×

zbMATH — the first resource for mathematics

A framework for model analysis across multiple experiment regimes: investigating effects of zinc on Xylella fastidiosa as a case study. (English) Zbl 1406.92483
Summary: Mathematical models are ubiquitous in analyzing dynamical biological systems. However, it might not be possible to explicitly account for the various sources of uncertainties in the model and the data if there is limited experimental data and information about the biological processes. The presence of uncertainty introduces problems with identifiability of the parameters of the model and determining appropriate regions to explore with respect to sensitivity and estimates of parameter values. Since the model analysis is likely dependent on the numerical estimates of the parameters, parameter identifiability should be addressed beforehand to capture biologically relevant parameter space. Here, we propose a framework which uses data from different experiment regimes to identify a region in the parameter space over which subsequent mathematical analysis can be conducted. Along with building confidence in the parameter estimates, it provides us with variations in the parameters due to changes in the experimental conditions. To determine significance of these variations, we conduct global sensitivity analysis, allowing us to make testable hypothesis for effects of changes in the experimental conditions on the biological system.
As a case study, we develop a model for growth dynamics and biofilm formation of a bacterial plant pathogen, and use our framework to identify possible effects of zinc on the bacterial populations in different metabolic states. The framework reveals underlying issues with parameter identifiability and identifies a suitable region in the parameter space, sensitivity analysis over which informs us about the parameters that might be affected by addition of zinc. Moreover, these parameters prove to be identifiable in this region.
MSC:
92D25 Population dynamics (general)
92C40 Biochemistry, molecular biology
Software:
LBFGS-B; LSODE
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Almeida, R. P.P.; Nunney, L., How do plant diseases caused by xylella fastidiosa emerge?, Plant Dis., 99, 1457-1467, (2015)
[2] Andersen, P. C.; Brodbeck, B. V.; Oden, S.; Shriner, A.; Leite, B., Influence of xylem fluid chemistry on planktonic growth, biofilm formation and aggregation of xylella fastidiosa, FEMS Microbiol. Lett., 274, 2, 210-217, (2007)
[3] Byrd, R. H.; Lu, P.; Nocedal, J.; Zhu, C., A limited memory algorithm for bound constrained optimization, SIAM J. Scient. Comput., 16, 5, 1190-1208, (1995) · Zbl 0836.65080
[4] Caflisch, R. E., Monte Carlo and quasi-Monte Carlo methods, Acta Numerica, 7, 1-49, (1998) · Zbl 0949.65003
[5] Chan, T. F.; Golub, G. H.; LeVeque, R. J., Algorithms for computing the sample variance: analysis and recommendations, Am. Stat., 37, 3, 242-247, (1983) · Zbl 0521.65098
[6] Chaplain, M. A.J., Multiscale mathematical modelling in biology and medicine, IMA J. Appl. Math., 76, 3, 371-388, (2011) · Zbl 1217.92055
[7] Cobine, P. A.; Cruz, L. F.; Navarrete, F.; Duncan, D.; Tygart, M.; De La Fuente, L., Xylella fastidiosa differentially accumulates mineral elements in biofilm and planktonic cells, PLoS ONE, 8, 1, e54936, (2013)
[8] Cogan, N. G.; Donahue, M. R.; Whidden, M.; De La Fuente, L., Pattern formation exhibited by biofilm formation within microfluidic chambers, Biophys. J., 104, 9, 1867-1874, (2013)
[9] Cruz, L. F.; Cobine, P. A.; De La Fuente, L., Calcium increases xylella fastidiosa surface attachment, biofilm formation, and twitching motility, Appl. Environ. Microbiol., 78, 5, 1321-1331, (2012)
[10] Davis, M. J.; Purcell, A. H.; Thomson, S. V., Pierce’s disease of grapevines: isolation of the causal bacterium, Science, 199, 4324, 75-77, (1978)
[11] Davis, M. J.; Purcell, A. H.; Thomson, S. V., Isolation media for the pierce’s disease bacterium., Phytopathology, 70, 5, 425-429, (1980)
[12] De La Fuente, L.; Burr, T. J.; Hoch, H. C., Autoaggregation of xylella fastidiosa cells is influenced by type i and type IV pili, Appl. Environ. Microbiol., 74, 17, 5579-5582, (2008)
[13] De La Fuente, L.; Parker, J. K.; Oliver, J. E.; Granger, S.; Brannen, P. M.; van Santen, E.; Cobine, P. A., The bacterial pathogen xylella fastidiosa affects the leaf ionome of plant hosts during infection, PLoS ONE, 8, 5, e62945, (2013)
[14] Gambetta, G. A.; Fei, J.; Rost, T. L.; Matthews, M. A., Leaf scorch symptoms are not correlated with bacterial populations during pierce’s disease, J. Exp. Bot., 58, 15-16, 4037-4046, (2007)
[15] Glasserman, P., Monte Carlo methods in financial engineering, Vol. 53, (2013), Springer Science & Business Media
[16] Hao, L.; Zaini, P. A.; Hoch, H. C.; Burr, T. J.; Mowery, P., Grape cultivar and sap culture conditions affect the development of xylella fastidiosa phenotypes associated with pierce’s disease, PLoS ONE, 11, 8, e0160978, (2016)
[17] Hopkins, D. L.; Purcell, A. H., Xylella fastidiosa: cause of pierce’s disease of grapevine and other emergent diseases, Plant Dis., 86, 10, 1056-1066, (2002)
[18] Jacques, M.-A.; Denancé, N.; Legendre, B.; Morel, E.; Briand, M.; Mississipi, S.; Durand, K.; Olivier, V.; Portier, P.; Poliakoff, F., New coffee plant-infecting xylella fastidiosa variants derived via homologous recombination, Appl. Environ. Microbiol., 82, 5, 1556-1568, (2016)
[19] Janissen, R.; Murillo, D. M.; Niza, B.; Sahoo, P. K.; Nobrega, M. M.; Cesar, C. L.; Temperini, M. L.A.; Carvalho, H. F.; De Souza, A. A.; Cotta, M. A., Spatiotemporal distribution of different extracellular polymeric substances and filamentation mediate xylella fastidiosa adhesion and biofilm formation, Sci. Rep., 5, (2015)
[20] Janse, J. D.; Obradovic, A., Xylella fastidiosa: its biology, diagnosis, control and risks, J. Plant Pathol., S35-S48, (2010)
[21] Jansen, M. J.W., Analysis of variance designs for model output, Comput. Phys. Commun., 117, 1-2, 35-43, (1999) · Zbl 1015.68218
[22] Killiny, N.; Almeida, R. P.P., Factors affecting the initial adhesion and retention of the plant pathogen xylella fastidiosa in the foregut of an insect vector, Appl. Environ. Microbiol., 80, 1, 420-426, (2014)
[23] Killiny, N.; Martinez, R. H.; Dumenyo, C. K.; Cooksey, D. A.; Almeida, R., The exopolysaccharide of xylella fastidiosa is essential for biofilm formation, plant virulence, and vector transmission, Mol. Plant-Microbe Interact., 26, 9, 1044-1053, (2013)
[24] Kolter, R.; Siegele, D. A.; Tormo, A., The stationary phase of the bacterial life cycle, Ann. Rev. Microbiol., 47, 1, 855-874, (1993)
[25] Kucherenko, S.; Song, S., Different numerical estimators for main effect global sensitivity indices, Reliab. Eng. Syst. Safety, 165, 222-238, (2017)
[26] Loconsole, G.; Potere, O.; Boscia, D.; Altamura, G.; Djelouah, K.; Elbeaino, T.; Frasheri, D.; Lorusso, D.; Palmisano, F.; Pollastro, P., Detection of xylella fastidiosa in olive trees by molecular and serological methods, J. Plant Pathol., 96, 1, 7-14, (2014)
[27] Marino, S.; Hogue, I. B.; Ray, C. J.; Kirschner, D. E., A methodology for performing global uncertainty and sensitivity analysis in systems biology, J. Theor. Biol., 254, 1, 178-196, (2008) · Zbl 1400.92013
[28] Monod, J., The growth of bacterial cultures, Ann. Rev. Microbiol., 3, 1, 371-394, (1949)
[29] Navarrete, F.; De La Fuente, L., Response of xylella fastidiosa to zinc: decreased culturability, increased exopolysaccharide production, and formation of resilient biofilms under flow conditions, Appl. Environ. Microbiol., 80, 3, 1097-1107, (2014)
[30] Navarrete, F.; De La Fuente, L., Zinc detoxification is required for full virulence and modification of the host leaf ionome by xylella fastidiosa, Mol. Plant-Microbe Interact., 28, 4, 497-507, (2015)
[31] Newman, K. L.; Almeida, R. P.P.; Purcell, A. H.; Lindow, S. E., Cell-cell signaling controls xylella fastidiosa interactions with both insects and plants, Proc. Natl. Acad. Sci. U.S.A., 101, 6, 1737-1742, (2004)
[32] Nocedal, J.; Wright, S., Numerical optimization, (2006), Springer Science & Business Media · Zbl 1104.65059
[33] Olmo, D.; Nieto, A.; Adrover, F.; Urbano, A.; Beidas, O.; Juan, A.; Marco-Noales, E.; López, M. M.; Navarro, I.; Monterde, A., First detection of xylella fastidiosa infecting Cherry (prunus avium) and polygala myrtifolia plants, in Mallorca island, Spain, Plant Dis., 101, 10, 1820-1822, (2017)
[34] Owen, A. B., Quasi-Monte Carlo sampling, Monte Carlo Ray Tracing, 1, 69-88, (2003)
[35] Owen, A. B., Better estimation of small sobol’sensitivity indices, ACM Trans. Model. Comput. Simul. (TOMACS), 23, 2, 11, (2013)
[36] Radhakrishnan, K.; Hindmarsh, A. C., Description and use of LSODE, the livermore solver for ordinary differential equations, Lawrence Livermore National Laboratory Report, (1993)
[37] Roper, M. C.; Greve, L. C.; Labavitch, J. M.; Kirkpatrick, B. C., Detection and visualization of an exopolysaccharide produced by xylella fastidiosa in vitro and in planta, Appl. Environ. Microbiol., 73, 22, 7252-7258, (2007)
[38] Saltelli, A.; Annoni, P.; Azzini, I.; Campolongo, F.; Ratto, M.; Tarantola, S., Variance based sensitivity analysis of model output. design and estimator for the total sensitivity index, Comput. Phys. Commun., 181, 2, 259-270, (2010) · Zbl 1219.93116
[39] Saponari, M.; Boscia, D.; Altamura, G.; Loconsole, G.; Zicca, S.; D’Attoma, G.; Morelli, M.; Palmisano, F.; Saponari, A.; Tavano, D., Isolation and pathogenicity of xylella fastidiosa associated to the olive quick decline syndrome in southern Italy, Sci. Rep., 7, 1, 17723, (2017)
[40] Simpson, A. J.G.; Reinach, F. C.; Arruda, P.; Abreu, F. A.; Acencio, M.; Alvarenga, R.; Alves, L. M.C.; Araya, J. E.; Baia, G. S.; Baptista, C. S., The genome sequence of the plant pathogen xylella fastidiosa, Nature, 406, 6792, 151, (2000)
[41] Sobol, I. M., Sensitivity estimates for nonlinear mathematical models, Math. Modell. Comput. Exp., 1, 4, 407-414, (1993) · Zbl 1039.65505
[42] Su, C.-C.; Chang, C. J.; Chang, C.-M.; Shih, H.-T.; Tzeng, K.-C.; Jan, F.-J.; Kao, C.-W.; Deng, W.-L., Pierce’s disease of grapevines in Taiwan: isolation, cultivation and pathogenicity of xylella fastidiosa, J. Phytopathol., 161, 6, 389-396, (2013)
[43] Sutton, S., Measurement of microbial cells by optical density, J. Validation Technol., 17, 1, 46, (2011)
[44] Tabak, J.; Mascagni, M.; Bertram, R., Mechanism for the universal pattern of activity in developing neuronal networks, J. Neurophysiol., 103, 4, 2208-2221, (2010)
[45] Thorne, E. T.; Stevenson, J. F.; Rost, T. L.; Labavitch, J. M.; Matthews, M. A., Pierce’s disease symptoms: comparison with symptoms of water deficit and the impact of water deficits, Am. J. Enol. Vitic., 57, 1, 1-11, (2006)
[46] Wells, J. M.; Raju, B. C.; Hung, H.-Y.; Weisburg, W. G.; Mandelco-Paul, L.; Brenner, D. J., Xylella fastidiosa gen. nov., sp. nov: Gram-negative, xylem-limited, fastidious plant bacteria related to xanthomonas spp., Int. J. Syst. Evol. Microbiol., 37, 2, 136-143, (1987)
[47] Zaini, P. A.; De La Fuente, L.; Hoch, H. C.; Burr, T. J., Grapevine xylem sap enhances biofilm development by xylella fastidiosa, FEMS Microbiol. Lett., 295, 1, 129-134, (2009)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.