with targeted therapy resistance. PLoS Comput. Biol., 15, 2019, e1007034, 10.1371/journal.pcbi.1007034.
Zhang, H., Chen, Y., Chen, Y., Noise Propagation in Gene Regulation Networks Involving Interlinked Positive and Negative Feedback Loops. PLoS One 7 (2012), e51840–e51848, 10.1371/journal.pone.0051840.
Berglund, N., Gentz, B., Noise-induced Phenomena in Slow-Fast Dynamical Systems: A Sample-Paths Approach, 2006, Springer Science and Business Media, 10.1007/1-84628-186-5.
Thompson, J.M.T., Sieber, J., Predicting climate tipping as a noisy bifurcation: a review. Int. J. Bifurcation Chaos 21 (2011), 399–423, 10.1142/S0218127411028519.
Ashwin, P., Wieczorek, S., Vitolo, R., Cox, P., Tipping points in open systems: bifurcation, noise-induced and rate-dependent examples in the climate system. Phil. Trans. Roy. Soc. A 370 (2012), 1166–1184, 10.1098/rsta.2011.0306.
Shi, J., Li, T., Chen, L., Towards a critical transition theory under different temporal scales and noise strengths. Phys. Rev. E 93 (2016), 032137–32213, 10.1103/PhysRevE.93.032137.
Ozbudak, E.M., Thattai, M., Lim, H.N., Shraiman, B.I., Van Oudenaarden, A., Multistability in the lactose utilization network of Escherichia coli. Nature 427 (2004), 737–740, 10.1038/nature02298.
Dai, L., Korolev, K.S., Gore, J., Carpenter, S.R., Relation between stability and resilience determines the performance of early warning signals under different environmental drivers. P. Natl. Acad. Sci. USA 112 (2015), 10056–10061, 10.1073/pnas.1418415112.
Sarkar, S., Sinha, S.K., Levine, H., Jolly, M.K., Dutta, P.S., Anticipating critical transitions in epithelial-hybrid-mesenchymal cell-fate determination. P. Natl. Acad. Sci. USA 116 (2019), 26343–26352, 10.1073/pnas.1913773116.
Izhikevich, E.M., Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting. 2007, MIT press, 10.7551/mitpress/2526.001.0001.
Sornette, D., Critical Phenomena in Natural Sciences. 2006, Springer Science and Business Media, 10.1017/CBO9781107415324.004.
Antoniou, D., Schwartz, S.D., Protein dynamics and enzymatic chemical barrier passage. J. Phys. Chem. B 115 (2011), 15147–15158, 10.1021/jp207876k.
Horsthemke, W., Lefever, R., Noise-Induced Transitions in Physics, Chemistry, and Biology, 1984, Springer Science & Business Media, 10.1007/3-540-36852-3_7.
Wieczorek, S., Ashwin, P., Luke, C.M., Cox, P.M., Excitability in ramped systems: The compost-bomb instability. Proc. R. Soc. A 467 (2011), 1243–1269, 10.1098/rspa.2010.0485.
Bonciolini, G., Ebi, D., Boujo, E., Noiray, N., Experiments and modelling of rate-dependent transition delay in a stochastic subcritical bifurcation. R. Soc. Open Sci., 5, 2018, 172078, 10.1098/rsos.172078.
Moejes, F.W., Matuszyńska, A., Adhikari, K., Bassi, R., Cariti, F., Cogne, G., Dikaios, I., Falciatore, A., Finazzi, G., Flori, S., et al. A systems-wide understanding of photosynthetic acclimation in algae and higher plants. J. Exp. Bot. 68 (2017), 2667–2681, 10.1093/jxb/erx137.
Zhou, J.X., Aliyu, M.D.S., Aurell, E., Huang, S., Quasi-potential landscape in complex multi-stable systems. J. R. Soc. Interface 9 (2012), 3539–3553, 10.1098/rsif.2012.0434.
Andrecut, M., Halley, J.D., Winkler, D.A., Huang, S., A general model for binary cell fate decision gene circuits with degeneracy: Indeterminacy and switch behavior in the absence of cooperativity. PLoS One, 6, 2011, e19358, 10.1371/journal.pone.0019358.
Stanoev, A., Schröter, C., Koseska, A., Robustness and timing of cellular differentiation through population-based symmetry breaking. Development, 148, 2021, dev197608, 10.1242/dev.197608.
Wang, J., Zhang, K., Xu, L., Wang, E., Quantifying the Waddington landscape and biological paths for development and differentiation. P. Nat. Acad. Sci. USA 108 (2011), 8257–8262, 10.1073/pnas.1017017108.
Alon, U., An Introduction to Systems Biology: Design Principles of Biological Circuits. 2006, CRC press, 10.1201/9781420011432.
O'Regan, S.M., Burton, D.L., How stochasticity influences leading indicators of critical transitions. Bull. Math. Biol. 80 (2018), 1630–1654, 10.1007/s11538-018-0429-z.
Liu, X.M., Xie, H.Z., Liu, L.G., Li, Z.B., Effect of multiplicative and additive noise on genetic transcriptional regulatory mechanism. Physica A 388 (2009), 392–398, 10.1016/j.physa.2008.10.030.
Sidney, R.C., Dunlop, M., Elowitz, M.B., A synthetic three-color reporter framework for monitoring genetic regulation and noise. J. Biol. Eng. 4 (2010), 1–12, 10.1186/1754-1611-4-10.
Wang, X., Li, L., Cheng, Y., Liu, Q., Construction of gene regulatory networks with colored noise. Neural Comput. Appl. 21 (2012), 1883–1891, 10.1007/s00521-011-0584-8.
Boettiger, C., From noise to knowledge: how randomness generates novel phenomena and reveals information. Ecol. Lett. 21 (2018), 1255–1267, 10.1111/ele.13085.
Gillespie, D.T., Chemical Langevin equation. J. Chem. Phys. 113 (2000), 297–306, 10.1063/1.481811.
Allen, L.J.S., An Introduction to Stochastic Processes with Applications to Biology. 2010, CRC press, 10.1201/b12537.
Van Kampen, N.G., Stochastic Processes in Physics and Chemistry, volume 1, 1992, Elsevier, 10.1016/B978-0-444-52965-7.X5000-4.
Hasty, J., Pradines, J., Dolnik, M., Collins, J.J., Noise-based switches and amplifiers forgene expression. P. Natl. Acad. Sci. USA 97 (2000), 2075–2080, 10.1073/pnas.040411297.
Holling, C.S., Engineering resilience versus ecological resilience. Engineering within ecological constraints, 31, 1996, 32, 10.17226/4919.
Bury, T.M., Bauch, C.T., Anand, M., Detecting and distinguishing tipping points using spectral early warning signals. J. R. Soc. Interface, 17, 2020, 20200482, 10.1098/rsif.2020.0482.
Guttal, V., Jayaprakash, C., Changing skewness: An early warning signal of regime shifts in ecosystems. Ecol. Lett. 11 (2008), 450–460, 10.1111/j.1461-0248.2008.01160.x.
Kéfi, S., Dakos, V., Scheffer, M., Van Nes, E.H., Rietkerk, M., Early warning signals also precede non-catastrophic transitions. Oikos 122 (2013), 641–648, 10.1111/j.1600-0706.2012.20838.x.
Boettiger, C., Ross, N., Hastings, A., Early warning signals: The charted and uncharted territories. Theor. Ecol. 6 (2013), 255–264, 10.1007/s12080-013-0192-6.
Dakos, V., Carpenter, S.R., van Nes, E.H., Scheffer, M., Resilience indicators: Prospects and limitations for early warnings of regime shifts. Phil. Trans. R. Soc. B. 370 (2015), 20130263–20130310, 10.1098/rstb.2013.0263.
Pavithran, I., Sujith, R.I., Effect of rate of change of parameter on early warning signals for critical transitions. Chaos, 31, 2021, 013116, 10.1063/5.0025533.
Brett, T.S., Drake, J.M., Rohani, P., Anticipating the emergence of infectious diseases. J. R. Soc. Interface, 14, 2017, 20170115, 10.1098/rsif.2017.0115.
Feng, S., Sáez, M., Wiuf, C., Feliu, E., Soyer, O.S., Core signalling motif displaying multistability through multi-state enzymes. J. R. Soc. Interface, 13, 2016, 20160524, 10.1098/rsif.2016.0524.
Weber, M., Buceta, J., Stochastic stabilization of phenotypic states: the genetic bistable switch as a case study. PLoS One, 8, 2013, e73487, 10.1371/journal.pone.0073487.
Strogatz, S.H., Nonlinear Dynamics and Chaos. 2015, CRC press, 10.1201/9780429492563.
Proverbio, D., Montanari, A.N., Skupin, A., Gonçalves, J., Buffering variability in cell regulation motifs close to criticality. Phys. Rev. E, 106, 2022, L032402, 10.1103/PhysRevE.106.L032402.
Rosso, O.A., Larrondo, H.A., Martin, M.T., Plastino, A., Fuentes, M.A., Distinguishing noise from chaos. Phys. Rev. Lett. 99 (2007), 154102–154104, 10.1103/PhysRevLett.99.154102.
Marco, E., Karp, R.L., Guo, G., Robson, P., Hart, A.H., Trippa, L., Yuan, G.C., Bifurcation analysis of single-cell gene expression data reveals epigenetic landscape. P. Natl. Acad. Sci. USA 111 (2014), E5643–E5650, 10.1073/pnas.1408993111.
Clements, C.F., Ozgul, A., Including trait-based early warning signals helps predict population collapse. Nat. Commun., 7, 2016, 10984, 10.1038/ncomms10984.
Bury, T.M., Sujith, R.I., Pavithran, I., Scheffer, M., Lenton, T.M., Anand, M., Bauch, C.T., Deep learning for early warning signals of tipping points. P. Natl. Acad. Sci. USA, 118, 2021, e2106140118, 10.1073/pnas.2106140118.
Laurence, E., Doyon, N., Dubé, L.J., Desrosiers, P., Spectral Dimension Reduction of Complex Dynamical Networks. Phys. Rev. X 9 (2019), 1–17, 10.1103/PhysRevX.9.011042.
Heino, M.T.J., Proverbio, D., Marchand, G., Resnicow, K., Hankonen, N., Attractor landscapes: A unifying conceptual model for understanding behaviour change across scales of observation. Health Psychol. Rev., 2022, 1–18, 10.1080/17437199.2022.2146598.
Weinans, E., Quax, R., van Nes, E.H., Leemput, I.A.v.d., Evaluating the performance of multivariate indicators of resilience loss. Sci. Rep. 11 (2021), 9148–9211, 10.1038/s41598-021-87839-y.
Dakos, V., Scheffer, M., van Nes, E.H., Brovkin, V., Petoukhov, V., Held, H., Slowing down as an early warning signal for abrupt climate change. P. Nat. Acad. Sci. USA 105 (2008), 14308–14312, 10.1353/elh.2014.0029.
Chen, N., Jayaprakash, C., Yu, K., Guttal, V., Rising variability, not slowing down, as a leading indicator of a stochastically driven abrupt transition in a dryland ecosystem. Am. Nat. 191 (2018), E1–E14, 10.1086/694821.
Deb, S., Bhandary, S., Sinha, S.K., Jolly, M.K., Dutta, P.S., Identifying critical transitions in complex diseases. J. Biosci., 47, 2022, 25, 10.1007/s12038-022-00258-7.
Haragus, M., Iooss, G., Local Bifurcation, Center Manifolds and Normal Forms in Infinte-Dimensional Dynamical Systems. 2010, Springer Science ∖and Business Media.
Namachchivaya, N.S., Leng, G., Equivalence of stochastic averaging and stochastic normal forms. J. Appl. Mech. 57 (1990), 1011–1017, 10.1115/1.2897619.
Khas'minskii, R.Z., A limit theorem for the solutions of differential equations with random right-hand sides. Theory Probab. Appl. 11 (1966), 390–406, 10.1137/1111038.
Taylor, J.R., An Introduction to Error Analysis. Mill Valley. 1997, University Science Books, 10.1063/1.882103.
Norman, T.M., Lord, N.D., Paulsson, J., Losick, R., Stochastic switching of cell fate in microbes. Annu. Rev. Microbiol. 69 (2015), 381–403, 10.1146/annurev-micro-091213-112852.
Bayram, M., Partal, T., Buyukoz, G.O., Numerical methods for simulation of stochastic differential equations. Adv. Differ. Equ-NY 2018 (2018), 1–10, 10.1186/s13662-018-1466-5.