The differential equation counterpart of an individual-based model for yeast population growth

Abstract

a b s t r a c tComputer simulations are increasingly used in biological fields. The amazing power, storage ability, and processing speeds available nowadays have enabled the implementation of computer individual-based models (IbMs) to simulate really complex biological populations. Computers can easily keep track of thousands of individuals (often called 'agents'), whose complex behaviours and large amounts of associated data were daunting only 20 years ago. As such, computer modelling has just entered a field where traditional PDE models used to reign alone. A study of the exchange and non-trivial relationship between these two fields, computer IbMs versus classic partial differential equations (PDEs), is appropriate. The aim of this paper is to compare both approaches through a relevant example, namely the evolution of a yeast population in a batch culture. Thus, this paper deals with the utilization of both classical mathematics and computer science in the solution of problems arising in microbiology. First, an IbM approach to study the evolution of a yeast batch culture is presented. Second, an equivalent PDE model is derived by using some techniques from the interacting particle systems field. Third, a comparison and discussion on the advantages and drawbacks of both modelling tools is given.

Exploring the lag phase and growth initiation of a yeast culture by means of an individual-based model

“…When microbial growth is considered starting from a few cells, the study of this evolution demands an individual-based approach. The two approaches, however, can converge to similar results as the size of the population increases (Gómez-Mourelo and Ginovart, 2009). Unlike continuous models, IbM is a bottom-up approach.…”

Analysis of the effect of inoculum characteristics on the first stages of a growing yeast population in beer fermentations by means of an individual-based model

“…For this study, we used INDISIM-YEAST as the individual-based simulator, which is based on the generic simulator INDISIM [9,[11][12][13][14]. Although the reader can refer to some previously published papers for a description of different parts of INDISIM-YEAST [11,12], a formal and brief description of this simulation model is presented below in order to make this study more self-contained and autonomous.…”

A connection between discrete individual-based and continuous population-based models: A forest modelling case study

“…In this line, two previous studies in the area of biology can be cited to illustrate quantitative results in the comparison of IBMs and PDEs, comparisons of the observed macroscopic and microscopic behaviour of an IBM with the corresponding differential equation counterpart of this IBM were shown. The first study is about an application to the upstream movement of elvers [52] and the second is a study on yeast populations [47] . These types of works provide a further insight into the possibilities of both modelling tools and their connections.…”

“…For instance, the way to obtain this equivalent PDE from a particular IBM has already been explained in two different cases: a cancer tumour invasion in a healthy surrounding tissue [46] , and a yeast population growth in a liquid medium [47] . …”