Quantifying emergence and self-organisation of Enterobacter cloacae microbial communities

Abstract

From microbial communities to cancer cells, many such complex collectives embody emergent and self-organising behaviour. Such behaviour drives cells to develop composite features such as formation of aggregates or expression of specific genes as a result of cell-cell interactions within a cell population. Currently, we lack universal mathematical tools for analysing the collective behaviour of biological swarms. To address this, we propose a multifractal inspired framework to measure the degree of emergence and self-organisation from scarce spatial (geometric) data and apply it to investigate the evolution of the spatial arrangement of Enterobacter cloacae aggregates. In a plate of semi-solid media, Enterobacter cloacae form a spatially extended pattern of high cell density aggregates. These aggregates nucleate from the site of inoculation and radiate outward to fill the entire plate. Multifractal analysis was used to characterise these patterns and calculate dynamics changes in emergence and self-organisation within the bacterial population. In particular, experimental results suggest that the new aggregates align their location with respect to the old ones leading to a decrease in emergence and increase in self-organisation.

Formation, collective motion, and merging of macroscopic bacterial aggregates

“…Enterobacter cloacae is a bacterial strain previously reported to be capable of large scale pattern formation, including moving bands of high cell density and aggregate formation (6,25). Here we focus on the aggregate formation, using a large culture dish and uniformly mixing cells into the culture medium at the beginning of the experiment.…”

Taming the Unknown Unknowns in Complex Systems: Challenges and Opportunities for Modeling, Analysis and Control of Complex (Biological) Collectives

“…Given the observed intra- and inter-patient physiological variability, the intelligence of MCPS should also be able to account for time-varying parameter uncertainty and modeled dynamics (unknown sensitivities to control variables), measurement and actuation delays, as well as the distributed nature of MCPS (distributed sensors and controllers). Having knowledge of the healthy physiological complexity of an individual (described through multi-fractal (Delignières et al, 2016), emergence (Balaban et al, 2018), self-organization (Balaban et al, 2018), and robustness metrics), can the MCPS controllers accurately determine (estimate) or retrieve the physiological state when facing sensor noise, adversarial events or actuator errors? Alternatively, can the MCPS controllers distinguish between sensor/actuator faults, abnormal medical conditions and external disturbances (e.g., mean, exercise, and stress levels)?…”

Mechanism for Measuring System Complexity Applying Sensitivity Analysis

“…Based on the fractal dimension as measure for self-similar objects, Balaban et al [26] proposes a metric for quantifying emergence and self-organisation extending fractal dimension to a function, since most of the fractal-like objects have multiple scaling rates. Thus the multifractal analysis investigates the statistical scaling laws of complex fragmented geometrical objects as bacteria aggregates.…”

“…Thus the multifractal analysis investigates the statistical scaling laws of complex fragmented geometrical objects as bacteria aggregates. Balaban et al [26] observe the evolution of the spatial arrangement of Enterobacter cloacae aggregates and apply multifractal analysis to calculate dynamics changes in emergence and self-organisation within the bacterial population. As experimental results, the emergence degree decreases as aggregates populate the plate while the self-organisation degree increases.…”