An Open Source Mesh Generation Platform for Biophysical Modeling Using Realistic Cellular Geometries

Abstract

Advances in imaging methods such as electron microscopy, tomography and other modalities are enabling high-resolution reconstructions of cellular and organelle geometries. Such advances pave the way for using these geometries for biophysical and mathematical modeling once these data can be represented as a geometric mesh, which, when carefully conditioned, enables the discretization and solution of partial differential equations. In this study, we outline the steps for a naïve user to approach GAMer 2, a mesh generation code written in C++ designed to convert structural datasets to realistic geometric meshes, while preserving the underlying shapes. We present two example cases, 1) mesh generation at the subcellular scale as informed by electron tomography, and 2) meshing a protein with structure from x-ray crystallography. We further demonstrate that the meshes generated by GAMer are suitable for use with numerical methods. Together, this collection of libraries and tools simplifies the process of constructing realistic geometric meshes from structural biology data. SIGNIFICANCE As biophysical structure determination methods improve, the rate of new structural data is increasing. New methods that allow the interpretation, analysis, and reuse of such structural information will thus take on commensurate importance. In particular, geometric meshes, such as those commonly used in graphics and mathematics, can enable a myriad of mathematical analysis. In this work, we describe GAMer 2, a mesh generation library designed for biological datasets. Using GAMer 2 and associated tools PyGAMer and BlendGAMer, biologists can robustly generate computer and algorithm friendly geometric mesh representations informed by structural biology data. We expect that GAMer 2 will be a valuable tool to bring realistic geometries to biophysical models.

Applications and Challenges of Machine Learning to Enable Realistic Cellular Simulations

“…Given a high quality and high resolution mesh representation of a structural geometry (see Figure 2 ), we can begin to probe structure-function relationships through mathematical modeling [ 11 , 112 ]. However, a single realistic geometry is not enough since it only captures a snapshot in time of the cellular geometry.…”

“… An illustration of complexity, size, quality, and local resolution of meshes typically needed for realistic simulation of biophysical systems. Meshes are generated using GAMer 2 [ 11 , 107 ]. (A) Example surface mesh of a dendritic spine with geometry informed by electron micrographs from Wu et al [ 24 ].…”

“…As biophysical methods have improved, the complexity of our mathematical and computational models is steadily increasing [ 7 – 9 ]. A major frontier for physics-based study of cellular processes will be to simulate biological processes in realistic cell shapes derived from various structural determination modalities [ 10 , 11 ]. For biological problems ranging from cognition to cancer, it has long been understood that cell shapes are often correlated with mechanism [ 12 – 16 ].…”

Biomembranes undergo complex, non-axisymmetric deformations governed by Kirchhoff-Love kinematics and revealed by a three dimensional computational framework

“…Indeed, the computation of membrane bending phenomena is significantly simplified with the axisymmetric assumption, but as we have shown recently [21], this may come at the cost of generality and precision in identifying the underlying physics, as lower-energy, low-symmetry kinematic modes and even entire mechanisms may be overlooked. With growing interest in curvature-mediated biophysical phenomena and in 3D imaging and reconstruction methods [25,26], there is a need for general purpose computational tools to enable fully three dimensional numerical simulations.…”

An Open-Source Mesh Generation Platform for Biophysical Modeling Using Realistic Cellular Geometries

“…We have also developed a new Python application programming interface (API) called PyGAMer and streamlined the GAMer Blender add-on called BlendGAMer. The complete explanation of the mathematics and underlying algorithms are available in (15)(16)(17)(18)(19)(20). In what follows, we provide an overview of the GAMer mesh generation capabilities for the general biophysicist.…”