Choosing an Appropriate Modelling Framework for Analysing Multispecies Co-culture Cell Biology Experiments

Spatial cumulant models enable spatially informed treatment strategies and analysis of local interactions in cancer systems

Theoretical and applied cancer studies that use individual-based models (IBMs) have been limited by the lack of a mathematical formulation that enables rigorous analysis of these models. However, spatial cumulant models (SCMs), which have arisen from theoretical ecology, describe population dynamics generated by a specific family of IBMs, namely spatio-temporal point processes (STPPs). SCMs are spatially resolved population models formulated by a system of differential equations that approximate the dynamics of two STPP-generated summary statistics: first-order spatial cumulants (densities), and second-order spatial cumulants (spatial covariances). We exemplify how SCMs can be used in mathematical oncology by modelling theoretical cancer cell populations comprising interacting growth factor-producing and non-producing cells. To formulate model equations, we use computational tools that enable the generation of STPPs, SCMs and mean-field population models (MFPMs) from user-defined model descriptions (Cornell et al. Nat Commun 10:4716, 2019). To calculate and compare STPP, SCM and MFPM-generated summary statistics, we develop an application-agnostic computational pipeline. Our results demonstrate that SCMs can capture STPP-generated population density dynamics, even when MFPMs fail to do so. From both MFPM and SCM equations, we derive treatment-induced death rates required to achieve non-growing cell populations. When testing these treatment strategies in STPP-generated cell populations, our results demonstrate that SCM-informed strategies outperform MFPM-informed strategies in terms of inhibiting population growths. We thus demonstrate that SCMs provide a new framework in which to study cell-cell interactions, and can be used to describe and perturb STPP-generated cell population dynamics. We, therefore, argue that SCMs can be used to increase IBMs' applicability in cancer research.

Modelling collective cell migration: neural crest as a model paradigm

A huge variety of mathematical models have been used to investigate collective cell migration. The aim of this brief review is twofold: to present a number of modelling approaches that incorporate the key factors affecting cell migration, including cell-cell and cell-tissue interactions, as well as domain growth, and to showcase their application to model the migration of neural crest cells. We discuss the complementary strengths of microscale and macroscale models, and identify why it can be important to understand how these modelling approaches are related. We consider neural crest cell migration as a model paradigm to illustrate how the application of different mathematical modelling techniques, combined with experimental results, can provide new biological insights. We conclude by highlighting a number of future challenges for the mathematical modelling of neural crest cell migration.

Co-Culture Systems for the Production of Secondary Metabolites: Current and Future Prospects

Microorganisms are the great sources of Natural Products (NPs); these are imperative to their survival apart from conferring competitiveness amongst each other within their environmental niches. Primary and secondary metabolites are the two major classes of NPs that help in cell development, where antimicrobial activity is closely linked with secondary metabolites. To capitalize on the effects of secondary metabolites, co-culture methods have been often used to develop an artificial microbial community that promotes the action of these metabolites. Different analytical techniques will subsequently be employed based on the metabolite specificity and sensitivity to further enhance the metabolite induction. Liquid Chromatography-Mass Spectrometry (LC-MS) and Gas Chromatography (GC)-MS are commonly used for metabolite separation while Nuclear Magnetic Resonance (NMR) and Mass Spectrometry (MS) have been used as tools to elucidate the structure of compounds. This review intends to discuss current systems in use for co-culture in addition to its advantages, with discourse into the investigation of specific techniques in use for the detailed study of secondary metabolites. Further advancements and focus on co-culture technologies are required to fully realize the massive potential in synthetic biological systems.