Biological network growth in complex environments: A computational framework

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.

Bone mineral density modeling via random field: normality, stationarity, sex and age dependence

“…Our approach uses covariance eigenpairs as bases for generating new BMD realizations. Most importantly, our approach is rather focused on exploring/explaining the spatio-temporal correlation structure, which somehow reflects the (mechano-)biological mechanisms of growth and adaptation [80] in the authors’ opinion.…”

“…ploring/explaining the spatio-temporal correlation structure, 498 which somehow reflects the (mechano-)biological mecha-499 nisms of growth and adaptation[80] in the authors' opinion.500 Conclusion 501 The understanding of uncertainties in bone density is of 502 paramount importance to biomechanics in the relation to 503 the understanding of bone mechanobiology, and it should 504 be properly incorporated into computational models. We introduced a random field model describing the fluctuation in bone density via the KLE.…”

Fourier Ring Correlation and Anisotropic Kernel Density Estimation Improve Deep Learning Based SMLM Reconstruction of Microtubules

“…The same approach can be used for higher dimensions, as multivariate Gaussian functions can easily be generalized to 3D, as demonstrated e.g. for spatial directional statistics simulations–see ( Paul and Kollmannsberger, 2020 ) for an implementation in python.…”

Network Modelling Methods for Precision Medicine

“…Like closeness centrality, harmonic centrality has great potential for analysis of biological networks, because it captures the intuition of the influence of a node decaying with the distance, while also naturally handling disconnected networks. Online resources for systems biology offer tools to compute harmonic centrality (e.g., [Zhang et al, 2016]), and this centrality measure is used in analysing simulations of growth of biological networks [Paul and Kollmannsberger, 2020]. We remark however that several papers use the term "harmonic centrality" to refer to a rather different centrality measure, e.g.…”