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.

Characterisation of the non-muscle α-actinins

Actinins are cytoskeleton proteins that cross-link actin filaments. Evolution of the actinin family resulted in the formation of Ca++-insensitive muscle isoforms (actinin-2 and- 3) and Ca++-sensitive non-muscle isoforms (actinin-1 and -4) with regard to their actin-binding function. Despite high sequence similarity, unique properties have been ascribed to actinin-4 compared with actinin-1. Actinin-4 is the predominant isoform reported to be associated with the cancer phenotype. Actinin-4, but not actinin-1, is essential for normal glomerular function in the kidney and and is able to translocate to the nucleus to regulate transcription. To understand the molecular basis for such isoform-specific functions I have comprehensively compared these proteins in terms of localisation, migration, alternative splicing, actin-binding properties, heterodimer formation and molecular interactions for the first time. This work characterises a number of commercially available actinin antibodies and in doing so, identifies actinin-1, -2 and -4 isoform-specific antibodies that enabled studies of actinin expression and localisation. This work identifies the actinin rod domain as the predominant domain that influences actinin localisation however localisation is likely to be effected by the entire actinin protein. si-RNA- mediated knockdown of actinin-1 and -4 did not affect migration in a number of cell lines highlighting that migration may only require a fraction of total non-muscle actinin levels. This work finds that the Ca++-insensitive variant of actinin-4 is expressed only in the nervous system and thus cannot be regarded as a smooth muscle isoform, as is the case for the Ca++-insensitive variant of actinin-1. This work also identifies a previously unreported exon 19a+19b expressing variant of actinin-4 in human skeletal muscle. This work finds that alternative splice variants of actinin-1 and -4 are co-expressed in a number of tissues, in particular the brain. In contrast to healthy brain, glioblastoma cells express Ca++-sensitive variants of both actinin-1 and -4. Actin-binding properties of actinin-1 and -4 are similar and are unlikely to explain isoform-specific functions. Surprisingly, this work reveals that actinin-1/-4 heterodimers, rather than homodimers, are the most abundant form of actinin in many cancer cell lines. Taken together this data suggests that actinin-1 and -4 cannot be viewed as distinct entities from each other but rather as proteins that can exist in both homodimeric and heterodimeric forms. Finally, this work employs yeast two-hybrid and proteomic approaches to identify actinin-interacting proteins. In doing so, this work identifies a number of putative actinin-4 specific interacting partners that may help to explain some of the unique functions attributed the actinin-4. The observation of alternative splice variants of actinin-1 and -4 combined with the observed potential of these proteins to form homodimers and heterodimers suggests that homodimers and heterodimers with novel actin-binding properties and interaction networks may exist. The ability to behave in this manner may have functional implications. This may be of importance considering that these proteins are central to such processes as cell migration and adhesion. This significantly alters our view of the non-muscle actinins.

Investigation of the function of the LNX family of E3 ubiquitin ligases in the nervous system

The Lnx1 (Ligand of Numb protein X 1) and Lnx2 genes belong to a family of PDZ domain-containing RING finger domain E3 ubiquitin ligases. mRNA expression for both genes have been reported in early murine central nervous system. However, there have been limited reports with regards to the expression patterns for both the proteins in vivo. Hence, we have attempted to characterize the significance of these proteins in the context of morphology and physiology of the central nervous system. Through our studies, we have attempted to examine closely the expression of these two genes in the murine central nervous system. We have also looked at novel interacting ligands for both proteins. Interacting partners have been examined with particular relevance to possible roles of their interactions with LNX1 and LNX2 in the functioning of the nervous system. Moreover, we have performed loss-of-function studies by way of creation and characterization of knockout mice.

Identification of RNA editing in the human exome and development of DARNED DatabaseSF

RNA editing is a biological phenomena that alters nascent RNA transcripts by insertion, deletion and/or substitution of one or a few nucleotides. It is ubiquitous in all kingdoms of life and in viruses. The predominant editing event in organisms with a developed central nervous system is Adenosine to Inosine deamination. Inosine is recognized as Guanosine by the translational machinery and reverse-transcriptase. In primates, RNA editing occurs frequently in transcripts from repetitive regions of the genome. In humans, more than 500,000 editing instances have been identified, by applying computational pipelines on available ESTs and high-throughput sequencing data, and by using chemical methods. However, the functions of only a small number of cases have been studied thoroughly. RNA editing instances have been found to have roles in peptide variants synthesis by non-synonymous codon substitutions, transcript variants by alterations in splicing sites and gene silencing by miRNAs sequence modifications. We established the Database of RNA EDiting (DARNED) to accommo-date the reference genomic coordinates of substitution editing in human, mouse and fly transcripts from published literatures, with additional information on edited genomic coordinates collected from various databases e.g. UCSC, NCBI. DARNED contains mostly Adenosine to Inosine editing and allows searches based on genomic region, gene ID, and user provided sequence. The Database is accessible at http://darned.ucc.ie RNA editing instances in coding region are likely to result in recoding in protein synthesis. This encouraged me to focus my research on the occurrences of RNA editing specific CDS and non-Alu exonic regions. By applying various filters on discrepancies between available ESTs and their corresponding reference genomic sequences, putative RNA editing candidates were identified. High-throughput sequencing was used to validate these candidates. All predicted coordinates appeared to be either SNPs or unedited.

Molecular genetics of the imprinted gene - SPROUTY3 (SPRY3)

Sprouty proteins are key regulators of cell growth and branching morphogenesis during development. Human SPRY3 which maps to the pseudoautosomal region 2, undergoes random X-inactivation in females and preferential Y-inactivation in males, behaving as though genetically X-linked. Spry3 is widely expressed in neuronal tissues, being found at high levels in the cerebellum and particularly in the Purkinje cells which, notably, are deficient in the autistic brain. Spry3 is also highly expressed in other ganglia in adults including retinal ganglion cells, dorsal root ganglion and superior cervical ganglion. SPRY3 enhancer can drive SPRY3 expression in the lung airway, which is consistent with a role in branching morphogenesis and the function of the original Drosophila Spry gene, which is critical for lung morphogenesis, providing a possible explanation for an observed anatomic abnormality in the autistic lung airway. In the human and mouse, the SPRY3 core promoter contains an AG-rich repeat and we found evidence of coexpression, promoter binding and regulation of SPRY3 expression by transcription factors EGR1, ZNF263 and PAX6. Spry3 over-expression in mouse superior cervical ganglion cells inhibits axon branching and Spry3 knockdown in those cells increases axon branching, consistent with known functions of other Sprouty proteins. Novel SPRY3 upstream transcripts that I characterised originate from three start sites in the X-linked F8A3 – TMLHE gene region, which is recently implicated in autism causation. Arising from these findings, I propose that the lung airway abnormality and low levels of blood carnitine found in autism suggest that deregulation of SPRY3 may underpin a subset of autism cases.