Subsystem eigenstate thermalization hypothesis for translation invariant systems.

The eigenstate thermalization hypothesis for translation invariant quantum spin systems has been proved recently by using random matrices. In this paper, we study the subsystem version of the eigenstate thermalization hypothesis for translation invariant quantum systems without referring to random matrices. We first find a relation between the quantum variance and the Belavkin-Staszewski relative entropy. Then, by showing the small upper bounds on the quantum variance and the Belavkin-Staszewski relative entropy, we prove the subsystem eigenstate thermalization hypothesis for translation invariant quantum systems with an algebraic speed of convergence in an elementary way. The proof holds for most of the translation invariant quantum lattice models with exponential or algebraic decays of correlations.

Formation, collective motion, and merging of macroscopic bacterial aggregates.

Chemotactic bacteria form emergent spatial patterns of variable cell density within cultures that are initially spatially uniform. These patterns are the result of chemical gradients that are created from the directed movement and metabolic activity of billions of cells. A recent study on pattern formation in wild bacterial isolates has revealed unique collective behaviors of the bacteria Enterobacter cloacae. As in other bacterial species, Enterobacter cloacae form macroscopic aggregates. Once formed, these bacterial clusters can migrate several millimeters, sometimes resulting in the merging of two or more clusters. To better understand these phenomena, we examine the formation and dynamics of thousands of bacterial clusters that form within a 22 cm square culture dish filled with soft agar over two days. At the macroscale, the aggregates display spatial order at short length scales, and the migration of cell clusters is superdiffusive, with a merging acceleration that is correlated with aggregate size. At the microscale, aggregates are composed of immotile cells surrounded by low density regions of motile cells. The collective movement of the aggregates is the result of an asymmetric flux of bacteria at the boundary. An agent-based model is developed to examine how these phenomena are the result of both chemotactic movement and a change in motility at high cell density. These results identify and characterize a new mechanism for collective bacterial motility driven by a transient, density-dependent change in motility.

Connecting single-cell properties to collective behavior in multiple wild isolates of the Enterobacter cloacae complex.

Some strains of motile bacteria self-organize to form spatial patterns of high and low cell density over length scales that can be observed by eye. One such collective behavior is the formation in semisolid agar media of a high cell density swarm band. We isolated 7 wild strains of the Enterobacter cloacae complex capable of forming this band and found its propagation speed can vary 2.5 fold across strains. To connect such variability in collective motility to strain properties, each strain's single-cell motility and exponential growth rates were measured. The band speed did not significantly correlate with any individual strain property; however, a multilinear analysis revealed that the band speed was set by a combination of the run speed and tumbling frequency. Comparison of variability in closely-related wild isolates has the potential to reveal how changes in single-cell properties influence the collective behavior of populations.

Single-cell variability of growth interactions within a two-species bacterial community.

Cell-cell interaction networks have been examined in many high diversity microbial communities using macroscale approaches. Microscale studies of multispecies communities are lacking and it remains unclear how macroscale trends scale down to small groups of cells. Experimental approaches using microfluidic devices have revealed heterogeneity in the behavior of single cells, however, this analysis has not been extended towards the variability of cell-cell interactions. Using a microwell device, we analyzed cell growth within hundreds of replicate microbial communities consisting of two species and small population sizes. The wells of the devices were inoculated with a coculture of Escherichia coli and Enterobacter cloacae. Each species expressed a unique fluorescent protein enabling simultaneously tracking of cell number for each species over time. Growth dynamics within the device were consistent with bulk measurements. The device enabled monitoring of replicate, isolated coculture populations at high magnification, revealing both the growth interaction between the two species and the variability of such cell-cell interactions within small groups of cells. The device enables new experimental measurements of the heterogeneity of interactions within small, multispecies populations of bacteria.

Lieb-Robinson bound at finite temperatures.

The Lieb-Robinson bound shows that the speed of propagating information in a nonrelativistic quantum lattice system is bounded by a finite velocity, which entails the clustering of correlations. In this paper, we extend the Lieb-Robinson bound to quantum systems at finite temperature by calculating the dynamical correlation function at nonzero temperature for systems whose interactions are, respectively, short range, exponentially decaying, and long range. We introduce a simple way of counting the clusters in a cluster expansion by using the combinatoric generating functions of graphs. Limitations and possible applications of the obtained bound are also discussed.

The Contribution of High-Order Metabolic Interactions to the Global Activity of a Four-Species Microbial Community.

The activity of a biological community is the outcome of complex processes involving interactions between community members. It is often unclear how to accurately incorporate these interactions into predictive models. Previous work has shown a range of positive and negative metabolic pairwise interactions between species. Here we examine the ability of a modified general Lotka-Volterra model with cell-cell interaction coefficients to predict the overall metabolic rate of a well-mixed microbial community comprised of four heterotrophic natural isolates, experimentally quantifying the strengths of two, three, and four-species interactions. Within this community, interactions between any pair of microbial species were positive, while higher-order interactions, between 3 or more microbial species, slightly modulated community metabolism. For this simple community, the metabolic rate of can be well predicted only with taking into account pairwise interactions. Simulations using the experimentally determined interaction parameters revealed that spatial heterogeneity in the distribution of cells increased the importance of multispecies interactions in dictating function at both the local and global scales.