TopoSPAM: Topology grounded Simulation Platform for morphogenesis and biological Active Matter

TL;DR

TopoSPAM introduces a topology-grounded, multiscale simulation platform for morphogenesis and biological active matter. It unifies meshfree continuum solvers for polar fluids with discrete 3D active vertex models and coarse-grained spring-lattice morphogenesis, all accessible through a Python/IPython interface atop the OpenFPM HPC framework. The platform explicitly leverages topological states such as defects and domains to navigate across scales, and demonstrates validated active hydrodynamics, tissue traction–driven morphogenesis, and curvature-programmed shape changes. While offering substantial capability, it notes limitations in fully coupled multiscale coupling, incomplete underlying biology, and potential stochastic extensions, outlining clear paths for future enhancement and broad applicability to biological physics.

Abstract

We present a topology grounded, multiscale simulation platform for morphogenesis and biological active matter. Morphogenesis and biological active matter represent keystone problems in biology with additional, far-reaching implications across the biomedical sciences. Addressing these problems will require flexible, cross-scale models of tissue shape, development, and dysfunction that can be tuned to understand, model, and predict relevant individual cases. Current approaches to simulating anatomical or cellular subsystems tend to rely on static, assumed shapes. Meanwhile, the potential for topology to provide natural dimensionality reduction and organization of shape and dynamical outcomes is not fully exploited. TopoSPAM combines ease of use with powerful simulation algorithms and methodological advances, including active nematic gels, topological-defect-driven shape dynamics, and an active 3D vertex model of tissues. It is capable of determining emergent flows and shapes across scales.

Figures (4)

• Figure 1: Modeling and simulation of biological active matter across scales. Cytoskeleton (left column): Microtubule mixtures with Kinesin-1 motor proteins exhibiting a bend instability (top panel) PhysRevLett.125.257801. An active polar fluid model (middle) captures the instability in the corresponding TopoSPAM Simulation (bottom panel). Cellular organoids (center column): Pancreatic organoids exhibiting spontaneous chiral rotations that are modeled with the 3D vertex model (top and middle) Tan:2024. The TopoSPAM simulation of the vertex model predicts the spontaneous chiral flows (bottom). Tissue 3D shape change (right column):Drosophila wing disc development (top) 10.7554/eLife.57964 modeled via a spring-lattice model (middle). The TopoSPAM simulation of the spring-lattice model predicts the three-dimensional development of the wing disc (bottom). Notice that the models are not restricted to the scales shown here. In particular, the active polar gel model can also be used across scales.
• Figure 2: Architecture and user interface of the TopoSPAM software suite. (A) The TopoSPAM architecture is centered around the IPython middleware using Jupyter as the user interface (top). From there, simulations can be set up and run on the scalable OpenFPM high-performance computing platform (left), leveraging its C++ expression system for targeting different hardware backends from laptops to supercomputers (bottom). Simulation results can directly be visualized from within the same Jupyter interface using the state-of-the-art visualization tools ParaView, PyVista, and matplotlib (right). Arrows: The IPython middleware generates the C++ code for OpenFPM, which in turn compiles it to hardware-specific optimized assembly code. Visualization is controlled from the IPython interface, while the data are fetched in the background from the hardware. (B) The IPython user interface of TopoSPAM. In this example, the user first imports the TopoSPAM model library and then selects the 2D active fluid model class. The model's documentation is shown inline. Then, the user sets the simulation parameters and runs the model on the target hardware.
• Figure 3: Active polar fluid solutions in 2D and 3D. (A) Two-dimensional active polar fluid with oscillatory polarity field as shown by the polarity streamlines and Frank free energy as color on the left, with resulting flow streamlines and magnitude of the flow velocity as color on the right. (B) Three-dimensional extensile active fluid undergoing an out-of-plane bend instability under confinement as shown by the polarity streamlines and Frank free energy as color (left) with flow streamlines and velocity as color (in- and out-of place flow directions indicated by the blue arrows) on the right. (C) Simulation of a rotating spiral defect in an active fluid confined to a 3D cylinder. (D) Simulation of a stable aster defect with no flow in an active fluid confined to a 3D cylinder.
• Figure 4: (A) Overview of the spring-lattice models for morphogenesis: Left column: Shape response of a group of cells to a specific collective cellular behavior. Middle column: coarse-grained shape patterns using the shape mechanisms of the left as building blocks. Right column: 3D shape obtained after letting the spring-lattice system relax to a geometrical configuration that satisfies force balance for the rest lengths imposed by their corresponding planar deformation pattern. From top to bottom: uniform radial elongations yield conical surfaces. Ratios of apical and basal areas manipulated to program a corrugated surface. Axisymmetric gradients of cell expansion decreasing along the radial direction yield a hyperbolic surface. (B) The shape development of the Drosophila imaginal leg disc elongation is an example of developmental morphogenesis (left) that could be captured by a spontaneous-strain deformation tensor that combines different "deformation modes" (middle). Radial elongation gradients transform a flat disk into an elongated dome. Each of the shown 3D surfaces is colored with respect to their Gaussian curvature (color bar).