The cellular Potts model (CPM) is a powerful computational method for simulating collective spatiotemporal dynamics of biological cells. To drive the dynamics, CPMs rely on physics-inspired Hamiltonians. However, as first principles remain elusive in biology, these Hamiltonians only approximate the full complexity of real multicellular systems. To address this limitation, we propose NeuralCPM, a more expressive cellular Potts model that can be trained directly on observational data. At the core of NeuralCPM lies the Neural Hamiltonian, a neural network architecture that respects universal symmetries in collective cellular dynamics. Moreover, this approach enables seamless integration of domain knowledge by combining known biological mechanisms and the expressive Neural Hamiltonian into a hybrid model. Our evaluation with synthetic and real-world multicellular systems demonstrates that NeuralCPM is able to model cellular dynamics that cannot be accounted for by traditional analytical Hamiltonians.

MOTIVATION: Biological tissues are dynamic and highly organized. Multi-scale models are helpful tools to analyse and understand the processes determining tissue dynamics. These models usually depend on parameters that need to be inferred from experimental data to achieve a quantitative understanding, to predict the response to perturbations, and to evaluate competing hypotheses. However, even advanced inference approaches such as approximate Bayesian computation (ABC) are difficult to apply due to the computational complexity of the simulation of multi-scale models. Thus, there is a need for a scalable pipeline for modeling, simulating, and parameterizing multi-scale models of multi-cellular processes. RESULTS: Here, we present FitMultiCell, a computationally efficient and user-friendly open-source pipeline that can handle the full workflow of modeling, simulating, and parameterizing for multi-scale models of multi-cellular processes. The pipeline is modular and integrates the modeling and simulation tool Morpheus and the statistical inference tool pyABC. The easy integration of high-performance infrastructure allows to scale to computationally expensive problems. The introduction of a novel standard for the formulation of parameter inference problems for multi-scale models additionally ensures reproducibility and reusability. By applying the pipeline to multiple biological problems, we demonstrate its broad applicability, which will benefit in particular image-based systems biology. AVAILABILITY AND IMPLEMENTATION: FitMultiCell is available open-source at https://gitlab.com/fitmulticell/fit.

Human airway epithelium (HAE) represents the primary site of viral infection for SARS-CoV-2. Comprising different cell populations, a lot of research has been aimed at deciphering the major cell types and infection dynamics that determine disease progression and severity. However, the cell type-specific replication kinetics, as well as the contribution of cellular composition of the respiratory epithelium to infection and pathology are still not fully understood. Although experimental advances, including Air-liquid interface (ALI) cultures of reconstituted pseudostratified HAE, as well as lung organoid systems, allow the observation of infection dynamics under physiological conditions in unprecedented level of detail, disentangling and quantifying the contribution of individual processes and cells to these dynamics remains challenging. Here, we present how a combination of experimental data and mathematical modelling can be used to infer and address the influence of cell type specific infectivity and tissue composition on SARS-CoV-2 infection dynamics. Using a stepwise approach that integrates various experimental data on HAE culture systems with regard to tissue differentiation and infection dynamics, we develop an individual cell-based model that enables investigation of infection and regeneration dynamics within pseudostratified HAE. In addition, we present a novel method to quantify tissue integrity based on image data related to the standard measures of transepithelial electrical resistance measurements. Our analysis provides a first aim of quantitatively assessing cell type specific infection kinetics and shows how tissue composition and changes in regeneration capacity, as e.g. in smokers, can influence disease progression and pathology. Furthermore, we identified key measurements that still need to be assessed in order to improve inference of cell type specific infection kinetics and disease progression. Our approach provides a method that, in combination with additional experimental data, can be used to disentangle the complex dynamics of viral infection and immunity within human airway epithelial culture systems.

Abstract Summary: Morpheus is a modeling environment for the simulation and integration of cell-based models with ordinary differential equations and reaction-diffusion systems. It allows rapid development of multiscale models in biological terms and mathematical expressions rather than programming code. Its graphical user interface supports the entire workflow from model construction and simulation to visualization, archiving and batch processing. Availability and implementation: Binary packages are available at http://imc.zih.tu-dresden.de/wiki/morpheus for Linux, Mac OSX and MS Windows. Contact: [email protected] Supplementary information: Supplementary data are available at Bioinformatics online.