Unification of aggregate growth models by emergence from cellular and intracellular mechanisms

Abstract

Multicellular aggregate growth is regulated by nutrient availability and removal of metabolites, but the specifics of growth dynamics are dependent on cell type and environment. Classical models of growth are based on differential equations. While in some cases these classical models match experimental observations, they can only predict growth of a limited number of cell types and so can only be selectively applied. Currently, no classical model provides a general mathematical representation of growth for any cell type and environment. This discrepancy limits their range of applications, which a general modelling framework can enhance. In this work, a hybrid cellular Potts model is used to explain the discrepancy between classical models as emergent behaviours from the same mathematical system. Intracellular processes are described using probability distributions of local chemical conditions for proliferation and death and simulated. By fitting simulation results to a generalization of the classical models, their emergence is demonstrated. Parameter variations elucidate how aggregate growth may behave like one classical growth model or another. Three classical growth model fits were tested, and emergence of the Gompertz equation was demonstrated. Effects of shape changes are demonstrated, which are significant for final aggregate size and growth rate, and occur stochastically.

Generating Agent-Based Multiscale Multicellular Spatiotemporal Models from Ordinary Differential Equations of Biological Systems, with Applications in Viral Infection

“…Indeed, previous works have performed related investigations of how spatial and cellular mechanisms affect emergent dynamics in biological systems of which non-spatial models have been developed. One such example described emergent growth dynamics in diffusion-limited systems on a cellular basis as affected by aggregate shape (16), which could be further investigated with regards to existing non-spatial models of organoid growth in vitro (32,33) using cellularization. Furthermore, operations defined in our cellularization method on spatial models may generate novel non-spatial model terms that are not obvious from a homogenized approach.…”

“…The ability to derive cell-based, spatiotemporal models from ODE models would enhance the utility of both types of models. Cell-based, spatiotemporal models can explicitly describe cellular and spatial mechanisms neglected by ODE models that affect the emergent dynamics and properties of multicellular systems, such as the influence of dynamic aggregate shape on diffusionlimited growth dynamics (16) and individual infected cells on the progression of viral infection (17). Likewise ODE models can inform cell-based, spatiotemporal models with efficient parameter fitting to experimental data, and can appropriately describe dynamics at coarser scales and distant locales with respect to a particular multicellular domain of interest (e.g., the population dynamics of a lymph node when explicitly modeling local viral infection).…”

Breast Cancer Reaction-Diffusion from Spectral-Spatial Analysis in Immunohistochemistry

“…No less important is the role of the diffusion process models in the approach to the clinically significant problems of patient-specific imaging-derived predictive models in response to neoadjuvant therapy of breast cancer. Several authors studied this problem (Weis et al ., 2013, 2015, 2017, Roque et al ., 2018, Jarrett et al ., 2018, Mang et al ., 2020), focusing on the coupling diffusion model to extracellular matrix stiffness, in connection with radiotherapy (Roniotis et al ., 2012, Holdsworth et al ., 2012, Borasi et al ., 2016) or synergy of radiation therapy and chemotherapy (Kibis and Buyuktahtakin 2018), surgical resection (Hathout et al ., 2016), necrosis density thresholds (Patel and Hathout 2017), radiation-induced necrosis (Narasimhan et al ., 2019), in vitro treatment of triple-negative breast cancer cell lines (Bowers et al ., 2020), in connection with in vitro growth (Ayensa-Jiménez et al ., 2020) or synthetic models of solid tumors (Sego et al ., 2020).…”

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

“…The ability to derive cell-based, spatiotemporal models from ordinary differential equation (ODE) models would enhance the utility of both types of models. Cell-based, spatiotemporal models can explicitly describe cellular and spatial mechanisms neglected by ODE models that affect the emergent dynamics and properties of multicellular systems, such as the influence of dynamic aggregate shape on diffusion-limited growth dynamics [ 16 ] and individual infected cells on the progression of viral infection [ 17 ]. Likewise, ODE models can inform cell-based, spatiotemporal models with efficient parameter fitting to experimental data, and can appropriately describe dynamics at coarser scales and distant locales with respect to a particular multicellular domain of interest (e.g., the population dynamics of a lymph node when explicitly modeling local viral infection).…”