Machine learning continuum models for cellular force generation

Mechanical behaviors of cells arise through the mechanochemical interactions of proteins which self-organize into organelles and cytoskeletal structures. However, no systematic strategy exists to identify the relevant collective variables representing protein distributions within the cell and link these to mechanical response at the cellular scale. Here, we show how machine learning can be used to build continuum models that relate protein distributions to forces. We train neural networks to map between fluorescent protein distributions and experimental traction stresses and observe that focal adhesion proteins alone are sufficient for accurate force predictions. By calculating the importance the network assigns to features of these protein distributions, we identify relevant analytical terms in a gradient expansion of the input protein signal. After performing sparse regression on a neural network-inspired library of terms, we obtain continuum equations relating protein localization and cell stresses.