Mitosis is the shortest phase of the cell cycle but visually the most outstanding. The key goal of mitosis is to accurately drive chromosome segregation. On one hand, DNA has to be condensed into characteristically shaped chromosomes. On the other hand, a very specialized structure needs to be built to conduct segregation, the mitotic spindle which is composed of microtubules organized into an antiparallel array between the two poles. The interaction between microtubules and chromosomes occurs at the kinetochore, a macromolecular complex assembled in mitosis at the centromere. The centromere/kinetochore monitors proper spindle microtubule attachment to each of the chromosomes, aligning them at the metaphase plate and also ensuring that chromosome segregation happens in perfect synchrony. Although centromeres are present in all eukaryotes, their basic structure and chromatin folding are still poorly understood. One of the aims of my work was to understand the function of the condensin complex specifically at the centromere during mitosis. Condensin I and II are pentameric protein complexes that are among the most abundant components of mitotic chromosomes. I have shown that condensin is important to confer stiffness to the innercentromeric chromatin once spindle microtubules interact with kinetochores in metaphase. Labile inner-centromeric regions delay mitotic progression by altering microtubule-kinetochore attachments and/or dynamics with a consequent increase in levels of Mad2 checkpoint protein bound to kinetochores. In the absence of condensin, kinetochores perform prominent “excursions” toward the poles trailing behind a thin thread of chromatin. These excursions are reversible suggesting that the centromeric chromatin behaves like an elastic polymer. During these excursions I noticed that only the inner centromeric chromatin was subjected to reversible deformations while the kinetochores (inner and outer plates) remained mostly unaltered. This suggested that the centromeric chromatin part of the inner kinetochore plate was organised differently from the subjacent chromatin. I went on to investigate how the centromeric chromatin is organised within the inner kinetochore domain. Super-resolution analyses of artificially unfolded centromeric chromatin revealed novel details of the vertebrate inner kinetochore domain. All together, the data allowed me to propose a new model for the centromeric chromatin folding: CENP-A domains are interspersed with H3 domains arranged in a linear segment that forms planar sinusoidal waves distributed in several layers. Both CENP-A and H3 arrays face the external surface, building a platform for CCAN proteins. CENP-C binds to more internal CENP-A blocks thereby crosslinking the layers. This organization of the chromatin explains the localisation and similar compliant behaviour that CENP-A and CENP-C showed when kinetochores come under tension. Other kinetochore proteins (the KMN complex) assemble in mitosis on top of the CCAN and bind microtubules. KMN binding may confer an extra degree of stability to the kinetochore by crosslinking CENP-C either directly or indirectly. My work and the testable model that I have developed for kinetochore organization provide a fundamental advance in our understanding of this specialized chromosomal substructure.

In this Master’s thesis, joint sequential inference of both parameters and states of stochastic volatility models is carried out using the SMC2 algorithm found in SMC2: an efficient algorithm for sequential analysis of state-space models, Nicolas Chopin, Pierre E. Jacob, Omiros Papaspiliopoulos. The models under study are the continuous time s.v. models (i) Heston, (ii) Bates, and (iii) SVCJ, where inference is based on options prices. It is found that the SMC2 performs well for the simpler models (i) and (ii), wheras filtering in (iii) performs worse. Furthermore, it is found that the FFT option price evaluation is the most computationally demanding step, and it is suggested to explore other avenues of computation, such as GPGPU-based computing. / I denna Masteruppsats estimeras sekventiellt parametrar och tillstånd i stokastiska volatilitetsmodeller nyttjandes SMC2 -algoritmen som återfinns i [1]. Modellerna som studeras är de kontinuerliga s.v.-modellerna (i) Heston, (ii) Bates och (iii) SVCJ, där inferens baseras på optionspriser. Vi finner att SMC2 presterar bra resultat för de enklare modellerna (i) och (ii) emedan filtrering för (iii) presterar sämre. Vi finner ytterligare att det beräkningsmässigt tyngsta steget är optionsprissättning nyttjandes FFT, därför föreslås det att undersöka andra beräkningssätt, såsom GPGPU-beräkning