Showing papers in "Journal of the Royal Society Interface in 2008"

Random walk models in biology.

Abstract: Mathematical modelling of the movement of animals, micro-organisms and cells is of great relevance in the fields of biology, ecology and medicine. Movement models can take many different forms, but the most widely used are based on the extensions of simple random walk processes. In this review paper, our aim is twofold: to introduce the mathematics behind random walks in a straightforward manner and to explain how such models can be used to aid our understanding of biological processes. We introduce the mathematical theory behind the simple random walk and explain how this relates to Brownian motion and diffusive processes in general. We demonstrate how these simple models can be extended to include drift and waiting times or be used to calculate first passage times. We discuss biased random walks and show how hyperbolic models can be used to generate correlated random walks. We cover two main applications of the random walk model. Firstly, we review models and results relating to the movement, dispersal and population redistribution of animals and micro-organisms. This includes direct calculation of mean squared displacement, mean dispersal distance, tortuosity measures, as well as possible limitations of these model approaches. Secondly, oriented movement and chemotaxis models are reviewed. General hyperbolic models based on the linear transport equation are introduced and we show how a reinforced random walk can be used to model movement where the individual changes its environment. We discuss the applications of these models in the context of cell migration leading to blood vessel growth (angiogenesis). Finally, we discuss how the various random walk models and approaches are related and the connections that underpin many of the key processes involved.

Biomaterials in orthopaedics.

Abstract: At present, strong requirements in orthopaedics are still to be met, both in bone and joint substitution and in the repair and regeneration of bone defects. In this framework, tremendous advances in the biomaterials field have been made in the last 50 years where materials intended for biomedical purposes have evolved through three different generations, namely first generation (bioinert materials), second generation (bioactive and biodegradable materials) and third generation (materials designed to stimulate specific responses at the molecular level). In this review, the evolution of different metals, ceramics and polymers most commonly used in orthopaedic applications is discussed, as well as the different approaches used to fulfil the challenges faced by this medical field.

Adaptive coevolutionary networks: a review

Abstract: Adaptive networks appear in many biological applications. They combine topological evolution of the network with dynamics in the network nodes. Recently, the dynamics of adaptive networks has been investigated in a number of parallel studies from different fields, ranging from genomics to game theory. Here we review these recent developments and show that they can be viewed from a unique angle. We demonstrate that all these studies are characterized by common themes, most prominently: complex dynamics and robust topological self-organization based on simple local rules.

Optical tweezers for single cells

Abstract: Optical tweezers (OT) have emerged as an essential tool for manipulating single biological cells and performing sophisticated biophysical/biomechanical characterizations. Distinct advantages of using tweezers for these characterizations include non-contact force for cell manipulation, force resolution as accurate as 100 aN and amiability to liquid medium environments. Their wide range of applications, such as transporting foreign materials into single cells, delivering cells to specific locations and sorting cells in microfluidic systems, are reviewed in this article. Recent developments of OT for nanomechanical characterization of various biological cells are discussed in terms of both their theoretical and experimental advancements. The future trends of employing OT in single cells, especially in stem cell delivery, tissue engineering and regenerative medicine, are prospected. More importantly, current limitations and future challenges of OT for these new paradigms are also highlighted in this review.

The effect of geometry on three-dimensional tissue growth

Abstract: Tissue formation is determined by uncountable biochemical signals between cells; in addition, physical parameters have been shown to exhibit significant effects on the level of the single cell. Beyond the cell, however, there is still no quantitative understanding of how geometry affects tissue growth, which is of much significance for bone healing and tissue engineering. In this paper, it is shown that the local growth rate of tissue formed by osteoblasts is strongly influenced by the geometrical features of channels in an artificial three-dimensional matrix. Curvature-driven effects and mechanical forces within the tissue may explain the growth patterns as demonstrated by numerical simulation and confocal laser scanning microscopy. This implies that cells within the tissue surface are able to sense and react to radii of curvature much larger than the size of the cells themselves. This has important implications towards the understanding of bone remodelling and defect healing as well as towards scaffold design in bone tissue engineering.

Boolean network models of cellular regulation: prospects and limitations

Abstract: Computer models are valuable tools towards an understanding of the cell's biochemical regulatory machinery. Possible levels of description of such models range from modelling the underlying biochemical details to top-down approaches, using tools from the theory of complex networks. The latter, coarse-grained approach is taken where regulatory circuits are classified in graph-theoretical terms, with the elements of the regulatory networks being reduced to simply nodes and links, in order to obtain architectural information about the network. Further, considering dynamics on networks at such an abstract level seems rather unlikely to match dynamical regulatory activity of biological cells. Therefore, it came as a surprise when recently examples of discrete dynamical network models based on very simplistic dynamical elements emerged which in fact do match sequences of regulatory patterns of their biological counterparts. Here I will review such discrete dynamical network models, or Boolean networks, of biological regulatory networks. Further, we will take a look at such models extended with stochastic noise, which allow studying the role of network topology in providing robustness against noise. In the end, we will discuss the interesting question of why at all such simple models can describe aspects of biology despite their simplicity. Finally, prospects of Boolean models in exploratory dynamical models for biological circuits and their mutants will be discussed.

Gyroid cuticular structures in butterfly wing scales: biological photonic crystals

Abstract: We present a systematic study of the cuticular structure in the butterfly wing scales of some papilionids (Parides sesostris and Teinopalpus imperialis) and lycaenids (Callophrys rubi, Cyanophrys remus, Mitoura gryneus and Callophrys dumetorum). Using published scanning and transmission electron microscopy (TEM) images, analytical modelling and computergenerated TEM micrographs, we find that the three-dimensional cuticular structures can be modelled by gyroid structures with various filling fractions and lattice parameters. We give a brief discussion of the formation of cubic gyroid membranes from the smooth endoplasmic reticulum in the scale’s cell, which dry and harden to leave the cuticular structure behind when the cell dies. The scales of C. rubi are a potentially attractive biotemplate for producing three-dimensional optical photonic crystals since for these scales the cuticle-filling fraction is nearly optimal for obtaining the largest photonic band gap in a gyroid structure.

Dynamic social networks and the implications for the spread of infectious disease

Abstract: Understanding the nature of human contact patterns is crucial for predicting the impact of future pandemics and devising effective control measures. However, few studies provide a quantitative description of the aspects of social interactions that are most relevant to disease transmission. Here, we present the results from a detailed diary-based survey of casual (conversational) and close contact (physical) encounters made by a small peer group of 49 adults who recorded 8661 encounters with 3528 different individuals over 14 non-consecutive days. We find that the stability of interactions depends on the intimacy of contact and social context. Casual contact encounters mostly occur in the workplace and are predominantly irregular, while close contact encounters mostly occur at home or in social situations and tend to be more stable. Simulated epidemics of casual contact transmission involve a large number of non-repeated encounters, and the social network is well captured by a random mixing model. However, the stability of the social network should be taken into account for close contact infections. Our findings have implications for the modelling of human epidemics and planning pandemic control policies based on social distancing methods.

Single-molecule biophysics: at the interface of biology, physics and chemistry

Abstract: Single-molecule methods have matured into powerful and popular tools to probe the complex behaviour of biological molecules, due to their unique abilities to probe molecular structure, dynamics and function, unhindered by the averaging inherent in ensemble experiments. This review presents an overview of the burgeoning field of single-molecule biophysics, discussing key highlights and selected examples from its genesis to our projections for its future. Following brief introductions to a few popular single-molecule fluorescence and manipulation methods, we discuss novel insights gained from single-molecule studies in key biological areas ranging from biological folding to experiments performed in vivo.

Influence of epidermal hydration on the friction of human skin against textiles.

Abstract: Friction and shear forces, as well as moisture between the human skin and textiles are critical factors in the formation of skin injuries such as blisters, abrasions and decubitus. This study investigated how epidermal hydration affects the friction between skin and textiles. The friction between the inner forearm and a hospital fabric was measured in the natural skin condition and in different hydration states using a force plate. Eleven males and eleven females rubbed their forearm against the textile on the force plate using defined normal loads and friction movements. Skin hydration and viscoelasticity were assessed by corneometry and the suction chamber method, respectively. In each individual, a highly positive linear correlation was found between skin moisture and friction coefficient (COF). No correlation was observed between moisture and elasticity, as well as between elasticity and friction. Skin viscoelasticity was comparable for women and men. The friction of female skin showed significantly higher moisture sensitivity. COFs increased typically by 43% (women) and 26% (men) when skin hydration varied between very dry and normally moist skin. The COFs between skin and completely wet fabric were more than twofold higher than the values for natural skin rubbed on a dry textile surface. Increasing skin hydration seems to cause gender-specific changes in the mechanical properties and/or surface topography of human skin, leading to skin softening and increased real contact area and adhesion.

Current techniques for single-cell lysis

Abstract: Owing to the small quantities of analytes and small volumes involved in single-cell analysis techniques, manipulation strategies must be chosen carefully. The lysis of single cells for downstream chemical analysis in capillaries and lab-on-a-chip devices can be achieved by optical, acoustic, mechanical, electrical or chemical means, each having their respective strengths and weaknesses. Selection of the most appropriate lysis method will depend on the particulars of the downstream cell lysate processing. Ultrafast lysis techniques such as the use of highly focused laser pulses or pulses of high voltage are suitable for applications requiring high temporal resolution. Other factors, such as whether the cells are adherent or in suspension and whether the proteins to be collected are desired to be native or denatured, will determine the suitability of detergent-based lysis methods. Therefore, careful selection of the proper lysis technique is essential for gathering accurate data from single cells.

The fixation probability of beneficial mutations

Abstract: The fixation probability, the probability that the frequency of a particular allele in a population will ultimately reach unity, is one of the cornerstones of population genetics. In this review, we give a brief historical overview of mathematical approaches used to estimate the fixation probability of beneficial alleles. We then focus on more recent work that has relaxed some of the key assumptions in these early papers, providing estimates that have wider applicability to both natural and laboratory settings. In the final section, we address the possibility of future work that might bridge the gap between theoretical results to date and results that might realistically be applied to the experimental evolution of microbial populations. Our aim is to highlight the concrete, testable predictions that have arisen from the theoretical literature, with the intention of further motivating the invaluable interplay between theory and experiment.

Formation of magnetite by bacteria and its application.

Abstract: Magnetic particles offer high technological potential since they can be conveniently collected with an external magnetic field. Magnetotactic bacteria synthesize bacterial magnetic particles (BacMPs) with well-controlled size and morphology. BacMPs are individually covered with thin organic membrane, which confers high and even dispersion in aqueous solutions compared with artificial magnetites, making them ideal biotechnological materials. Recent molecular studies including genome sequence, mutagenesis, gene expression and proteome analyses indicated a number of genes and proteins which play important roles for BacMP biomineralization. Some of the genes and proteins identified from these studies have allowed us to express functional proteins efficiently onto BacMPs, through genetic engineering, permitting the preservation of the protein activity, leading to a simple preparation of functional protein–magnetic particle complexes. They were applicable to high-sensitivity immunoassay, drug screening and cell separation. Furthermore, fully automated single nucleotide polymorphism discrimination and DNA recovery systems have been developed to use these functionalized BacMPs. The nano-sized fine magnetic particles offer vast potential in new nano-techniques.

The effect of opinion clustering on disease outbreaks

Abstract: Many high-income countries currently experience large outbreaks of vaccine-preventable diseases such as measles despite the availability of highly effective vaccines. This phenomenon lacks an explanation in countries where vaccination rates are rising on an already high level. Here, we build on the growing evidence that belief systems, rather than access to vaccines, are the primary barrier to vaccination in high-income countries, and show how a simple opinion formation process can lead to clusters of unvaccinated individuals, leading to a dramatic increase in disease outbreak probability. In particular, the effect of clustering on outbreak probabilities is strongest when the vaccination coverage is close to the level required to provide herd immunity under the assumption of random mixing. Our results based on computer simulations suggest that the current estimates of vaccination coverage necessary to avoid outbreaks of vaccine-preventable diseases might be too low.

Biomaterials for the central nervous system.

Abstract: Biomaterials are widely used to help treat neurological disorders and/or improve functional recovery in the central nervous system (CNS). This article reviews the application of biomaterials in (i) shunting systems for hydrocephalus, (ii) cortical neural prosthetics, (iii) drug delivery in the CNS, (iv) hydrogel scaffolds for CNS repair, and (v) neural stem cell encapsulation for neurotrauma. The biological and material requirements for the biomaterials in these applications are discussed. The difficulties that the biomaterials might face in each application and the possible solutions are also reviewed in this article.

Quantifying social distancing arising from pandemic influenza

Abstract: Local epidemic curves during the 1918-1919 influenza pandemic were often characterized by multiple epidemic waves. Identifying the underlying cause(s) of such waves may help manage future pandemics. We investigate the hypothesis that these waves were caused by people avoiding potentially infectious contacts-a behaviour termed 'social distancing'. We estimate the effective disease reproduction number and from it infer the maximum degree of social distancing that occurred during the course of the multiple-wave epidemic in Sydney, Australia. We estimate that, on average across the city, people reduced their infectious contact rate by as much as 38%, and that this was sufficient to explain the multiple waves of this epidemic. The basic reproduction number, R0, was estimated to be in the range of 1.6-2.0 with a preferred estimate of 1.8, in line with other recent estimates for the 1918-1919 influenza pandemic. The data are also consistent with a high proportion (more than 90%) of the population being initially susceptible to clinical infection, and the proportion of infections that were asymptomatic (if this occurs) being no higher than approximately 9%. The observed clinical attack rate of 36.6% was substantially lower than the 59% expected based on the estimated value of R0, implying that approximately 22% of the population were spared from clinical infection. This reduction in the clinical attack rate translates to an estimated 260 per 100000 lives having been saved, and suggests that social distancing interventions could play a major role in mitigating the public health impact of future influenza pandemics.

Assessing the risk of bluetongue to UK livestock: uncertainty and sensitivity analyses of a temperature-dependent model for the basic reproduction number

Abstract: Since 1998 bluetongue virus (BTV), which causes bluetongue, a non-contagious, insect-borne infectious disease of ruminants, has expanded northwards in Europe in an unprecedented series of incursions, suggesting that there is a risk to the large and valuable British livestock industry. The basic reproduction number, R0, provides a powerful tool with which to assess the level of risk posed by a disease. In this paper, we compute R0 for BTV in a population comprising two host species, cattle and sheep. Estimates for each parameter which influences R0 were obtained from the published literature, using those applicable to the UK situation wherever possible. Moreover, explicit temperature dependence was included for those parameters for which it had been quantified. Uncertainty and sensitivity analyses based on Latin hypercube sampling and partial rank correlation coefficients identified temperature, the probability of transmission from host to vector and the vector to host ratio as being most important in determining the magnitude of R0. The importance of temperature reflects the fact that it influences many processes involved in the transmission of BTV and, in particular, the biting rate, the extrinsic incubation period and the vector mortality rate.

Range and severity of a plant disease increased by global warming.

Abstract: Climate change affects plants in natural and agricultural ecosystems throughout the world but little work has been done on the effects of climate change on plant disease epidemics. To illustrate such effects, a weather-based disease forecasting model was combined with a climate change model predicting UK temperature and rainfall under high- and low-carbon emissions for the 2020s and 2050s. Multi-site data collected over a 15-year period were used to develop and validate a weather-based model forecasting severity of phoma stem canker epidemics on oilseed rape across the UK. This was combined with climate change scenarios to predict that epidemics will not only increase in severity but also spread northwards by the 2020s. These results provide a stimulus to develop models to predict the effects of climate change on other plant diseases, especially in delicately balanced agricultural or natural ecosystems. Such predictions can be used to guide policy and practice in adapting to effects of climate change on food security and wildlife.

On methods for studying stochastic disease dynamics

Abstract: Models that deal with the individual level of populations have shown the importance of stochasticity in ecology, epidemiology and evolution. An increasingly common approach to studying these models is through stochastic (event-driven) simulation. One striking disadvantage of this approach is the need for a large number of replicates to determine the range of expected behaviour. Here, for a class of stochastic models called Markov processes, we present results that overcome this difficulty and provide valuable insights, but which have been largely ignored by applied researchers. For these models, the so-called Kolmogorov forward equation (also called the ensemble or master equation) allows one to simultaneously consider the probability of each possible state occurring. Irrespective of the complexities and nonlinearities of population dynamics, this equation is linear and has a natural matrix formulation that provides many analytical insights into the behaviour of stochastic populations and allows rapid evaluation of process dynamics. Here, using epidemiological models as a template, these ensemble equations are explored and results are compared with traditional stochastic simulations. In addition, we describe further advantages of the matrix formulation of dynamics, providing simple exact methods for evaluating expected eradication (extinction) times of diseases, for comparing expected total costs of possible control programmes and for estimation of disease parameters.

A multiscale model of thrombus development.

Abstract: A two-dimensional multiscale model is introduced for studying formation of a thrombus (clot) in a blood vessel. It involves components for modelling viscous, incompressible blood plasma; non-activated and activated platelets; blood cells; activating chemicals; fibrinogen; and vessel walls and their interactions. The macroscale dynamics of the blood flow is described by the continuum Navier–Stokes equations. The microscale interactions between the activated platelets, the platelets and fibrinogen and the platelets and vessel wall are described through an extended stochastic discrete cellular Potts model. The model is tested for robustness with respect to fluctuations of basic parameters. Simulation results demonstrate the development of an inhomogeneous internal structure of the thrombus, which is confirmed by the preliminary experimental data. We also make predictions about different stages in thrombus development, which can be tested experimentally and suggest specific experiments. Lastly, we demonstrate that the dependence of the thrombus size on the blood flow rate in simulations is close to the one observed experimentally.

Adhesion formation of primary human osteoblasts and the functional response of mesenchymal stem cells to 330 nm deep microgrooves

Abstract: 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 330 nm deep and either 10, 25 or 100 μm 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, 1.7 K 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; 100 μm wide groove/ridge arrays did not significantly affect adhesion formation yet induced upregulation of genes involved in skeletal development and increased osteospecific function; 25 μm wide groove/ridge arrays were associated with a reduction in SMA and an increase in FX formation; and 10 μm 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.

The combined role of wear particles, macrophages and lymphocytes in the loosening of total joint prostheses.

Abstract: This review considers the causes of loosening of prosthetic joint replacement paying attention to the biological mechanisms rather than other effects that are physical, such as component fracture and other failure related to mechanical problems. Infection accounts for approximately 1.5 per cent of joint loosening and when it occurs it is a cause of serious concern to the surgeon. The loosening of prosthetic joints in the absence of infection is by far the most common reason for revision surgery and is known as aseptic loosening. While this may be multifactorial in terms of causation, and non-biological factors may contribute significantly in a particular individual, a significant part is undoubtedly played by the generation of wear debris, mainly from the bearing surfaces of the joint, and the cellular reaction to this in the implant bed. Phagocytic cells (macrophages and multinucleated giant cells) are the ones that remove foreign material from the tissues, and the ways in which these cells function in the interface between implant and bone are described. Mediators produced locally include numerous cytokines, enzymes and integrins. There is evidence for interactions between macrophages and locally recruited lymphocytes, which may or may not give rise to an immunologically mediated process. Sensitization of individuals having metal implants in place has been shown by positive skin tests or blood lymphocyte transformation tests and in these cases has been accompanied by loosening and failure of the replacement joint. The question remains as to whether this process is also present in a proportion of individuals with aseptic loosening in the absence of clearly defined clinical evidence of sensitization. Numerous studies performed by the author's group and, latterly, by others suggest that the cellular reactions detected in the tissues in cases of aseptic loosening are indeed those of contact sensitization. There is good evidence to show that a type IV cell-mediated immune reaction is taking place, with TH1 cell involvement and active antigen presentation. The extent to which sensitization is present in individual cases of aseptic loosening remains a subject for further work and this needs all the sophisticated molecular methods now available to modern biology to be applied in appropriate prospective clinical studies coupled with experimental models in vitro and in vivo. Immunological processes may play a more important part in joint loosening than previously considered.

Eliminating human tuberculosis in the twenty-first century.

Abstract: Recognizing that tuberculosis (TB) is still the leading cause of human death from a curable infection, the international health community has set ambitious targets for disease control. One target is to eliminate TB by 2050; that is, to cut the annual incidence of new cases to less than 1 per million population. National TB control programmes are working to eliminate TB mainly by intensifying efforts to find and cure patients with active disease. Here, we use mathematical modelling to show that, while most TB patients can be cured with present drug regimens, the 2050 target is far more likely to be achieved with a combination of diagnostics, drugs and vaccines that can detect and treat both latent infection and active disease. We find that the coupling of control methods is particularly effective because treatments for latent infection and active disease act in synergy. This synergistic effect offers new perspectives on the cost-effectiveness of treating latent TB infection and the impact of possible new TB vaccines. Our results should be a stimulus to those who develop, manufacture and implement new technology for TB control, and to their financial donors.

Periodic travelling waves in cyclic populations: field studies and reaction-diffusion models.

Abstract: Periodic travelling waves have been reported in a number of recent spatio-temporal field studies of populations undergoing multi-year cycles. Mathematical modelling has a major role to play in understanding these results and informing future empirical studies. We review the relevant field data and summarize the statistical methods used to detect periodic waves. We then discuss the mathematical theory of periodic travelling waves in oscillatory reaction–diffusion equations. We describe the notion of a wave family, and various ecologically relevant scenarios in which periodic travelling waves occur. We also discuss wave stability, including recent computational developments. Although we focus on oscillatory reaction–diffusion equations, a brief discussion of other types of model in which periodic travelling waves have been demonstrated is also included. We end by proposing 10 research challenges in this area, five mathematical and five empirical.

Selective activation of mechanosensitive ion channels using magnetic particles

Abstract: This study reports the preliminary development of a novel magnetic particle-based technique that permits the application of highly localized mechanical forces directly to specific regions of an ion-channel structure. We demonstrate that this approach can be used to directly and selectively activate a mechanosensitive ion channel of interest, namely TREK-1. It is shown that manipulation of particles targeted against the extended extracellular loop region of TREK-1 leads to changes in whole-cell currents consistent with changes in TREK-1 activity. Responses were absent when particles were coated with RGD (Arg–Gly–Asp) peptide or when magnetic fields were applied in the absence of magnetic particles. It is concluded that changes in whole-cell current are the result of direct force application to the extracellular loop region of TREK-1 and thus these results implicate this region of the channel structure in mechano-gating. It is hypothesized that the extended loop region of TREK-1 may act as a tension spring that acts to regulate sensitivity to mechanical forces, in a nature similar to that described for MscL. The development of a technique that permits the direct manipulation of mechanosensitive ion channels in real time without the need for pharmacological drugs has huge potential benefits not only for basic biological research of ion-channel gating mechanisms, but also potentially as a tool for the treatment of human diseases caused by ion-channel dysfunction.

Sliding-induced adhesion of stiff polymer microfibre arrays. I. Macroscale behaviour

Abstract: The adhesive pads of geckos provide control of normal adhesive force by controlling the applied shear force. This frictional adhesion effect is one of the key principles used for rapid detachment in animals running up vertical surfaces. We developed polypropylene microfibre arrays composed of vertical, 0.3 μm radius fibres with elastic modulus of 1 GPa which show this effect for the first time using a stiff polymer. In the absence of shear forces, these fibres show minimal normal adhesion. However, sliding parallel to the substrate with a spherical probe produces a frictional adhesion effect which is not seen in the flat control. A cantilever model for the fibres and the spherical probe indicates a strong dependence on the initial fibre angle. A novel feature of the microfibre arrays is that adhesion improves with use. Repeated shearing of fibres temporarily increases maximum shear and pull-off forces.

Likelihood-based estimation of continuous-time epidemic models from time-series data: application to measles transmission in London.

Abstract: We present a new statistical approach to analyse epidemic time-series data. A major difficulty for inference is that (i) the latent transmission process is partially observed and (ii) observed quantities are further aggregated temporally. We develop a data augmentation strategy to tackle these problems and introduce a diffusion process that mimicks the susceptible–infectious–removed (SIR) epidemic process, but that is more tractable analytically. While methods based on discrete-time models require epidemic and data collection processes to have similar time scales, our approach, based on a continuous-time model, is free of such constraint. Using simulated data, we found that all parameters of the SIR model, including the generation time, were estimated accurately if the observation interval was less than 2.5 times the generation time of the disease. Previous discrete-time TSIR models have been unable to estimate generation times, given that they assume the generation time is equal to the observation interval. However, we were unable to estimate the generation time of measles accurately from historical data. This indicates that simple models assuming homogenous mixing (even with age structure) of the type which are standard in mathematical epidemiology miss key features of epidemics in large populations.

Frictional and elastic energy in gecko adhesive detachment.

Abstract: Geckos use millions of adhesive setae on their toes to climb vertical surfaces at speeds of over 1 m s(-1). Climbing presents a significant challenge for an adhesive since it requires both strong attachment and easy, rapid removal. Conventional pressure-sensitive adhesives are either strong and difficult to remove (e.g. duct tape) or weak and easy to remove (e.g. sticky notes). We discovered that the energy required to detach adhering tokay gecko setae (W(d)) is modulated by the angle (theta) of a linear path of detachment. Gecko setae resist detachment when dragged towards the animal during detachment (theta = 30 degrees ) requiring W(d) = 5.0+/-0.86(s.e.) J m(-2) to detach, largely due to frictional losses. This external frictional loss is analogous to viscous internal frictional losses during detachment of pressure-sensitive adhesives. We found that, remarkably, setae possess a built-in release mechanism. Setae acted as springs when loaded in tension during attachment and returned elastic energy when detached along the optimal path (theta=130 degrees ), resulting in W(d) = -0.8+/-0.12 J m(-2). The release of elastic energy from the setal shaft probably causes spontaneous release, suggesting that curved shafts may enable easy detachment in natural, and synthetic, gecko adhesives.

Biological switches and clocks.

Abstract: To introduce this special issue on biological switches and clocks, we review the historical development of mathematical models of bistability and oscillations in chemical reaction networks. In the 1960s and 1970s, these models were limited to well-studied biochemical examples, such as glycolytic oscillations and cyclic AMP signalling. After the molecular genetics revolution of the 1980s, the field of molecular cell biology was thrown wide open to mathematical modellers. We review recent advances in modelling the gene–protein interaction networks that control circadian rhythms, cell cycle progression, signal processing and the design of synthetic gene networks.

Optimal foraging: Lévy pattern or process?

Abstract: Many different species have been suggested to forage according to a Levy walk in which the distribution of step lengths is heavy-tailed. Theoretical research has shown that a Levy 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 Levy walk model. It is shown that it may be very difficult, in practice, to distinguish between the Brownian and the Levy 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 Levy model.