Gas flow in plant microfluidic networks controlled by capillary valves

The fluidic memristor as a collective phenomenon in elastohydrodynamic networks

Fluid flow networks are ubiquitous and can be found in a broad range of contexts, from human-made systems such as water supply networks to living systems like animal and plant vasculature. In many cases, the elements forming these networks exhibit a highly non-linear pressure-flow relationship. Although we understand how these elements work individually, their collective behavior remains poorly understood. In this work, we combine experiments, theory, and numerical simulations to understand the main mechanisms underlying the collective behavior of soft flow networks with elements that exhibit negative differential resistance. Strikingly, our theoretical analysis and experiments reveal that a minimal network of nonlinear resistors, which we have termed a 'fluidic memristor', displays history-dependent resistance. This new class of element can be understood as a collection of hysteresis loops that allows this fluidic system to store information, and it can be directly used as a tunable resistor in fluidic setups. Our results provide insights that can inform other applications of fluid flow networks in soft materials science, biomedical settings, and soft robotics, and may also motivate new understanding of the flow networks involved in animal and plant physiology.

Ageing-induced shrinkage of intervessel pit membranes in xylem of Clematis vitalba modifies its mechanical properties as revealed by atomic force microscopy

Bordered pit membranes of angiosperm xylem are anisotropic, mesoporous media between neighbouring conduits, with a key role in long distance water transport. Yet, their mechanical properties are poorly understood. Here, we aim to quantify the stiffness of intervessel pit membranes over various growing seasons. By applying an AFM-based indentation technique "Quantitative Imaging" we measured the effective elastic modulus (E ^effective) of intervessel pit membranes of Clematis vitalba in dependence of size, age, and hydration state. The indentation-deformation behaviour was analysed with a non-linear membrane model, and paired with magnetic resonance imaging to visualise sap-filled and embolised vessels, while geometrical data of bordered pits were obtained using electron microscopy. E ^effective was transformed to the geometrically independent apparent elastic modulus E ^apparent and to aspiration pressure P _b. The material stiffness (E ^apparent) of fresh pit membranes was with 57 MPa considerably lower than previously suggested. The estimated pressure for pit membrane aspiration was 2.20+28 MPa. Pit membranes from older growth rings were shrunken, had a higher material stiffness and a lower aspiration pressure than current year ones, suggesting an irreversible, mechanical ageing process. This study provides an experimental-stiffness analysis of hydrated intervessel pit membranes in their native state. The estimated aspiration pressure suggests that membranes are not deflected under normal field conditions. Although absolute values should be interpreted carefully, our data suggest that pit membrane shrinkage implies increasing material stiffness, and highlight the dynamic changes of pit membrane mechanics and their complex, functional behaviour for fluid transport.

Functional xylem characteristics associated with drought-induced embolism in angiosperms

Hydraulic failure resulting from drought-induced embolism in the xylem of plants is a key determinant of reduced productivity and mortality. Methods to assess this vulnerability are difficult to achieve at scale, leading to alternative metrics and correlations with more easily measured traits. These efforts have led to the longstanding and pervasive assumed mechanistic link between vessel diameter and vulnerability in angiosperms. However, there are at least two problems with this assumption that requires critical re-evaluation: (1) our current understanding of drought-induced embolism does not provide a mechanistic explanation why increased vessel width should lead to greater vulnerability, and (2) the most recent advancements in nanoscale embolism processes suggest that vessel diameter is not a direct driver. Here, we review data from physiological and comparative wood anatomy studies, highlighting the potential anatomical and physicochemical drivers of embolism formation and spread. We then put forward key knowledge gaps, emphasising what is known, unknown and speculation. A meaningful evaluation of the diameter-vulnerability link will require a better mechanistic understanding of the biophysical processes at the nanoscale level that determine embolism formation and spread, which will in turn lead to more accurate predictions of how water transport in plants is affected by drought.

Catastrophic hydraulic failure and tipping points in plants

Water inside plants forms a continuous chain from water in soils to the water evaporating from leaf surfaces. Failures in this chain result in reduced transpiration and photosynthesis and are caused by soil drying and/or cavitation-induced xylem embolism. Xylem embolism and plant hydraulic failure share several analogies to 'catastrophe theory' in dynamical systems. These catastrophes are often represented in the physiological and ecological literature as tipping points when control variables exogenous (e.g., soil water potential) or endogenous (e.g., leaf water potential) to the plant are allowed to vary on time scales much longer than time scales associated with cavitation events. Here, plant hydraulics viewed from the perspective of catastrophes at multiple spatial scales is considered with attention to bubble expansion within a xylem conduit, organ-scale vulnerability to embolism, and whole-plant biomass as a proxy for transpiration and hydraulic function. The hydraulic safety-efficiency tradeoff, hydraulic segmentation and maximum plant transpiration are examined using this framework. Underlying mechanisms for hydraulic failure at fine scales such as pit membranes and cell-wall mechanics, intermediate scales such as xylem network properties and at larger scales such as soil-tree hydraulic pathways are discussed. Understudied areas in plant hydraulics are also flagged where progress is urgently needed.

A biological nanofoam: The wall of coniferous bisaccate pollen

The outer layer of the pollen grain, the exine, plays a key role in the survival of terrestrial plant life. However, the exine structure in different groups of plants remains enigmatic. Here, modern and fossil coniferous bisaccate pollen were examined to investigate the detailed three-dimensional structure and properties of the pollen wall. X-ray nanotomography and volume electron microscopy are used to provide high-resolution imagery, revealing a solid nanofoam structure. Atomic force microscopy measurements were used to compare the pollen wall with other natural and synthetic foams and to demonstrate that the mechanical properties of the wall in this type of pollen are retained for millions of years in fossil specimens. The microscopic structure of this robust biological material has potential applications in materials sciences and also contributes to our understanding of the evolutionary success of conifers and other plants over geological time.

Air spread through a wetted deformable membrane: Implications for the mechanism of soft valves in plants

Plants have a special structure, torus-margo (TM) pit, which comprises a thickened torus at the center encircled by a highly porous margo. It is regarded as a key evolutionary structure to enable stable water transport, minimizing the air spread in the vessels. However, its valve-like dynamics to regulate two-phase flows still remains unclear even at a single pit level. Here, we study the air spreading dynamics using a bioinspired model of this soft pit valve. We divide it into the initial onset and the consecutive air-spreads, and propose the criteria of TM structures as the valve-like function. To delay the onset of air spread, the margo region should be thin and deformable enough to seal the pit aperture with the torus before the air penetration. Even after the onset, the membranes whose maximum pore size is smaller than its thickness can avoid continuous air-spread. The criteria also fit properly into botanical data on the morphologies of TM pits, implying that their valve-like behaviors may alleviate the tradeoff between hydraulic safety and efficiency at the single pit level. Our study would help to understand of the mechanistic pit-level strategy and also can provide insight into fluidic systems to control interfacial phenomena.

Bending and Stretching of Soft Pores Enable Passive Control of Fluid Flows

Programmable valves and actuators are widely used in man-made systems to provide sophisticated control of fluid flows. In nature, however, this process is frequently achieved using passive soft materials. Here we study how elastic deformations of cylindrical pores embedded in a flexible membrane enable passive flow control. We develop biomimetic valves with variable pore radius, membrane radius, and thickness. Our experiments reveal a mechanism where small deformations bend the membrane and constrict the pore-thus reducing flow-while larger deformations stretch the membrane, expand the pore, and enhance flow. We develop a theory capturing this highly nonmonotonic behavior, and validate the scaling across a broad range of material and geometric parameters. Our results suggest that intercompartmental flow control in living systems can be encoded entirely in the physical attributes of soft materials. Moreover, this design could enable autonomous flow control in man-made systems.

Investigating Effects of Bordered Pit Membrane Morphology and Properties on Plant Xylem Hydraulic Functions-A Case Study from 3D Reconstruction and Microflow Modelling of Pit Membranes in Angiosperm Xylem

Pit membranes in between neighboring conduits of xylem play a crucial role in plant water transport. In this review, the morphological characteristics, chemical composition and mechanical properties of bordered pit membranes were summarized and linked with their functional roles in xylem hydraulics. The trade-off between xylem hydraulic efficiency and safety was closely related with morphology and properties of pit membranes, and xylem embolism resistance was also determined by the pit membrane morphology and properties. Besides, to further investigate the effects of bordered pit membranes morphology and properties on plant xylem hydraulic functions, here we modelled three-dimensional structure of bordered pit membranes by applying a deposition technique. Based on reconstructed 3D pit membrane structures, a virtual fibril network was generated to model the microflow pattern across inter-vessel pit membranes. Moreover, the mechanical behavior of intervessel pit membranes was estimated from a single microfibril's mechanical property. Pit membranes morphology varied among different angiosperm and gymnosperm species. Our modelling work suggested that larger pores of pit membranes do not necessarily contribute to major flow rate across pit membranes; instead, the obstructed degree of flow pathway across the pit membranes plays a more important role. Our work provides useful information for studying the mechanism of microfluid flow transport across pit membranes and also sheds light on investigating the response of pit membranes both at normal and stressed conditions, thus improving our understanding on functional roles of pit membranes in xylem hydraulic function. Further work could be done to study the morphological and mechanical response of bordered pit membranes under different dehydrated conditions, as well as the related microflow behavior, based on our constructed model.

Air spreading through wetted cellulose membranes: Implications for the safety function of hydraulic valves in plants

Plants transport water against the risk of cavitation inside xylem vessels, called "embolism." As one of their hydraulic strategies, pit membranes composed of cellulose fibers have been known as safety valves that prevent the spreading of embolism towards adjacent xylem vessels. However, detailed observation of embolism spreading through a pit membrane is still lacking. Here, we hypothesized that the pit membranes normally remain to be wetted in xylem vessels and noticed in particular the hydraulic role of water film on air spreading that has been overlooked previously. For the hydrodynamic study of the embolism spreading through a wetted pit membrane, we investigated the penetration and spreading dynamics of air plugs through the wetted cellulose membrane in a channel flow. Air spreading exhibits two types of dynamics: continuous and discrete spreading. We elucidated the correlation of dynamic characteristics of air flow and pressure variations according to membrane thickness. Our study speculates that the thickness of pit membranes affects the behaviors of water film captured by cellulose fibers, and it is a crucial criterion for the reversible gating of further spreading of embolism throughout xylem networks.

A network model links wood anatomy to xylem tissue hydraulic behaviour and vulnerability to cavitation

Plant xylem response to drought is routinely represented by a vulnerability curve (VC). Despite the significance of VCs, the connection between anatomy and tissue-level hydraulic response to drought remains a subject of inquiry. We present a numerical model of water flow in flowering plant xylem that combines current knowledge on diffuse-porous anatomy and embolism spread to explore this connection. The model produces xylem networks and uses different parameterizations of intervessel connection vulnerability to embolism spread: the Young-Laplace equation and pit membrane stretching. Its purpose is upscaling processes occurring on the microscopic length scales, such as embolism propagation through pit membranes, to obtain tissue-scale hydraulics. The terminal branch VC of Acer glabrum was successfully reproduced relying only on real observations of xylem tissue anatomy. A sensitivity analysis shows that hydraulic performance and VC shape and location along the water tension axis are heavily dependent on anatomy. The main result is that the linkage between pit-scale and vessel-scale anatomical characters, along with xylem network topology, affects VCs significantly. This work underscores the importance of stepping up research related to the three-dimensional network structure of xylem tissues. The proposed model's versatility makes it an important tool to explore similar future questions.

From the sap's perspective: The nature of vessel surfaces in angiosperm xylem

PREMISE OF THE STUDY

Xylem sap in angiosperms moves under negative pressure in conduits and cell wall pores that are nanometers to micrometers in diameter, so sap is always very close to surfaces. Surfaces matter for water transport because hydrophobic ones favor nucleation of bubbles, and surface chemistry can have strong effects on flow. Vessel walls contain cellulose, hemicellulose, lignin, pectins, proteins, and possibly lipids, but what is the nature of the inner, lumen-facing surface that is in contact with sap?

METHODS

Vessel lumen surfaces of five angiosperms from different lineages were examined via transmission electron microscopy and confocal and fluorescence microscopy, using fluorophores and autofluorescence to detect cell wall components. Elemental composition was studied by energy-dispersive X-ray spectroscopy, and treatments with phospholipase C (PLC) were used to test for phospholipids.

KEY RESULTS

Vessel surfaces consisted mainly of lignin, with strong cellulose signals confined to pit membranes. Proteins were found mainly in inter-vessel pits and pectins only on outer rims of pit membranes and in vessel-parenchyma pits. Continuous layers of lipids were detected on most vessel surfaces and on most pit membranes and were shown by PLC treatment to consist at least partly of phospholipids.

CONCLUSIONS

Vessel surfaces appear to be wettable because lignin is not strongly hydrophobic and a coating with amphiphilic lipids would render any surface hydrophilic. New questions arise about these lipids and their possible origins from living xylem cells, especially about their effects on surface tension, surface bubble nucleation, and pit membrane function.

Surface Acoustic Waves to Drive Plant Transpiration

Emerging fields of research in electronic plants (e-plants) and agro-nanotechnology seek to create more advanced control of plants and their products. Electronic/nanotechnology plant systems strive to seamlessly monitor, harvest, or deliver chemical signals to sense or regulate plant physiology in a controlled manner. Since the plant vascular system (xylem/phloem) is the primary pathway used to transport water, nutrients, and chemical signals-as well as the primary vehicle for current e-plant and phtyo-nanotechnology work-we seek to directly control fluid transport in plants using external energy. Surface acoustic waves generated from piezoelectric substrates were directly coupled into rose leaves, thereby causing water to rapidly evaporate in a highly localized manner only at the site in contact with the actuator. From fluorescent imaging, we find that the technique reliably delivers up to 6x more water/solute to the site actuated by acoustic energy as compared to normal plant transpiration rates and 2x more than heat-assisted evaporation. The technique of increasing natural plant transpiration through acoustic energy could be used to deliver biomolecules, agrochemicals, or future electronic materials at high spatiotemporal resolution to targeted areas in the plant; providing better interaction with plant physiology or to realize more sophisticated cyborg systems.

Threats to xylem hydraulic function of trees under 'new climate normal' conditions

Climate models predict increases in frequency and intensity of extreme environmental conditions, such as changes to minimum and maximum temperatures, duration of drought periods, intensity of rainfall/snowfall events and wind strength. These local extremes, rather than average climatic conditions, are closely linked to woody plant survival, as trees cope with such events over long lifespans. While the xylem provides trees with structural strength and is considered the most robust part of a tree's structure, it is also the most physiologically vulnerable as tree survival depends on its ability to sustain water supply to the tree crown under variable environmental conditions. Many structural, functional and biological tree properties evolved to protect xylem from loss of transport function because of embolism or to restore xylem transport capacity following embolism formation. How 'the new climate normal' conditions will affect these evolved strategies is yet to be seen. Our understanding of xylem physiology and current conceptual models describing embolism formation and plant recovery from water stress, however, can provide insight into near-future challenges that woody plants will face. In addition, knowledge of species-specific properties of xylem function may help guide mitigation of climate change impacts on woody plants in natural and agricultural tree communities.

Vulnerability to drought-induced cavitation in poplars: synthesis and future opportunities

Vulnerability to drought-induced cavitation is a key trait of plant water relations. Here, we summarize the available literature on vulnerability to drought-induced cavitation in poplars (Populus spp.), a genus of agronomic, ecological and scientific importance. Vulnerability curves and vulnerability parameters (including the water potential inducing 50% loss in hydraulic conductivity, P50) were collected from 37 studies published between 1991 and 2014, covering a range of 10 species and 12 interspecific hybrid crosses. Results of our meta-analysis confirm that poplars are among the most vulnerable woody species to drought-induced cavitation (mean P50  = -1.44 and -1.55 MPa across pure species and hybrids, respectively). Yet, significant variation occurs among species (P50 range: 1.43 MPa) and among hybrid crosses (P50 range: 1.12 MPa), within species and hybrid crosses (max. P50 range reported: 0.8 MPa) as well as in response to environmental factors including nitrogen fertilization, irradiance, temperature and drought (max. P50 range reported: 0.75 MPa). Potential implications and gaps in knowledge are discussed in the context of poplar cultivation, species adaptation and climate modifications. We suggest that poplars represent a valuable model for studies on drought-induced cavitation, especially to elucidate the genetic and molecular basis of cavitation resistance in Angiosperms.

Exploring the Klinkenberg effect at different scales

Simulations of microflows usually require sophisticated numerical tools. Nevertheless in the slip regime, the hydrodynamic equation with slip boundary condition may be sufficient to account for the so-called Klinkenberg effect. We propose to visit this effect using a basic network of microchannels in which the Knudsen number is multiplied by two or four by introducing successive derivations to the channel. We derived an equivalent hydraulic conductivity up to second order. Theoretical results are compared both with the results of the Navier-Stokes equations with slip condition and with those obtained using a Bhatnagar-Gross-Krook-Hermite model developed especially for flows with a large spectrum of Knudsen numbers (typically 10^{-4}<K_{n}<10). A criterion is provided in order to distinguish the slip regime from the transitional one in this multiscale network.

Modelling the mechanical behaviour of pit membranes in bordered pits with respect to cavitation resistance in angiosperms

BACKGROUND AND AIMS

Various correlations have been identified between anatomical features of bordered pits in angiosperm xylem and vulnerability to cavitation, suggesting that the mechanical behaviour of the pits may play a role. Theoretical modelling of the membrane behaviour has been undertaken, but it requires input of parameters at the nanoscale level. However, to date, no experimental data have indicated clearly that pit membranes experience strain at high levels during cavitation events.

METHODS

Transmission electron microscopy (TEM) was used in order to quantify the pit micromorphology of four tree species that show contrasting differences in vulnerability to cavitation, namely Sorbus aria, Carpinus betulus, Fagus sylvatica and Populus tremula. This allowed anatomical characters to be included in a mechanical model that was based on the Kirchhoff-Love thin plate theory. A mechanistic model was developed that included the geometric features of the pits that could be measured, with the purpose of evaluating the pit membrane strain that results from a pressure difference being applied across the membrane. This approach allowed an assessment to be made of the impact of the geometry of a pit on its mechanical behaviour, and provided an estimate of the impact on air-seeding resistance.

KEY RESULTS

The TEM observations showed evidence of residual strains on the pit membranes, thus demonstrating that this membrane may experience a large degree of strain during cavitation. The mechanical modelling revealed the interspecific variability of the strains experienced by the pit membrane, which varied according to the pit geometry and the pressure experienced. The modelling output combined with the TEM observations suggests that cavitation occurs after the pit membrane has been deflected against the pit border. Interspecific variability of the strains experienced was correlated with vulnerability to cavitation. Assuming that air-seeding occurs at a given pit membrane strain, the pressure predicted by the model to achieve this mechanical state corresponds to experimental values of cavitation sensitivity (P50).

CONCLUSIONS

The results provide a functional understanding of the importance of pit geometry and pit membrane structure in air-seeding, and thus in vulnerability to cavitation.