Research Papers

Study of Protein Facilitated Water and Nutrient Transport in Plant Phloem

[+] Author and Article Information
Tsun-kay Jackie Sze, Jin Liu

School of Mechanical and Materials Engineering,
Washington State University,
Pullman, WA 99164

Prashanta Dutta

School of Mechanical and Materials Engineering,
Washington State University,
Pullman, WA 99164
e-mail: dutta@mail.wsu.edu

1Corresponding author.

Manuscript received January 8, 2014; final manuscript received January 15, 2014; published online February 19, 2014. Assoc. Editor: Sushanta K Mitra.

J. Nanotechnol. Eng. Med 4(3), 031005 (Feb 19, 2014) (9 pages) Paper No: NANO-14-1001; doi: 10.1115/1.4026519 History: Received January 08, 2014; Revised January 15, 2014

Biological systems use transporter proteins to create concentration gradients for a variety of purposes. In plant, sucrose transporter proteins play a vital role in driving fluid flow through the phloem by generating chemical potential. In this study, we investigate these nanoscale phenomena of protein directed active transport in a microscale biological system. We presented a mathematical model for protein facilitated sucrose loading considering six different states of the sucrose transporter protein. In addition, we developed a quasi-one dimensional transport model to study protein facilitated pumping mechanisms in plant phloem. Here we specifically study the influence of transporter protein reaction rates, apoplast proton concentration, membrane electrical potential, and cell membrane hydraulic permeability on flow through the phloem. This study reveals that increasing companion cell side deprotonation rate significantly enhances the sieve tube sugar concentrations, which results in much higher water transport. Lower apoplast pH increases the transport rate, but the flow control is less noticeable for a pH less than 5. A more negative membrane electrical potential difference will significantly accelerate the transporter proteins' ability to pump water and nutrients. Higher companion cell and sieve element membrane hydraulic permeability also promotes flows through the phloem; however, the flow difference is less noticeable at higher permeabilities when near typical plant cell membrane ranges.

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Grahic Jump Location
Fig. 2

(a) Proton sucrose transporter protein, where sucrose molecules are moved from the apoplast into the cytoplasm of the companion cell (CC). (b) Individual protein states during active loading of sucrose from the apoplast to the CC. There are a total of six states with 12 rate constants composed of forward kn and reverse kn reactions. Reactant concentrations on both sides of the membrane are included, where the apoplast side sucrose concentration is Se and the companion cell side sucrose concentration is S. Since the companion cell is connected to the sieve element (Fig. 1(c)), it is assumed that both companion cell and sieve element have the same reactant concentrations.

Grahic Jump Location
Fig. 1

(a) Transport of sugar and water through the four regions of sieve tube: a source region represented as leaf, transport region through the petiole, transport region through the stem, and unloading region in the root. (b) The sieve tube consists of sieve elements with sieve plates separating individual elements. We consider each sieve element with a length L and height h. Sieve plates have a thickness Lp and a sieve plate pore radius rp. Water flows through the membrane from the surrounding apoplast (blank space) into the sieve element and neighboring companion cell. (c) Companion cells are considered as interconnected with neighboring sieve elements by plasmodesmata approximated as annular pores. The companion cell and sieve element cell are separated from the apoplast by the cell membrane, which contains aquaporins. It is assumed that the sugar transporter proteins are only present at the membrane of companion cell. The sucrose transporter protein and its different states are further illustrated in Fig. 2.

Grahic Jump Location
Fig. 3

Schematic of control volumes used in this model for (a) continuity, (b) momentum, and (c) chemical species mass conservation equations. For continuity we consider mass added due to streamwise flow, sugar loaded, and water loaded by osmotic pressures. The momentum equation includes forces due to thermodynamic pressure, wall shear stress, sieve plate drag, and additional body forces. In the case of the mass conservation equation for chemical species, we consider streamwise species flux and flux due to species loading.

Grahic Jump Location
Fig. 4

Distribution along sieve tube for (a) wall flow velocity, (b) average velocity, (c) pressure and water potential difference, and (d) sucrose concentration. The modeled sieve tube is decomposed into three sections: leaf, petiole (between leaf and stem region), and stem. Simulation results are based on a k5 of 4.3 s−1, an apoplast pH of 6.1, a membrane electrical potential difference of −140 mV, and a cell membrane permeability of 6 × 10−14 m Pa−1 s−1.

Grahic Jump Location
Fig. 8

Sieve tube average velocity at the sink end (s = L3) for different cell membrane hydraulic permeabilities. All other conditions are the same as Fig. 4. Membrane hydraulic permeability is shown on a log scale.

Grahic Jump Location
Fig. 7

The effect of membrane electrical potential difference on fluid velocity at the sink end (s = L3). All other conditions are the same as Fig. 4. A more negative membrane electrical potential difference implies a more negative charge in the companion cell.

Grahic Jump Location
Fig. 5

Influence of companion cell side deprotonation rate constant k5 on (a) sieve tube sugar concentration at starting end (s = 0) and (b) sieve tube average velocity at the sink end (s = L3). All other conditions are the same as Fig. 4.

Grahic Jump Location
Fig. 6

The influence of apoplast proton concentration on fluid velocity at the sink end (s = L3). All other conditions are the same as Fig. 4.



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