@article{BerberichKurzReinhardetal.2021,
  author    = {Berberich, Andreas and Kurz, Andreas and Reinhard, Sebastian and Paul, Torsten Johann and Burd, Paul Ray and Sauer, Markus and Kollmannsberger, Philip},
  title     = {Fourier Ring Correlation and anisotropic kernel density estimation improve deep learning based SMLM reconstruction of microtubules},
  series = {Frontiers in Bioinformatics},
  volume    = {1},
  journal   = {Frontiers in Bioinformatics},
  doi       = {10.3389/fbinf.2021.752788},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-261686},
  year      = {2021},
  abstract  = {Single-molecule super-resolution microscopy (SMLM) techniques like dSTORM can reveal biological structures down to the nanometer scale. The achievable resolution is not only defined by the localization precision of individual fluorescent molecules, but also by their density, which becomes a limiting factor e.g., in expansion microscopy. Artificial deep neural networks can learn to reconstruct dense super-resolved structures such as microtubules from a sparse, noisy set of data points. This approach requires a robust method to assess the quality of a predicted density image and to quantitatively compare it to a ground truth image. Such a quality measure needs to be differentiable to be applied as loss function in deep learning. We developed a new trainable quality measure based on Fourier Ring Correlation (FRC) and used it to train deep neural networks to map a small number of sampling points to an underlying density. Smooth ground truth images of microtubules were generated from localization coordinates using an anisotropic Gaussian kernel density estimator. We show that the FRC criterion ideally complements the existing state-of-the-art multiscale structural similarity index, since both are interpretable and there is no trade-off between them during optimization. The TensorFlow implementation of our FRC metric can easily be integrated into existing deep learning workflows.},
  language  = {en}
}
@article{PaulKollmannsberger2020,
  author    = {Paul, Torsten Johann and Kollmannsberger, Philip},
  title     = {Biological network growth in complex environments: A computational framework},
  series = {PLoS Computational Biology},
  volume    = {16},
  journal   = {PLoS Computational Biology},
  number    = {11},
  doi       = {10.1371/journal.pcbi.1008003},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-231373},
  year      = {2020},
  abstract  = {Spatial biological networks are abundant on all scales of life, from single cells to ecosystems, and perform various important functions including signal transmission and nutrient transport. These biological functions depend on the architecture of the network, which emerges as the result of a dynamic, feedback-driven developmental process. While cell behavior during growth can be genetically encoded, the resulting network structure depends on spatial constraints and tissue architecture. Since network growth is often difficult to observe experimentally, computer simulations can help to understand how local cell behavior determines the resulting network architecture. We present here a computational framework based on directional statistics to model network formation in space and time under arbitrary spatial constraints. Growth is described as a biased correlated random walk where direction and branching depend on the local environmental conditions and constraints, which are presented as 3D multilayer grid. To demonstrate the application of our tool, we perform growth simulations of a dense network between cells and compare the results to experimental data from osteocyte networks in bone. Our generic framework might help to better understand how network patterns depend on spatial constraints, or to identify the biological cause of deviations from healthy network function. Author summary We present a novel modeling approach and computational implementation to better understand the development of spatial biological networks under the influence of external signals. Our tool allows us to study the relationship between local biological growth parameters and the emerging macroscopic network function using simulations. This computational approach can generate plausible network graphs that take local feedback into account and provide a basis for comparative studies using graph-based methods.},
  language  = {en}
}