Generation of multicellular spatiotemporal models of population dynamics from ordinary differential equations, with applications in viral infection

BACKGROUND

The biophysics of an organism span multiple scales from subcellular to organismal and include processes characterized by spatial properties, such as the diffusion of molecules, cell migration, and flow of intravenous fluids. Mathematical biology seeks to explain biophysical processes in mathematical terms at, and across, all relevant spatial and temporal scales, through the generation of representative models. While non-spatial, ordinary differential equation (ODE) models are often used and readily calibrated to experimental data, they do not explicitly represent the spatial and stochastic features of a biological system, limiting their insights and applications. However, spatial models describing biological systems with spatial information are mathematically complex and computationally expensive, which limits the ability to calibrate and deploy them and highlights the need for simpler methods able to model the spatial features of biological systems.

RESULTS

In this work, we develop a formal method for deriving cell-based, spatial, multicellular models from ODE models of population dynamics in biological systems, and vice versa. We provide examples of generating spatiotemporal, multicellular models from ODE models of viral infection and immune response. In these models, the determinants of agreement of spatial and non-spatial models are the degree of spatial heterogeneity in viral production and rates of extracellular viral diffusion and decay. We show how ODE model parameters can implicitly represent spatial parameters, and cell-based spatial models can generate uncertain predictions through sensitivity to stochastic cellular events, which is not a feature of ODE models. Using our method, we can test ODE models in a multicellular, spatial context and translate information to and from non-spatial and spatial models, which help to employ spatiotemporal multicellular models using calibrated ODE model parameters. We additionally investigate objects and processes implicitly represented by ODE model terms and parameters and improve the reproducibility of spatial, stochastic models.

CONCLUSION

We developed and demonstrate a method for generating spatiotemporal, multicellular models from non-spatial population dynamics models of multicellular systems. We envision employing our method to generate new ODE model terms from spatiotemporal and multicellular models, recast popular ODE models on a cellular basis, and generate better models for critical applications where spatial and stochastic features affect outcomes.

Data-driven multiscale modeling reveals the role of metabolic coupling for the spatio-temporal growth dynamics of yeast colonies

BACKGROUND

Multicellular entities like mammalian tissues or microbial biofilms typically exhibit complex spatial arrangements that are adapted to their specific functions or environments. These structures result from intercellular signaling as well as from the interaction with the environment that allow cells of the same genotype to differentiate into well-organized communities of diversified cells. Despite its importance, our understanding how this cell-cell and metabolic coupling lead to functionally optimized structures is still limited.

RESULTS

Here, we present a data-driven spatial framework to computationally investigate the development of yeast colonies as such a multicellular structure in dependence on metabolic capacity. For this purpose, we first developed and parameterized a dynamic cell state and growth model for yeast based on on experimental data from homogeneous liquid media conditions. The inferred model is subsequently used in a spatially coarse-grained model for colony development to investigate the effect of metabolic coupling by calibrating spatial parameters from experimental time-course data of colony growth using state-of-the-art statistical techniques for model uncertainty and parameter estimations. The model is finally validated by independent experimental data of an alternative yeast strain with distinct metabolic characteristics and illustrates the impact of metabolic coupling for structure formation.

CONCLUSIONS

We introduce a novel model for yeast colony formation, present a statistical methodology for model calibration in a data-driven manner, and demonstrate how the established model can be used to generate predictions across scales by validation against independent measurements of genetically distinct yeast strains.

Modeling cell-cell communication for immune systems across space and time

Communicating is crucial for cells to coordinate their behaviors. Immunological processes, involving diverse cytokines and cell types, are ideal for developing frameworks for modeling coordinated behaviors of cells. Here, we review recent studies that combine modeling and experiments to reveal how immune systems use autocrine, paracrine, and juxtacrine signals to achieve behaviors such as controlling population densities and hair regenerations. We explain that models are useful because one can computationally vary numerous parameters, in experimentally infeasible ways, to evaluate alternate immunological responses. For each model, we focus on the length-scales and time-scales involved and explain why integrating multiple length-scales and time-scales in a model remain challenging. We suggest promising modeling strategies for meeting this challenge and their practical consequences.