ECOP Subgroup Contributed Talks

Alberto Tenore

University Federico II of Naples, Italy

"A model on phototrophic granular biofilms: microbial ecology and reactor performance"

This talk addresses the mathematical modelling of phototrophic granular biofilms, spherical, dense aggregates constituted by a relevant phototrophic component and developed in presence of light. These biofilm granules are typically cultivated within bioreactors, and represent an innovative technology in the field of wastewater treatment. Specifically, the presented model describes both the growth of phototrophic granules and the related wastewater treatment process occurring in the bioreactor. The biofilm granule has been modelled as a free boundary domain with radial symmetry, which evolves over time as a result of microbial growth, attachment and detachment processes. Hyperbolic and parabolic partial differential equations (PDEs) have been considered to model at mesoscale the transport and growth of sessile biomass and the diffusion and conversion of soluble substrates. The macroscale behaviour of the system has been modelled through first order impulsive ordinary differential equations (IDEs), which reproduce a sequencing batch reactor (SBR) configuration. Phototrophic biomass has been considered for the first time in granular biofilms, and cyanobacteria and microalgae have been accounted separately, to model their different growth and granulation abilities. To describe the key role of cyanobacteria in the photogranulation process, the attachment velocity of all suspended microbial species has been modelled as a function of the cyanobacteria concentration in suspended form. The model takes into account the main biological processes involved in photogranules-based systems: metabolic activity of cyanobacteria, microalgae, heterotrophic and nitrifying bacteria, microbial decay, EPS secrection, symbiotic and competitive interactions between different species, light-dark cycle, light attenuation across the granule and photoinhibion phenomena. The model has been integrated numerically, and the results show its consistency in describing the photogranules evolution and ecology, and highlight the advantages of the photogranules-based technology, analyzing the effects of the influent wastewater composition and light conditions on the process.
Additional authors: Maria Rosaria Mattei, Department of Mathematics and Applications, University Federico II of Naples, Italy; Luigi Frunzo, Department of Mathematics and Applications, University Federico II of Naples, Italy.

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Alejandro Anderson

University of Idaho

"Contribution of waiting times therapies on mathematical models to tackle antimicrobial-drug resistance"

Antimicrobial resistance is a global health concern that requires all possible means of control it. To avoid the onset of multidrug-resistant strains each drug is subject to a maximum time of administration and to a minimum time of administration for effectiveness, referred to as Waiting Time Constraints (WTCs) on biomedical treatments. Treatment with drug combinations and appropriated WT specifications can be modeled by a nonlinear switched system, where a mode (or subsystem) represents the specific administrated drug and the schedule of drugs is associated with an optimal control problem that aims to reduce therapeutic escape. From a dynamic perspective, WTCs significantly alter the regions of the state space of the system that can be feasibly stabilized as they prevent excessive or insufficient time spent in a given mode. Indeed, the literature lacks results on this subject except for recent outcomes for the linear case. Understanding the regions that can be feasibly stabilized is as important as control developing or system modeling; without them no well-posed control can be formulated. Nonetheless, the regions that can be feasibly stabilized by predictive controllers for a nonlinear switched system of antimicrobial resistance, where drugs are subject to WTCs, remain unknown. In this work we present and analyze a series of algorithms to compute stabilizing regions for a switched mathematical model under WTC. The results applied to antibiotic-sensitive and resistance bacteria dynamic population during the course of multi-antibiotic treatment of an infected host addresses the following problems: (i) the existence and characterization of general regions of the state space wherein controlled states trajectories under WTC can feasibly (and indefinitely) remain inside; (ii) when the conditions on WTC to avoid the emergence of resistance allows the existence of feasible and stable control strategies for the success of multiple drug treatment in suppressing the infection; and (iii) when the condition on WTC for the treatment regimen predicts the failure of the treatment due to resistance.
Additional authors: Esteban A. Hernandez-Vargas; Department of Mathematics and Statistical Science, University of Idaho

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Fordyce A. Davidson

University of Dundee

"Competitive outcome in biofilms: a race for space"

Bacteria can form dense communities called biofilms, where cells are embedded in a self-produced extracellular matrix. Exploiting competitive interactions between strains within the biofilm context can have potential applications in biological, medical, and industrial systems. By combining mathematical modelling with experimental assays, we reveal that spatial structure and competitive dynamics within biofilms are significantly affected by the location and density of the founder cells used to inoculate the biofilm. Using a species-independent theoretical framework describing colony biofilm formation, we show that the observed spatial structure and relative strain biomass in a mature biofilm comprising two isogenic strains can be mapped directly to the geographical distributions of founder cells. Moreover, we define a predictor of competitive outcome that accurately forecasts relative abundance of strains based solely on the founder cells potential for radial expansion - a result we confirmed experimentally. Consequently, we reveal that variability of competitive outcome in biofilms inoculated at low founder density is a natural consequence of the random positioning of founding cells in the inoculum. Extension of our study to non-isogenic strains that interact through local antagonisms, shows that even for strains with different competition strengths, a race for space remains the dominant mode of competition in low founder density biofilms. Our results, verified by experimental assays using Bacillus subtilis, highlight the importance of spatial dynamics on competitive interactions within biofilms and hence to related applications
Additional authors: Lukas Eigentler, University of Dundee*; Margarita Kalamara, University of Dundee; Graeme Ball, University of Dundee; Cait E. MacPhee, University of Edinburgh; Nicola R. Stanley-Wall, University of Dundee; Fordyce A. Davidson, University of Dundee . *Current address University Bielefeld, Germany.

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Jessica Renz

University of Bergen

"Learning and predicting the pathways of AMR evolution with hypercubic inference"

Understanding the evolution of antimicrobial resistance (AMR) is central for their treatment. In this talk, I want to show a possible way to address this problem from a statistical point of view, namely the hypercubic inference, which we developed and introduced during the last years at the University of Bergen. The basis of this model is a hypercubic transition graph, whose nodes represent possible resistance states and the edges between correspond to the different evolutionary steps. This new approach allows us to efficiently make predictions about the most likely evolutionary pathways leading to AMR and learn their structure and variability, even if we have incomplete datasets with uncertain states. For this we can either use Bayesian inference via Monte Carlo Markov Chain methods or a frequentist approach for the estimation of likelihoods, whereby we only need cross-sectional datasets. While we focus here on AMR, hypercubic inference can be and has been used in a very wide range of problems involving evolutionary accumulation and disease progression, including ovarian cancer, severe malaria, genome and behavioral evolution, and educational progress. The focus of the talk will be the introduction and explanation of the methods themselves, whereby I will address both the advantages and strengths of using a hypercubic structure, but also open problems and ongoing work. In addition, I will also present the results of concrete current applications to real AMR datasets from Klebsiella pneumoniae and Escherichia coli and discuss some biological insights that can be derived from them.

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