Comparing two strategies of counter-defence against plant toxins: A modeling study on plant-herbivore interactions

Various herbivorous insects prefer plants of the Brassicaceae family as their hosts, although they are toxic. The two-component chemical defence system of the Brassicaceae against herbivores consists of glucosinolates (GLS) and the activating enzyme myrosinase. GLS hydrolysis by myrosinase leads to isothiocyanate (ITC) products, which are toxic and deterrent to many insect herbivores. Some insects that feed on Brassicaceae, however, have evolved speciﬁc adaptations (called counter-defences) against GLS. Two diﬀerent types of counter-defences can be distinguished: a preemptive counter-defence that prevents the GLS from being hydrolysed to ITC due to metabolic redirection and direct counter-defence, where the ITC is formed, but then metabolized to a non-toxic conjugate. Preemptive counter-defence is believed to be more eﬃcient due to the lower exposure to ITC


Introduction
One of the best studied plant chemical defences are the glucosinolates (GLS), found principally in the Brassicaceae and related families.GLS are accompanied by a glucohydrolase called myrosinase that upon herbivory converts GLS into active forms, which are toxic and deterrent to herbivores (Halkier et al. 2006;Wittstock et al. 2003).The most widespread active forms of GLS are isothiocyanates (ITC), which have been demonstrated to be toxic to many insect herbivores (Wittstock et al. 2010;Sun et al. 2019).Despite the GLS-myrosinase system, some insects are observed to feed on GLS-containing plants.In several cases, these insects have been demonstrated to possess different types of detoxification enzymes (Jeschke et al. 2016;Zou et al. 2016;Schramm et al. 2012).
Specialist feeding insects that feed exclusively on GLS-containing plants often convert GLS prior to myrosinase activation to a metabolite that is not activated by myrosinase.This detoxification scheme can be referred to as a preemptive counter-defence, because it avoids the formation of toxic ITC.For example, larvae of the large cabbage white (Pieris rapae) redirect GLS hydrolysis to form less toxic nitriles by using a nitrile-specifier protein (NSP) (Wittstock et al. 2004).Another example is provided by the larvae of the diamondback moth (Plutella xylostella) that desulfate GLS before they can be hydrolyzed (Ratzka et al. 2002).However, a portion of GLS can escape being metabolized by these preemptive mechanisms and produce ITC products via myrosinase-catalysed hydrolysis (Jeschke et al. 2017).
Another adaption of some specialist feeders is to absorb or accumulate GLS in their bodies for their own defence (Petschenka et al. 2016;Beran et al. 2019;Yang et al. 2020;Sporer et al. 2021).For example, larvae of the turnip sawfly (Athalia rosae L.) store the GLS of their host plants in their haemolymph (Müller et al. 2001), while larvae and also the adults of horseradish flea beetles (Phyllotreta armoraciae) absorb GLS (Sporer et al. 2021).Hydrolysis of GLS by myrosinase is avoided by rapid adsorption after ingestion and by partial inhibition of myrosinase activity (Sporer et al. 2021).This adaptation can also be considered a type of preemptive counter-defence.However, a portion of GLS can escape the sequestration process and produce ITC through myrosinase-catalyzed hydrolysis (Yang et al. 2020;Sporer et al. 2021).
In contrast to specialist feeders, generalists feed only occasionally on GLS-containing plants and typically do not possess preemptive detoxification systems.Once ITC has been formed, part of it is detoxified directly via conjugation to the tripeptide glutathione (GSH) (Yu 1987;Wadleigh et al. 1988;Schramm et al. 2012).Therefore, we call this adaptation direct counter-defence.Experimental studies have reported that lepidopteran generalists (e.g.Spodoptera littoralis, S. exigua, Trichoplusia ni, Mamestra brassicae and Helicoverpa armigera) employ this detoxification strategy.In this case, a major portion of the ITC is not conjugated to GSH, but is released in the faeces (Schramm et al. 2012;Jeschke et al. 2017).
Experimental studies show that specialist feeders generally perform significantly better on GLS-containing plants than generalists (Li et al. 2000;Hopkins et al. 2009;Sarosh et al. 2010;Rohr et al. 2011) presumably due to lower exposure to ITC.For example, when the preemptive desulfation detoxification system of P.
xylostella was knocked-down by interference RNA, the level of ITC present in the gut increased by over ten-fold (Sun et al. 2019).Thus, preemptive counter-defence appears to be superior to direct counterdefence.However, it is not clear if preemptive detoxification actually involves less ITC exposure than direct detoxification, and this is difficult to measure experimentally at short intervals in a time course.
Here, we attempt to model the metabolism of GLS in specialist and generalist feeders to determine the theoretical exposure of insects to ITC during preemptive vs. direct detoxification.Mathematical modelling helps to understand the change in substrate concentration (plant defence compounds in our case) over time (Johnson et al. 2011;Srinivasan 2022;Knoke et al. 2009).By developing two different ordinary differential equation models, we simulate the dynamics of ITC concentrations in these two cases.Our results show less ITC exposure for insects with a preemptive counter-defence than for those relying on direct counter-defence, where the overall exposures to ITC (for specialists and generalists, respectively) are obtained from the area under the ITC curves (Wagner et al. 1985;Schuster et al. 2019).Our models also help to explain how both counter-defences may entirely degrade the host plant defence.

Models and results
We develop two different deterministic models, one for preemptive counter-defence and the other for direct counter-defence.For the model formulation, we assume herbivory and plant GLS degradation are simultaneous processes.Therefore, plant GLS degradation (either by myrosinase or the preemptive detoxification by specialists) starts as soon as herbivory begins.On the other hand, ITC detoxification (direct detoxification by generalists) starts as soon as the ITC contact detoxification enzymes.For simplicity, we assume that GLS are only a constitutive plant defence (Dicke 1998), i.e. that they are present in plants in a fixed amount, and their accumulation is not induced by herbivory.

Preemptive counter-defence
In case of insects with a preemptive detoxification system, let α be the rate constant of plant GLS degradation by the preemptive detoxification enzyme, whereas β be the rate constant of ITC formation by the hydrolysis of GLS that escape preemptive detoxification.Further, the free ITC in the insect gut are released in the faeces with a rate constant, γ.Based on mass-action kinetics, the rate equations are: where S P is the plant GLS concentration and T P is the ITC concentration at time t for insects with preemptive counter-defence.The model ( 1) has an equilibrium point (0, 0), which is asymptotically stable.So, without doubt, the preemptive counter-defence can degrade the ITC concentration to 0. Since the model ( 1) is a simple linear ODE system, the equations can be solved analytically: where S P0 is the initial plant GLS concentration that insects with a preemptive detoxification system are exposed to.The time-course of model ( 1) is shown in Figure 1 (A).

Direct counter-defence
In the case of insects with a direct detoxification system, let δ be the rate constant at which plant GLS are hydrolysed to ITC by myrosinase, µ be the rate constant at which ITC is reacted to produce ITC-conjugates, whereas with a rate constant η, the unmetabolized ITC gets released in the faeces.Eventually, the active portion of ITC is decreased with an overall rate constant µ + η.The rate equations are: where the subscript D refers to direct counter-defence.The only equilibrium point of model ( 3) is (0, 0), which is also asymptotically stable.Similar to the preemptive counter-defence, direct counter-defence can also degrade the ITC concentration to 0. The time-course of model ( 3) is shown in Figure 1 (B).Due to its simplicity, model (3) can also be solved analytically: where S D0 is the initial plant GLS concentration that insects with a direct detoxification are exposed to.2b) and (4b), we obtain: It is worth noting that the parameter δ does not appear in the formula for AU C D .Moreover, note that S P0 and S D0 are not necessarily equal to each other.The feeding capacity of insects with preemptive counterdefence may differ from the insects with direct counter-defence, if they feed on plants of different size, or they stop feeding in the middle and move to a different patch of plants.

Comparison
To make a comparison under equal conditions, we assume that insects with preemptive and direct detoxification systems feed on plants or patches of plants that are identical in GLS concentration.Therefore, insects with the two types of detoxification are initially exposed to an equal volume of plant GLS, i.e.
S P0 = S D0 = S 0 .By comparing the ITC exposure eqs.( 5a) and (5b), proving AU C P < AU C D is enough to explain why the negative effects of ITC are higher in insects with direct rather than preemptory detoxification.Hence, to prove: From the available experimental results, we can establish some relationships among the parameters of the inequality (6).
Property 1.For an insect with a preemptive detoxification system, only a small amount of GLS escape to form ITC, whereas most of the GLS is detoxified, determined by GC-MS analysis (Wittstock et al. 2004), LC-MS analysis and direct radioactivity measurement (Jeschke et al. 2017).Thus, we obtain β < α.
Property 2. In direct detoxification, the major portion of free ITC is excreted unmetabolized, whereas a smaller portion is converted to non-toxic conjugates, measured by LC-MS analysis and flux measurements with radioactive labelling (Schramm et al. 2012;Jeschke et al. 2017).Hence, µ is very small and µ < η.
Property 3. Without loss of generality, we consider γ ≈ η (but not equal) by assuming that the excretion mechanism is more or less the same for all insects.Therefore, µ < γ, following prop.(2).
Theorem 1. AU C P < AU C D or inequality ( 6) is always true for β ≤ α.
In the second case, the inequality (6) can be transformed into: The l.h.s. of inequality ( 6) is < 1 for any α and β, while the r.h.s. of inequality ( 6) is ≥ 1.This implies inequality (6).
Theorem 1 explains that if β ≤ α is satisfied, preemptive counter-defence is stronger than direct counterdefence, shown in Figure 2.However, it does not mean that β > α makes preemptive counter-defence inferior, see Figure 3 (A).On the contrary, it can be proved that preemptive counter-defence remains superior under the conditions stated in the following theorem (below).Moreover, it is justified to assume that β ̸ ≫ α because if preemptive counter-defence is observed in plant-insect interactions, it is always found to be efficient enough that not almost the entire plant GLS is hydrolysed to ITC.Proof.In case of γ ≥ µ + η, the proof is similar to case (1) of Theorem (1).
This case is of special interest because the superiority of preemptive counter-defence is then less intuitive.
Remark 1. Theoretically, a direct counter-defence may perform better if β > α, µ ̸ → 0 and η being significantly greater than γ, shown in Figure 3 (B).However, that is an unrealistic case, because γ and η should not differ much and µ is expected to be much lower than γ and η, explained in props.( 1), ( 2) and (3).
Remark 2. We did not make a direct comparison between the dynamic ITC concentrations T P and T D , because to verify whether or not T D − T P > 0, we need to establish relations among the parameters α, β and δ.It can be assumed that δ < α + β, because insects with direct counter-defence, feed slowly on toxic hosts (Jeschke et al. 2021;Zalucki et al. 2021).However, we have to be more specific to make such parameter comparisons.Fortunately, AU C D in eq. ( 5b) is free of δ.Therefore, we do not require a relation between α, β and δ to compare between the quantified toxin exposures AU C P and AU C D (eq. ( 6)).

Discussion
Insect herbivores employ two different strategies to detoxify activated plant defences like GLS.There is no a priori reason why herbivores could not possess both preemptory and direct counter-defences, except the potentially high metabolic costs.Our work shows that 1.A preemptive counter-defence always outcompetes a direct counter-defence, as explained by Theorems 1 and 2.
2. Although the ITC exposure is comparatively low when a preemptive counter-defence is operating, it is not negligible, because AU C P is a positive value.A negligible exposure to ITC is possible if AU C P → 0, which can only be attained through β ≪ α.
The universal superiority of preemptive vs. direct counter-defence guarantees that herbivores possessing this strategy have an advantage over other herbivores on toxic host plants because they minimize contact with toxins.The toxic effects of ITC on feeding insects exposed to this toxin (AU C P or AU C D ), cause reductions in feeding rate, growth and survival (Sun et al. 2019;Jeschke et al. 2021;Zalucki et al. 2021).Thus, a low ITC exposure (AU C P ) obviously implies only minor effects on insect feeding behavior, growth and mortality (Li et al. 2000;Hopkins et al. 2009;Rohr et al. 2011), whereas a high AU C D value leads to poor feeding behaviour, slow growth and a high mortality rate (Jeschke et al. 2021;Zalucki et al. 2021).
The lower exposure to ITC in preemptive detoxification (AU C P ) versus direct detoxification (AU C D ) may have an empirical basis due to the location of these reactions in the insect.The preemptive detoxification reactions of GLS, such as desulfation, are known to occur extracellularly in the insect gut lumen by acting on GLS in the plant tissue being digested (Sun et al. 2019).In contrast, once ITC are formed by GLS breakdown in the gut, the direct detoxification reaction, conjugation with glutathione, occurs intracellularly.
The ITC formed thus need to cross through a membrane and enter a cell before being detoxified (Jeschke et al. 2016).This longer path to the site of detoxification in direct counter-defence, allows more opportunities for the ITC to react with target sites than in preemptory detoxification.
The effectiveness of preemptive detoxification does not necessarily mean that insects employing this strategy completely escape the adverse effect of ITC.As described in point (3) above, negative effects occur as long as β ≪ α does not hold.That could explain why some experimental studies report that insect species known to be preemptive detoxifiers of GLS are affected by ITC (Mewis et al. 2005(Mewis et al. , 2006;;Gols et al. 2007Gols et al. , 2008)).For the preemptively detoxifying P. xylostella, larvae feeding on plants without any GLS at all perform significantly better than those on GLS-containing plants, suggesting that some exposure to ITC occurs despite an effective detoxification strategy (Sun et al. 2019).However, preemptory detoxification has also been documented to be very effective, with many studies reporting that species with this strategy are only marginally affected by the GLS-myrosinase defence system of their host plants (Slansky et al. 1977;Blau et al. 1978;Broadway 1995;Li et al. 2000;Sarosh et al. 2010;Rohr et al. 2011).In such cases, β is likely to be much less than α.
Our results may also apply to insects that sequester GLS in their own defence, as these are also reported avoiding the negative effects of ITC (Müller 2009;Müller et al. 2006;Beran et al. 2019;Sporer et al. 2021).
This phenomenon is explainable from the model (1) by assuming α to be the absorption or sequestration rate of GLS, where β remains the rate of GLS hydrolysis.In fact, quick sequestration certainly leads to the situation β ≪ α, a conclusion supported experimentally by the rapid absorption of GLS measured in insect guts of sequestering herbivores (Petschenka et al. 2016;Abdalsamee et al. 2014;Sporer et al. 2021).
In natural systems, many plants of the Brassicaceae that produce GLS constitutively have also been found to accumulate higher concentrations after herbivore damage (Textor et al. 2009;van Dam et al. 1993;Agrawal 1998).Experimental studies report that such GLS induction has noticeable adverse effects on insect herbivores (Agrawal 2000;Agrawal et al. 2003;van Dam et al. 2000).Therefore, accommodating the induction of GLS in model ( 1) or (3) could be of interest in future studies of defence vs. counterdefence paradigms during plant-herbivore interactions.Intuitively, we can say that the induction of GLS may drastically increase the ITC exposure (i.e.AU C P and AU C D ).As a result, the toxic effect of ITC can be raised.
Our study adds to experimental results indicating that herbivore feeding on GLS-containing plants can be costly, even for preemptory detoxification systems.Thus, it may seem puzzling that specialist herbivores with such detoxification systems use plant GLS or ITC content as a cue for their oviposition and feeding preference (Mewis et al. 2002;Renwick 2002;Miles et al. 2005;Badenes-Perez et al. 2020), and thus prefer GLC-containing plants compared to plants without GLS despite the costs.A possible explanation is the reduced competition enjoyed on GLS-containing plants because of their generally toxic nature to most herbivores.From an evolutionary perspective, feeding on plants with GLS or other toxins must benefit herbivores.Otherwise, the evolutionary origin of detoxification traits (Dobzhansky 1968;Darwin 1859) is hard to understand.Comparative fitness studies on toxic vs. non-toxic plants, both with and without competition, may help explain the shift to toxic plants.

Figure 2 :
Figure 2: Area enclosed by ITC concentrations during the herbivory period, obtained from model eq.(1) and model eq.(3), respectively.Parameter values, same as in Figure 1.