Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-24T11:07:50.279Z Has data issue: false hasContentIssue false
  • English
  • Français

Mathematical Models for Expansive Growth of Cells withWalls

Published online by Cambridge University Press:  10 July 2013

J.K.E. Ortega  and
S.W.J. Welch
Get access

Abstract

Plants, algae, and fungi are essential for nearly all life on earth. Throughphotosynthesis, plants and algae convert solar energy to chemical energy in the form oforganic compounds that sustains essentially all life on earth. In addition, plants andalgae convert the carbon dioxide produced by respiring organisms to oxygen that is neededfor respiration. Fungi decompose complex organic compounds produced by respiring organismsso that molecules can be recycled in photosynthesis and respiration. Plants, algae, andfungi have one important feature in common, their cells have walls. Expansive growth andits regulation are central to the life and development of plant, algal, and fungal cells,i.e. cells with walls. In recent decades there has been an explosion of informationrelevant to expansive growth of cells with walls. Mathematical models have beenconstructed in an attempt to organize and evaluate this information, to gain insight, toevaluate hypotheses, and to assist in the selection and development of new experimentalstudies. In this article some of the mathematical models constructed to study expansivegrowth of cells with walls are reviewed. It is nearly impossible to review all relevantresearch conducted in this area. Instead, the review focuses on the development ofmathematical equations that have been used to model expansive growth, morphogenesis, andgrowth rate regulation of cells with walls. Also, relevant experimental findings arereviewed, conceptual models are presented, and suggestions for future research areproposed. The authors have attempted to provide an overview that is accessible toresearchers that are not working in this field.

Keywords

plantsalgaefungigrowth modelsgrowth equationsaugmented growth equations
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 8 , Issue 4 , 2013 , pp. 35 - 61
Copyright
© EDP Sciences, 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ahlquist, C.N., Gamow, R.I.. Phycomyces mechanical behavior of stage II and stage IV. Plant Physiol., 51 (1973), 586–587. CrossRefGoogle ScholarPubMed
Ambrosi, D., Ateshian, G.A., Arruda, E.M., Cowin, S.C., Dumais, J., Goriely, A., Holzapfel, G.A., Humphrey, J.D., Kemkemer, R., Kuhl, E., Olberding, J.E., Taber, L.A., Garikipati, K.. Perspectives on biological growth and remodeling. J Mech. Phys. Solids, 59 (2011), 863–883. CrossRefGoogle ScholarPubMed
Bartnicki-Garcia, S., Bracker, C.E., Glerz, G., Lopez-Franco, R., Lu, H.. Mapping the growth of fungal hyphae orthogonal cell wall expansion during tip growth and the role of turgor. Biophys J., 79 (2000) 2382–2390. CrossRefGoogle Scholar
Baskin, T.I.. Anisotropic expansion of the plant cell wall. Annu Rev Cell Dev Biol, 21 (2005), 203–222. CrossRefGoogle ScholarPubMed
E.C. Bingham. Fluidity and Plasticity. McGraw-Hill, New York, 1922.
Bove, J., Vaillancourt, B., Kroeger, J., Hepler, P.K., Wiseman, P.W., Geitmann, A.. Magnitude and Direction of Vesicle Dynamics in Growing Pollen Tubes Using Spatiotemporal Image Correlation Spectroscopy and Fluorescence Recovery after Photobleaching. Plant Physiol., 147 (2008), 1646–1658. CrossRefGoogle Scholar
Boyer, J.S.. Cell wall biosynthesis and the molecular mechanism of plant enlargement. Funct. Plant Biol., 36 (2009), 383–394. CrossRefGoogle Scholar
Campas, O., Mahadevan, L.. Shape and dynamics of tip-growing cells. Current Biol., 19 (2009), 2102–2107. CrossRefGoogle ScholarPubMed
Carpita, N.C., Gibeaut, D.M.. Structural models of primary cell wall in flowering plants: Consistency of molecular structure with the physical properties of the walls during growth. Plant J., 3 (1993), 1–30. CrossRefGoogle ScholarPubMed
Castle, E.S.. Spiral growth and the reversal of spiraling in Phycomyces, and their bearing on primary wall structure. Am J Botany, 29 (1942), 664–672. CrossRefGoogle Scholar
Chaplain, M.A.J.. The strain energy function of an ideal plant cell wall. J Theor. Biol., 163 (1993), 77–97. CrossRefGoogle Scholar
Chebli, Y., Geitmann, A.. Mechanical principles governing pollen tube growth. Funct. Plant Sci Biotech., 1 (2007), 232–245. Google Scholar
E. Cerda-Olmedo, E.D. Lipson. Phycomyces. Cold Spring Harbor Laboratory Press, Cold Spring Harbor, New York, 1987.
Cosgrove, D.J.. Cell wall yield properties of growing tissue evaluation by in vivo stress relaxation. Plant Physiol., 78 (1985), 347–356. CrossRefGoogle ScholarPubMed
Cosgrove, D.J.. Wall relaxation in growing stems: comparison of four species and assessment of measurement techniques. Planta, 171 (1987), 266–278. CrossRefGoogle ScholarPubMed
Cosgrove, D.J.. Assembly and enlargement of the primary cell wall in plants. Annu. Rev. Cell Dev. Biol., 13 (1997), 171–201. CrossRefGoogle ScholarPubMed
Cosgrove, D.J.. Loosening of plant cell walls by expansions. Nature, 407 (2000), 321–326. CrossRefGoogle Scholar
Cosgrove, D.J.. Growth of the plant cell wall. Nat. Rev. Mol. Cell Biol., 6 (2005), 850–861 (doi:10.1038/nrm1746). CrossRefGoogle Scholar
Dumais, J., Shaw, S.L., Steele, C.R., Long, S.R., Ray, P.M.. An anisotropic-viscoplastic model of plant cell morphogenesis by tip growth. Int. J Dev. Biol., 50 (2006), 209–222. CrossRefGoogle ScholarPubMed
Dyson, R.J., Jensen, O.E.. A fibre-reinforced fluid model of anisotropic plant cell growth. J Fluid Mech., 655 (2010), 472–503. CrossRefGoogle Scholar
Dyson, R.J., Band, L.R., Jensen, O.E.. A model of cross-link kinetics in the expanding plant cell wall: Yield stress and enzyme action. J Theor Biol., 307 (2012), 125–136. CrossRefGoogle Scholar
Gasser, T.C., Ogden, R.W., Holzapfel, G.A.. Hyperelastic modelling of arterial layers with distributed collagen fibre orientations. J Roy Soc. Interface, 3 (2006), 15–35. CrossRefGoogle Scholar
Geitmann, A., Li, Y.Q., Cresti, M.. The role of the cytoskeleton and dyctyosome activity in the pulsatory growth of Nicotiana tabacum and Petunia hybrida. Bot. Acta, 109 (1996), 102–109. CrossRefGoogle Scholar
Geitmann, A., Ortega, J.K.E.. Mechanics and modeling of plant cell growth. Trends Plant Sci., 14 (2009), 467–478. CrossRefGoogle ScholarPubMed
Gierz, G., Bartnicki-Garcia, S.. A three-dimensional model of fungal morphogenesis based on the vesicle supply center concept. J Theor. Biol., 208 (2001), 151–164. CrossRefGoogle ScholarPubMed
Green, J.E.F., Friedman, A.. The extensional flow of a thin sheet of incompressible, transversly isotropic fluid. Europ. J Appl. Math., 3 (2008), 225–257. Google Scholar
Green, P.B.. Growth Physics in Nitella: a Method for Continuous in Vivo Analysis of Extensibility Based on a Micro-manometer Technique for Turgor Pressure. Plant Physiol., 43 (1968), 1169–1184. CrossRefGoogle Scholar
Green, P.B.. Cell Morphogenesis. Ann. Rev. Plant Physiol., 20 (1969), 365–394. CrossRefGoogle Scholar
Green, P.B., Erickson, R.O., Buggy, J.. Metabolic and physical control of cell elongation rate: in vivo studies in Nitella. Plant Physiol., 47 (1971), 423–430. CrossRefGoogle Scholar
I.B. Heath. Tip growth in plant and fungal cells. Academic Press, Inc., San Diego, CA , 1990.
Holdaway-Clarke, T., Hepler, P.. Control of pollen tube growth: role of ion gradients and fluxes. New Phytol., 159 (2003), 539–563. CrossRefGoogle Scholar
Huang, R., Becker, A.A., Jones, I.A.. Modelling cell wall growth using a fibre-reinforced hyperelastic-viscoplastic constitutive law. J Mech. Phys. Solids, 60 (2012), 750-783. CrossRefGoogle Scholar
Kroeger, J.H., Geitmann, A., Grant, M.. Model for calcium dependent oscillatory growth in pollen tubes. J Theor. Biol., 253 (2008), 363–374. CrossRefGoogle ScholarPubMed
Kroeger, J.H., Zerzour, R., Geitmann, A.. Regulator or driving force? The role of turgor pressure in oscillatory plant cell growth. PLoS One, 6 (2011), e18549. CrossRefGoogle ScholarPubMed
Kroeger, J.H., Geitmann, A.. Pollen tube growth: Getting a grip on cell biology through modeling. Mech. Res. Comm., 42 (2012), 32–39. CrossRefGoogle Scholar
Lewicka, S.. General and analytic solutions of the Ortega equation. Plant Physiol., 142 (2006), 1493–1510. CrossRefGoogle ScholarPubMed
Liu, J., Piette, B.M.A.G., Deeks, M.J., Franklin-Tong, V.E., Hussey, P.J.. A compartmental model analysis of integrative and self-regulatory ion dynamics in pollen tube growth Plos One, 5 (2010), e13157. CrossRefGoogle ScholarPubMed
Lockhart, J.A.. An analysis of irreversible plant cell elongation J Theor. Biol., 8 (1965), 264–275. CrossRefGoogle Scholar
Marga, F., Grandbois, M., Cosgrove, D.J., Baskin, T.I.. Cell wall extension results in the coordinate separation of parallel microfibrils: evidence from scanning electron microscopy and atomic force microscopy. Plant J., 43 (2005), 181–190. CrossRefGoogle Scholar
Messerli, M.A., Greton, R., Jaffe, L.F., Robinson, K.R.. Periodic increases in elongation rate precede increases in cytosolic Ca2+ during pollen tube growth. Dev. Biol., 222 (2000), 84–98. CrossRefGoogle Scholar
Molz, F.J., Boyer, J.S.. Growth-induced water potential in plant cells and tissue. Plant Physiol., 62 (1978), 423–429. CrossRefGoogle Scholar
Murphy, R., Ortega, J.K.E.. A new pressure probe method to determine the average volumetric elastic modulus of cells in plant tissue. Plant Physiol., 107 (1995), 995–1005. CrossRefGoogle Scholar
Murphy, R., Ortega, J.K.E.. A study of the stationary volumetric elastic modulus during dehydration and rehydration of stems of pea seedlings. Plant Physiol., 110 (1996), 1309–1316. CrossRefGoogle ScholarPubMed
Nonami, H., Boyer, J.S.. Direct demonstration of a growth-induced water potential gradient. Plant Physiol., 102 (1993), 13–19. CrossRefGoogle ScholarPubMed
Ortega, J.K.E.. Augmented growth equation for cell wall expansion. Plant Physiol., 79 (1985), 318–320. CrossRefGoogle ScholarPubMed
Ortega, J.K.E.. Governing equations for plant cell growth. Physiol. Plant, 79 (1990), 116–121. CrossRefGoogle Scholar
Ortega, J.K.E.. A quantitative biophysical perspective of expansive growth for cells with walls. Ed. SG Pandalai, Rec. Res. Dev. Biophys, Transworld Research Network, Kerala, India. 3 (2004), 297–324. Google Scholar
Ortega, J.K.E.. Plant cell growth in tissue. Plant Physiol., 154 (2010), 1244–1253. CrossRefGoogle ScholarPubMed
Ortega, J.K.E.. Growth rate regulation of cells with walls: The sporangiophores of Phycomyces blakesleeanus used as a model system. Rec. Res. Dev. Plant Physiol., 5 (2012), 1–19. Google Scholar
Ortega, J.K.E., Gamow, R.I.. The problem of handedness reversal during the spiral growth of Phycomyces. J Theor. Biol., 47 (1974), 317–332. CrossRefGoogle ScholarPubMed
Ortega, J.K.E., Keanini, R.G., Manica, K.J.. Pressure probe technique to study transpiration in Phycomyces sporangiophores. Plant Physiol., 87 (1988), 11–14. CrossRefGoogle ScholarPubMed
Ortega, J.K.E., Manica, K.J., Keanini, R.G.. Phycomyces: Turgor pressure behavior during the light and avoidance growth response. Photochem. Photobiol., 48 (1988), 697–703. CrossRefGoogle Scholar
Ortega, J.K.E., Zehr, E.G., Keanini, R.G.. In vivo creep and stress relaxation experiments to determine the wall extensibility and yield threshold for the sporangiophores of Phycomyces. Biophys. J., 56 (1989), 465–475. CrossRefGoogle ScholarPubMed
Ortega, J.K.E., Lesh-Laurie, G.E., Espinosa, M.A., Ortega, E.L., Manos, S.M., Cunning, M.D., Olson, J.E.C.. Helical growth of stage-IVb sporangiophores Phycomyces blakesleeanus: the relationship between rotation and elongation growth rates. Planta, 216 (2003), 716–722. Google ScholarPubMed
Ortega, J.K.E., Munoz, C.M., Blakley, S.E., Truong, J.T., Ortega, E.L.. Stiff mutant genes of Phycomyces affect turgor pressure and wall mechanical properties to regulate elongation growth rate. Frontiers in Plant Science, 3 (2012), 1–12. CrossRefGoogle ScholarPubMed
Ortega, J.K.E., Smith, M.E., Erazo, A.J., Espinosa, M.A., Bell, S.A., Zehr, E.G.. A comparison of cell-wall-yielding properties for two developmental stages of Phycomyces sporangiophores: Determination by in-vivo creep experiments. Planta, 183 (1991), 613–619. CrossRefGoogle ScholarPubMed
Parre, E., Geitmann, A.. Pectin and the role of the physical properties of the cell wall in pollen tube growth of Solanum chacoense. Planta, 220 (2005), 582–592. CrossRefGoogle ScholarPubMed
Parton, R., Fischer-Parton, S., Watahiki, M., Trewavas, A.. Dynamics of the apical vesicle accumulation and the rate of growth are related in individual pollen tubes J Cell Sci., 114 (2001), 2685–2695. Google ScholarPubMed
Passioura, J.B., Fry, S.C.. Turgor and cell expansion: beyond the Lockhart equation. Austral. J Plant Physiol., 19 (1992), 565–576. CrossRefGoogle Scholar
Pietruszka, M.. Solutions for a local equation of anisotropic plant cell growth: an analytical study of expansin activity. J Royal Soc. Int., 8 (2011), 975–987. CrossRefGoogle ScholarPubMed
Pietruszka, M.. Special solutions to the Ortega Equation. J Plant Growth Regul., 32 (2013), 102–107. CrossRefGoogle Scholar
Proseus, T.E., Boyer, J.S.. Calcium deprivation disrupts enlargement of Chara corallina cells: further evidence for the calcium pectate cycle. J Exp. Bot., 63 (2012), 3953–3958. CrossRefGoogle ScholarPubMed
Proseus, T.E., Ortega, J.K.E., Boyer, J.S.. Separating growth from elastic deformation during cell enlargement. Plant Physiol., 119 (1999), 775–784. CrossRefGoogle ScholarPubMed
Proseus, T.E., Zhu, G.L., Boyer, J.S.. Turgor, temperature and the growth of plant cells:using Chara corallina as a model system. J. Exp. Bot., 51 (2000), 1481–1494. CrossRefGoogle ScholarPubMed
Richmond, P.A., Métraux, J.-P., Taiz, L.. Cell expansion patterns and directionality of wall mechanical properties in Nitella Plant Physiol., 65 (1980), 211–217. CrossRefGoogle ScholarPubMed
Rodriguez, E.K., Hoger, A., McCulloch, A.. Stress-dependent finite growth in soft elastic tissue. J. Biomechanics, 27 (1994), 455–467. CrossRefGoogle Scholar
Roelofsen, P.A.. The origin of spiral growth in Phycomyces sporangiophores. Record of Travaux Botaniques Neerlandais, 42 (1950), 72–110. Google Scholar
Roelofsen, P.. Cell wall structure in the growth zone of Phycomyces sporangiophores. II. Double refraction and electron microscopy. The origin of spiral growth in Phycomyces sporangiophores. Biochemica et Biophysica Acta, 6 (1951), 357–373. CrossRefGoogle Scholar
Rojas, E.R., Hotton, S., Dumais, J.. Chemically-mediated Mechanical expansion of the pollen tube cell wall. Biophys. J., 101 (2011), 1844–1853. CrossRefGoogle ScholarPubMed
J. Ruiz-Herrera. Fungal cell wall: Structure, synthesis, and assembly. CRC Press, New York, 2012.
J.C. Simo, T.J.R. Hughes. Computational Inelasticity. Springer, New York, 1998.
Spencer, A.J.M.. A theory of viscoplasticity for fabric-reinforced composites. J Mech. Phys. Solids, 49 (2001), 2667–2687. CrossRefGoogle Scholar
Taiz, L.. Plant Cell Expansion: Regulation of Cell Wall Mechanical Properties. Ann. Rev. Plant Physiol., 35 (1984), 585–657. CrossRefGoogle Scholar
Tang, A.-C., Boyer, J.S.. Xylem tension affect growth-induced water potential and daily elongation of maize leaves. J Exp. Bot., 59 (2008), 753–764. CrossRefGoogle Scholar
Vandiver, R., Goriely, A.. Tissue tension and axial growth of cylindrical structures in plants and elastic tissues. Europhys. Letter, 84 (2008), 58004. CrossRefGoogle Scholar
Veytsmann, B., Cosgrove, D.J.. A model of cell wall expansion based on thermodynamics of polymer networks. Biophys. J., 75 (1998), 2240–2250. CrossRefGoogle Scholar
J.G.H. Wessel. Tip growth in plant and fungal cells. IB Heath (Ed.), Academic Press, Inc., San Diego, CA (1990), 1–29.
Yan, A., Xu, G., Yang, Z.-B.. Calcium participates in feedback regulation of the oscillating ROP1 Rho GTPase in pollen tubes. PNAS, 106 (2009), 22002–22007. CrossRefGoogle ScholarPubMed