# Development of Relevant Approaches to Mathematically Model Increasingly Complex Microbially-driven Processes

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# A simplified approach shines light on complex microbial systems

Predictive models support fields from pharmaceutical development to investing. Simplifying underlying models to accommodate integration of high-level analyses has enabled a step change in qualitative insight regarding complex microbe-based processes for a sustainable future.

Fundamental Research

Mathematics help us make sense of the world, establishing concrete cause-and-effect relationships. For example, a 20 % discount on your EUR 1000 refrigerator provides a savings of 0.20*1000 = EUR 200. Mathematical descriptions and models are even more necessary for scientists and engineers who attempt to describe processes of incredible complexity in fields from medicine and climate science to economics and manufacturing. With the support of the Marie Skłodowska-Curie Actions Individual Fellowships (MSCA-IF) programme, the DRAMATIC project developed improved mathematical models to help us better harness the power of microbial life for the benefit of people and the environment. Specifically, the global fellowship recipient Matthew Wade of Newcastle University integrated mathematical theory commonly used to describe industrial processes into models of engineered biological systems (EBS).

## Simplifying models facilitates integration with high-level maths

An EBS is any biological process that is manipulated and managed using engineering principles. A wastewater treatment plant is a common example. Currently, process disturbances, faults and even failure are commonly addressed based on empirical knowledge. Predictive models must balance detail (that may, or may not, increase accuracy given inherent uncertainty) against computation time and computational load to be useful. By reducing model complexity without sacrificing the required accuracy, scientists can make the models amenable to rigorous mathematical analyses.

## The proof is in the pudding

This is exactly what Wade has done. He explains: “Mathematical analysis tools, typically in the domain of theorists, can be applied to simplified models of EBS to investigate the qualitative dynamics of the system. This can help identify unexpected or emergent behaviour, guide experimental studies and enable optimisation of parameters for improved process control.” Wade’s methodology can lead to tailored models rather than commonly used off-the-shelf simulators constrained by fixed parameter sets. Wade developed a method to perform bifurcation analysis for the study of deammonification, an energy efficient process universally accepted for the treatment of ammonium rich sewage. Bifurcation analysis describes how the long term behaviour predicted by the model changes, as key control parameters in the model change. Wade’s open-access code and analysis enhanced the understanding of how selected control parameters can suppress the growth of organisms that adversely impact the performance of the process by increasing energy and carbon demand.

## Quality and not quantity

While lesser detail and simplifying assumptions of the underlying predictive model may reduce quantitative accuracy, qualitative insights are vital to planning and optimisation of biological treatment processes. This is especially true at a time when resource and energy efficiency are priorities. Further, in many cases, reduced models can be studied analytically using generalised descriptions for microbial growth, potentially yielding even more powerful insights as the properties will hold true for all parameter values. Wade concludes: “The environmental, economic and social constraints on our water, energy and food supplies are increasing. It is critical to ensure that the EBS linked to these resources are not only optimised but resilient and flexible to future demands. DRAMATIC has demonstrated the important and necessary role of mathematical analysis in understanding and managing EBS.”

## Keywords

DRAMATIC, model, mathematical, EBS, microbial, bifurcation analysis, deammonification, engineered biological systems, wastewater

29 May 2020