Trophic interactions induce spatial self-organization of microbial consortia on rough surfaces

The spatial context of microbial interactions common in natural systems is largely absent in traditional pure culture-based microbiology. The understanding of how interdependent microbial communities assemble and coexist in limited spatial domains remains sketchy. A mechanistic model of cell-level interactions among multispecies microbial populations grown on hydrated rough surfaces facilitated systematic evaluation of how trophic dependencies shape spatial self-organization of microbial consortia in complex diffusion fields. The emerging patterns were persistent irrespective of initial conditions and resilient to spatial and temporal perturbations. Surprisingly, the hydration conditions conducive for self-assembly are extremely narrow and last only while microbial cells remain motile within thin aqueous films. The resulting self-organized microbial consortia patterns could represent optimal ecological templates for the architecture that underlie sessile microbial colonies on natural surfaces. Understanding microbial spatial self-organization offers new insights into mechanisms that sustain small-scale soil microbial diversity; and may guide the engineering of functional artificial microbial consortia.


Representing hydrated soil surfaces
We developed a spatially-explicit and individual-based model 17,23 for systematically studying the spatial and temporal dynamics of multispecies cell-level trophic interactions in the context of the self-assembly of microbial consortia, The simulation domain modeled abstracts natural soil surfaces into a two dimensional network of roughness/capillary elements arranged on a regular lattice 6,23 comprised of 100 × 87 sites that span a domain with physical size of 17.2 × 17.2 mm. The aqueous phase within the (capillary) network geometry varies with external conditions (soil matric potential) and gives rise to formation of hydraulicallyconnected habitats (represented by connected aqueous bonds) that facilitate nutrient diffusion pathways, cell motion and thus the nature of local interactions (nutrient interception, etc.).
Previous studies have shown that key transport properties and connectivity of the aqueous phase in the model surface roughness networks mimic macroscopic transport and water holding behavior of soils for different matric potential values (or relative humidity) 23 . To evaluate the role of surface roughness, we considered homogeneous networks (HM, a network consists of identical roughness elements/channels), and equivalent heterogeneous networks (HT, networks consisting of roughness elements drawn from a statistical distribution of sizes).

Modeling microbial growth kinetics
Microbial growth rate and metabolic reactions for conditions where two nutrients limit growth were described by Monod-type kinetics as 39 , where Y is apparent yield (conversion of nutrients intercepted to biomass). The key physiological parameters were summarized in Table 2

Modeling self-motion of individual microbial cells
The self-motion of microbial cells is an important trait that confers advantages for survival in patchy and heterogeneous environments 1 . Self-motion also promotes other biophysical interactions such as ability to self-organization that wins response to chemotactic gradients 23,41 . Flagellated and other forms of cell motions 42 on soil surfaces become rapidly restricted with reduction in soil aqueous phase content. These restrictions are attributed to enhanced cell-wall viscous drag in thin films, followed by capillary pinning as air-water interfaces interact with microbial cells in unsaturated soil 3,23 . The effects of surface hydration state on individual cell motion and thus on population dispersion rates were expressed by relationship between cell size and effective water film thickness, d(ψ) 23 . For a given matric potential value (), the resulting cell velocity (V) considering capillary and hydrodynamic limitations is obtained as: , with V 0 is mean cell velocity in bulk water, and F C and F λ are the capillary pinning force and the cell-wall viscous drag forces opposing motion driven by the maximum self-propulsion force, and F M is resistant force in bulk water 6 . Hence, the drying of a soil surface not only impede individual cell motion due to thinning of film thickness, but also results in fragmentation of previouslylinked microbial aqueous habitats thereby reducing both ranges of microbial motions and diffusive fluxes 1,3,7,23 . For cell motions in response to chemotactic gradients 1,42 , we first evaluate the hydration-constrained mean cell velocity, V(), as a function of local aqueous film thickness. Next, we assign a displacement vector that depends on nutrient (chemoattractant) gradient by weighing chemotactic and random motility components using complementary weight factors, ζ and 1-ζ, where ζ is the normalized dimensionless nutrient gradient defined as the ratio of local to maximal nutrient gradients, with ζ = 0 for entirely random cell motility 6 . The cell net displacement is expressed as: with R  describing direction of random displacement of a cell along (with value of 1) or against (with value of -1) nutrient gradient, and τ is median value of microbial run time.

Simulated hydration and heterogeneity scenarios
Substituting parameter values for consortium II into equation (S5) one obtains,

Analytical prediction of critical Trophic Interactions Distance (TID)
The spatial self-organization of microbial consortia emerges through collective interactions among individual cells of consortium members and their local aqueous and nutrient environments. These interactions are shaped by acquisition of essential nutrients and other environmental stimuli 45 . The spatial separation between the initially unorganized yet trophically interlinked consortium members is critical for the triggering of subsequent spatial self-organization. The analysis identifies the critical distance for activation of trophic interactions as the key biophysical parameter. This critical distance is partially defined by the maximum displacement distance for a cell assuming no nutrients interception (relying entirely on its own inner energy storage, expressed as cell dry biomass) for the physical conditions of the surface 23, 46 . An estimate of this distance is given by 47 : where V is microbial median cell velocity on the hydrated rough surface 31 , τ is median value of microbial run time 47 , and T C is the survival time of a cell that only utilizes its own stored energy (cell dry biomass) without nutrient supply 48 estimated as, where Q B,0 is the median value of dry biomass of an active cell, and Q B,min is the threshold value of its dry biomass below which a cell turns inactive (a cell switches off its metabolism or simply dies). The other component to this critical distance is determined from the diffusion range (distance) a by-product that a producer species generates. More specifically, it is important to consider a region with concentration values above the threshold required for the maintenance of the consumer species (e.g., sp3). We denote the steady state radius of this maintenance concentration (of the by-product) originating from a producer cell or from a cell cluster as L D estimated as 2 , where D eff is nutrient effective diffusion coefficient on a hydrated rough surface 31 , [N * ] is the critical nutrient concentration for consumer cell self-maintenance calculated as, , and Q N is the amount of the point source (dry mass) which we approximated the amount of by-product generated by the producer species as: , with β is the by-product yield, Y the apparent yield (conversion of nutrient intercepted to biomass), and Q B,T is the total dry biomass of the population of the producer species developed at T C after inoculation estimated as, where n is the number of cells of the producer colony or cluster modifying or serving as the nutrient source. For illustrative purposes we have selected a value of n=100 for the analysis (similar to the inoculation density in the simulations), noting that the TID range is not sensitive to this value across several orders of magnitude of n. The effective specific growth rate of the producer species at nutrient concentration of [N] is expressed as: . Note that Q B,T was adjusted according to the total available initial nutrient mass which (for uniform concentration) is proportional to the effective water film thickness of the rough surface 6,23 , d(ψ). The parameter d max (ψ) is the maximum film thickness under wet surface condition, considered in this study as thickness under -0.5 kPa of water matric potential. Equations (S11) and (S13) enable the estimation of the trophic interactions distance (TID) defined as the maximal initial separation distance between consortium members for activation of trophic interactions calculated as (note that for L D ≤0, TID≡0), The TID reflects the interplay of hydration-mediated diffusion and motility, and threshold concentrations for setting the conditions for self-assembly and formation of consortia on heterogeneous rough surfaces.