Counterexample-Guided Polynomial Loop Invariant Generation by Lagrange Interpolation

We apply multivariate Lagrange interpolation to synthesize polynomial quantitative loop invariants for probabilistic programs. We reduce the computation of an quantitative loop invariant to solving constraints over program variables and unknown coefficients. Lagrange interpolation allows us to find constraints with less unknown coefficients. Counterexample-guided refinement furthermore generates linear constraints that pinpoint the desired quantitative invariants. We evaluate our technique by several case studies with polynomial quantitative loop invariants in the experiments

Interplay between transglutaminases and heparan sulphate in progressive renal scarring

Transglutaminase-2 (TG2) is a new anti-fibrotic target for chronic kidney disease, for its role in altering the extracellular homeostatic balance leading to excessive build-up of matrix in kidney. However, there is no confirmation that TG2 is the only transglutaminase involved, neither there are strategies to control its action specifically over that of the conserved family-members. In this study, we have profiled transglutaminase isozymes in the rat subtotal nephrectomy (SNx) model of progressive renal scarring. All transglutaminases increased post-SNx peaking at loss of renal function but TG2 was the predominant enzyme. Upon SNx, extracellular TG2 deposited in the tubulointerstitium and peri-glomerulus via binding to heparan sulphate (HS) chains of proteoglycans and co-associated with syndecan-4. Extracellular TG2 was sufficient to activate transforming growth factor-β1 in tubular epithelial cells, and this process occurred in a HS-dependent way, in keeping with TG2-affinity for HS. Analysis of heparin binding of the main transglutaminases revealed that although the interaction between TG1 and HS is strong, the conformational heparin binding site of TG2 is not conserved, suggesting that TG2 has a unique interaction with HS within the family. Our data provides a rationale for a novel anti-fibrotic strategy specifically targeting the conformation-dependent TG2-epitope interacting with HS

Detection of Functional Modes in Protein Dynamics

Proteins frequently accomplish their biological function by collective atomic motions. Yet the identification of collective motions related to a specific protein function from, e.g., a molecular dynamics trajectory is often non-trivial. Here, we propose a novel technique termed “functional mode analysis” that aims to detect the collective motion that is directly related to a particular protein function. Based on an ensemble of structures, together with an arbitrary “functional quantity” that quantifies the functional state of the protein, the technique detects the collective motion that is maximally correlated to the functional quantity. The functional quantity could, e.g., correspond to a geometric, electrostatic, or chemical observable, or any other variable that is relevant to the function of the protein. In addition, the motion that displays the largest likelihood to induce a substantial change in the functional quantity is estimated from the given protein ensemble. Two different correlation measures are applied: first, the Pearson correlation coefficient that measures linear correlation only; and second, the mutual information that can assess any kind of interdependence. Detecting the maximally correlated motion allows one to derive a model for the functional state in terms of a single collective coordinate. The new approach is illustrated using a number of biomolecules, including a polyalanine-helix, T4 lysozyme, Trp-cage, and leucine-binding protein

Bare Bones Pattern Formation: A Core Regulatory Network in Varying Geometries Reproduces Major Features of Vertebrate Limb Development and Evolution

BACKGROUND: Major unresolved questions regarding vertebrate limb development concern how the numbers of skeletal elements along the proximodistal (P-D) and anteroposterior (A-P) axes are determined and how the shape of a growing limb affects skeletal element formation. There is currently no generally accepted model for these patterning processes, but recent work on cartilage development (chondrogenesis) indicates that precartilage tissue self-organizes into nodular patterns by cell-molecular circuitry with local auto-activating and lateral inhibitory (LALI) properties. This process is played out in the developing limb in the context of a gradient of fibroblast growth factor (FGF) emanating from the apical ectodermal ridge (AER). RESULTS: We have simulated the behavior of the core chondrogenic mechanism of the developing limb in the presence of an FGF gradient using a novel computational environment that permits simulation of LALI systems in domains of varying shape and size. The model predicts the normal proximodistal pattern of skeletogenesis as well as distal truncations resulting from AER removal. Modifications of the model's parameters corresponding to plausible effects of Hox proteins and formins, and of the reshaping of the model limb, bud yielded simulated phenotypes resembling mutational and experimental variants of the limb. Hypothetical developmental scenarios reproduce skeletal morphologies with features of fossil limbs. CONCLUSIONS: The limb chondrogenic regulatory system operating in the presence of a gradient has an inherent, robust propensity to form limb-like skeletal structures. The bare bones framework can accommodate ancillary gene regulatory networks controlling limb bud shaping and establishment of Hox expression domains. This mechanism accounts for major features of the normal limb pattern and, under variant geometries and different parameter values, those of experimentally manipulated, genetically aberrant and evolutionary early forms, with no requirement for an independent system of positional information

Development of a Scoring System to Evaluate the Severity of Craniocervical Spinal Cord Compression in Patients with Mucopolysaccharidosis IVA (Morquio A Syndrome)

Background: As spinal cord compression at the craniocervical junction (CCJ) is a life-threatening manifestation in patients with mucopolysaccharidosis (MPS) IVA, surgical decompression should be performed before damage becomes irreversible. We evaluated the diagnostic value of several examinations for determining the need for decompression surgery. Methods: We retrospectively analysed results of clinical neurological examination, somatosensory evoked potential (SEP) and magnetic resonance imaging (MRI) in 28 MPS IVA patients. A scoring system – based on the severity of findings – was used to compare results of patients with and without indication for decompression surgery. Individual test scores and two composite scores were evaluated for their potential to assess severity of CCJ impairment. Results: Sixteen patients had an indication for surgery; 12 of them had undergone surgery. Twelve patients had no indication for surgery; none had received surgery. Neurological (P = 0.004), MRI (P < 0.001) and atlantoaxial subluxation (P = 0.006) scores, but not SEP and odontoid hypoplasia scores, differed significantly between patients with and without surgical indication. Both the abbreviated CCJ score, i.e. sum of neurological and MRI scores, and the extended CCJ score, i.e. sum of abbreviated CCJ and atlantoaxial subluxation score, discriminated between patients with and without surgical indication (abbreviated: 0–2 points vs 2–5 points, P < 0.001; extended: 0–3 points vs 3–7 points; P < 0.001). Although CCJ instability plays a major role in cervical cord pathology, decompression surgery without occipito-cervical stabilisation may yield good postoperative results. Conclusions: The abbreviated and extended CCJ scores are objective, transparent and reproducible tools for assessing the CCJ pathology and the need for surgery