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.

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.

The fluidity of Trypanosoma brucei ′s dense coat of GPI-anchored variant surface glycoproteins (VSGs) is fundamental for the survival of the parasite. In order to maintain the integrity of the coat, it is recycled on the time scale of a few minutes. This is surprisingly fast as endo- and exocytosis take place in the same small membrane invagination called the flagellar pocket. Here, we present measurements of VSG dynamics on the single-molecule level in living trypanosomes. A large number of short protein trajectories sampling the parasite's surface were analysed in two distinct scenarios: diffusion and directed motion. To this end, we employed a previously published algorithm and implemented two extensions to consider rim effects as well as localisations errors inherent to single-mole tracking. Neglect of the latter can have a significant distortive effect on the measured diffusion coefficient; in our case resulting in an underestimation by 20%. We found large heterogeneity in the local diffusion coefficients and velocities with a surprisingly high average value of D = 1.00 μm 2/s and v = 1.99 μm/s, respectively. To decide on the locally dominant motion mode, we present a guideline based on random walk simulations. We find that VSG dynamics is indeed dominated by diffusion. Complementary simulations on long time scales not accessible in the experiment showed that passive VSG randomisation is fast enough to prevent re-endocytosis newly exocytosed VSGs and to accomplish turnover of the full VSG coat within a few minutes.

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 images. To demonstrate the application of our tool, we perform growth simulations of the osteocyte lacuno-canalicular system in bone and of the zebrafish sensory nervous system. 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 summaryWe 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 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. Introduction 1 Complex biological networks such as the neural connectome are striking examples of large-2 scale functional structures arising from a locally controlled growth process [1,2]. The resulting 3 network architecture is not only genetically determined, but depends on biological and physical 4interactions with the microenvironment during the growth process [3,4]. In this context, 5 evolution has shaped diverse spatial networks on all length scales, from the cytoskeletal 6 network in cells [5], to multicellular networks such as the vascular system [6] or the osteocyte 7 1/19 lacuno-canalicular network [7], to macroscopic networks of slime molds [8], mycelia [9] and 8 plants [10]. Sophisticated imaging techniques together with large-scale automated analysis 9provide increasingly detailed views of the architecture of biological networks, revealing e.g. 10 how neurons are wired together in the brain [11]. After extracting the topological connectivity 11 from such image data, quantitative methods from the physics of complex networks can 12 be applied to compare different types of networks and to uncover common organizational 13 principles [12][13][1...