Transition probability of Brownian motion in the octant and its application to default modeling

We derive a semi-analytic formula for the transition probability of three-dimensional Brownian motion in the positive octant with absorption at the boundaries. Separation of variables in spherical coordinates leads to an eigenvalue problem for the resulting boundary value problem in the two angular components. The main theoretical result is a solution to the original problem expressed as an expansion into special functions and an eigenvalue which has to be chosen to allow a matching of the boundary condition. We discuss and test several computational methods to solve a finite-dimensional approximation to this nonlinear eigenvalue problem. Finally, we apply our results to the computation of default probabilities and credit valuation adjustments in a structural credit model with mutual liabilities

Investigating the Effects of Mutant FUS on Stress Response in Amyotrophic Lateral Sclerosis: A Thesis

During stress, eukaryotes regulate protein synthesis in part through formation of cytoplasmic, non-membrane-bound complexes called stress granules (SGs). SGs transiently store signaling proteins and stalled translational complexes in response to stress stimuli (e.g. oxidative insult, DNA damage, temperature shifts and ER dysfunction). The functional outcome of SGs is proper translational regulation and signaling, allowing cells to overcome stress. The fatal motor neuron disease Amyotrophic Lateral Sclerosis (ALS) develops in an age-related manner and is marked by progressive neuronal death, with cytoplasmic protein aggregation, excitotoxicity and increased oxidative stress as major hallmarks. Fused in Sarcoma/Translocated in Liposarcoma (FUS) is an RNA-binding protein mutated in ALS with roles in RNA and DNA processing. Most ALS-associated FUS mutations cause FUS to aberrantly localize in the cytoplasm due to a disruption in the nuclear localization sequence. Intriguingly, pathological inclusions in human FUSALS cases contain aggregated FUS as well as several SG-associated proteins. Further, cytoplasmic mutant FUS incorporates into SGs, which increases SG volume and number, delays SG assembly, accelerates SG disassembly, and alters SG dynamics. I posit that mutant FUS association with stress granules is a toxic gain-of-function in ALS that alters the function of SGs by interaction with SG components. Here, I show that mutant FUS incorporates in to SGs via its Cterminal RGG motifs, the methylation of which is not required for this localization. Further, I identify protein interactions specific to full-length mutant FUS under stress conditions that are potentially capable of interacting with FUS in SGs. Finally, I demonstrate a potential change in the protein composition of SGs upon incorporation of mutant FUS. These findings advance the field of ALS and SG biology, thereby providing groundwork for future investigation

Pathways and gene networks mediating the regulatory effects of cannabidiol, a nonpsychoactive cannabinoid, in autoimmune T cells.

BackgroundOur previous studies showed that the non-psychoactive cannabinoid, cannabidiol (CBD), ameliorates the clinical symptoms in mouse myelin oligodendrocyte glycoprotein (MOG)35-55-induced experimental autoimmune encephalomyelitis model of multiple sclerosis (MS) as well as decreases the memory MOG35-55-specific T cell (TMOG) proliferation and cytokine secretion including IL-17, a key autoimmune factor. The mechanisms of these activities are currently poorly understood.MethodsHerein, using microarray-based gene expression profiling, we describe gene networks and intracellular pathways involved in CBD-induced suppression of these activated memory TMOG cells. Encephalitogenic TMOG cells were stimulated with MOG35-55 in the presence of spleen-derived antigen presenting cells (APC) with or without CBD. mRNA of purified TMOG was then subjected to Illumina microarray analysis followed by ingenuity pathway analysis (IPA), weighted gene co-expression network analysis (WGCNA) and gene ontology (GO) elucidation of gene interactions. Results were validated using qPCR and ELISA assays.ResultsGene profiling showed that the CBD treatment suppresses the transcription of a large number of proinflammatory genes in activated TMOG. These include cytokines (Xcl1, Il3, Il12a, Il1b), cytokine receptors (Cxcr1, Ifngr1), transcription factors (Ier3, Atf3, Nr4a3, Crem), and TNF superfamily signaling molecules (Tnfsf11, Tnfsf14, Tnfrsf9, Tnfrsf18). "IL-17 differentiation" and "IL-6 and IL-10-signaling" were identified among the top processes affected by CBD. CBD increases a number of IFN-dependent transcripts (Rgs16, Mx2, Rsad2, Irf4, Ifit2, Ephx1, Ets2) known to execute anti-proliferative activities in T cells. Interestingly, certain MOG35-55 up-regulated transcripts were maintained at high levels in the presence of CBD, including transcription factors (Egr2, Egr1, Tbx21), cytokines (Csf2, Tnf, Ifng), and chemokines (Ccl3, Ccl4, Cxcl10) suggesting that CBD may promote exhaustion of memory TMOG cells. In addition, CBD enhanced the transcription of T cell co-inhibitory molecules (Btla, Lag3, Trat1, and CD69) known to interfere with T/APC interactions. Furthermore, CBD enhanced the transcription of oxidative stress modulators with potent anti-inflammatory activity that are controlled by Nfe2l2/Nrf2 (Mt1, Mt2a, Slc30a1, Hmox1).ConclusionsMicroarray-based gene expression profiling demonstrated that CBD exerts its immunoregulatory effects in activated memory TMOG cells via (a) suppressing proinflammatory Th17-related transcription, (b) by promoting T cell exhaustion/tolerance, (c) enhancing IFN-dependent anti-proliferative program, (d) hampering antigen presentation, and (d) inducing antioxidant milieu resolving inflammation. These findings put forward mechanism by which CBD exerts its anti-inflammatory effects as well as explain the beneficial role of CBD in pathological memory T cells and in autoimmune diseases

Semi-analytical solution of a McKean-Vlasov equation with feedback through hitting a boundary

In this paper, we study the non-linear diffusion equation associated with a particle system where the common drift depends on the rate of absorption of particles at a boundary. We provide an interpretation as a structural credit risk model with default contagion in a large interconnected banking system. Using the method of heat potentials, we derive a coupled system of Volterra integral equations for the transition density and for the loss through absorption. An approximation by expansion is given for a small interaction parameter. We also present a numerical solution algorithm and conduct computational tests

Outcomes of mentored, grant‐funded fellowship training in haemostasis /thrombosis: findings from a nested case–control survey study

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/91228/1/j.1365-2516.2011.02626.x.pd

Post-CNS-inflammation expression of CXCL12 promotes the endogenous myelin/neuronal repair capacity following spontaneous recovery from multiple sclerosis-like disease

Background: Demyelination and axonal degeneration, hallmarks of multiple sclerosis (MS), are associated with the central nervous system (CNS) inflammation facilitated by C-X-C motif chemokine 12 (CXCL12) chemokine. Both in MS and in experimental autoimmune encephalomyelitis (EAE), the deleterious CNS inflammation has been associated with upregulation of CXCL12 expression in the CNS. We investigated the expression dynamics of CXCL12 in the CNS with progression of clinical EAE and following spontaneous recovery, with a focus on CXCL12 expression in the hippocampal neurogenic dentate gyrus (DG) and in the corpus callosum (CC) of spontaneously recovered mice, and its potential role in promoting the endogenous myelin/neuronal repair capacity. Methods: CNS tissue sections from mice with different clinical EAE phases or following spontaneous recovery and in vitro differentiated adult neural stem cell cultures were analyzed by immunofluorescent staining and confocal imaging for detecting and enumerating neuronal progenitor cells (NPCs) and oligodendrocyte precursor cells (OPCs) and for expression of CXCL12. Results: Our expression dynamics analysis of CXCL12 in the CNS with EAE progression revealed elevated CXCL12 expression in the DG and CC, which persistently increases following spontaneous recovery even though CNS inflammation has subsided. Correspondingly, the numbers of NPCs and OPCs in the DG and CC, respectively, of EAE-recovered mice increased compared to that of naive mice (NPCs, p 20 %) of the CXCL12(+) NPCs and OPCs co-express the CXCL12 receptor, CXCR4, and their numbers significantly increase with recovery from EAE not only relative to naive mice (p < 0.0002) but also to mice with ongoing EAE (p < 0.004). Conclusions: These data link CXCL12 expression in the DG and CC of EAE-recovering mice to the promotion of neuro/oligodendrogenesis generating CXCR4(+)CXCL12(+) neuronal and oligodendrocyte progenitor cells endowed with intrinsic neuro/oligondendroglial differentiation potential. These findings highlight the post-CNS-inflammation role of CXCL12 in augmenting the endogenous myelin/neuronal repair capacity in MS-like disease, likely via CXCL12/CXCR4 autocrine signaling

The Promise of Systems Biology Approaches for Revealing Host Pathogen Interactions in Malaria.

Despite global eradication efforts over the past century, malaria remains a devastating public health burden, causing almost half a million deaths annually (WHO, 2016). A detailed understanding of the mechanisms that control malaria infection has been hindered by technical challenges of studying a complex parasite life cycle in multiple hosts. While many interventions targeting the parasite have been implemented, the complex biology o