Comparing two classes of biological distribution systems using network analysis

Exploring discrete space-time models for information transfer: Analogies from mycelial networks to the cosmic web

Fungal mycelium networks are large scale biological networks along which nutrients, metabolites flow. Recently, we discovered a rich spectrum of electrical activity in mycelium networks, including action-potential spikes and trains of spikes. Reasoning by analogy with animals and plants, where travelling patterns of electrical activity perform integrative and communicative mechanisms, we speculated that waves of electrical activity transfer information in mycelium networks. Using a new discrete space-time model with emergent radial spanning-tree topology, hypothetically comparable mycelial morphology and physically comparable information transfer, we provide physical arguments for the use of such a model, and by considering growing mycelium network by analogy with growing network of matter in the cosmic web, we develop mathematical models and theoretical concepts to characterise the parameters of the information transfer.

The Robust Lamina Cribrosa Vasculature: Perfusion and Oxygenation Under Elevated Intraocular Pressure

Purpose

Elevated intraocular pressure (IOP) is thought to cause lamina cribrosa (LC) blood vessel distortions and potentially collapse, adversely affecting LC hemodynamics, reducing oxygenation, and triggering, or contributing to, glaucomatous neuropathy. We assessed the robustness of LC perfusion and oxygenation to vessel collapses.

Methods

From histology, we reconstructed three-dimensional eye-specific LC vessel networks of two healthy monkey eyes. We used numerical simulations to estimate LC perfusion and from this the oxygenation. We then evaluated the effects of collapsing a fraction of LC vessels (0%-36%). The collapsed vessels were selected through three scenarios: stochastic (collapse randomly), systematic (collapse strictly by the magnitude of local experimentally determined IOP-induced compression), and mixed (a combination of stochastic and systematic).

Results

LC blood flow decreased linearly as vessels collapsed-faster for stochastic and mixed scenarios and slower for the systematic one. LC regions suffering severe hypoxia (oxygen <8 mm Hg) increased proportionally to the collapsed vessels in the systematic scenario. For the stochastic and mixed scenarios, severe hypoxia did not occur until 15% of vessels collapsed. Some LC regions had higher perfusion and oxygenation as vessels collapsed elsewhere. Some severely hypoxic regions maintained normal blood flow. Results were equivalent for both networks and patterns of experimental IOP-induced compression.

Conclusions

LC blood flow was sensitive to distributed vessel collapses (stochastic and mixed) and moderately vulnerable to clustered collapses (systematic). Conversely, LC oxygenation was robust to distributed vessel collapses and sensitive to clustered collapses. Locally normal flow does not imply adequate oxygenation. The actual nature of IOP-induced vessel collapse remains unknown.

Optimal mechanical interactions direct multicellular network formation on elastic substrates

Cells self-organize into functional, ordered structures during tissue morphogenesis, a process that is evocative of colloidal self-assembly into engineered soft materials. Understanding how intercellular mechanical interactions may drive the formation of ordered and functional multicellular structures is important in developmental biology and tissue engineering. Here, by combining an agent-based model for contractile cells on elastic substrates with endothelial cell culture experiments, we show that substrate deformation-mediated mechanical interactions between cells can cluster and align them into branched networks. Motivated by the structure and function of vasculogenic networks, we predict how measures of network connectivity like percolation probability and fractal dimension as well as local morphological features including junctions, branches, and rings depend on cell contractility and density and on substrate elastic properties including stiffness and compressibility. We predict and confirm with experiments that cell network formation is substrate stiffness dependent, being optimal at intermediate stiffness. We also show the agreement between experimental data and predicted cell cluster types by mapping a combined phase diagram in cell density substrate stiffness. Overall, we show that long-range, mechanical interactions provide an optimal and general strategy for multicellular self-organization, leading to more robust and efficient realizations of space-spanning networks than through just local intercellular interactions.

Analysis of the emerging physical network in young mycelia

Filamentous fungi develop intricate hyphal networks that support mycelial foraging and transport of resources. These networks have been analyzed recently using graph theory, enabling the development of models that seek to predict functional traits. However, attention has focused mainly on mature colonies. Here, we report the extraction and analysis of the graph corresponding to Trichoderma atroviride mycelia only a few hours after conidia germination. To extract the graph for a given mycelium, a mosaic conformed of multiple bright-field, optical microscopy images is digitally processed using freely available software. The resulting graphs are characterized in terms of number of nodes and edges, average edge length, total mycelium length, hyphal growth unit, maximum edge length and mycelium diameter, for colonies between 8 h and 14 h after conidium germination. Our results show that the emerging hyphal network grows first by hyphal elongation and branching, and then it transitions to a stage where hyphal-hyphal interactions become significant. As a tangled hyphal network develops with decreasing hyphal mean length, the mycelium maintains long (∼2 mm) hyphae-a behavior that suggests a combination of aggregated and dispersed architectures to support foraging. Lastly, analysis of early network development in Podospora anserina reveals striking similarity with T. atroviride, suggesting common mechanisms during initial colony formation in filamentous fungi.

Vessel network extraction and analysis of mouse pulmonary vasculature via X-ray micro-computed tomographic imaging

In this work, non-invasive high-spatial resolution three-dimensional (3D) X-ray micro-computed tomography (μCT) of healthy mouse lung vasculature is performed. Methodologies are presented for filtering, segmenting, and skeletonizing the collected 3D images. Novel methods for the removal of spurious branch artefacts from the skeletonized 3D image are introduced, and these novel methods involve a combination of distance transform gradients, diameter-length ratios, and the fast marching method (FMM). These new techniques of spurious branch removal result in the consistent removal of spurious branches without compromising the connectivity of the pulmonary circuit. Analysis of the filtered, skeletonized, and segmented 3D images is performed using a newly developed Vessel Network Extraction algorithm to fully characterize the morphology of the mouse pulmonary circuit. The removal of spurious branches from the skeletonized image results in an accurate representation of the pulmonary circuit with significantly less variability in vessel diameter and vessel length in each generation. The branching morphology of a full pulmonary circuit is characterized by the mean diameter per generation and number of vessels per generation. The methods presented in this paper lead to a significant improvement in the characterization of 3D vasculature imaging, allow for automatic separation of arteries and veins, and for the characterization of generations containing capillaries and intrapulmonary arteriovenous anastomoses (IPAVA).

Substrate and cell fusion influence on slime mold network dynamics

The acellular slime mold Physarum polycephalum provides an excellent model to study network formation, as its network is remodelled constantly in response to mass gain/loss and environmental conditions. How slime molds networks are built and fuse to allow for efficient exploration and adaptation to environmental conditions is still not fully understood. Here, we characterize the network organization of slime molds exploring homogeneous neutral, nutritive and adverse environments. We developed a fully automated image analysis method to extract the network topology and followed the slime molds before and after fusion. Our results show that: (1) slime molds build sparse networks with thin veins in a neutral environment and more compact networks with thicker veins in a nutritive or adverse environment; (2) slime molds construct long, efficient and resilient networks in neutral and adverse environments, whereas in nutritive environments, they build shorter and more centralized networks; and (3) slime molds fuse rapidly and establish multiple connections with their clone-mates in a neutral environment, whereas they display a late fusion with fewer connections in an adverse environment. Our study demonstrates that slime mold networks evolve continuously via pruning and reinforcement, adapting to different environmental conditions.

Reorderability of node-filtered order complexes

Growing graphs describe a multitude of developing processes from maturing brains to expanding vocabularies to burgeoning public transit systems. Each of these growing processes likely adheres to proliferation rules that establish an effective order of node and connection emergence. When followed, such proliferation rules allow the system to properly develop along a predetermined trajectory. But rules are rarely followed. Here we ask what topological changes in the growing graph trajectories might occur after the specific but basic perturbation of permuting the node emergence order. Specifically, we harness applied topological methods to determine which of six growing graph models exhibit topology that is robust to randomizing node order, termed global reorderability, and robust to temporally local node swaps, termed local reorderability. We find that the six graph models fall upon a spectrum of both local and global reorderability, and furthermore we provide theoretical connections between robustness to node pair ordering and robustness to arbitrary node orderings. Finally, we discuss real-world applications of reorderability analyses and suggest possibilities for designing reorderable networks.

Optimizing biologically inspired transport networks by control

Transportation networks with intrinsic flow dynamics governed by the Kirchhoff's current law are ubiquitous in natural and engineering systems. There has been recent work on designing optimal transportation networks based on biological principles with the goal to minimize the total dissipation associated with the flow. Despite being biologically inspired, e.g., adaptive network design based on slime mold Physarum polycephalum, such methods generally lead to suboptimal networks due to the difficulty in finding a global or nearly global optimum of the nonconvex optimization function. Here we articulate a design paradigm that combines engineering control and biological principles to realize optimal transportation networks. In particular, we show how small control signals applied only to a fraction of edges in an adaptive network can lead to solutions that are far more optimal than those based solely on biological principles. We also demonstrate that control signals, if not properly designed, can lead to networks that are less optimal. Incorporating control principle into biology-based optimal network design has broad applications not only in biomedical science and engineering but also in other disciplines such as civil engineering for designing resilient infrastructure systems.

Spatial Embedding Imposes Constraints on Neuronal Network Architectures

Recent progress towards understanding circuit function has capitalized on tools from network science to parsimoniously describe the spatiotemporal architecture of neural systems. Such tools often address systems topology divorced from its physical instantiation. Nevertheless, for embedded systems such as the brain, physical laws directly constrain the processes of network growth, development, and function. We review here the rules imposed by the space and volume of the brain on the development of neuronal networks, and show that these rules give rise to a specific set of complex topologies. These rules also affect the repertoire of neural dynamics that can emerge from the system, and thereby inform our understanding of network dysfunction in disease. We close by discussing new tools and models to delineate the effects of spatial embedding.