Frontiers in Mathematical Biology

Fragmentation of bacterial flocs

Erin Byrne

Harvey Mudd College

Multicellular communities are a dominant, if not the predominant, form of bacterial growth. Growing affixed to a surface, they are termed biofilms. When growing freely suspended in aqueous environments, they are usually referred to as flocs. Flocculated growth is important in conditions as varied as bloodstream infections (where flocs can be seen under the microscope) to algal blooms (where they can be seen from low earth orbit). Understanding the distribution of floc sizes in a disperse collection of bacterial colonies is a significant experimental and theoretical challenge. One analytical approach is the application of the Smoluchowski coagulation equations, a group of PDEs that track the evolution of a particle size distribution over time. The equations are characterized by kernels describing the result of floc collisions as well as hydrodynamic-mediated fragmentation into daughter aggregates. The post-fragmentation probability density of daughter flocs is one of the least well-understood aspects of modeling flocculation. A wide variety of functional forms have been used over the years for describing fragmentation, and few have had experimental data to aid in its construction. In this talk, we discuss the use of 3D positional data of Klebsiella pneumoniae bacterial flocs in suspension, along with the knowledge of hydrodynamic properties of a laminar flow field, to construct a probability density function of floc volumes after a fragmentation event. Computational results are provided which predict that the primary fragmentation mechanism for medium to large flocs is erosion, as opposed to the binary fragmentation mechanism (i.e. a fragmentation that results in two similarly-sized daughter flocs) that has traditionally been assumed.