BIOSYSTMe Bio S Modelbased approach Purpose Improve understanding
BIOSYST-Me. Bio. S
Model-based approach Purpose Improve understanding Optimization Control BIOSYST-Me. Bio. S Macroscale approach Mannapperuma et al. (1991); Lammertyn et al. (2003) Geometry: intact fruit Gas transport coupled with respiration kinetics
Gas transport properties Macroscale approach Volume-averaged parameter Effective parameters Liquid phase 1 -ε BIOSYST-Me. Bio. S Ci, l ε Ci, g Gas phase Measurement Biological variability DCO 2 > DO 2 Anisotropic diffusivity Apparant values Deff
Microscopic overview of tissue Parenchyma tissue structure Grouped cells Random distribution of cells and pores Cell wall Plasma membranes BIOSYST-Me. Bio. S Transport phenomena Geometry required Two phases Gas Liquid Cell membrane Passive transport Active transport Intra-cellular enzymatic reactions Plant Cell wall (Albert et al. , 1994)
Objective BIOSYST-Me. Bio. S To verify the applicability of a microscale modelling approach to the gas transport at tissue level in a multiscale framework To quantify the pathways of gas transport in relation to the microstructure of fruit tissue
BIOSYST-Me. Bio. S www. biw. kuleuven. be Microscale modelling of gas transport in pears Q. Tri Ho, Hibru K. Mebatsion, Bert E. Verlinden, Pieter Verboven, Stefan Vandewalle and Bart M. Nicolaï
Geometry model Light microscopy images Parenchyma tissues of ‘Conference’ pear Resolution 1 pixel~0. 735µm Digitization of image BIOSYST-Me. Bio. S Geometry model generation (Mebatsion et al, 2006) Ellipse tessellation algorithm
Ellipse tesselation TEM image of Conference pear BIOSYST-Me. Bio. S Cells Cell Intercellular space Cell wall
Concept of gas transport Gas exchange of fruit Air filled intercellular space BIOSYST-Me. Bio. S At the interface Liquid Pore Intra-cell O 2, g ADP +Pi O 2, l ATP Mitochondrio synthase n Cytosol CO 2, g CO 2, l ATP HCO 3 - Work
Model of O 2 transport in tissue Assumption Cell was assumed gas phase with effective diffusivity DO 2, w Passive gas transport through cell membrane Henry’s law at the inter-phase Model equation (Fick’s second law of diffusion) BIOSYST-Me. Bio. S Pore, cell wall (i= pore, cellwall) O 2 consumption at intra-cell Michaelis-Menten reaction Flux through cell membrane with C*O 2, l the equilibrated O 2 concentration outside of the membrane
Model of CO 2 transport in tissue CO 2, l Fraction of spieces BIOSYST-Me. Bio. S Fraction of CO 2 spieces in liquid phase CO 32 HCO 3 - H 2 CO 3 p. H
Model of CO 2 transport in tissue BIOSYST-Me. Bio. S In pore, cell wall: the same as Eq of O 2 In cellular liquid phase O 2 Mitochondrio n k 1 H 2 CO 3 CO 2, l+ H 2 O k 2 ka 1 HCO 3+H+ CO 2, g
BIOSYST-Me. Bio. S Physical parameters of microscale model Model parameters O 2 microscale model CO 2 microscale model Diffusivity -Pore -Cell wall DO 2, gas=1. 6× 10 -5 m 2 s-1 (1) DO 2, liquid =2. 01× 10 -9 m 2 s-1 (1) DO 2, w = 5× 10 -9 m 2 s-1 DCO 2, gas=1. 6× 10 -5 m 2 s-1 (1) DCO 2, liquid =1. 67× 10 -9 m 2 s-1 (1) DCO 2, w = 5× 10 -9 m 2 s-1 Cell wall thickness 0. 73 µm 0. 73µm Membrane permeability Thickness L=6 -10 nm (2) DO 2, membrane =2. 91× 10 -9 m 2 s-1 (3) h. O 2 = 3. 63× 10 -2 m s-1 * h. CO 2 = 3. 5× 10 -3 m s-1 (4) h. HCO 3 -= 4. 3× 10 -6 m s-1 (4) Henry’s constant HO 2 =1. 371× 10 -2 mol m-3 Pa-1 (1) HCO 2 =0. 3876 mol m-3 Pa-1 (1) Reaction rate constant (1)Lide k 1 =0. 039 s-1 (5) k 2 =23 s-1 (5) Ka 1 =2. 5 × 10 -4 mol L-1 (5) (1996), (2) Gunning and Steer (1996), (3) Uchida et al. (1992), (4)Geers and Gros (2000), (5) Jolly (1991)
Numerical solution Meshing 125050 elements Solution BIOSYST-Me. Bio. S Finite element method Comsol 3. 3 (Comsol AB, Stockholm) Estimation of Dtissue, eff C 2 Steady state Boundary condition Side 1: C 1 ; Side 2: C 2 Ltissue Isolated boundary C 1
Results BIOSYST-Me. Bio. S Simulation of O 2 transport
BIOSYST-Me. Bio. S Simulation of CO 2 transport
Effect of vacuole in the model Occupy 30 -90% of cell volume Storage function Maintain internal acidic p. H BIOSYST-Me. Bio. S Lumped p. H intra-cell model Constant p. H in the cell (DH+=9. 3× 10 -9 m 2/s, Geers and Gros, 2000) p. Hintra-cell=5 Model with vacuole Constant p. H in the cytoplasm and vacuole Regulation of p. H in the cytoplasm and vacuole p. Hcytoplasm=7, p. Hvacuole=4. 82
BIOSYST-Me. Bio. S Lumped p. H intra-cell versus intra-cell including vacuole
Comparison of lumped p. H intracellular model and intra-cell including vacuole Model including vacuole BIOSYST-Me. Bio. S Simulated results Cytoplas m Intra cell CCO 2, l (mol/m 3) 2. 094516 2. 108099 2. 103486 2. 09849 CHCO 3 - (mol/m 3) 0. 271265 0. 088299 0. 15045 0. 09103 CCO 2, l, Total (mol/m 3) 2. 365781 2. 196398 2. 253936 2. 18952 p. H DCO 2 (m 2/s) 7 Vacuole Lumped method 4. 82 2. 565× 10 -9 4. 998776 5 2. 6× 10 -9
Estimated O 2 diffusivity of pear tissue BIOSYST-Me. Bio. S DO 2, cell wall =5× 10 -9 m 2/s Cell wall thickness= 0. 73 µm (TEM, Mebatsion 2006, unpublished data) 9 different geometries DO 2, tissue (m 2/s) Micro scale Ellipse Tesselation Measurement (Macro scale) (3. 93 1. 00) × 10 -10 (2. 87 0. 45) 10 -10 (Ho et al. , 2006) (4. 3 1. 7) 10 -10 (Schotsmans et al. , 2003)
Estimated CO 2 diffusivity of pear tissue BIOSYST-Me. Bio. S Dw, CO 2 cell= 5× 10 -9 m 2/s Cell wall thickness= 0. 73 µm (TEM, Mebatsion 2006, unpublished data) 9 different geometries DCO 2, tissue (m 2/s) Micro scale (3. 12 0. 77)× 10 -9 Measurement (Macro scale) (2. 6 0. 36) 10 -9 (Ho et al. , 2006) (1. 73 1. 15) 10 -9 (Schotsmans et al. , 2003)
Current work Toward 3 D model BIOSYST-Me. Bio. S Digitization vs. mapping X-ray image Digitial geometry 13853 elements Mapping parameters 16896 elements
BIOSYST-Me. Bio. S Solution using mapping parameters Solution based on digitial geometry Solution using mapping parameters DO 2=1. 29 e-9 m 2/s DO 2=1. 33 e-9 m 2/s
3 D geometry based on mapping Geometry information BIOSYST-Me. Bio. S Synchrotron X-ray tomography Resolution 1 pixel~1. 4µm Pore distribution
3 D geometry based on mapping Geometry meshing Lagrange-linear cube Edge dim ~ 2. 8µm Nr of elements: 3968750 (3968750 DOFs) BIOSYST-Me. Bio. S Solving Comsol script 1. 1 (Comsol 3. 3) GMRES HPC Clusters CPU freq: 2000 -2400 MHz Used Mem: 5792736 kb Processing time: 12. 25 h
3 D geometry based on mapping Postprocessing BIOSYST-Me. Bio. S Scripts written in Matlab Running on cluster CPU freq: 2000 -2400 MHz Used Mem: 6. 5 Mb
Primary 3 D simulation BIOSYST-Me. Bio. S O 2 diffusion in tissue CO 2, gas (mol/m 3) O 2 gas concentration CO 2, l (mol/m 3) O 2 liquid concentration
Primary 3 D simulation BIOSYST-Me. Bio. S O 2 diffusion in different tissues CO 2, gas (mol/m 3) Epidermis Subepidermis Cortex
3 D diffusivity results Epidermis Porosity Dg DO 2, eff 0. 0204 1. 6 10 -5 1. 22 10 -10 Measurements (1. 86 0. 78) 10 -10 (Ho et al. , 2006) BIOSYST-Me. Bio. S (0. 33 0. 24) 10 -10 (Schotsmans et al. , 2003) Subepidermis 0. 0364 1. 6 10 -5 8. 58 E 10 -10 Cortex tissue 0. 0554 1. 6 10 -5 2. 83 E 10 -7 (2. 87 0. 45) 10 -10 (Ho et al. , 2006) (4. 3 1. 7) 10 -10 (Schotsmans et al. , 2003)
BIOSYST-Me. Bio. S Conclusions A model was presented to study gas transport at the microscale O 2 mainly transports in the gas phase of intercellular space and cell wall networks CO 2 transfer in both gas and liquid phase Macroscopic diffusivity was estimated using microscale simulations Future: 3 D simulations based on synchrotron X-ray tomography 500 micron
BIOSYST-Me. Bio. S Thank you
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