The ISME Journal (2017) 11, 166–175 © 2017 International Society for Microbial Ecology All rights reserved 1751-7362/17 OPEN www.nature.com/ismej ORIGINAL ARTICLE A quantitative analysis of the direct and indirect costs of nitrogen fixation: a model based on Azotobacter vinelandii Keisuke Inomura1, Jason Bragg2 and Michael J Follows1 1Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA, USA and 2Research School of Biology, Australian National University, Canberra, ACT, Australia Nitrogen fixation is advantageous in microbial competition when bioavailable nitrogen is scarce, but has substantial costs for growth rate and growth efficiency. To quantify these costs, we have developed a model of a nitrogen-fixing bacterium that constrains mass, electron and energy flow at the scale of the individual. When tested and calibrated with laboratory data for the soil bacterium Azotobacter vinelandii, the model reveals that the direct energetic cost of nitrogen fixation is small relative to the cost of managing intracellular oxygen. It quantifies the costs and benefits of several potential oxygen protection mechanisms present in nature including enhanced respiration (respiratory protection) as well as the production of extracellular polymers as a barrier to O2 diffusion, and increasing cell size. The latter mechanisms lead to higher growth efficiencies relative to respiratory protection alone. This simple, yet mechanistic framework provides a quantitative model of nitrogen fixation, which can be applied in ecological simulations. The ISME Journal (2017) 11, 166–175; doi:10.1038/ismej.2016.97; published online 14 October 2016 Introduction 16 molecules of ATP to reduce each N2 molecule to two molecules of NH (Sohm et al., 2011). All organisms need nitrogen for the synthesis of 3 À þ important molecules including nucleic acids and N2 þ 8e þ 8H þ 16ATP þ 16H2O-2NH3 proteins. Nitrogen pervades the environment in the þ H2 þ 16ADP þ 16Pi ð1Þ form of N2 gas, yet it is often a limiting resource on land and in aquatic environments. Nitrogen fixation Although the energetic expense of breaking the provides some marine and terrestrial prokaryotes dinitrogen triple bond is high, this direct cost may with an ecological advantage but is typically not necessarily be the greatest challenge faced associated with low growth efficiencies and rates by nitrogen-fixing cells. Nitrogenase consists of an – – – (Kuhla and Oelze, 1988a, b; LaRoche and Breitbarth, Fe protein and a Mo Fe protein and other metal 2005; Berman-Frank et al., 2007; Goebel et al., 2007), cofactors whose activity is decreased upon exposure placing significant constraints on the relative to oxygen (Gallon, 1981). Thus, aerobic nitrogen fitness of nitrogen fixers and their biogeography. fixers have developed numerous strategies to protect Here we address the question of what underpins nitrogenase from oxygen, particularly in oxygenic the low growth efficiency of nitrogen fixers and phototrophs. For example, in Anabaena and Nostoc develop a quantitative analysis that forms the basis the nitrogen-fixing cells also become heterocysts, for trait-based ecological and biogeochemical losing the ability to fix carbon and building a thick models. cell coating, which is less permeable to oxygen One contribution to the low growth rate/efficiency (Neilson et al., 1971; Wolk, 1996; Golden and Yoon, of nitrogen fixers is the direct cost of reducing 2003) demanding an exchange of metabolites dinitrogen. Nitrogen fixation is catalyzed by the between cells, as do nitrogen fixers in symbiotic nitrogenase enzyme, and uses 8 electrons and at least relationships with other species. Free-living, uni- cellular aerobic nitrogen fixers use other strategies, including the separation of oxygenic photosynthesis Correspondence: K Inomura, Department of Earth, Atmospheric and nitrogen fixation between day and night and Planetary Sciences, Massachusetts Institute of Technology, (for example, Colón-López et al., 1997; Misra, 1999; Room 54-1425, 77 Massachusetts Avenue, Cambridge, MA 02139, Tucker et al., 2001; Berman-Frank et al., 2003; Saito USA. E-mail: [email protected] et al., 2011; Großkopf and LaRoche, 2012). Hetero- Received 30 March 2016; revised 1 June 2016; accepted 7 June trophic, soil-dwelling nitrogen fixers, such as 2016; published online 14 October 2016 Azotobacter vinlandii, use elevated rates of Direct and indirect costs of nitrogen fixation K Inomura et al 167 Figure 1 Continuous cultures of Azotobacter vinelandii with observed data (circles) redrawn from Kuhla and Oelze (1988b). Solid lines are the corresponding simulations from this work. (a) Protein-specific sucrose consumption rate, (b) standing stock of protein, all with respect to dilution (and growth) rate, D (x axis) and oxygen concentration (colored points/lines). The legend indicates oxygen concentration. respiration to deplete intracellular oxygen (Poole rate increased with oxygen concentration. The and Hill, 1997). They also produce an extracellular sensitivity to oxygen manifests largely as a 'main- polymeric substance that impedes oxygen invasion tenance' effect, increasing overall carbohydrate (Sabra et al., 2000), and they maintain larger cell consumption (Figure 1a) because the cell must be sizes (Post et al., 1982), which likely also reduces the equally clear of oxygen even at very low growth and specific oxygen-invasion rate. nitrogen fixation rates. Azotobacter encodes and Each of these strategies demands that the organism expresses cytochrome bd, which has high oxygen invests resources in nitrogen fixation that could consumption relative to ATP production (Poole and otherwise be used for other activities, such as carbon Hill, 1997). The reduction of growth efficiency with fixation or biosynthesis, offsetting the ecological increasing oxygen concentration was also reflected advantage of nitrogen fixation. The resulting reduc- in a lower standing stock of protein (Kuhl and Oelze, tion in growth rate and/or efficiency is the key to 1988b) in Figure 1b. At the lowest oxygen concen- understanding the biogeography of nitrogen fixation tration (12 μM) there was a sharp change in the slope in the environment (for example, Staal et al., 2003; at a dilution rate of ~ 0.1 per day. Monteiro et al., 2010; Dutkiewicz et al., 2012). However, it was noted that the increase in In current ecological and biogeochemical simula- respiration is not linear with oxygen concentration, tions, this cost is typically empirically imposed increasing less rapidly at concentrations above (for example, Krishnamurthy et al., 2007; μ Dutkiewicz et al., 2012; Stukel et al., 2014). Here 70 M (Oelze, 2000) suggesting that other protection we present a mechanistic and quantitative approach mechanisms must also be at play. A. vinelandii is to modeling the cost of nitrogen fixation and its also observed to increase in cell size in more associated oxygen management. Although the model oxygenated cultures (Post et al., 1982) and to form represents a generalized approach, we focus on an external alginate capsule as a barrier to oxygen the heterotrophic, nitrogen-fixing soil bacterium, diffusion, which increases in molecular weight and A. vinelandii, for which extensive, quantitative gluronic acid content with higher oxygen conditions laboratory characterizations have been published (Sabra et al., 2000). (for example, Post et al., 1982, 1983a, b; Kuhla and The thorough characterization of the energetics of Oelze, 1988a, b; Allman et al., 1990; Poole and Hill, A. vinelandii in the laboratory (for example, Post 1997; Oelze, 2000; Dixon and Kahn, 2004). et al., 1982; Bühler, et al., 1987a, b; Kuhla and Oelze, Laboratory cultures of Azotobacter (for example, 1988a, b; Oelze 2000) provides an excellent oppor- Kuhla and Oelze, 1988a, b) have demonstrated a tunity to develop a quantitative, mechanistic model decrease in growth efficiency at all growth rates as of nitrogen-fixer physiology, which we can employ the ambient concentration of oxygen in the medium both as a diagnostic tool and in dynamic ecological was increased. This was manifested as an increased simulations. Shortly, we will present such a model, carbohydrate cost, which has been interpreted as but first we consider the general principle that enhanced energetically uncoupled respiration underpins it. (exceeding the level required for biosynthesis; Nagai and Aiba, 1972; Kuhla and Oelze, 1988b) to manage intracellular oxygen concentration and Materials and methods maintain functional nitrogenase, hereafter termed ‘respiratory protection’ (Dalton and Postgate, 1969; In this section, we describe the core equations of the Poole and Hill, 1997). This is illustrated in Figure 1a model. The entire equations are summarized in (data in circles; lines represent a model discussed Supplementary Material S4 and the nomenclature later), in which the specific sucrose consumption is provided in Supplementary Material S5. The ISME Journal Direct and indirect costs of nitrogen fixation K Inomura et al 168 Intracellular oxygen balance [O2]C = 0 in Equation (4) and re-arranging: Oxygen management is a key cost for nitrogen fixers ÀÁ : that we seek to quantitatively model. First consider R ¼ 4prk ½O þP À mQ Y O2 BIO þ R ð5Þ the rate of change of the intracellular oxygen, P O2 2 O2 C S m QO2 (mol O2 per cell) in a spherical microbe: The required RP is the difference between sources dQ ÀÁ due to oxygenesis and diffusive invasion, and the O2 ¼ P þ 4prk ½O ½O ðR þ R þ R Þ demand from