On Measurability Properties of Stochastic Processes

This paper does not contain anything new, and, in fact, it deals with a rather old-fashioned subject: the theorem of Chung-Doob [CD 64] and Meyer [Me66] (cf. also [DM 78]) on the existence of a progressively measurable modification of a measurable, adapted process. The raison d'€tre of this paper is that in our seminar at Mannheim periodically with new students the need comes up to understand the construction of the Itö-integral, and that in most of the common literat ure the details of a certain argument (see below) are not given or only hinted at. This paper attempts to provide that. argument in rather much - maybe even unnecessary - detail, so that the student can understand the probably most direct approach to the stochastic integral with respect to a Brownian motion as the limit of approximations of Riemann type

Progressive Stochastic Processes and an Application to the Itô Integral

An elementary proof of the theorem of Chung-Doob-Meyer on the existence of a progressively measurable modification of a measurable adapted process is given. It is shown how this result can be applied to the construction of the Itô integral with respect to a Brownian motion

MSH6- or PMS2-deficiency causes re-replication in DT40 B cells, but it has little effect on immunoglobulin gene conversion or on repair of AID-generated uracils

The mammalian antibody repertoire is shaped by somatic hypermutation (SHM) and class switch recombination (CSR) of the immunoglobulin (Ig) loci of B lymphocytes. SHM and CSR are triggered by non-canonical, error-prone processing of G/U mismatches generated by activation-induced deaminase (AID). In birds, AID does not trigger SHM, but it triggers Ig gene conversion (GC), a ‘homeologous' recombination process involving the Ig variable region and proximal pseudogenes. Because recombination fidelity is controlled by the mismatch repair (MMR) system, we investigated whether MMR affects GC in the chicken B cell line DT40. We show here that Msh6−/− and Pms2−/− DT40 cells display cell cycle defects, including genomic re-replication. However, although IgVλ GC tracts in MMR-deficient cells were slightly longer than in normal cells, Ig GC frequency, donor choice or the number of mutations per sequence remained unaltered. The finding that the avian MMR system, unlike that of mammals, does not seem to contribute towards the processing of G/U mismatches in vitro could explain why MMR is unable to initiate Ig GC in this species, despite initiating SHM and CSR in mammalian cells. Moreover, as MMR does not counteract or govern Ig GC, we report a rare example of ‘homeologous' recombination insensitive to MM

FAN1 interaction with ubiquitylated PCNA alleviates replication stress and preserves genomic integrity independently of BRCA2

Interstrand cross-link (ICL) hypersensitivity is a characteristic trait of Fanconi anemia (FA). Although FANCD2-associated nuclease 1 (FAN1) contributes to ICL repair, FAN1 mutations predispose to karyomegalic interstitial nephritis (KIN) and cancer rather than to FA. Thus, the biological role of FAN1 remains unclear. Because fork stalling in FAN1-deficient cells causes chromosomal instability, we reasoned that the key function of FAN1 might lie in the processing of halted replication forks. Here, we show that FAN1 contains a previously-uncharacterized PCNA interacting peptide (PIP) motif that, together with its ubiquitin-binding zinc finger (UBZ) domain, helps recruit FAN1 to ubiquitylated PCNA accumulated at stalled forks. This prevents replication fork collapse and controls their progression. Furthermore, we show that FAN1 preserves replication fork integrity by a mechanism that is distinct from BRCA2-dependent homologous recombination. Thus, targeting FAN1 activities and its interaction with ubiquitylated PCNA may offer therapeutic opportunities for treatment of BRCA-deficient tumors.This work was funded by the Swiss National Science Foundation (grant no. 310030B-133123 and 31003A- 149989) and by the European Research Council grant “Myriam” (294537), both to J.J

FAN1 interaction with ubiquitylated PCNA alleviates replication stress and preserves genomic integrity independently of BRCA2

Interstrand cross-link (ICL) hypersensitivity is a characteristic trait of Fanconi anemia (FA). Although FANCD2-associated nuclease 1 (FAN1) contributes to ICL repair, FAN1 mutations predispose to karyomegalic interstitial nephritis (KIN) and cancer rather than to FA. Thus, the biological role of FAN1 remains unclear. Because fork stalling in FAN1-deficient cells causes chromosomal instability, we reasoned that the key function of FAN1 might lie in the processing of halted replication forks. Here, we show that FAN1 contains a previously-uncharacterized PCNA interacting peptide (PIP) motif that, together with its ubiquitin-binding zinc finger (UBZ) domain, helps recruit FAN1 to ubiquitylated PCNA accumulated at stalled forks. This prevents replication fork collapse and controls their progression. Furthermore, we show that FAN1 preserves replication fork integrity by a mechanism that is distinct from BRCA2-dependent homologous recombination. Thus, targeting FAN1 activities and its interaction with ubiquitylated PCNA may offer therapeutic opportunities for treatment of BRCA-deficient tumors

Chromosome Missegregation Associated with RUVBL1 Deficiency

RUVBL1 (RuvB-like1) and RUVBL2 (RuvB-like 2) are integral components of multisubunit protein complexes involved in processes ranging from cellular metabolism, transcription and chromatin remodeling to DNA repair. Here, we show that although RUVBL1 and RUVBL2 are known to form heterodimeric complexes in which they stabilize each other, the subunits separate during cytokinesis. In anaphase-to-telophase transition, RUVBL1 localizes to structures of the mitotic spindle apparatus, where it partially co-localizes with polo-like kinase 1 (PLK1). The ability of PLK1 to phosphorylate RUVBL1-but not RUVBL2-in vitro and their physical association in vivo suggest that this kinase differentially regulates the function of the RuvB-like proteins during mitosis. We further show that siRNA-mediated knock-down of RuvB-like proteins causes severe defects in chromosome alignment and segregation. In addition, we show that the ATPase activity of RUVBL1 is indispensable for cell proliferation. Our data thus demonstrate that RUVBL1 is essential for efficient mitosis and proliferation

Progressive stochastic processes and an application to the Itô integral

An elementary proof of the theorem of Chung–Doob–Meyer on the existence of a progressively measurable modification of a measurable adapted process is given. It is shown how this result can be applied to the construction of the Itô integral with respect to a Brownian motion

<i>In vitro</i> phosphorylation of RUVBL1 by PLK1.

<p><b>(A)</b> Protein sequences were obtained from <a href="http://www.ncbi.nlm.nih.gov/" target="_blank">http://www.ncbi.nlm.nih.gov</a> and scanned for PLK1 consensus motifs [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0133576#pone.0133576.ref037" target="_blank">37</a>]. Corresponding sequences of human RUVBL2 are shown by comparison below the alignments. Crucial amino acids are shown in gray. <b>(B)</b> The indicated amounts of His-tagged RUVBL1 or RUVBL2 were incubated with PLK1 in the presence of [γ-³²P]ATP and protein phosphorylation was monitored by autoradiography. <b>(C)</b> Bands corresponding to phosphorylated RUVBL1 were excised and in-gel digested with trypsin. Eluted peptides were separated in two dimensions by their hydrophobicity and charge. Potential sequences were assigned to the obtained phosphopeptide patterns after autoradiography. Trypsin digestion sites are indicated with K•X. <b>(D)</b> Purified His-tagged RUVBL1 mutants were incubated with PLK1 in the presence of [γ-³²P]ATP and protein phosphorylation was monitored by autoradiography.</p

RUVBL1 depletion affects the length of mitosis and results in lagging chromosomes.

<p><b>(A)</b> HeLa cells were transfected with the indicated siRNA oligos and analyzed by RT-PCR and immunoblot 48 h post-transfection. <b>(B)</b> Confocal live imaging after siRNA-mediated knock-down was performed. The figure shows stills of control or RUVBL1 siRNA-treated cells. Lagging chromosomes are indicated with arrowheads. DNA is shown in cyan and α-tubulin in red. <b>(C)</b> Early mitotic progression was analyzed by measuring the time from prophase (nuclear envelope breakdown: NEB) to anaphase onset (left panel). Mitotic exit was estimated by measuring the period of time from anaphase onset until accomplished cytokinesis (right panel). The bottom and top of the boxes represent the first and third quartiles, respectively. Horizontal lines inside the boxes represent the median of the data points (n = 100). Whiskers span the 10th and 90th percentiles, with individual dots showing data points that lie outside of these percentiles. Statistical significance was determined by Mann–Whitney test and <i>p</i>-values are indicated above. <b>(D)</b> Occurrence of aberrant mitotic phenotypes was quantified by analyzing 100 cell divisions in each cell line.</p