Informatics derived materials databases for multifunctional properties

In this review, we provide an overview of the development of quantitative structure–property relationships incorporating the impact of data uncertainty from small, limited knowledge data sets from which we rapidly develop new and larger databases. Unlike traditional database development, this informatics based approach is concurrent with the identification and discovery of the key metrics controlling structure–property relationships; and even more importantly we are now in a position to build materials databases based on design ‘intent’ and not just design parameters. This permits for example to establish materials databases that can be used for targeted multifunctional properties and not just one characteristic at a time as is presently done. This review provides a summary of the computational logic of building such virtual databases and gives some examples in the field of complex inorganic solids for scintillator applications.     

Materials Nanoarchitecturing via Cation‐Mediated Protein Assembly: Making Limpet Teeth without Mineral

Teeth are designed to deliver high forces while withstanding the generated stresses. Aside from isolated mineral‐free exception (e.g., marine polychaetes and squids), minerals are thought to be indispensable for tooth‐hardening and durability. Here, the unmineralized teeth of the giant keyhole limpet (Megathura crenulata) are shown to attain a stiffness, which is twofold higher than any known organic biogenic structures. In these teeth, protein and chitin fibers establish a stiff compact outer shell enclosing a less compact core. The stiffness and its gradients emerge from a concerted interaction across multiple length‐scales: packing of hydrophobic proteins and folding into secondary structures mediated by Ca²⁺ and Mg²⁺ together with a strong spatial control in the local fiber orientation. These results integrating nanoindentation, acoustic microscopy, and finite‐element modeling for probing the tooth's mechanical properties, spatially resolved small‐ and wide‐angle X‐ray scattering for probing the material ordering on the micrometer scale, and energy‐dispersive X‐ray scattering combined with confocal Raman microscopy to study structural features on the molecular scale, reveal a nanocomposite structure hierarchically assembled to form a versatile damage‐tolerant protein‐based tooth, with a stiffness similar to mineralized mammalian bone, but without any mineral.     

Characterization of microstructures using contour tree connectivity for fluid flow analysis

Quantifying the connectivity of material microstructures is important for a wide range of applications from filters to biomaterials. Currently, the most used measure of connectivity is the Euler number, which is a topological invariant. Topology alone, however, is not sufficient for most practical purposes. In this study, we use our recently introduced connectivity measure, called the contour tree connectivity (CTC), to study microstructures for flow analysis. CTC is a new structural connectivity measure that is based on contour trees and algebraic graph theory. To test CTC, we generated a dataset composed of 120 samples and six different types of artificial microstructures. We compared CTC against the Euler parameter (EP), the parameter for connected pairs, the nominal opening dimension (d_nom) and the permeabilities estimated using direct pore scale modelling. The results show that d_nom is highly correlated with permeability (R² = 0.91), but cannot separate the structural differences. The groups are best classified with feature combinations that include CTC. CTC provides new information with a different connectivity interpretation that can be used to analyse and design materials with complex microstructures.     

Supermacroprous chitosan–agarose–gelatin cryogels: in vitro characterization and in vivo assessment for cartilage tissue engineering

The study focuses on the synthesis of a novel polymeric scaffold having good porosity and mechanical characteristics synthesized by using natural polymers and their optimization for application in cartilage tissue engineering. The scaffolds were synthesized via cryogelation technology using an optimized ratio of the polymer solutions (chitosan, agarose and gelatin) and cross-linker followed by the incubation at sub-zero temperature (−12°C). Microstructure examination of the chitosan–agarose–gelatine (CAG) cryogels was done using scanning electron microscopy (SEM) and fluorescent microscopy. Mechanical analysis, such as the unconfined compression test, demonstrated that cryogels with varying chitosan concentrations, i.e. 0.5–1% have a high compression modulus. In addition, fatigue tests revealed that scaffolds are suitable for bioreactor studies where gels are subjected to continuous cyclic strain. In order to confirm the stability, cryogels were subjected to high frequency (5 Hz) with 30 per cent compression of their original length up to 1 × 10⁵ cycles, gels did not show any significant changes in their mass and dimensions during the experiment. These cryogels have exhibited degradation capacity under aseptic conditions. CAG cryogels showed good cell adhesion of primary goat chondrocytes examined by SEM. Cytotoxicity of the material was checked by MTT assay and results confirmed the biocompatibility of the material. In vivo biocompatibility of the scaffolds was checked by the implantation of the scaffolds in laboratory animals. These results suggest the potential of CAG cryogels as a good three-dimensional scaffold for cartilage tissue engineering.     

Host–guest chemistry of mesoporous silicas: precise design of location,density and orientation of molecular guests in mesopores

Mesoporous solids, which were prepared from inorganic-surfactant mesostructured materials, have been investigated due to their very large surface area and high porosity, pore size uniformity and variation, periodic pore arrangement and possible pore surface modification. Morphosyntheses from macroscopic morphologies such as bulk monolith and films, to nanoscopic ones, nanoparticles and their stable suspension, make mesoporous materials more attractive for applications and detailed characterization. This class of materials has been studied for such applications as adsorbents and catalysts, and later on, for optical, electronic, environmental and bio-related ones. This review summarizes the studies on the chemistry of mesoporous silica and functional guest species (host–guest chemistry) to highlight the present status and future applications of the host–guest hybrids.     

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.     

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.     

Structural performance of a climbing cactus: making the most of softness

Climbing plants must reach supports and navigate gaps to colonize trees. This requires a structural organization ensuring the rigidity of so-called ‘searcher’ stems. Cacti have succulent stems adapted for water storage in dry habitats. We investigate how a climbing cactus Selenicereus setaceus develops its stem structure and succulent tissues for climbing. We applied a ‘wide scale’ approach combining field-based bending, tensile and swellability tests with fine-scale rheological, compression and anatomical analyses in laboratory conditions. Gap-spanning ‘searcher’ stems rely significantly on the soft cortex and outer skin of the stem for rigidity in bending (60–94%). A woody core contributes significantly to axial and radial compressive strength (80%). Rheological tests indicated that storage moduli were consistently higher than loss moduli indicating that the mucilaginous cortical tissue behaved like a viscoelastic solid with properties similar to physical or chemical hydrogels. Rheological and compression properties of the soft tissue changed from young to old stages. The hydrogel–skin composite is a multi-functional structure contributing to rigidity in searcher stems but also imparting compliance and benign failure in environmental situations when stems must fail. Soft tissue composites changing in function via changes in development and turgescence have a great potential for exploring candidate materials for technical applications.     

Accuracy of the Michaelis–Menten approximation when analysing effects of molecular noise

Quantitative biology relies on the construction of accurate mathematical models, yet the effectiveness of these models is often predicated on making simplifying approximations that allow for direct comparisons with available experimental data. The Michaelis–Menten (MM) approximation is widely used in both deterministic and discrete stochastic models of intracellular reaction networks, owing to the ubiquity of enzymatic activity in cellular processes and the clear biochemical interpretation of its parameters. However, it is not well understood how the approximation applies to the discrete stochastic case or how it extends to spatially inhomogeneous systems. We study the behaviour of the discrete stochastic MM approximation as a function of system size and show that significant errors can occur for small volumes, in comparison with a corresponding mass-action system. We then explore some consequences of these results for quantitative modelling. One consequence is that fluctuation-induced sensitivity, or stochastic focusing, can become highly exaggerated in models that make use of MM kinetics even if the approximations are excellent in a deterministic model. Another consequence is that spatial stochastic simulations based on the reaction–diffusion master equation can become highly inaccurate if the model contains MM terms.     

Integration of intrinsic muscle properties,feed-forward and feedback signals for generating and stabilizing hopping

It was hypothesized that a tight integration of feed-forward and feedback-driven muscle activation with the characteristic intrinsic muscle properties is a key feature of locomotion in challenging environments. In this simulation study it was investigated whether a combination of feed-forward and feedback signals improves hopping stability compared with those simulations with one individual type of activation. In a reduced one-dimensional hopping model with a Hill-type muscle (one contractile element, neither serial nor parallel elastic elements), the level of detail of the muscle''s force–length–velocity relation and the type of activation generation (feed-forward, feedback and combination of both) were varied to test their influence on periodic hopping. The stability of the hopping patterns was evaluated by return map analysis. It was found that the combination of feed-forward and proprioceptive feedback improved hopping stability. Furthermore, the nonlinear Hill-type representation of intrinsic muscle properties led to a faster reduction of perturbations than a linear approximation, independent of the type of activation. The results emphasize the ability of organisms to exploit the stabilizing properties of intrinsic muscle characteristics.     

Pattern formation in stromatolites: insights from mathematical modelling

To this day, computer models for stromatolite formation have made substantial use of the Kardar–Parisi–Zhang (KPZ) equation. Oddly enough, these studies yielded mutually exclusive conclusions about the biotic or abiotic origin of such structures. We show in this paper that, at our current state of knowledge, a purely biotic origin for stromatolites can neither be proved nor disproved by means of a KPZ-based model. What can be shown, however, is that whatever their (biotic or abiotic) origin might be, some morphologies found in actual stromatolite structures (e.g. overhangs) cannot be formed as a consequence of a process modelled exclusively in terms of the KPZ equation and acting over sufficiently large times. This suggests the need to search for alternative mathematical approaches to model these structures, some of which are discussed in this paper.     

Insertions and deletions in the RNA sequence–structure map

Genotype–phenotype maps link genetic changes to their fitness effect and are thus an essential component of evolutionary models. The map between RNA sequences and their secondary structures is a key example and has applications in functional RNA evolution. For this map, the structural effect of substitutions is well understood, but models usually assume a constant sequence length and do not consider insertions or deletions. Here, we expand the sequence–structure map to include single nucleotide insertions and deletions by using the RNAshapes concept. To quantify the structural effect of insertions and deletions, we generalize existing definitions for robustness and non-neutral mutation probabilities. We find striking similarities between substitutions, deletions and insertions: robustness to substitutions is correlated with robustness to insertions and, for most structures, to deletions. In addition, frequent structural changes after substitutions also tend to be common for insertions and deletions. This is consistent with the connection between energetically suboptimal folds and possible structural transitions. The similarities observed hold both for genotypic and phenotypic robustness and mutation probabilities, i.e. for individual sequences and for averages over sequences with the same structure. Our results could have implications for the rate of neutral and non-neutral evolution.     

Rapid intra-adrenal feedback regulation of glucocorticoid synthesis

The hypothalamic–pituitary–adrenal axis is a vital neuroendocrine system that regulates the secretion of glucocorticoid hormones from the adrenal glands. This system is characterized by a dynamic ultradian hormonal oscillation, and in addition is highly responsive to stressful stimuli. We have recently shown that a primary mechanism generating this ultradian rhythm is a systems-level interaction where adrenocorticotrophin hormone (ACTH) released from the pituitary stimulates the secretion of adrenal glucocorticoids, which in turn feedback at the level of the pituitary to rapidly inhibit ACTH secretion. In this study, we combine experimental physiology and mathematical modelling to investigate intra-adrenal mechanisms regulating glucocorticoid synthesis. Our modelling results suggest that glucocorticoids can inhibit their own synthesis through a very rapid (within minutes), presumably non-genomic, intra-adrenal pathway. We present further evidence for the existence of a short time delay in this intra-adrenal inhibition, and also that at the initiation of each ACTH stimulus, this local feedback mechanism is rapidly antagonized, presumably via activation of the specific ACTH receptor (MC2R) signalling pathway. This mechanism of intra-adrenal inhibition enables the gland to rapidly release glucocorticoids while at the same time preventing uncontrolled release of glucocorticoids in response to large surges in ACTH associated with stress.     

Implementation and acceleration of optimal control for systems biology

Optimal control theory provides insight into complex resource allocation decisions. The forward–backward sweep method (FBSM) is an iterative technique commonly implemented to solve two-point boundary value problems arising from the application of Pontryagin’s maximum principle (PMP) in optimal control. The FBSM is popular in systems biology as it scales well with system size and is straightforward to implement. In this review, we discuss the PMP approach to optimal control and the implementation of the FBSM. By conceptualizing the FBSM as a fixed point iteration process, we leverage and adapt existing acceleration techniques to improve its rate of convergence. We show that convergence improvement is attainable without prohibitively costly tuning of the acceleration techniques. Furthermore, we demonstrate that these methods can induce convergence where the underlying FBSM fails to converge. All code used in this work to implement the FBSM and acceleration techniques is available on GitHub at https://github.com/Jesse-Sharp/Sharp2021.     

Mathematical modelling of atheroma plaque formation and development in coronary arteries

Atherosclerosis is a vascular disease caused by inflammation of the arterial wall, which results in the accumulation of low-density lipoprotein (LDL) cholesterol, monocytes, macrophages and fat-laden foam cells at the place of the inflammation. This process is commonly referred to as plaque formation. The evolution of the atherosclerosis disease, and in particular the influence of wall shear stress on the growth of atherosclerotic plaques, is still a poorly understood phenomenon. This work presents a mathematical model to reproduce atheroma plaque growth in coronary arteries. This model uses the Navier–Stokes equations and Darcy''s law for fluid dynamics, convection–diffusion–reaction equations for modelling the mass balance in the lumen and intima, and the Kedem–Katchalsky equations for the interfacial coupling at membranes, i.e. endothelium. The volume flux and the solute flux across the interface between the fluid and the porous domains are governed by a three-pore model. The main species and substances which play a role in early atherosclerosis development have been considered in the model, i.e. LDL, oxidized LDL, monocytes, macrophages, foam cells, smooth muscle cells, cytokines and collagen. Furthermore, experimental data taken from the literature have been used in order to physiologically determine model parameters. The mathematical model has been implemented in a representative axisymmetric geometrical coronary artery model. The results show that the mathematical model is able to qualitatively capture the atheroma plaque development observed in the intima layer.     

The contagious nature of imprisonment: an agent-based model to explain racial disparities in incarceration rates

We build an agent-based model of incarceration based on the susceptible–infected–suspectible (SIS) model of infectious disease propagation. Our central hypothesis is that the observed racial disparities in incarceration rates between Black and White Americans can be explained as the result of differential sentencing between the two demographic groups. We demonstrate that if incarceration can be spread through a social influence network, then even relatively small differences in sentencing can result in large disparities in incarceration rates. Controlling for effects of transmissibility, susceptibility and influence network structure, our model reproduces the observed large disparities in incarceration rates given the differences in sentence lengths for White and Black drug offenders in the USA without extensive parameter tuning. We further establish the suitability of the SIS model as applied to incarceration by demonstrating that the observed structural patterns of recidivism are an emergent property of the model. In fact, our model shows a remarkably close correspondence with California incarceration data. This work advances efforts to combine the theories and methods of epidemiology and criminology.     

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.     

Social network architecture and the maintenance of deleterious cultural traits

How have changes in communications technology affected the way that misinformation spreads through a population and persists? To what extent do differences in the architecture of social networks affect the spread of misinformation, relative to the rates and rules by which individuals transmit or eliminate different pieces of information (cultural traits)? Here, we use analytical models and individual-based simulations to study how a ‘cultural load’ of misinformation can be maintained in a population under a balance between social transmission and selective elimination of cultural traits with low intrinsic value. While considerable research has explored how network architecture affects percolation processes, we find that the relative rates at which individuals transmit or eliminate traits can have much more profound impacts on the cultural load than differences in network architecture. In particular, the cultural load is insensitive to correlations between an individual''s network degree and rate of elimination when these quantities vary among individuals. Taken together, these results suggest that changes in communications technology may have influenced cultural evolution more strongly through changes in the amount of information flow, rather than the details of who is connected to whom.