Physical and Morphological Constraints on Transport in Nodules

Abstract

MATERIALS AND METHODS Estimation of Flows. We will approach the quantification of the flows from a realistic agronomic goal of a nitrogen fixation rate of 2 kg N ha-' day-' (13). We will consider a soybean crop with a plant population of 2 x 105 plants ha-' and with 100 nodules/ plant. Each nodule then will be assumed to fix nitrogen at a rate of about 1 x 10-9 g N s-'. This number will be used to estimate first the required flow of glucose and then of 02.Glucose is required in the nitrogen fixation process as a source of energy and carbon skeletons and as the substrate for sustaining maintenance respiration in the nodule. On the basis of the theoretical considerations of Penning de Vires (10, 11), it is possible to construct the following reaction for the fixation of 1 g N: 15.5 g glucose + 6 g2 + 1 g N2 x 7 g amino acids + 10.7 g CO2 + 4.8 g H20 Experimentally, Ryle et al. (12) measured the CO2 loss from nodules of soybean, cowpea, and clover. Expressing this loss/g nitrogen fixed, full-grown, nonsenesced nodules were found to lose 3 to 4 g C/g N fixed. Converting this ratio to CO2 loss yields 4 x 44/12 = 14.7 g CO2 evolved, or 4.0 g more than derived above. This excess CO2 loss can be attributed to maintenance respiration and represents an additional glucose requirement of about 2.7 g. Approximately 18 g glucose is used by the nodule during its fixation of 1 g N or, to meet the agronomic goals, about 18 x 10-9 g glucose s-1 needs to be imported by a nodule.A similar approach can be used to estimate the 02 requirement.From the reaction above, 6 g 02 is required in fixation itself and maintenance respiration requires 2.9 g 02. Consequently, approximately 8.9 g 02 is required during the fixation of 1 g N, and the agronomic goal requires 8.9 x 10-9 g 02 s' to be obtained by a nodule from the surrounding atmosphere.Model. A second-order differential equation can be used to define material transport in the nodule after invoking several simplifying assumptions. It is assumed that the nodule is a uniform, homogeneous sphere because this geometry reasonably approximates many nodules and it allows an analytic solution. The biochemical events of N2 fixation are assumed to be reasonably 143 www.plantphysiol.org on May 7, 2018 -Published by Downloaded from

Mathematical Modeling of Oxygen Diffusion and Respiration in Legume Root Nodules

“…The mathematical model of Sinclair and Goudriaan (21) established that a layer of water on the order of 50 ,m thick would provide a diffusion resistance consistent with experimental data. The actual baffler is presumably more complex, with 02 diffusion both through cells and through intercellular spaces filled with air or water.…”

“…The unsteady-state 02 method for determining nodule permeability was tested using data generated by the model. The accuracy of the method was confirmed, provided that certain assumptions (full oxygenation of leghemoglobin under pure 02 and uniform conditions in the nodule interior) are met.A diffusion barrier in legume root nodules restricts 02 flux into the nodule and thereby protects nitrogenase from inactivation by 02 (21,22). The responses of nodules to such seemingly unrelated factors as drought, nitrate, and defoliation all apparently involve changes in the gas permeability of this barrier (8,10,14,17,23,24 Variable gas permeability of nodules might result from changes in (a) the number or size of gas-filled radial pores through the barrier, (b) the thickness of water plugs in radial pores, (c) the extent of flooding between layers of cells, or (d) flooding of airspaces in the central zone.…”

Response to Drought Stress of Nitrogen Fixation (Acetylene Reduction) Rates by Field-Grown Soybeans

“…Drought stress decreases nitrogen fixation rates as measured by both acetylene reduction (1,7,(17)(18)(19)(20)(21)(22) and 'sN uptake (16). While some researchers have concluded that this loss of nodule activity is due to an inhibition ofphotosynthesis (8,9,13), Sprent (22) concluded that nitrogen fixation is more sensitive than photosynthesis to drought stress.…”

“…They presumed that the depressed oxygen uptake was caused by either a loss ofoxygen conductance through the nodule or by inhibition of oxygen requiring reactions, or perhaps by both. Restricted oxygen conductance has been shown by theoretical arguments to be an important feature of viable, well-watered nodules (16).…”

Measurement of Legume Nodule Respiration and O2 Permeability by Noninvasive Spectrophotometry of Leghemoglobin

“…Similar permeability changes occur in response to acetylene exposure (12) or with increased or decreased external 02 concentration (23,27). Studies with microelectrodes (19,27) and theoretical considerations (18) suggest that nodule permeability is limited mainly by one or more layers of tightly packed cells in the nodule cortex.…”