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Bacterial colonies growing on solid surfaces can exhibit robust expansion kinetics, with constant radial growth and saturating vertical expansion, suggesting a common developmental program. Here, we study this process for Escherichia coli cells using a combination of modeling and experiments. We show that linear radial colony expansion is set by the verticalization of interior cells due to mechanical constraints rather than radial nutrient gradients as commonly assumed. In contrast, vertical expansion slows down from an initial linear regime even while radial expansion continues linearly. This vertical slowdown is due to limitation of cell growth caused by vertical nutrient gradients, exacerbated by concurrent oxygen depletion. Starvation in the colony interior results in a distinct death zone which sets in as vertical expansion slows down, with the death zone increasing in size along with the expanding colony. Thus, our study reveals complex heterogeneity within simple monoclonal bacterial colonies, especially along the vertical dimension. The intricate dynamics of such emergent behavior can be understood quantitatively from an interplay of mechanical constraints and nutrient gradients arising from obligatory metabolic processes. Bacterial colonies growing on solid surfaces can exhibit robust expansion kinetics, with constant radial growth and saturating vertical expansion. Here, the authors use modeling and experiments to show that colony growth dynamics are driven by an interplay of mechanical constraints and nutrient gradients arising from obligatory metabolic processes.

Many biogeochemical functions involve bacteria utilizing solid substrates. However, little is known about the coordination of bacterial growth with the kinetics of attachment to and detachment from such substrates. In this quantitative study of Vibrio sp. 1A01 growing on chitin particles, we reveal the heterogeneous nature of the exponentially growing culture comprising two co-existing subpopulations: a minority replicating on chitin particles and a non-replicating majority which was planktonic. This partition resulted from a high rate of cell detachment from particles. Despite high detachment, sustained exponential growth of cells on particles was enabled by the enrichment of extracellular chitinases excreted and left behind by detached cells. The ‘inheritance’ of these chitinases sustains the colonizing subpopulation despite its reduced density. This simple mechanism helps to circumvent a trade-off between growth and dispersal, allowing particle-associated marine heterotrophs to explore new habitats without compromising their fitness on the habitat they have already colonized. Chitin-degrading bacteria split into on- and away-from-particles subpopulations. Only on-particle cells grow and most disperse after replication, leaving chitinases behind. High dispersal is sustained by remaining cells thriving on leftover chitinases.

Sinking particulate organic carbon out of the surface ocean sequesters carbon on decadal to millennial timescales. Predicting the particulate carbon flux is therefore critical for understanding both global carbon cycling and the future climate. Microbes play a crucial role in particulate organic carbon degradation, but the impact of depth-dependent microbial dynamics on ocean-scale particulate carbon fluxes is poorly understood. Here we scale-up essential features of particle-associated microbial dynamics to understand the large-scale vertical carbon flux in the ocean. Our model provides mechanistic insight into the microbial contribution to the particulate organic carbon flux profile. We show that the enhanced transfer of carbon to depth can result from populations struggling to establish colonies on sinking particles due to diffusive nutrient loss, cell detachment, and mortality. These dynamics are controlled by the interaction between multiple biotic and abiotic factors. Accurately capturing particle-microbe interactions is essential for predicting variability in large-scale carbon cycling. Micro-scale microbial community dynamics can substantially alter the fate of sinking particulates in the ocean thus playing a key role in setting the vertical flux of particulate carbon in the ocean.

Metabolic cross-feeding plays vital roles in promoting ecological diversity. While some microbes depend on exchanges of essential nutrients for growth, the forces driving the extensive cross-feeding needed to support the coexistence of free-living microbes are poorly understood. Here we characterize bacterial physiology under self-acidification and establish that extensive excretion of key metabolites following growth arrest provides a collaborative, inter-species mechanism of stress resistance. This collaboration occurs not only between species isolated from the same community, but also between unrelated species with complementary (glycolytic vs. gluconeogenic) modes of metabolism. Cultures of such communities progress through distinct phases of growth-dilution cycles, comprising of exponential growth, acidification-triggered growth arrest, collaborative deacidification, and growth recovery, with each phase involving different combinations of physiological states of individual species. Our findings challenge the steady-state view of ecosystems commonly portrayed in ecological models, offering an alternative dynamical view based on growth advantages of complementary species in different phases. Microbes can cooperate and share resources via metabolic cross-feeding. Here, the authors show that excretion of key metabolites following acid stress provides a collaborative, inter-species mechanism of stress resistance.

Many biogeochemical functions involve bacteria utilizing solid substrates. However, little is known about the coordination of bacterial growth with the kinetics of attachment to and detachment from such substrates. In this quantitative study of Vibrio sp. 1A01 growing on chitin particles, we reveal the heterogeneous nature of the exponentially growing culture, comprised of two co-existing subpopulations: a minority replicating on chitin particles and a non-replicating majority which was planktonic. This partition resulted from a high rate of cell detachment from particles. Despite high detachment, sustained exponential growth of cells on particles was enabled by the enrichment of extra-cellular chitinases excreted and left behind by detached cells. The “inheritance” of these chitinases sustains the colonizing subpopulation despite its reduced density. This simple mechanism helps to circumvent a tradeoff between growth and dispersal, allowing particle-associated marine heterotrophs to explore new habitats without compromising their fitness on the habitat they have already colonized.

Bacterial colony growth on hard agar is commonplace in microbiology; yet, what occurs inside a growing colony is complex even in the simplest cases. Robust colony expansion kinetics featuring a linear radial growth and a saturating vertical growth indicates a common developmental program which is elucidated here for Escherichia coli cells using a combination of modeling and experiments. Radial colony expansion is found to be limited by mechanical factors rather than nutrients as commonly assumed. In contrast, vertical expansion is limited by glucose depletion inside the colony, an effect compounded by reduced growth yield due to anaerobiosis. Carbon starvation in the colony interior results in substantial cell death within 1-2 days, with a distinct death zone that expands with the growing colony. Overall, the development of simple colonies lacking EPS production and differentiation is dictated by an interplay of mechanical constraints and emergent nutrient gradients arising from obligatory metabolic processes.

The roughening phase diagram of the d=3 Ising model with uniaxially anisotropic interactions is calculated for the entire range of anisotropy, from decoupled planes to the isotropic model to the solid-on-solid model, using hard-spin mean-field theory. The phase diagram contains the line of ordering phase transitions and, at lower temperatures, the line of roughening phase transitions, where the interface between ordered domains roughens. Upon increasing the anisotropy, roughening transition temperatures settle after the isotropic case, whereas the ordering transition temperature increases to infinity. The calculation is repeated for the d=2 Ising model for the full range of anisotropy, yielding no roughening transition.

The left-right chiral and ferromagnetic-antiferromagnetic double spin-glass clock model, with the crucially even number of states q=4 and in three dimensions d=3, has been studied by renormalization-group theory. We find, for the first time to our knowledge, four different spin-glass phases, including conventional, chiral, and quadrupolar spin-glass phases, and phase transitions between spin-glass phases. The chaoses, in the different spin-glass phases and in the phase transitions of the spin-glass phases with the other spin-glass phases, with the non-spin-glass ordered phases, and with the disordered phase, are determined and quantified by Lyapunov exponents. It is seen that the chiral spin-glass phase is the most chaotic spin-glass phase. The calculated phase diagram is also otherwise very rich, including regular and temperature-inverted devil's staircases and reentrances.

The chiral clock spin-glass model with q=5 states, with both competing ferromagnetic-antiferromagnetic and left-right chiral frustrations, is studied in d=3 spatial dimensions by renormalization-group theory. The global phase diagram is calculated in temperature, antiferromagnetic bond concentration p, random chirality strength, and right-chirality concentration c. The system has a ferromagnetic phase, a multitude of different chiral phases, a chiral spin-glass phase, and a critical (algebraically) ordered phase. The ferromagnetic and chiral phases accumulate at the disordered phase boundary and form a spectrum of devil's staircases, where different ordered phases characteristically intercede at all scales of phase-diagram space. Shallow and deep reentrances of the disordered phase, bordered by fragments of regular and temperature-inverted devil's staircases, are seen. The extremely rich phase diagrams are presented as continuously and qualitatively changing videos.

The chiral spin-glass Potts system with q=3 states is studied in d=2 and 3 spatial dimensions by renormalization-group theory and the global phase diagrams are calculated in temperature, chirality concentration p, and chirality-breaking concentration c, with determination of phase chaos and phase-boundary chaos. In d=3, the system has ferromagnetic, left-chiral, right-chiral, chiral spin-glass, and disordered phases. The phase boundaries to the ferromagnetic, left- and right-chiral phases show, differently, an unusual, fibrous patchwork (microreentrances) of all four (ferromagnetic, left-chiral, right-chiral, chiral spin-glass) ordered ordered phases, especially in the multicritical region. The chaotic behavior of the interactions, under scale change, are determined in the chiral spin-glass phase and on the boundary between the chiral spin-glass and disordered phases, showing Lyapunov exponents in magnitudes reversed from the usual ferromagnetic-antiferromagnetic spin-glass systems. At low temperatures, the boundaries of the left- and right-chiral phases become thresholded in p and c. In the d=2, the chiral spin-glass system does not have a spin-glass phase, consistently with the lower-critical dimension of ferromagnetic-antiferromagnetic spin glasses. The left- and right-chirally ordered phases show reentrance in chirality concentration p.