The viscoelastic behaviour of a biological material is central to its functioning and is an indicator of its health. The Fung quasi-linear viscoelastic (QLV) model, a standard tool for characterizing biological materials, provides excellent fits to most stress–relaxation data by imposing a simple form upon a material's temporal relaxation spectrum. However, model identification is challenging because the Fung QLV model's ‘box’-shaped relaxation spectrum, predominant in biomechanics applications, can provide an excellent fit even when it is not a reasonable representation of a material's relaxation spectrum. Here, we present a robust and simple discrete approach for identifying a material's temporal relaxation spectrum from stress–relaxation data in an unbiased way. Our ‘discrete QLV’ (DQLV) approach identifies ranges of time constants over which the Fung QLV model's typical box spectrum provides an accurate representation of a particular material's temporal relaxation spectrum, and is effective at providing a fit to this model. The DQLV spectrum also reveals when other forms or discrete time constants are more suitable than a box spectrum. After validating the approach against idealized and noisy data, we applied the methods to analyse medial collateral ligament stress–relaxation data and identify the strengths and weaknesses of an optimal Fung QLV fit.

Biological information is stored in DNA, RNA and protein sequences, which can be understood as genotypes that are translated into phenotypes. The properties of genotype–phenotype (GP) maps have been studied in great detail for RNA secondary structure. These include a highly biased distribution of genotypes per phenotype, negative correlation of genotypic robustness and evolvability, positive correlation of phenotypic robustness and evolvability, shape-space covering, and a roughly logarithmic scaling of phenotypic robustness with phenotypic frequency. More recently similar properties have been discovered in other GP maps, suggesting that they may be fundamental to biological GP maps, in general, rather than specific to the RNA secondary structure map. Here we propose that the above properties arise from the fundamental organization of biological information into ‘constrained' and ‘unconstrained' sequences, in the broadest possible sense. As ‘constrained' we describe sequences that affect the phenotype more immediately, and are therefore more sensitive to mutations, such as, e.g. protein-coding DNA or the stems in RNA secondary structure. ‘Unconstrained' sequences, on the other hand, can mutate more freely without affecting the phenotype, such as, e.g. intronic or intergenic DNA or the loops in RNA secondary structure. To test our hypothesis we consider a highly simplified GP map that has genotypes with ‘coding' and ‘non-coding' parts. We term this the Fibonacci GP map, as it is equivalent to the Fibonacci code in information theory. Despite its simplicity the Fibonacci GP map exhibits all the above properties of much more complex and biologically realistic GP maps. These properties are therefore likely to be fundamental to many biological GP maps.

Nature presents multiple intriguing examples of processes that proceed with high precision and regularity. This remarkable stability is frequently counter to modellers' experience with the inherent stochasticity of chemical reactions in the regime of low-copy numbers. Moreover, the effects of noise and nonlinearities can lead to ‘counterintuitive’ behaviour, as demonstrated for a basic enzymatic reaction scheme that can display stochastic focusing (SF). Under the assumption of rapid signal fluctuations, SF has been shown to convert a graded response into a threshold mechanism, thus attenuating the detrimental effects of signal noise. However, when the rapid fluctuation assumption is violated, this gain in sensitivity is generally obtained at the cost of very large product variance, and this unpredictable behaviour may be one possible explanation of why, more than a decade after its introduction, SF has still not been observed in real biochemical systems. In this work, we explore the noise properties of a simple enzymatic reaction mechanism with a small and fluctuating number of active enzymes that behaves as a high-gain, noisy amplifier due to SF caused by slow enzyme fluctuations. We then show that the inclusion of a plausible negative feedback mechanism turns the system from a noisy signal detector to a strong homeostatic mechanism by exchanging high gain with strong attenuation in output noise and robustness to parameter variations. Moreover, we observe that the discrepancy between deterministic and stochastic descriptions of stochastically focused systems in the evolution of the means almost completely disappears, despite very low molecule counts and the additional nonlinearity due to feedback. The reaction mechanism considered here can provide a possible resolution to the apparent conflict between intrinsic noise and high precision in critical intracellular processes.

In HIV-infected patients, an individual's set point viral load (SPVL) strongly predicts disease progression. Some think that SPVL is evolving, indicating that the virulence of the virus may be changing, but the data are not consistent. In addition, the widespread use of antiretroviral therapy (ART) has the potential to drive virulence evolution. We develop a simple deterministic model designed to answer the following questions: what are the expected patterns of virulence change in the initial decades of an epidemic? Could administration of ART drive changes in virulence evolution and, what is the potential size and direction of this effect? We find that even without ART we would not expect monotonic changes in average virulence. Transient decreases in virulence following the peak of an epidemic are not necessarily indicative of eventual evolution to avirulence. In the short term, we would expect widespread ART to cause limited downward pressure on virulence. In the long term, the direction of the effect is determined by a threshold condition, which we define. We conclude that, given the surpassing benefits of ART to the individual and in reducing onward transmission, virulence evolution considerations need have little bearing on how we treat.

We present a novel method for the unsupervised discovery of behavioural motifs in larval Drosophila melanogaster and Caenorhabditis elegans. A motif is defined as a particular sequence of postures that recurs frequently. The animal's changing posture is represented by an eigenshape time series, and we look for motifs in this time series. To find motifs, the eigenshape time series is segmented, and the segments clustered using spline regression. Unlike previous approaches, our method can classify sequences of unequal duration as the same motif. The behavioural motifs are used as the basis of a probabilistic behavioural annotator, the eigenshape annotator (ESA). Probabilistic annotation avoids rigid threshold values and allows classification uncertainty to be quantified. We apply eigenshape annotation to both larval Drosophila and C. elegans and produce a good match to hand annotation of behavioural states. However, we find many behavioural events cannot be unambiguously classified. By comparing the results with ESA of an artificial agent's behaviour, we argue that the ambiguity is due to greater continuity between behavioural states than is generally assumed for these organisms.

Currently, most of the basic mechanisms governing tumour–immune system interactions, in combination with modulations of tumour-associated vasculature, are far from being completely understood. Here, we propose a mathematical model of vascularized tumour growth, where the main novelty is the modelling of the interplay between functional tumour vasculature and effector cell recruitment dynamics. Parameters are calibrated on the basis of different in vivo immunocompromised Rag1–/– and wild-type (WT) BALB/c murine tumour growth experiments. The model analysis supports that tumour vasculature normalization can be a plausible and effective strategy to treat cancer when combined with appropriate immunostimulations. We find that improved levels of functional tumour vasculature, potentially mediated by normalization or stress alleviation strategies, can provide beneficial outcomes in terms of tumour burden reduction and growth control. Normalization of tumour blood vessels opens a therapeutic window of opportunity to augment the antitumour immune responses, as well as to reduce intratumoral immunosuppression and induced hypoxia due to vascular abnormalities. The potential success of normalizing tumour-associated vasculature closely depends on the effector cell recruitment dynamics and tumour sizes. Furthermore, an arbitrary increase in the initial effector cell concentration does not necessarily imply better tumour control. We evidence the existence of an optimal concentration range of effector cells for tumour shrinkage. Based on these findings, we suggest a theory-driven therapeutic proposal that optimally combines immuno- and vasomodulatory interventions.

The distribution of firms' growth and firms' sizes is a topic under intense scrutiny. In this paper, we show that a thermodynamic model based on the maximum entropy principle, with dynamical prior information, can be constructed that adequately describes the dynamics and distribution of firms' growth. Our theoretical framework is tested against a comprehensive database of Spanish firms, which covers, to a very large extent, Spain's economic activity, with a total of 1 155 142 firms evolving along a full decade. We show that the empirical exponent of Pareto's law, a rule often observed in the rank distribution of large-size firms, is explained by the capacity of economic system for creating/destroying firms, and that can be used to measure the health of a capitalist-based economy. Indeed, our model predicts that when the exponent is larger than 1, creation of firms is favoured; when it is smaller than 1, destruction of firms is favoured instead; and when it equals 1 (matching Zipf's law), the system is in a full macroeconomic equilibrium, entailing ‘free’ creation and/or destruction of firms. For medium and smaller firm sizes, the dynamical regime changes, the whole distribution can no longer be fitted to a single simple analytical form and numerical prediction is required. Our model constitutes the basis for a full predictive framework regarding the economic evolution of an ensemble of firms. Such a structure can be potentially used to develop simulations and test hypothetical scenarios, such as economic crisis or the response to specific policy measures.

In this paper, we examine the role of lies in human social relations by implementing some salient characteristics of deceptive interactions into an opinion formation model, so as to describe the dynamical behaviour of a social network more realistically. In this model, we take into account such basic properties of social networks as the dynamics of the intensity of interactions, the influence of public opinion and the fact that in every human interaction it might be convenient to deceive or withhold information depending on the instantaneous situation of each individual in the network. We find that lies shape the topology of social networks, especially the formation of tightly linked, small communities with loose connections between them. We also find that agents with a larger proportion of deceptive interactions are the ones that connect communities of different opinion, and, in this sense, they have substantial centrality in the network. We then discuss the consequences of these results for the social behaviour of humans and predict the changes that could arise due to a varying tolerance for lies in society.

Real-world attacks can be interpreted as the result of competitive interactions between networks, ranging from predator–prey networks to networks of countries under economic sanctions. Although the purpose of an attack is to damage a target network, it also curtails the ability of the attacker, which must choose the duration and magnitude of an attack to avoid negative impacts on its own functioning. Nevertheless, despite the large number of studies on interconnected networks, the consequences of initiating an attack have never been studied. Here, we address this issue by introducing a model of network competition where a resilient network is willing to partially weaken its own resilience in order to more severely damage a less resilient competitor. The attacking network can take over the competitor's nodes after their long inactivity. However, owing to a feedback mechanism the takeovers weaken the resilience of the attacking network. We define a conservation law that relates the feedback mechanism to the resilience dynamics for two competing networks. Within this formalism, we determine the cost and optimal duration of an attack, allowing a network to evaluate the risk of initiating hostilities.

Small metazoan paddlers, such as crustacean larvae (nauplii), are abundant, ecologically important and active swimmers, which depend on exploiting viscous forces for locomotion. The physics of micropaddling at low Reynolds number was investigated using a model of swimming based on slender-body theory for Stokes flow. Locomotion of nauplii of the copepod Bestiolina similis was quantified from high-speed video images to obtain precise measurements of appendage movements and the resulting displacement of the body. The kinematic and morphological data served as inputs to the model, which predicted the displacement in good agreement with observations. The results of interest did not depend sensitively on the parameters within the error of measurement. Model tests revealed that the commonly attributed mechanism of ‘feathering’ appendages during return strokes accounts for only part of the displacement. As important for effective paddling at low Reynolds number is the ability to generate a metachronal sequence of power strokes in combination with synchronous return strokes of appendages. The effect of feathering together with a synchronous return stroke is greater than the sum of each factor individually. The model serves as a foundation for future exploration of micropaddlers swimming at intermediate Reynolds number where both viscous and inertial forces are important.

Rapid technological advances have led to the production of different types of biological data and enabled construction of complex networks with various types of interactions between diverse biological entities. Standard network data analysis methods were shown to be limited in dealing with such heterogeneous networked data and consequently, new methods for integrative data analyses have been proposed. The integrative methods can collectively mine multiple types of biological data and produce more holistic, systems-level biological insights. We survey recent methods for collective mining (integration) of various types of networked biological data. We compare different state-of-the-art methods for data integration and highlight their advantages and disadvantages in addressing important biological problems. We identify the important computational challenges of these methods and provide a general guideline for which methods are suited for specific biological problems, or specific data types. Moreover, we propose that recent non-negative matrix factorization-based approaches may become the integration methodology of choice, as they are well suited and accurate in dealing with heterogeneous data and have many opportunities for further development.

Elastic objects across a wide range of scales deform under local changes of their intrinsic properties, yet the shapes are glocal, set by a complicated balance between local properties and global geometric constraints. Here, we explore this interplay during the inversion process of the green alga Volvox, whose embryos must turn themselves inside out to complete their development. This process has recently been shown to be well described by the deformations of an elastic shell under local variations of its intrinsic curvatures and stretches, although the detailed mechanics of the process have remained unclear. Through a combination of asymptotic analysis and numerical studies of the bifurcation behaviour, we illustrate how appropriate local deformations can overcome global constraints to initiate inversion.

Casemaker caddisfly (Hesperophylax occidentalis) larvae use adhesive silk fibres to construct protective shelters under water. The silk comprises a distinct peripheral coating on a viscoelastic fibre core. Caddisworm silk peroxinectin (csPxt), a haem-peroxidase, was shown to be glycosylated by lectin affinity chromatography and tandem mass spectrometry. Using high-resolution H2O2 and peroxidase-dependent silver ion reduction and nanoparticle deposition, imaged by electron microscopy, csPxt activity was shown to be localized in the peripheral layer of drawn silk fibres. CsPxt catalyses dityrosine cross-linking within the adhesive peripheral layer post-draw, initiated perhaps by H2O2 generated by a silk gland-specific superoxide dismutase 3 (csSOD3) from environmental reactive oxygen species present in natural water. CsSOD3 was also shown to be a glycoprotein and is likely localized in the peripheral layer. Using a synthetic fluorescent phenolic copolymer and confocal microscopy, it was shown that csPxt catalyses oxidative cross-linking to external polyphenolic compounds capable of diffusive interpenetration into the fuzzy peripheral coating, including humic acid, a natural surface-active polyphenol. The results provide evidence of enzyme-mediated covalent cross-linking of a natural bioadhesive to polyphenol conditioned interfaces as a mechanism of permanent adhesion underwater.

Transport networks distribute resources and information in many human and biological systems. Their construction requires optimization and balance of conflicting criteria such as robustness against disruptions, transport efficiency and building cost. The colonies of the polydomous Australian meat ant Iridomyrmex purpureus are a striking example of such a decentralized network, consisting of trails that connect spatially separated nests. Here we study the rules that underlie network construction in these ants. We find that a simple model of network growth, which we call the minimum linking model (MLM), is sufficient to explain the growth of real ant colonies. For larger networks, the MLM shows a qualitative similarity with a Euclidean minimum spanning tree, prioritizing cost and efficiency over robustness. We introduce a variant of our model to show that a balance between cost, efficiency and robustness can be also reproduced at larger scales than ant colonies. Remarkably, such a balance is influenced by a parameter reflecting the specific features of the modelled transport system. The extended MLM could thus be a suitable source of inspiration for the construction of cheap and efficient transport networks with non-zero robustness, suggesting possible applications in the design of human-made networks.