Journal of The Royal Society Interface

Published by Royal Society, The
Online ISSN: 1742-5662
This issue marks the fifth anniversary of the launch of Journal of the Royal Society Interface in May 2004. After consulting widely, it became apparent that the traditional distinction between the physical sciences, including mathematics, and the biological sciences was becoming ever more problematic. Such a division ignored the scientific challenges and opportunities which were increasingly emerging at their interface. It was recognised that interdisciplinary, multidisciplinary and cross-disciplinary research was flourishing, but that a forum for its publication and promotion was lacking, especially by a journal which did not favour either side of the physical science/life science divide. In my first editorial, I stated the ambition that Journal of the Royal Society Interface would empower the advance of cross-disciplinary science and that ‘our success would depend on the quality and impact of the submitted papers we publish.’ I am delighted to report that such an aspiration is being realised. Submissions have shown a consistent year-on-year increase, which has necessitated a corresponding rise in the number of issues, from four in our first full year of publication to one a month in 2008. The quality of articles has followed a similar trajectory. The Journal's impact factor is already above three making it fifth in ISI's multi-disciplinary category. It is thus not surprising that Journal of the Royal Society Interface has attracted some of the world's most renowned researchers. The range of submissions, both research articles and review papers, is also impressive; tissue engineering of replacement skin, self-healing materials, optical tweezers, diamond and biology, bio-inspired adhesive pads and the hyperelastic modelling of arterial layers are but a few of the distinctive subjects covered in the last five years. Another source of satisfaction has been the acceptance of our themed publication, Interface Focus. Beginning in 2008 with an issue on biological switches and clocks, we now aim to publish six issues a year on topics such as synthetic biology and the bio–nano-interface. Interface Focus offers a special opportunity for both authors and readers to define a particular field through a collection of related articles, with the benefit of knowing that all have passed through the Royal Society's stringent peer-review process. I would like to thank my colleagues on the editorial board for their role in the development of Journal of the Royal Society Interface. Not only have they offered me guidance and acted as referees, but they have also submitted their own work for publication. I would also like to thank both the Royal Society and the publishing team for their support, with special thanks to Dr Tim Holt for his outstanding service as Publishing Editor. I look forward to overseeing the Journal's continued progress over the coming years and hope that you, either as an author, referee and/or reader, will continue your valued participation. Footnotes • © 2009 The Royal Society
Simulating the dynamics of primary seeding. (A) shows the total tumour burden for three different conditions where the removal rate was fixed at λ = 10 −5 and return probability was taken to be p = 10 −2 , 10 −3 and 10 −4 respectively. (B) illustrates the model dynamics when the parameters λ and p are varied systematically, and shows that accelerated tumour growth only occurs for large values of the leaving rate λ and the return probability p. The parameter regions corresponding to primary and secondary seeding are encircled in the figure, and the error bars show the estimated error in the Fermi estimate. These results suggest that only secondary seeding has the capability of accelerating tumor progression, while primary seeding occurs with rates that do not alter the rate of tumour progression.
Two models of circulating tumour cell (CTC) dynamics have been proposed to explain the phenomenon of tumour 'self-seeding', whereby CTCs repopulate the primary tumour and accelerate growth: primary seeding, where cells from a primary tumour shed into the vasculature and return back to the primary themselves; and secondary seeding, where cells from the primary first metastasize into a secondary tissue and form microscopic secondary deposits, which then shed cells into the vasculature returning to the primary. These two models are difficult to distinguish experimentally, yet the differences between them is of great importance to both our understanding of the metastatic process and also for designing methods of intervention. Therefore, we developed a mathematical model to test the relative likelihood of these two phenomena in the subset of tumours whose shed CTCs first encounter the lung capillary bed, and show that secondary seeding is several orders of magnitude more likely than primary seeding. We suggest how this difference could affect tumour evolution, progression and therapy, and propose several possible methods of experimental validation.
Everyone's walking style is unique, and it has been shown that both humans and computers are very good at recognizing known gait patterns. It is therefore unsurprising that dynamic foot pressure patterns, which indirectly reflect the accelerations of all body parts, are also unique, and that previous studies have achieved moderate-to-high classification rates (CRs) using foot pressure variables. However, these studies are limited by small sample sizes (n < 30), moderate CRs (CR ≃ 90%), or both. Here we show, using relatively simple image processing and feature extraction, that dynamic foot pressures can be used to identify n = 104 subjects with a CR of 99.6 per cent. Our key innovation was improved and automated spatial alignment which, by itself, improved CR to over 98 per cent, a finding that pointedly emphasizes inter-subject pressure pattern uniqueness. We also found that automated dimensionality reduction invariably improved CRs. As dynamic pressure data are immediately usable, with little or no pre-processing required, and as they may be collected discreetly during uninterrupted gait using in-floor systems, foot pressure-based identification appears to have wide potential for both the security and health industries.
Many different species have been suggested to forage according to a Lévy walk in which the distribution of step lengths is heavy-tailed. Theoretical research has shown that a Lévy exponent of approximately 2 can provide a higher foraging efficiency than other exponents. In this paper, a composite search model is presented for non-destructive foraging behaviour based on Brownian (i.e. non-heavy-tailed) motion. The model consists of an intensive search phase, followed by an extensive phase, if no food is found in the intensive phase. Quantities commonly observed in the field, such as the distance travelled before finding food and the net displacement in a fixed time interval, are examined and compared with the results of a Lévy walk model. It is shown that it may be very difficult, in practice, to distinguish between the Brownian and the Lévy models on the basis of observed data. A mathematical expression for the optimal time to switch from intensive to extensive search mode is derived, and it is shown that the composite search model provides higher foraging efficiency than the Lévy model.
Examples of recent pathway discoveries via 13 C tracing. 
Procedures for metabolism analysis through GC-MS-based isotopic labelling.
After feeding microbes with a defined (13)C substrate, unique isotopic patterns (isotopic fingerprints) can be formed in their metabolic products. Such labelling information not only can provide novel insights into functional pathways but also can determine absolute carbon fluxes through the metabolic network via metabolic modelling approaches. This technique has been used for finding pathways that may have been mis-annotated in the past, elucidating new enzyme functions, and investigating cell metabolisms in microbial communities. In this review paper, we summarize the applications of (13)C approaches to analyse novel cell metabolisms for the past 3 years. The isotopic fingerprints (defined as unique isotopomers useful for pathway identifications) have revealed the operations of the Entner-Doudoroff pathway, the reverse tricarboxylic acid cycle, new enzymes for biosynthesis of central metabolites, diverse respiration routes in phototrophic metabolism, co-metabolism of carbon nutrients and novel CO(2) fixation pathways. This review also discusses new isotopic methods to map carbon fluxes in global metabolisms, as well as potential factors influencing the metabolic flux quantification (e.g. metabolite channelling, the isotopic purity of (13)C substrates and the isotopic effect). Although (13)C labelling is not applicable to all biological systems (e.g. microbial communities), recent studies have shown that this method has a significant value in functional characterization of poorly understood micro-organisms, including species relevant for biotechnology and human health.
How do enzymes work? What is the physical basis of the phenomenal rate enhancements achieved by enzymes? Do we have a theoretical framework that accounts for observed catalytic rates? These are the foremost questions-with particular emphasis on tunnelling phenomena-debated at this Discussion Meeting by the leading practitioners in the field.
(a) Trajectories of prey (solid curve) and predator (dashed curve) populations of the deterministic LV system and the data points (circles, prey data; triangles, predator data). (b) Parameters inferred by the ABC rejection sampler.  
(a) Histograms of the approximate marginal posterior distributions of parameters a 0 , n, b and a of the deterministic repressilator model. (b) The normalized 95% interquantile ranges (qr) of each population. The narrower the interval for a given tolerance e t , the more sensitive the model is to the corresponding parameter. The interquantile range reached in population 9 is determined by the added experimental noise. As e 9 was chosen accordingly, one cannot proceed by lowering the tolerance further. The sharp change in the interquantile ranges, which occurs, for example, for parameter a 0 between populations 1 and 2, can be explained by the steep gradient of the likelihood surface along a 0 . (c) The output (i.e. the accepted particles) of the ABC SMC algorithm as two-dimensional scatterplots. The particles from population 1 are in yellow, particles from population 4 in black, particles from population 7 in blue and those from the last population in red. Islands of particles are observed in population 4 and they can be explained by the multimodality of the fourth intermediate distribution. (d ) PCA of the set of accepted particles (population 9). Owing to the dependence of the PCA on the scaling of original variables, the PCA was performed on the correlation matrix. The first PC explains 70.0% of the total variance, the second 24.6%, the third 5.3% and the fourth 0.1% of the variance. Pie charts show the fraction of the length of PCs explained by individual parameters.  
(a) The probability density function of a mixture of two normal distributions, ð1=2Þfð0; 1=100ÞC ð1=2Þfð0; 1Þ, taken as a toy example used for a comparison of ABC SMC with ABC PRC. (b,c) Plots show how the variance of approximated intermediate distributions p t changes with populations (t Z1, ., 10 on the x-axis). The red curves plot the variance of the ABC SMC population and the blue curves the variance of the non-weighted ABC PRC populations. The perturbation kernel in both algorithms is uniform, K t Z sU ðK1; 1Þ. In (b), sZ1.5 and this results in poor estimation of the posterior variance with the ABC PRC algorithm. In (c), s is updated in each population so that it expands over the whole population range. Such s is big enough for non-weighted ABC PRC to perform equally well as ABC SMC.
Histograms of the approximated posterior distributions of parameters (a) g, (b) v, (c) d and (d ) S(0) of the SIR model with a latent phase of infection (3.12).  
Approximate Bayesian computation (ABC) methods can be used to evaluate posterior distributions without having to calculate likelihoods. In this paper, we discuss and apply an ABC method based on sequential Monte Carlo (SMC) to estimate parameters of dynamical models. We show that ABC SMC provides information about the inferability of parameters and model sensitivity to changes in parameters, and tends to perform better than other ABC approaches. The algorithm is applied to several well-known biological systems, for which parameters and their credible intervals are inferred. Moreover, we develop ABC SMC as a tool for model selection; given a range of different mathematical descriptions, ABC SMC is able to choose the best model using the standard Bayesian model selection apparatus.
Glioblastoma multiforme (GBM) is a highly invasive primary brain tumour that has poor prognosis despite aggressive treatment. A hallmark of these tumours is diffuse invasion into the surrounding brain, necessitating a multi-modal treatment approach, including surgery, radiation and chemotherapy. We have previously demonstrated the ability of our model to predict radiographic response immediately following radiation therapy in individual GBM patients using a simplified geometry of the brain and theoretical radiation dose. Using only two pre-treatment magnetic resonance imaging scans, we calculate net rates of proliferation and invasion as well as radiation sensitivity for a patient's disease. Here, we present the application of our clinically targeted modelling approach to a single glioblastoma patient as a demonstration of our method. We apply our model in the full three-dimensional architecture of the brain to quantify the effects of regional resistance to radiation owing to hypoxia in vivo determined by [(18)F]-fluoromisonidazole positron emission tomography (FMISO-PET) and the patient-specific three-dimensional radiation treatment plan. Incorporation of hypoxia into our model with FMISO-PET increases the model-data agreement by an order of magnitude. This improvement was robust to our definition of hypoxia or the degree of radiation resistance quantified with the FMISO-PET image and our computational model, respectively. This work demonstrates a useful application of patient-specific modelling in personalized medicine and how mathematical modelling has the potential to unify multi-modality imaging and radiation treatment planning.
There is still limited understanding of key determinants of spatial spread of influenza. The 1918 pandemic provides an opportunity to elucidate spatial determinants of spread on a large scale. To better characterize the spread of the 1918 major wave, we fitted a range of city-to-city transmission models to mortality data collected for 246 population centres in England and Wales and 47 cities in the US. Using a gravity model for city-to-city contacts, we explored the effect of population size and distance on the spread of disease and tested assumptions regarding density dependence in connectivity between cities. We employed Bayesian Markov Chain Monte Carlo methods to estimate parameters of the model for population, infectivity, distance and density dependence. We inferred the most likely transmission trees for both countries. For England and Wales, a model that estimated the degree of density dependence in connectivity between cities was preferable by deviance information criterion comparison. Early in the major wave, long distance infective interactions predominated, with local infection events more likely as the epidemic became widespread. For the US, with fewer more widely dispersed cities, statistical power was lacking to estimate population size dependence or the degree of density dependence, with the preferred model depending on distance only. We find that parameters estimated from the England and Wales dataset can be applied to the US data with no likelihood penalty.
The analysis of undulatory swimming gaits requires knowledge of the fluid forces acting on the animal body during swimming. In his classical 1952 paper, Taylor analysed this problem using a 'resistive-force' theory. The theory was used to characterize the undulatory gaits that result in the smallest energy dissipation to the fluid for a given swim velocity. The optimal gaits thus found were compared with data recorded from movies of a snake and a leech swimming. This report identifies and corrects a mathematical error in Taylor's paper, showing that his theory applies even better to animals of circular cross section.
Overview of the questionnaire used for model classification. 
Questions and responses used to create RM index. 
Mathematical models of mosquito-borne pathogen transmission originated in the early twentieth century to provide insights into how to most effectively combat malaria. The foundations of the Ross-Macdonald theory were established by 1970. Since then, there has been a growing interest in reducing the public health burden of mosquito-borne pathogens and an expanding use of models to guide their control. To assess how theory has changed to confront evolving public health challenges, we compiled a bibliography of 325 publications from 1970 through 2010 that included at least one mathematical model of mosquito-borne pathogen transmission and then used a 79-part questionnaire to classify each of 388 associated models according to its biological assumptions. As a composite measure to interpret the multidimensional results of our survey, we assigned a numerical value to each model that measured its similarity to 15 core assumptions of the Ross-Macdonald model. Although the analysis illustrated a growing acknowledgement of geographical, ecological and epidemiological complexities in modelling transmission, most models during the past 40 years closely resemble the Ross-Macdonald model. Modern theory would benefit from an expansion around the concepts of heterogeneous mosquito biting, poorly mixed mosquito-host encounters, spatial heterogeneity and temporal variation in the transmission process.
Stochastic model of the Fort Dix outbreak. Initially, model runs start with a single infectious individual and 49 susceptible individuals. Individuals then move through compartments stochastically based on the current R 0 and the serial interval being simulated. The simulation runs until there are no infectious individuals remaining. 
Plot showing the level of support of different values for R 0 and the serial interval based on the results of our simulations. Lighter shading represents values with greater support from simulation results, as indicated by the likelihood of observing the given epidemics, given the values for R 0 and serial interval. The central white region is the supported region representing the most probable values for R 0 and the serial interval (the supported region is a concept from likelihood-based statistics and is roughly equivalent to the 95% confidence interval (Clayton & Mills 1993)). 
Estimates of the basic reproductive number for influenza appearing in the literature along with our estimate of the basic reproductive number from the Fort Dix outbreak. Estimates are shown for interpandemic influenza, 1918, 1957 and 1968. To fit all the estimates in a graph and still show detail of most estimates (between 1.5 and 2.0), a log scale has been used on the x-axis. Squares, point estimates; lines surrounding point estimates, confidence or supported intervals; lines alone, ranges (or ranges of estimates created using several different techniques). Sources of estimates are listed on the left (Spicer 1979; Rvachev & Longini 1985; Longini et al. 1986; Flahault et al. 1988; Fraser et al. 2004; Longini et al. 2004; Mills et al. 2004; Ferguson et al. 2005; Gani et al. 2005; Liao et al. 2005; Longini et al. 2005; Wearing et al. 2005; Chowell et al. 2006; Ferguson et al. 2006; Sertsou et al. 2006; Viboud et al. 2006; Chowell et al. 2007; Massad et al. 2007). 
Abstarct The 1976 outbreak of A/New Jersey/76 influenza in Fort Dix is a rare example of an influenza virus with documented human to human transmission that failed to spread widely. Despite extensive epidemiological investigation, no attempt has been made to quantify the transmissibility of this virus. The World Health Organization and the United States Government view containment of emerging influenza strains as central to combating pandemic influenza. Computational models predict that it may be possible to contain an emergent pandemic influenza if virus transmissibility is low. The A/New Jersey/76 outbreak at the United States Army Training Center at Fort Dix, New Jersey in January 1976 caused 13 hospitalizations, 1 death and an estimated 230 cases. To characterize viral transmission in this epidemic, we estimated the basic reproductive number and serial interval using deterministic epidemic models and stochastic simulations. We estimated the basic reproductive number for this outbreak to be 1.2 (supported interval 1.1–1.4), the serial interval to be 1.9 days (supported interval 1.6–3.8 days), and that the virus had at least six serial human to human transmissions. This places the transmissibility of A/New Jersey/76 virus at the lower end of circulating flu strains, well below the threshold for control.
Double immunofluorescence labelling of chicken retinae for violet opsin marking the violet cones ((i) magenta fluorescence) and for Cry1a ((ii) green fluorescence). The two images in each row show the two labels in the same patch of retina. Treatment of the chickens: (a) pre-treatment in daylight, 30 min in sunlight (S); (b) pre-treatment in daylight, 30 min in total darkness (D); (c) 30 min pre-treatment in darkness, 5 min in 373 nm UV light (D–UV). The scale bar represents 50 µm (applies to all panels).
Amount of Cry1a immunolabelled with an antiserum against an epitope near the C-terminus of Cry1a after exposure to narrow-bandwidth lights of different wavelengths. UV, 373 nm ultraviolet; B, 424 nm blue; T, 502 nm turquoise; G, 565 nm green; Y, 590 nm yellow; R, 645 nm red (control labelling of these fields with the antiserum against violet opsin is shown in the electronic supplementary material, figure S1). The scale bar represents 50 µm (applies to all panels).
Flavin cycle of cryptochrome indicating where our antiserum (AS) might bind. Nt, nitrogen-terminus; Ct, carboxy-terminus of the protein, with the antiserum-binding epitope in red; in parentheses, radical pairs. Black arrows indicate light-independent reactions.
The radical pair model proposes that the avian magnetic compass is based on radical pair processes in the eye, with cryptochrome, a flavoprotein, suggested as receptor molecule. Cryptochrome 1a (Cry1a) is localized at the discs of the outer segments of the UV/violet cones of European robins and chickens. Here, we show the activation characteristics of a bird cryptochrome in vivo under natural conditions. We exposed chickens for 30 min to different light regimes and analysed the amount of Cry1a labelled with an antiserum against an epitope at the C-terminus of this protein. The staining after exposure to sunlight and to darkness indicated that the antiserum labels only an illuminated, activated form of Cry1a. Exposure to narrow-bandwidth lights of various wavelengths revealed activated Cry1a at UV, blue and turquoise light. With green and yellow, the amount of activated Cry1a was reduced, and with red, as in the dark, no activated Cry1a was labelled. Activated Cry1a is thus found at all those wavelengths at which birds can orient using their magnetic inclination compass, supporting the role of Cry1a as receptor molecule. The observation that activated Cry1a and well-oriented behaviour occur at 565 nm green light, a wavelength not absorbed by the fully oxidized form of cryptochrome, suggests that a state other than the previously suggested Trp(•)/FAD(•) radical pair formed during photoreduction is crucial for detecting magnetic directions.
Most of the mathematical models that were developed to study the UK 2001 foot-and-mouth disease epidemic assumed that the infectiousness of infected premises was constant over their infectious periods. However, there is some controversy over whether this assumption is appropriate. Uncertainty about which farm infected which in 2001 means that the only method to determine if there were trends in farm infectiousness is the fitting of mechanistic mathematical models to the epidemic data. The parameter values that are estimated using this technique, however, may be influenced by missing and inaccurate data. In particular to the UK 2001 epidemic, this includes unreported infectives, inaccurate farm infection dates and unknown farm latent periods. Here, we show that such data degradation prevents successful determination of trends in farm infectiousness.
Estimates for the prevalence of sheep infected with classical scrapie are essential for assessing the efficacy of control strategies that have been implemented in Great Britain (GB). Here a back-calculation approach was used to estimate the prevalence in the GB national flock by integrating data on reported cases and the results of abattoir and fallen stock surveys for 2002. Prevalence estimates ranged from 0.33 to 2.06%, depending on the estimates used for the frequencies of prion protein (PrP) genotypes in the national flock and the stage of incubation at which the diagnostic tests used are able to detect infected animals. The risk of infection was found to be higher than that of clinical disease, especially in those PrP genotypes that have a later age at onset of clinical disease. Moreover, results suggest that a high proportion (more than 55%) of infected animals surviving to disease onset die on farm before clinical signs become apparent, which helps account for the high observed prevalence in the fallen stock compared with the abattoir survey. The analyses indicated that attention needs to be given to identifying the stage of incubation at which diagnostic tests are able to detect infected animals and obtaining better demographic data for the GB national flock.
( a ) The relationship between root mean square deviation between models and the correct structure ( x -axis) and the scoring function ( y -axis). There are some models (lower left-most points) that have both the lowest score and are the most accurate. Panel ( b ) shows the lowest scoring model (blue) superimposed onto the real structure (gold). In addition to the correct secondary structure being in the correct position, the side chains also substantially superimpose. (Figure reproduced courtesy of D. Baker, University of Washington, Seattle, USA.) 
Has the protein folding problem been solved? On the first day of this Discussion Meeting, John Moult (University of Maryland, USA) pointed out that commentaries announcing the solving of the protein folding problem have a long history and, so far, these have all been the product of over-enthusiasm.
One fascinating recent discovery in microbiology is that bacteria can communicate with each other—and there is increasing evidence that bacterial communication is also very important for higher organisms. The process of communication is termed ‘quorum sensing (QS)’; it is a density-dependent
The epidemic time line. The solid line shows the current number of notified farms. The dashed line gives the predicted median number of undetected infections, given the available information up to that time.
reflects the same patterns that were
Active disease surveillance during epidemics is of utmost importance in detecting and eliminating new cases quickly, and targeting such surveillance to high-risk individuals is considered more efficient than applying a random strategy. Contact tracing has been used as a form of at-risk targeting, and a variety of mathematical models have indicated that it is likely to be highly efficient. However, for fast-moving epidemics, resource constraints limit the ability of the authorities to perform, and follow up, contact tracing effectively. As an alternative, we present a novel real-time Bayesian statistical methodology to determine currently undetected (occult) infections. For the UK foot-and-mouth disease (FMD) epidemic of 2007, we use real-time epidemic data synthesized with previous knowledge of FMD outbreaks in the UK to predict which premises might have been infected, but remained undetected, at any point during the outbreak. This provides both a framework for targeting surveillance in the face of limited resources and an indicator of the current severity and spatial extent of the epidemic. We anticipate that this methodology will be of substantial benefit in future outbreaks, providing a compromise between targeted manual surveillance and random or spatially targeted strategies.
Overview of the serological data (bars) and fit of the model with school holiday (lines). Panels show results for the various age groups. Bars show the serological data aggregated in titre classes (,20, 20-40, 40-80, 80-160, 160-320 and 320-640). Black bars and black lines denote pre-pandemic data and pre-pandemic model fit, respectively. Blue bars and lines show the post-pandemic data and post-pandemic model fit. Note that no serological data are available in young children (1-4 years) and that only pre-pandemic data are included in the oldest age group (65þ years). 
Overview of the hospitalization data (red lines) and model fits (black lines). The red line shows daily incidence of symptoms onset for influenza A requiring hospitalization. The area shaded in yellow indicates the timing of the school holiday. The solid and dashed black lines give fits of the models with and without school holiday, respectively. The shaded black area represents the 95% credible interval of the model with school holiday, and grey dashed lines indicate the Poisson 95% confidence interval of the number of hospitalizations in the model with school holiday. 
Age-specific estimates of pre-existing immunity and infection attack rates. Coloured dots indicate samples from the posterior distribution, and black dots represent medians of the posterior distribution. 
Obtaining a quantitative understanding of the transmission dynamics of influenza A is important for predicting healthcare demand and assessing the likely impact of intervention measures. The pandemic of 2009 provides an ideal platform for developing integrative analyses as it has been studied intensively, and a wealth of data sources is available. Here, we analyse two complementary datasets in a disease transmission framework: cross-sectional serological surveys providing data on infection attack rates, and hospitalization data that convey information on the timing and duration of the pandemic. We estimate key epidemic determinants such as infection and hospitalization rates, and the impact of a school holiday. In contrast to previous approaches, our novel modelling of serological data with mixture distributions provides a probabilistic classification of individual samples (susceptible, immune and infected), propagating classification uncertainties to the transmission model and enabling serological classifications to be informed by hospitalization data. The analyses show that high levels of immunity among persons 20 years and older provide a consistent explanation of the skewed attack rates observed during the pandemic and yield precise estimates of the probability of hospitalization per infection (1-4 years: 0.00096 (95%CrI: 0.00078-0.0012); 5-19 years: 0.00036 (0.00031-0.0044); 20-64 years: 0.0015 (0.00091-0.0020); 65+ years: 0.0084 (0.0028-0.016)). The analyses suggest that in The Netherlands, the school holiday period reduced the number of infectious contacts between 5- and 9-year-old children substantially (estimated reduction: 54%; 95%CrI: 29-82%), thereby delaying the unfolding of the pandemic in The Netherlands by approximately a week.
This paper presents new computational and modelling tools for studying the dynamics of an epidemic in its initial stages that use both available incidence time series and data describing the population's infection network structure. The work is motivated by data collected at the beginning of the H1N1 pandemic outbreak in Israel in the summer of 2009. We formulated a new discrete-time stochastic epidemic SIR (susceptible-infected-recovered) model that explicitly takes into account the disease's specific generation-time distribution and the intrinsic demographic stochasticity inherent to the infection process. Moreover, in contrast with many other modelling approaches, the model allows direct analytical derivation of estimates for the effective reproductive number (R(e)) and of their credible intervals, by maximum likelihood and Bayesian methods. The basic model can be extended to include age-class structure, and a maximum likelihood methodology allows us to estimate the model's next-generation matrix by combining two types of data: (i) the incidence series of each age group, and (ii) infection network data that provide partial information of 'who-infected-who'. Unlike other approaches for estimating the next-generation matrix, the method developed here does not require making a priori assumptions about the structure of the next-generation matrix. We show, using a simulation study, that even a relatively small amount of information about the infection network greatly improves the accuracy of estimation of the next-generation matrix. The method is applied in practice to estimate the next-generation matrix from the Israeli H1N1 pandemic data. The tools developed here should be of practical importance for future investigations of epidemics during their initial stages. However, they require the availability of data which represent a random sample of the real epidemic process. We discuss the conditions under which reporting rates may or may not influence our estimated quantities and the effects of bias.
Percentage of D. magna offspring infected with the microsporidian parasite O. bayeri from infected mothers who reproduced by parthenogenesis (asexual), selfing (monoclonal populations) or mostly outcrossing (polyclonal populations). Note, the selfing and outbreeding treatment are part of the same mesocosm field experiment, while the asexual treatment was done under different conditions in the laboratory. 
Dynamics of prevalence of the microsporidium O. bayeri in five natural rock pool populations of D. magna over one summer season. 
Dynamics of host and parasite in the epidemiological model for one host type. (a) Dynamics of total, infected and healthy host population over one summer season. (b) Dynamics of prevalence for different starting prevalences (from 10 to 90%) in the early season. (c) Dynamics of prevalence for different levels of parasite-induced host fecundity reduction from fZ0.5 (infected hosts have only 50% fecundity relative to healthy hosts) to fZ1.0 (no effect on fecundity). Other parameter settings used: X init Z50, Y init Z50, S init Z10, KZ2000, bZ0.25, fZ0.8, mZ0.05, aZ0.05, gZ0.05, bZ0.0001. 
Population size of two competing host types with an initial difference in their prevalence of infection. The solid lines indicate the population with 85% prevalence at the start of the season. The stippled line shows a competing host type with 98% prevalence. Parameter settings used as in figure 3, except: X 1,init Z15, Y 1,init Z85, X 2,init Z2, Y 2,init Z98. 
The advantage of host type 1 over type 2 in relation to their prevalence at the beginning of the season. Parameter settings as in figure 3, except for the initial values of X and Y of the two host types. 
Because host-parasite interactions are often specific to the host and parasite genotype, it may be important whether a host reproduces by selfing or outcrossing. The latter is associated with higher genetic diversity among the offspring and may reduce parasite success. Here, we test whether outbred offspring of Daphnia magna have an advantage over selfed offspring in the presence of a parasite transmitted from mothers to offspring. Using outdoor mesocosms, we set up monoclonal and polyclonal host populations of D. magna infected with a prevalence of 100% with the horizontally and vertically transmitted microsporidian parasite Octosporea bayeri. These populations diapaused after sexual reproduction and hatchlings were screened for signs of O. bayeri. Parasite prevalence was 98.9% for hatchlings from the monoclonal treatment, but only 85.2% among the hatchlings from the polyclonal populations, indicating a short-term benefit for outbreeding. This benefit occurs, we hypothesize, not owing to inbreeding depression, but because the vertically transmitted parasite is less able to establish itself in the relatively new genetic environment of the outbred offspring, as compared to the more stable environment when transmitted to selfed offspring. To quantify the fitness consequences of this 14% prevalence difference, we studied the within-season epidemiology of O. bayeri, using an epidemiological model. We then examined whether descendants of outbred offspring produce more resting eggs than the descendants of selfed offspring. The data and our model show that Daphnia which are uninfected at the beginning of the growth season have a large advantage when the entire season is considered. Our data support the Red Queen hypothesis which states that in the presence of coevolving parasites, outbreeding is favoured in the host.
The basic engineering principles used to characterize skin biomechanics. (a) The Linear Standard Solid Model; (b) a typical creep curve; (c) the basis of oscillatory testing, where G 0 and G 00 can be derived from M/M 0 , the amplitude ratio, and l, the phase lag. 
Currently commercially available or marketed dermo-epidermal skin constructs. PEO, polyethylene oxide terephthalate; PBT, polybutylene terephthalate; HAM, hyaluronic acid membrane (microperforated); auto, autologous; allo, allogeneic; xeno, xenogeneic; recomb, recombinant; synth, synthetic. 
Situations where normal autografts cannot be used to replace damaged skin often lead to a greater risk of mortality, prolonged hospital stay and increased expenditure for the National Health Service. There is a substantial need for tissue-engineered skin bioconstructs and research is active in this field. Significant progress has been made over the years in the development and clinical use of bioengineered components of the various skin layers. Off-the-shelf availability of such constructs, or production of sufficient quantities of biological materials to aid rapid wound closure, are often the only means to help patients with major skin loss. The aim of this review is to describe those materials already commercially available for clinical use as well as to give a short insight to those under development. It seeks to provide skin scientists/tissue engineers with the information required to not only develop in vitro models of skin, but to move closer to achieving the ultimate goal of an off-the-shelf, complete full-thickness skin replacement.
Regression plot of the first and second SAXS peaks of channel-(open triangles) and sphere-type (shaded circles) amorphous barb nanostructures. The colour of each triangle or circle is coded to the approximate colour of the corresponding feather (UV colours in black). The thin vertical and horizontal lines at each data point indicate the standard error of the mean (s.e.m). The solid blue and green lines with corresponding slopes of 2 and p 3 indicate the expected positional ratios for the second SAXS peak based on experimental observations of spinodal and nucleated, close-packed sphere morphologies, respectively. The solid and dashed grey lines, respectively, indicate the 95% confidence interval of the regressions.
Single-scattering SAXS reflectance predictions for the primary optical peaks of channel (a –i) and sphere-type ( j –r) amorphous barb nanostructures. SAXS single-scattering reflectance predictions (black lines) and measured normal incidence reflectance curves (coloured lines) for (a) UV (black) belly feather barbs of Charmosyna papou (Psittacidae), (b) violet primary feather barbs of Acryllium vulturinum (Psittacidae), (c) royal blue rump feather barbs of S. sialis (Turdidae), (d) sky blue rump feather barbs of Alcedo atthis (Alcedinidae), (e) deep azure blue back feather barbs of Irena puella (Irenidae), ( f ) electric blue wing covert feather barbs of Pitta maxima (Pittidae), (g) emerald green back feather barbs of Ailuroedus buccoides (Ptilonorhynchidae ), (h) emerald green back feather barbs of Charmosyna papou (Psittacidae), (i) emerald green back feather barbs of Calyptomena whitehadi (Eurylaimidae), ( j ) deep blue throat feather barbs of Tangara chilensis (Thraupidae), (k) royal blue wing covert feather barbs of Wetmorethraupis sterrhopteron (Thraupidae), (l ) violet scapular feather barbs of Conirostrum albifrons (Thraupidae), (m) dark turquoise blue back feather barbs of C. maynana (Cotingidae), (n) sky blue back feather barbs of male Tersina viridis (Thraupidae), (o) azure blue rump feather barbs of Lepidothrix serena (Pipridae), ( p) golden yellow crown feather barbs of Lepidothrix vilasboasi (Pipridae), (q) electric green back feather barbs of Chloronis riefferii (Thraupidae), (r) golden crown feather barbs of Tangara larvata (Thraupidae). The colour of the measured reflectance curves is approximately coded to the colour of the feather barbs based on the spectral position of the primary reflectance peak.  
Non-iridescent structural colours of feathers are a diverse and an important part of the phenotype of many birds. These colours are generally produced by three-dimensional, amorphous (or quasi-ordered) spongy β-keratin and air nanostructures found in the medullary cells of feather barbs. Two main classes of three-dimensional barb nanostructures are known, characterized by a tortuous network of air channels or a close packing of spheroidal air cavities. Using synchrotron small angle X-ray scattering (SAXS) and optical spectrophotometry, we characterized the nanostructure and optical function of 297 distinctly coloured feathers from 230 species belonging to 163 genera in 51 avian families. The SAXS data provided quantitative diagnoses of the channel- and sphere-type nanostructures, and confirmed the presence of a predominant, isotropic length scale of variation in refractive index that produces strong reinforcement of a narrow band of scattered wavelengths. The SAXS structural data identified a new class of rudimentary or weakly nanostructured feathers responsible for slate-grey, and blue-grey structural colours. SAXS structural data provided good predictions of the single-scattering peak of the optical reflectance of the feathers. The SAXS structural measurements of channel- and sphere-type nanostructures are also similar to experimental scattering data from synthetic soft matter systems that self-assemble by phase separation. These results further support the hypothesis that colour-producing protein and air nanostructures in feather barbs are probably self-assembled by arrested phase separation of polymerizing β-keratin from the cytoplasm of medullary cells. Such avian amorphous photonic nanostructures with isotropic optical properties may provide biomimetic inspiration for photonic technology.
Feather nanostructure and colour-producing mechanism in iridescent duck feathers. (a) Representative cross section of an iridescent feather barbule taken from the speculum feather of a mallard (A. platyrhynchos) showing measured parameters a (lattice constant), 2r (melanosome diameter) and d (cortex thickness). Inset shows Fourier transformation of region pictured in (a), illustrating hexagonal periodicity of melanosomes. (b) Photograph of a female mallard showing location of speculum (s) and light microscope image of a feather barb (inset). (c) Band structure diagram of two-dimensional hexagonal lattice of melanin rods (r/a ¼ 0.44; RI ¼ 2.0) embedded in keratin (RI ¼ 1.56); lines represent modes for s-(E-field parallel to rods; dashed lines) and p-polarized light (E-field perpendicular to rods; solid lines), and black arrow shows location of partial photonic band gap (PBG). Inset shows schematic diagram of barbule cross section (unit cell, purple hexagon), depicting light incident along G-M (blue arrow), M-X (green arrow) and X-G directions (red arrow). (d ) Plot of feather reflectance at corresponding frequencies in (c) with wavelength shown on secondary y-axis; black arrow shows location of partial PBG as in (c). 
The colours of birds are diverse but limited relative to the colours they can perceive. This mismatch may be partially caused by the properties of their colour-production mechanisms. Aside from pigments, several classes of highly ordered nanostructures (thin films, amorphous three-dimensional arrays) can produce a range of colours. However, the variability of any single nanostructural class has rarely been explored. Dabbling ducks are a speciose clade with substantial interspecific variation in the iridescent coloration of their wing patches (specula). Here, we use electron microscopy, spectrophotometry, polarization and refractive index-matching experiments, and optical modelling to examine these colours. We show that, in all species examined, speculum colour is produced by a photonic heterostructure consisting of both a single thin-film of keratin and a two-dimensional hexagonal lattice of melanosomes in feather barbules. Although the range of possible variations of this heterostructure is theoretically broad, only relatively close-packed, energetically stable variants producing more saturated colours were observed, suggesting that ducks are either physically constrained to these configurations or are under selection for the colours that they produce. These data thus reveal a previously undescribed biophotonic structure and suggest that both physical variability and constraints within single nanostructural classes may help explain the broader patterns of colour across Aves.
Matrix of confusion of training set of best optimized SVM model. 
Overall performances of 'Ro4' and SVM models for the two available PPI bioassays. EF, enrichment factor. 
Over the last 10 years, protein-protein interactions (PPIs) have shown increasing potential as new therapeutic targets. As a consequence, PPIs are today the most screened target class in high-throughput screening (HTS). The development of broad chemical libraries dedicated to these particular targets is essential; however, the chemical space associated with this 'high-hanging fruit' is still under debate. Here, we analyse the properties of 40 non-redundant small molecules present in the 2P2I database ( to define a general profile of orthosteric inhibitors and propose an original protocol to filter general screening libraries using a support vector machine (SVM) with 11 standard Dragon molecular descriptors. The filtering protocol has been validated using external datasets from PubChem BioAssay and results from in-house screening campaigns. This external blind validation demonstrated the ability of the SVM model to reduce the size of the filtered chemical library by eliminating up to 96% of the compounds as well as enhancing the proportion of active compounds by up to a factor of 8. We believe that the resulting chemical space identified in this paper will provide the scientific community with a concrete support to search for PPI inhibitors during HTS campaigns.
Central tendency of footprints. (a) Laetoli G-1 mean in perspective. (b) Laetoli G-1 mean as greyscale depth map (n ¼ 11). (c) Habitually shod human mean as greyscale depth map (five male and five female adults, 10 trials each) walking in moist fine-sand. (b,c) Black areas indicate XY reference plane. Darker shades within the 'footprints' indicate greater mean depth. Dimensions in millimetre; resolution 1 mm 2 . (False-colour plots in electronic supplementary material, figure S1, individual records in false colour in electronic supplementary material, figures S5 and S6.) (Online version in colour.)  
Statistical comparison of G-1 and habitually shod human footprints. Heel is to left, toe to right, medial above and lateral below in each plot. Black or white outside 'prints' indicate XY reference plane, inside 'prints', regions of no difference. Brighter areas indicate larger differences. (a) Raw statistical parametric map (SPM(t)), constructed from pixel-level t-tests. Lighter regions indicate where the means differ most. (b) Thresholded inference image (height threshold t. 2.5, cluster-size threshold 10 pixels) showing topological significance p of the immediately adjacent suprathreshold clusters. Significance of the t-values is greatest under the medial midfoot, hallux and anterior heel. Dimensions normalized by registration. (False colour maps in electronic supplementary material, figure S2.) (Online version in colour.)
Foot pressure in orang-utan and bonobo bipedalism. Mean peak-pressure for (a) elicited bipedalism of a hand-reared orang-utan (n ¼ 10); (b) voluntary bipedalism of naturally reared bonobos (n ¼ 11). Individual records in electronic supplementary material, figures S7 and S8. (c) A footprint from a habitually barefoot human from modern Ileret, showing an apparent mid-tarsal break (resolution 1 mm 2 ). Dimensions in millimetres, pixels 25 mm 2 . Darkest areas indicate the zero-data reference plane. Intense pixels within the foot-pressure record or footprint indicate (a,b) higher relative peak pressures; (c) greater relative depth. Light pixels to upper left of (a) and (b) are made by hallux, and indicate low pressure and highly variable posture. Intense pixels within the pressure record in (a) and (b): bottom, heel-region maximum, middle: mid-tarsal maximum, top: lateralmetatarsal maximum. (d) Bonobo mean pressure; (e) Ileret footprint, after manual registration with (d); ( f ) subtraction of (d) and (e). In the subtraction, dark surround indicates no difference, dark areas 'inside' the 'print' indicate areas of no difference, brighter areas indicate stronger differences. Dimensions normalized by registration. (False colour maps in electronic supplementary material, figure S3.) (Online version in colour.)  
Predicted foot pressure in alternative simulated A. afarensis gaits. Predicted foot pressure (impulse, Ns, over 40 mm 2 areas) from a simulation of A. afarensis in: (a,b) BHBK gait; (c,d ) upright gait. (a,c) Results with chimpanzee-like mass distribution; (b,d ) with human-like mass distribution. Dark areas 'outside' the 'prints' indicate the zero-data reference plane, dark areas within the 'prints' the highest predicted pressure, lighter areas lower pressure. (False colour maps in electronic supplementary material, figure S4.) (Online version in colour.)  
It is commonly held that the major functional features of the human foot (e.g. a functional longitudinal medial arch, lateral to medial force transfer and hallucal (big-toe) push-off) appear only in the last 2 Myr, but functional interpretations of footbones and footprints of early human ancestors (hominins) prior to 2 million years ago (Mya) remain contradictory. Pixel-wise topographical statistical analysis of Laetoli footprint morphology, compared with results from experimental studies of footprint formation; foot-pressure measurements in bipedalism of humans and non-human great apes; and computer simulation techniques, indicate that most of these functional features were already present, albeit less strongly expressed than in ourselves, in the maker of the Laetoli G-1 footprint trail, 3.66 Mya. This finding provides strong support to those previous studies which have interpreted the G-1 prints as generally modern in aspect.
Potentiodynamic polarization and impedance tests were carried out on 316L stainless steel with culturing murine fibroblast L929 cells to elucidate the corrosion behaviour of 316L steel with L929 cells and to understand the electrochemical interface between 316L steel and cells, respectively. Potential step test was carried out on 316L steel with type I collagen coating and culturing L929 cells to compare the effects of collagen and L929 cells. The open-circuit potential of 316L steel slightly shifted in a negative manner and passive current density increased with cells, indicating a decrease in the protective ability of passive oxide film. The pitting potential decreased with cells, indicating a decrease in the pitting corrosion resistance. In addition, a decrease in diffusivity at the interface was indicated from the decrease in the cathodic current density and the increase in the diffusion resistance parameter in the impedance test. The anodic peak current in the potential step test decreased with cells and collagen. Consequently, the corrosion resistance of 316L steel decreases with L929 cells. In addition, collagen coating would provide an environment for anodic reaction similar to that with culturing cells.
Pre- (open circles) and post-exposure (filled circles) latencies for 30 Hz, 65 nT as well as fibreglass sham, stainless steel control and 0 nT (mu-metal positive control). The five entries for each of the eight conditions refer to the five experimental days. Error bars correspond to ±standard error of the mean (s.e.m.). Where s.e.m. bars are not evident, they fall within the symbols. The ANOVA analysis showed a significant three-way interaction between day (5, repeated) by pre–post (2, repeated) by condition (8, independent) (F2,28 = 5.30, p < 0.001, η2 = 0.14).
Pre- (open circles) and post-exposure (filled circles) latencies for 30 Hz, 65 nT and four 30 Hz, 33 nT exposures as well as a fibreglass sham, a stainless steel control and a 0 nT mu-metal positive control. The five entries for each of the eight conditions refer to the five experimental days. Error bars correspond to±standard error of the mean (s.e.m.). Where s.e.m. bars are not evident, they fall within the symbols. The ANOVA analysis showed a significant three-way interaction between day (5, repeated) by pre–post (2, repeated) by condition (8, independent) (F2,28 = 4.00, p < 0.001, η2 = 0.11).
Pre- (open circles) and post-exposure (filled circles) latencies for a 44 µT static field exposure as well as a fibreglass sham, a stainless steel control and a 0 nT mu-metal positive control. The five entries for each of the four conditions refer to the five experimental days. Error bars correspond to ±standard error of the mean (s.e.m.). Where SEM bars are not evident, they fall within the symbols. The ANOVA analysis showed a significant three-way interaction between day (5, repeated) by pre–post (2, repeated) by condition (4, independent) (F2,38 = 5.98, p < 0.001, η2 = 0.13).
Magnetoreception in the animal kingdom has focused primarily on behavioural responses to the static geomagnetic field and the slow changes in its magnitude and direction as animals navigate/migrate. There has been relatively little attention given to the possibility that weak extremely low-frequency magnetic fields (wELFMF) may affect animal behaviour. Previously, we showed that changes in nociception under an ambient magnetic field-shielded environment may be a good alternative biological endpoint to orientation measurements for investigations into magnetoreception. Here we show that nociception in mice is altered by a 30 Hz field with a peak amplitude more than 1000 times weaker than the static component of the geomagnetic field. When mice are exposed to an ambient magnetic field-shielded environment 1 h a day for five consecutive days, a strong analgesic (i.e. antinociception) response is induced by day 5. Introduction of a static field with an average magnitude of 44 µT (spatial variability of ±3 µT) marginally affects this response, whereas introduction of a 30 Hz time-varying field as weak as 33 nT has a strong effect, reducing the analgesic effect by 60 per cent. Such sensitivity is surprisingly high. Any purported detection mechanisms being considered will need to explain effects at such wELFMF.
Adhesion quantification of S-phase HOBs and characterization of experimental substrates. (a-c) Adhesion-associated vinculin was immunolabelled, images were scored with a straight white line, and analysed by image analysis software. Substrates were 330 nm deep and had widths of (d ) 100 mm, (e) 25 mm and ( f ) 10 mm. 
Tri-fluorescent labelling of adhesion complexes and stress fibre organization in S-Phase HOBs on experimental substrates. (a) HOBs cultured on planar controls formed well-organized stress fibres and numerous SMAs. (b) Osteoblasts on 100 mm grooves possessed a well-developed actin cytoskeleton. Adhesions were large and numerous. (c) HOBs cultured on 25 mm grooves developed an organized actin cytoskeleton. Adhesion formation was reduced relative to planar controls. (d ) HOBs cultured on 10 mm groove arrays disrupted cellular spreading. Adhesion formation was influenced by groove orientation. BarZ50 mm; red, actin; green, vinculin; blue, S-phase nuclei. 
Dual immunolabelling of the tubulin cytoskeleton and S-phase nuclei of HOBs on experimental substrates. (a,b) HOBs cultured on control and 100 mm groove substrates formed organized tubulin networks. Tubulin density decreased with increasing distance from the nucleus. (c) HOBs on 25 mm grooves demonstrated increased contact guidance. Cells were less spread and possessed a denser tubulin network. (d ) Contact guidance was increased in cells on 10 mm groove substrates. S-phase HOBs formed a dense and polarized microtubule network. BarZ50 mm. 
Scanning electron immunolabelling of adhesion complexes in HOBs on experimental substrates. (a) HOBs cultured on flat pMMA formed numerous focal complexes. (b) Diffuse 100 mm grooves did not affect adhesion formation. (c) HOBs on 25 mm grooves formed adhesions predominantly on the raised ridge areas (indicated in insert). (d ) HOBs cultured on 10 mm grooves influenced cellular and adhesion orientation, aligning both HOBs and adhesion complexes with groove direction. 
Adhesion complex distribution in S-phase HOBs on experimental substrates. (a) FXs measuring less than 1 mm in length were most abundant in HOBs on 25 mm grooves. Distribution of FXs approaching 2 mm in length was increased on flat and 100 mm groove substrates. All experimental substrates show a similar decline in adhesion complex distribution as FA lengths approach 4 mm. (b) SMAs are most pronounced in HOBs cultured on control substrates. SMA frequency declines on all substrates as length increases (diamonds, flat; triangles, 100 mm grooves; crosses, 25 mm grooves; squares, 10 mm grooves). 
The surface microtexture of an orthopaedic device can regulate cellular adhesion, a process fundamental in the initiation of osteoinduction and osteogenesis. Advances in fabrication techniques have evolved to include the field of surface modification; in particular, nanotechnology has allowed for the development of experimental nanoscale substrates for investigation into cell nanofeature interactions. Here primary human osteoblasts (HOBs) were cultured on ordered nanoscale groove/ridge arrays fabricated by photolithography. Grooves were 330nm deep and either 10, 25 or 100microm in width. Adhesion subtypes in HOBs were quantified by immunofluorescent microscopy and cell-substrate interactions were investigated via immunocytochemistry with scanning electron microscopy. To further investigate the effects of these substrates on cellular function, 1.7K gene microarray analysis was used to establish gene regulation profiles of mesenchymal stem cells cultured on these nanotopographies. Nanotopographies significantly affected the formation of focal complexes (FXs), focal adhesions (FAs) and supermature adhesions (SMAs). Planar control substrates induced widespread adhesion formation; 100microm wide groove/ridge arrays did not significantly affect adhesion formation yet induced upregulation of genes involved in skeletal development and increased osteospecific function; 25microm wide groove/ridge arrays were associated with a reduction in SMA and an increase in FX formation; and 10microm wide groove/ridge arrays significantly reduced osteoblast adhesion and induced an interplay of up- and downregulation of gene expression. This study indicates that groove/ridge topographies are important modulators of both cellular adhesion and osteospecific function and, critically, that groove/ridge width is important in determining cellular response.
Chemical composition (at%) of surfaces before and after incubation with FBS as determined by XPS analysis.
This study investigated the possibility of incorporating alpha-tocopherol (vitamin E) into poly(3hydroxybutyrate) (P(3HB))/Bioglass composites, which are being developed for bone tissue engineering matrices. P(3HB) films with 20wt% Bioglass and 10wt% vitamin E were prepared using the solvent casting technique. Addition of vitamin E significantly improved the hydrophilicity of the composites along with increasing the total protein adsorption. The presence of protein adsorbed on the composite surface was further confirmed using X-ray photoelectron spectroscopy analysis. Preliminary cell culture studies using MG-63 human osteoblasts showed that the addition of vitamin E in the P(3HB)/20wt% Bioglass films significantly increased cell proliferation. The results achieved in this study confirmed the possibility of incorporating vitamin E as a suitable additive in P(3HB)/Bioglass composites to engineer the surface of the composites by promoting higher protein adsorption and increasing the hydrophilicity.
For decades, a link between increased levels of iron and areas of Alzheimer's disease (AD) pathology has been recognized, including AD lesions comprised of the peptide β-amyloid (Aβ). Despite many observations of this association, the relationship between Aβ and iron is poorly understood. Using X-ray microspectroscopy, X-ray absorption spectroscopy, electron microscopy and spectrophotometric iron(II) quantification techniques, we examine the interaction between Aβ(1-42) and synthetic iron(III), reminiscent of ferric iron stores in the brain. We report Aβ to be capable of accumulating iron(III) within amyloid aggregates, with this process resulting in Aβ-mediated reduction of iron(III) to a redox-active iron(II) phase. Additionally, we show that the presence of aluminium increases the reductive capacity of Aβ, enabling the redox cycling of the iron. These results demonstrate the ability of Aβ to accumulate iron, offering an explanation for previously observed local increases in iron concentration associated with AD lesions. Furthermore, the ability of iron to form redox-active iron phases from ferric precursors provides an origin both for the redox-active iron previously witnessed in AD tissue, and the increased levels of oxidative stress characteristic of AD. These interactions between Aβ and iron deliver valuable insights into the process of AD progression, which may ultimately provide targets for disease therapies.
Novel Ca-Si-Ti-based sphene (CaTiSiO5) ceramics possess excellent chemical stability and cytocompatibility. The aim of this study was to prepare sphene coating on titanium alloy (Ti-6Al-4V) for orthopaedic applications using the plasma spray method. The phase composition, surface and interface microstructure, coating thickness, surface roughness and bonding strength of the plasma-sprayed sphene coating were analysed using X-ray diffraction, scanning electron microscopy, atomic force microscopy and the standard mechanical testing of the American Society for Testing and Materials, respectively. The results indicated that sphene coating was obtained with a uniform and dense microstructure at the interface of the Ti-6Al-4V surface and the thickness and surface roughness of the coating were approximately 150 and 10 microm, respectively. Plasma-sprayed sphene coating on Ti-6Al-4V possessed a significantly improved bonding strength and chemical stability compared with plasma-sprayed hydroxyapatite (HAp) coating. Plasma-sprayed sphene coating supported human osteoblast-like cell (HOB) attachment and significantly enhanced HOB proliferation and differentiation compared with plasma-sprayed HAp coating and uncoated Ti-6Al-4V. Taken together, plasma-sprayed sphene coating on Ti-6Al-4V possessed excellent bonding strength, chemical stability and cellular bioactivity, indicating its potential application for orthopaedic implants.
Raman spectra of air-dried whole blood ( a ), a single red blood cell ( b ), and the corpuscle found in the Iceman tissue sample A ( c ). All spectra show peaks at 1586, 1395, 1308 and 747 cm 2 1 , which are characteristic of porphyrin. Apart from 
Raman peak assignment of Iceman sample A.
Raman peaks assigned for Iceman sample B.
The distribution of Young's moduli from the corpuscle of Iceman sample B and contemporary single RBCs. Young's modulus for the mummy particles (grey) is significantly lower than Young's modulus for the recent RBCs (black).
Changes in elasticity and structures of red blood cells (RBCs) are important indicators of disease, and this makes them interesting for medical studies. In forensics, blood analyses represent a crucial part of crime scene investigations. For these reasons, the recovery and analysis of blood cells from ancient tissues is of major interest. In this study, we show that RBCs were preserved in Iceman tissue samples for more than 5000 years. The morphological and molecular composition of the blood corpuscle is verified by atomic force microscope and Raman spectroscopy measurements. The cell size and shape approximated those of healthy, dried, recent RBCs. Raman spectra of the ancient corpuscle revealed bands that are characteristic of haemoglobin. Additional vibrational modes typical for other proteinaceous fragments, possibly fibrin, suggested the formation of a blood clot. The band intensities, however, were approximately an order of magnitude weaker than those of recent RBCs. This fact points to a decrease in the RBC-specific metalloprotein haemoglobin and, thus, to a degradation of the cells. Together, the results show the preservation of RBCs in the 5000 year old mummy tissue and give the first insights into their degradation.
Protein structure prediction is one of the major challenges in bioinformatics today. Throughout the past five decades, many different algorithmic approaches have been attempted, and although progress has been made the problem remains unsolvable even for many small proteins. While the general objective is to predict the three-dimensional structure from primary sequence, our current knowledge and computational power are simply insufficient to solve a problem of such high complexity. Some prediction algorithms do, however, appear to perform better than others, although it is not always obvious which ones they are and it is perhaps even less obvious why that is. In this review, the reported performance results from 18 different recently published prediction algorithms are compared. Furthermore, the general algorithmic settings most likely responsible for the difference in the reported performance are identified, and the specific settings of each of the 18 prediction algorithms are also compared. The average normalized r.m.s.d. scores reported range from 11.17 to 3.48. With a performance measure including both r.m.s.d. scores and CPU time, the currently best-performing prediction algorithm is identified to be the I-TASSER algorithm. Two of the algorithmic settings—protein representation and fragment assembly—were found to have definite positive influence on the running time and the predicted structures, respectively. There thus appears to be a clear benefit from incorporating this knowledge in the design of new prediction algorithms.
The abdominal aorta (AA) in older individuals can develop an aneurysm, which is of increasing concern in our ageing population. The structural integrity of the ageing aortic wall, and hence aneurysm, depends primarily on effective elastin and multiple families of oriented collagen fibres. In this paper, we show that a structurally motivated phenomenological 'four-fibre family' constitutive relation captures the biaxial mechanical behaviour of both the human AA, from ages less than 30 to over 60, and abdominal aortic aneurysms. Moreover, combining the statistical technique known as non-parametric bootstrap with a modal clustering method provides improved confidence intervals for estimated best-fit values of the eight associated constitutive parameters. It is suggested that this constitutive relation captures the well-known loss of structural integrity of elastic fibres owing to ageing and the development of abdominal aneurysms, and that it provides important insight needed to construct growth and remodelling models for aneurysms, which in turn promise to improve our ability to predict disease progression.
Complementary advances in medical imaging, vascular biology and biomechanics promise to enable computational modelling of abdominal aortic aneurysms to play increasingly important roles in clinical decision processes. Using a finite-element-based growth and remodelling model of evolving aneurysm geometry and material properties, we show that regional variations in material anisotropy, stiffness and wall thickness should be expected to arise naturally and thus should be included in analyses of aneurysmal enlargement or wall stress. In addition, by initiating the model from best-fit material parameters estimated for non-aneurysmal aortas from different subjects, we show that the initial state of the aorta may influence strongly the subsequent rate of enlargement, wall thickness, mechanical behaviour and thus stress in the lesion. We submit, therefore, that clinically reliable modelling of the enlargement and overall rupture-potential of aneurysms may require both a better understanding of the mechanobiological processes that govern the evolution of these lesions and new methods of determining the patient-specific state of the pre-aneurysmal aorta (or correlation to currently unaffected portions thereof) through knowledge of demographics, comorbidities, lifestyle, genetics and future non-invasive or minimally invasive tests.
Maximum principal Cauchy stress computed with the abdominal aortic aneurysm (AAA) tube model. (a) Prediction that neglected collagen turnover ( passive model). (b) Prediction that accounted for collagen turnover and used parameters (l new min ¼ 0:97; l new max ¼ 1:21; _ r þ max ¼ 5:3 Â 10 À3 ðsr day) À1 ) leading to homeostasis. (c) Prediction that accounted for collagen turnover and used parameters ðl new min ¼ 0:98; l new max ¼ 1:22; _ r þ max ¼ 5:3 Â 10 À3 ðsr day) À1 ) that matched the growth of small AAAs. 
A better understanding of the inherent properties of vascular tissue to adapt to its mechanical environment is crucial to improve the predictability of biomechanical simulations. Fibrillar collagen in the vascular wall plays a central role in tissue adaptation owing to its relatively short lifetime. Pathological alterations of collagen turnover may fail to result in homeostasis and could be responsible for abdominal aortic aneurysm (AAA) growth at later stages of the disease. For this reason our previously reported multiscale constitutive framework (Martufi, G. & Gasser, T. C. 2011 J. Biomech. 44, 2544-2550 (doi:10.1016/j.jbiomech.2011.07.015)) has been enriched by a collagen turnover model. Specifically, the framework's collagen fibril level allowed a sound integration of vascular wall biology, and the impact of collagen turnover on the macroscopic properties of AAAs was studied. To this end, model parameters were taken from the literature and/or estimated from clinical follow-up data of AAAs (on average 50.7 mm-large). Likewise, the in vivo stretch of the AAA wall was set, such that 10 per cent of collagen fibres were engaged. Results showed that the stretch spectrum, at which collagen fibrils are deposed, is the most influential parameter, i.e. it determines whether the vascular geometry grows, shrinks or remains stable over time. Most importantly, collagen turnover also had a remarkable impact on the macroscopic stress field. It avoided high stress gradients across the vessel wall, thus predicted a physiologically reasonable stress field. Although the constitutive model could be successfully calibrated to match the growth of small AAAs, a rigorous validation against experimental data is crucial to further explore the model's descriptive and predictive capabilities.
The relationship between Doppler measurements, size and growth rate in fetal growth restriction has not been defined. We used functional linear discriminant analysis (FLDA) to investigate these parameters taking account of the difficulties inherent in exploring relationships between repeated observations from a small number of cases. In 40 fetuses with severe growth restriction, serial abdominal circumference (AC), umbilical, middle cerebral artery (MCA) and ductus venosus Doppler pulsatility index measurements were recorded. In 11 singleton fetuses with normal growth, umbilical artery pulsatility index only was measured. Data were expressed as z-scores in relation to gestation and analysed longitudinally using FLDA. In severe growth restriction, the Spearman correlation coefficients between umbilical artery pulsatility index and AC z-score, MCA pulsatility index and AC z-score and ductus venosus pulsatility index z-score and AC z-score were, respectively: -0.36, p = 4.4 × 10(-7); 0.70, p = 1.1 × 10(-17) and -0.50, p = 8.1 × 10(-4). No relationship was seen between Doppler parameters and growth rate. There was no relationship between umbilical artery pulsatility index and AC nor growth rate in normally grown fetuses. In severe fetal growth restriction, Doppler changes are related to absolute fetal AC size, not growth rate.
The established method of polarized microscopy in combination with a universal stage is used to determine the layer-specific distributed collagen fibre orientations in 11 human non-atherosclerotic thoracic and abdominal aortas and common iliac arteries (63 ± 15.3 years, mean ± s.d.). A dispersion model is used to quantify over 37 000 recorded fibre angles from tissue samples. The study resulted in distinct fibre families, fibre directions, dispersion and thickness data for each layer and all vessels investigated. Two fibre families were present for the intima, media and adventitia in the aortas, with often a third and sometimes a fourth family in the intima in the respective axial and circumferential directions. In all aortas, the two families were almost symmetrically arranged with respect to the cylinder axis, closer to the axial direction in the adventitia, closer to the circumferential direction in the media and in between in the intima. The same trend was found for the intima and adventitia of the common iliac arteries; however, there was only one preferred fibre alignment present in the media. In all locations and layers, the observed fibre orientations were always in the tangential plane of the walls, with no radial components and very small dispersion through the wall thickness. A wider range of in-plane fibre orientations was present in the intima than in the media and adventitia. The mean total wall thickness for the aortas and the common iliac artery was 1.39 and 1.05 mm, respectively. For the aortas, a slight thickening of the intima and a thinning of the media in increasingly distal regions were observed. A clear intimal thickening was present distal to the branching of the celiac arteries. All data, except for the media of the common iliac arteries, showed two prominent collagen fibre families for all layers so that two-fibre family models seem most appropriate.
A clinical photograph of peri-implant soft tissue overgrowth associated with a CPTi BAHA fixture. Up to 33% of patients suffer from peri-implant skin inflammation, which can necessitate implant removal. Interrupted line indicates circumferential incision line for tissue explanation.  
Globally, more than 1000 tonnes of titanium (Ti) is implanted into patients in the form of biomedical devices on an annual basis. Ti is perceived to be 'biocompatible' owing to the presence of a robust passive oxide film (approx. 4 nm thick) at the metal surface. However, surface deterioration can lead to the release of Ti ions, and particles can arise as the result of wear and/or corrosion processes. This surface deterioration can result in peri-implant inflammation, leading to the premature loss of the implanted device or the requirement for surgical revision. Soft tissues surrounding commercially pure cranial anchorage devices (bone-anchored hearing aid) were investigated using synchrotron X-ray micro-fluorescence spectroscopy and X-ray absorption near edge structure. Here, we present the first experimental evidence that minimal load-bearing Ti implants, which are not subjected to macroscopic wear processes, can release Ti debris into the surrounding soft tissue. As such debris has been shown to be pro-inflammatory, we propose that such distributions of Ti are likely to effect to the service life of the device.
Fish must orient in three dimensions as they navigate through space, but it is unknown whether they are assisted by a sense of depth. In principle, depth can be estimated directly from hydrostatic pressure, but although teleost fish are exquisitely sensitive to changes in pressure, they appear unable to measure absolute pressure. Teleosts sense changes in pressure via changes in the volume of their gas-filled swim-bladder, but because the amount of gas it contains is varied to regulate buoyancy, this cannot act as a long-term steady reference for inferring absolute pressure. In consequence, it is generally thought that teleosts are unable to sense depth using hydrostatic pressure. Here, we overturn this received wisdom by showing from a theoretical physical perspective that absolute depth could be estimated during fast, steady vertical displacements by combining a measurement of vertical speed with a measurement of the fractional rate of change of swim-bladder volume. This mechanism works even if the amount of gas in the swim-bladder varies, provided that this variation occurs over much longer time scales than changes in volume during displacements. There is therefore no a priori physical justification for assuming that teleost fish cannot sense absolute depth by using hydrostatic pressure cues.
Hypothetical mechanism for the EnvZ/OmpR signal transduction system in Escherichia coli. The mechanism is represented in (a) where the terminal (light orange) and nonterminal (dark blue) complexes are labeled. The parameter values used for numerical simulations are given in (b).  
Quasi-stationary distributions of X A with α = 1 and various values of β and M. As M → ∞ the quasi-stationary distributions approach the overlain Poisson distributions (10) (solid line). The iterative procedure of [33, 34, 38] was used to construct the plots.
It has recently been shown that structural conditions on the reaction network, rather than a 'fine-tuning' of system parameters, often suffice to impart 'absolute concentration robustness' (ACR) on a wide class of biologically relevant, deterministically modelled mass-action systems. We show here that fundamentally different conclusions about the long-term behaviour of such systems are reached if the systems are instead modelled with stochastic dynamics and a discrete state space. Specifically, we characterize a large class of models that exhibit convergence to a positive robust equilibrium in the deterministic setting, whereas trajectories of the corresponding stochastic models are necessarily absorbed by a set of states that reside on the boundary of the state space, i.e. the system undergoes an extinction event. If the time to extinction is large relative to the relevant timescales of the system, the process will appear to settle down to a stationary distribution long before the inevitable extinction will occur. This quasi-stationary distribution is considered for two systems taken from the literature, and results consistent with ACR are recovered by showing that the quasi-stationary distribution of the robust species approaches a Poisson distribution.
The kinetic energy of flying insect prey is a formidable challenge for orb-weaving spiders. These spiders construct two-dimensional, round webs from a combination of stiff, strong radial silk and highly elastic, glue-coated capture spirals. Orb webs must first stop the flight of insect prey and then retain those insects long enough to be subdued by the spiders. Consequently, spider silks rank among the toughest known biomaterials. The large number of silk threads composing a web suggests that aerodynamic dissipation may also play an important role in stopping prey. Here, we quantify energy dissipation in orb webs spun by diverse species of spiders using data derived from high-speed videos of web deformation under prey impact. By integrating video data with material testing of silks, we compare the relative contributions of radial silk, the capture spiral and aerodynamic dissipation. Radial silk dominated energy absorption in all webs, with the potential to account for approximately 100 per cent of the work of stopping prey in larger webs. The most generous estimates for the roles of capture spirals and aerodynamic dissipation show that they rarely contribute more than 30 per cent and 10 per cent of the total work of stopping prey, respectively, and then only for smaller orb webs. The reliance of spider orb webs upon internal energy absorption by radial threads for prey capture suggests that the material properties of the capture spirals are largely unconstrained by the selective pressures of stopping prey and can instead evolve freely in response to alternative functional constraints such as adhering to prey.
Another phase-contrast three-dimensional rendering of the specimen presumably shows the so-called Purkinje cells. The grey-scale values correspond to the white bar in the histogram in figure 6c. 
Human brain tissue belongs to the most impressive and delicate three-dimensional structures in nature. Its outstanding functional importance in the organism implies a strong need for brain imaging modalities. Although magnetic resonance imaging provides deep insights, its spatial resolution is insufficient to study the structure on the level of individual cells. Therefore, our knowledge of brain microstructure currently relies on two-dimensional techniques, optical and electron microscopy, which generally require severe preparation procedures including sectioning and staining. X-ray absorption microtomography yields the necessary spatial resolution, but since the composition of the different types of brain tissue is similar, the images show only marginal contrast. An alternative to absorption could be X-ray phase contrast, which is known for much better discrimination of soft tissues but requires more intricate machinery. In the present communication, we report an evaluation of the recently developed X-ray grating interferometry technique, applied to obtain phase-contrast as well as absorption-contrast synchrotron radiation-based microtomography of human cerebellum. The results are quantitatively compared with synchrotron radiation-based microtomography in optimized absorption-contrast mode. It is demonstrated that grating interferometry allows identifying besides the blood vessels, the stratum moleculare, the stratum granulosum and the white matter. Along the periphery of the stratum granulosum, we have detected microstructures about 40 µm in diameter, which we associate with the Purkinje cells because of their location, size, shape and density. The detection of individual Purkinje cells without the application of any stain or contrast agent is unique in the field of computed tomography and sets new standards in non-destructive three-dimensional imaging.
XANES spectra showing a comparison of (a) reference spectra from synthetic magnetite and horse spleen ferritin and pigeon haemoglobin; (b) reference spectra of ferritin and haemoglobin compared to that from iron anomaly A, showing good fit with ferritin; and (c) reference spectrum of magnetite and that from iron anomaly D, showing good fit.
Maps of the coronal section of a pigeon brain consisting of (a) X-ray transmission map (black-yellow) with superimposed iron fluorescence map (red-white) with 500 mm resolution; (b) iron fluorescence map at 20 mm resolution, with 5 mm resolution wireframe image inset of iron anomaly A consisting primarily of ferritin-like iron compounds; and (c) iron fluorescence wireframe map at 5 mm resolution of iron anomaly D, consisting primarily of magnetite.
( a ) Normalized XANES spectra comparing synthetic magnetite standards before and after chemical processing, embedding and baking in Kapton. ( b ) Relative XANES spectra showing the lack of background iron signal from the Kapton film compared with the signal from a standard magnetite sample. 
This work describes a novel method for the detection, identification and mapping of anomalous iron compounds in mammalian brain tissue using X-ray absorption spectroscopy. We have located and identified individual iron anomalies in an avian tissue model associated with ferritin, biogenic magnetite and haemoglobin with a pixel resolution of less than 5 microm. This technique represents a breakthrough in the study of both intra- and extra-cellular iron compounds in brain tissue. The potential for high-resolution iron mapping using microfocused X-ray beams has direct application to investigations of the location and structural form of iron compounds associated with human neurodegenerative disorders--a problem which has vexed researchers for 50 years.
Modularity, inference and identity. (a) Engineering modularity exposes restricted functionality through interfaces, while hiding internal complexity behind barriers. (b) Modularity for biological models must allow for the possibility that any molecule may interact with any other molecule. E is an enzyme that converts A to B. Module 1 contains A but not E or B while module 2 contains E but not A or B. Composing modules 1 and 2 results in a new species, B, not previously present in either module. A module must work correctly in contexts determined by other modules whose characteristics are not known in advance of module composition. Little b's computational infrastructure uses reasoning to infer the presence of the highlighted entities. (c) Unique identities must encode information about location. E converts A to B and is present in both the cytoplasm compartment and the nucleus compartment. However, A is only present in the cytoplasm. The system should infer that B is present in the cytoplasm but, in the absence of other information, should not infer that it is present in the nucleus. (d ) Membranes are complex locations. T transports X unidirectionally across a membrane. T is oriented in membrane m1 of vesicle v1 to transport X into v1 but is oppositely oriented in membrane m2 of vesicle v2. If X is present in the cytoplasm compartment then the computational infrastructure should infer that it is in v1 but, in the absence of other information, should not infer that it is in v2. In little b, membranes encode information about their two adjacent volume compartments and molecules are oriented by locating them in either the standard (default) membrane or its inverse. The behaviour of T and X can be described once but then works correctly irrespective of T 's location.
Modular construction of developmental networks in arbitrary cellular lattices. (a) Polygonal lattice of cells. The user provides the vertex coordinates to little b's generic lattice module, which creates an internal representation of the lattice. (b) The segment polarity gene regulation network after von Dassow et al. (2000). (Adapted by permission from Macmillan Publishers Ltd: Nature 406, 188-192, copyright 2001.) The positive feedback of Wingless protein ( WG) on its mRNA (wg) and the repression of Engrailed mRNA (en) by cleaved Cubitus Interruptus (CN) are both included. Labels show the interactions (cZWGen and cZPTCCID) that are varied in figure 6. Little b can take any polygonal lattice and any network of reactions and put the two together in a modular way. Each cell acquires a copy of the regulatory network and two adjacent cells interact across their common membrane segment using the same mechanism as in von Dassow et al. (2000). The bookkeeping scheme required to identify each species in each location is automatically worked out by little b and used to build the model equations.
Segment polarization in different cellular lattices. (a) Image of a Drosophila embryo, with the extracted cellular lattice superimposed. (b) Four lattices showing the pre-pattern where Wingless (red) and Engrailed (green) are high. For correct segmentation, the regulatory network must stabilize this pre-pattern, starting from the pre-pattern as initial condition. (c,d ) Correct (filled square) or incorrect (cross) segmentation for the lattices listed on the right. The half-maximal value, k_c (horizontal axis), and the Hill coefficient, v_c (vertical axis), of a Hill function, x v_c /((k_c) v_c Cx v_c ), describing one of the connections c in figure 5b, are varied. The half-maximal value varies horizontally on a log scale, while the Hill coefficient takes either a low (1 or 1.5) or high (5) value. The parameter values other than v c and k c are obtained from two previously defined parameter sets (von Dassow et al. 2000), as described in §2, and are listed in the electronic supplementary material, table 1. (c) Intercellular transcriptional activation of Engrailed by Wingless (cZWGen). (d ) Intracellular cleavage of Cubitus Interruptus by Patched (cZPTCCID).
Mathematical models are increasingly used to understand how phenotypes emerge from systems of molecular interactions. However, their current construction as monolithic sets of equations presents a fundamental barrier to progress. Overcoming this requires modularity, enabling sub-systems to be specified independently and combined incrementally, and abstraction, enabling generic properties of biological processes to be specified independently of specific instances. These, in turn, require models to be represented as programs rather than as datatypes. Programmable modularity and abstraction enables libraries of modules to be created, which can be instantiated and reused repeatedly in different contexts with different components. We have developed a computational infrastructure that accomplishes this. We show here why such capabilities are needed, what is required to implement them and what can be accomplished with them that could not be done previously.
DNA strand displacement techniques have been used to implement a broad range of information processing devices, from logic gates, to chemical reaction networks, to architectures for universal computation. Strand displacement techniques enable computational devices to be implemented in DNA without the need for additional components, allowing computation to be programmed solely in terms of nucleotide sequences. A major challenge in the design of strand displacement devices has been to enable rapid analysis of high-level designs while also supporting detailed simulations that include known forms of interference. Another challenge has been to design devices capable of sustaining precise reaction kinetics over long periods, without relying on complex experimental equipment to continually replenish depleted species over time. In this paper, we present a programming language for designing DNA strand displacement devices, which supports progressively increasing levels of molecular detail. The language allows device designs to be programmed using a common syntax and then analysed at varying levels of detail, with or without interference, without needing to modify the program. This allows a trade-off to be made between the level of molecular detail and the computational cost of analysis. We use the language to design a buffered architecture for DNA devices, capable of maintaining precise reaction kinetics for a potentially unbounded period. We test the effectiveness of buffered gates to support long-running computation by designing a DNA strand displacement system capable of sustained oscillations.
Ecological monitoring aims to provide estimates of pest species abundance-this information being then used for making decisions about means of control. For invertebrate species, population size estimates are often based on trap counts which provide the value of the population density at the traps' location. However, the use of traps in large numbers is problematic as it is costly and may also be disruptive to agricultural procedures. Therefore, the challenge is to obtain a reliable population size estimate from sparse spatial data. The approach we develop in this paper is based on the ideas of numerical integration on a coarse grid. We investigate several methods of numerical integration in order to understand how badly the lack of spatial data can affect the accuracy of results. We first test our approach on simulation data mimicking spatial population distributions of different complexity. We show that, rather counterintuitively, a robust estimate of the population size can be obtained from just a few traps, even when the population distribution has a highly complicated spatial structure. We obtain an estimate of the minimum number of traps required to calculate the population size with good accuracy. We then apply our approach to field data to confirm that the number of trap/sampling locations can be much fewer than has been used in many monitoring programmes. We also show that the accuracy of our approach is greater that that of the statistical method commonly used in field studies. Finally, we discuss the implications of our findings for ecological monitoring practice and show that the use of trap numbers 'smaller than minimum' may still be possible but it would result in a paradigm shift: the population size estimates should be treated probabilistically and the arising uncertainty may introduce additional risk in decision-making.
Cell polarization is a ubiquitous process which results in cellular constituents being organized into discrete intracellular spatial domains. It occurs in a variety of cell types, including epithelial cells, immune system cells and neurons. A key player in this process is the Par protein family whose asymmetric localization to anterior and posterior parts of the cell is crucial for proper division and cell fate specification. In this paper, we explore a stochastic analogue of the temporal model of Par protein interactions first developed in Dawes & Munro (Dawes and Munro 2011 Biophys. J. 101, 1412-1422. (doi:10.1016/j.bpj.2011.07.030)). We focus on how protein abundance influences the behaviour of both the deterministic and stochastic versions of the model. In Dawes & Munro (2011), it was found that bistable behaviour in the temporal model of Par protein led to the existence of complementary domains in the corresponding spatio-temporal model. Here, we find that the corresponding temporal stochastic model permits switching behaviour (the model solution 'jumps' between steady states) for lower protein abundances, whereas for higher protein abundances the stochastic and deterministic models are in good agreement (the model solution evolves to one of two steady states). This led us to the testable hypothesis that cells with lower abundances of Par protein may be more sensitive to external cues, whereas cells with higher abundances of Par protein may be less sensitive to external cues. In order to gain more control over the precise abundance of Par protein, we proposed and explored a second model (again, examining both deterministic and stochastic versions) in which the total number of Par molecules is conserved. We found that this model required an additional dimerization reaction in the cytoplasm in order for bistable and switching behaviour to be found. Once this additional reaction was included, we found that both the first and second models gave qualitatively similar results but in different regions of the parameter space, suggesting a further regulatory mechanism that cells could potentially use to modulate their response to external signals. © 2015 The Author(s) Published by the Royal Society. All rights reserved.
Top-cited authors
Aldo R. Boccaccini
  • Friedrich-Alexander-University of Erlangen-Nürnberg
J.A.P. Heesterbeek
  • Utrecht University
Odo Diekmann
  • Utrecht University
Vincent A A Jansen
  • Royal Holloway, University of London
Sebastian Funk
  • London School of Hygiene and Tropical Medicine