A history of the study of solid tumour growth: The contribution of mathematical modelling

A miscellany of new strategies, experimental techniques and theoretical approaches are emerging in the ongoing battle against cancer. Nevertheless, as new, ground-breaking discoveries relating to many and diverse areas of cancer research are made, scientists often have recourse to mathematical modelling in order to elucidate and interpret these experimental findings. Indeed, experimentalists and clinicians alike are becoming increasingly aware of the possibilities afforded by mathematical modelling, recognising that current medical techniques and experimental approaches are often unable to distinguish between various possible mechanisms underlying important aspects of tumour development. This short treatise presents a concise history of the study of solid tumour growth, illustrating the development of mathematical approaches from the early decades of the twentieth century to the present time. Most importantly these mathematical investigations are interwoven with the associated experimental work, showing the crucial relationship between experimental and theoretical approaches, which together have moulded our understanding of tumour growth and contributed to current anti-cancer treatments. Thus, a selection of mathematical publications, including the influential theoretical studies by Burton, Greenspan, Liotta et al., McElwain and co-workers, Adam and Maggelakis, and Byrne and co-workers are juxtaposed with the seminal experimental findings of Gray et al. on oxygenation and radio-sensitivity, Folkman on angiogenesis, Dorie et al. on cell migration and a wide variety of other crucial discoveries. In this way the development of this field of research through the interactions of these different approaches is illuminated, demonstrating the origins of our current understanding of the disease.     

Plant growth and architectural modelling and its applications. Preface

Over the last decade, a growing number of scientists around the world have invested in research on plant growth and architectural modelling and applications (often abbreviated to plant modelling and applications, PMA). By combining physical and biological processes, spatially explicit models have shown their ability to help in understanding plant–environment interactions. This Special Issue on plant growth modelling presents new information within this topic, which are summarized in this preface. Research results for a variety of plant species growing in the field, in greenhouses and in natural environments are presented. Various models and simulation platforms are developed in this field of research, opening new features to a wider community of researchers and end users. New modelling technologies relating to the structure and function of plant shoots and root systems are explored from the cellular to the whole-plant and plant-community levels.     

Biology by numbers: mathematical modelling in developmental biology

In recent years, mathematical modelling of developmental processes has earned new respect. Not only have mathematical models been used to validate hypotheses made from experimental data, but designing and testing these models has led to testable experimental predictions. There are now impressive cases in which mathematical models have provided fresh insight into biological systems, by suggesting, for example, how connections between local interactions among system components relate to their wider biological effects. By examining three developmental processes and corresponding mathematical models, this Review addresses the potential of mathematical modelling to help understand development.     

Mathematical and computational approaches can complement experimental studies of host–pathogen interactions

In addition to traditional and novel experimental approaches to study host–pathogen interactions, mathematical and computer modelling have recently been applied to address open questions in this area. These modelling tools not only offer an additional avenue for exploring disease dynamics at multiple biological scales, but also complement and extend knowledge gained via experimental tools. In this review, we outline four examples where modelling has complemented current experimental techniques in a way that can or has already pushed our knowledge of host–pathogen dynamics forward. Two of the modelling approaches presented go hand in hand with articles in this issue exploring fluorescence resonance energy transfer and two-photon intravital microscopy. Two others explore virtual or ' in silico ' deletion and depletion as well as a new method to understand and guide studies in genetic epidemiology. In each of these examples, the complementary nature of modelling and experiment is discussed. We further note that multi-scale modelling may allow us to integrate information across length (molecular, cellular, tissue, organism, population) and time (e.g. seconds to lifetimes). In sum, when combined, these compatible approaches offer new opportunities for understanding host–pathogen interactions.     

How to understand species’ niches and range dynamics: a demographic research agenda for biogeography

Range dynamics causes mismatches between a species’ geographical distribution and the set of suitable environments in which population growth is positive (the Hutchinsonian niche). This is because source–sink population dynamics cause species to occupy unsuitable environments, and because environmental change creates non‐equilibrium situations in which species may be absent from suitable environments (due to migration limitation) or present in unsuitable environments that were previously suitable (due to time‐delayed extinction). Because correlative species distribution models do not account for these processes, they are likely to produce biased niche estimates and biased forecasts of future range dynamics. Recently developed dynamic range models (DRMs) overcome this problem: they statistically estimate both range dynamics and the underlying environmental response of demographic rates from species distribution data. This process‐based statistical approach qualitatively advances biogeographical analyses. Yet, the application of DRMs to a broad range of species and study systems requires substantial research efforts in statistical modelling, empirical data collection and ecological theory. Here we review current and potential contributions of these fields to a demographic understanding of niches and range dynamics. Our review serves to formulate a demographic research agenda that entails: (1) advances in incorporating process‐based models of demographic responses and range dynamics into a statistical framework, (2) systematic collection of data on temporal changes in distribution and abundance and on the response of demographic rates to environmental variation, and (3) improved theoretical understanding of the scaling of demographic rates and the dynamics of spatially coupled populations. This demographic research agenda is challenging but necessary for improved comprehension and quantification of niches and range dynamics. It also forms the basis for understanding how niches and range dynamics are shaped by evolutionary dynamics and biotic interactions. Ultimately, the demographic research agenda should lead to deeper integration of biogeography with empirical and theoretical ecology.     

Are all prey created equal? A review and synthesis of differential predation on prey in substandard condition

Our understanding of predator-prey interactions in fishes has been influenced largely by research assuming that the condition of the participants is normal. However, fish populations today often reside in anthropogenically altered environments and are subjected to many kinds of stressors, which may reduce their ecological performance by adversely affecting their morphology, physiology, or behaviour. One consequence is that either the predator or prey, or both, may be in a substandard condition at the time of an interaction. We reviewed the literature on predator-prey interactions in fishes where substandard prey were used as experimental groups. Although most of this research indicates that such prey are significantly more vulnerable to predation, prey condition has rarely been considered in ecological theory regarding predator-prey interactions. The causal mechanisms for increased vulnerability of substandard prey to predation include a failure to detect predators, lapses in decision-making, poor fast-start performance, inability to shoal effectively, and increased prey conspicuousness. Despite some problems associated with empirical predator-prey studies using substandard prey, their results can have theoretical and applied uses, such as in ecological modelling or justification of corrective measures to be implemented in the wild. There is a need for more corroborative field experimentation, a better understanding of the causal mechanisms behind differential predation, and increased incorporation of prey condition into the research of predator-prey modellers and theoreticians. If the concept of prey condition is considered in predator-prey interactions, our understanding of how such interactions influence the structure and dynamics of fish communities is likely to change, which should prove beneficial to aquatic ecosystems.     

Integrating demography,dispersal and interspecific interactions into bird distribution models

Species’ ranges are primarily limited by the physiological (abiotic) tolerance of the species, described by their fundamental niche. Additionally, demographic processes, dispersal, and interspecific interactions with other species are shaping species distributions, resulting in the realised niche. Understanding the complex interplay between these drivers is vital for making robust biodiversity predictions to novel environments. Correlative species distribution models have been widely used to predict biodiversity response but also remain criticised, as they are not able to properly disentangle the abiotic and biotic drivers shaping species’ niches. Recent developments have thus focussed on 1) integrating demography and dispersal into species distribution models, and on 2) integrating interspecific interactions. Here, I review recent demographic and multi‐species modelling approaches and discuss critical aspects of these models that remain underexplored in general and in respect to birds, for example, the complex life histories of birds and other animals as well as the scale dependence of interspecific interactions. I conclude by formulating modelling guidelines for integrating the abiotic and biotic processes that limit species’ ranges, which will help to disentangle the complex roles of demography, dispersal and interspecific interactions in shaping species niches. Throughout, I pinpoint complexities of avian life cycles that are critical for consideration in the models and identify data requirements for operationalizing the different modelling steps.     

靶向宿主致病菌sRNA的发现及其靶标确定的实验技术进展

人类时常暴露于充满各种致病菌的环境中,这些致病菌与人体细胞或组织之间存在多种相互作用。在相互作用的过程中,细菌通过调节自身毒性、侵袭性等致病性,以适应宿主环境并生存下来,同样,宿主细胞也会通过调动自身的免疫系统来抵抗致病菌的入侵。然而,大多数研究者主要聚焦于致病菌sRNA (small RNA, sRNA)自身生理功能的研究,致病菌与宿主相互作用的认识仍然处于起步阶段。因此,如何使用高灵敏性、高分辨率的方法研究致病菌与宿主之间的相互作用成为当前研究面临的一大难题。本文综合国内外相关研究,概述了目前研究致病菌与宿主相互作用常用的技术方法及实验流程,提高对其机制原理的理解,为致病菌sRNA-宿主靶标的相关研究提供技术参考。     

Bioinformatic strategies for better understanding of immune function

Novartis Foundation sponsored a Symposium which brought together a group of experimental immunologists, theoretical immunologists, and bioinformaticians to discuss the new field of immunoinformatics. The discussion focused on immunological databases, antigen processing and presentation, immunogenomics, host-pathogen interactions, and mathematical modelling of the immune system. A main conclusion of the meeting is the critical role played by immunoinformatics in current immunology research. In particular, immunoinformatics provides a foundation for the emerging fields of systems immunology and immunogenomics.     

Female polymorphism, frequency dependence, and rapid evolutionary dynamics in natural populations

Rapid evolutionary change over a few generations has been documented in natural populations. Such changes are observed as organisms invade new environments, and they are often triggered by changed interspecific interactions, such as differences in predation regimes. However, in spite of increased recognition of antagonistic male-female mating interactions, there is very limited evidence that such intraspecific interactions could cause rapid evolutionary dynamics in nature. This is because ecological and longitudinal data from natural populations have been lacking. Here we show that in a color-polymorphic damselfly species, male-female mating interactions lead to rapid evolutionary change in morph frequencies between generations. Field data and computer simulations indicate that these changes are driven by sexual conflict, in which morph fecundities are negatively affected by frequency- and density-dependent male mating harassment. These frequency-dependent processes prevent population divergence by maintaining a female polymorphism in most populations. Although these results contrast with the traditional view of how sexual conflict enhances the rate of population divergence, they are consistent with a recent theoretical model of how females may form discrete genetic clusters in response to male mating harassment.     

Heterogeneity in biofilms

Biofilms, accumulations of microorganisms at interfaces, have been described for every aqueous system supporting life. The structure of these microbial communities ranges from monolayers of scattered single cells to thick, mucous structures of macroscopic dimensions (microbial mats; algal-microbial associations; trickling filter biofilms). During recent years the structure of biofilms from many different environments has been documented and evaluated by use of a broad variety of microscopic, physico-chemical and molecular biological techniques, revealing a generally complex 3D structure. Parallel to these investigations more and more complex mathematical models and simulations were developed to explain the development, structures, and interactions of biofilms. The forces determining the spatial structure of biofilms, including microcolonies, extracellular polymeric substances (EPS), and channels, are still the subject of controversy. To achieve conclusive explanations for the structures observed in biofilms the cooperation of both fields of investigation, modelling and experimental research, is necessary. The expanding field of molecular techniques not only allows more and more detailed documentation of the spatial distribution of species, but also of functional activities of single cells in their biofilm environment. These new methods will certainly reveal new insights in the mechanisms involved in the developmental processes involved in the formation and behavior of biofilms.     

Clonal plants and facilitation research: bridging the gap

Over the last twenty years there has been increasing interest in facilitative plant-plant interactions. Research has examined the relationships between the role of plant interactions and gradients of environmental severity, the consequences of facilitation for biodiversity at a range of scales and the integration of facilitation into mainstream ecological theories. However, there appears to be a lack of research that explicitly links facilitation and the study of plant clonality. This is surprising given the common co-occurrence of high levels of facilitation and clonality in some systems, for example arctic and alpine environments, and the possibility for clonality to play a role in regulating facilitation processes. I propose a number of areas where there is considerable potential for bringing these two topics together, including the re-analysis of large-scale databases and multi-site experiments, the development of modelling approaches combining both facilitation and clonality and the testing of these approaches through field experimentation. I also discuss some of the studies that are starting to address this research gap, and that indicate how we might in future bring these research topics closer together.     

Moving from pattern to process: coexistence mechanisms under intermediate disturbance regimes

Coexistence mechanisms that require environmental variation to operate contribute importantly to the maintenance of biodiversity. One famous hypothesis of diversity maintenance under disturbance is the intermediate disturbance hypothesis (IDH). The IDH proposes patterns of peaked diversity under intermediate disturbance regimes, based on a tension between competitively superior species and species which can rapidly colonize following disturbance. We review the literature, and describe recent research that suggests that more than one underlying mechanism can generate this unimodal diversity pattern in disturbed environments. Several exciting emerging research areas are identified, including interactions between disturbance types, operation of the IDH in multi‐trophic systems, and changes in disturbance regimes. However, empirical work is still focussed on describing the IDH pattern, with little emphasis on identifying its mechanistic basis. We discuss how to extend methods for identifying different coexistence mechanisms, developed in the theoretical literature, to experimental research. In an attempt to operationalize these various ideas we outline a hypothetical IDH research programme. A solid understanding of the life history attributes of the component species and their responses to disturbance will facilitate identification of the coexistence mechanism(s) underlying the IDH pattern, and provide a framework by which empirical and theoretical results can be more fully integrated.     

On the use of advanced modelling techniques to investigate the conformational discrepancy between two X-ray structures of the AppA BLUF domain

The conformation of the blue light utilising flavin domain of the signalling protein AppA in the dark state is a matter of intensive research, both experimental and theoretical, and has not yet unambiguously been determined. Two contradicting X-ray structures of the dark state have been published previously. We aim at resolving this seeming contradiction by exploring conformational pathways between the two X-ray structures using advanced modelling techniques, such as local-elevation searching and sampling, soft-core non-bonded interactions and protocols of successively biasing the sampling of sets of torsional angles which adopt different values in the two alternative X-ray structures. The results suggest a high energetic barrier for a change in the Trp104 side chain from a ‘Trp-in’ to a ‘Trp-out’ conformation or vice versa, and illustrate the complexity to model conformational transitions involving a large number of degrees of freedom.     

Competition among plants: Concepts, individual-based modelling approaches, and a proposal for a future research strategy

Competition is a key process in plant populations and communities. We thus need, if we are to predict the responses of ecological systems to environmental change, a comprehensive and mechanistic understanding of plant competition. Considering competition, however, only at the population level is not sufficient because plant individuals usually are different, interact locally, and can adapt their behaviour to the current state of themselves and of their biotic and abiotic environment. Therefore, simulation models that are individual-based and spatially explicit are increasingly used for studying competition in plant systems. Many different individual-based modelling approaches exist to represent competition, but it is not clear how good they are in reflecting essential aspects of plant competition. We therefore first summarize current concepts and theories addressing plant competition. Then, we review individual-based approaches for modelling competition among plants. We distinguish between approaches that are used for more than 10 years and more recent ones. We identify three major gaps that need to be addressed more in the future: the effects of plants on their local environment, adaptive behaviour, and below-ground competition. To fill these gaps, the representation of plants and their interactions have to be more mechanistic than most existing approaches. Developing such new approaches is a challenge because they are likely to be more complex and to require more detailed knowledge and data on individual-level processes underlying competition. We thus need a more integrated research strategy for the future, where empirical and theoretical ecologists as well as computer scientists work together on formulating, implementing, parameterization, testing, comparing, and selecting the new approaches.     

The intercalation of imidazoacridinones into DNA induces conformational changes in their side chain

Imidazoacridinones (IAs) are a new group of highly active antitumor compounds. The intercalation of the IA molecule into DNA is the preliminary step in the mode of action of these compounds. There are no experimental data about the structure of an intercalation complex formed by imidazoacridinones. Therefore the design of new potentially better compounds of this group should employ the molecular modelling techniques. The results of molecular dynamics simulations performed for four IA analogues are presented. Each of the compounds was studied in two systems: i) in water, and ii) in the intercalation complex with dodecamer duplex d(GCGCGCGCGCGC)2. Significant differences in the conformation of the side chain in the two environments were observed for all studied IAs. These changes were induced by electrostatic as well as van der Waals interactions between the intercalator and DNA. Moreover, the results showed that the geometry of the intercalation complex depends on: i) the chemical constitution of the side chain, and ii) the substituent in position 8 of the ring system.     

Plant functional types and disturbance dynamics – Introduction

Abstract. Plant functional traits and types are useful concepts in relation to disturbance responses of natural and managed ecosystems. To explore their applicability in greater depth, a set of 12 papers presents a broad range of issues from methodologies to the results of particular trait studies in the field, and modelling approaches. So far, empirical studies have only allowed us to identify a few functional traits that are consistently associated with disturbance. To determine the trait variations associated with climate, disturbance history and current disturbance regime as well as the interactions between these factors, global-scale comparisons of numerous individual studies are required. Significant advances toward this ambitious goal are presented in these papers, and include: (1) the articulation of experimental and analytical methodologies for individual studies that could usefully contribute to a global comparison; (2) the identification of core traits that can be used in the further search for disturbance-related traits common to a range of environments; (3) further information on vegetation response to disturbance in terms of trait representation, and the identification of attribute syndromes; (4) the identification of issues for modelling disturbance dynamics using functional types.