Universal spectrum of normal modes in low-temperature glasses

We report an analytical study of the vibrational spectrum of the simplest model of jamming, the soft perceptron. We identify two distinct classes of soft modes. The first kind of modes are related to isostaticity and appear only in the close vicinity of the jamming transition. The second kind of modes instead are present everywhere in the glass phase and are related to the hierarchical structure of the potential energy landscape. Our results highlight the universality of the spectrum of normal modes in disordered systems, and open the way toward a detailed analytical understanding of the vibrational spectrum of low-temperature glasses.Low-energy excitations in disordered glassy systems have received a great deal of attention because of their multiple interesting features and their importance for thermodynamic and transport properties of low-temperature glasses. Much debate has been concentrated around the deviation of the spectrum from the Debye law for solids, due to an excess of low-energy excitations, known as the “boson peak” (1).The vibrational spectrum of glasses is a natural problem of random matrix theory. In fact, the Hessian of a disordered system is a random matrix due to the random position of particles in the sample. The distribution of the particles induces nontrivial correlations between the matrix elements. Many attempted to explain the observed spectrum of eigenvalues by replacing the true statistical ensemble with some simpler ones, in which correlations are neglected or treated in approximate ways (2–11). However, most of these models are not microscopically grounded, thus making it difficult to assess which of the proposed mechanisms are the most relevant and understand their interplay.In this work we will focus on two ways of inducing a boson peak in random matrix models. First, it has been suggested that the boson peak is due to the vicinity to the jamming transition where glasses are isostatic (12, 13). Isostaticity means that the number of degrees of freedom is exactly equal to the number of interactions. Isostaticity implies marginal mechanical stability (MMS): cutting one particle contact induces an unstable soft mode that allows particles to slide without paying any energy cost (14, 15). From this hypothesis, scaling laws have been derived that characterize the spectrum as a function of the distance from an isostatic point (11, 12, 16). Second, it has been proposed that low-temperature glasses have a complex energy landscape with a hierarchical distribution of energy minima and barriers (17). Minima are marginally stable (18) and display anomalous soft modes (11, 19) related to the lowest energy barriers (20–22). We will denote this second kind of marginality as landscape marginal stability (LMS).Both mechanisms described above are highly universal. LMS is a generic property of mean-field strongly disordered models (18). MMS holds for a broad class of simple random matrix models (6, 10, 11, 16) and for realistic glass models (12, 23, 24) at the isostatic point. Universality motivates the introduction of a broad class of continuous constraint satisfaction problems (CCSP) (25), in which a set of constraints is imposed on a set of continuous variables. In the satisfiable (SAT) phase, all of the constraints can be satisfied, whereas this is impossible in the unsatisfiable (UNSAT) phase. A sharp SAT–UNSAT transition separates the two phases: jamming can be seen as a particular instance of this transition. In fact, (i) jamming properties are within numerical precision superuniversal, i.e., independent of the spatial dimension d for all d ≥ 2 (26, 27), (ii) they can be analytically predicted through the exact solution in d → ∞ (17, 28), and (iii) the perceptron model of neural networks, a prototypical CCSP, displays a jamming transition with the same exponents (25). Based on universality, both for analytical and numerical computations, the perceptron appears to be the simplest model^† where low-temperature glassy behavior can be studied (25).Here, we exploit this simplicity and characterize analytically the vibrational spectrum of the perceptron at zero temperature in the glass phase. Our main results are (i) the spectrum is given by a Marchenko–Pastur law with parameters that can be computed analytically; (ii) it closely resembles the one of soft sphere glass models in all d ≥ 2; (iii) it displays soft modes coming from marginal stabilities of both kinds (LMS and MMS), allowing us to unify both contributions and understand their interplay. Our results are based on the replica method and random matrix theory, and for the first time, to our knowledge, we are able to derive all of the critical properties of jamming within the analytic solution of a well-defined microscopic model.     

NF-κB contributes to MMP1 expression in breast cancer spheroids causing paracrine PAR1 activation and disintegrations in the lymph endothelial barrier in vitro

RELA, RELB, CREL, NFKB1 and NFKB2, and the upstream regulators NEMO and NIK were knocked-down in lymph endothelial cells (LECs) and in MDA-MB231 breast cancer spheroids to study the contribution of NF-κB in vascular barrier breaching. Suppression of RELA, NFKB1 and NEMO inhibited “circular chemo-repellent induced defects” (CCIDs), which form when cancer cells cross the lymphatic vasculature, by ~20–30%. Suppression of RELB, NFKB2 and NIK inhibited CCIDs by only ~10–15%. In MDA-MB231 cells RELA and NFKB1 constituted MMP1 expression, which caused the activation of PAR1 in adjacent LECs. The knock-down of MMP1 in MDA-MB231 spheroids and pharmacological inhibition of PAR1 in LECs inhibited CCID formation by ~30%. Intracellular Ca²⁺ release in LECs, which was induced by recombinant MMP1, was suppressed by the PAR1 inhibitor {"type":"entrez-protein","attrs":{"text":"SCH79797","term_id":"1052762130","term_text":"SCH79797"}}SCH79797, thereby confirming a functional intercellular axis: RELA/NFKB1 – MMP1 (MDA-MB231) – PAR1 (LEC). Recombinant MMP1 induced PAR1-dependent phosphorylation of MLC2 and FAK in LECs, which is indicative for their activity and for directional cell migration such as observed during CCID formation. The combined knock-down of the NF-κB pathways in LECs and MDA-MB231 spheroids inhibited CCIDs significantly stronger than knock-down in either cell type alone. Also the knock-down of ICAM-1 in LECs (a NF-κB endpoint with relevance for CCID formation) and knock-down of MMP1 in MDA-MB231 augmented CCID inhibition. This evidences that in both cell types NF-κB significantly and independently contributes to tumour-mediated breaching of the lymphatic barrier. Hence, inflamed tumour tissue and/or vasculature pose an additional threat to cancer progression.     

Monosomy of chromosome 17 in breast cancer during interpretation of HER2 gene amplification

Monosomy of chromosome 17 may affect the assessment of HER2 amplification. Notably, the prevalence ranges from 1% up to 49% due to lack of consensus in recognition. We sought to investigate the impact of monosomy of chromosome 17 to interpretation of HER2 gene status. 201 breast carcinoma were reviewed for HER2 gene amplification and chromosome 17 status. FISH analysis was performed by using double probes (LSI/CEP). Absolute gene copy number was also scored per each probe. HER2 FISH test was repeated on serial tissue sections, ranging in thickness from 3 to 20 µm. Ratio was scored and subsequently corrected by monosomy after gold control test using the aCGH method to overcome false interpretation due to artefactual nuclear truncation. HER2 immunotests was performed on all cases. 26/201 cases were amplified (13%). Single signals per CEP17 were revealed in 7/201 (3.5%) cases. Five out of 7 cases appeared monosomic with aCGH (overall, 5/201, 2.5%) and evidenced single signals in >60% of nuclei after second-look on FISH when matching both techniques. Among 5, one case showed amplification with a pattern 7/1 (HER2/CEP17>2) of copies (3+ at immunotest); three cases revealed single signals per both probes (LSI/CEP=1) and one case revealed a 3:1 ratio; all last 4 cases showed 0/1+ immunoscore. We concluded that: 1) monosomy of chromosome 17 may be observed in 2.5% of breast carcinoma; 2) monosomy of chromosome 17 due to biological reasons rather than nuclear truncation was observed when using the cut-off of 60% of nuclei harboring single signals; 3) the skewing of the ratio due to single centromeric 17 probe may lead to false positive evaluation; 4) breast carcinomas showing a 3:1 ratio (HER2/CEP17) usually show negative 0/1+ immunoscore and <6 gene copy number at FISH.     

Second-generation arthroscopic autologous chondrocyte implantation for the treatment of degenerative cartilage lesions

Purpose

Degenerative cartilage lesions present a negative joint environment, which may have a negative effect on the process of cartilage regeneration. The aim of this study is to analyze the clinical outcome obtained with the treatment for isolated degenerative knee cartilage lesions by second-generation arthroscopic autologous chondrocyte implantation (ACI).

Methods

Fifty-eight consecutive patients affected by focal degenerative chondral lesions of the femoral condyles and trochlea were treated by second-generation arthroscopic ACI. The mean age at surgery was 34.7?±?9.1?years and the average defect size was 2.3?±?0.9?cm². The patients were prospectively evaluated with IKDC, EQ-VAS, and Tegner scores preoperatively, at 2 and 6?years.

Results

A statistically significant improvement was observed in all scores from the basal evaluation to the final follow-up. The IKDC subjective score improved from 39.3?±?13.6 to 68.8?±?22.7 and 68.5?±?23.9 at the 2- and 6-year follow-ups, respectively, with a significant improvement (P?Conclusions Despite a significant improvement, the results were lower with respect to the outcome reported in different study populations, and the number of failures was markedly higher, too. Tissue-engineered cartilage implantation is a promising approach for the treatment of degenerative chondral lesions, but graft properties, besides mechanical and biochemical joint environment, have to be improved.

Level of evidence

Case series, Level IV.