Report

Teaser, summary, work performed and final results

Periodic Reporting for period 1 - DRAMATIC (Development of Relevant Approaches to Mathematically Model Increasingly Complex Microbially-driven Processes)

Teaser

Mathematical models are commonplace in biology. In environmental engineering applications such as water and wastewater treatment, waste stabilisation and biofuel production, modelling of these processes is important to understand the behaviour of the microbial communities that...

Summary

Mathematical models are commonplace in biology. In environmental engineering applications such as water and wastewater treatment, waste stabilisation and biofuel production, modelling of these processes is important to understand the behaviour of the microbial communities that drive them. This is especially relevant in view of the significant challenges related to global warming and decreasing fossil fuel resources, which have emphasised the need to seek alternative, low-cost, carbon neutral and renewable sources of energy, as well as improving the efficiency and effectiveness of processes dealing with biological waste treatment. These have been addressed in Europe by EU directives that seek to support policy and research in a range of areas related to alternative and improved technologies for managing energy demand, environmental quality and societal needs. Together with the theoretical mathematics supporting the models, there is a growing need to be able to communicate the information gained from their analysis in a way that is transparent and accessible to practitioners who can apply this knowledge to their process. Ultimately, this will lead to greater acceptance of the often challenging mathematical approaches required to fully understand or predict the behaviour of microbial systems.

Mathematical modelling has played a key role in understanding and predicting the fundamental characteristics and behaviour of ecological systems for over a century. In microbial ecology it has developed as an important discipline due to recent advances in the fields of environmental microbiology, mathematical biology and ecological modelling.

In recent years, there has been a shift in the focus of modelling efforts away from conventional approaches to applications requiring expertise from a spectrum of scientific discipline. However, with the acquisition of greater understanding of microbial kinetics from molecular biology and biochemistry, scientists are now able to explore microbial ecosystems at a greater resolution, in which the concept of microbes as chemical units are no longer sufficient. In these systems, modelling has attempted to reveal the dynamics and interactions of microbial communities from simple co-cultures in dedicated experimental devices (‘chemostats’) through to more complex systems with highly diverse functionality. Whilst it is acknowledged that mechanistic approaches to modelling have helped make sense of empirical observations in microbial systems, one must still consider the underlying objective of any modelling exercise, the outputs and precision required, and the effort needed to parameterise and simulate the model under the desired conditions. Most models describe populations at a macroscopic level, without incorporating knowledge at the individual scale, justifying the deterministic nature of these models under the implicit assumption that the population size is large enough to average out variability. As the quantity and quality of data continues to improve, modelling must move apace. The UK Government has set out thematic priorities for the EU Horizon 2020 programme on “Modelling, simulation and prediction to explore control of pathways and develop opportunities for synthetic biology” and “system modelling to optimise performance” as key to development across biotechnology sectors. Further, the Biotechnology-based industrial products and processes strand of the Horizon 2020 industrial leadership pillar directs research and innovation in “gaining insight on the dynamics of microbial communities”.

Objective 1: To comprehensively analyse microbial communities at a scale that allows rigorous mathematical study of their behaviour

Objective 2: To develop, incorporate and compare alternative approaches to microbial population modelling

Objective 3: Development of software tools that can be utilised by the scientific community to facilitate rapid determination of characteristics and behaviour of

Work performed

Working towards the objectives, initially three systems were identified as candidate system for model development, being reducible and open to mathematical analysis:

(i) A model describing an anaerobic community comprising three organisms degrading mono-chlorophenol to methane as a food-web;

(ii) Analysis of a simplified zero-dimensional model (i.e., no consideration of spatial effects) of the Partial Nitritation/Anammox (PN/A) shortcut nitrification process;

(iii) A reduced model of the anaerobic digestion process describing a tri-culture of a sulphate-reducing bacteria and two methanogens;

With this Fellowship, the deterministic, structured models developed in WP1 were suitable for deriving fundamental knowledge and demonstrating the qualitative behaviour of system dynamics. When translating theoretical knowledge into practical application, the use of a singular model is typically not sufficient, and whilst some models may adequately represent system dynamics under simulation conditions, they may be inefficient. Here, a series of alternative approaches and advances on existing models were explored. Several more advanced models and approaches were investigated:

(i) Extension of the PN/A model to include effects of nutrient gradients through the sessile phase of the system

(ii) Inclusion of thermodynamics and a method to describe metabolic pathway switching

(iii) Competition-cooperation model using Delay Differential Equations

(iv) Data-driven modelling for biological engineered systems: hybrid models & machine learning

Final results

Progress beyond the state-of-the-art:

- Analytical proof of a Hopf bifurcation and conditions for persistence of a general three-tiered model of chlorophenol mineralisation with extraneous substrate addition;
- New and more efficient numerical method for solving the boundary value problem in a one dimensional biofilm
- A novel approach to optimise a kinetic model of anaerobic digestion with the incorporation of thermodynamic functions

Expected results:

- An individual based modelling approach that incorporates bacterial morphology and chemotactic behaviour, coupled to microfluidic studies and advanced visualisation techniques
- A comparison of modelling approaches for biological engineered systems (e.g., complexity and functional requirements for varied engineering objectives)

Potential impacts:

- The Fellow will gain mathematical competency and expertise of dynamical systems modelling to enhance his existing capabilities and knowledge on microbial ecology and modelling;
- The Fellow will gain a greater understanding of the challenges and opportunities related to impacts on European Society including better use of resources, improved treatment processes, and the development of bioprocess engineering to meet the human and environmental challenges of the modern world;
- The Fellow will be competitive at the highest level with regard to acquisition of funding to support research independence and will have closer connections with industry in which his research will deliver impact;
- Modelling insights that will be incorporated into future research work by the Fellow and other academics. Connections with industry in which model results may further existing tools used for process design and operation.

Website & more info

More info: https://github.com/MI-SIM/DRAMATIC.