Structural mechanics of filamentous cyanobacteria

Filamentous cyanobacteria, forming long strands of connected cells, are one of the earliest and most successful forms of life on Earth. They exhibit self-organized behaviour, forming large-scale patterns in structures like biomats and stromatolites. The mechanical properties of these rigid structures have contributed to their biological success and are important to applications like algae-based biofuel production. For active polymers like these cyanobacteria, one of the most important mechanical properties is the bending modulus, or flexural rigidity. Here, we quantify the bending stiffness of three species of filamentous cyanobacteria, of order Oscillatoriales, using a microfluidic flow device where single filaments are deflected by fluid flow. This is complemented by measurements of Young’s modulus of the cell wall, via nanoindentation, and the cell wall thickness. We find that the stiffness of the cyanobacteria is well-captured by a simple model of a flexible rod, with most stress carried by a rigid outer wall. Finally, we connect these results to the curved shapes that these cyanobacteria naturally take while gliding, and quantify the forces generated internally to maintain this shape. The measurements can be used to model interactions between cyanobacteria, or with their environment, and how their collective behaviour emerges from such interactions.     

Fast free-energy-based neutral set size estimates for the RNA genotype–phenotype map

The genotype–phenotype (GP) map of RNA secondary structure links each RNA sequence to its corresponding secondary structure. Previous research has shown that the large-scale structural properties of GP maps, such as the size of neutral sets in genotype space, can influence evolutionary outcomes. In order to use neutral set sizes, efficient and accurate computational methods are needed to compute them. Here, we propose a new method, which is based on free energy estimates and is much faster than existing sample-based methods. Moreover, this approach can give insight into the reasons behind neutral set size variations, for example, why structures with fewer stacks tend to have larger neutral set sizes. In addition, we generalize neutral set size calculations from the previously studied many-to-one framework, where each sequence folds into a single energetically preferred structure, to a fuller many-to-many framework, where several low-energy structures are included. We find that structures with high neutral sets in one framework also tend to have large neutral sets in the other framework for a range of parameters and thus the choice of GP map does not fundamentally affect which structures have the largest neutral set sizes.     

The radial growth phase of malignant melanoma: multi-phase modelling,numerical simulations and linear stability analysis

Cutaneous melanoma is disproportionately lethal despite its relatively low incidence and its potential for cure in the early stages. The aim of this study is to foster understanding of the role of microstructure on the occurrence of morphological changes in diseased skin during melanoma evolution. The authors propose a biomechanical analysis of its radial growth phase, investigating the role of intercellular/stromal connections on the initial stages of epidermis invasion. The radial growth phase of a primary melanoma is modelled within the multi-phase theory of mixtures, reproducing the mechanical behaviour of the skin layers and of the epidermal–dermal junction. The theoretical analysis takes into account those cellular processes that have been experimentally observed to disrupt homeostasis in normal epidermis. Numerical simulations demonstrate that the loss of adhesiveness of the melanoma cells both to the basal laminae, caused by deregulation mechanisms of adherent junctions, and to adjacent keratynocytes, consequent to a downregulation of E-cadherin, are the fundamental biomechanical features for promoting tumour initiation. Finally, the authors provide the mathematical proof of a long wavelength instability of the tumour front during the early stages of melanoma invasion. These results open the perspective to correlate the early morphology of a growing melanoma with the biomechanical characteristics of its micro-environment.     

Demographic buffering: titrating the effects of birth rate and imperfect immunity on epidemic dynamics

Host demography can alter the dynamics of infectious disease. In the case of perfectly immunizing infections, observations of strong sensitivity to demographic variation have been mechanistically explained through analysis of the susceptible–infected–recovered (SIR) model that assumes lifelong immunity following recovery from infection. When imperfect immunity is incorporated into this framework via the susceptible–infected–recovered–susceptible (SIRS) model, with individuals regaining full susceptibility following recovery, we show that rapid loss of immunity is predicted to buffer populations against the effects of demographic change. However, this buffering is contrary to the dependence on demography recently observed for partially immunizing infections such as rotavirus and respiratory syncytial virus. We show that this discrepancy arises from a key simplification embedded in the SIR(S) framework, namely that the potential for differential immune responses to repeat exposures is ignored. We explore the minimum additional immunological information that must be included to reflect the range of observed dependencies on demography. We show that including partial protection and lower transmission following primary infection is sufficient to capture more realistic reduced levels of buffering, in addition to changes in epidemic timing, across a range of partially and fully immunizing infections. Furthermore, our results identify key variables in this relationship, including R₀.     

Leg stiffness of sprinters using running-specific prostheses

Running-specific prostheses (RSF) are designed to replicate the spring-like nature of biological legs (bioL) during running. However, it is not clear how these devices affect whole leg stiffness characteristics or running dynamics over a range of speeds. We used a simple spring–mass model to examine running mechanics across a range of speeds, in unilateral and bilateral transtibial amputees and performance-matched controls. We found significant differences between the affected leg (AL) of unilateral amputees and both ALs of bilateral amputees compared with the bioL of non-amputees for nearly every variable measured. Leg stiffness remained constant or increased with speed in bioL, but decreased with speed in legs with RSPs. The decrease in leg stiffness in legs with RSPs was mainly owing to a combination of lower peak ground reaction forces and increased leg compression with increasing speeds. Leg stiffness is an important parameter affecting contact time and the force exerted on the ground. It is likely that the fixed stiffness of the prosthesis coupled with differences in the limb posture required to run with the prosthesis limits the ability to modulate whole leg stiffness and the ability to apply high vertical ground reaction forces during sprinting.     

Modelling cholera epidemics: the role of waterways,human mobility and sanitation

We investigate the role of human mobility as a driver for long-range spreading of cholera infections, which primarily propagate through hydrologically controlled ecological corridors. Our aim is to build a spatially explicit model of a disease epidemic, which is relevant to both social and scientific issues. We present a two-layer network model that accounts for the interplay between epidemiological dynamics, hydrological transport and long-distance dissemination of the pathogen Vibrio cholerae owing to host movement, described here by means of a gravity-model approach. We test our model against epidemiological data recorded during the extensive cholera outbreak occurred in the KwaZulu-Natal province of South Africa during 2000–2001. We show that long-range human movement is fundamental in quantifying otherwise unexplained inter-catchment transport of V. cholerae, thus playing a key role in the formation of regional patterns of cholera epidemics. We also show quantitatively how heterogeneously distributed drinking water supplies and sanitation conditions may affect large-scale cholera transmission, and analyse the effects of different sanitation policies.     

Through the eyes of a bird: modelling visually guided obstacle flight

Various flight navigation strategies for birds have been identified at the large spatial scales of migratory and homing behaviours. However, relatively little is known about close-range obstacle negotiation through cluttered environments. To examine obstacle flight guidance, we tracked pigeons (Columba livia) flying through an artificial forest of vertical poles. Interestingly, pigeons adjusted their flight path only approximately 1.5 m from the forest entry, suggesting a reactive mode of path planning. Combining flight trajectories with obstacle pole positions, we reconstructed the visual experience of the pigeons throughout obstacle flights. Assuming proportional–derivative control with a constant delay, we searched the relevant parameter space of steering gains and visuomotor delays that best explained the observed steering. We found that a pigeon''s steering resembles proportional control driven by the error angle between the flight direction and the desired opening, or gap, between obstacles. Using this pigeon steering controller, we simulated obstacle flights and showed that pigeons do not simply steer to the nearest opening in the direction of flight or destination. Pigeons bias their flight direction towards larger visual gaps when making fast steering decisions. The proposed behavioural modelling method converts the obstacle avoidance behaviour into a (piecewise) target-aiming behaviour, which is better defined and understood. This study demonstrates how such an approach decomposes open-loop free-flight behaviours into components that can be independently evaluated.     

Regulation of the membrane wrapping transition of a cylindrical target by cytoskeleton adhesion

The adsorption of external objects to the cell membrane often triggers cellular responses involving large deformations. In phagocytosis, upon contact with the target, the cell creates large extensions that wrap around the target and ultimately lead to its engulfment. Although active force generation, in particular by actin polymerization, is required for completion of this process, the elastic deformation of the cell membrane upon adhesion to an external object might play an important part in its initiation. In this paper, the elastic deformation of a bilayer owing to the binding of a cylindrical object is studied, taking into account the membrane bending rigidity and the surface tension, the membrane adhesion to both the external target and inner cytoskeleton. The problem is studied within the framework of the Helfrich–Hamiltonian and using force balance relations and the proper boundary conditions that are related to the adhesion energy coefficients. It is shown that membrane wrapping around the target may be a continuous or abrupt transition upon increasing the target binding energy, depending on the value of the parameter. The degree of wrapping and the shape of the membrane in the vicinity of the object are computed numerically, and analytical expressions are given for the boundaries separating the different wrapping regimes in the parameter space.     

Experimental study of the Ca–Mg–Zn system using diffusion couples and key alloys

Nine diffusion couples and 32 key samples were prepared to map the phase diagram of the Ca–Mg–Zn system. Phase relations and solubility limits were determined for binary and ternary compounds using scanning electron microscopy, electron probe microanalysis and x-ray diffraction (XRD). The crystal structure of the ternary compounds was studied by XRD and electron backscatter diffraction. Four ternary intermetallic (IM) compounds were identified in this system: Ca₃Mg_xZn_15−x (4.6 ⩽ x ⩽ 12 at 335 °C, IM1), Ca_14.5Mg_15.8Zn_69.7 (IM2), Ca₂Mg₅Zn₁₃ (IM3) and Ca_1.5Mg_55.3Zn_43.2 (IM4). Three binary compounds were found to have extended solid solubility into ternary systems: CaZn₁₁, CaZn₁₃ and Mg₂Ca form substitutional solid solutions where Mg substitutes for Zn atoms in the first two compounds, and Zn substitutes for both Ca and Mg atoms in Mg₂Ca. The isothermal section of the Ca–Mg–Zn phase diagram at 335 °C was constructed on the basis of the obtained experimental results. The morphologies of the diffusion couples in the Ca–Mg–Zn phase diagram at 335 °C were studied. Depending on the terminal compositions of the diffusion couples, the two-phase regions in the diffusion zone have either a tooth-like morphology or contain a matrix phase with isolated and/or dendritic precipitates.     

A tractable genotype–phenotype map modelling the self-assembly of protein quaternary structure

The mapping between biological genotypes and phenotypes is central to the study of biological evolution. Here, we introduce a rich, intuitive and biologically realistic genotype–phenotype (GP) map that serves as a model of self-assembling biological structures, such as protein complexes, and remains computationally and analytically tractable. Our GP map arises naturally from the self-assembly of polyomino structures on a two-dimensional lattice and exhibits a number of properties: redundancy (genotypes vastly outnumber phenotypes), phenotype bias (genotypic redundancy varies greatly between phenotypes), genotype component disconnectivity (phenotypes consist of disconnected mutational networks) and shape space covering (most phenotypes can be reached in a small number of mutations). We also show that the mutational robustness of phenotypes scales very roughly logarithmically with phenotype redundancy and is positively correlated with phenotypic evolvability. Although our GP map describes the assembly of disconnected objects, it shares many properties with other popular GP maps for connected units, such as models for RNA secondary structure or the hydrophobic-polar (HP) lattice model for protein tertiary structure. The remarkable fact that these important properties similarly emerge from such different models suggests the possibility that universal features underlie a much wider class of biologically realistic GP maps.     

Wet shells and dry tales: the evolutionary ‘Just-So’ stories behind the structure–function of biominerals

The ability of evolution to shape organic form involves the interactions of multiple systems of constraints, including fabrication, phylogeny and function. The tendency to place function above everything else has characterized some of the historical biological literature as a series of ‘Just-So’ stories that provided untested explanations for individual features of an organism. A similar tendency occurs in biomaterials research, where features for which a mechanical function can be postulated are treated as an adaptation. Moreover, functional adaptation of an entire structure is often discussed based on the local characterization of specimens kept in conditions that are far from those in which they evolved. In this work, environmental- and frequency-dependent mechanical characterization of the shells of two cephalopods, Nautilus pompilius and Argonauta argo, is used to demonstrate the importance of multi-scale environmentally controlled characterization of biogenic materials. We uncover two mechanistically independent strategies to achieve deformable, stiff, strong and tough highly mineralized structures. These results are then used to critique interpretations of adaptation in the literature. By integrating the hierarchical nature of biological structures and the environment in which they exist, biomaterials testing can be a powerful tool for generating functional hypotheses that should be informed by how these structures are fabricated and their evolutionary history.     

Spatial heterogeneity enhances and modulates excitability in a mathematical model of the myometrium

The muscular layer of the uterus (myometrium) undergoes profound changes in global excitability prior to parturition. Here, a mathematical model of the myocyte network is developed to investigate the hypothesis that spatial heterogeneity is essential to the transition from local to global excitation which the myometrium undergoes just prior to birth. Each myometrial smooth muscle cell is represented by an element with FitzHugh–Nagumo dynamics. The cells are coupled through resistors that represent gap junctions. Spatial heterogeneity is introduced by means of stochastic variation in coupling strengths, with parameters derived from physiological data. Numerical simulations indicate that even modest increases in the heterogeneity of the system can amplify the ability of locally applied stimuli to elicit global excitation. Moreover, in networks driven by a pacemaker cell, global oscillations of excitation are impeded in fully connected and strongly coupled networks. The ability of a locally stimulated cell or pacemaker cell to excite the network is shown to be strongly dependent on the local spatial correlation structure of the couplings. In summary, spatial heterogeneity is a key factor in enhancing and modulating global excitability.     

(Ni,Co)Se2/NiCo‐LDH Core/Shell Structural Electrode with the Cactus‐Like (Ni,Co)Se2 Core for Asymmetric Supercapacitors

Supercapacitors (SCs) have been widely studied as a class of promising energy‐storage systems for powering next‐generation E‐vehicles and wearable electronics. Fabricating hybrid‐types of electrode materials and designing smart nanoarchitectures are effective approaches to developing high‐performance SCs. Herein, first, a Ni‐Co selenide material (Ni,Co)Se₂ with special cactus‐like structure as the core, to scaffold the NiCo‐layered double hydroxides (LDHs) shell, is designed and fabricated. The cactus‐like structural (Ni,Co)Se₂ core, as a highly conductive and robust support, promotes the electron transport as well as hinders the agglomeration of LDHs. The synergistic contributions from the two types of active materials together with the superior properties of the cactus‐like nanostructure enable the (Ni,Co)Se₂/NiCo‐LDH hybrid electrode to exhibit a high capacity of ≈170 mA h g^?1 (≈1224 F g^?1), good rate performance, and long durability. The as‐assembled (Ni,Co)Se₂/NiCo‐LDH//PC (porous carbon) asymmetric supercapacitor (ASC) with an operating voltage of 1.65 V delivers a high energy density of 39 W h kg^?1 at a power density of 1650 W kg^?1. Therefore, the cactus‐like core/shell structure offers an effective pathway to engineer advanced electrodes. The assembled flexible ASC is demonstrated to effectively power electronic devices.     

Scaling law and enhancement of lift generation of an insect-size hovering flexible wing

We report a comprehensive scaling law and novel lift generation mechanisms relevant to the aerodynamic functions of structural flexibility in insect flight. Using a Navier–Stokes equation solver, fully coupled to a structural dynamics solver, we consider the hovering motion of a wing of insect size, in which the dynamics of fluid–structure interaction leads to passive wing rotation. Lift generated on the flexible wing scales with the relative shape deformation parameter, whereas the optimal lift is obtained when the wing deformation synchronizes with the imposed translation, consistent with previously reported observations for fruit flies and honeybees. Systematic comparisons with rigid wings illustrate that the nonlinear response in wing motion results in a greater peak angle compared with a simple harmonic motion, yielding higher lift. Moreover, the compliant wing streamlines its shape via camber deformation to mitigate the nonlinear lift-degrading wing–wake interaction to further enhance lift. These bioinspired aeroelastic mechanisms can be used in the development of flapping wing micro-robots.     

Hydrodynamics of diatom chains and semiflexible fibres

Diatoms are non-motile, unicellular phytoplankton that have the ability to form colonies in the form of chains. Depending upon the species of diatoms and the linking structures that hold the cells together, these chains can be quite stiff or very flexible. Recently, the bending rigidities of some species of diatom chains have been quantified. In an effort to understand the role of flexibility in nutrient uptake and aggregate formation, we begin by developing a three-dimensional model of the coupled elastic–hydrodynamic system of a diatom chain moving in an incompressible fluid. We find that simple beam theory does a good job of describing diatom chain deformation in a parabolic flow when its ends are tethered, but does not tell the whole story of chain deformations when they are subjected to compressive stresses in shear. While motivated by the fluid dynamics of diatom chains, our computational model of semiflexible fibres illustrates features that apply widely to other systems. The use of an adaptive immersed boundary framework allows us to capture complicated buckling and recovery dynamics of long, semiflexible fibres in shear.     

Analytical model for instantaneous lift and shape deformation of an insect-scale flapping wing in hover

In the analysis of flexible flapping wings of insects, the aerodynamic outcome depends on the combined structural dynamics and unsteady fluid physics. Because the wing shape and hence the resulting effective angle of attack are a priori unknown, predicting aerodynamic performance is challenging. Here, we show that a coupled aerodynamics/structural dynamics model can be established for hovering, based on a linear beam equation with the Morison equation to account for both added mass and aerodynamic damping effects. Lift strongly depends on the instantaneous angle of attack, resulting from passive pitch associated with wing deformation. We show that both instantaneous wing deformation and lift can be predicted in a much simplified framework. Moreover, our analysis suggests that resulting wing kinematics can be explained by the interplay between acceleration-related and aerodynamic damping forces. Interestingly, while both forces combine to create a high angle of attack resulting in high lift around the midstroke, they offset each other for phase control at the end of the stroke.     

Time and dose-dependent risk of pneumococcal pneumonia following influenza: a model for within-host interaction between influenza and Streptococcus pneumoniae

A significant fraction of seasonal and in particular pandemic influenza deaths are attributed to secondary bacterial infections. In animal models, influenza virus predisposes hosts to severe infection with both Streptococcus pneumoniae and Staphylococcus aureus. Despite its importance, the mechanistic nature of the interaction between influenza and pneumococci, its dependence on the timing and sequence of infections as well as the clinical and epidemiological consequences remain unclear. We explore an immune-mediated model of the viral–bacterial interaction that quantifies the timing and the intensity of the interaction. Taking advantage of the wealth of knowledge gained from animal models, and the quantitative understanding of the kinetics of pathogen-specific immunological dynamics, we formulate a mathematical model for immune-mediated interaction between influenza virus and S. pneumoniae in the lungs. We use the model to examine the pathogenic effect of inoculum size and timing of pneumococcal invasion relative to influenza infection, as well as the efficacy of antivirals in preventing severe pneumococcal disease. We find that our model is able to capture the key features of the interaction observed in animal experiments. The model predicts that introduction of pneumococcal bacteria during a 4–6 day window following influenza infection results in invasive pneumonia at significantly lower inoculum size than in hosts not infected with influenza. Furthermore, we find that antiviral treatment administered later than 4 days after influenza infection was not able to prevent invasive pneumococcal disease. This work provides a quantitative framework to study interactions between influenza and pneumococci and has the potential to accurately quantify the interactions. Such quantitative understanding can form a basis for effective clinical care, public health policies and pandemic preparedness.     

Voltage- and current-activated metal–insulator transition in VO2-based electrical switches: a lifetime operation analysis

Vanadium dioxide is an intensively studied material that undergoes a temperature-induced metal–insulator phase transition accompanied by a large change in electrical resistivity. Electrical switches based on this material show promising properties in terms of speed and broadband operation. The exploration of the failure behavior and reliability of such devices is very important in view of their integration in practical electronic circuits. We performed systematic lifetime investigations of two-terminal switches based on the electrical activation of the metal–insulator transition in VO₂ thin films. The devices were integrated in coplanar microwave waveguides (CPWs) in series configuration. We detected the evolution of a 10 GHz microwave signal transmitted through the CPW, modulated by the activation of the VO₂ switches in both voltage- and current-controlled modes. We demonstrated enhanced lifetime operation of current-controlled VO₂-based switching (more than 260 million cycles without failure) compared with the voltage-activated mode (breakdown at around 16 million activation cycles). The evolution of the electrical self-oscillations of a VO₂-based switch induced in the current-operated mode is a subtle indicator of the material properties modification and can be used to monitor its behavior under various external stresses in sensor applications.     

In vivo optic nerve head biomechanics: performance testing of a three-dimensional tracking algorithm

Measurement of optic nerve head (ONH) deformations could be useful in the clinical management of glaucoma. Here, we propose a novel three-dimensional tissue-tracking algorithm designed to be used in vivo. We carry out preliminary verification of the algorithm by testing its accuracy and its robustness. An algorithm based on digital volume correlation was developed to extract ONH tissue displacements from two optical coherence tomography (OCT) volumes of the ONH (undeformed and deformed). The algorithm was tested by applying artificial deformations to a baseline OCT scan while manipulating speckle noise, illumination and contrast enhancement. Tissue deformations determined by our algorithm were compared with the known (imposed) values. Errors in displacement magnitude, orientation and strain decreased with signal averaging and were 0.15 µm, 0.15° and 0.0019, respectively (for optimized algorithm parameters). Previous computational work suggests that these errors are acceptable to provide in vivo characterization of ONH biomechanics. Our algorithm is robust to OCT speckle noise as well as to changes in illumination conditions, and increasing signal averaging can produce better results. This algorithm has potential be used to quantify ONH three-dimensional strains in vivo, of benefit in the diagnosis and identification of risk factors in glaucoma.     

Probabilistic patterns of interaction: the effects of link-strength variability on food web structure

Patterns of species interactions affect the dynamics of food webs. An important component of species interactions that is rarely considered with respect to food webs is the strengths of interactions, which may affect both structure and dynamics. In natural systems, these strengths are variable, and can be quantified as probability distributions. We examined how variation in strengths of interactions can be described hierarchically, and how this variation impacts the structure of species interactions in predator–prey networks, both of which are important components of ecological food webs. The stable isotope ratios of predator and prey species may be particularly useful for quantifying this variability, and we show how these data can be used to build probabilistic predator–prey networks. Moreover, the distribution of variation in strengths among interactions can be estimated from a limited number of observations. This distribution informs network structure, especially the key role of dietary specialization, which may be useful for predicting structural properties in systems that are difficult to observe. Finally, using three mammalian predator–prey networks (two African and one Canadian) quantified from stable isotope data, we show that exclusion of link-strength variability results in biased estimates of nestedness and modularity within food webs, whereas the inclusion of body size constraints only marginally increases the predictive accuracy of the isotope-based network. We find that modularity is the consequence of strong link-strengths in both African systems, while nestedness is not significantly present in any of the three predator–prey networks.