## Abstract

Microbial communities are complex systems, and the fundamental mechanisms that control their dynamics and composition are still largely unknown. Here we show that such systems have a previously unexplored level of complexity: their microscopic details related to gene expression influence their macroscopic properties such as the population dynamics. We provide an experimental proof of concept showing that proteome allocation dramatically affects the outcome of competition assays between strains of *Escherichia coli*. We also provide an essential model that predicts our findings.

Microbes are among the most abundant life forms on Earth [1]. They inhabit almost every habitat of our planet, and have continuously surprised us for their ability to survive in places that were thought to be inhospitable and barren. For example, microbial communities have been found in the deep terrestrial subsurface [2, 3], and it has been estimated that the first five kilometers beneath the Earth’s surface could be habitable for them [4]. Because of their ubiquity, microbial communities play fundamental roles in countless natural processes of vital importance, from the digestion and overall health of their host organism [5] to climate regulation [6, 7]. Despite their importance, however, we still know very little about the fundamental mechanisms that regulate microbial communities, partly because we are only able to grow in the lab a very small fraction of all the bacteria found in nature [8], and partly because microbial communities are complex, non-linear systems whose dynamics is difficult to predict. Such difficulty arises because microbial communities are comprised of multiple agents (e.g., different species) linked by numerous kinds of interactions, and often the properties of the whole system cannot be inferred directly from the properties of its constituent parts alone. For these reasons, scientists from many disciplines have long been fascinated by the challenging theoretical questions posed by the study of microbial communities’ structure and dynamics, and serious efforts have been made to understand how competition [9–11] and metabolic interactions [12, 13] allow such systems to maintain very high levels of biodiversity.

Recent studies have shown that the structure and composition of microbial communities are tightly linked to the metabolism of the species that comprise them [14, 15] (e.g., communities with different taxonomic composition can nevertheless exhibit the same metabolic functional structure [16, 17]). We can therefore speculate that the ways with which they consume different resources for growth and proliferation can affect the dynamics of the entire community. On the other end, nutrient uptake is affected by the other functions that cells must perform to grow and proliferate, and the balance between such functions is governed by the allocation of the cell proteome to different tasks. It is therefore important to understand how microbial community dynamics is influenced by the proteome allocation of its members, and new insights in this direction might help us make more powerful predictions on how microbial communities assemble and evolve [18, 19].

Scott et al. [20] discovered that, despite the complexity of bacterial metabolism, there are very simple relationships that link the fraction of the proteome allocated for nutrient uptake and protein synthesis to bacterial growth rates in isolation, and that reducing such fraction by forcing cells to express useless proteins reduces their growth rate. Such phenomenological relationships are very powerful because they show that there are simple laws describing how bacterial growth is influenced by proteome allocation and gene expression. These laws have recently been applied in many different contexts [21] and have been shown to be an incredibly effective tool to improve our knowledge of microbial metabolism: they have for example helped explaining the occurrence of overflow metabolism in *Escherichia coli* [22] and improving the predictive power of Flux Balance Analysis [23]. However, the experiments by Scott et al. [21] have been performed with bacterial cultures grown in isolation and in exponential phase, and so it is unclear whether one can use their results to predict the dynamics of a multi-strain community in which multiple strains compete for the same resources in a temporally-variable environment.

In this Letter, we build on Scott et al. [20] and show that one can use the relationship between proteome allocation and bacterial growth rate to predict the population dynamics of a simple community composed of two strains of *E. coli* competing for the same resources in environments that vary temporally between high and low nutrient availability, i.e. between exponential and stationary growth phase. We show that by manipulating the proteome allocation of one of the two strains, we can control the population dynamics to the point of changing the outcome of competition. We also provide an essential community dynamics model that allows us to make verifiable predictions.

In our experiment, we used two strains of *E. coli* (which we call “strain 1” and “strain 2”, Figure 1a) that were engineered so that strain 1 expresses a yellow fluorescent protein (mVenus) constitutively, while strain 2 expresses a red one (mKate2Hyb) constitutively. These fluorescent proteins allowed us to distinguish the two strains at the flow cytometer and measure their relative frequency in the communities (Figure 1c). Furthermore, strain 1 carries a plasmid with a gene encoding for an additional red fluorescent protein (mCherry), whose production can be induced titratably by adding Isopropyl *β*-D-1-thiogalactopyranoside (IPTG) (a molecular mimic of allolactose that cannot be metabolized by *E. coli*) to the medium. By increasing the concentration of IPTG in the medium, we were thus able to change the overall proteome allocation of the strain, as sketched in Figure 1b, by diverting cellular resources to the production of the protein mCherry. At the start of the experiment, we mixed the two strains in liquid medium, where they competed for nutrients and glucose as the sole common carbon source, at eight different concentrations of IPTG (six technical replicates per IPTG concentration). We re-diluted the cultures daily in fresh medium at a 1:100 ratio for eight days and measured the relative abundances of the two strains at each transfer using flow cytometry. In the Supplemental Material we provide more detailed information on the strains and on the experimental protocol [24].

From a theoretical point of view, the phenomenological framework by Scott et al. [20] prescribes that the proteome of a bacterial strain *σ* can be minimally divided into three sectors: a fraction allocated for nutrient uptake and metabolization, a fraction allocated for biomass production (i.e., protein synthesis) and a fraction allocated for “housekeeping” functions (which they observed to be incompressible); since they are fractions, these three quantities must sum to one:

Given this minimal division of the proteome, Scott et al. [20] have shown that and can be written as linear functions of the growth rate *g _{σ}* as follows:
where

*κ*is the “nutritional capacity” of the (only) energy source used by the strains, is the “translational capacity” of strain

^{n}*σ*(which measures the speed of mRNA translation),

*ρ*is a conversion factor and is an “incompressible core” of . From Eqs (2a) and (2b) we can express in terms of , so that Eq (1) can be rewritten as where Φ

_{σ}_{σ}can be interpreted as the total fraction of species

*σ*’s proteome allocated to metabolism and growth.

In our experiment, the two strains started at low density and had enough time to reach saturation before being transferred to fresh medium. As a first approximation, we can write down a minimal model in which the two strains are always growing in the exponential phase, i.e. *ṁ _{σ}* =

*m*, where

_{σ}η_{σ}φ_{σ}*m*is the biomass of species

_{σ}*σ*,

*η*=

_{σ}*κ*/

^{n}*ρ*and we write

_{σ}*φ*instead of . Eq (3) can be rewritten as

_{σ}*φ*(1 +

_{σ}*γ*) = Φ

_{σ}_{σ}with . In this approximation, we are not taking into account that cultures are diluted at regular intervals and that the common energy source may run out before the next dilution is made. Nevertheless, in the Supplemental Material [24] we show that results are unaltered when these facts are taken into account. We can set

*η*

_{1}=

*η*

_{2}=

*η*and

*γ*

_{1}=

*γ*

_{2}=

*γ*since these two strains were engineered starting from the same

*E. coli*ancestor strain. Simple computations [24] show that the relative abundance

*f*

_{1}(

*t*) of strain

*σ*= 1 for small

*t*grows linearly in time with rate: and that the rate of growth of

*f*

_{2}(

*t*) is Λ

_{2}= −Λ

_{1}. The outcome of competition will thus be determined by the sign of Φ

_{1}– Φ

_{2}: if Φ

_{1}> Φ

_{2}(i.e., strain 1 allocates a larger fraction of its proteome to metabolism and biomass production than strain 2) then Λ

_{1}>0, Λ

_{2}< 0 and therefore strain 1 will outcompete strain 2; the opposite will happen if Φ

_{1}< Φ

_{2}. Coexistence between the two strains will be possible only when Φ

_{1}= Φ

_{2}. The system thus exhibits two regimes where only one of the two strains will survive, separated by the coexistence point Φ

_{1}= Φ

_{2}.

Experimentally, increasing the concentration of IPTG corresponds to lowering Φ_{1}, because cellular resources are diverted to the production of the fluorescent protein mCherry. Writing , where *φ _{U}* is the fraction of proteome allocated by strain 1 for the (useless) synthesis of mCherry, the rates Λ

_{1}and Λ

_{2}can be written as linear functions of

*φ*with slopes and intercepts of equal magnitude but opposite sign, i.e. where and

_{U}Because the relationship between IPTG concentration and the fluorescence intensity of cells due to the production of mCherry is nonlinear [24], we calibrated the IPTG concentration with the fluorescent intensity of the cells in the arbitrary units returned by the flow cytometer, so that we could express Λ_{1} and Λ_{2} as functions of the latter [24] (and we are assuming that the measured fluorescent intensity of the cells is proportional to the quantity of fluorescent protein expressed by the cells, i.e. to *φ _{U}*). As shown in Figure 2, the two experimentally-measured rates Λ

_{1}and Λ

_{2}are indeed linear functions of the fluorescence intensity due to the production of mCherry, as predicted by our theoretical framework. Indeed, a linear fit returns slopes and intercepts that are identical in magnitude within the errors. By manipulating the IPTG concentration, we were able to explore the three predicted regimes of the system. In the absence of IPTG and at low concentrations of it, strain 1 outcompeted strain 2 (Λ

_{1}> 0). At an IPTG concentration of approximately 30

*μ*M, the two strains coexisted by maintaining a stable relative fraction. At IPTG concentrations larger than 30

*μ*M, strain 1 was outcompeted by strain 2 (i.e., Λ

_{1}< 0).

We found that in the absence of IPTG strain 1 had a fitness advantage over strain 2, i.e. the frequency of strain 1 in the community increased over time. In our theoretical framework, such an advantage means that . Based on our calculations, we can perform an order-of-magnitude estimate of this difference from Eqs (6a) and (6b):

In order to estimate *δ*Φ, we can take *ℓ* from our fits and calculate λ as follows. First, we compute *f*_{1}(0) and *f*_{2}(0) from our data as the mean values of the initial conditions for the relative abundances of the two strains. The other parameters, i.e. *κ ^{n}*,

*ρ*and

*κ*, were not measured in our experiment, but we can use the values estimated in [20] for strains with the same genetic background, i.e. strain MG1655 [24]. This indirect estimate limits the accuracy of

^{t}*δ*Φ, but it allows us to evaluate its order of magnitude. With these choices [25], we obtain λ ~ 0.33 and

*δ*Φ ~ 1%.

We have also repeated our experiment with two other strains, strains 3 and 4, that are respectively identical to strains 1 and 2, but with reversed fluorescent protein colors (see Figure S.9): strain 3 constantly expresses a red fluorescent protein and carries a plasmid that allows it to produce a yellow fluorescent protein (Venus YFP) when IPTG is present in the culture medium, and strain 4 constantly expresses a yellow fluorescent protein. All the details of these strains and the results of this second experiment are reported in the Supplemental Material [24]. Despite not being able to span all the regimes exhibited by the system in this case, due to the fact that expressing Venus YFP has a smaller effect on growth rate than expressing mCherry [24], the results are consistent with the ones reported here.

In this Letter we have presented a proof of concept showing how proteome allocation has a central role in shaping and affecting the dynamics of microbial communities. Our experiment shows that changing proteome allocation by inducing the expression of a useless protein, thereby reducing the proteome fraction that cells of one strain allocate to growth and proliferation, has an important effect on the outcome of competition assays and the rate at which a strain increases in frequency in the community and the other one goes extinct. We have also provided a simple community dynamics model capable of explaining our observations. We can thus argue that microbial communities exhibit an additional level of complexity that makes their study even more challenging and intellectually stimulating: in addition to the nontrivial interactions between their constituent parts at the species, strains and individuals level, the properties of such systems will be determined also by how phenomena at both the microscopic (i.e., gene expression and proteome allocation) and macroscopic (i.e. population dynamics) scales influence each other. This work thus provides a first conceptual bridge at the interplay between microbial physiology and community dynamics. In particular, our work constitutes a first step towards the development of the study of microbial competition through population dynamics models grounded on the microscopic properties of microbial communities.

Direct competition for the same common energy source is only one of the many known chemical interactions that can take place in a microbial community [26]: from the exchange of useful metabolites [27, 28] to the production of toxins and antibiotics [29], there are several different ways in which bacteria can allocate their proteome that can have a major impact on community dynamics and structure. This is especially important for engineering synthetic communities in which each member needs to perform a given task, because one needs to balance the production of given a gene product with the growth rate of the strain that produces it, ensuring that the gene product is sufficiently abundant to perform its function and that the strain grows sufficiently fast to persist in the community. Our work shows that these kinds of phenomena must be taken into account in models of community dynamics in order to better understand the fundamental mechanisms that regulate microbial communities.

## ACKNOWLEDGMENTS

We thank David R Nelson and Andrew W Murray for hosting L. P.-M. during the experiments. We thank Daniel Eaton for providing the background bacterial strains. A. M. and L. P.-M. acknowledge the Cariparo Foundation for funding. S. S. acknowledges the University of Padua for STARS2018 grants. A. G. was supported by research fellowships from the Swiss National Science Foundation, Projects P2ELP2_168498 and P400PB_180823.