Resilience in hierarchical fluid flow networks

Photosynthesis of rice leaves with a parallel venation is highly tolerant to vein severing

Vein severing in plants caused by leaf damage is common in fields where crops are cultivated. It is hypothesized that leaves with complex reticulate venation can withstand hydraulic disturbances caused by vein severing, thereby preserving leaf carbon assimilation. However, limited research focuses on vein damage of leaves with parallel venation. We studied how vein-severing affected the photosynthetic traits of rice (Oryza sativa) leaves in seconds, minutes and days, under varying water-demand conditions and differing extents of water supply disruption. Rice leaves completely lost their photosynthetic capacity within 2.5 minutes after excision. Severing the midrib resulted in reduced light-saturated photosynthetic rate (A), stomatal conductance (gsw ) and transpiration rate (E) by 2.6, 6.8 and 5.9%, respectively, already after thirty minutes. We further investigated the photosynthetic trait responses to various extents of leaf width severing, while keeping the midrib functional. Surprisingly, A, gsw and E in the downstream area of the severed leaves largely remained stable, showing minimal variation across different leaf width severing ratios. These traits declined only slightly even under increased ambient light intensity and leaf-to-air vapor pressure deficit. This sustained photosynthesis post-severing is attributed to the efficient lateral water transport. Long-term leaf damage slightly but not significantly, impacted the downstream photosynthetic traits within five days post-severing. However, a more pronounced reduction in gas exchange during leaf senescence was observed nine days after severing. These findings suggested that rice leaves can tolerate hydraulic disturbances from vein severing and maintain functionality under various conditions, which is crucial for crop yield stability. However, long-term consequences require further investigation.

Dual communities in spatial networks

Both human-made and natural supply systems, such as power grids and leaf venation networks, are built to operate reliably under changing external conditions. Many of these spatial networks exhibit community structures. Here, we show that a relatively strong connectivity between the parts of a network can be used to define a different class of communities: dual communities. We demonstrate that traditional and dual communities emerge naturally as two different phases of optimized network structures that are shaped by fluctuations and that they both suppress failure spreading, which underlines their importance in understanding the shape of real-world supply networks.

Gigantic floating leaves occupy a large surface area at an economical material cost

The giant Amazonian waterlily (genus Victoria) produces the largest floating leaves in the plant kingdom. The leaves' notable vasculature has inspired artists, engineers, and architects for centuries. Despite the aesthetic appeal and scale of this botanical enigma, little is known about the mechanics of these extraordinary leaves. For example, how do these leaves achieve gigantic proportions? We show that the geometric form of the leaf is structurally more efficient than those of other smaller species of waterlily. In particular, the spatially varying thickness and regular branching of the primary veins ensures the structural integrity necessary for extensive coverage of the water surface, enabling optimal light capture despite a relatively low leaf biomass. Leaf gigantism in waterlilies may have been driven by selection pressures favoring a large surface area at an economical material cost, for outcompeting other plants in fast-drying ephemeral pools.

Linking xylem network failure with leaf tissue death

Global warming is expected to dramatically accelerate forest mortality as temperature and drought intensity increase. Predicting the magnitude of this impact urgently requires an understanding of the process connecting atmospheric drying to plant tissue damage. Recent episodes of forest mortality worldwide have been widely attributed to dry conditions causing acute damage to plant vascular systems. Under this scenario vascular embolisms produced by water stress are thought to cause plant death, yet this hypothetical trajectory has never been empirically demonstrated. Here we provide foundational evidence connecting failure in the vascular network of leaves with tissue damage caused during water stress. We observe a catastrophic sequence initiated by water column breakage under tension in leaf veins which severs local leaf tissue water supply, immediately causing acute cellular dehydration and irreversible damage. By highlighting the primacy of vascular network failure in the death of leaves exposed to drought or evaporative stress our results provide a strong mechanistic foundation upon which models of plant damage in response to dehydration can be confidently structured.

Network isolators inhibit failure spreading in complex networks

In our daily lives, we rely on the proper functioning of supply networks, from power grids to water transmission systems. A single failure in these critical infrastructures can lead to a complete collapse through a cascading failure mechanism. Counteracting strategies are thus heavily sought after. In this article, we introduce a general framework to analyse the spreading of failures in complex networks and demostrate that not only decreasing but also increasing the connectivity of the network can be an effective method to contain damages. We rigorously prove the existence of certain subgraphs, called network isolators, that can completely inhibit any failure spreading, and we show how to create such isolators in synthetic and real-world networks. The addition of selected links can thus prevent large scale outages as demonstrated for power transmission grids.

Optimal Elasticity of Biological Networks

Reinforced elastic sheets surround us in daily life, from concrete shell buildings to biological structures such as the arthropod exoskeleton or the venation network of dicotyledonous plant leaves. Natural structures are often highly optimized through evolution and natural selection, leading to the biologically and practically relevant problem of understanding and applying the principles of their design. Inspired by the hierarchically organized scaffolding networks found in plant leaves, here we model networks of bending beams that capture the discrete and nonuniform nature of natural materials. Using the principle of maximal rigidity under natural resource constraints, we show that optimal discrete beam networks reproduce the structural features of real leaf venation. Thus, in addition to its ability to efficiently transport water and nutrients, the venation network also optimizes leaf rigidity using the same hierarchical reticulated network topology. We study the phase space of optimal mechanical networks, providing concrete guidelines for the construction of elastic structures. We implement these natural design rules by fabricating efficient, biologically inspired metamaterials.

Brain folding shapes the branching pattern of the middle cerebral artery

The folds of the brain offer a particular challenge for the subarachnoid vascular grid. The primitive blood vessels that occupy this space, when the brain is flat, have to adapt to an everchanging geometry while constructing an efficient network. Surprisingly, the result is a non-redundant arterial system easily challenged by acute occlusions. Here, we generalize the optimal network building principles of a flat surface growing into a folded configuration and generate an ideal middle cerebral artery (MCA) configuration that can be directly compared with the normal brain anatomy. We then describe how the Sylvian fissure (the fold in which the MCA is buried) is formed during development and use our findings to account for the differences between the ideal and the actual shaping pattern of the MCA. Our results reveal that folding dynamics condition the development of arterial anastomosis yielding a network without loops and poor response to acute occlusions.

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.