Modelling the role of enzymatic pathways in the metabolism of docosahexaenoic acid by monocytes and its association with osteoarthritic pain.

Chronic pain is a major cause of disability and suffering in osteoarthritis (OA) patients. Endogenous specialised pro-resolving molecules (SPMs) curtail pro-inflammatory responses. One of the SPM intermediate oxylipins, 17-hydroxydocasahexaenoic acid (17-HDHA, a metabolite of docosahexaenoic acid (DHA)), is significantly associated with OA pain (Valdes et al., 2017). The aim of this multidisciplinary work is to develop a mathematical model to describe the contributions of enzymatic pathways (and the genes that encode them) to the metabolism of DHA by monocytes and to the levels of the down-stream metabolites, 17-HDHA and 14-hydroxydocasahexaenoic acid (14-HDHA), motivated by novel clinical data from a study involving 30 participants with OA. The data include measurements of oxylipin levels, mRNA levels, measures of OA severity and self-reported pain scores. We propose a system of ordinary differential equations to characterise associations between the different datasets, in order to determine the homeostatic concentrations of DHA, 17-HDHA and 14-HDHA, dependent upon the gene expression of the associated metabolic enzymes. Using parameter-fitting methods, local sensitivity and uncertainty analysis, the model is shown to fit well qualitatively to experimental data. The model suggests that up-regulation of some ALOX genes may lead to the down-regulation of 17-HDHA and that dosing with 17-HDHA increases the production of resolvins, which helps to down-regulate the inflammatory response. More generally, we explore the challenges and limitations of modelling real data, in particular individual variability, and also discuss the value of gathering additional experimental data motivated by the modelling insights.

Multimodal assessment improves neuroprognosis performance in clinically unresponsive critical-care patients with brain injury.

Accurately predicting functional outcomes for unresponsive patients with acute brain injury is a medical, scientific and ethical challenge. This prospective study assesses how a multimodal approach combining various numbers of behavioral, neuroimaging and electrophysiological markers affects the performance of outcome predictions. We analyzed data from 349 patients admitted to a tertiary neurointensive care unit between 2009 and 2021, categorizing prognoses as good, uncertain or poor, and compared these predictions with observed outcomes using the Glasgow Outcome Scale-Extended (GOS-E, levels ranging from 1 to 8, with higher levels indicating better outcomes). After excluding cases with life-sustaining therapy withdrawal to mitigate the self-fulfilling prophecy bias, our findings reveal that a good prognosis, compared with a poor or uncertain one, is associated with better one-year functional outcomes (common odds ratio (95% CI) for higher GOS-E: OR = 14.57 (5.70-40.32), P < 0.001; and 2.9 (1.56-5.45), P < 0.001, respectively). Moreover, increasing the number of assessment modalities decreased uncertainty (OR = 0.35 (0.21-0.59), P < 0.001) and improved prognostic accuracy (OR = 2.72 (1.18-6.47), P = 0.011). Our results underscore the value of multimodal assessment in refining neuroprognostic precision, thereby offering a robust foundation for clinical decision-making processes for acutely brain-injured patients. ClinicalTrials.gov registration: NCT04534777 .

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.

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.

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.

Multicellular Mathematical Modelling of Mesendoderm Formation in Amphibians.

The earliest cell fate decisions in a developing embryo are those associated with establishing the germ layers. The specification of the mesoderm and endoderm is of particular interest as the mesoderm is induced from the endoderm, potentially from an underlying bipotential group of cells, the mesendoderm. Mesendoderm formation has been well studied in an amphibian model frog, Xenopus laevis, and its formation is driven by a gene regulatory network (GRN) induced by maternal factors deposited in the egg. We have recently demonstrated that the axolotl, a urodele amphibian, utilises a different topology in its GRN to specify the mesendoderm. In this paper, we develop spatially structured mathematical models of the GRNs governing mesendoderm formation in a line of cells. We explore several versions of the model of mesendoderm formation in both Xenopus and the axolotl, incorporating the key differences between these two systems. Model simulations are able to reproduce known experimental data, such as Nodal expression domains in Xenopus, and also make predictions about how the positional information derived from maternal factors may be interpreted to drive cell fate decisions. We find that whilst cell-cell signalling plays a minor role in Xenopus, it is crucial for correct patterning domains in axolotl.

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.

Characterizing the dynamics of mental representations: the temporal generalization method.

Parsing a cognitive task into a sequence of operations is a central problem in cognitive neuroscience. We argue that a major advance is now possible owing to the application of pattern classifiers to time-resolved recordings of brain activity [electroencephalography (EEG), magnetoencephalography (MEG), or intracranial recordings]. By testing at which moment a specific mental content becomes decodable in brain activity, we can characterize the time course of cognitive codes. Most importantly, the manner in which the trained classifiers generalize across time, and from one experimental condition to another, sheds light on the temporal organization of information-processing stages. A repertoire of canonical dynamical patterns is observed across various experiments and brain regions. This method thus provides a novel way to understand how mental representations are manipulated and transformed.

A model of subjective report and objective discrimination as categorical decisions in a vast representational space.

Subliminal perception studies have shown that one can objectively discriminate a stimulus without subjectively perceiving it. We show how a minimalist framework based on Signal Detection Theory and Bayesian inference can account for this dissociation, by describing subjective and objective tasks with similar decision-theoretic mechanisms. Each of these tasks relies on distinct response classes, and therefore distinct priors and decision boundaries. As a result, they may reach different conclusions. By formalizing, within the same framework, forced-choice discrimination responses, subjective visibility reports and confidence ratings, we show that this decision model suffices to account for several classical characteristics of conscious and unconscious perception. Furthermore, the model provides a set of original predictions on the nonlinear profiles of discrimination performance obtained at various levels of visibility. We successfully test one such prediction in a novel experiment: when varying continuously the degree of perceptual ambiguity between two visual symbols presented at perceptual threshold, identification performance varies quasi-linearly when the stimulus is unseen and in an 'all-or-none' manner when it is seen. The present model highlights how conscious and non-conscious decisions may correspond to distinct categorizations of the same stimulus encoded by a high-dimensional neuronal population vector.

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 ß-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.

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

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.

Mathematical modelling of toxicity associated with intracellular chromium reduction.

Chromium is a known allergen and carcinogen, but the mechanisms by which damage is caused are not clearly understood. Based on experimental literature, we devise a conceptual model examining the intracellular reduction of chromium through reductants such as glutathione and ascorbic acid. From this, we build a mathematical model describing these events in detail and we use this to clarify the key steps in the process of chromium reduction within cells.In particular, we consider the free radicals which are generated as a result of chromium reduction and that are likely to cause most harm to the cell. To explore the practical implications of the model predication, we investigate what the effects of a single eight hours of exposure and multiple eight hour exposures over the course of 3 days with increasing extracellular chromium concentration are. The dependence on initial chromium concentration is of particular significance with the proportions of the various chromium states changing as well as free radical generation increasing with greater chromium exposure.

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.

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.

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.