Concentration-dependent unloading as a necessary assumption for a closed form mathematical model of osmotically driven pressure flow in phloem
Previous attempts to model steady state Münch pressure flow in phloem (Christy and Ferrier. [1973]. Plant Physiol. 52: 531-538; and Ferrier et al. [1974]. Plant Physiol. 54: 589-600) lack sufficient equations, and results were produced which do not represent correct mathematical solutions. Additiona...
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Veröffentlicht in: | Plant physiology (Bethesda) 1976-10, Vol.58 (4), p.556-562 |
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creator | Goeschl, J D Magnuson, C E Demichele, D W Sharpe, P J |
description | Previous attempts to model steady state Münch pressure flow in phloem (Christy and Ferrier. [1973]. Plant Physiol. 52: 531-538; and Ferrier et al. [1974]. Plant Physiol. 54: 589-600) lack sufficient equations, and results were produced which do not represent correct mathematical solutions. Additional equations for the present closed form model were derived by assuming that unloading of a given solute is dependent upon the concentration of that solute in the sieve tube elements. Examples of linear and enzymic type unloading mechanisms are given, although other concentration-dependent mechanisms could be substituted. A method for a numerical solution is outlined, and proof of convergence is presented along with some representative data and the speed of computer calculations. The model provides the minimal set of equations for describing the Münch pressure flow hypothesis as it might operate in plants. |
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[1973]. Plant Physiol. 52: 531-538; and Ferrier et al. [1974]. Plant Physiol. 54: 589-600) lack sufficient equations, and results were produced which do not represent correct mathematical solutions. Additional equations for the present closed form model were derived by assuming that unloading of a given solute is dependent upon the concentration of that solute in the sieve tube elements. Examples of linear and enzymic type unloading mechanisms are given, although other concentration-dependent mechanisms could be substituted. A method for a numerical solution is outlined, and proof of convergence is presented along with some representative data and the speed of computer calculations. 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The model provides the minimal set of equations for describing the Münch pressure flow hypothesis as it might operate in plants.</description><subject>Loading rate</subject><subject>Mathematical constants</subject><subject>Mathematical models</subject><subject>Phloem</subject><subject>Plants</subject><subject>Sieve elements</subject><subject>Sieve tubes</subject><subject>Solutes</subject><subject>Water pressure</subject><subject>Zero</subject><issn>0032-0889</issn><issn>1532-2548</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1976</creationdate><recordtype>article</recordtype><recordid>eNpVUUtv1DAQthAVXQonrgj51gPKYsfjxDlwQKvykCr1AD1b3tjedeVHsJOi_gl-M1521cLF45n5vnl9CL2hZE0pgQ_TtOZiDWvOu2doRTlrm5aDeI5WhNQ_EWI4Ry9LuSOEUEbhBTqnXceHnvYr9HuT4mjinNXsUmy0mUzU1cdL9ElpF3dYFaxwNKMpReWH6pYlTAc0tinX1OhTMfrgBBzUvDf1caPyOCRtPE4WpxLS35B_wDq7exPxlGu5JRtsffqFXQ3sfTLhFTqzyhfz-mQv0O3nqx-br831zZdvm0_XzQgc5ob1QPQgqNUChGKq64aRMyBtaxWjou7NlCUd1VTAtt9u1UiAEF3PIUQHlrML9PFYd1q2wejjBbycsgt1R5mUk_9notvLXbqXHGoNWvmXJ35OPxdTZhlcGY33Kpq0FNkzBqIHOHR6f0SOOZWSjX1sQok86CenSXIhQVb9Kvrdv3M9YU-CVcDbI-CuzCk_5qHtgA_8iW9VkmqXXZG33-nQ91V53tfB_wAzcqx5</recordid><startdate>19761001</startdate><enddate>19761001</enddate><creator>Goeschl, J D</creator><creator>Magnuson, C E</creator><creator>Demichele, D W</creator><creator>Sharpe, P J</creator><general>American Society of Plant Physiologists</general><scope>FBQ</scope><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7X8</scope><scope>5PM</scope></search><sort><creationdate>19761001</creationdate><title>Concentration-dependent unloading as a necessary assumption for a closed form mathematical model of osmotically driven pressure flow in phloem</title><author>Goeschl, J D ; Magnuson, C E ; Demichele, D W ; Sharpe, P J</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c454t-3740d981fd848a3a669c534022fa3180033af061d184b7bbac0400d0328864f53</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1976</creationdate><topic>Loading rate</topic><topic>Mathematical constants</topic><topic>Mathematical models</topic><topic>Phloem</topic><topic>Plants</topic><topic>Sieve elements</topic><topic>Sieve tubes</topic><topic>Solutes</topic><topic>Water pressure</topic><topic>Zero</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Goeschl, J D</creatorcontrib><creatorcontrib>Magnuson, C E</creatorcontrib><creatorcontrib>Demichele, D W</creatorcontrib><creatorcontrib>Sharpe, P J</creatorcontrib><collection>AGRIS</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>MEDLINE - Academic</collection><collection>PubMed Central (Full Participant titles)</collection><jtitle>Plant physiology (Bethesda)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Goeschl, J D</au><au>Magnuson, C E</au><au>Demichele, D W</au><au>Sharpe, P J</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Concentration-dependent unloading as a necessary assumption for a closed form mathematical model of osmotically driven pressure flow in phloem</atitle><jtitle>Plant physiology (Bethesda)</jtitle><addtitle>Plant Physiol</addtitle><date>1976-10-01</date><risdate>1976</risdate><volume>58</volume><issue>4</issue><spage>556</spage><epage>562</epage><pages>556-562</pages><issn>0032-0889</issn><eissn>1532-2548</eissn><abstract>Previous attempts to model steady state Münch pressure flow in phloem (Christy and Ferrier. [1973]. Plant Physiol. 52: 531-538; and Ferrier et al. [1974]. Plant Physiol. 54: 589-600) lack sufficient equations, and results were produced which do not represent correct mathematical solutions. Additional equations for the present closed form model were derived by assuming that unloading of a given solute is dependent upon the concentration of that solute in the sieve tube elements. Examples of linear and enzymic type unloading mechanisms are given, although other concentration-dependent mechanisms could be substituted. A method for a numerical solution is outlined, and proof of convergence is presented along with some representative data and the speed of computer calculations. 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language | eng |
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source | Alma/SFX Local Collection; JSTOR; EZB Electronic Journals Library |
subjects | Loading rate Mathematical constants Mathematical models Phloem Plants Sieve elements Sieve tubes Solutes Water pressure Zero |
title | Concentration-dependent unloading as a necessary assumption for a closed form mathematical model of osmotically driven pressure flow in phloem |
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