Deep Neural Cellular Potts Models

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.

Researchers in the life sciences use the cellular Potts model (CPM) to simulate (parts of) a living organism, for instance to find out how biological cells interact and collectively achieve a well-proportioned and functional body plan. So far, it has been difficult to set up and gradually improve the interaction formulas, termed Hamiltonians, inside such a CPM, as thousands of different types of molecules contribute to cell-cell interactions in unexplored ways. To address this challenge, we propose NeuralCPM, a CPM with a Neural Hamiltonian as interaction formula. The Neural Hamiltonian is a neural network that can be trained directly on experimental data like microscopy videos. This approach guarantees fundamental physical and biological properties, thanks to the embedding into the CPM formalism, but now allows for realistic simulations of complex processes as we demonstrate for synthetic and real biological experiments.