Investigation of p75 neurotrophin receptor and the role of its post-translational modifications in tumour cell motility and invasiveness

The p75 neurotrophin receptor (p75NTR) is a member of the tumour necrosis factor superfamily, which relies on the recruitment of cytosolic protein partners - including the TNF receptor associated factor 6 (TRAF6) E3 ubiquitin ligase - to produce cellular responses such as apoptosis, survival, and inhibition of neurite outgrowth. Recently,p75NTR was also shown to undergo γ-secretase-mediated regulated intramembrane proteolysis, and the receptor ICD was found to migrate to the nucleus where it regulates gene transcription. Moreover, γ-secretase-mediated proteolysis was shown to be involved in glioblastoma cell migration and invasion. In this study we report that TRAF6-mediated K63-linked polyubiquitination at multiple or alternative lysine residues influences p75NTR-ICD stability in vitro. In addition, we found that TRAF6-mediated ubiquitination of p75NTR is not influenced by inhibition of dynamin. Moreover, we report beta-transducin repeats-containing protein (β-TrCP) as a novel E3- ligase that ubiquitinates p75NTR, which is independent of serine phosphorylation of the p75NTR destruction motif. In contrast to its influence on other substrates, co-expression of β-TrCP did not reduce p75NTR stability. We created U87-MG glioblastoma cell lines stably expressing wild type, γ-secretaseresistant and constitutively cleaved receptor, as well as the ICD-stabilized mutant K301R. Interestingly, only wild-type p75NTR induces increased glioblastoma cell migration, which could be reversed by application of γ-secretase inhibitor. Microarray and qRT-PCR analysis of mRNA transcripts in these cell lines yielded several promising genes that might be involved in glioblastoma cell migration and invasion, such as cadherin 11 and matrix metalloproteinase 12. Analysis of potential transcription factor binding sites revealed that transcription of these genes might be regulated by well known p75NTR signalling cascades such as NF-κB or JNK signalling, which are independent of γ-secretase-mediated cleavage of the receptor. In contrast, while p75NTR overexpression was confirmed in melanoma cell lines and a patient sample of melanoma metastasis to the brain, inhibition of γ-secretase did not influence melanoma cell migration. Collectively, this study provides several avenues to better understand the physiological importance of posttranslational modifications of p75NTR and the significance of the receptor in glioblastoma cell migration and invasion.

Financial modelling with 2-EPT probability density functions

The class of all Exponential-Polynomial-Trigonometric (EPT) functions is classical and equal to the Euler-d’Alembert class of solutions of linear differential equations with constant coefficients. The class of non-negative EPT functions defined on [0;1) was discussed in Hanzon and Holland (2010) of which EPT probability density functions are an important subclass. EPT functions can be represented as ceAxb, where A is a square matrix, b a column vector and c a row vector where the triple (A; b; c) is the minimal realization of the EPT function. The minimal triple is only unique up to a basis transformation. Here the class of 2-EPT probability density functions on R is defined and shown to be closed under a variety of operations. The class is also generalised to include mixtures with the pointmass at zero. This class coincides with the class of probability density functions with rational characteristic functions. It is illustrated that the Variance Gamma density is a 2-EPT density under a parameter restriction. A discrete 2-EPT process is a process which has stochastically independent 2-EPT random variables as increments. It is shown that the distribution of the minimum and maximum of such a process is an EPT density mixed with a pointmass at zero. The Laplace Transform of these distributions correspond to the discrete time Wiener-Hopf factors of the discrete time 2-EPT process. A distribution of daily log-returns, observed over the period 1931-2011 from a prominent US index, is approximated with a 2-EPT density function. Without the non-negativity condition, it is illustrated how this problem is transformed into a discrete time rational approximation problem. The rational approximation software RARL2 is used to carry out this approximation. The non-negativity constraint is then imposed via a convex optimisation procedure after the unconstrained approximation. Sufficient and necessary conditions are derived to characterise infinitely divisible EPT and 2-EPT functions. Infinitely divisible 2-EPT density functions generate 2-EPT Lévy processes. An assets log returns can be modelled as a 2-EPT Lévy process. Closed form pricing formulae are then derived for European Options with specific times to maturity. Formulae for discretely monitored Lookback Options and 2-Period Bermudan Options are also provided. Certain Greeks, including Delta and Gamma, of these options are also computed analytically. MATLAB scripts are provided for calculations involving 2-EPT functions. Numerical option pricing examples illustrate the effectiveness of the 2-EPT approach to financial modelling.