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Host-symbiont interaction model explains non-monotonic response of soybean growth and seed production to nano-CeO2 exposure Tin Klanjscek, Erik B Muller, Patricia A. Holden, and Roger M. Nisbet Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.6b06618 • Publication Date (Web): 23 Mar 2017 Downloaded from http://pubs.acs.org on March 26, 2017

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Environmental Science & Technology

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Host-symbiont interaction model

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explains non-monotonic response of

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soybean growth and seed production

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to nano-CeO2 exposure

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Tin Klanjšček*1,2, Erik B. Muller3, Patricia A. Holden4, Roger M. Nisbet1

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Santa Barbara, CA 93106-9610, USA

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Department of Ecology, Evolution and Marine Biology, University of California Santa Barbara,

Ruđer Bošković Institute, Zagreb, 10000 Croatia Marine Science Institute, University of California Santa Barbara, Santa Barbara, CA 93106-

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9610, USA

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Barbara, Santa Barbara, CA 93106-5131, USA

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* corresponding author, Tin Klanjscek, ORCID: 0000-0002-9341-344X

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Address: Ruđer Bošković Institute, P.O. Box 180, Bijenička 54, HR-10000 Zagreb, Croatia.

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E-mail: [email protected], [email protected]

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Phone: +38514561131; Fax: +38514680242

Bren School of Environmental Science and Management, University of California Santa

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ACS Paragon Plus Environment

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Abstract

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Recent nanotoxicity studies have demonstrated non-monotonic dose-response mechanisms for

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planted soybean that have a symbiotic relationship with bacteroids in their root nodules:

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reduction of growth and seed production was greater for low, as compared to high, exposures.

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To investigate mechanistic underpinnings of the observed patterns, we formulated an energy

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budget model coupled to a toxicokinetic module describing bioaccumulation, and two

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toxicodynamic modules describing respectively toxic effects on host plant and symbionts. By

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fitting data on plants exposed to engineered CeO2 nanoparticles to the newly formulated model,

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we show that the non-monotonic patterns can be explained as the interaction of two, individually

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monotonic, dose-response processes: one for the plant, and the other for the symbiont. We

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further validate the newly formulated model by showing that, without the need for additional

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parameters, the model successfully predicts changes in dinitrogen fixation potential as a

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function of exposure (dinitrogen fixation potential data not used in model fitting). The symbiont

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buffers overall toxicity only when, in the absence of exposure to a toxicant, it has a parasitic

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interaction with the host plant. If the interaction is mutualistic or commensal, there is no

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buffering and only monotonic toxic responses are possible. Since the model is based on general

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biological principles, we expect it to be applicable to other similar symbiotic systems, especially

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other nodule-forming legumes.

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Introduction

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Ecological nanotoxicology bridges multiple levels of biological organization to help understand

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and minimize negative impacts of an ever-increasing input of engineered nanomaterials (ENMs)

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on ecosystem function and resulting ecosystem services(1). Recent efforts in ecological

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nanotoxicology include coherent experimental and theoretical efforts to investigate mechanisms

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of ENM action and toxicity on many aquatic and terrestrial (eco)systems (e.g. Xia et al. (2) and


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references therein). These efforts have identified a number of mechanisms specific to ENMs

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and materials that comprise ENMs. In particular, elevated oxidative stress has for long been

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identified as a major contributor to cellular damage resulting from ENM exposure (3–6). The

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cascading effects of oxidative stress from biochemical, to individual, to population-level scales

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of biological organization have been modeled using Dynamic Energy Budget (DEB) models (7–

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9). These models assume that exposure increases oxidative stress, which results in damage to

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cells and potentially to whole organisms; in particular, Klanjscek et al. (10) developed theory

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showing that with only some non-restrictive assumptions, correlation between exposure, ROS,

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and cellular damage is expected. In the absence of other confounding factors, this would at the

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organism level translate into a monotonic dose-response pattern, i.e. negative effects that

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increase with exposure. Such monotonic responses in many endpoints to metal oxide

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nanoparticles have been reported for a number of plants (see Du et al. (11) for a comprehensive

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review).

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Recent studies on effects of CeO2 nanoparticles on soybean revealed a much more complex

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pattern of impacts. Prior publications (6,12) report on a large number of endpoints

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characterizing the effects on soybean of exposure to three levels of CeO2 nanoparticle. Of

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particular importance was their finding that dinitrogen fixation potential was impacted, as has

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been observed for some other plants (13) (but see Moll et al. (14), who found no change in

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dinitrogen fixation by clover in response to nano-CeO2 exposure). Since dinitrogen fixation is an

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important function directly related to ecosystem services (food production and nutrient cycling),

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the impact could have far-reaching consequences. Prior publications (6,12) report that some

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measured quantities such as bioaccumulation, oxidative stress, and leaf damage, exhibit

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monotonic dose-responses. Other endpoints, however, exhibit a non-monotone, zig-zagged or

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U-shaped dose-response. Stem length, pods and seeds per plant, leaf cover, dry mass, and

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growth rate exhibit the largest effects for the smallest exposure (0.1 g/kg), while increasing the


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exposure (to 0.5 g/kg and 1 g/kg) reduces the toxic effect. Effects of the exposure on the plant

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may interact with the control on dinitrogen fixation to produce the atypical correlations between

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exposure, oxidative stress, and other measured quantities (6).

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From a modelling perspective, the non-monotone patterns suggest two competing processes,

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one of which promotes, while the other mitigates the response. For example, Conolly and Lutz

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(15) give four instances of non-monotone dose-responses involving competing molecular

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processes. In the soybean studies described above (6,12), the promoting process is most

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pronounced for low exposures, and the second process mitigates responses for mid- and high

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exposures (with the potential for the promoting process to again dominate for large exposures).

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Noting that endpoints exhibiting ‘standard’ toxicity patterns relate to mechanisms of toxicity (e.g.

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oxidative stress), while the non-monotone patterns (e.g. growth rate) relate to energy utilization,

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we hypothesize that understanding the origins of the patterns requires a coherent inclusion of

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mechanisms governing both energetics and toxicity.

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We investigate the hypothesis by creating a simple model that is able to integrate

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measurements relating to both toxicity and energetics. The model differs from previous models

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describing non-monotonic dose-response curves, in that one of the processes modeled involves

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inter-organism interactions rather than molecular kinetics. Starting with a bioenergetic module

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capturing energy utilization for growth and reproduction, we (i) implement a rudimentary

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symbiotic interaction between the plant and bacteroids, (ii) integrate a toxicokinetic module (16)

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for cerium bioaccumulation, and (iii) couple the toxicokinetic module to a toxicodynamic module

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(17) that describes toxic effects on the plant and bacteroids. We fit the model to the measured

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growth curves, bioaccumulation, and measures of reproductive output. We use data on

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dinitrogen fixation potential to ground-truth the model and guide discussion of our results.

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Methods

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The model consists of three integrated modules: a bioenergetic module describing acquisition

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and utilization of energy, a toxicokinetic module describing the distribution of cerium within the

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compartments of the energy budget module, and a toxicodynamic module capturing the toxic

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effects (Figure 1). An overview of model equations, state variables, parameters, and units is

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provided in Table 1.

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Figure 1: Overview of the model with energy budget, toxicokinetic, and toxicodynamic modules. Net

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production flux (P) is the rate of production of utilizable photosynthesized energy left after subtracting the

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maintenance needs of the plant, and accounting for the net energy loss or gain from supporting dinitrogen

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fixation by bacteroids. The production flux is either committed to growth of the above- and below-ground

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biomass (both proportional to total plant somatic biomass (excluding seeds), W), or reproductive output (S

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or ∑, see text for definitions), with the ratio of the two commitments determined by Θ. Bioaccumulation

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due to exposure of the root increases the bioaccumulated toxicant, Q, which affects the production flux by

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decreasing photosynthesis and/or increasing maintenance, and reducing the interaction with N2-fixing

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bacteroids (e.g. by instituting bacteroid mortality in response to the toxicant burden).

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Our bioenergetics module tracks the utilization of energy from photosynthesis (Figure 1).

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Photosynthesis results in gross production of photosynthate, Φ, part of which is used to meet

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maintenance requirements and provide energy to support dinitrogen fixation by bacteroids. We

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use the term production flux (P) to represent the rate at which the remaining energy becomes

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available to support growth and reproduction, with a fraction Θ of the production flux assigned to

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reproduction, and (1- Θ) to increase in plant biomass (growth). Both reproduction and growth

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are assumed to be proportional to energy invested. We further assume:


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1. environmental conditions are constant;

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2. the ratio of above and below-ground biomass is constant (see Figure S1);

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3. production flux is proportional to plant biomass;

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4. bioaccumulation is proportional to the root biomass;

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5. investment to reproduction starts at a fixed age denoted by tS;

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6. in the absence of exposure to a toxicant, bacteroid biomass is proportional to below-

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ground biomass, but contributes negligibly to the weight of the plant; 7. both the energy demands of the bacteroids and their contributions to the production flux are proportional to their biomass.

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Assumption 6 ensures that the dynamics of bacteroid biomass can be represented

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mathematically from the below-ground biomass, while assumption 2 ensures that both above-

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and below-ground biomass can be represented by a single state variable (plant biomass).

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Hence, through assumptions 2 and 6, the two state variables of the bioenergetic model (plant

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biomass and reproductive output) account for four compartments: above-ground and below-

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ground biomass, reproductive buffer, and bacteroids. Although we do not explicitly include

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nitrogen dynamics in the model, the parameters linked to assumption 7 allow both positive and

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negative net impact of N2-fixing bacteroids on production flux. We make no prior assumptions

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about the impact of bacteroids on plant energy budgets, but infer this impact from the data and

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model fits. The symbionts may, depending on species and environment, operate as mutualists

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or parasites.

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Protein biosynthesis represents a major cost of seed production and is, therefore, important for

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estimating energy committed to reproduction. Data on seed production collected by the

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experiment in Priester et al. (12) included seed count for each plant, and protein density of

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seeds (mg protein per g of seed dry weight). However, total seed protein content could not be

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determined because total seed weight per plant was not measured.


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To extract as much information on seeds as possible, we used additional assumptions to create

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two plausible measures of reproduction. First, by assuming that all seeds are of equal size,

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weight, and protein density, we could use the recorded seed count, S, as a measure of

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reproduction. Second, we assumed all seeds have equal mass. Then, we defined scaled seed

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protein, ∑, as the seed count multiplied by the protein density. The scaled seed protein

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represents total protein content of seeds scaled to mass of a single seed, thus representing

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protein content. Since ∑ is the product of the two endpoints (scaled seed protein and seed

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count), it scores both seed count and protein content.

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The toxicokinetic module accounts for uptake of toxicant by the plant. Cerium, administered in

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the form of nano-CeO2 has been shown to bioaccumulate primarily in the root, with some

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transport to the aboveground biomass (12) including in the form of nano-CeO2 (18) that exerts

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oxidative stress in the leaves (6). Using a common approach in cases where physico-chemical

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details of toxicant transport are not known (e.g. Ashauer and Escher (19) and Jager et al. (20)),

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we assumed that (i) the concentration of bioavailable cerium is proportional to nominal

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concentration, (ii) toxicant uptake by the plant is a linear function of outside toxicant

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concentration and the soil-plant interface area (which, in turn, is proportional to root biomass –

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giving rise to Assumption 4 above), and (iii) the bioaccumulated toxicant is evenly distributed in

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the root, with no transport to above-ground biomass.

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The toxicodynamic module has two sub-modules that capture effects of bioaccumulated toxicant

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on the plant and on the bacteroids. The plant sub-module (fP) reduces the production flux, while

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the bacteroid sub-module (fR) reduces the total activity of bacteroids and their net contribution to

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the production flux (shown to be negative during parameter estimation). While specifying

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functional forms for the toxicodynamic sub-modules, we focused on minimizing the number of

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parameters while keeping the overall response to exposure flexible yet realistic. The functional

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forms needed to have no effect when there is no exposure (i.e. fP,R(0)=1), and converge to


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maximum effect for large internal cerium concentration. Hill functions satisfy the requirements,

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and are often utilized when investigating concentration-dependent effects of biological systems.

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We used Hill functions to construct the toxicodynamic sub-modules presented in the main text

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(Table 1). In the SI, we assess sensitivity of our analysis on the choice of functional form of the

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toxicodynamic module by considering four alternative functional forms featuring (i) constant

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negative effect upon exposure, (ii) exponential decay as a function of bioaccumulated toxicant

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concentration, (iii) exponential decay towards a non-zero asymptote, and (iv) logarithmic

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response. A total of 10 combinations of functional forms for the two sub-modules were

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investigated (SI, Table S1).

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Additional analysis using the original choice of toxicodynamc functions was performed to

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ascertain the sensitivity of the unimodal effect to model parameters. We used two metrics to

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characterize the strength of the unimodal response: the magnitudes of the initial decline, and of

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the subsequent recovery. Details are in section “Parameter Sensitivity Analysis” of the SI.

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Parameter estimation

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The parameters in Table 1 were estimated by fitting to the following data from Priester et al.

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(12): final biomass measurements of the leaf, stem, root, and nodule biomass, final

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concentrations of cerium in roots and leaves, timing of flowering, final seed count, and time

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series of plant height. Additionally, we used data on final fraction of protein in seeds from the

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same experiments (6).

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The fraction of below-ground biomass (qW) was estimated as the mean of final ratios of below-

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ground and total dry weights (without seed weight). Time of maturation (ts) was taken to be

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equal to the date of first observation of flowers. The time series used as a proxy for growth

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(stem height) was converted to the state variable (biomass, W) using parameter δ calculated by


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least squares fitting of the total biomass to final height measurements (Figure S1, bottom left

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plot). The average of the initial plant height measurements for each treatment was used as the

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initial height for all plants in that treatment in simulations, and converted to W using δ. The

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toxicant partitioning coefficient (vQ) was estimated as the mean of the ratios of measured final

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toxicant concentrations in leaf and root biomass using data for medium and high exposures (the

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low exposure data were not used because bioaccumulation was extremely low). Note that

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photosynthate (Φ) is only implicitly used, and that units of Φ (photosynthate units, ups) can be

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set without any loss of generality. Since only the linear combination of yW and φ is used, we

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choose such ups that φyW=1 ups(J day)-1.

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Models were fitted to data by maximizing likelihoods while assuming deviations between models

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and data were due to additive normally distributed error. First, growth-related parameters, pT

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and Θ. were estimated from stem length data series. Parameters of the toxicokinetic and

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toxicodynamic modules (specific to each module), reproductive yield (yS and y∑), and the net

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energetic effect of dinitrogen fixation to the production flux (in terms of proportion, qR), were

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estimated using growth series of exposed plants, data on bioaccumulation, and the reproductive

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output by maximizing a sum of (1) log-likelihood function for growth series, and (2) log-likelihood

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function for endpoints (bioaccumulation and a reproductive output). Both log-likelihood functions

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were based on additive normally distributed error, with optimizations performed using the

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Nelder-Mead simplex algorithm.

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Note that growth data only allow estimates of the total production flux, so they could not be used

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to fit the net contribution of bacteroids to plant growth, qR. Importantly, however, responses of

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growth and reproduction to exposure allowed us to differentiate between contributions of

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bacteroids and the plant to the production flux.


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Results

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Our hypothesis on the type of the symbiotic interaction is sufficient to explain the

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observed patterns in growth, bioaccumulation, and reproduction. The model fits presented

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in the first three plot columns of Figure 2 (titles ‘Growth’, ‘Bioaccumulation’, and ‘Reproduction’)

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illustrate that the model is able to capture important features of the observed dynamics:

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non-monotonic (negative) effect of exposure on plant (stem height) growth that is stronger for low exposures than for higher exposures,

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bioaccumulation pattern that increases monotonically with exposure, and

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non-monotonic pattern (lowest exposure begets the strongest effect) of reproductive

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responses to exposure.

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The reproductive patterns were simulated using a single set of initial conditions for all

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exposures. The agreement between the data and the model improves further when the initial

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condition is allowed to vary to match initial conditions used for the growth curves (Figure S3).

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Figure 2: Model fits of the impact of nano-CeO2 exposure on soybean growth, bioaccumulation, and

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reproduction, and predictions of bacteroid activity. Each row shows data and model runs for growth (first

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column), bioaccumulation (second column), reproduction (third column), and predicted N2-fixing bacteroid

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activity (fourth column). Top row has been simulated using scaled seed protein, and the second row using


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seed count as a measure of reproductive output. Toxicodynamic modules listed in Table 1 (with only two

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free parameters) have been used. Data plotted in the first three columns were used to fit the model:

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growth curves (first column), cerium bioaccumulation (second column), and two measures of reproduction

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(third column): recorded seed count (top), and scaled seed protein (bottom). The last column compares

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predicted bacteroid activity with data on measured N2 fixation potential (normalized to root nodule dry

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biomass (12)) as a proportion of the largest mean. The black curve represents model predictions of root

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nodule bacteroid activity (normalized to maximum value) as a function of exposure. Blue lines, stars:

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control (no exposure). Red lines, circles: low exposure (0.1 g/kg). Green lines, triangles upwards: medium

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exposure (0.5 g/kg). Cyan lines, triangles downwards: high exposure (1 g/kg). Black lines: simulations.

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In the absence of exposure, contribution of root nodule symbioses to plant growth is

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negative (for particular experimental conditions). Although it is impossible to use only data

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for the control to distinguish relative contributions to the production flux of the plant’s own

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assimilation and of the net contribution from bacteroid activity, the data on toxicity help

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distinguish the two. In particular, the increase in plant growth and reproduction observed at the

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highest relative to the intermediate exposure level can only be achieved for negative

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contributions of the symbioses to the production flux (qR0), our model would predict

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that all toxicity patterns should be monotonic. However, mechanistic insight into the transition

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from parasitism to mutualism would require a model that recognizes explicitly the nitrogen

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fluxes, for example by invoking the formalism of dynamic energy budget theory as in one study

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of the symbiosis of corals and their symbionts (29).

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All legume-bacteroid symbioses are clearly potentially susceptible to the environmentally-

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induced toxicity buffering mediated by the symbiotic interactions modeled here, but other similar

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symbiotic systems may be susceptible as well. Plants and ectomycorrhizal fungi respond to

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manipulation of the fungal community (30) and plant growth could thereby be buffered against

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toxicity in environments where a fungal species (directly or indirectly) competes with the plant

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for specific nutrients. Indeed, buffering of toxicity for a focal species through indirect effects


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mediated by interaction with natural enemies is common in nature (31). We have here

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demonstrated that similar responses are likely when a host organism interacts with its endo-

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symbionts.

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Supporting Information: cover sheet; argumentation to support height as a measure of weight;

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list of alternative toxicodynamic modules; simulations for all toxicodynamic modules with a

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unique initial condition; simulations for all toxicodynamic modules with interpolated initial

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conditions; parameter values; parameter sensitivity analysis; and toxicokinetics and

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toxicodynamics.

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ACKNOWLEDGEMENTS

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We thank J.H. Priester for providing data in digital form and helping with useful information and

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insights, Y. Wang and J. Rohr for valuable discussions and advice, and T. Jager for sharing

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statistical programs. This research was primarily funded by the National Science Foundation

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(NSF) and the U.S. Environmental Protection Agency (EPA) under Cooperative Agreements

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DBI-0830117 and 1266377 (to P.A.H and R.M.N.) and by the US Environmental Protection

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Agency under STAR grant 835797 to RMN and EM. Additional funding was provided by the

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Croatian National Science Foundation (HRZZ) under the project 2202-ACCTA. Any opinions,

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findings, and conclusions expressed in this material are those of the author(s) and do not

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necessarily reflect those of the NSF, the EPA, or the HRZZ. This work has not been subjected

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to EPA review and no official endorsement should be inferred.

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Page 22 of 25

Table 1: Summary of model dynamics.

MODEL EQUATIONS State variable Total plant dry biomass, W (g) Seed count, S (count), or Scaled seed protein (∑)

Dynamics

Parameters and units

dW = yW (1 − Θ) P dt

yW - growth yield (g/J)

dS = yS ΘP dt

yS - reproductive yield (seeds/J) yΣ - scaled seed protein yield in

OR

milligrams of protein per Joule time

dΣ = yΣ Θ P dt Bioaccumulated cerium in the plant, Q (mg of

gram of plant dry mass

dQ = vQ qW X AW dt

( mg Jg )

vQ - bioaccumulation rate constant

    mg(Ce)     g(root) day  g (CeO2 ) kg ( soil )    

cerium)

qW - fraction of below-ground biomass in total biomass (g(root)/g(plant))

X A - environmental toxicant concentration (g(CeO2)/kg(soil)) FUNCTIONALS Gross production of photosynthate, Φ

Φ = ϕW

φ - biomass-specific gross production rate (ups/(day g))


22

Page 23 of 25


(ups/day) Net production flux, P

P = pT

(J/day)

fW + f R qR Φ (1 + qR )

pT –net production yield (J/ups) qR – net contribution or detraction to the production flux of supporting bacteroids and dinitrogen fixation (n.d.)

Fraction of P dedicated to reproduction (dimensionless)

Below-ground cerium

θ - reproductive switch rate (day-1) t < tS 0  Θ = θ (t − t S ) tS ≤ t ≤ θ −1 + tS ,  tS – age at the onset of reproduction otherwise 1

(

(day)

CB =

concentration, CB (mg

qQ Q

qQ – cerium partitioning coefficient

qW W

between above- and below-ground

Ce/g biomass) Reduction of

)

biomass (n.d.)

fP =

photosynthesis and/or increase in plant

1 γP

 C  1+  B   CP 50 

.

CP50 – below-ground toxicant concentration (proportional to total concentration) for which the

maintenance in response

production (P) is reduced by 50%

to the burden (CB)

(mg/g)

(dimensionless)

γ P - strength of the effect, set to γ P = 1 in fitting (n.d.)

Reduction of net energetic cost (or benefit) of dinitrogen

fR =

1 γR

 C  1+  B   CR 50 

.

CR50 – below-ground cerium concentration for which 50% of bacteroids die (mg/g)


23


fixation in response to

γ R - strength of the effect,

the burden (CB)

set to γ R = 2 in fitting (n.d.)

Page 24 of 25

(dimensionless) Although ten different sets of the toxicodynamic modules (fP and fR) were investigated (Table S1, results shown in Figure S2 and Figure S3), only modules used to generate Figure 2 are listed below; for the nine other combinations of toxicodynamic modules, see Table S1. The units of reproductive yield listed in the table apply only when seeds are considered as the reproductive endpoint. Parameter values for the toxicodynamic modules used for Figure 2 are given in Table S2. The abbreviation ‘ups’ denotes (proprietary) units of photosynthate, and ‘n.d.’ denotes ‘non-dimensional’.


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