Microorganisms living within our bodies and outside, move through complex and porous terrains. At the micro-scale, their constant search for favorable living conditions is ruled more by their interactions with surfaces in their confined environments than external gradients.

In a recent article in the Proceedings of the National Academy of Sciences (PNAS), scientists at the Max Planck Institute for Dynamics and Self-Organization (MPIDS), the University of Bayreuth, and the University of Loughborough publish their results on microbial navigation based on mathematical simulation studies and microfluidic experimentations.

The article titled, “Emergent probability fluxes in confined microbial navigation” reveals principles that describe and predict the movement and organization of microbes in confined spaces, buttressing the development of novel technologies.

Principles underlying the organization of ‘active matter’ like moving microbes can have direct implications for future technologies, such as guiding the trajectory of photosynthetic microorganisms such that their flux can propel a generator that directly converts sunlight into mechanical energy. These basic principles may also find application in the pharmaceutical and healthcare sector.

“A potential application in the medical sector is the development of micro-robots delivering drugs to their specific destination in an efficient manner,” says Oliver Bäumchen, PhD, a scientist at MPIDS and the University of Bayreuth and a senior co-author on the study.

Research groups led by Oliver Bäumchen, PhD, (left) and Marco Mazza, PhD, (right) conducted the study.

Microfluidics is the behavior, control, and regulation of fluids that are geometrically restricted to tiny spaces.  Physical principles that govern interaction with surface structures override volumetric principles at such minute scales. Active matter physics, an interdisciplinary field, explores the principles behind the behavior and self-organization of living organisms.

“As microbes are often challenged with navigating through confined spaces, we were asking ourselves if there is a pattern behind the microbial navigation in a defined compartment”, the authors note. “At what level does such order start emerging? Specifically, is there a lower bound in either the number of participating microbes or the available space for regularities to affect the activity of the cells?”

Although the movement of a single microbe can appear erratic, the sum of fluidic and surface forces generates striking patterns in the dynamic organizations of microbial groups. To look closely at these patterns, the researchers follow a single moving microbe and experimentally determine the ‘probability flux’ of its movements.

This they do by subdividing a defined compartment into sectors and determining the probability of directional movement into each sector. In this way, they create a map to predict the navigation behavior of the microbe.

The microbe does not move randomly through space, as one might expect, the authors observe. Instead, the average pattern of the microbe’s motion is both highly organized and symmetrical, and the map of the microbe’s movement patterns shows a defined distribution of probability fluxes.

“In particular the strength of the flux was found to depend on the curvature of the adjacent solid interface: a higher degree of curvature resulted in a stronger flux” explain the lead authors of the study, Jan Cammann, PhD student at Loughborough University, and Fabian Schwarzendahl, PhD, a researcher at the MPIDS.

The researchers conduct the experiments in chambers of 2D arrays–elliptical microfluidic compartments about 22 microns high—manufactured using soft-lithography. Before filling the chambers with the cell culture, the authors treat the microfluidic device and a covering glass microscope slide with air plasma to increase the affinity of these surfaces to water. They then place a droplet of the diluted cell suspension at the entry point of the microfluidic device, such that the compartment array is completely filled with the cell suspension. They then press the glass slide over it to seal the compartment, creating a quasi 2D environment that confines the surfaces at the top and bottom, preventing the microbe from moving out of the plane.

Marco Mazza, PhD, lead scientist at MPIDS, and his group have created a model to predict the probabilities of the microbe’s flow in different directions, based on observing the microbe’s pattern of movement in the microfluidic array. They then apply this model to compartments with more complex surface curves. These results are experimentally verified by Bäumchen’s lab.

“It turns out that the curvature of the interface is the dominating factor which directly determines the flux of the self-propelling microbe,” says Bäumchen.

The model defined in the current study constitutes a fundamental observation that can be applied to other areas of active matter physics.

“With our model, we can basically statistically predict where the object of interest will be in the next moment”, says Mazza. “This could not only significantly improve our understanding of the organization of life but also help to engineer technical devices.”