Liliana Model Set 43 46

Liliana Model Set 43 46

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The metabolic capabilities of the species and the local environment shape the microbial interactions in a community either through the exchange of metabolic products or the competition for the resources. Cells are often arranged in close proximity to each other, creating a crowded environment that unevenly reduce the diffusion of nutrients. Herein, we investigated how the crowding conditions and metabolic variability among cells shape the dynamics of microbial communities. For this, we developed CROMICS, a spatio-temporal framework that combines techniques such as individual-based modeling, scaled particle theory, and thermodynamic flux analysis to explicitly incorporate the cell metabolism and the impact of the presence of macromolecular components on the nutrients diffusion. This framework was used to study two archetypical microbial communities (i) Escherichia coli and Salmonella enterica that cooperate with each other by exchanging metabolites, and (ii) two E. coli with different production level of extracellular polymeric substances (EPS) that compete for the same nutrients. In the mutualistic community, our results demonstrate that crowding enhanced the fitness of cooperative mutants by reducing the leakage of metabolites from the region where they are produced, avoiding the resource competition with non-cooperative cells. Moreover, we also show that E. coli EPS-secreting mutants won the competition against the non-secreting cells by creating less dense structures (i.e. increasing the spacing among the cells) that allow mutants to expand and reach regions closer to the nutrient supply point. A modest enhancement of the relative fitness of EPS-secreting cells over the non-secreting ones were found when the crowding effect was taken into account in the simulations. The emergence of cell-cell interactions and the intracellular conflicts arising from the trade-off between growth and the secretion of metabolites or EPS could provide a local competitive advantage to one species, either by supplying more cross-feeding metabolites or by creating a less dense neighborhood.

Microbial communities play a key role in biogeochemical cycles, bioremediation, and human health. In crowded microbial systems such as biofilms and cellular aggregates, the close proximity between individual cells reduces the free space for the nutrients diffusion. To model the heterogeneous nature of these microbial systems, we developed CROMICS, a framework that integrates the information about the metabolic capabilities of each individual cell as well as the size and location of cells and macromolecules in the medium. The interactions among the individuals arise naturally through competition for or the exchange of metabolites. We show how the presence of mutants and a reduced diffusion in crowded environments can perturb the local availability of nutrients and therefore modify the dynamics of a microbial community. The discovered mechanisms underlying the microbial interactions in crowded systems together with the developed framework represent a valuable starting point for future studies of the interplay of human microbiome and host metabolism, the pathogen invasion, and the evaluation of antibiotic effectiveness.

Citation: Angeles-Martinez L, Hatzimanikatis V (2021) Spatio-temporal modeling of the crowding conditions and metabolic variability in microbial communities. PLoS Comput Biol 17(7): e1009140.

List of abbreviations: Beps+, Multispecies biofilm composed by E. coli wild type and eps+ mutans; Beps++, Multispecies biofilm composed by E. coli wild type and eps++ mutans; cLBM, Crowding adaptation of the lattice Bolzmann method; CN, Crank-Nicholson method; CROMICS, Crowding-modeling of in-silico community systems; eps+, E. coli mutant that secretes 0.11 g gDW-1 of EPS; eps++, E. coli mutant that secretes 0.43 g gDW-1 of EPS; EPS, Extracellular polymeric substances; GEM, Genome-scale metabolic models; IbM, Individual-based modeling; nmse, Normalized mean squared error; NN, Neural network; SPT, Scaled particle theory; TFA, Thermodynamic flux analysis; WT, Wild type cell

CROMICS allows the spatio-temporal modeling of microbial communities, wherein the heterogeneous aspects of the system, such as metabolic capabilities of the species and crowding conditions, can be incorporated. Thus, the effect of the spatial restrictions imposed by the presence of cells (and other macromolecules secreted to the medium) on the diffusion of nutrients and metabolites exchanged by the microorganisms arises naturally in the simulation. Here, the system is divided into small boxes or regions, where cells can uptake the nutrients locally available in a box. The simulation consists of three iterative steps (Fig 1). At every time step Δt, (i) the growth rate and exchange metabolic fluxes of each microorganism are obtained from GEMs using either TFA or neural networks (NN) [24] specially trained for such purpose. NNs reduce the computational burden associated to the computation of the metabolic fluxes (see Methods). These metabolic fluxes are used to update the mass and volume of the cells as well as the amount (or concentration) of metabolites in each region. Then, (ii) the metabolites are allowed to diffuse to other regions, whose crowding conditions have changed due to the size increment of the cells. The effective diffusion is computed as [25], where the activity coefficient γmet (calculated using SPT) represents the ratio between the total volume and the available volume for metabolite met in each region of the system. The metabolite diffusion in a 2D or 3D system can be computed using a crowding adaptation of either the semi-implicit Crank-Nicholson appoach [26] or the lattice Boltzmann method (cLBM) [27]. Finally, (iii) the cell division and re-distribution of species in the system is computed following IbM rules.

Following our previous case study, we simulated the co-growth of S. enterica and E. coli ΔmetB, using an initial species ratio of 50:50 and assuming that cells occupied 40% of the box volume. S. enterica species consisted of subpopulations meth- and meth+. Twenty bacterial spots were inoculated in the system with an equal number of individuals of E. coli and S. enterica, but only one spot (identified as colony A) contained meth+, we tested three different initial number of meth+ cells 70, 60, and 50 (corresponding to a relative abundance of 8.8%, 7.5%, and 6.3%, respectively). All cells were randomly allocated in the bacterial spots. See the model setup in Methods. Community model 1.

Modeling approaches like CROMICS can contribute to efforts to bridge the gap between the modeling of single cell metabolisms and whole populations. The versatility of these approaches allows one to explore the interplay between the physical restrictions imposed by cell growth and macromolecule secretion that negatively affect the nutrients diffusion and the dependence of the cell metabolism on the local availability of nutrients in microbial systems.

The spatio-temporal microbial modeling developed in CROMICS is an iterative process that integrates information about (i) the cell metabolism, (ii) the diffusion of metabolites, and (iii) the redistribution of individual cells in the system (Fig 1). CROMICS requires an input of the parameters (e.g. diffusion coefficients, Michaelis-Menten constants) and the initial set up of the system (GEM, initial seed of cells and metabolites). The system is discretized on a regular lattice, with meshing sizes Δx, Δy, and Δz along the spatial coordinates. 2D systems are simulated by assuming a monolayer of rectangular (or cubic) prism boxes.

Once the uptake flux limits vUf,ex,met are set based on the effective nutrient concentration in the medium (Eqs 1 and 2), then the growth rate νbio and exchange flux of metabolites to/from the cell νf,ex,met [mmol gDW-1 h-1] can be calculated by TFA (which involves mass conservation and thermodynamics constraints) [21] or alternatively by NN [24]. See details in S1 Text Metabolic flux estimations. Other stoichiometric models and constraints can also be applied. When no feasible flux solution was found due to the starvation conditions, the cell was allowed to shrink with a rate vshrinkage to satisfy the cell maintenance requirements, i.e., νbio = vshrinkage. νbio and νf,ex,met were used to update cell mass Mcell and the amount of metabolite ρmet in each box for the next time t + Δt, so that(5)(6)

GEM models for the methionine-secreting S. enterica and E. coli ΔmetB were constructed as described by Harcombe et al. [19]. For the E. coli iJ01366 core [45], the reaction catalyzed by the cystathionine-γ-synthase was blocked in the GEM model to prevent the synthesis of methionine. For S. enterica iRR1083 [46], the biomass reaction was modified to consume 0.5 mmol gDW-1 of intracellular methionine balanced by the production of the same amount of methionine that will be secreted to the medium. Furthermore, to simulate the metabolic variability of S. enterica (see below), the ratio of methionine: biomass (rmeth) in the biomass reaction was constrained either to 0.5 or 0 mmol gDW-1. In this way, different subpopulations were characterized by the methionine production, where a cell with rmeth = 0 corresponds to S. enterica wild type (WT) that does not secrete methionine (identified as meth-), while rmeth = 0.5 corresponds to methionine-secreting S. enterica mutant (meth+).

NNs significantly reduce the runtime required for metabolic flux estimations, e.g. the exchange fluxes of 10,000 bacteria are computed in approximately 0.04 s (based on the GEM model of E. coli) using Matlab in a 12-core Intel Xeon E5, CPU 2.7 GHz. Comparatively, the runtime required by TFA for the parallel computation of metabolic distributions (by maximizing the growth rate vbio, using CPLEX) of a similar number of bacteria is about 93 min, and with reduced GEM models [47], the time required is 32 min. Thus, NNs reduce the computational cost associated with the cellular metabolic response in spatio-temporal simulations that require a fine time discretization Δt, with a large number of cells and/or when the metabolic model used is computationally expensive (e.g. genome-scale models of metabolism and macromolecular expression). However, training the NNs requires previous knowledge of the prevalent metabolite exchanged among the species to select the most important metabolites to track. The use of TFA or other stochiometric-based models could be more appropriate in more complex problems, such as when the metabolic flux distributions of a species are very sensitive to small amounts of multiple substrates. 1e1e36bf2d