Information inequalities and Generalized Graph Entropies

In this article, we discuss the problem of establishing relations between information measures assessed for network structures. Two types of entropy based measures namely, the Shannon entropy and its generalization, the R\'{e}nyi entropy have been considered for this study. Our main results involve establishing formal relationship, in the form of implicit inequalities, between these two kinds of measures when defined for graphs. Further, we also state and prove inequalities connecting the classical partition-based graph entropies and the functional-based entropy measures. In addition, several explicit inequalities are derived for special classes of graphs.Comment: A preliminary version. To be submitted to a journa

Connections between Classical and Parametric Network Entropies

This paper explores relationships between classical and parametric measures of graph (or network) complexity. Classical measures are based on vertex decompositions induced by equivalence relations. Parametric measures, on the other hand, are constructed by using information functions to assign probabilities to the vertices. The inequalities established in this paper relating classical and parametric measures lay a foundation for systematic classification of entropy-based measures of graph complexity

Information Indices with High Discriminative Power for Graphs

In this paper, we evaluate the uniqueness of several information-theoretic measures for graphs based on so-called information functionals and compare the results with other information indices and non-information-theoretic measures such as the well-known Balaban index. We show that, by employing an information functional based on degree-degree associations, the resulting information index outperforms the Balaban index tremendously. These results have been obtained by using nearly 12 million exhaustively generated, non-isomorphic and unweighted graphs. Also, we obtain deeper insights on these and other topological descriptors when exploring their uniqueness by using exhaustively generated sets of alkane trees representing connected and acyclic graphs in which the degree of a vertex is at most four

Quantitative real-time RT-PCR of CD24 mRNA in the detection of prostate cancer

BACKGROUND: Gene expression profiling has recently shown that the mRNA for CD24 is overexpressed in prostate carcinomas (Pca) compared to benign or normal prostate epithelial tissues. Immunohistochemical studies have reported the usefulness of anti-CD24 for detecting prostate cancer over the full range of prostate specimens encountered in surgical pathology, e.g. needle biopsies, transurethral resection of prostate chips, or prostatectomies. It is a small mucin-like cell surface protein and thus promises to become at least a standard adjunctive stain for atypical prostate biopsies. We tested the usefulness of real-time RT-PCR for specific and sensitive detection of CD24 transcripts as a supplementary measure for discriminating between malignant and benign lesions in prostatic tissues. METHODS: Total RNA was isolated from snap-frozen chips in 55 cases of benign prostatic hyperplasia (BPH) and from frozen sections in 59 prostatectomy cases. The latter contain at least 50% malignant epithelia. Relative quantification of CD24 transcripts was performed on the LightCycler instrument using hybridization probes for detection and porphobilinogen deaminase transcripts (PBGD) for normalization. RESULTS: Normalized CD24 transcript levels showed an average 2.69-fold increase in 59 Pca-cases (mean 0.21) when compared to 55 cases of BPH (mean 0.08). This difference was highly significant (p < 0.0001). The method has a moderate specificity (47.3%) but a high sensitivity (86.4%) if the cutoff is set at 0.0498. CD24 expression levels among Pca cases were not statistically associated with the tumor and lymph-node stage, the grading (WHO), the surgical margins, or the Gleason score. CONCLUSION: The present study demonstrates the feasibility of quantitative CD24 RNA transcript detection in prostatic tissues even without previous laser microdissection

Increased expression of transcription factor TFAP2α correlates with chemosensitivity in advanced bladder cancer

<p>Abstract</p> <p>Background</p> <p>The standard treatment for patients with advanced transitional cell carcinoma of the bladder is platin based chemotherapy. Only approximately 50% of the patients respond to chemotherapy. Therefore, molecular predictive markers for identification of chemotherapy sensitive subgroups of patients are highly needed. We selected the transcription factor <it>TFAP2α </it>from a previously identified gene expression signature for chemotherapy response.</p> <p>Methods</p> <p><it>TFAP2α </it>expression and localization was assessed by immunohistochemistry using a tissue microarray (TMA) containing 282 bladder cancer tumors from patients with locally advanced (pT2-T4_band N_1-3) or metastatic (M₁) disease. All patients had received cisplatin containing chemotherapy. Furthermore, QPCR analysis of three <it>TFAP2α </it>isoforms was performed on tumor specimens of advanced muscle invasive bladder cancers (T2-4). Using the bladder cell lines T24 and SW780 the relation of <it>TFAP2α </it>and cisplatin and gemcitabine sensitivity as well as cell proliferation was examined using siRNA directed <it>TFAP2α </it>knockdown.</p> <p>Results</p> <p>TFAP2α protein expression was analyzed on a TMA with cores from 282 advanced bladder cancer tumors from patients treated with cisplatin based combinational chemotherapy. <it>TFAP2α </it>was identified as a strong independent predictive marker for a good response and survival after cisplatin-containing chemotherapy in patients with advanced bladder cancer. Strong TFAP2α nuclear and cytoplasmic staining predicted good response to chemotherapy in patients with lymph node metastasis, whereas weak TFAP2α nuclear staining predicted good response in patients without lymph node metastasis. In vitro studies showed that siRNA mediated knockdown of TFAP2α increased the proliferation of SW780 cells and rendered the cells less sensitive to cisplatin and gemcitabine. In contrast to that T24 bladder cells with mutated p53 showed to be more drug sensitive upon TFAP2α depletion.</p> <p>Conclusions</p> <p>High levels of nuclear and cytoplasmic TFAP2α protein were a predictor of increased overall survival and progression free survival in patients with advanced bladder cancer treated with cisplatin based chemotherapy. TFAP2α knockdown increased the proliferation of the SW780 bladder cells and reduced cisplatin and gemcitabine induced cell death. The inverse effect was observed in the <it>TP53 </it>mutated T24 cell line where TFAP2α silencing augmented cisplatin and gemcitabine sensitivity and did not stimulate proliferation.</p

Extraction of Accurate Biomolecular Parameters from Single-Molecule Force Spectroscopy Experiments

The atomic force microscope (AFM) is able to manipulate biomolecules and their complexes with exquisite force sensitivity and distance resolution. This capability, complemented by theoretical models, has greatly improved our understanding of the determinants of mechanical strength in proteins and revealed the diverse effects of directional forces on the energy landscape of biomolecules. In unbinding experiments, the interacting partners are usually immobilized on their respective substrates via extensible linkers. These linkers affect both the force and contour length (Lc) of the complex at rupture. Surprisingly, while the former effect is well understood, the latter is largely neglected, leading to incorrect estimations of Lc, a parameter that is often used as evidence for the detection of specific interactions and remodeling events and for the inference of interaction regions. To address this problem, a model that predicts contour length measurements from single-molecule forced-dissociation experiments is presented that considers attachment position on the AFM tip, geometric effects, and polymer dynamics of the linkers. Modeled data are compared with measured contour length distributions from several different experimental systems, revealing that current methods underestimate contour lengths. The model enables nonspecific interactions to be identified unequivocally, allows accurate determination of Lc, and, by comparing experimental and modeled distributions, enables partial unfolding events before rupture to be identified unequivocally