Alterations in gap junction connexin43/connexin45 ratio mediate a transition from quiescence to excitation in a mathematical model of the myometrium

The smooth muscle cells of the uterus contract in unison during delivery. These cells achieve coordinated activity via electrical connections called gap junctions which consist of aggregated connexin proteins such as connexin43 and connexin45. The density of gap junctions governs the excitability of the myometrium (among other factors). An increase in gap junction density occurs immediately prior to parturition. We extend a mathematical model of the myometrium by incorporating the voltage-dependence of gap junctions that has been demonstrated in the experimental literature. Two functional subtypes exist, corresponding to systems with predominantly connexin43 and predominantly connexin45, respectively. Our simulation results indicate that the gap junction protein connexin45 acts as a negative modulator of uterine excitability, and hence, activity. A network with a higher proportion of connexin45 relative to connexin43 is unable to excite every cell. Connexin45 has much more rapid gating kinetics than connexin43 which we show limits the maximum duration of a local burst of activity. We propose that this effect regulates the degree of synchronous excitation attained during a contraction. Our results support the hypothesis that as labour approaches, connexin45 is downregulated to allow action potentials to spread more readily through the myometrium.     

Synergy of cell–cell repulsion and vacuolation in a computational model of lumen formation

A key step in blood vessel development (angiogenesis) is lumen formation: the hollowing of vessels for blood perfusion. Two alternative lumen formation mechanisms are suggested to function in different types of blood vessels. The vacuolation mechanism is suggested for lumen formation in small vessels by coalescence of intracellular vacuoles, a view that was extended to extracellular lumen formation by exocytosis of vacuoles. The cell–cell repulsion mechanism is suggested to initiate extracellular lumen formation in large vessels by active repulsion of adjacent cells, and active cell shape changes extend the lumen. We used an agent-based computer model, based on the cellular Potts model, to compare and study both mechanisms separately and combined. An extensive sensitivity analysis shows that each of the mechanisms on its own can produce lumens in a narrow region of parameter space. However, combining both mechanisms makes lumen formation much more robust to the values of the parameters, suggesting that the mechanisms may work synergistically and operate in parallel, rather than in different vessel types.     

Surfactancy in a tadpole model of proteins

We model the environment of eukaryotic nuclei by representing macromolecules by only their entropic properties, with globular molecules represented by spherical colloids and flexible molecules by polymers. We put particular focus on proteins with both globular and intrinsically disordered regions, which we represent with ‘tadpole’ constructed by grafting single polymers and colloids together. In Monte Carlo simulations, we find these tadpoles support phase separation via depletion flocculation, and demonstrate several surfactant behaviours, including being found preferentially at interfaces and forming micelles in single phase solution. Furthermore, the model parameters can be tuned to give a tadpole a preference for either bulk phase. However, we find entropy too weak to drive these behaviours by itself at likely biological concentrations.     

A mathematical model of wound healing and subsequent scarring

Wound healing is a complex process involving the delicate interaction between elements that vary widely in nature and size scales, from the nanometre level, such as molecules, to cells measured in micrometres, and fibres with width and length measured on both scales. Hybrid approaches, where each species is represented by a model on an appropriate size scale, have received attention recently. In this study, we provide a review of earlier work on such hybrid models of wound healing. General models for each of the element types involved in dermal wound healing used in this research are described: cells, modelled as discrete individuals; chemicals, modelled as continua; and fibres, modelled with a novel tensorial representation. Techniques for integrating such disparate models are outlined. A six-species model (fibrin, collagen, macrophages, fibroblasts, transforming growth factor-β (TGF-β) and tissue plasminogen activator) of dermal wound healing is presented. The role of the cytokine TGF-β in the healing cascade is investigated using the model, along with its role in the degree of scarring in the healed tissue.     

Data-driven modelling of group formation in the fission–fusion dynamics of Bechstein’s bats

Communal roosting in Bechstein’s bat colonies is characterized by the formation of several groups that use different day roosts and that regularly dissolve and re-merge (fission–fusion dynamics). Analysing data from two colonies of different sizes over many years, we find that (i) the number of days that bats stay in the same roost before changing follows an exponential distribution that is independent of the colony size and (ii) the number and size of groups that bats formed for roosting depend on the size of the colony, such that above a critical colony size two to six groups of different sizes are formed. To model these two observations, we propose an agent-based model in which agents make their decisions about roosts based on both random and social influences. For the latter, they copy the roost preference of another agent which models the transfer of the respective information. Our model is able to reproduce both the distribution of stay length in the same roost and the emergence of groups of different sizes dependent on the colony size. Moreover, we are able to predict the critical system size at which the formation of different groups emerges without global coordination. We further comment on dynamics that bridge the roosting decisions on short time scales (less than 1 day) with the social structures observed at long time scales (more than 1 year).     

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.     

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.     

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.     

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.     

A mathematical model to evaluate the role of agility enablers and criteria in a manufacturing environment

Modern manufacturing arena necessitates the need for responsiveness by practicing agile manufacturing (AM) principles. AM imposes the transformation of the manufacturing organisation so as to respond to dynamic market changes. This article focuses towards the application of graph theory (GT) for conceptual modelling the agile system and to compute the dependencies among the individual agile enabler, criteria and attributes as a top-down approach. Using GT approach, digraphs were systematically constructed for agile enablers and variable permanent matrix values were computed for different scenarios and the relative importance of agility enablers were determined. The permanent values of ‘Management responsibility’ enabler and technology enabler are found to be 920 (minimum) and 3529?×?10¹⁴, respectively for the existing situation, whereas for the practically base case situation, it was found to be 1185 (minimum) and 5081.17?×?10¹⁴ (maximum), respectively. The Comprehensive Agility Index was found to be 1.3996?×?10⁴⁵, which can be even used to benchmark with other best-in-class agile organisations.     

Simultaneous reconstruction of evolutionary history and epidemiological dynamics from viral sequences with the birth–death SIR model

The evolution of RNA viruses, such as human immunodeficiency virus (HIV), hepatitis C virus and influenza virus, occurs so rapidly that the viruses'' genomes contain information on past ecological dynamics. Hence, we develop a phylodynamic method that enables the joint estimation of epidemiological parameters and phylogenetic history. Based on a compartmental susceptible–infected–removed (SIR) model, this method provides separate information on incidence and prevalence of infections. Detailed information on the interaction of host population dynamics and evolutionary history can inform decisions on how to contain or entirely avoid disease outbreaks. We apply our birth–death SIR method to two viral datasets. First, five HIV type 1 clusters sampled in the UK between 1999 and 2003 are analysed. The estimated basic reproduction ratios range from 1.9 to 3.2 among the clusters. All clusters show a decline in the growth rate of the local epidemic in the middle or end of the 1990s. The analysis of a hepatitis C virus genotype 2c dataset shows that the local epidemic in the Córdoban city Cruz del Eje originated around 1906 (median), coinciding with an immigration wave from Europe to central Argentina that dates from 1880 to 1920. The estimated time of epidemic peak is around 1970.     

Prediction of human protein–protein interaction by a mixed Bayesian model and its application to exploring underlying cancer-related pathway crosstalk

Protein–protein interaction (PPI) prediction method has provided an opportunity for elucidating potential biological processes and disease mechanisms. We integrated eight features involving proteomic, genomic, phenotype and functional annotation datasets by a mixed model consisting of full connected Bayesian (FCB) model and naive Bayesian model to predict human PPIs, resulting in 40 447 PPIs which contain 2740 common PPIs with the human protein reference database (HPRD) by a likelihood ratio cutoff of 512. Then we applied them to exploring underlying pathway crosstalk where pathways were derived from the pathway interaction database. Two pathway crosstalk networks (PCNs) were constructed based on PPI sets. The PPI sets were derived from two different sources. One source was strictly the HPRD database while the other source was a combination of HPRD and PPIs predicted by our mixed Bayesian method. We demonstrated that PCNs based on the mixed PPI set showed much more underlying pathway interactions than the HPRD PPI set. Furthermore, we mapped cancer-causing mutated somatic genes to PPIs between significant pathway crosstalk pairs. We extracted highly connected clusters from over-represented subnetworks of PCNs, which were enriched for mutated gene interactions that acted as crosstalk links. Most of the pathways in top ranking clusters were shown to play important roles in cancer. The clusters themselves showed coherent function categories pertaining to cancer development.     

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.     

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.     

A dynamic dose–response model to account for exposure patterns in risk assessment: a case study in inhalation anthrax

The most commonly used dose–response models implicitly assume that accumulation of dose is a time-independent process where each pathogen has a fixed risk of initiating infection. Immune particle neutralization of pathogens, however, may create strong time dependence; i.e. temporally clustered pathogens have a better chance of overwhelming the immune particles than pathogen exposures that occur at lower levels for longer periods of time. In environmental transmission systems, we expect different routes of transmission to elicit different dose–timing patterns and thus potentially different realizations of risk. We present a dose–response model that captures time dependence in a manner that incorporates the dynamics of initial immune response. We then demonstrate the parameter estimation of our model in a dose–response survival analysis using empirical time-series data of inhalational anthrax in monkeys in which we find slight dose–timing effects. Future dose–response experiments should include varying the time pattern of exposure in addition to varying the total doses delivered. Ultimately, the dynamic dose–response paradigm presented here will improve modelling of environmental transmission systems where different systems have different time patterns of exposure.     

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.     

Nonlinear flight dynamics and stability of hovering model insects

Current analyses on insect dynamic flight stability are based on linear theory and limited to small disturbance motions. However, insects'' aerial environment is filled with swirling eddies and wind gusts, and large disturbances are common. Here, we numerically solve the equations of motion coupled with the Navier–Stokes equations to simulate the large disturbance motions and analyse the nonlinear flight dynamics of hovering model insects. We consider two representative model insects, a model hawkmoth (large size, low wingbeat frequency) and a model dronefly (small size, high wingbeat frequency). For small and large initial disturbances, the disturbance motion grows with time, and the insects tumble and never return to the equilibrium state; the hovering flight is inherently (passively) unstable. The instability is caused by a pitch moment produced by forward/backward motion and/or a roll moment produced by side motion of the insect.     

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.