Mathematical Modeling

Developing effective strategies for managing microbial communities

Microorganisms grow and decay in the environment, engineered system, and the human body.  These activities, which are linked to multiple components and processes at scales from molecular to global, transform and transfer energy, materials, structures, and genetic information.  For example, microorganisms grow on diverse energy sources:  e.g., phototrophy in photobioreactors (PBRs), anode respiration in microbial electrochemical systems (MXCs), and uranium reduction in groundwater.  Materials microorganisms transform can be soluble, particulate, gaseous, and electrochemical.  Processes in microbiological systems can range from fast to slow:  e.g., in a microbial fuel cell (MFC), acid-base equilibrium is infinitely fast, but transport of alkalinity is slow, leading to a strong pH gradient.  Microorganisms establish communities in self-forming aggregates:  e.g., flocs, biofilm, and granules.

Researchers at the Swette Center from Environmental Biotechnology develop and apply novel mathematical models that translate the multiple facets of microbiological activities into a useful quantitative framework.  We derive kinetic and thermodynamic models that describe microbiological physiology:  e.g., the Nernst-Monod equation for understanding bacterial electrochemistry; inhibition and promotion models for microbial processes linked to aqueous chemistry and photosynthesis; and Unified Theory for Soluble Microbial Products (SMPs) for tracking soluble and solid materials of microbial origin.  Our models describe microorganisms growing in communities, including in biofilms.  We link these frameworks into overall process-based models that tell us how real-world systems function – and why.  Integrating physical, chemical, and microbiological processes is computationally challenging, and we have developed efficient computational frameworks for unique settings:  CASADM, CCBATCH and PCBIOFILM.  Our ultimate goal:  identifying the processes and parameters that control performance and formulating effective strategies for managing microbial communities.

A typical H2-concentration profile in the permeation test in a membrane biofilm reactor (MBfR). A virtual gas layer with a negligible thickness is added to correlate the H2 concentrations in the membrane and diffusion layer. For more information, click here.  

An illustration of three processes that follow the ARB reaction in microbial electrochemical cells (MXCs):  mass transport, conduction and acid-base reactions.  For more information, click here.