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2.  Wavelet analysis in ecology and epidemiology: impact of statistical tests 
Wavelet analysis is now frequently used to extract information from ecological and epidemiological time series. Statistical hypothesis tests are conducted on associated wavelet quantities to assess the likelihood that they are due to a random process. Such random processes represent null models and are generally based on synthetic data that share some statistical characteristics with the original time series. This allows the comparison of null statistics with those obtained from original time series. When creating synthetic datasets, different techniques of resampling result in different characteristics shared by the synthetic time series. Therefore, it becomes crucial to consider the impact of the resampling method on the results. We have addressed this point by comparing seven different statistical testing methods applied with different real and simulated data. Our results show that statistical assessment of periodic patterns is strongly affected by the choice of the resampling method, so two different resampling techniques could lead to two different conclusions about the same time series. Moreover, our results clearly show the inadequacy of resampling series generated by white noise and red noise that are nevertheless the methods currently used in the wide majority of wavelets applications. Our results highlight that the characteristics of a time series, namely its Fourier spectrum and autocorrelation, are important to consider when choosing the resampling technique. Results suggest that data-driven resampling methods should be used such as the hidden Markov model algorithm and the ‘beta-surrogate’ method.
doi:10.1098/rsif.2013.0585
PMCID: PMC3869155  PMID: 24284892
wavelet analysis; statistical testing; ecology; epidemiology
3.  Fish responses to flow velocity and turbulence in relation to size, sex and parasite load 
Riverine fish are subjected to heterogeneous flow velocities and turbulence and may use this to their advantage by selecting regions that balance energy expenditure for station holding while maximizing energy gain through feeding opportunities. This study investigated microhabitat selection by guppies Poecilia reticulata in terms of flow characteristics generated by hemisphere boulders in an open channel flume. Velocity and turbulence influenced the variation in swimming behaviour with respect to size, sex and parasite intensity. With increasing body length, fish swam further and more frequently between boulder regions. Larger guppies spent more time in the areas of high-velocity and low-turbulence regions beside the boulders, whereas smaller guppies frequented the low-velocity and high-turbulence regions directly behind the boulders. Male guppies selected the regions of low velocity, indicating possible reduced swimming ability owing to hydrodynamic drag imposed by their fins. With increasing Gyrodactylus turnbulli burden, fish spent more time in regions with moderate velocity and lowest turbulent kinetic energy which were the most spatially and temporally homogeneous in terms of velocity and turbulence. These findings highlight the importance of heterogeneous flow conditions in river channel design owing to the behavioural variability within a species in response to velocity and turbulence.
doi:10.1098/rsif.2013.0814
PMCID: PMC3869156  PMID: 24284893
riverine habitat; acoustic Doppler velocimetry; turbulence; Poecilia reticulata; Gyrodactylus turnbulli
4.  Boronic acid-modified magnetic materials for antibody purification 
Aminophenyl boronic acids can form reversible covalent ester interactions with cis-diol-containing molecules, serving as a selective tool for binding glycoproteins as antibody molecules that possess oligosaccharides in both the Fv and Fc regions. In this study, amino phenyl boronic acid (APBA) magnetic particles (MPs) were applied for the magnetic separation of antibody molecules. Iron oxide MPs were firstly coated with dextran to avoid non-specific binding and then with 3-glycidyloxypropyl trimethoxysilane to allow further covalent coupling of APBA (APBA_MP). When contacted with pure protein solutions of human IgG (hIgG) and bovine serum albumin (BSA), APBA_MP bound 170 ± 10 mg hIgG g−1 MP and eluted 160 ± 5 mg hIgG g−1 MP, while binding only 15 ± 5 mg BSA g−1 MP. The affinity constant for the interaction between hIgG and APBA_MP was estimated as 4.9 × 105 M−1 (Ka) with a theoretical maximum capacity of 492 mg hIgG adsorbed g−1 MP (Qmax), whereas control particles bound a negligible amount of hIgG and presented an estimated theoretical maximum capacity of 3.1 mg hIgG adsorbed g−1 MP (Qmax). APBA_MPs were also tested for antibody purification directly from CHO cell supernatants. The particles were able to bind 98% of IgG loaded and to recover 95% of pure IgG (purity greater than 98%) at extremely mild conditions.
doi:10.1098/rsif.2013.0875
PMCID: PMC3869159  PMID: 24258155
magnetic particles; amino phenyl boronic acid; antibodies; glycosylated proteins
5.  Unveiling a mechanism for species decline in fragmented habitats: fragmentation induced reduction in encounter rates 
Several studies have reported that fragmentation (e.g. of anthropogenic origin) of habitats often leads to a decrease in the number of species in the region. An important mechanism causing this adverse ecological impact is the change in the encounter rates (i.e. the rates at which individuals meet other organisms of the same or different species). Yet, how fragmentation can change encounter rates is poorly understood. To gain insight into the problem, here we ask how landscape fragmentation affects encounter rates when all other relevant variables remain fixed. We present strong numerical evidence that fragmentation decreases search efficiencies thus encounter rates. What is surprising is that it falls even when the global average densities of interacting organisms are held constant. In other words, fragmentation per se can reduce encounter rates. As encounter rates are fundamental for biological interactions, it can explain part of the observed diminishing in animal biodiversity. Neglecting this effect may underestimate the negative outcomes of fragmentation. Partial deforestation and roads that cut through forests, for instance, might be responsible for far greater damage than thought. Preservation policies should take into account this previously overlooked scientific fact.
doi:10.1098/rsif.2013.0887
PMCID: PMC3869160  PMID: 24258156
forest fragmentation; encounter rates; foraging; population decreasing; Lévy processes
6.  Non-lithographic patterning of phage-displayed peptides with wrinkled elastomers 
The development of controlled patterning of phage (viruses) could expand opportunities for both fundamental studies and creating various materials platforms. Inducing the elastomeric instability of PDMS film provides a non-lithographic, tuneable, controlled method for generating micro/nanoscale wrinkle patterns. Phage display has emerged as a powerful method for selecting peptides that possess enhanced selectivity and binding affinity toward a variety of targets. In this report, we demonstrate the non-lithographic patterning of phage-displayed peptides with wrinkled elastomers. Our results show that the phage-displayed peptides can be patterned on specific locations in controlled and tuneable ways, be transferred to other substrates and induce the self-assembly of hybrid materials. We anticipate that these results could open up exciting opportunities in fundamental studies and in applications ranging from sensors, hybrid materials, self-assembly, surface and interface, to micro/nanoelectronics.
doi:10.1098/rsif.2013.0893
PMCID: PMC3869161  PMID: 24284895
non-lithographic patterning; phage-displayed peptides; wrinkle patterns; self-assembly
7.  Human responses to multiple sources of directional information in virtual crowd evacuations 
The evacuation of crowds from buildings or vehicles is one example that highlights the importance of understanding how individual-level interactions and decision-making combine and lead to the overall behaviour of crowds. In particular, to make evacuations safer, we need to understand how individuals make movement decisions in crowds. Here, we present an evacuation experiment with over 500 participants testing individual behaviour in an interactive virtual environment. Participants had to choose between different exit routes under the influence of three different types of directional information: static information (signs), dynamic information (movement of simulated crowd) and memorized information, as well as the combined effect of these different sources of directional information. In contrast to signs, crowd movement and memorized information did not have a significant effect on human exit route choice in isolation. However, when we combined the latter two treatments with additional directly conflicting sources of directional information, for example signs, they showed a clear effect by reducing the number of participants that followed the opposing directional information. This suggests that the signals participants observe more closely in isolation do not simply overrule alternative sources of directional information. Age and gender did not consistently explain differences in behaviour in our experiments.
doi:10.1098/rsif.2013.0904
PMCID: PMC3869162  PMID: 24258157
decision-making; crowd behaviour; emergency evacuations; virtual environment; route choice; directional information
8.  Connecting fractional anisotropy from medical images with mechanical anisotropy of a hyperviscoelastic fibre-reinforced constitutive model for brain tissue 
Brain tissue modelling has been an active area of research for years. Brain matter does not follow the constitutive relations for common materials and loads applied to the brain turn into stresses and strains depending on tissue local morphology. In this work, a hyperviscoelastic fibre-reinforced anisotropic law is used for computational brain injury prediction. Thanks to a fibre-reinforcement dispersion parameter, this formulation accounts for anisotropic features and heterogeneities of the tissue owing to different axon alignment. The novelty of the work is the correlation of the material mechanical anisotropy with fractional anisotropy (FA) from diffusion tensor images. Finite-element (FE) models are used to investigate the influence of the fibre distribution for different loading conditions. In the case of tensile–compressive loads, the comparison between experiments and simulations highlights the validity of the proposed FA–k correlation. Axon alignment affects the deformation predicted by FE models and, when the strain in the axonal direction is large with respect to the maximum principal strain, decreased maximum deformations are detected. It is concluded that the introduction of fibre dispersion information into the constitutive law of brain tissue affects the biofidelity of the simulations.
doi:10.1098/rsif.2013.0914
PMCID: PMC3869163  PMID: 24258158
brain tissue; constitutive modelling; fibre dispersion; anisotropy
9.  Vision-based flight control in the hawkmoth Hyles lineata 
Vision is a key sensory modality for flying insects, playing an important role in guidance, navigation and control. Here, we use a virtual-reality flight simulator to measure the optomotor responses of the hawkmoth Hyles lineata, and use a published linear-time invariant model of the flight dynamics to interpret the function of the measured responses in flight stabilization and control. We recorded the forces and moments produced during oscillation of the visual field in roll, pitch and yaw, varying the temporal frequency, amplitude or spatial frequency of the stimulus. The moths’ responses were strongly dependent upon contrast frequency, as expected if the optomotor system uses correlation-type motion detectors to sense self-motion. The flight dynamics model predicts that roll angle feedback is needed to stabilize the lateral dynamics, and that a combination of pitch angle and pitch rate feedback is most effective in stabilizing the longitudinal dynamics. The moths’ responses to roll and pitch stimuli coincided qualitatively with these functional predictions. The moths produced coupled roll and yaw moments in response to yaw stimuli, which could help to reduce the energetic cost of correcting heading. Our results emphasize the close relationship between physics and physiology in the stabilization of insect flight.
doi:10.1098/rsif.2013.0921
PMCID: PMC3869164  PMID: 24335557
flight control; flight dynamics; insect flight; optomotor; hawkmoth; Hyles lineata
10.  Mechanically driven accumulation of microscale material at coupled solid–fluid interfaces in biological channels 
The accumulation of microscale materials at solid–fluid interfaces in biological channels is often the initial stage of certain growth processes, which are present in some forms of atherosclerosis. The objective of this work is to develop a relatively simple model for such accumulation, which researchers can use to qualitatively guide their analyses. Specifically, the approach is to construct rate equations for the accumulation at the solid–fluid interface as a function of the intensity of the shear stress. The accumulation of material subsequently reduces the cross-sectional area of the channel until the fluid-induced shear stress at the solid–fluid interface reaches a critical value, which terminates the accumulation rate. Characteristics of the model are explored analytically and numerically.
doi:10.1098/rsif.2013.0922
PMCID: PMC3869165  PMID: 24284896
accumulation; solid–fluid interfaces; channel flow
11.  Space–time correlations in urban sprawl 
Understanding demographic and migrational patterns constitutes a great challenge. Millions of individual decisions, motivated by economic, political, demographic, rational and/or emotional reasons underlie the high complexity of demographic dynamics. Significant advances in quantitatively understanding such complexity have been registered in recent years, as those involving the growth of cities but many fundamental issues still defy comprehension. We present here compelling empirical evidence of a high level of regularity regarding time and spatial correlations in urban sprawl, unravelling patterns about the inertia in the growth of cities and their interaction with each other. By using one of the world's most exhaustive extant demographic data basis—that of the Spanish Government's Institute INE, with records covering 111 years and (in 2011) 45 million people, distributed among more than 8000 population nuclei—we show that the inertia of city growth has a characteristic time of 15 years, and its interaction with the growth of other cities has a characteristic distance of 80 km. Distance is shown to be the main factor that entangles two cities (60% of total correlations). The power of our current social theories is thereby enhanced.
doi:10.1098/rsif.2013.0930
PMCID: PMC3869166  PMID: 24258159
urban growth; social dynamics; space–time correlations
12.  Calcium waves initiating from the anomalous subdiffusive calcium sparks 
The objective of the study is to investigate the propagation of Ca2+ waves in full-width cardiac myocytes and carry out sensitivity analysis to study the effects of various physiological parameters on global Ca2+ waves. Based on the anomalous subdiffusion of Ca2+ sparks, a mathematical model was proposed to characterize the Ca2+ waves. The computed results were in agreement with the experimental measurements using confocal microscopy. This model includes variables of current through the Ca2+ release unit (CRU; ICRU), duration of current flow through CRU (Topen), Ca2+ sensitivity parameter (K), the longitudinal and transverse spatial separation of CRUs (lx and ly, where x denotes longitudinal direction (x-axis) and y denotes transverse direction (y-axis)) and Ca2+ diffusion coefficients (Dx, Dy). The spatio-temporal mechanism of the anomalous Ca2+ sparks led to results that were different from those based on Fick's law. The major findings were reported as: ICRU affected the dynamic properties of Ca2+ waves more significantly than Topen; the effect of K on the properties of Ca2+ waves was negligible; ly affected the amplitude significantly, but lx affected the longitudinal velocity significantly; in turn, the limitation and significance of the study are discussed.
doi:10.1098/rsif.2013.0934
PMCID: PMC3869167  PMID: 24335558
calcium wave; anomalous subdiffusion; calcium spark; numerical simulation; cardiac myocyte
13.  Modelling and simulation of low-density lipoprotein transport through multi-layered wall of an anatomically realistic carotid artery bifurcation 
A high concentration of low-density lipoprotein (LDL) is recognized as one of the principal risk factors for development of atherosclerosis. This paper reports on modelling and simulations of the coupled mass (LDL concentration) and momentum transport through the arterial lumen and the multi-layered arterial wall of an anatomically realistic carotid bifurcation. The mathematical model includes equations for conservation of mass, momentum and concentration, which take into account a porous layer structure, the biological membranes and reactive source/sink terms in different layers of the arterial wall, as proposed in Yang & Vafai (2006). A four-layer wall model of an arterial wall with constant thickness is introduced and initially tested on a simple cylinder geometry where realistic layer properties are specified. Comparative assessment with previously published results demonstrated proper implementation of the mathematical model. Excellent agreement for the velocity and LDL concentration distributions in the arterial lumen and in the artery wall are obtained. Then, an anatomically realistic carotid artery bifurcation is studied. This is the main novelty of the presented research. We find a strong dependence between underlying blood flow pattern (and consequently the wall shear stress distributions) and the uptake of the LDL concentration in the artery wall. The radial dependency of interactions between the diffusion, convection and chemical reactions within the multi-layered artery wall is crucial for accurate predictions of the LDL concentration in the media. It is shown that a four-layer wall model produced qualitatively good agreement with the experimental results of Meyer et al. (1996) in predicting levels of LDL within the media of a rabbit aorta under identical transmural pressure conditions. Finally, it is demonstrated that the adopted model represents a good initial platform for future numerical investigations of the initial stage of atherosclerosis for patient-specific geometries.
doi:10.1098/rsif.2013.0941
PMCID: PMC3869169  PMID: 24284897
low-density lipoprotein transport; multi-layered artery wall; numerical simulation; atherosclerosis
14.  Global warming alters sound transmission: differential impact on the prey detection ability of echolocating bats 
Climate change impacts the biogeography and phenology of plants and animals, yet the underlying mechanisms are little known. Here, we present a functional link between rising temperature and the prey detection ability of echolocating bats. The maximum distance for echo-based prey detection is physically determined by sound attenuation. Attenuation is more pronounced for high-frequency sound, such as echolocation, and is a nonlinear function of both call frequency and ambient temperature. Hence, the prey detection ability, and thus possibly the foraging efficiency, of echolocating bats and susceptible to rising temperatures through climate change. Using present-day climate data and projected temperature rises, we modelled this effect for the entire range of bat call frequencies and climate zones around the globe. We show that depending on call frequency, the prey detection volume of bats will either decrease or increase: species calling above a crossover frequency will lose and species emitting lower frequencies will gain prey detection volume, with crossover frequency and magnitude depending on the local climatic conditions. Within local species assemblages, this may cause a change in community composition. Global warming can thus directly affect the prey detection ability of individual bats and indirectly their interspecific interactions with competitors and prey.
doi:10.1098/rsif.2013.0961
PMCID: PMC3869170  PMID: 24335559
echolocation; foraging; global warming; sensory ecology; species interactions
15.  Optimal indolence: a normative microscopic approach to work and leisure 
Dividing limited time between work and leisure when both have their attractions is a common everyday decision. We provide a normative control-theoretic treatment of this decision that bridges economic and psychological accounts. We show how our framework applies to free-operant behavioural experiments in which subjects are required to work (depressing a lever) for sufficient total time (called the price) to receive a reward. When the microscopic benefit-of-leisure increases nonlinearly with duration, the model generates behaviour that qualitatively matches various microfeatures of subjects’ choices, including the distribution of leisure bout durations as a function of the pay-off. We relate our model to traditional accounts by deriving macroscopic, molar, quantities from microscopic choices.
doi:10.1098/rsif.2013.0969
PMCID: PMC3869171  PMID: 24284898
work; leisure; normative; microscopic; reinforcement learning; economics
16.  Three-dimensional vortex wake structure of flapping wings in hovering flight 
Flapping wings continuously create and send vortices into their wake, while imparting downward momentum into the surrounding fluid. However, experimental studies concerning the details of the three-dimensional vorticity distribution and evolution in the far wake are limited. In this study, the three-dimensional vortex wake structure in both the near and far field of a dynamically scaled flapping wing was investigated experimentally, using volumetric three-component velocimetry. A single wing, with shape and kinematics similar to those of a fruitfly, was examined. The overall result of the wing action is to create an integrated vortex structure consisting of a tip vortex (TV), trailing-edge shear layer (TESL) and leading-edge vortex. The TESL rolls up into a root vortex (RV) as it is shed from the wing, and together with the TV, contracts radially and stretches tangentially in the downstream wake. The downwash is distributed in an arc-shaped region enclosed by the stretched tangential vorticity of the TVs and the RVs. A closed vortex ring structure is not observed in the current study owing to the lack of well-established starting and stopping vortex structures that smoothly connect the TV and RV. An evaluation of the vorticity transport equation shows that both the TV and the RV undergo vortex stretching while convecting downwards: a three-dimensional phenomenon in rotating flows. It also confirms that convection and secondary tilting and stretching effects dominate the evolution of vorticity.
doi:10.1098/rsif.2013.0984
PMCID: PMC3869174  PMID: 24335561
flapping wing; vortex wake; far wake; volumetric visualization; induced flow; hovering
17.  Collective thermoregulation in bee clusters 
Swarming is an essential part of honeybee behaviour, wherein thousands of bees cling onto each other to form a dense cluster that may be exposed to the environment for several days. This cluster has the ability to maintain its core temperature actively without a central controller. We suggest that the swarm cluster is akin to an active porous structure whose functional requirement is to adjust to outside conditions by varying its porosity to control its core temperature. Using a continuum model that takes the form of a set of advection–diffusion equations for heat transfer in a mobile porous medium, we show that the equalization of an effective ‘behavioural pressure’, which propagates information about the ambient temperature through variations in density, leads to effective thermoregulation. Our model extends and generalizes previous models by focusing the question of mechanism on the form and role of the behavioural pressure, and allows us to explain the vertical asymmetry of the cluster (as a consequence of buoyancy-driven flows), the ability of the cluster to overpack at low ambient temperatures without breaking up at high ambient temperatures, and the relative insensitivity to large variations in the ambient temperature. Our theory also makes testable hypotheses for the response of the cluster to external temperature inhomogeneities and suggests strategies for biomimetic thermoregulation.
doi:10.1098/rsif.2013.1033
PMCID: PMC3869176  PMID: 24335563
thermoregulation; honeybees; swarms; active porous media
18.  Network morphospace 
Journal of the Royal Society Interface  2015;12(103):20140881.
The structure of complex networks has attracted much attention in recent years. It has been noted that many real-world examples of networked systems share a set of common architectural features. This raises important questions about their origin, for example whether such network attributes reflect common design principles or constraints imposed by selectional forces that have shaped the evolution of network topology. Is it possible to place the many patterns and forms of complex networks into a common space that reveals their relations, and what are the main rules and driving forces that determine which positions in such a space are occupied by systems that have actually evolved? We suggest that these questions can be addressed by combining concepts from two currently relatively unconnected fields. One is theoretical morphology, which has conceptualized the relations between morphological traits defined by mathematical models of biological form. The second is network science, which provides numerous quantitative tools to measure and classify different patterns of local and global network architecture across disparate types of systems. Here, we explore a new theoretical concept that lies at the intersection between both fields, the ‘network morphospace’. Defined by axes that represent specific network traits, each point within such a space represents a location occupied by networks that share a set of common ‘morphological’ characteristics related to aspects of their connectivity. Mapping a network morphospace reveals the extent to which the space is filled by existing networks, thus allowing a distinction between actual and impossible designs and highlighting the generative potential of rules and constraints that pervade the evolution of complex systems.
doi:10.1098/rsif.2014.0881
PMCID: PMC4305402  PMID: 25540237
evolution; complexity; graph theory; Pareto optimality; brain connectivity
19.  Collective sensing and collective responses in quorum-sensing bacteria 
Journal of the Royal Society Interface  2015;12(103):20140882.
Bacteria often face fluctuating environments, and in response many species have evolved complex decision-making mechanisms to match their behaviour to the prevailing conditions. Some environmental cues provide direct and reliable information (such as nutrient concentrations) and can be responded to individually. Other environmental parameters are harder to infer and require a collective mechanism of sensing. In addition, some environmental challenges are best faced by a group of cells rather than an individual. In this review, we discuss how bacteria sense and overcome environmental challenges as a group using collective mechanisms of sensing, known as ‘quorum sensing’ (QS). QS is characterized by the release and detection of small molecules, potentially allowing individuals to infer environmental parameters such as density and mass transfer. While a great deal of the molecular mechanisms of QS have been described, there is still controversy over its functional role. We discuss what QS senses and how, what it controls and why, and how social dilemmas shape its evolution. Finally, there is a growing focus on the use of QS inhibitors as antibacterial chemotherapy. We discuss the claim that such a strategy could overcome the evolution of resistance. By linking existing theoretical approaches to data, we hope this review will spur greater collaboration between experimental and theoretical researchers.
doi:10.1098/rsif.2014.0882
PMCID: PMC4305403  PMID: 25505130
quorum sensing; collective behaviour; systems biology; social evolution
20.  Minimal within-host dengue models highlight the specific roles of the immune response in primary and secondary dengue infections 
Journal of the Royal Society Interface  2015;12(103):20140886.
In recent years, the within-host viral dynamics of dengue infections have been increasingly characterized, and the relationship between aspects of these dynamics and the manifestation of severe disease has been increasingly probed. Despite this progress, there are few mathematical models of within-host dengue dynamics, and the ones that exist focus primarily on the general role of immune cells in the clearance of infected cells, while neglecting other components of the immune response in limiting viraemia. Here, by considering a suite of mathematical within-host dengue models of increasing complexity, we aim to isolate the critical components of the innate and the adaptive immune response that suffice in the reproduction of several well-characterized features of primary and secondary dengue infections. By building up from a simple target cell limited model, we show that only the innate immune response is needed to recover the characteristic features of a primary symptomatic dengue infection, while a higher rate of viral infectivity (indicative of antibody-dependent enhancement) and infected cell clearance by T cells are further needed to recover the characteristic features of a secondary dengue infection. We show that these minimal models can reproduce the increased risk of disease associated with secondary heterologous infections that arises as a result of a cytokine storm, and, further, that they are consistent with virological indicators that predict the onset of severe disease, such as the magnitude of peak viraemia, time to peak viral load, and viral clearance rate. Finally, we show that the effectiveness of these virological indicators to predict the onset of severe disease depends on the contribution of T cells in fuelling the cytokine storm.
doi:10.1098/rsif.2014.0886
PMCID: PMC4305404  PMID: 25519990
dengue; mathematical model; viral dynamics; immune response; cytokine storm; disease severity
21.  Multi-scale modelling of the dynamics of cell colonies: insights into cell-adhesion forces and cancer invasion from in silico simulations 
Journal of the Royal Society Interface  2015;12(103):20141080.
Studying the biophysical interactions between cells is crucial to understanding how normal tissue develops, how it is structured and also when malfunctions occur. Traditional experiments try to infer events at the tissue level after observing the behaviour of and interactions between individual cells. This approach assumes that cells behave in the same biophysical manner in isolated experiments as they do within colonies and tissues. In this paper, we develop a multi-scale multi-compartment mathematical model that accounts for the principal biophysical interactions and adhesion pathways not only at a cell–cell level but also at the level of cell colonies (in contrast to the traditional approach). Our results suggest that adhesion/separation forces between cells may be lower in cell colonies than traditional isolated single-cell experiments infer. As a consequence, isolated single-cell experiments may be insufficient to deduce important biological processes such as single-cell invasion after detachment from a solid tumour. The simulations further show that kinetic rates and cell biophysical characteristics such as pressure-related cell-cycle arrest have a major influence on cell colony patterns and can allow for the development of protrusive cellular structures as seen in invasive cancer cell lines independent of expression levels of pro-invasion molecules.
doi:10.1098/rsif.2014.1080
PMCID: PMC4305411  PMID: 25519994
individual-based modelling; cell population modelling; cell-adhesion forces; E-cadherin
22.  Modelling the spatial heterogeneity and molecular correlates of lymphocytic infiltration in triple-negative breast cancer 
Journal of the Royal Society Interface  2015;12(103):20141153.
Lymphocytic infiltration is associated with a favourable prognosis and predicts response to chemotherapy in many cancer types, including the aggressive triple-negative breast cancer (TNBC). However, it is not well understood owing to the high levels of spatial heterogeneity within tumours, which is difficult to analyse by traditional pathological assessment. This paper describes an unbiased methodology to statistically model the spatial distribution of lymphocytes among tumour cells based on automated analysis of haematoxylin-and-eosin-stained whole-tumour section images, which is applied to two independent TNBC cohorts of 181 patients with matched microarray gene expression data. The novelty of the proposed methodology is the fusion of image analysis and statistical modelling for an integrative understanding of intratumour heterogeneity of lymphocytic infiltration. Using this methodology, a quantitative measure of intratumour lymphocyte ratio is developed and found to be significantly associated with disease-specific survival in both TNBC cohorts independent to standard clinical parameters. The proposed image-based measure compares favourably to a number of gene expression signatures of immune infiltration. In addition, heterogeneous immune infiltration at the morphological level is reflected at the molecular scale and correlated with increased expression of CTLA4, the target of ipilimumab. Taken together, these results support the fusion of high-throughput image analysis and statistical modelling to offer reproducible and robust biomarkers for the objective identification of patients with poor prognosis and treatment options.
doi:10.1098/rsif.2014.1153
PMCID: PMC4305416  PMID: 25505134
image analysis; immune response; tumour microenvironment; statistical modelling
23.  Magnetic field effects as a result of the radical pair mechanism are unlikely in redox enzymes 
Journal of the Royal Society Interface  2015;12(103):20141155.
Environmental exposure to electromagnetic fields is potentially carcinogenic. The radical pair mechanism is considered the most feasible mechanism of interaction between weak magnetic fields encountered in our environment and biochemical systems. Radicals are abundant in biology, both as free radicals and reaction intermediates in enzyme mechanisms. The catalytic cycles of some flavin-dependent enzymes are either known or potentially involve radical pairs. Here, we have investigated the magnetic field sensitivity of a number of flavoenzymes with important cellular roles. We also investigated the magnetic field sensitivity of a model system involving stepwise reduction of a flavin analogue by a nicotinamide analogue—a reaction known to proceed via a radical pair. Under the experimental conditions used, magnetic field sensitivity was not observed in the reaction kinetics from stopped-flow measurements in any of the systems studied. Although widely implicated in radical pair chemistry, we conclude that thermally driven, flavoenzyme-catalysed reactions are unlikely to be influenced by exposure to external magnetic fields.
doi:10.1098/rsif.2014.1155
PMCID: PMC4305418  PMID: 25505136
magnetic field effects; radical pair mechanism; flavoproteins; hydride transfer; environmental magnetic fields
24.  A patient-specific computational model of hypoxia-modulated radiation resistance in glioblastoma using 18F-FMISO-PET 
Journal of the Royal Society Interface  2015;12(103):20141174.
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 [18F]-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.
doi:10.1098/rsif.2014.1174
PMCID: PMC4305419  PMID: 25540239
hypoxia; mathematical modelling; radiation resistance; glioblastoma; patient-specific
25.  The virtue of innovation: innovation through the lenses of biological evolution 
Journal of the Royal Society Interface  2015;12(103):20141183.
We rehearse the processes of innovation and discovery in general terms, using as our main metaphor the biological concept of an evolutionary fitness landscape. Incremental and disruptive innovations are seen, respectively, as successful searches carried out locally or more widely. They may also be understood as reflecting evolution by mutation (incremental) versus recombination (disruptive). We also bring a platonic view, focusing on virtue and memory. We use ‘virtue’ as a measure of efforts, including the knowledge required to come up with disruptive and incremental innovations, and ‘memory’ as a measure of their lifespan, i.e. how long they are remembered. Fostering innovation, in the evolutionary metaphor, means providing the wherewithal to promote novelty, good objective functions that one is trying to optimize, and means to improve one's knowledge of, and ability to navigate, the landscape one is searching. Recombination necessarily implies multi- or inter-disciplinarity. These principles are generic to all kinds of creativity, novel ideas formation and the development of new products and technologies.
doi:10.1098/rsif.2014.1183
PMCID: PMC4305420  PMID: 25505138
innovation; evolutionary computing; philosophy of science

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