On the mathematical modeling of wound healing angiogenesis in skin as a reaction-transport process

Over the last 30 years, numerous research groups have attempted to provide mathematical descriptions of the skin wound healing process. The development of theoretical models of the interlinked processes that underlie the healing mechanism has yielded considerable insight into aspects of this critical phenomenon that remain difficult to investigate empirically. In particular, the mathematical modeling of angiogenesis, i.e., capillary sprout growth, has offered new paradigms for the understanding of this highly complex and crucial step in the healing pathway. With the recent advances in imaging and cell tracking, the time is now ripe for an appraisal of the utility and importance of mathematical modeling in wound healing angiogenesis research. The purpose of this review is to pedagogically elucidate the conceptual principles that have underpinned the development of mathematical descriptions of wound healing angiogenesis, specifically those that have utilized a continuum reaction-transport framework, and highlight the contribution that such models have made toward the advancement of research in this field. We aim to draw attention to the common assumptions made when developing models of this nature, thereby bringing into focus the advantages and limitations of this approach. A deeper integration of mathematical modeling techniques into the practice of wound healing angiogenesis research promises new perspectives for advancing our knowledge in this area. To this end we detail several open problems related to the understanding of wound healing angiogenesis, and outline how these issues could be addressed through closer cross-disciplinary collaboration.

Efficient simulation of stochastic chemical kinetics with the Stochastic Bulirsch-Stoer extrapolation method

Background Biochemical systems with relatively low numbers of components must be simulated stochastically in order to capture their inherent noise. Although there has recently been considerable work on discrete stochastic solvers, there is still a need for numerical methods that are both fast and accurate. The Bulirsch-Stoer method is an established method for solving ordinary differential equations that possesses both of these qualities. Results In this paper, we present the Stochastic Bulirsch-Stoer method, a new numerical method for simulating discrete chemical reaction systems, inspired by its deterministic counterpart. It is able to achieve an excellent efficiency due to the fact that it is based on an approach with high deterministic order, allowing for larger stepsizes and leading to fast simulations. We compare it to the Euler τ-leap, as well as two more recent τ-leap methods, on a number of example problems, and find that as well as being very accurate, our method is the most robust, in terms of efficiency, of all the methods considered in this paper. The problems it is most suited for are those with increased populations that would be too slow to simulate using Gillespie’s stochastic simulation algorithm. For such problems, it is likely to achieve higher weak order in the moments. Conclusions The Stochastic Bulirsch-Stoer method is a novel stochastic solver that can be used for fast and accurate simulations. Crucially, compared to other similar methods, it better retains its high accuracy when the timesteps are increased. Thus the Stochastic Bulirsch-Stoer method is both computationally efficient and robust. These are key properties for any stochastic numerical method, as they must typically run many thousands of simulations.

Stochastic dynamics of interacting haematopoietic stem cell niche lineages

Since we still know very little about stem cells in their natural environment, it is useful to explore their dynamics through modelling and simulation, as well as experimentally. Most models of stem cell systems are based on deterministic differential equations that ignore the natural heterogeneity of stem cell populations. This is not appropriate at the level of individual cells and niches, when randomness is more likely to affect dynamics. In this paper, we introduce a fast stochastic method for simulating a metapopulation of stem cell niche lineages, that is, many sub-populations that together form a heterogeneous metapopulation, over time. By selecting the common limiting timestep, our method ensures that the entire metapopulation is simulated synchronously. This is important, as it allows us to introduce interactions between separate niche lineages, which would otherwise be impossible. We expand our method to enable the coupling of many lineages into niche groups, where differentiated cells are pooled within each niche group. Using this method, we explore the dynamics of the haematopoietic system from a demand control system perspective. We find that coupling together niche lineages allows the organism to regulate blood cell numbers as closely as possible to the homeostatic optimum. Furthermore, coupled lineages respond better than uncoupled ones to random perturbations, here the loss of some myeloid cells. This could imply that it is advantageous for an organism to connect together its niche lineages into groups. Our results suggest that a potential fruitful empirical direction will be to understand how stem cell descendants communicate with the niche and how cancer may arise as a result of a failure of such communication.

Temporal and environmental influences on the vocal behaviour of a nocturnal bird

Temporal and environmental variation in vocal activity can provide information on avian behaviour and call function not available to short-term experimental studies. Intersexual differences in this variation can provide insight into selection effects. Yet factors influencing vocal behaviour have not been assessed in many birds, even those monitored by acoustic methods. This applies to the New Zealand kiwi (Apterygidae), for which call censuses are used extensively in conservation monitoring, yet which have poorly understood acoustic ecology. We investigated little spotted kiwi Apteryx owenii vocal behaviour over 3 yr, measuring influences on vocal activity in both sexes from time of night, season, weather conditions and lunar cycle. We tested hypotheses that call rate variation reflects call function, foraging efficiency, historic predation risk and variability in sound transmission, and that there are inter-sexual differences in call function. Significant seasonal variation showed that vocalisations were important in kiwi reproduction, and inter-sexual synchronisation of call rates indicated that contact, pair-bonding or resource defence were key functions. All weather variables significantly affected call rates, with elevated calling during increased humidity and ground moisture indicating a relation between vocal activity and foraging conditions. A significant decrease in calling activity on cloudy nights, combined with no moonlight effect, suggests an impact of light pollution in this species. These influences on vocal activity provide insight into kiwi call function, have direct consequences for conservation monitoring of kiwi, and have wider implications in understanding vocal behaviour in a range of nocturnal birds

A model to explain specific cellular communications and cellular harmony: - a hypothesis of coupled cells and interactive coupling molecules

Background The various cell types and their relative numbers in multicellular organisms are controlled by growth factors and related extracellular molecules which affect genetic expression pathways. However, these substances may have both/either inhibitory and/or stimulatory effects on cell division and cell differentiation depending on the cellular environment. It is not known how cells respond to these substances in such an ambiguous way. Many cellular effects have been investigated and reported using cell culture from cancer cell lines in an effort to define normal cellular behaviour using these abnormal cells. A model is offered to explain the harmony of cellular life in multicellular organisms involving interacting extracellular substances. Methods A basic model was proposed based on asymmetric cell division and evidence to support the hypothetical model was accumulated from the literature. In particular, relevant evidence was selected for the Insulin-Like Growth Factor system from the published data, especially from certain cell lines, to support the model. The evidence has been selective in an attempt to provide a picture of normal cellular responses, derived from the cell lines. Results The formation of a pair of coupled cells by asymmetric cell division is an integral part of the model as is the interaction of couplet molecules derived from these cells. Each couplet cell will have a receptor to measure the amount of the couplet molecule produced by the other cell; each cell will be receptor-positive or receptor-negative for the respective receptors. The couplet molecules will form a binary complex whose level is also measured by the cell. The hypothesis is heavily supported by selective collection of circumstantial evidence and by some direct evidence. The basic model can be expanded to other cellular interactions. Conclusions These couplet cells and interacting couplet molecules can be viewed as a mechanism that provides a controlled and balanced division-of-labour between the two progeny cells, and, in turn, their progeny. The presence or absence of a particular receptor for a couplet molecule will define a cell type and the presence or absence of many such receptors will define the cell types of the progeny within cell lineages.

Genetics of rheumatoid arthritis contributes to biology and drug discovery

A major challenge in human genetics is to devise a systematic strategy to integrate disease-associated variants with diverse genomic and biological data sets to provide insight into disease pathogenesis and guide drug discovery for complex traits such as rheumatoid arthritis (RA)1. Here we performed a genome-wide association study meta-analysis in a total of >100,000 subjects of European and Asian ancestries (29,880 RA cases and 73,758 controls), by evaluating ~10 million single-nucleotide polymorphisms. We discovered 42 novel RA risk loci at a genome-wide level of significance, bringing the total to 101 (refs 2, 3, 4). We devised an in silico pipeline using established bioinformatics methods based on functional annotation5, cis-acting expression quantitative trait loci6 and pathway analyses7, 8, 9—as well as novel methods based on genetic overlap with human primary immunodeficiency, haematological cancer somatic mutations and knockout mouse phenotypes—to identify 98 biological candidate genes at these 101 risk loci. We demonstrate that these genes are the targets of approved therapies for RA, and further suggest that drugs approved for other indications may be repurposed for the treatment of RA. Together, this comprehensive genetic study sheds light on fundamental genes, pathways and cell types that contribute to RA pathogenesis, and provides empirical evidence that the genetics of RA can provide important information for drug discovery.

Convergence of regenerative medicine and synthetic biology to develop standardized and validated models of human diseases with clinical relevance

In order to progress beyond currently available medical devices and implants, the concept of tissue engineering has moved into the centre of biomedical research worldwide. The aim of this approach is not to replace damaged tissue with an implant or device but rather to prompt the patient's own tissue to enact a regenerative response by using a tissue-engineered construct to assemble new functional and healthy tissue. More recently, it has been suggested that the combination of Synthetic Biology and translational tissue-engineering techniques could enhance the field of personalized medicine, not only from a regenerative medicine perspective, but also to provide frontier technologies for building and transforming the research landscape in the field of in vitro and in vivo disease models.

miR-514a regulates the tumour suppressor NF1 and modulates BRAFi sensitivity in melanoma

To identify ‘melanoma-specific’ microRNAs (miRNAs) we used an unbiased microRNA profiling approach to comprehensively study cutaneous melanoma in relation to other solid malignancies, which revealed 233 differentially expressed (≥ 2 fold, p < 0.05) miRNAs. Among the top 20 most significantly different miRNAs was hsa-miR-514a-3p. miR-514a is a member of a cluster of miRNAs (miR-506-514) involved in initiating melanocyte transformation and promotion of melanoma growth. We found miR-514a was expressed in 38/55 (69%) melanoma cell lines but in only 1/34 (3%) other solid cancers. To identify miR-514a regulated targets we conducted a miR-514a-mRNA ‘pull-down’ experiment, which revealed hundreds of genes, including: CTNNB1, CDK2, MC1R, and NF1, previously associated with melanoma. NF1 was selected for functional validation because of its recent implication inacquired resistance to BRAFV600E-targeted therapy. Luciferase-reporter assays confirmed NF1 as a direct target of miR-514a and over-expression of miR-514a in melanoma cell lines inhibited NF1 expression, which correlated with increased survival of BRAFV600E cells treated with PLX4032. These data provide another mechanism for the dysregulation of the MAPK pathway which may contribute to the profound resistance associated with current RAF-targeted therapies.

Effects of methyl eugenol feeding on mating compatibility of Asian population of Bactrocera dorsalis (Diptera: Tephritidae) with African population and with B. carambolae

Males of some species included in the Bactrocera dorsalis complex are strongly attracted to methyl eugenol (ME) (1,2-dimethoxy-4-(2-propenyl) benzene), a natural compound occurring in a variety of plant species. ME feeding of males of the B. dorsalis complex is known to enhance their mating competitiveness. Within B. dorsalis, recent studies show that Asian and African populations of B. dorsalis are sexually compatible, while populations of B. dorsalis and Bactrocera carambolae are relatively incompatible. The objectives of this study were to examine whether ME feeding by males affects mating compatibility between Asian and African populations of B. dorsalis and ME feeding reduces male mating incompatibility between B. dorsalis (Asian population) and B. carambolae. The data confirmed that Asian and African populations of B. dorsalis are sexually compatible for mating and showed that ME feeding only increased the number of matings. Though ME feeding also increased the number of matings of B. dorsalis (Asian population) and B. carambolae males but the sexual incompatibility between both species was not reduced by treatment with ME. These results conform to the efforts resolving the biological species limits among B. dorsalis complex and have implications for fruit fly control programs in fields and horticultural trade.

Effects of laboratory colonization on Bactrocera dorsalis (Diptera, Tephritidae) mating behaviour: ‘what a difference a year makes

Laboratory-reared insects are widely known to have significantly reduced genetic diversity in comparison to wild populations; however, subtle behavioural changes between laboratory-adapted and wild or ‘wildish’ (i.e., within one or very few generations of field collected material) populations are less well understood. Quantifying alterations in behaviour, particularly sexual, in laboratory-adapted insects is important for mass-reared insects for use in pest management strategies, especially those that have a sterile insect technique component. We report subtle changes in sexual behaviour between ‘wildish’ Bactrocera dorsalis flies (F1 and F2) from central and southern Thailand and the same colonies 12 months later when at six generations from wild. Mating compatibility tests were undertaken under standardised semi-natural conditions, with number of homo/heterotypic couples and mating location in field cages analysed via compatibility indices. Central and southern populations of B. dorsalis displayed positive assortative mating in the 2010 trials but mated randomly in the 2011 trials. ‘Wildish’ southern Thailand males mated significantly earlier than central Thailand males in 2010; this difference was considerably reduced in 2011, yet homotypic couples from southern Thailand still formed significantly earlier than all other couple combinations. There was no significant difference in couple location in 2010; however, couple location significantly differed among pair types in 2011 with those involving southern Thailand females occurring significantly more often on the tree relative to those with central Thailand females. Relative participation also changed with time, with more southern Thailand females forming couples relative to central Thailand females in 2010; this difference was considerably decreased by 2011. These results reveal how subtle changes in sexual behaviour, as driven by laboratory rearing conditions, may significantly influence mating behaviour between laboratory-adapted and recently colonised tephritid fruit flies over a relatively short period of time.

Trapping to monitor tephritid movement: Results, best practice, and assessment of alternatives

Movement of tephritid flies underpins their survival, reproduction, and ability to establish in new areas and is thus of importance when designing effective management strategies. Much of the knowledge currently available on tephritid movement throughout landscapes comes from the use of direct or indirect methods that rely on the trapping of individuals. Here, we review published experimental designs and methods from mark-release-recapture (MRR) studies, as well as other methods, that have been used to estimate movement of the four major tephritid pest genera (Bactrocera, Ceratitis, Anastrepha, and Rhagoletis). In doing so, we aim to illustrate the theoretical and practical considerations needed to study tephritid movement. MRR studies make use of traps to directly estimate the distance that tephritid species can move within a generation and to evaluate the ecological and physiological factors that influence dispersal patterns. MRR studies, however, require careful planning to ensure that the results obtained are not biased by the methods employed, including marking methods, trap properties, trap spacing, and spatial extent of the trapping array. Despite these obstacles, MRR remains a powerful tool for determining tephritid movement, with data particularly required for understudied species that affect developing countries. To ensure that future MRR studies are successful, we suggest that site selection be carefully considered and sufficient resources be allocated to achieve optimal spacing and placement of traps in line with the stated aims of each study. An alternative to MRR is to make use of indirect methods for determining movement, or more correctly, gene flow, which have become widely available with the development of molecular tools. Key to these methods is the trapping and sequencing of a suitable number of individuals to represent the genetic diversity of the sampled population and investigate population structuring using nuclear genomic markers or non-recombinant mitochondrial DNA markers. Microsatellites are currently the preferred marker for detecting recent population displacement and provide genetic information that may be used in assignment tests for the direct determination of contemporary movement. Neither MRR nor molecular methods, however, are able to monitor fine-scale movements of individual flies. Recent developments in the miniaturization of electronics offer the tantalising possibility to track individual movements of insects using harmonic radar. Computer vision and radio frequency identification tags may also permit the tracking of fine-scale movements by tephritid flies by automated resampling, although these methods come with the same problems as traditional traps used in MRR studies. Although all methods described in this chapter have limitations, a better understanding of tephritid movement far outweighs the drawbacks of the individual methods because of the need for this information to manage tephritid populations.

Diet-induced hypercholesterolemia promotes androgen-independent prostate cancer metastasis via IQGAP1 and caveolin-1

Obesity and metabolic syndrome are associated with several cancers, however, the molecular mechanisms remain to be fully elucidated. Recent studies suggest that hypercholesterolemia increases intratumoral androgen signaling in prostate cancer, but it is unclear whether androgenindependent mechanisms also exist. Since hypercholesterolemia is associated with advanced, castrate-resistant prostate cancer, in this study, we aimed to determine whether and how hypercholesterolemia affects prostate cancer progression in the absence of androgen signaling. We demonstrate that diet-induced hypercholesterolemia promotes orthotopic xenograft PC-3 cell metastasis, concomitant with elevated expression of caveolin-1 and IQGAP1 in xenograft tumor tissues. In vitro cholesterol treatment of PC-3 cells stimulated migration and increased IQGAP1 and caveolin-1 protein level and localization to a detergent-resistant fraction. Down-regulation of caveolin-1 or IQGAP1 in PC-3 cells reduced migration and invasion in vitro, and hypercholesterolemia-induced metastasis in vivo. Double knock-down of caveolin-1 and IQGAP1 showed no additive effect, suggesting that caveolin-1 and IQGAP1 act via the same pathway. Taken together, our data show that hypercholesterolemia promotes prostate cancer metastasis independent of the androgen pathway, in part by increasing IQGAP1 and caveolin-1. These results have broader implications for managing metastasis of cancers in general as IQGAP1 and hypercholesterolemia are implicated in the progression of several cancers.

Estimating cell diffusivity and cell proliferation rate by interpreting IncuCyte ZOOM™ assay data using the Fisher-Kolmogorov model

Background: Standard methods for quantifying IncuCyte ZOOM™ assays involve measurements that quantify how rapidly the initially-vacant area becomes re-colonised with cells as a function of time. Unfortunately, these measurements give no insight into the details of the cellular-level mechanisms acting to close the initially-vacant area. We provide an alternative method enabling us to quantify the role of cell motility and cell proliferation separately. To achieve this we calibrate standard data available from IncuCyte ZOOM™ images to the solution of the Fisher-Kolmogorov model. Results: The Fisher-Kolmogorov model is a reaction-diffusion equation that has been used to describe collective cell spreading driven by cell migration, characterised by a cell diffusivity, D, and carrying capacity limited proliferation with proliferation rate, λ, and carrying capacity density, K. By analysing temporal changes in cell density in several subregions located well-behind the initial position of the leading edge we estimate λ and K. Given these estimates, we then apply automatic leading edge detection algorithms to the images produced by the IncuCyte ZOOM™ assay and match this data with a numerical solution of the Fisher-Kolmogorov equation to provide an estimate of D. We demonstrate this method by applying it to interpret a suite of IncuCyte ZOOM™ assays using PC-3 prostate cancer cells and obtain estimates of D, λ and K. Comparing estimates of D, λ and K for a control assay with estimates of D, λ and K for assays where epidermal growth factor (EGF) is applied in varying concentrations confirms that EGF enhances the rate of scratch closure and that this stimulation is driven by an increase in D and λ, whereas K is relatively unaffected by EGF. Conclusions: Our approach for estimating D, λ and K from an IncuCyte ZOOM™ assay provides more detail about cellular-level behaviour than standard methods for analysing these assays. In particular, our approach can be used to quantify the balance of cell migration and cell proliferation and, as we demonstrate, allow us to quantify how the addition of growth factors affects these processes individually.

Spectral analysis of pair-correlation bandwidth: Application to cell biology images

Images from cell biology experiments often indicate the presence of cell clustering, which can provide insight into the mechanisms driving the collective cell behaviour. Pair-correlation functions provide quantitative information about the presence, or absence, of clustering in a spatial distribution of cells. This is because the pair-correlation function describes the ratio of the abundance of pairs of cells, separated by a particular distance, relative to a randomly distributed reference population. Pair-correlation functions are often presented as a kernel density estimate where the frequency of pairs of objects are grouped using a particular bandwidth (or bin width), Δ>0. The choice of bandwidth has a dramatic impact: choosing Δ too large produces a pair-correlation function that contains insufficient information, whereas choosing Δ too small produces a pair-correlation signal dominated by fluctuations. Presently, there is little guidance available regarding how to make an objective choice of Δ. We present a new technique to choose Δ by analysing the power spectrum of the discrete Fourier transform of the pair-correlation function. Using synthetic simulation data, we confirm that our approach allows us to objectively choose Δ such that the appropriately binned pair-correlation function captures known features in uniform and clustered synthetic images. We also apply our technique to images from two different cell biology assays. The first assay corresponds to an approximately uniform distribution of cells, while the second assay involves a time series of images of a cell population which forms aggregates over time. The appropriately binned pair-correlation function allows us to make quantitative inferences about the average aggregate size, as well as quantifying how the average aggregate size changes with time.

New genetic loci link adipose and insulin biology to body fat distribution

Body fat distribution is a heritable trait and a well-established predictor of adverse metabolic outcomes, independent of overall adiposity. To increase our understanding of the genetic basis of body fat distribution and its molecular links to cardiometabolic traits, here we conduct genome-wide association meta-analyses of traits related to waist and hip circumferences in up to 224,459 individuals. We identify 49 loci (33 new) associated with waist-to-hip ratio adjusted for body mass index (BMI), and an additional 19 loci newly associated with related waist and hip circumference measures (P < 5 × 10−8). In total, 20 of the 49 waist-to-hip ratio adjusted for BMI loci show significant sexual dimorphism, 19 of which display a stronger effect in women. The identified loci were enriched for genes expressed in adipose tissue and for putative regulatory elements in adipocytes. Pathway analyses implicated adipogenesis, angiogenesis, transcriptional regulation and insulin resistance as processes affecting fat distribution, providing insight into potential pathophysiological mechanisms.