On the inference of function from structure using biomechanical modelling and simulation of extinct organisms

Biomechanical modelling and simulation techniques offer some hope for unravelling the complex inter-relationships of structure and function perhaps even for extinct organisms, but have their limitations owing to this complexity and the many unknown parameters for fossil taxa. Validation and sensitivity analysis are two indispensable approaches for quantifying the accuracy and reliability of such models or simulations. But there are other subtleties in biomechanical modelling that include investigator judgements about the level of simplicity versus complexity in model design or how uncertainty and subjectivity are dealt with. Furthermore, investigator attitudes toward models encompass a broad spectrum between extreme credulity and nihilism, influencing how modelling is conducted and perceived. Fundamentally, more data and more testing of methodology are required for the field to mature and build confidence in its inferences.     

Homology modelling and spectroscopy, a never-ending love story

Homology modelling is normally the technique of choice when experimental structure data are not available but three-dimensional coordinates are needed, for example, to aid with detailed interpretation of results of spectroscopic studies. Herein, the state of the art of homology modelling will be described in the light of a series of recent developments, and an overview will be given of the problems and opportunities encountered in this field. The major topic, the accuracy and precision of homology models, will be discussed extensively due to its influence on the reliability of conclusions drawn from the combination of homology models and spectroscopic data. Three real-world examples will illustrate how both homology modelling and spectroscopy can be beneficial for (bio)medical research.     

Bridging from molecular simulation to biochemical networks

How can we make the connection between the three-dimensional structures of individual proteins and understanding how complex biological systems involving many proteins work? The modelling and simulation of protein structures can help to answer this question for systems ranging from multimacromolecular complexes to organelles and cells. On one hand, multiscale modelling and simulation techniques are advancing to permit the spatial and temporal properties of large systems to be simulated using atomic-detail structures. On the other hand, the estimation of kinetic parameters for the mathematical modelling of biochemical pathways using protein structure information provides a basis for iterative manipulation of biochemical pathways guided by protein structure. Recent advances include the structural modelling of protein complexes on the genomic level, novel coarse-graining strategies to increase the size of the system and the time span that can be simulated, and comparative molecular field analyses to estimate enzyme kinetic parameters.     

Mathematical modelling of the cellular mechanics of plants

The complex mechanical behaviour of plant tissues reflects the complexity of their structure and material properties. Modelling has been widely used in studies of how cell walls, single cells and tissue respond to loading, both externally applied loading and loads on the cell wall resulting from changes in the pressure within fluid-filled cells. This paper reviews what approaches have been taken to modelling and simulation of cell wall, cell and tissue mechanics, and to what extent models have been successful in predicting mechanical behaviour. Advances in understanding of cell wall ultrastructure and the control of cell growth present opportunities for modelling to clarify how growth-related mechanical properties arise from wall polymeric structure and biochemistry.     

Modelling the past: new generation approaches to understanding biological patterns in the fossil record

The history of life on this planet is gleaned from analysing how fossils are distributed through time and space. While these patterns are now rather securely known, at least for well-studied parts of the world, their interpretation remains far from simple. Fossils preserve only partial data from which to reconstruct their biology and the geological record is incomplete and biased, so that taxonomic ranges and palaeocommunity structure are imperfectly known. To better understand the often highly complex deep-time processes that gave rise to the empirical fossil record, palaeontologists have turned to modelling the past. Here, we summarize a series of 11 papers that showcase where modelling the past is being applied to advance our understanding across a wide spectrum of current palaeontological endeavours.     

Ecological time-series analysis through structural modelling with latent constructs: concepts, methods and applications

Time-series analyses in ecology usually involve the use of autoregressive modelling through direct and/or delayed difference equations, which severely restricts the ability of the modeler to structure complex causal relationships within a multivariate frame. This is especially problematic in the field of population regulation, where the proximate and ultimate causes of fluctuations in population size have been hotly debated for decades. Here it is shown that this debate can benefit from the implementation of structural modelling with latent constructs (SEM) to time-series analysis in ecology. A nonparametric bootstrap scheme illustrates how this modelling approach can circumvent some problems posed by the climate-ecology interface. Stochastic Monte Carlo simulation is further used to assess the effects of increasing time-series length and different parameter estimation methods on the performance of several model fit indexes. Throughout, the advantages and limitations of the SEM method are highlighted.     

Protein motifs and data-base searching

Protein structure and sequence motifs are now recognized for many different protein families and topologies. To aid identification and use of these motifs in modelling and prediction, it has become necessary to establish consistent data bases of protein structure, including not only coordinates, but also derived data such as secondary structure location and solvent accessibilities. This article describes first attempts to construct such data bases and explains how they can be used.     

An investigation into effects of long-distance seed dispersal on organelle population genetic structure and colonization rate: a model analysis

A simulation-based modelling approach is used to examine the effects of stratified seed dispersal (representing the distribution of the majority of dispersal around the maternal parent and also rare long-distance dispersal) on the genetic structure of maternally inherited genomes and the colonization rate of expanding plant populations. The model is parameterized to approximate postglacial oak colonization in the UK, but is relevant to plant populations that exhibit stratified seed dispersal. The modelling approach considers the colonization of individual plants over a large area (three 500 km x 10 km rolled transects are used to approximate a 500 km x 300 km area). Our approach shows how the interaction of plant population dynamics with stratified dispersal can result in a spatially patchy haplotype structure. We show that while both colonization speeds and the resulting genetic structure are influenced by the characteristics of the dispersal kernel, they are robust to changes in the periodicity of long-distance events, provided the average number of long-distance dispersal events remains constant. We also consider the effects of additional physical and environmental mechanisms on plant colonization. Results show significant changes in genetic structure when the initial colonization of different haplotypes is staggered over time and when a barrier to colonization is introduced. Environmental influences on survivorship and fecundity affect both the genetic structure and the speed of colonization. The importance of these mechanisms in relation to the postglacial spread and genetic structure of oak in the UK is discussed.     

Dynamics on the manifold: Identifying computational dynamical activity from neural population recordings

The question of how the collective activity of neural populations gives rise to complex behaviour is fundamental to neuroscience. At the core of this question lie considerations about how neural circuits can perform computations that enable sensory perception, decision making, and motor control. It is thought that such computations are implemented through the dynamical evolution of distributed activity in recurrent circuits. Thus, identifying dynamical structure in neural population activity is a key challenge towards a better understanding of neural computation. At the same time, interpreting this structure in light of the computation of interest is essential for linking the time-varying activity patterns of the neural population to ongoing computational processes. Here, we review methods that aim to quantify structure in neural population recordings through a dynamical system defined in a low-dimensional latent variable space. We discuss advantages and limitations of different modelling approaches and address future challenges for the field.     

Application of the finite-element method to simulation of damage to the human skull as a consequence of missile impact on a multi-layered composite crash helmet

Finite-element analysis is a powerful technique which could be applicable to the study of a wide range of circumstances where the frame and/or the vital organs of the body are subjected to extreme loading conditions. This paper reports the results of an exploratory investigation in which the performance of a crash helmet in protecting the skull from an impacting load is modelled. The immediate objective is to show how a typical crash helmet design of glass-reinforced plastic (GRP) outer casing with quasi-foam-like liner can, with a suitable choice of material properties, attenuate the transfer of energy from the impacting mass such that the damage intensity to the skull is minimized. A simplified structure for both helmet and skull shape is adopted and the skull is modelled as being supported on an elastic foundation. The material properties used are representative rather than being accurately matched to experimentally determined ones. Several aspects of the modelling technique are worthy of particular note: the simulation of material anisotropy by means of multiple reinforcement layers with varying orientation, the use of dashpot elements for energy attenuation and the incorpotation of multipoint constraint between the skull and the helmet lining to ensure integrity of the model with correct stiffness matrix values and allowing independent monitoring of all stress levels at the mating interface region. The results of the modelling show that the specific limited objectives can be met but also indicate how vitally important information could be obtained from similar but more detailed studies which included representative modelling of the body organs and skeleton.     

Infectious disease transmission and contact networks in wildlife and livestock

The use of social and contact networks to answer basic and applied questions about infectious disease transmission in wildlife and livestock is receiving increased attention. Through social network analysis, we understand that wild animal and livestock populations, including farmed fish and poultry, often have a heterogeneous contact structure owing to social structure or trade networks. Network modelling is a flexible tool used to capture the heterogeneous contacts of a population in order to test hypotheses about the mechanisms of disease transmission, simulate and predict disease spread, and test disease control strategies. This review highlights how to use animal contact data, including social networks, for network modelling, and emphasizes that researchers should have a pathogen of interest in mind before collecting or using contact data. This paper describes the rising popularity of network approaches for understanding transmission dynamics in wild animal and livestock populations; discusses the common mismatch between contact networks as measured in animal behaviour and relevant parasites to match those networks; and highlights knowledge gaps in how to collect and analyse contact data. Opportunities for the future include increased attention to experiments, pathogen genetic markers and novel computational tools.     

How to make predictions about future infectious disease risks

Formal, quantitative approaches are now widely used to make predictions about the likelihood of an infectious disease outbreak, how the disease will spread, and how to control it. Several well-established methodologies are available, including risk factor analysis, risk modelling and dynamic modelling. Even so, predictive modelling is very much the 'art of the possible', which tends to drive research effort towards some areas and away from others which may be at least as important. Building on the undoubted success of quantitative modelling of the epidemiology and control of human and animal diseases such as AIDS, influenza, foot-and-mouth disease and BSE, attention needs to be paid to developing a more holistic framework that captures the role of the underlying drivers of disease risks, from demography and behaviour to land use and climate change. At the same time, there is still considerable room for improvement in how quantitative analyses and their outputs are communicated to policy makers and other stakeholders. A starting point would be generally accepted guidelines for 'good practice' for the development and the use of predictive models.     

Power-law models of signal transduction pathways

The mathematical modelling of signal transduction pathways has become a valuable aid to understanding the complex interactions involved in intracellular signalling mechanisms. An important aspect of the mathematical modelling process is the selection of the model type and structure. Until recently, the convention has been to use a standard kinetic model, often with the Michaelis-Menten steady state assumption. However this model form, although valuable, is only one of a number of choices, and the aim of this article is to consider the mathematical structure and essential features of an alternative model form--the power-law model. Specifically, we analyse how power-law models can be applied to increase our understanding of signal transduction pathways when there may be limited prior information. We distinguish between two kinds of power law models: a) Detailed power-law models, as a tool for investigating pathways when the structure of protein-protein interactions is completely known, and; b) Simplified power-law models, for the analysis of systems with incomplete structural information or insufficient quantitative data for generating detailed models. If sufficient data of high quality are available, the advantage of detailed power-law models is that they are more realistic representations of non-homogenous or crowded cellular environments. The advantages of the simplified power-law model formulation are illustrated using some case studies in cell signalling. In particular, the investigation on the effects of signal inhibition and feedback loops and the validation of structural hypotheses are discussed.     

A mathematical and statistical framework for modelling dispersal

Mechanistic and phenomenological dispersal modelling of organisms has long been an area of intensive research. Recently, there has been an increased interest in intermediate models between the two. Intermediate models include major mechanisms that affect dispersal, in addition to the dispersal curve of a phenomenological model. Here we review and describe the mathematical and statistical framework for phenomenological dispersal modelling. In the mathematical development we describe modelling of dispersal in two dimensions from a point source, and in one dimension from a line or area source. In the statistical development we describe applicable observation distributions, and the procedures of model fitting, comparison, checking, and prediction. The procedures are also demonstrated using data from dispersal experiments. The data are hierarchically structured, and hence, we fit hierarchical models. The Bayesian modelling approach is applied, which allows us to show the uncertainty in the parameter estimates and in predictions. Finally, we show how to account for the effect of wind speed on the estimates of the dispersal parameters. This serves as an example of how to strengthen the coupling in the modelling between the phenomenon observed in an experiment and the underlying process – something that should be striven for in the statistical modelling of dispersal.     

Network modelling of gene regulation

Gene regulatory network (GRN) modelling has gained increasing attention in the past decade. Many computational modelling techniques have been proposed to facilitate the inference and analysis of GRN. However, there is often confusion about the aim of GRN modelling, and how a gene network model can be fully utilised as a tool for systems biology. The aim of the present article is to provide an overview of this rapidly expanding subject. In particular, we review some fundamental concepts of systems biology and discuss the role of network modelling in understanding complex biological systems. Several commonly used network modelling paradigms are surveyed with emphasis on their practical use in systems biology research.     

Landscape simplification shapes pathogen prevalence in plant‐pollinator networks

Species interaction networks, which play an important role in determining pathogen transmission and spread in ecological communities, can shift in response to agricultural landscape simplification. However, we know surprisingly little about how landscape simplification‐driven changes in network structure impact epidemiological patterns. Here, we combine mathematical modelling and data from eleven bipartite plant‐pollinator networks observed along a landscape simplification gradient to elucidate how changes in network structure shape disease dynamics. Our empirical data show that landscape simplification reduces pathogen prevalence in bee communities via increased diet breadth of the dominant species. Furthermore, our empirical data and theoretical model indicate that increased connectance reduces the likelihood of a disease outbreak and decreases variance in prevalence among bee species in the community, resulting in a dilution effect. Because infectious diseases are implicated in pollinator declines worldwide, a better understanding of how land use change impacts species interactions is therefore critical for conserving pollinator health.     

The SWISS-MODEL workspace: a web-based environment for protein structure homology modelling

MOTIVATION: Homology models of proteins are of great interest for planning and analysing biological experiments when no experimental three-dimensional structures are available. Building homology models requires specialized programs and up-to-date sequence and structural databases. Integrating all required tools, programs and databases into a single web-based workspace facilitates access to homology modelling from a computer with web connection without the need of downloading and installing large program packages and databases. RESULTS: SWISS-MODEL workspace is a web-based integrated service dedicated to protein structure homology modelling. It assists and guides the user in building protein homology models at different levels of complexity. A personal working environment is provided for each user where several modelling projects can be carried out in parallel. Protein sequence and structure databases necessary for modelling are accessible from the workspace and are updated in regular intervals. Tools for template selection, model building and structure quality evaluation can be invoked from within the workspace. Workflow and usage of the workspace are illustrated by modelling human Cyclin A1 and human Transmembrane Protease 3. AVAILABILITY: The SWISS-MODEL workspace can be accessed freely at http://swissmodel.expasy.org/workspace/     

How molecular modelling can better broaden the understanding of glycosylations

Glycosylations are among the most ubiquitous post-translational modifications (PTMs) in proteins, and the effects of their perturbations are seen in various diseases such as cancers, diabetes and arthritis to name a few. Yet they remain one of the most enigmatic aspects of protein structure and function. On the other hand, molecular modelling techniques have been rapidly bridging this knowledge gap since the last decade. In this review, we discuss how these techniques have proven to be indispensable for a better understanding of the role of glycosylations in glycoprotein structure and function.     

Collective variable modelling of nucleic acids.

Collective variable models continue to contribute to our knowledge of nucleic acids. The past year has seen considerable progress both in modelling sequence-dependent effects on nucleic acid conformation and in understanding how proteins or external stresses influence nucleic acid structure. Algorithmic developments have also allowed collective models to be applied to studies of thermal fluctuations and dynamics. For larger systems, models with varying degrees of resolution are being refined and applied to nucleic acids containing hundreds or thousands of nucleotides.     

Testing causal structure in the biogeography of avian extinctions on oceanic islands

In their recent comment in this journal, T. M. Blackburn and colleagues called into question the use of standardized partial regression modelling (also called path analysis and structural equation modelling) when null expectations for regression coefficients are not zero. Here, we answer their critique by showing how randomization can be used to illuminate and interpret causal modelling in analyses that have non-zero expectations. Causal modelling is a powerful tool that can yield novel insights in biogeography when properly interpreted.