Jordi Ferrer

Individual-based Modelling: An Essential Tool for Microbiology

Micro-organisms play a central role in every ecosystem and in the global biomass cycle. They are strongly involved in many fields of human interest, from medicine to the food industry and waste control. Nevertheless, most micro-organisms remain almost unknown, and nearly 99% of them have not yet been successfully cultured in vitro. Therefore, new approaches and new tools must be developed in order to understand the collective behaviour of microbial communities in any natural or artificial setting. In particular, theoretical and practical methodologies to deal with such systems at a mesoscopic level of description (covering the range from 100 to 108 cells) are required. Individual-based modelling (IBM) has become a widely used tool for describing complex systems made up of autonomous entities, such as ecosystems and social networks. Individual-based models (IBMs) provide some advantages over the traditional whole-population models: (a) they are bottom-up approaches, so they describe the behaviour of a system as a whole by establishing procedural rules for the individuals and for their interactions, and thus allow more realistic assumptions for the model of the individuals than population models do; (b) they permit the introduction of randomness and individual variability, so they can reproduce the diversity found in real systems; and (c) they can account for individual adaptive behaviour to their environmental conditions, so the evolution of the whole system arises from the dynamics that govern individuals in their pursuit of optimal fitness. However, they also present some drawbacks: they lack the clarity of continuous models and may easily become rambling, which makes them difficult to analyse and communicate. All in all, IBMs supply a holistic description of microbial systems and their emerging properties. They are specifically appropriate to deal with microbial communities in non-steady states, and spatially explicit IBMs are particularly appropriate to study laboratory and natural microbiological systems with spatial heterogeneity. In this paper, we review IBM methodology applied to microbiology. We also present some results obtained from the application of Individual Discrete Simulations, an IBM of ours, to the study of bacterial communities, yeast cultures and Plasmodium falciparum-infected erythrocytes in vitro cultures of Plasmodium falciparum-infected erythrocytes.

Mathematical modelling methodologies in predictive food microbiology: A SWOT analysis

Predictive microbiology is the area of food microbiology that attempts to forecast the quantitative evolution of microbial populations over time. This is achieved to a great extent through models that include the mechanisms governing population dynamics. Traditionally, the models used in predictive microbiology are whole-system continuous models that describe population dynamics by means of equations applied to extensive or averaged variables of the whole system. Many existing models can be classified by specific criteria. We can distinguish between survival and growth models by seeing whether they tackle mortality or cell duplication. We can distinguish between empirical (phenomenological) models, which mathematically describe specific behaviour, and theoretical (mechanistic) models with a biological basis, which search for the underlying mechanisms driving already observed phenomena. We can also distinguish between primary, secondary and tertiary models, by examining their treatment of the effects of external factors and constraints on the microbial community. Recently, the use of spatially explicit Individual-based Models (IbMs) has spread through predictive microbiology, due to the current technological capacity of performing measurements on single individual cells and thanks to the consolidation of computational modelling. Spatially explicit IbMs are bottom-up approaches to microbial communities that build bridges between the description of micro-organisms at the cell level and macroscopic observations at the population level. They provide greater insight into the mesoscale phenomena that link unicellular and population levels. Every model is built in response to a particular question and with different aims. Even so, in this research we conducted a SWOT (Strength, Weaknesses, Opportunities and Threats) analysis of the different approaches (population continuous modelling and Individual-based Modelling), which we hope will be helpful for current and future researchers.

Analysis and IbM simulation of the stages in bacterial lag phase: Basis for an updated definition

The lag phase is the initial phase of a culture that precedes exponential growth and occurs when the conditions of the culture medium differ from the pre-inoculation conditions. It is usually defined by means of cell density because the number of individuals remains approximately constant or slowly increases, and it is quantified with the lag parameter lambda. The lag phase has been studied through mathematical modelling and by means of specific experiments. In recent years, Individual-based Modelling (IbM) has provided helpful insights into lag phase studies. In this paper, the definition of lag phase is thoroughly examined. Evolution of the total biomass and the total number of bacteria during lag phase is tackled separately. The lag phase lasts until the culture reaches a maximum growth rate both in biomass and cell density. Once in the exponential phase, both rates are constant over time and equal to each other. Both evolutions are split into an initial phase and a transition phase, according to their growth rates. A population-level mathematical model is presented to describe the transitional phase in cell density. INDividual DIScrete SIMulation (INDISIM) is used to check the outcomes of this analysis. Simulations allow the separate study of the evolution of cell density and total biomass in a batch culture, they provide a depiction of different observed cases in lag evolution at the individual-cell level, and are used to test the population-level model. The results show that the geometrical lag parameter lambda is not appropriate as a universal definition for the lag phase. Moreover, the lag phase cannot be characterized by a single parameter. For the studied cases, the lag phases of both the total biomass and the population are required to fully characterize the evolution of bacterial cultures. The results presented prove once more that the lag phase is a complex process that requires a more complete definition. This will be possible only after the phenomena governing the population dynamics at an individual level of description, and occurring during the lag and exponential growth phases, are well understood.

Individual-based modelling and simulation of microbial processes: yeast fermentation and multi-species composting

Controlled microbial activity is the core of many industrial processes. Such dynamic microbial processes must be carefully studied to optimize their application. They are usually tackled by means of continuous mathematical modelling at the population level (top-down). An alternative approach is individual-based modelling (IbM) (bottom-up). INDISIM is a discrete and spatially explicit IbM. It sets the rules that govern each microbe and its interaction with its local environment, as well as the significant environmental processes. Then it performs simulations that include a large number of microbes, and the behaviour of the whole system emerges. The rules are changed to reproduce the behaviour of microbes depending on the system to be studied. Two adaptations of INDISIM to study yeast fermentations and multi-species composting are presented in this article (INDISIM-YEAST and INDISIM-COMP), proof of INDISIMs versatility. A few representative results are also shown.

Effect of the haematocrit layer geometry on Plasmodium falciparum static thin-layer in vitro cultures

BackgroundIn vitro cultivation of Plasmodium falciparum is usually carried out through the continuous preservation of infected erythrocytes deposited in static thin layers of settled haematocrit. This technique, called the candle-jar method, was first achieved by Trager and Jensen in 1976 and has undergone slight modifications since then. However, no systematic studies concerning the geometry of the haematocrit layer have been carried out. In this work, a thorough investigation of the effects of the geometric culturing conditions on the parasites development is presented.MethodsSeveral experimental trials exploring different settings have been carried out, covering haematocrit layer depths that ranged from 6 mm to 3 mm and separation between the walls of the culturing device that ranged from 7.5 mm to 9 mm. The obtained results have been analysed and compared to different system-level models and to an Individual-Based Model.ConclusionIn line with the results, a mechanism governing the propagation of the infection which limits it to the vicinity of the interface between the haematocrit layer and the culture medium is deduced, and the most appropriate configurations are proposed for further experimental assays.

Thermodynamic Concepts in the Study of Microbial Populations: Age Structure in Plasmodium falciparum Infected Red Blood Cells

Variability is a hallmark of microbial systems. On the one hand, microbes are subject to environmental heterogeneity and undergo changeable conditions in their immediate surroundings. On the other hand, microbial populations exhibit high cellular diversity. The relation between microbial diversity and variability of population dynamics is difficult to assess. This connection can be quantitatively studied from a perspective that combines in silico models and thermodynamic methods and interpretations. The infection process of Plasmodium falciparum parasitizing human red blood cells under laboratory cultivation conditions is used to illustrate the potential of Individual-based models in the context of predictive microbiology and parasitology. Experimental data from several in vitro cultures are compared to the outcome of an individual-based model and analysed from a thermodynamic perspective. This approach allows distinguishing between intrinsic and external constraints that give rise to the diversity in the infection forms, and it provides a criterion to quantitatively define transient and stationary regimes in the culture. Increasing the ability of models to discriminate between different states of microbial populations enhances their predictive capability which finally leads to a better the control over culture systems. The strategy here presented is of general application and it can substantially improve modelling of other types of microbial communities.

Contribution of Individual-based Models in malaria elimination strategy design

Background Global strategies to fight malaria consist of three components: medical coverage scale-up in the affected regions, sustained control of the disease and increasing local elimination. These strategies normally consider long-term temporal scales of the order of the decade and are typically formulated either in technical terms or through mathematical models that are not easily communicated to non-experts (e.g. local people that act as malaria control technicians and local governments). Yet, global strategies finally lie on local specific interventions, carried out by agents with a limited scope of action and covering short spans. Field actions against malaria typically have to struggle against logistic limitations and must be very well coordinated in order to succeed. There is a need for models that can connect field actors with strategy designers in order to tackle the specific constraints of each particular intervention, and to redefine objectives on the fly, in accordance with the field results.