Matrix models for quantifying competitive intransitivity from species abundance data

In a network of competing species, a competitive intransitivity occurs when the ranking of competitive abilities does not follow a linear hierarchy (A > B > C but C > A). A variety of mathematical models suggests that intransitive networks can prevent or slow down competitive exclusion and maintain biodiversity by enhancing species coexistence. However, it has been difficult to assess empirically the relative importance of intransitive competition because a large number of pairwise species competition experiments are needed to construct a competition matrix that is used to parameterize existing models. Here we introduce a statistical framework for evaluating the contribution of intransitivity to community structure using species abundance matrices that are commonly generated from replicated sampling of species assemblages. We provide metrics and analytical methods for using abundance matrices to estimate species competition and patch transition matrices by using reverse-engineering and a colonization-competition model. These matrices provide complementary metrics to estimate the degree of intransitivity in the competition network of the sampled communities. Benchmark tests reveal that the proposed methods could successfully detect intransitive competition networks, even in the absence of direct measures of pairwise competitive strength. To illustrate the approach, we analyzed patterns of abundance and biomass of five species of necrophagous Diptera and eight species of their hymenopteran parasitoids that co-occur in beech forests in Germany. We found evidence for a strong competitive hierarchy within communities of flies and parasitoids. However, for parasitoids, there was a tendency towards increasing intransitivity in higher weight classes, which represented larger resource patches. These tests provide novel methods for empirically estimating the degree of intransitivity in competitive networks from observational datasets. They can be applied to experimental measures of pairwise species interactions, as well as to spatio-temporal samples of assemblages in homogenous environments or environmental gradients.

Numerical assessment on the effective mechanical stimuli for matrix-associated metabolism in chondrocyte-seeded constructs

The self-regeneration capacity of articular cartilage is limited, due to its avascular and aneural nature. Loaded explants and cell cultures demonstrated that chondrocyte metabolism can be regulated via physiologic loading. However, the explicit ranges of mechanical stimuli that correspond to favourable metabolic response associated with extracellular matrix (ECM) synthesis are elusive. Unsystematic protocols lacking this knowledge produce inconsistent results. This study aims to determine the intrinsic ranges of physical stimuli that increase ECM synthesis and simultaneously inhibit nitric oxide (NO) production in chondrocyte-agarose constructs, by numerically re-evaluating the experiments performed by Tsuang et al. (2008). Twelve loading patterns were simulated with poro-elastic finite element models in ABAQUS. Pressure on solid matrix, von Mises stress, maximum principle stress and pore pressure were selected as intrinsic mechanical stimuli. Their development rates and magnitudes at the steady state of cyclic loading were calculated with MATLAB at the construct level. Concurrent increase in glycosaminoglycan and collagen was observed at 2300 Pa pressure and 40 Pa/s pressure rate. Between 0-1500 Pa and 0-40 Pa/s, NO production was consistently positive with respect to controls, whereas ECM synthesis was negative in the same range. A linear correlation was found between pressure rate and NO production (R = 0.77). Stress states identified in this study are generic and could be used to develop predictive algorithms for matrix production in agarose-chondrocyte constructs of arbitrary shape, size and agarose concentration. They could also be helpful to increase the efficacy of loading protocols for avascular tissue engineering. Copyright (c) 2010 John Wiley \& Sons, Ltd.

Gelatinase B [matrix metalloproteinase (MMP)-9] and collagenases (MMP-8/-13) are upregulated in cerebrospinal fluid during aseptic and bacterial meningitis in children

We investigated the protein expression of gelatinases [matrix metalloproteinase (MMP)-2 and -9] and collagenases (MMP-8 and -13) in cerebrospinal fluid (CSF) from patients with bacterial (BM, n = 17) and aseptic (AM, n = 14) meningitis. In both, MMP-8 and -9 were increased in 100% of patients, whereas MMP-13 was detectable in 53% and 82% respectively. Three patients with clinical signs of meningitis, without CSF pleocytosis, scored positive for all three MMPs. MMP-8 appeared in two isoforms, granulocyte-type [polymorphonuclear cell (PMN)] and fibroblast/macrophage (F/M) MMP-8. Analysis of kinetic changes from serial lumbar punctures showed that these MMPs are independently regulated, and correlate only partly with CSF cytosis or levels of the endogenous inhibitor, tissue inhibitor of matrix metalloproteinase-1. In vitro, T cells, peripheral blood mononuclear cells (PBMCs) and granulocytes (PMN) release MMP-8 and -9, whereas MMP-13 could be found only in the former two cell types. Using models of exogenous (n-formyl-Met-Leu-Phe, T cell receptor cross-linking) and host-derived stimuli (interleukin-2), the kinetics and the release of the MMP-8, -9 and -13 showed strong variation between these immune cells and suggest release from preformed stocks. In addition, MMP-9 is also synthesized de novo in PBMCs and T cells. In conclusion, invading immune cells contribute only partially to MMPs in CSF during meningitis, and parenchymal cells are an equally relevant source. In this context, in patients with clinical signs of meningitis, but without CSF pleocytosis, MMPs seem to be a highly sensitive marker for intrathecal inflammation. The present data support the concept that broad-spectrum enzyme inhibition targeting gelatinases and collagenases is a potential strategy for adjunctive therapy in infectious meningitis.

Matrix metalloproteinase inhibition lowers mortality and brain injury in experimental pneumococcal meningitis

Pneumococcal meningitis (PM) results in high mortality rates and long-lasting neurological deficits. Hippocampal apoptosis and cortical necrosis are histopathological correlates of neurofunctional sequelae in rodent models and are frequently observed in autopsy studies of patients who die of PM. In experimental PM, inhibition of matrix metalloproteinases (MMPs) and/or tumor necrosis factor (TNF)-converting enzyme (TACE) has been shown to reduce brain injury and the associated impairment of neurocognitive function. However, none of the compounds evaluated in these studies entered clinical development. Here, we evaluated two second-generation MMP and TACE inhibitors with higher selectivity and improved oral availability. Ro 32-3555 (Trocade, cipemastat) preferentially inhibits collagenases (MMP-1, -8, and -13) and gelatinase B (MMP-9), while Ro 32-7315 is an efficient inhibitor of TACE. PM was induced in infant rats by the intracisternal injection of live Streptococcus pneumoniae. Ro 32-3555 and Ro 32-7315 were injected intraperitoneally, starting at 3 h postinfection. Antibiotic (ceftriaxone) therapy was initiated at 18 h postinfection, and clinical parameters (weight, clinical score, mortality rate) were recorded. Myeloperoxidase activities, concentrations of cytokines and chemokines, concentrations of MMP-2 and MMP-9, and collagen concentrations were measured in the cerebrospinal fluid. Animals were sacrificed at 42 h postinfection, and their brains were assessed by histomorphometry for hippocampal apoptosis and cortical necrosis. Both compounds, while exhibiting disparate MMP and TACE inhibitory profiles, decreased hippocampal apoptosis and cortical injury. Ro 32-3555 reduced mortality rates and cerebrospinal fluid TNF, interleukin-1β (IL-1β) and collagen levels, while Ro 32-7315 reduced weight loss and cerebrospinal fluid TNF and IL-6 levels.

In pneumococcal meningitis a novel water-soluble inhibitor of matrix metalloproteinases and TNF-alpha converting enzyme attenuates seizures and injury of the cerebral cortex

Matrix metalloproteinases (MMPs) and TNF-alpha converting enzyme (TACE) contribute to the pathophysiology of bacterial meningitis. To date, MMP-inhibitors studied in models of meningitis were compromised by their hydrophobic nature. We investigated the pharmacokinetics and the effect of TNF484, a water-soluble hydroxamate-based inhibitor of MMP and TACE, on disease parameters and brain damage in a neonatal rat model of pneumococcal meningitis. At 1 mg/kg q6h TNF484 reduced soluble TNF-alpha and the collagen degradation product hydroxyproline in the cerebrospinal fluid. Clinically, TNF484 attenuated the incidence of seizures and was neuroprotective in the cortex. Water-soluble MMP-inhibitors may hold promise in the therapy of bacterial meningitis.

Matrix metalloproteinases: multifunctional effectors of inflammation in multiple sclerosis and bacterial meningitis

Matrix metalloproteinases (MMPs) are a family of Zn2+-dependent endopeptidases targeting extracellular matrix (ECM) compounds as well as a number of other proteins. Their proteolytic activity acts as an effector mechanism of tissue remodeling in physiologic and pathologic conditions, and as modulator of inflammation. In the context of neuro-inflammatory diseases, MMPs have been implicated in processes such as (a) blood-brain barrier (BBB) and blood-nerve barrier opening, (b) invasion of neural tissue by blood-derived immune cells, (c) shedding of cytokines and cytokine receptors, and (d) direct cellular damage in diseases of the peripheral and central nervous system. This review focuses on the role of MMPs in multiple sclerosis (MS) and bacterial meningitis (BM), two neuro-inflammatory diseases where current therapeutic approaches are insufficient to prevent severe disability in the majority of patients. Inhibition of enzymatic activity may prevent MMP-mediated neuronal damage due to an overactive or deviated immune response in both diseases. Downregulation of MMP release may be the molecular basis for the beneficial effect of IFN-beta and steroids in MS. Instead, synthetic MMP inhibitors offer the possibility to shut off enzymatic activity of already activated MMPs. In animal models of MS and BM, they efficiently attenuated clinical disease symptoms and prevented brain damage due to excessive metalloproteinase activity. However, the required target profile for the therapeutic use of this novel group of compounds in human disease is not yet sufficiently defined and may be different depending on the type and stage of disease. Currently available MMP inhibitors show little target-specificity within the MMP family and may lead to side-effects due to interference with physiological functions of MMPs. Results from human MS and BM indicate that only a restricted number of MMPs specific for each disease is up-regulated. MMP inhibitors with selective target profiles offer the possibility of a more efficient therapy of MS and BM and may enter clinical trials in the near future.

Specimen specific parameter identification of ovine lumbar intervertebral discs: On the influence of fibre-matrix and fibre-fibre shear interactions.

Numerical models of the intervertebral disc, which address mechanical questions commonly make use of the difference in water content between annulus and nucleus, and thus fluid and solid parts are separated. Despite this simplification, models remain complex due to the anisotropy and nonlinearity of the annulus and regional variations of the collagen fibre density. Additionally, it has been shown that cross-links make a large contribution to the stiffness of the annulus. Because of this complex composite structure, it is difficult to reproduce several sets of experimental data with one single set of material parameters. This study addresses the question to which extent the ultrastructure of the intervertebral disc should be modelled so that its moment-angle behaviour can be adequately described. Therefore, a hyperelastic constitutive law, based on continuum mechanical principles was derived, which does not only consider the anisotropy from the collagen fibres, but also interactions among the fibres and between the fibres and the ground substance. Eight ovine lumbar intervertebral discs were tested on a custom made spinal loading simulator in flexion/extension, lateral bending and axial rotation. Specimen-specific geometrical models were generated using CT images and T2 maps to distinguish between annulus fibrosus and nucleus pulposus. For the identification of the material parameters the annulus fibrosus was described with two scenarios: with and without fibre-matrix and fibre-fibre interactions. Both scenarios showed a similar behaviour on a load displacement level. Comparing model predictions to the experimental data, the mean RMS of all specimens and all load cases was 0.54±0.15° without the interaction and 0.54±0.19° when the fibre-matrix and fibre-fibre interactions were included. However, due to the increased stiffness when cross-links effects were included, this scenario showed more physiological stress-strain relations in uniaxial and biaxial stress states. Thus, the present study suggests that fibre-matrix and fibre-fibre interactions should be considered in the constitutive law when the model addresses questions concerning the stress field of the annulus fibrosus.

Chow–Liu trees are sufficient predictive models for reproducing key features of functional networks of periictal EEG time-series

Seizure freedom in patients suffering from pharmacoresistant epilepsies is still not achieved in 20–30% of all cases. Hence, current therapies need to be improved, based on a more complete understanding of ictogenesis. In this respect, the analysis of functional networks derived from intracranial electroencephalographic (iEEG) data has recently become a standard tool. Functional networks however are purely descriptive models and thus are conceptually unable to predict fundamental features of iEEG time-series, e.g., in the context of therapeutical brain stimulation. In this paper we present some first steps towards overcoming the limitations of functional network analysis, by showing that its results are implied by a simple predictive model of time-sliced iEEG time-series. More specifically, we learn distinct graphical models (so called Chow–Liu (CL) trees) as models for the spatial dependencies between iEEG signals. Bayesian inference is then applied to the CL trees, allowing for an analytic derivation/prediction of functional networks, based on thresholding of the absolute value Pearson correlation coefficient (CC) matrix. Using various measures, the thus obtained networks are then compared to those which were derived in the classical way from the empirical CC-matrix. In the high threshold limit we find (a) an excellent agreement between the two networks and (b) key features of periictal networks as they have previously been reported in the literature. Apart from functional networks, both matrices are also compared element-wise, showing that the CL approach leads to a sparse representation, by setting small correlations to values close to zero while preserving the larger ones. Overall, this paper shows the validity of CL-trees as simple, spatially predictive models for periictal iEEG data. Moreover, we suggest straightforward generalizations of the CL-approach for modeling also the temporal features of iEEG signals.

All-loop anomalous dimensions in integrable λ-deformed σ-models

We calculate the all-loop anomalous dimensions of current operators in λ-deformed σ-models. For the isotropic integrable deformation and for a semi-simple group G we compute the anomalous dimensions using two different methods. In the first we use the all-loop effective action and in the second we employ perturbation theory along with the Callan–Symanzik equation and in conjunction with a duality-type symmetry shared by these models. Furthermore, using CFT techniques we compute the all-loop anomalous dimension of bilinear currents for the isotropic deformation case and a general G . Finally we work out the anomalous dimension matrix for the cases of anisotropic SU(2) and the two couplings, corresponding to the symmetric coset G/H and a subgroup H, splitting of a group G.

Two distinct filopodia populations at the growth cone allow to sense nanotopographical extracellular matrix cues to guide neurite outgrowth

BACKGROUND The process of neurite outgrowth is the initial step in producing the neuronal processes that wire the brain. Current models about neurite outgrowth have been derived from classic two-dimensional (2D) cell culture systems, which do not recapitulate the topographical cues that are present in the extracellular matrix (ECM) in vivo. Here, we explore how ECM nanotopography influences neurite outgrowth. METHODOLOGY/PRINCIPAL FINDINGS We show that, when the ECM protein laminin is presented on a line pattern with nanometric size features, it leads to orientation of neurite outgrowth along the line pattern. This is also coupled with a robust increase in neurite length. The sensing mechanism that allows neurite orientation occurs through a highly stereotypical growth cone behavior involving two filopodia populations. Non-aligned filopodia on the distal part of the growth cone scan the pattern in a lateral back and forth motion and are highly unstable. Filopodia at the growth cone tip align with the line substrate, are stabilized by an F-actin rich cytoskeleton and enable steady neurite extension. This stabilization event most likely occurs by integration of signals emanating from non-aligned and aligned filopodia which sense different extent of adhesion surface on the line pattern. In contrast, on the 2D substrate only unstable filopodia are observed at the growth cone, leading to frequent neurite collapse events and less efficient outgrowth. CONCLUSIONS/SIGNIFICANCE We propose that a constant crosstalk between both filopodia populations allows stochastic sensing of nanotopographical ECM cues, leading to oriented and steady neurite outgrowth. Our work provides insight in how neuronal growth cones can sense geometric ECM cues. This has not been accessible previously using routine 2D culture systems.