Christopher T. Lee , Justin G. Laughlin , Nils Angliviel de La Beaumelle, Rommie E. Amaro, J. Andrew McCammon, Ravi Ramamoorthi, Michael Holst, Padmini Rangamani
Recent advances in electron microscopy have enabled the imaging of single cells in 3D at nanometer length scale resolutions. An uncharted frontier for in silico biology is the ability to simulate cellular processes using these observed geometries. Enabling such simulations requires watertight meshing of electron micrograph images into 3D volume meshes, which can then form the basis of computer simulations of such processes using numerical techniques such as the finite element method. In this paper, we describe the use of our recently rewritten mesh processing software, GAMer 2, to bridge the gap between poorly conditioned meshes generated from segmented micrographs and boundary marked tetrahedral meshes which are compatible with simulation. We demonstrate the application of a workflow using GAMer 2 to a series of electron micrographs of neuronal dendrite morphology explored at three different length scales and show that the resulting meshes are suitable for finite element simulations. This work is an important step towards making physical simulations of biological processes in realistic geometries routine. Innovations in algorithms to reconstruct and simulate cellular length scale phenomena based on emerging structural data will enable realistic physical models and advance discovery at the interface of geometry and cellular processes. We posit that a new frontier at the intersection of computational technologies and single cell biology is now open.
Understanding structure-function relationships at cellular length scales (nm to μm) is one of the central goals of modern cell biology. While structural determination techniques are routine for very small and large scales such as molecular and tissue, high-resolution images of mesoscale subcellular scenes were historically elusive . This was primarily due to the diffraction limits of visible light and the limitations of X-ray and Electron Microscopy (EM) hardware. Over the past decade, technological improvements such as improved direct electron detectors have enabled the practical applications of techniques such as volume electron microscopy
GAMer 2 development
GAMer 2 is a complete rewrite of GAMer in C++ using the CASC data structure  as the underlying mesh representation. Prior versions of GAMer were susceptible to segmentation faults under certain conditions, which is now fixed in this major update. In addition to improving the run-time stability, we have added error handling code to produce actionable notes for the convenience of the end-user. GAMer 2 continues to be licensed under LGPL v2.1 and the source code can be downloaded from GitHub (https://github.com/ctlee/gamer) .
The relationship between cellular shape and function is being uncovered as systems, structural biology, and physical simulations converge. Beyond traditional compartmentalization, plasma membrane curvature and cellular ultrastructure have been shown to affect the diffusion and localization of molecular species in cells [100, 116]. For example, fluorescence experiments have shown that the dendritic spine necks act as a diffusion barrier to calcium ions, preventing ions from entering the dendritic shaft . Complementary to this and other experiments, various physical models solving reaction-diffusion equations in idealized geometries have been developed to further interrogate the structure-function relationships [51, 100, 111, 117–119].
We would like to thank Prof. Pietro De Camilli and coworkers for sharing their datasets from Wu et al. . We also thank Dr. Matthias Haberl, Mr. Evan Campbell, Profs. Brenda Bloodgood and Mark Ellisman for helpful discussion and suggestions. CTL especially thanks Dr. John B. Moody, and Mr. Mason V. Holst for discussions on GAMer 2 code development along with Dr. Tom Bartol for additional help with using Blender and the design of Blender add-ons. We thank Ms. Miriam Bell, Ms. Kiersten Scott, Ms. Jennifer Fromm, and Dr. Donya Ohadi for critical comments and suggestions for improving this manuscript.
Citation: Lee CT, Laughlin JG, Angliviel de La Beaumelle N, Amaro RE, McCammon JA, Ramamoorthi R, et al. (2020) 3D mesh processing using GAMer 2 to enable reaction-diffusion simulations in realistic cellular geometries. PLoS Comput Biol 16(4): e1007756. https://doi.org/10.1371/journal.pcbi.1007756
Editor: Hugues Berry, Inria, FRANCE
Received: July 22, 2019; Accepted: March 1, 2020; Published: April 6, 2020
Copyright: © 2020 Lee et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: The latest GAMer 2 code can be found on GitHub https://github.com/ctlee/gamer. Snapshots of GAMer 2 are also archived on Zenodo https://doi.org/10.5281/zenodo.2340294. High resolution versions of supplemental movies and meshes can be found at https://github.com/RangamaniLabUCSD/Lee-Laughlin-GAMer2. The EM data used in this work are from Wu, Y.; Whiteus, C.; Xu, C. S.; Hayworth, K. J.; Weinberg, R. J.; Hess, H. F.; Camilli, P. D. Contacts between the Endoplasmic Reticulum and Other Membranes in Neurons. PNAS 2017, 114 (24), E4859–E4867. https://doi.org/10.1073/pnas.1701078114. The original EM datasets are available by request from the corresponding author of this work, Pietro de Camilli (Pietro.email@example.com), as pursuant to PNAS data availability guidelines.
Funding: CTL, REA, JAM, and MH are supported in part by the National Institutes of Health (https://www.nih.gov) under grant number P41-GM103426. CTL, and JAM are also supported by the National Institutes of Health (https://www.nih.gov) under RO1-GM31749. CTL also acknowledges support from the National institutes of Health (https://www.nih.gov) Molecular Biophysics Training Grant T32-GM008326 and a Hartwell Foundation Postdoctoral Fellowship. RR was supported in part by the Ronald L. Graham endowed chair. MH was supported in part by the National Science Foundation (https://www.nsf.gov) under awards DMS-CM1620366 and DMS-FRG1262982. PR was supported by the Air Force Office of Scientific Research (AFOSR, https://www.wpafb.af.mil/afrl/afosr/) Multidisciplinary University Research Initiative (MURI) FA9550-18-1-0051 and JGL was supported by a fellowship from the UCSD Center for Transscale Structural Biology and Biophysics/Virtual Molecular Cell Consortium (https://vmcc.ucsd.edu/). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing interests: I have read the journals policy and the authors of this manuscript have the following competing interests: R.E.A. has equity interest in, is a cofounder of, and on the scientific advisory board of Actavalon, Inc.