Microbial Potlatch: Cell-level adaptation of leakiness of metabolites leads to resilient symbiosis among diverse cells

Microbial communities display extreme diversity, facilitated by the secretion of chemicals that can create new niches. However, it is unclear why cells often secrete even essential metabolites after evolution. By noting that cells can enhance their own growth rate by leakage of essential metabolites, we show that such leaker cells can benefit from coexistence with cells that consume the leaked chemicals in the environment. This leads to an unusual form of mutualism between “leaker” and “consumer” cells, resulting in frequency-dependent coexistence of multiple microbial species, as supported by extensive simulations. Remarkably, such symbiotic relationships generally evolve when each species adapts its leakiness to optimize its own growth rate under crowded conditions and nutrient limitations, leading to ecosystems with diverse species exchanging many metabolites with each other. In addition, such ecosystems are resilient against structural and environmental perturbations. Thus, we present a new basis for diverse, complex microbial ecosystems.

In the present paper, we examined whether and how cell-cell interactions mediated by secreted 59 metabolites can lead to stable coexistence of diverse microbial species (or strains or mutants), 60 rather than the dominance of a single ttest species. We rst show that "leaker" and "consumer" 61 species (i.e., cells that bene t by leaking some chemicals and those that bene t by consuming them, 62 respectively) can immediately develop a mutualistic relationship. We then explore the conditions 63 under which such "leaker-consumer mutualism" is observed and stable. 64 Based on the idea of leaker-consumer mutualism, we will further show that when each coexist-65 ing cell species optimizes its own growth (which may result from adaptation within a generation or 66 evolution over generations), the coexistence of diverse species is achieved and the overall growth 67 rate of the microbial community is enhanced. This novel scenario for symbiosis among diverse 68 species will explain why the single " ttest" species does not dominate as a result of evolution. Fur-69 thermore, we will show that systems with exchange of metabolites among diverse species are where (↵) is the growth rate of each cell species, and Ñ í ≥ ↵ p (↵) (↵) is the average growth rate of 102 all species (Kaneko, 2016). 103 We then investigated the steady state of the population dynamics of multiple species with dif-104 ferent reaction networks, and examined whether they can coexist in a common environment. . CC-BY 4.0 International license available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint this version posted November 7, 2020. ; https://doi.org/10.1101/2020.11.06.370924 doi: bioRxiv preprint

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A simple example of leaker-consumer mutualism: symbiosis between two species 107 In order to exemplify the leaker-consumer mutualism, we rst consider the simplest situation: sym-108 biosis between two cell species in which the leaker cells secrete an essential metabolite and the 109 consumer cells consume it to facilitate their growth.

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For the sake of simplicity, the network structure of the example in Yamagishi et al. (2020)-a 111 simple reaction network that consists of substrate S, enzyme E, ribosome rb, metabolites M 1 and 112 M 2 , biomass BM-is adopted both for the leaker and consumer cells ( Fig. 2A). The equations for 113 the reactions are given below, and the rate constants given below are di erent for the leaker and 114 consumer cells: SôM 2 where the growth rate is de ned as the rate of synthesis of biomass BM from its precursor M 2 , such thus, the leakage (uptake) of M 1 is bene cial only for the former (latter) ( Fig. 2A).

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Our numerical simulations show that the mutualism between the leaker and consumer cells is are large, the leaker and consumer cells can still coexist, but their growth 138 rate is lower than that observed when leaker cells grow in isolation. Thus, parasitism, rather than 139 mutualism, is realized in such cases (Region P in Fig. 2C). This is because excess leakage of nec-140 essary chemical M 1 is disadvantageous to the leaker. Figure 2C, however, also indicates that the . CC-BY 4.0 International license available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint this version posted November 7, 2020. ; https://doi.org/10.1101/2020.11.06.370924 doi: bioRxiv preprint when the degradation rate R deg or environment size V env is too large to allow for su cient accu-

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. CC-BY 4.0 International license available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint this version posted November 7, 2020. ; https://doi.org/10.1101/2020.11.06.370924 doi: bioRxiv preprint Symbiosis among randomly generated networks because of cell-level adaptation 152 To investigate the possibility of leaker-consumer mutualism and symbiosis among more cell species 153 with diverse chemicals, we further considered a model including a variety of cell species with ran-154 domly chosen catalytic networks. The transport of chemicals from one cell species to another can 155 be bidirectional if their membranes are permeable to diverse chemicals, which may lead to a com-156 plex symbiotic relationship. For simplicity, we mainly considered reaction networks including only 157 catalytic reactions such as i + k ô j + k with a catalyst k (the simplest multibody reactions; see also 158 Yamagishi et al. (2020)) and equal rate constants (set at unity), and only a single nutrient (chemical 159 0) is supplied externally. 160 We rst generated a "species pool" containing N = 50 randomly generated networks, and these  (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint this version posted November 7, 2020. ; https://doi.org/10.1101/2020.11.06.370924 doi: bioRxiv preprint  The vertical axis represents the growth rate of each cell species ↵ in isolation, (↵) iso . Cyan and pink arrows indicate the leakage and uptake of each chemical component, respectively. Symbiosis among multiple species increases the growth rate to symbiosis (as indicated on the top), which is higher than the growth rate of each cell species in isolation, (↵) iso . In the numerical simulation, the parameters were set to n = 20, S env = 0.03, V env = 3, D (env) S = 10, D S = 1, R deg = 5 ù 10 *5 , N enzyme = n_5.

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. CC-BY 4.0 International license available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint this version posted November 7, 2020. ; https://doi.org/10.1101/2020.11.06.370924 doi: bioRxiv preprint Cell-level adaptation via leak advantage frequently leads to symbiosis 185 We then statistically examined how frequently such symbiosis was realized (Fig. 4). Figure 4A shows 186 the frequency of symbiotic coexistence of multiple species in a single-nutrient condition. As the 187 number of chemical components n increases, the coexistence of more species is more likely. For 188 n = 30, symbiotic coexistence is achieved for almost all the trials, as long as the cell species with the 189 fastest growth in isolation has at least one leak-advantage chemical. Here, recall that the frequency 190 of leak advantage in isolation increases with n (Yamagishi et al., 2020). 191 In addition, symbiosis is achieved frequently with a wide range of environmental parameters 192 S env and V env (and R deg ) (Fig. 4BC and Fig. S4). Notably, Fig. 4B demonstrates that the frequency 193 of symbiosis decreases as the size of the environment V env increases, unless the environment is 194 too small (V env Ù 1, i.e., the total volume of cells equals that of the environment). Note here that 195 increase in V env (and/or R deg ) weakens cell-cell interactions because the secreted chemicals are di-196 luted; consequently, the growth change due to consumption is suppressed while that due to leak-  (Fig. S5). Interestingly, the frequency of 217 coexistence of multiple species is much smaller (Fig. 4D).

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Notably, when adaptive changes in the di usion coe cients at the cell level are allowed, leak-  , 1971; Hassell and May, 1973). Consistently, for the case with 227 randomly pre-xed di usion coe cients, the frequency of parasitic (symbiotic) relationships de-228 creases (increases) as the number of coexisting species increases (Fig. S6B). Hence, the likelihood 229 of coexistence is lower when the di usion coe cients are xed.

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To further corroborate these results, we also generated a model with null di usion coe cients 231 for chemicals that confer leak advantage (in isolated conditions) and positive random coe cients 232 for chemicals that do not. In this situation, leakage is always disadvantageous in isolated conditions.

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In the absence of leakage of leak-advantage chemicals, the frequency of symbiosis and the average 234 8 of 17 . CC-BY 4.0 International license available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint this version posted November 7, 2020. ; https://doi.org/10.1101/2020.11.06.370924 doi: bioRxiv preprint number of coexisting species were further reduced (Fig. 4D), even though growth promotion due 235 to the uptake of metabolites could still occur.  . CC-BY 4.0 International license available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint this version posted November 7, 2020. ; https://doi.org/10.1101/2020.11.06.370924 doi: bioRxiv preprint Resilience of symbiosis mediated by metabolite exchange 237 Thus far, we investigated if and how symbiosis of diverse cell species with tangled forms of metabo-238 lite exchange is achieved as a result of cell-level adaptation of di usion coe cients. Lastly, we ex-239 amined the stability of communities consisting of diverse cell species that exchange metabolites.

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In particular, we focused on the resilience of symbiotic relationships against the removal of 241 a species that coexisted. In most cases, the removal of one species from the community does 242 not cause the successive extinction of any other species in the community (Fig. 5A). In contrast 243 to the extinction of species in a hierarchical ecosystem with trophic levels, where the removal of 244 some keystone/core species leads to an avalanche of extinctions of downstream species in the hi-245 erarchy (Paine, 1969; Mills et al., 1993; Goyal and Maslov, 2018), such an avalanche of species 246 extinctions hardly occurs in our model (Fig. 5A). In other words, we rarely observe the existence of 247 keystone/core species whose absence prevents many other species from coexisting, and removal 248 of which leads to the extinction of all other species. Hence, the present system with metabolite 249 exchange has a high degree of resilience.

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As shown in Fig. 5A, we did observe a few cases in which removal of one species causes the 251 extinction of most species. In such non-resilient cases, the removed species tended to be ones 252 that dominantly leaked chemicals into the environment. In general, the resilience of the system  nents (i.e., both S Cell and S Chem are large), the system tends to be resilient (Fig. 5B). S Cell and S Chem 265 are also strongly correlated (Fig. 5B), such that when many cell species contribute to leakage, many 266 components are leaked, and vice versa. We now consider two extreme situations to illustrate this 267 correlation: if S Chem = 0 (i.e., only one chemical is leaked to the environment), then S Cell must be 0 268 due to Gause's rule. In contrast, when S Chem is large, S Cell is unlikely to be zero because a large S Chem 269 allows the coexistence of many cells, which in turn can leak more chemicals, leading to large S Cell . CC-BY 4.0 International license available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint this version posted November 7, 2020. ; https://doi.org/10.1101/2020.11.06.370924 doi: bioRxiv preprint . CC-BY 4.0 International license available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint this version posted November 7, 2020. ; https://doi.org/10.1101/2020.11.06.370924 doi: bioRxiv preprint

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In this paper, we elucidated how symbiosis mediated by the exchange of various metabolites 273 among diverse cell species is possible, based on the advantages of metabolite leakage for leaker 274 cells. Resilient symbiosis among diverse species can be achieved when each cell species is allowed 275 to adaptively change the degree of leakage and uptake of metabolites. 276 First, we described the mechanism and conditions for mutualism between leaker and consumer 277 cells. As the density of cells (with leak advantage) is increased, the metabolites secreted by the anisms to suppress such leakage that may be disadvantageous. In this respect, our results will 292 complement the BQH: some microbial cells secrete chemicals just because this process is bene -293 cial for them. In this sense, the "richer" cells "donate" their products to "poorer" cells for the sake of  . CC-BY 4.0 International license available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint this version posted November 7, 2020. ; https://doi.org/10.1101/2020.11.06.370924 doi: bioRxiv preprint removal of its members. In contrast, if only few cell species leak a few chemicals, the ecosystem 322 would have a unidirectional structure similar to a "food chain." In such cases, keystone/core species 323 could exist, and the system would not be resilient to removal of such species. Empirical studies sug-324 gest that diverse microbial communities are more resistant to environmental disturbances than 325 monocultures (Giri et al., 2020). Experimentally estimating S Cell or S Chem in these microbial commu-326 nities and investigating their relationship with their resilience could be interesting. 327 Theoretically, we nd that coexistence of diverse species is achieved by incorporating multilevel 328 dynamics at the intercellular (population) and intracellular (metabolic) levels and cannot be cap-329 tured by standard Lotka-Volterra-type population dynamics. Microbial ecosystems with metabo-330 lite exchange via the environment are expected to behave di erently from those with simple food 331 chain or food web structures that are often considered in Lotka-Volterra-type population dynam-332 ics, as the interactions between di erent cell species depend not only on their populations but 333 also on the exchanged chemicals, which depend on their intracellular states (Liao et al., 2020). For  The premise of the present study was that the leakage of even essential metabolites can be ben-  363 Finally, let us discuss whether a leak advantage would be eliminated through the course of evo-364 lution by incorporating appropriate gene-regulation of enzymatic activity, which is a well-known 365 means to optimize cell growth (Jacob and Monod, 1961). If only a single cell species exists, such 366 optimization of gene regulation might be possible to eliminate the leak advantage by evolution. . CC-BY 4.0 International license available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint this version posted November 7, 2020. ; https://doi.org/10.1101/2020.11.06.370924 doi: bioRxiv preprint gresses under the environmental conditions with interacting cells, nding such a solution, even if 373 it exists, would take many generations. Before such isolated optimization is reached, other cells 374 that consume secreted chemicals could either emerge through mutation or invade from elsewhere,  (Goldford et al., 2018; Ponomarova and Patil, 2015). 381 Moreover, a recent study on phylogeny suggested that such leakage of essential metabolites has 382 been promoted through evolution and adaptation (Braakman et al., 2017). 383 In summary, we have shown that cell-level adaptation of leakiness of (essential) metabolites 384 spontaneously establishes symbiotic relationships. This "microbial potlatch" generally emerges 385 when the intracellular metabolic network is complex, the environment is crowded, and nutrient 386 supply is limited. The present study provides a basis for complex microbial ecosystems with diverse