Sleep in people with and without intellectual disabilities: a systematic review and meta-analysis

BACKGROUND

Sleep problems are regularly reported in people with intellectual disabilities. Recent years have seen a substantial increase in studies comparing sleep in people with intellectual disabilities to control participants, with an increase in the use of validated, objective measures. Emerging patterns of differences in sleep time and sleep quality warrant pooled investigation.

METHODS

A systematic search was conducted across three databases (Ovid Embase, PsycInfo and Medline) and returned all papers comparing sleep in people with intellectual disabilities to a control group, published since the last meta-analysis on the topic. A quality framework was employed to rate the risk of bias across studies. Separate meta-analyses of sleep duration and sleep quality were conducted. Subgrouping compared findings for those studies with participants with genetic syndromes or neurodevelopmental conditions and those with heterogeneous intellectual disability.

RESULTS

Thirteen new papers were identified and combined with those from the previous meta-analysis to provide 34 papers in total. Quality of studies was generally rated highly, though sampling provided risk of bias and adaptive functioning was rarely measured. People with intellectual disability associated with genetic syndromes or neurodevelopmental conditions sleep for shorter time periods (standardised mean difference = .26) and experience worse sleep quality (standardised mean difference = .68) than their peers. People with intellectual disability of heterogeneous origin show no difference in sleep time but have poorer sleep quality. There was some evidence that age moderated these effects.

CONCLUSIONS

People with intellectual disability have poorer sleep than those without. Subtle patterns suggest that aetiology of intellectual disability moderates the topography of these difficulties, with further work needed to differentiate common and distinct mechanisms across groups.

Fiber reinforced hydrated networks recapitulate the poroelastic mechanics of articular cartilage

The role of poroelasticity on the functional performance of articular cartilage has been established in the scientific literature since the 1960s. Despite the extensive knowledge on this topic there remain few attempts to design for poroelasticity and to our knowledge no demonstration of an engineered poroelastic material that approaches the physiological performance. In this paper, we report on the development of an engineered material that begins to approach physiological poroelasticity. We quantify poroelasticity using the fluid load fraction, apply mixture theory to model the material system, and determine cytocompatibility using primary human mesenchymal stem cells. The design approach is based on a fiber reinforced hydrated network and uses routine fabrication methods (electrohydrodynamic deposition) and materials (poly[ɛ-caprolactone] and gelatin) to develop the engineered poroelastic material. This composite material achieved a mean peak fluid load fraction of 68%, displayed consistency with mixture theory, and demonstrated cytocompatibility. This work creates a foundation for designing poroelastic cartilage implants and developing scaffold systems to study chondrocyte mechanobiology and tissue engineering. STATEMENT OF SIGNIFICANCE: Poroelasticity drives the functional mechanics of articular cartilage (load bearing and lubrication). In this work we develop the design rationale and approach to produce a poroelastic material, known as a fiber reinforced hydrated network (FiHy™), that begins to approach the native performance of articular cartilage. This is the first engineered material system capable of exceeding isotropic linear poroelastic theory. The framework developed here enables fundamental studies of poroelasticity and the development of translational materials for cartilage repair.

Distribution of the Red Imported Fire Ant Solenopsis invicta (Hymenoptera: Formicidae) in Central Florida Pastures

Habitat disturbance has been found to facilitate the introduction of a wide range of species, including the red imported fire ant Solenopsis invicta Buren (Hymenoptera: Formicidae: Myrmicinae). Despite the link between S. invicta colonization and disturbance, little is known about how different intensities or types of disturbance might impact S. invicta populations. In this study, we used S. invicta populations in cattle pastures to understand how variation in disturbance type and frequency correlates with the density of S. invicta mounds. In total, 56 plots were surveyed for mound abundance during both the wet and dry seasons on a subtropical south Florida ranch. Explanatory variables were grouped into five categories based on disturbance type: 1) historic pasture conversion; 2) modern pasture management (mowing, dragging, chopping, or aerating); 3) grazing intensity (a measure vegetation height and dung pat abundance); 4) distance to human-made and natural localized disturbance (roads, ditches, and wetlands); and 5) abiotic conditions (soil temperature, soil moisture). Overall, the average number of mounds per plot was not significantly different between seasons, but was significantly higher in intensive pastures, which are converted to nonnative forage grasses than in seminative pastures during the dry season. Time since soil disturbance (aeration and chopping of pasture) was a significant predictor of S. invicta densities in both dry and wet seasons, with an increase in time since disturbance being associated with higher mound densities. Other forms of pasture management that did not disturb the soil, such as dragging and mowing, as well as distance to localized disturbances (wetlands, roads, and ditches) were not found to have a significant correlation in either season.

Mathematical modelling of contact dermatitis from nickel and chromium

Dermal exposure to metal allergens can lead to irritant and allergic contact dermatitis (ACD). In this paper we present a mathematical model of the absorption of metal ions, hexavalent chromium and nickel, into the viable epidermis and compare the localised irritant and T-lymphocyte (T-cell) mediated immune responses. The model accounts for the spatial-temporal variation of skin health, extra and intracellular allergen concentrations, innate immune cells, T-cells, cytokine signalling and lymph node activity up to about 6 days after contact with these metals; repair processes associated with withdrawal of exposure to both metals is not considered in the current model, being assumed secondary during the initial phases of exposure. Simulations of the resulting system of PDEs are studied in one-dimension, i.e. across skin depth, and three-dimensional scenarios with the aim of comparing the responses to the two ions in the cases of first contact (no T-cells initially present) and second contact (T-cells initially present). The results show that on continuous contact, chromium ions elicit stronger skin inflammation, but for nickel, subsequent re-exposure stimulates stronger responses due to an accumulation of cytotoxic T-cell mediated responses which characterise ACD. Furthermore, the surface area of contact to these metals has little effect on the speed of response, whilst sensitivity is predicted to increase with the thickness of skin. The modelling approach is generic and should be applicable to describe contact dermatitis from a wide range of allergens.

Single-trial detection of event-related fields in MEG from the presentation of happy faces: Results of the Biomag 2016 data challenge

The recognition of brain evoked responses at the single-trial level is a challenging task. Typical non-invasive brain-computer interfaces based on event-related brain responses use eletroencephalograhy. In this study, we consider brain signals recorded with magnetoencephalography (MEG), and we expect to take advantage of the high spatial and temporal resolution for the detection of targets in a series of images. This study was used for the data analysis competition held in the 20th International Conference on Biomagnetism (Biomag) 2016, wherein the goal was to provide a method for single-trial detection of even-related fields corresponding to the presentation of happy faces during the rapid presentation of images of faces with six different facial expressions (anger, disgust, fear, neutrality, sadness, and happiness). The datasets correspond to 204 gradiometers signals obtained from four participants. The best method is based on the combination of several approaches, and mainly based on Riemannian geometry, and it provided an area under the ROC curve of 0.956±0.043. The results show that a high recognition rate of facial expressions can be obtained at the signal-trial level using advanced signal processing and machine learning methodologies.

Finite indentation of highly curved elastic shells

Experimentally measuring the elastic properties of thin biological surfaces is non-trivial, particularly when they are curved. One technique that may be used is the indentation of a thin sheet of material by a rigid indenter, while measuring the applied force and displacement. This gives immediate information on the fracture strength of the material (from the force required to puncture), but it is also theoretically possible to determine the elastic properties by comparing the resulting force–displacement curves with a mathematical model. Existing mathematical studies generally assume that the elastic surface is initially flat, which is often not the case for biological membranes. We previously outlined a theory for the indentation of curved isotropic, incompressible, hyperelastic membranes (with no bending stiffness) which breaks down for highly curved surfaces, as the entire membrane becomes wrinkled. Here, we introduce the effect of bending stiffness, ensuring that energy is required to change the shell shape without stretching, and find that commonly neglected terms in the shell equilibrium equation must be included. The theory presented here allows for the estimation of shape- and size-independent elastic properties of highly curved surfaces via indentation experiments, and is particularly relevant for biological surfaces.

Delayed response to abnormal lithium results is no longer necessary

A survey of one year's lithium results for a hearth district of 170 000 disclosed unacceptable delays in checking abnormally high values. Only 17% of moderately elevated levels were rechecked within a week. The problem was most marked with patients monitored in general practice, but one particularly high result in a patient monitored in psychiatric out-patients remained unchecked for over three weeks as a result of poor communication between general practitioner and psychiatrist. A trial of an on-the-spot monitoring service using new technology has simplified procedures and reduced to zero the number of results taking over a week to check.

Instant lithium monitoring

Lithium therapy for affective disorders has been estimated to result in savings of hospital beds in the National Health Service of £23 million each year. In order to maintain and justify this saving we must invest to provide careful monitoring of serum lithium concentrations in patients living in the community. In recent years the advent of lithium clinics has done much to improve the compliance and safety of lithium therapy (Masterton et al, 1988), but we believe that there may be scope for further improvement both in the service to the patient and in encouragement of the patient to comply.

A mathematical model of the human metabolic system and metabolic flexibility

In healthy subjects some tissues in the human body display metabolic flexibility, by this we mean the ability for the tissue to switch its fuel source between predominantly carbohydrates in the postprandial state and predominantly fats in the fasted state. Many of the pathways involved with human metabolism are controlled by insulin and insulin-resistant states such as obesity and type-2 diabetes are characterised by a loss or impairment of metabolic flexibility. In this paper we derive a system of 12 first-order coupled differential equations that describe the transport between and storage in different tissues of the human body. We find steady state solutions to these equations and use these results to nondimensionalise the model. We then solve the model numerically to simulate a healthy balanced meal and a high fat meal and we discuss and compare these results. Our numerical results show good agreement with experimental data where we have data available to us and the results show behaviour that agrees with intuition where we currently have no data with which to compare.

The resolution of inflammation: a mathematical model of neutrophil and macrophage interactions

There is growing interest in inflammation due to its involvement in many diverse medical conditions, including Alzheimer's disease, cancer, arthritis and asthma. The traditional view that resolution of inflammation is a passive process is now being superceded by an alternative hypothesis whereby its resolution is an active, anti-inflammatory process that can be manipulated therapeutically. This shift in mindset has stimulated a resurgence of interest in the biological mechanisms by which inflammation resolves. The anti-inflammatory processes central to the resolution of inflammation revolve around macrophages and are closely related to pro-inflammatory processes mediated by neutrophils and their ability to damage healthy tissue. We develop a spatially averaged model of inflammation centring on its resolution, accounting for populations of neutrophils and macrophages and incorporating both pro- and anti-inflammatory processes. Our ordinary differential equation model exhibits two outcomes that we relate to healthy and unhealthy states. We use bifurcation analysis to investigate how variation in the system parameters affects its outcome. We find that therapeutic manipulation of the rate of macrophage phagocytosis can aid in resolving inflammation but success is critically dependent on the rate of neutrophil apoptosis. Indeed our model predicts that an effective treatment protocol would take a dual approach, targeting macrophage phagocytosis alongside neutrophil apoptosis.

Two different network topologies yield bistability in models of mesoderm and anterior mesendoderm specification in amphibians

Understanding the Gene Regulatory Networks (GRNs) that underlie development is a major question for systems biology. The establishment of the germ layers is amongst the earliest events of development and has been characterised in numerous model systems. The establishment of the mesoderm is best characterised in the frog Xenopus laevis and has been well studied both experimentally and mathematically. However, the Xenopus network has significant differences from that in mouse and humans, including the presence of multiple copies of two key genes in the network, Mix and Nodal. The axolotl, a urodele amphibian, provides a model with all the benefits of amphibian embryology but crucially only a single Mix and Nodal gene required for the specification of the mesoderm. Remarkably, the number of genes within the network is not the only difference. The interaction between Mix and Brachyury, two transcription factors involved in the establishment of the endoderm and mesoderm respectively, is not conserved. While Mix represses Brachyury in Xenopus, it activates Brachyury in axolotl. Thus, whilst the topology of the networks in the two species differs, both are able to form mesoderm and endoderm in vivo. Based on current knowledge of the structure of the mesendoderm GRN we develop deterministic models that describe the time evolution of transcription factors in a single axolotl cell and compare numerical simulations with previous results from Xenopus. The models are shown to have stable steady states corresponding to mesoderm and anterior mesendoderm, with the in vitro model showing how the concentration of Activin can determine cell fate, while the in vivo model shows that β-catenin concentration can determine cell fate. Moreover, our analysis suggests that additional components must be important in the axolotl network in the specification of the full range of tissues.

•

We present models of mesendoderm specification in the urodele amphibian, the axolotl.

•

in vitro and in vivo models are simulated and compared with experimental data.

•

The model topology differs from that of the anuran amphibian, Xenopus laevis.

•

Steady states representing mesoderm and anterior mesendoderm are found in both models.

•

Both the axolotl and Xenopus topologies can account for similar qualitative data.

Buckling of a growing tissue and the emergence of two-dimensional patterns

•

We model the growth of gut epithelial cells cultured upon a deformable substrate.

•

Growth generates buckling instabilities, contributing to crypt formation in vivo.

•

Variations in mechanical properties have little effect on resulting configurations.

•

Configurations are controlled by growth patterns & interactions with strata below.

The process of biological growth and the associated generation of residual stress has previously been considered as a driving mechanism for tissue buckling and pattern selection in numerous areas of biology. Here, we develop a two-dimensional thin plate theory to simulate the growth of cultured intestinal epithelial cells on a deformable substrate, with the goal of elucidating how a tissue engineer might best recreate the regular array of invaginations (crypts of Lieberkühn) found in the wall of the mammalian intestine. We extend the standard von Kármán equations to incorporate inhomogeneity in the plate’s mechanical properties and surface stresses applied to the substrate by cell proliferation. We determine numerically the configurations of a homogeneous plate under uniform cell growth, and show how tethering to an underlying elastic foundation can be used to promote higher-order buckled configurations. We then examine the independent effects of localised softening of the substrate and spatial patterning of cellular growth, demonstrating that (within a two-dimensional framework, and contrary to the predictions of one-dimensional models) growth patterning constitutes a more viable mechanism for control of crypt distribution than does material inhomogeneity.

Single-trial decoding of auditory novelty responses facilitates the detection of residual consciousness

Detecting residual consciousness in unresponsive patients is a major clinical concern and a challenge for theoretical neuroscience. To tackle this issue, we recently designed a paradigm that dissociates two electro-encephalographic (EEG) responses to auditory novelty. Whereas a local change in pitch automatically elicits a mismatch negativity (MMN), a change in global sound sequence leads to a late P300b response. The latter component is thought to be present only when subjects consciously perceive the global novelty. Unfortunately, it can be difficult to detect because individual variability is high, especially in clinical recordings. Here, we show that multivariate pattern classifiers can extract subject-specific EEG patterns and predict single-trial local or global novelty responses. We first validate our method with 38 high-density EEG, MEG and intracranial EEG recordings. We empirically demonstrate that our approach circumvents the issues associated with multiple comparisons and individual variability while improving the statistics. Moreover, we confirm in control subjects that local responses are robust to distraction whereas global responses depend on attention. We then investigate 104 vegetative state (VS), minimally conscious state (MCS) and conscious state (CS) patients recorded with high-density EEG. For the local response, the proportion of significant decoding scores (M=60%) does not vary with the state of consciousness. By contrast, for the global response, only 14% of the VS patients' EEG recordings presented a significant effect, compared to 31% in MCS patients' and 52% in CS patients'. In conclusion, single-trial multivariate decoding of novelty responses provides valuable information in non-communicating patients and paves the way towards real-time monitoring of the state of consciousness.

Modelling auxin efflux carrier phosphorylation and localization

Regulation of the activity and localization of PIN-FORMED (PIN) membrane proteins, which facilitate efflux of the plant hormone auxin from cells, is important for plants to respond to environmental stimuli and to develop new organs. The protein kinase PINOID (PID) is involved in regulating PIN phosphorylation, and this is thought to affect PIN localization by biasing recycling towards shootwards (apical) (rather than rootwards (basal)) membrane domains. PID has been observed to undergo transient internalization following auxin treatment, and it has been suggested that this may be a result of calcium-dependent sequestration of PID by the calcium-binding protein TOUCH3 (TCH3). We present a mathematical formulation of these processes and examine the resulting steady-state and time-dependent behaviours in response to transient increases in cytosolic calcium. We further combine this model with one for the recycling of PINs in polarized cells and also examine its behaviour. The results provide insight into the behaviour observed experimentally and provide the basis for subsequent studies of the tissue-level implications of these subcellular processes for phenomena such as gravitropism.

Wave pinning and spatial patterning in a mathematical model of Antivin/Lefty-Nodal signalling

Nodal signals are key regulators of mesoderm and endoderm development in vertebrate embryos. It has been observed experimentally that in Xenopus embryos the spatial range of Nodal signals is restricted by the signal Antivin (also known as Lefty). Nodal signals can activate both Nodal and Antivin, whereas Antivin is thought to antagonise Nodal by binding either directly to it or to its receptor. In this paper we develop a mathematical model of this signalling network in a line of cells. We consider the heterodimer and receptor-mediated inhibition mechanisms separately and find that, in both cases, the restriction by Antivin to the range of Nodal signals corresponds to wave pinning in the model. Our analysis indicates that, provided Antivin diffuses faster than Nodal, either mechanism can robustly account for the experimental data. We argue that, in the case of Xenopus development, it is wave pinning, rather than Turing-type patterning, that is underlying Nodal-Antivin dynamics. This leads to several experimentally testable predictions, which are discussed. Furthermore, for heterodimer-mediated inhibition to prevent waves of Nodal expression from propagating, the Nodal-Antivin complex must be turned over, and diffusivity of the complex must be negligible. In the absence of molecular mechanisms regulating these, we suggest that Antivin restricts Nodal signals via receptor-mediated, and not heterodimer-mediated, inhibition.

Multiple travelling-wave solutions in a minimal model for cell motility

Two-phase flow models have been used previously to model cell motility. In order to reduce the complexity inherent with describing the many physical processes, we formulate a minimal model. Here we demonstrate that even the simplest 1D, two-phase, poroviscous, reactive flow model displays various types of behaviour relevant to cell crawling. We present stability analyses that show that an asymmetric perturbation is required to cause a spatially uniform, stationary strip of cytoplasm to move, which is relevant to cell polarization. Our numerical simulations identify qualitatively distinct families of travelling-wave solutions that coexist at certain parameter values. Within each family, the crawling speed of the strip has a bell-shaped dependence on the adhesion strength. The model captures the experimentally observed behaviour that cells crawl quickest at intermediate adhesion strengths, when the substrate is neither too sticky nor too slippy.

Ruminal degradability and whole-tract digestibility of protein and fibre fractions in fenugreek haylage

Doepel, L., Montgomery, J. E., Beauchemin, K. A., King, J. R. and Acharya, S. N. 2012. Ruminal degradability and whole-tract digestibility of protein and fibre fractions in fenugreek haylage. Can. J. Anim. Sci. 92: 211–217. The purpose of this study was to evaluate the digestibility of fenugreek forage compared with alfalfa in dairy cows. Alfalfa and two genotypes of fenugreek, Quatro and F70, were harvested and prepared as plastic-wrapped high-moisture bales. Fourteen weeks after baling, forage samples were obtained for determination of ruminal degradation and whole-tract digestibility. To determine ruminal degradation, forage samples were placed in polyester bags and incubated in the rumen for various time points (up to 168 h) in lactating Holstein cows. Digestibility in the rumen, intestine and the whole digestive tract was estimated by incubating samples in the rumen, followed by measurements of intestinal digestibility using the mobile bag technique in two non-lactating Holstein cows. Effective ruminal degradability of DM was lower for F70 than for alfalfa, while for ADF and NDF it was equivalent in all forages. Whole-tract disappearance of DM, CP, ADF and NDF was lower for F70 than Quatro. In general, Quatro and alfalfa were similar in terms of ruminal degradation and digestion in the rumen, intestine and whole-tract, while F70 tended to be of lower quality.

Inhibition of quorum sensing in a computational biofilm simulation

Bacteria communicate through small diffusible molecules in a process known as quorum sensing. Quorum-sensing inhibitors are compounds which interfere with this, providing a potential treatment for infections associated with bacterial biofilms. We present an individual-based computational model for a developing biofilm. Cells are aggregated into particles for computational efficiency, but the quorum-sensing mechanism is modelled as a stochastic process on the level of individual cells. Simulations are used to investigate different treatment regimens. The response to the addition of inhibitor is found to depend significantly on the form of the positive feedback in the quorum-sensing model; in cases where the model exhibits bistability, the time at which treatment is initiated proves to be critical for the effective prevention of quorum sensing and hence potentially of virulence.

The isolation of spatial patterning modes in a mathematical model of juxtacrine cell signalling

Juxtacrine signalling mechanisms are known to be crucial in tissue and organ development, leading to spatial patterns in gene expression. We investigate the patterning behaviour of a discrete model of juxtacrine cell signalling due to Owen & Sherratt (1998, Mathematical modelling of juxtacrine cell signalling. Math. Biosci., 153, 125-150) in which ligand molecules, unoccupied receptors and bound ligand-receptor complexes are modelled. Feedback between the ligand and receptor production and the level of bound receptors is incorporated. By isolating two parameters associated with the feedback strength and employing numerical simulation, linear stability and bifurcation analysis, the pattern-forming behaviour of the model is analysed under regimes corresponding to lateral inhibition and induction. Linear analysis of this model fails to capture the patterning behaviour exhibited in numerical simulations. Via bifurcation analysis, we show that since the majority of periodic patterns fold subcritically from the homogeneous steady state, a wide variety of stable patterns exists at a given parameter set, providing an explanation for this failure. The dominant pattern is isolated via numerical simulation. Additionally, by sampling patterns of non-integer wavelength on a discrete mesh, we highlight a disparity between the continuous and discrete representations of signalling mechanisms: in the continuous case, patterns of arbitrary wavelength are possible, while sampling such patterns on a discrete mesh leads to longer wavelength harmonics being selected where the wavelength is rational; in the irrational case, the resulting aperiodic patterns exhibit 'local periodicity', being constructed from distorted stable shorter wavelength patterns. This feature is consistent with experimentally observed patterns, which typically display approximate short-range periodicity with defects.

Multiscale modelling of auxin transport in the plant-root elongation zone

In the root elongation zone of a plant, the hormone auxin moves in a polar manner due to active transport facilitated by spatially distributed influx and efflux carriers present on the cell membranes. To understand how the cell-scale active transport and passive diffusion combine to produce the effective tissue-scale flux, we apply asymptotic methods to a cell-based model of auxin transport to derive systematically a continuum description from the spatially discrete one. Using biologically relevant parameter values, we show how the carriers drive the dominant tissue-scale auxin flux and we predict how the overall auxin dynamics are affected by perturbations to these carriers, for example, in knockout mutants. The analysis shows how the dominant behaviour depends on the cells' lengths, and enables us to assess the relative importance of the diffusive auxin flux through the cell wall. Other distinguished limits are also identified and their potential roles discussed. As well as providing insight into auxin transport, the study illustrates the use of multiscale (cell to tissue) methods in deriving simplified models that retain the essential biology and provide understanding of the underlying dynamics.

Continuum limits of pattern formation in hexagonal-cell monolayers

Intercellular signalling is key in determining cell fate. In closely packed tissues such as epithelia, juxtacrine signalling is thought to be a mechanism for the generation of fine-grained spatial patterns in cell differentiation commonly observed in early development. Theoretical studies of such signalling processes have shown that negative feedback between receptor activation and ligand production is a robust mechanism for fine-grained pattern generation and that cell shape is an important factor in the resulting pattern type. It has previously been assumed that such patterns can be analysed only with discrete models since significant variation occurs over a lengthscale concomitant with an individual cell; however, considering a generic juxtacrine signalling model in square cells, in O'Dea and King (Math Biosci 231(2):172-185 2011), a systematic method for the derivation of a continuum model capturing such phenomena due to variations in a model parameter associated with signalling feedback strength was presented. Here, we extend this work to derive continuum models of the more complex fine-grained patterning in hexagonal cells, constructing individual models for the generation of patterns from the homogeneous state and for the transition between patterning modes. In addition, by considering patterning behaviour under the influence of simultaneous variation of feedback parameters, we construct a more general continuum representation, capturing the emergence of the patterning bifurcation structure. Comparison with the steady-state and dynamic behaviour of the underlying discrete system is made; in particular, we consider pattern-generating travelling waves and the competition between various stable patterning modes, through which we highlight an important deficiency in the ability of continuum representations to accommodate certain dynamics associated with discrete systems.

Mathematical modelling of the Aux/IAA negative feedback loop

The hormone auxin is implicated in regulating a diverse range of developmental processes in plants. Auxin acts in part by inducing the Aux/IAA genes. The associated pathway comprises multiple negative feedback loops (whereby Aux/IAA proteins can repress Aux/IAA genes) that are disrupted by auxin mediating the turnover of Aux/IAA protein. In this paper, we develop a mathematical model of a single Aux/IAA negative feedback loop in a population of identical cells. The model has a single steady-state. We explore parameter space to uncover a number of dynamical regimes. In particular, we identify the ratio between the Aux/IAA protein and mRNA turnover rates as a key parameter in the model. When this ratio is sufficiently small, the system can evolve to a stable limit cycle, corresponding to an oscillation in Aux/IAA expression levels. Otherwise, the steady-state is either a stable-node or a stable-spiral. These observations may shed light on recent experimental results.

An integrative computational model for intestinal tissue renewal

OBJECTIVES

The luminal surface of the gut is lined with a monolayer of epithelial cells that acts as a nutrient absorptive engine and protective barrier. To maintain its integrity and functionality, the epithelium is renewed every few days. Theoretical models are powerful tools that can be used to test hypotheses concerning the regulation of this renewal process, to investigate how its dysfunction can lead to loss of homeostasis and neoplasia, and to identify potential therapeutic interventions. Here we propose a new multiscale model for crypt dynamics that links phenomena occurring at the subcellular, cellular and tissue levels of organisation.

METHODS

At the subcellular level, deterministic models characterise molecular networks, such as cell-cycle control and Wnt signalling. The output of these models determines the behaviour of each epithelial cell in response to intra-, inter- and extracellular cues. The modular nature of the model enables us to easily modify individual assumptions and analyse their effects on the system as a whole.

RESULTS

We perform virtual microdissection and labelling-index experiments, evaluate the impact of various model extensions, obtain new insight into clonal expansion in the crypt, and compare our predictions with recent mitochondrial DNA mutation data.

CONCLUSIONS

We demonstrate that relaxing the assumption that stem-cell positions are fixed enables clonal expansion and niche succession to occur. We also predict that the presence of extracellular factors near the base of the crypt alone suffices to explain the observed spatial variation in nuclear beta-catenin levels along the crypt axis.

Bistability in a model of mesoderm and anterior mesendoderm specification in Xenopus laevis

In this paper we develop a model of mesendoderm specification in Xenopus laevis based on an existing gene regulation network. The mesendoderm is a population of cells that may contribute to either the mesoderm or endoderm. The model that we develop encompasses the time evolution of transcription factor concentrations in a single cell and is shown to have stable steady states that correspond to mesoderm and anterior mesendodermal cell types, but not endoderm (except in cells where Goosecoid expression is inhibited). Both in vitro and in vivo versions of the model are developed and analysed, the former indicating how cell fate is determined in large part by the concentration of Activin administered to a cell, with the model results comparing favourably with current quantitative experimental data. A numerical investigation of the in vivo model suggests that cell fate is determined largely by a VegT and beta-Catenin pre-pattern, subsequently being reinforced by Nodal. We argue that this sensitivity of the model to a VegT and beta-Catenin pre-pattern indicates that a key VegT self-limiting mechanism (for which there is experimental evidence) is absent from the model. Furthermore, we find that the lack of a steady state corresponding to endoderm is entirely consistent with current in vivo data, and that the in vivo model corresponds to mesendoderm specification on the dorsal, but not the ventral, side of the embryo.

Travelling-wave behaviour in a multiphase model of a population of cells in an artificial scaffold

This paper analyses travelling-wave behaviour in a recently-formulated multiphase model for the growth of biological tissue that comprises motile cells and water inside a porous scaffold. The model arises in the context of tissue engineering, and its purpose is to study how cells migrate and proliferate inside porous biomaterials. In suitable limits, tissue growth in the model is shown to occur in the form of travelling waves that can propagate either forwards or backwards, depending on the values of the parameters. In the case where the drag force between the scaffold and the cells is non-zero, the growth of the aggregate can be analysed in terms of the propagation of a constant-speed wavefront in a semi-infinite domain. A numerical (shooting) method is described for calculating the wave speed, and detailed results for how the speed varies with respect to the parameters are given. In the case where the drag force is zero, the size of the aggregate is shown either to grow or to shrink exponentially with time. These results may be of importance in determining the experimental factors that control tissue invasiveness in scaffolds thereby allowing greater control over engineered tissue growth.

Ganciclovir Population Pharmacokinetics in Neonates Following Intravenous Administration of Ganciclovir and Oral Administration of a Liquid Valganciclovir Formulation

Cytomegalovirus (CMV) is the most common viral congenital infection, producing both sensorineural hearing loss and mental retardation. Our objective was to assess the population pharmacokinetics of a research-grade oral valganciclovir solution in neonates with symptomatic congenital CMV disease. Twenty-four neonates received 6 weeks of antiviral therapy. Ganciclovir and valganciclovir were measured by liquid chromatography/tandem mass spectroscopy. NONMEM version VI beta was used for population analyses. All profiles were consistent with a one-compartment model. Postnatal age, body surface area, and gender did not improve the model fit after body weight was taken into account. The typical value of clearance (l/h), distribution volume (l), and bioavailability of ganciclovir were 0.146 x body weight (WT)(1.68), 1.15 x WT, and 53.6%, respectively. Although these results cannot be extrapolated to extemporaneously compounded valganciclovir preparations, they provide the foundation on which a commercial-grade valganciclovir oral solution may be a viable option for administration to neonates.

Multiphase modelling of cell behaviour on artificial scaffolds: effects of nutrient depletion and spatially nonuniform porosity

This paper contains analysis of a recently formulated multiphase model for the growth of biological tissue that comprises motile cells and water inside a rigid scaffold material. The model is extended here to include a term describing cell proliferation which is mediated by the supply of a diffusible nutrient and to include the case where the scaffold porosity varies in space. Numerical solutions of the model equations are presented for different values of the parameters. Comparison is drawn between the different types of growth that arise when using static or dynamic methods for seeding the scaffold with cells. Analytical solutions are presented for the limiting cases in which the coefficient of drag between the cells and the scaffold is very large or zero. In the limit of large time, solutions reveal preferential tissue growth in the vicinity of the scaffold edge due to depletion of nutrient by the cells, consistent with experimental results. However, it is shown that reducing the coefficient of drag between the scaffold and the cells overcomes the effects of nutrient depletion by increasing cell mobility, thereby leading to improved uniformity of the cell distribution within the scaffold.

A multi-phase mathematical model of quorum sensing in a maturing Pseudomonas aeruginosa biofilm

It is well known that sessile bacteria have a strong tendency to exist in a biofilm phenotype, whereby bacterial cells aggregate and produce a gel-like extracellular matrix, which, in an infection scenario, offers a significant barrier to attack by conventional antibiotics and the immune system. In this paper we develop a multi-phase model of a maturing Pseudomonas aeruginosa biofilm, allowing for the production and secretion of exopolysaccharide (EPS). The primary quorum-sensing system of P. aeruginosa (namely the lasR system) is believed to be required for full biofilm development, and we thus take the synthesis of EPS to be regulated by the cognate signal molecule, 3-oxo-C12-HSL. We also take EPS and signal production, along with bacterial growth, to be limited by oxygen availability, thus factoring in the nutrient poor conditions deep inside the biofilm. We use simulations to examine the role played by quorum sensing in the biofilm maturation process, and to investigate the effect of anti-quorum sensing and antibiotic treatments on EPS concentration, signal level, bacterial numbers and biofilm growth rate. In addition, we undertake analysis of the associated travelling-wave behaviour.

Crypt dynamics and colorectal cancer: advances in mathematical modelling

Mathematical modelling forms a key component of systems biology, offering insights that complement and stimulate experimental studies. In this review, we illustrate the role of theoretical models in elucidating the mechanisms involved in normal intestinal crypt dynamics and colorectal cancer. We discuss a range of modelling approaches, including models that describe cell proliferation, migration, differentiation, crypt fission, genetic instability, APC inactivation and tumour heterogeneity. We focus on the model assumptions, limitations and applications, rather than on the technical details. We also present a new stochastic model for stem-cell dynamics, which predicts that, on average, APC inactivation occurs more quickly in the stem-cell pool in the absence of symmetric cell division. This suggests that natural niche succession may protect stem cells against malignant transformation in the gut. Finally, we explain how we aim to gain further understanding of the crypt system and of colorectal carcinogenesis with the aid of multiscale models that cover all levels of organization from the molecular to the whole organ.

Modelling the effect of caveolae on G-protein activation

In this paper, we study the effects on G-protein activation of a non-uniform distribution of signalling components. The spatial heterogeneity is attributed to caveolae, a specific membrane microdomain which has been observed to redistribute and concentrate signalling molecules. Diffusive coagulation-fragmentation equations are used to describe the aggregation of caveolin homo-oligomers and the subsequent formation of caveolae. A system of reaction-diffusion equation is thus formulated and, in order to describe the restrictions imposed by caveolae on the movement of receptors and G-protein, a segregation coefficient is introduced which serves to regulate the preference of the species to segregate according to the concentration of caveolae. The results demonstrate that the heterogeneous distribution of the signalling components and the efficiency of G-protein activation can vary significantly, depending on the concentration of caveolae.

Modelling antibiotic- and anti-quorum sensing treatment of a spatially-structured Pseudomonas aeruginosa population

The bacterial cell to cell signalling system known as quorum sensing (QS) is essential for the regulation of virulence in many pathogens and offers a specific biochemical target for novel antibacterial therapies. Expanding on earlier work, in which consideration was given to the primary QS system (lasR system) in a homogeneous population of the common human pathogen Pseudomonas aeruginosa, we build a simple spatial model of an early-stage P. aeruginosa biofilm subject to treatment with topically applied anti-QS drugs (of two specific kinds) and conventional antibiotics. In the case of a slowly growing biofilm we show that both kinds of anti-quorum sensing drug are effective in reducing the level of the relevant signal molecule (3-oxo-C12-homoserine lactone; henceforth AHL), in each case obtaining an explicit bound on the steady-state AHL profile in terms of a prescribed surface drug concentration. Using numerical methods, we are also able to reproduce the hysteretic phenomena exhibited by the homogeneous model, in particular showing that for each kind of anti-QS drug there is a parameter regime in which a catastrophic collapse occurs in the steady-state AHL concentration as the surface drug concentration passes some critical value; an alternative way of interpreting this result is to say that, for a prescribed surface drug concentration, there is a critical biofilm depth such that treatment is successful until this depth is reached, but fails thereafter. In the thick-biofilm limit we show that the critical concentration of each drug increases exponentially with the biofilm thickness (or, conversely, that the critical depth increases logarithmically with surface drug concentration); this is dramatically different to the behaviour observed in the corresponding homogeneous model, where the critical concentrations grow linearly with bacterial carrying capacity, and thus highlights the relative difficulty of treating a large, spatially-structured population with diffusing antibacterials.

Thin-film theories for two-phase reactive flow models of active cell motion

The aim of this paper is to develop a broadly-applicable and self-consistent thin-film biphasic modelling framework for the full crawling cycle of a single animal cell. A hierarchy of thin-film two-phase 'reactive flow' models is derived; between them these cover a wide range of biologically relevant parameter regimes. The mathematical properties and biological implications of the resulting systems of high-order nonlinear degenerate parabolic-elliptic evolution equations are investigated. Linear-stability arguments suggest the formation of highly localized regions of high or low network density associated with small irregular oscillations or 'ruffling' of the plasma membrane. Local analyses at the contact line identify the classes of admissible contact-line conditions, through which we study for the first time the effect on the cell-scale motion of the 'mesoscopic' contact-line physics, which consists of the chemical and mechanical mechanisms for protrusive and retractive force generation near the outer cell periphery. One of the formulations is used to develop a minimal model for cell body translocation over a thin pseudopod, which predicts that myosin-driven contraction is not essential for rapid translocation. An analytic prediction for the translocation speed is given in terms of the network viscosity and slip coefficient (a parameter measuring the adhesion strength), of the membrane tension and of the thicknesses of the pseudopod and actin cortex; this is in good agreement with the translocation speed of osteoblasts on biomaterial substrates commonly used for orthopaedic implants. Limitations of the modelling approach and directions for future work are outlined.

Modelling cell signalling and differentiation in the urothelium

Urothelial cells line the bladder. If the urothelium is damaged, it is vital that it repairs itself quickly. Experimental results shedding light on how this repair process works are presented, revealing in particular the dependence of the response on the length of time for which the drug Troglitazone (TZ) is applied. A simple mathematical model for the basic mechanism (comprising ordinary differential equations) is then developed and analysed, seeking specifically to clarify and quantify the mechanisms governing the dependence of the cell differentiation response on the TZ administration time, rather than providing a comprehensive model of differentiation. Through biologically justified simplifications, analysis reveals that the model gives results in accord with the experimental observations, and suggests new experiments that may aid further understanding. Directions in which this preliminary modelling of the PPAR gamma (peroxisome proliferator activated receptor gamma) pathway could be usefully extended are also indicated.

Deterministic and stochastic modelling of endosome escape by Staphylococcus aureus: ?quorum? sensing by a single bacterium

Deterministic and stochastic models describing quorum sensing by Staphylococcus aureus within an endosome, and the subsequent escape via the production of virulence factors, are developed and analysed. Particular attention is given to a biologically-relevant asymptotic limit of the problem, for which the solutions, including the endosome escape time, can be explicitly characterised in terms of the model parameters.

Mathematical modelling of therapies targeted at bacterial quorum sensing

Bacteria commonly use diffusible signal molecules to synchronise their behaviour by facilitating population dependent co-ordination. This cell-to-cell signalling mechanism is known as quorum sensing (QS) and provides a way of ensuring that certain genes are 'switched on' only when a certain signal concentration (typically corresponding to a large population density) has been reached. In this paper we focus on the QS system of the human pathogen Pseudomonas aeruginosa, which employs a complex hierarchy of QS signalling systems, which regulate the formation of multiple exoproducts, swarming and biofilm differentiation. In P. aeruginosa, the signal molecules are N-acylated homoserine lactones (AHLs; e.g., N-(3-oxododecanoyl)-homoserine lactone [3-oxo-C12-HSL]), which bind to transcriptional regulator proteins (LasR in the case of 3-oxo-C12-HSL) to activate the expression of target genes including lasI, which codes for the 3-oxo-C12-HSL synthase. Since the virulence of P. aeruginosa is controlled by QS, agents (QSBs) designed to block this cell-to-cell communication have potential as novel antibacterials. By drawing on existing models for the reaction kinetics of this system, we model a growing population subject to treatment with two kinds of QSB, together with a conventional antibiotic. The first kind of QSB is assumed to act by diffusing through the cell membrane and then destabilising/sequestering LasR, while the second kind remains outside the cell and degrades the AHL signal molecule itself. Numerical and mathematical analysis of the resulting systems of ordinary differential equations reveals in particular that, while a sufficiently high dose of QSB is, in all cases considered, able to reduce the AHL concentration (and hence virulence) to a negligible level, the qualitative response to treatment is sensitive to parameter values.

Cell-signalling repression in bacterial quorum sensing

In this paper we expand on two mathematical models for investigating the role of three distinct repression mechanisms within the so-called quorum sensing (QS) cell-signalling process of bacterial colonies growing (1) in liquid cultures and (2) in biofilms. The repression mechanisms studied are (i) reduction of cell signalling molecule (QSM) production by a constitutively produced agent degrading the messenger RNA of a crucial enzyme (QSE), (ii) lower QSM production rate due to a negative feedback process and (iii) loss of QSMs by binding directly to a constitutively produced agent; the first two mechanisms are known to be employed by the pathogenic bacterium Pseudomonas aeruginosa and the last is relevant to the plant pathogen Agrobacterium tumefaciens. The modelling approach assumes that the bacterial colony consists of two sub-populations, namely down- and up-regulated cells, that differ in the rates at which they produce QSMs, while QSM concentration governs the switching between sub-populations. Parameter estimates are obtained by curve-fitting experimental data (involving P. aeruginosa growth in liquid culture, obtained as part of this study) to solutions of model (1). Asymptotic analysis of the model (1) shows that mechanism (i) is necessary, but not sufficient, to predict the observed saturation of QSM levels in an exponentially growing colony; either mechanism (ii) or (iii) also needs to be incorporated to obtain saturation. Consequently, only a fraction of the population will become up-regulated. Furthermore, only mechanisms (i) and (iii) affect the main timescales for up-regulation. Repression was found to play a less significant role in a biofilms, but mechanisms (i)-(iii) were nevertheless found to reduce the ultimate up-regulated cell fraction and mechanisms (i) and (iii) to increase the timescale for substantial up-regulation and to decrease the wave speed of an expanding front of QS activity.

Modelling host tissue degradation by extracellular bacterial pathogens

Extracellular bacterial pathogens such as Pseudomonas aeruginosa are able to penetrate into host tissues (given an initial breech in the outer barrier, e.g. a wound) through the action of exo-toxins and degradative exo-enzymes. A mathematical model of this process is presented which, in the absence of significant immune response, predicts the progression of the bacteria into the tissue as a travelling wave whose velocity can be determined explicitly in terms of the model parameters. Simple in vitro experiments in protein-based matrices are performed which yield results consistent with this behaviour. A complementary in vitro experimental system with distinct qualitative behaviour is also studied, giving further insight and confidence in the modelling approach.

Modelling the early growth of ductal carcinoma in situ of the breast

The growth of a tumour in a rigid walled cylindrical duct is examined in order to model the initial stages of tumour cell expansion in ductal carcinoma in situ (DCIS) of the breast. A nutrient-limited growth model is formulated, in which cell movement is described by a Stokes flow constitutive relation. The effects on the shape of the tumour boundary of the material properties (i.e. the viscosity) and the extent to which the cells adhere to the duct wall are studied using numerical and asymptotic methods. It is shown how stable, non-planar, interface configurations result and that, during these initial stages, before the duct wall has been breached, few cells die and a nutrient-rich model is usually sufficient to capture the behaviour. Finally, we discuss the relevance of this approach to DCIS and suggest possible avenues for further work.

Modelling of signalling via G-protein coupled receptors: pathway-dependent agonist potency and efficacy

A mathematical model is constructed to study promiscuous coupling of receptors to G-proteins and to simulate events leading to the activation of multiple effector pathways within a cell. The model is directed at a better understanding of the factors that determine the efficacy and potency of a drug. Assuming that the receptors can exist in multiple conformational states, and allowing for agonist specific conformation, a system of ordinary differential equations is constructed and subsequently pathway-dependent agonist efficacy and potency order is predicted. A simple case of the compartmentalization of receptors and G-proteins is also given, using the current model to illustrate the effects of spatial heterogeneity on the predicted response.

Interactions between a uniformly proliferating tumour and its surroundings: uniform material properties

The stability of a planar tumour growing into neighbouring tissue is examined and, in particular, its dependence on the properties of the tumour and of the surrounding material studied. An abundant supply of nutrient is assumed, so the proliferation of cells is uninhibited (resulting in exponential growth). We consider two possible constitutive relations. Darcy's law and Stokes flow, in describing the deformation of the tissue and the resulting model takes the form of a coupled system comprising a nonlinear reaction-diffusion-convection equation for the tumour cell concentration and an elliptic system for the deformation and stress fields. Using a combination of linear-stability analysis, numerical methods and thin-film approximations. the evolution of the advancing tumour boundary is determined. It is shown that when the tumour and surrounding material properties are the same, a planar interface is always linearly unstable, with the Stokes flow problem being reducible to the Darcy one. We treat the subsequent (nonlinear) evolution and suggest possible extensions to this work.

Plant reserves of perennial grasses subjected to drought and defoliation stresses on the Northern Tablelands of New South Wales, Australia

The effects of defoliation intensity and drought severity on levels of water-soluble carbohydrate (WSC), fructan, and etiolated regrowth of 6 important perennial grasses were investigated. The experiment was conducted under a rain-out shelter at Armidale, NSW, Australia, using 6 perennial grass species (Phalaris aquatica cv. Sirosa, Festuca arundinacea cv. Demeter, Dactylis glomerata cv. Porto, Lolium perenne cv. Victorian, Microlaena stipoides cv. Shannon, and Austrodanthonia richardsonii cv. Taranna) subjected to 3 moisture regimes (non-stress moisture, and moderate and severe drought) and 2 defoliation intensities (moderate and severe) over 2 seasonal sequences (spring–summer and summer–autumn).The range in WSC, fructan, and etiolated regrowth of the species varied, with Festuca and Lolium having the highest WSC and fructan concentrations. Austrodanthonia had the lowest WSC concentration of the species. Unlike the introduced species, the natives did not store fructans. The species varied in their response to the treatments imposed. Festuca and Phalaris had the highest etiolated regrowth and showed the greatest effect of defoliation intensity. Etiolated regrowth appeared to be a sensitive measure of plant status, showing the fragile nature of some of the species.The effect of defoliation intensity and drought varied with season. Defoliation intensity had little effect on carbohydrate reserves of all species, except Festuca, during summer of the spring–summer experimental season. During the summer–autumn experimental season, severe defoliation reduced the rate of accumulation during the period December–April. Drought affected carbohydrate accumulation and utilisation. Carbohydrates that had been accumulated at the end of spring of the spring–summer experimental season in plants affected by drought were utilised during summer. However, if drought commenced in summer, carbohydrate accumulation continued for 120 days in all species studied, and 180 days in Lolium and Phalaris.Autumn appeared to be a period when plant reserves were particularly susceptible to stress. The importance of WSC, fructans, and etiolated regrowth as measures of plant reserves, and their role in persistence were discussed.

A mathematical model of partial-thickness burn-wound infection by Pseudomonas aeruginosa: quorum sensing and the build-up to invasion

Pseudomonas aeruginosa remains a significant pathogen in burn-wound infection, its pathogenicity being associated with the production of a cocktail of virulence determinants which is regulated by a population-density-dependent mechanism termed quorum sensing. Quorum sensing is effected through the production and binding of signalling molecules. Here we present a mathematical model for the early stages of the infection process by P. aeruginosa in burn wounds which accounts for the quorum sensing system and for the diffusion of signalling molecules in the burn-wound environment. The results of the model and the effects of important parameters are discussed in detail. For example, the effect of the degradation rate of signalling molecules and its significance for anti-signalling therapies is discussed.