A simplest steady-state Munch-like model of phloem translocation, with source and pathway and sink

Functional Plant Biology

Volumn 36, Issue 7, 2009, Pages 629-644

  Pickard, William F ^a   Abraham Shrauner, Barbara ^a  

^a WASHINGTON UNIVERSITY IN ST LOUIS   (United States)

Author keywords

biological fluid mechanics; Li nard equation; M nch mechanism; osmosis; phloem transport

Indexed keywords

EID: 77953223886     PISSN: 14454408     EISSN: None     Source Type: Journal    
DOI: 10.1071/FP08278     Document Type: Article

References (50)

1. Batchelor GK (1967) 'An introduction to fluid dynamics.' (Cambridge University Press: Cambridge)
2. Behnke HD (1989) Structure of the phloem. In 'Transport of photoassimilates'. (Eds DA Baker, JA Milburn) pp. 79-136. (Longman Scientific & Technical: Harlow, UK)
3. Bluman GW, Cole JD (1969) The general similarity solution of the heat equation. Journal of Mathematics and Mechanics 18, 1025-1042.
4. Bluman GW, Reid GJ, Kumei S (1988) New classes of symmetries for partial differential equations. Journal of Mathematical Physics 29, 806-811. doi: 10.1063/1.527974
5. Canny MJ (1973) 'Phloem translocation.' (Cambridge University Press: Cambridge)
6. Canny MJ (1977) Flow and transport in plants. Annual Review of Fluid Mechanics 9, 275-296. doi: 10.1146/annurev.fl.09.010177.001423
7. Carslaw HS, Jaeger JC (1959) 'Conduction of heat in solids.' 2nd edn. (Oxford University Press: Oxford)
8. Chellam S, Wiesner MR, Dawson C (1995) Laminar flow in porous ducts. Reviews in Chemical Engineering 11, 53-99.
9. Clarkson PA, Kruskal MD (1989) New similarity reductions of the Boussinesq equation. Journal of Mathematical Physics 30, 2201-2213. doi: 10.1063/1.528613
10. Diamond JM, Bossert WH (1967) Standing-gradient osmotic flow. Journal of General Physiology 50, 2061-2083. doi: 10.1085/jgp.50.8.2061
11. Ellington CP, Pedley TJ (Eds) (1995) 'Biological fluid dynamics.' (Company of Biologists: Cambridge)
12. Feng ZS (2002) On explicit exact solutions for the Lienard equation and its applications. Physics Letters [Part A] 293, 50-56. doi: 10.1016/S0375- 9601(01)00823-4
13. Gamalei YV (2007) The role of mesophyll cell tonoplast in determining the route of phloem loading. Russian Journal of Plant Physiology: a Comprehensive Russian Journal on Modern Phytophysiology 54, 1-9. doi: 10.1134/ S1021443707010013 (Pubitemid 46072619)
14. Gould N, Thorpe MR, Koroleva O, Minchin PEH (2005) Phloem hydrostatic pressure relates to solute loading rate: a direct test of the Münch hypothesis. Functional Plant Biology 32, 1019-1026. doi: 10.1071/FP05036 (Pubitemid 43293174)
15. Hocking PJ (1980) The composition of phloem exudate and xylem sap from tree tobacco (Nicotiana glauca Grah.). Annals of Botany 45, 633-643.
16. Hölttä T, Vesala T, Sevanto S, Perämäki M, Nikinmaa E (2006) Modeling xylem and phloem water flows in trees according to cohesion theory and Münch hypothesis. Trees (Berlin) 20, 67-78. doi: 10.1007/s00468-005-0014-6 (Pubitemid 41831004)
17. Huang X, Zhu L (2005) Uniqueness of limit cycles in a generalized Liénard system. Journal of the Indian Institute of Science 85, 307-316. (Pubitemid 44560850)
18. Ince EL (1956) 'Ordinary differential equations.' (Dover Publications: New York)
19. Jordan DW, Smith P (1990) 'Nonlinear ordinary differential equations.' (Clarendon Press: Oxford)
20. Kamm RD (2002) Cellular fluid mechanics. Annual Review of Fluid Mechanics 34, 211-232. doi: 10.1146/annurev.fluid.34.082401.165302 (Pubitemid 35372022)
21. Langhaar HL (1951) 'Dimensional analysis and the theory of models.' (Wiley: New York)
22. Mandelbrojt S (1972) 'Dirichlet series.' (D. Riedel Publishing: Dordrecht, The Netherlands)
23. Milburn JA, Kallarackal J (1989) Physiological aspects of translocation. In 'Transport of photoassimilates'. (Eds DA Baker, JA Milburn) pp. 264-305. (Longman Scientific & Technical: Harlow, UK)
24. Minchin PEH, Lacointe A (2005) New understanding on phloem physiology and possible consequences for modelling long-distance carbon transport. New Phytologist 166, 771-779. doi: 10.1111/j.1469-8137.2005.01323.x (Pubitemid 40717680)
25. Münch E (1930) 'Die Stoffbewegungen in der Pflanze.' (Gustav Fischer: Jena, Germany)
26. Neto C, Evans DR, Bonaccurso E, Butt HJ, Craig VSJ (2005) Boundary slip in Newtonian liquids: a review of experimental studies. Reports on Progress in Physics 68, 2859-2897. doi: 10.1088/0034-4885/68/12/R05 (Pubitemid 41435120)
27. Parthasarathy MV (1975) Sieve-element structure. Encyclopedia of Plant Physiology 1, 3-38.
28. Peters WS, Knoblauch M, Warmann SA, Schnetter R, Shen AQ, Pickard WF (2007) Tailed forisomes of Canavalia gladiata: a new model to study Ca2+-driven protein contractility. Annals of Botany 100, 101-109. doi: 10.1093/aob/mcm080 (Pubitemid 47355809)
29. Peters WS, Knoblauch M, Warmann SA, Schnetter R, Pickard WF, Shen AQ (2008) Anisotropic contraction in forisomes: simple models won't fit. Cell Motility and the Cytoskeleton 65, 368-378. doi: 10.1002/cm.20266 (Pubitemid 351657152)
30. Pickard WF (1981) The ascent of sap in plants. Progress in Biophysics and Molecular Biology 37, 181-229. doi: 10.1016/0079-6107(82)90023-2
31. Pickard WF (2003) The riddle of root pressure. I. Putting Maxwell's demon to rest. Functional Plant Biology 30, 121-134. doi: 10.1071/FP02035 (Pubitemid 36325742)
32. Pickard WF (2008) Modelling the swelling assay for aquaporin expression. Journal of Mathematical Biology 57, 883-903. doi: 10.1007/s00285-008-0196-9
33. Pickard WF, Hill RL (1975) An application of g-scintigraphy to the observation of basipetal transport in moonflower. Planta 125, 289-301. doi: 10.1007/BF00385605
34. Pickard WF, Minchin PEH, Troughton JH (1978) Real time studies of carbon-11 translocation in moonflower. II. The effects of metabolic and photosynthetic activity and of water stress. Journal of Experimental Botany 29, 1003-1009.
35. Polya G (1957) 'How to solve it: a new aspect of mathematical method.' 2nd edn. (Doubleday: Garden City, NY)
36. Rand RH (1983) Fluid mechanics of green plants. Annual Review of Fluid Mechanics 15, 29-45. doi: 10.1146/annurev.fl.15.010183.000333
37. Squires TM, Quake SR (2005) Microfluidics: fluid physics at the nanoliter scale. Reviews of Modern Physics 77, 977-1026. doi: 10.1103/RevModPhys.77.977 (Pubitemid 43272528)
38. Taylor GI (1953) Dispersion of soluble matter in solvent flowing slowly through a tube. Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences 219, 186-203. doi: 10.1098/rspa.1953.0139
39. Taylor GI (1954) Conditions under which dispersion of a solute in a stream of solvent can be used to measure molecular diffusion. Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences 225, 473-477. doi: 10.1098/rspa.1954.0216
40. Thompson MV (2006) Phloem: the long and short of it. Trends in Plant Science 11, 26-32. doi: 10.1016/j.tplants.2005.11.009 (Pubitemid 43053975)
41. Thompson MV, Holbrook NM (2003) Application of a single-solute non-steady-state phloem model to the study of long-distance assimilate transport. Journal of Theoretical Biology 220, 419-455. doi: 10.1006/jtbi.2003.3115 (Pubitemid 36293159)
42. Uys L, Botha FC, Hofmeyr JHS, Rohwer JM (2007) Kinetic model of sucrose accumulation in maturing sugarcane culm tissue. Phytochemistry 68, 2375-2392. doi: 10.1016/j.phytochem.2007.04.023 (Pubitemid 47211193)
43. van Bel AJE (2003) The phloem, a miracle of ingenuity. Plant, Cell & Environment 26, 125-149. doi: 10.1046/j.1365-3040.2003.00963.x (Pubitemid 36117284)
44. Van den Broeck C (1990) Taylor dispersion revisited. Physica A 168, 677-696. doi: 10.1016/0378-4371(90)90023-L
45. Van Dyke M (1964) 'Perturbation methods in fluid mechanics.' (Academic Press: New York)
46. Wardlaw IF (1974) Phloem transport: physical chemical or impossible. Annual Review of Plant Physiology 25, 515-539. doi: 10.1146/annurev.pp.25. 060174.002503
47. Zhang WH, Zhou Y, Dibley KE, Tyerman SD, Furbank RT, Patrick JW (2007) Nutrient loading of developing seeds. Functional Plant Biology 34, 314-331. doi: 10.1071/FP06271 (Pubitemid 46641455)
48. Ziegler H (1975) Nature of transported substances. Encyclopedia of Plant Physiology 1, 59-100.
49. Zimmermann MH (1957) Translocation of organic substances in trees. II. The translocation mechanism in the phloem of white ash (Fraxinus americana L.). Plant Physiology 32, 399-404.
50. Zimmermann MH, Ziegler H (1975) List of sugars and sugar alcohols in sieve-tube exudates. Encyclopedia of Plant Physiology 1, 480-503.