Concepts

The concept behind microbenthos models is to generate partial differential equations of various analytes/variables that constitute the relationships between the entities of the model. So the starting point for creating microbenthic models is to write down the constitutive relationships between chemical or metabolic processes and their dependencies on environmental conditions.

Example of partial differential equations that can be built and solved

The special case of microbenthic systems emerges from the extremely steep gradients of most environmental parameters within a few millimeters, i.e. irradiance intensity, oxygen, sulfide, biomass, etc. Microbial mats constitute very dense, laminated populations of different microbial groups that occupy the niches created by the microenvironments and exploit them through adapted and specific metabolic processes.

Microbial mats are typically modelled as diffusive-reactive systems, i.e. the dominant mode of mass transport is physical diffusion of solutes. This diffusion occurs within the porespaces of the sediment matrix, which are considered to be occupied by microbial populations. The “reactive” aspect refers to the presence of a large number of “local” sources and sinks within the mat system. Indeed, a vast array of metabolic pathways can be found within a few millimeters of microbial mats, with one population thriving off the side-products of another populations main process. Furthermore, the various metabolisms have responses to multiple environmental parameters, responding to some with inhibition, to others with saturation and preferences for an optimum level. This could be with respect to light, or temperature, or oxygen or any other environmental parameters.

MicroBenthos recognizes that while the process of physical diffusion is simple to model, the larger challenge is to have a flexible way to experiment with in silico microbial mats, that can exhibit various types of metabolic responses. So MicroBenthos helps in converting constitutive relationships for metabolic processes, e.g. oxygenic photosynthesis is inhibited by oxygen and sulfide and has an optimal light level, into mathematical equations and compiling several of these into highly non-linear, coupled, partial differential equations. This is done through symbolic computation (using sympy) and abstractions at the level useful for microbial mats (sediment, diffusive boundary layer, microbial biomass, etc) and then iteratively solving the differential equations (using fipy) as the model clock evolves.

The Tutorials provide a hands-on path towards creating and studying your own in silico microbial mats which can include features such as:

  • solar irradiance

  • photopigment absorption

  • microbial metabolisms (respiration, photosynthesis, etc)

  • abiotic (geo)chemical processess

  • biomass synthesis and growth

  • … and more to come

References

  • Rutger de Wit, Frank P. van den Ende, Hans van Gemerden; Mathematical simulation of the interactions among cyanobacteria, purple sulfur bacteria and chemotrophic sulfur bacteria in microbial mat communities, FEMS Microbiology Ecology, Volume 17, Issue 2, 1 June 1995, Pages 117–135 (DOI)

  • Hans van Gemerden; Microbial mats: A joint venture, Marine Geology, Volume 113, Issues 1-2, July 1993, Pages 3-25 (DOI)

  • J. E. Guyer, D. Wheeler & J. A. Warren, FiPy: Partial Differential Equations with Python, Computing in Science & Engineering 11 (3) pp. 6-15 (2009), (DOI)