Mathematical models on the impact of noise and dyadic molecular structures on the properties of a cardiac myocyte

In cardiac myocytes (heart muscle cells), coupling of electric signal known as the action potential to contraction of the heart depends crucially on calcium-induced calcium release (CICR) in a microdomain known as the dyad. During CICR, the peak number of free calcium ions (Ca) present in the dyad is small, typically estimated to be within range 1-100. Since the free Ca ions mediate CICR, noise in Ca signaling due to the small number of free calcium ions influences Excitation-Contraction (EC) coupling gain. Noise in Ca signaling is only one noise type influencing cardiac myocytes, e.g., ion channels playing a central role in action potential propagation are stochastic machines, each of which gates more or less randomly, which produces gating noise present in membrane currents. How various noise sources influence macroscopic properties of a myocyte, how noise is attenuated and taken advantage of are largely open questions. In this thesis, the impact of noise on CICR, EC coupling and, more generally, macroscopic properties of a cardiac myocyte is investigated at multiple levels of detail using mathematical models. Complementarily to the investigation of the impact of noise on CICR, computationally-efficient yet spatially-detailed models of CICR are developed. The results of this thesis show that (1) gating noise due to the high-activity mode of L-type calcium channels playing a major role in CICR may induce early after-depolarizations associated with polymorphic tachycardia, which is a frequent precursor to sudden cardiac death in heart failure patients; (2) an increased level of voltage noise typically increases action potential duration and it skews distribution of action potential durations toward long durations in cardiac myocytes; and that (3) while a small number of Ca ions mediate CICR, Excitation-Contraction coupling is robust against this noise source, partly due to the shape of ryanodine receptor protein structures present in the cardiac dyad.

Stochastic Filtering

The stochastic filtering has been in general an estimation of indirectly observed states given observed data. This means that one is discussing conditional expected values as being one of the most accurate estimation, given the observations in the context of probability space. In my thesis, I have presented the theory of filtering using two different kind of observation process: the first one is a diffusion process which is discussed in the first chapter, while the third chapter introduces the latter which is a counting process. The majority of the fundamental results of the stochastic filtering is stated in form of interesting equations, such the unnormalized Zakai equation that leads to the Kushner-Stratonovich equation. The latter one which is known also by the normalized Zakai equation or equally by Fujisaki-Kallianpur-Kunita (FKK) equation, shows the divergence between the estimate using a diffusion process and a counting process. I have also introduced an example for the linear gaussian case, which is mainly the concept to build the so-called Kalman-Bucy filter. As the unnormalized and the normalized Zakai equations are in terms of the conditional distribution, a density of these distributions will be developed through these equations and stated by Kushner Theorem. However, Kushner Theorem has a form of a stochastic partial differential equation that needs to be verify in the sense of the existence and uniqueness of its solution, which is covered in the second chapter.

Computing the Stochastic Complexity of Simple Probabilistic Graphical Models

Minimum Description Length (MDL) is an information-theoretic principle that can be used for model selection and other statistical inference tasks. There are various ways to use the principle in practice. One theoretically valid way is to use the normalized maximum likelihood (NML) criterion. Due to computational difficulties, this approach has not been used very often. This thesis presents efficient floating-point algorithms that make it possible to compute the NML for multinomial, Naive Bayes and Bayesian forest models. None of the presented algorithms rely on asymptotic analysis and with the first two model classes we also discuss how to compute exact rational number solutions.

Dessy : desktop search and synchronization

Current smartphones have a storage capacity of several gigabytes. More and more information is stored on mobile devices. To meet the challenge of information organization, we turn to desktop search. Users often possess multiple devices, and synchronize (subsets of) information between them. This makes file synchronization more important. This thesis presents Dessy, a desktop search and synchronization framework for mobile devices. Dessy uses desktop search techniques, such as indexing, query and index term stemming, and search relevance ranking. Dessy finds files by their content, metadata, and context information. For example, PDF files may be found by their author, subject, title, or text. EXIF data of JPEG files may be used in finding them. User–defined tags can be added to files to organize and retrieve them later. Retrieved files are ranked according to their relevance to the search query. The Dessy prototype uses the BM25 ranking function, used widely in information retrieval. Dessy provides an interface for locating files for both users and applications. Dessy is closely integrated with the Syxaw file synchronizer, which provides efficient file and metadata synchronization, optimizing network usage. Dessy supports synchronization of search results, individual files, and directory trees. It allows finding and synchronizing files that reside on remote computers, or the Internet. Dessy is designed to solve the problem of efficient mobile desktop search and synchronization, also supporting remote and Internet search. Remote searches may be carried out offline using a downloaded index, or while connected to the remote machine on a weak network. To secure user data, transmissions between the Dessy client and server are encrypted using symmetric encryption. Symmetric encryption keys are exchanged with RSA key exchange. Dessy emphasizes extensibility. Also the cryptography can be extended. Users may tag their files with context tags and control custom file metadata. Adding new indexed file types, metadata fields, ranking methods, and index types is easy. Finding files is done with virtual directories, which are views into the user’s files, browseable by regular file managers. On mobile devices, the Dessy GUI provides easy access to the search and synchronization system. This thesis includes results of Dessy synchronization and search experiments, including power usage measurements. Finally, Dessy has been designed with mobility and device constraints in mind. It requires only MIDP 2.0 Mobile Java with FileConnection support, and Java 1.5 on desktop machines.

Adhesion,Presence and Antifouling of Deinococcus geothermalis in Paper Machine Environment

This thesis has two items: biofouling and antifouling in paper industry. Biofouling means unwanted microbial accumulation on surfaces causing e.g. disturbances in industrial processes, contamination of medical devices or of water distribution networks. Antifouling focuses on preventing accumulation of the biofilms in undesired places. Deinococcus geothermalis is a pink-pigmented, thermophilic bacterium, and extremely resistant towards radiation, UV-light and desiccation and known as a biofouler of paper machines forming firm and biocide resistant biofilms on the stainless steel surfaces. The compact structure of biofilm microcolonies of D. geothermalis E50051 and the adhesion into abiotic surfaces were investigated by confocal laser scanning microscope combined with carbohydrate specific fluorescently labelled lectins. The extracellular polymeric substance in D. geothermalis microcolonies was found to be a composite of at least five different glycoconjugates contributing to adhesion, functioning as structural elements, putative storages for water, gliding motility and likely also to protection. The adhesion threads that D. geothermalis seems to use to adhere on an abiotic surface and to anchor itself to the neighbouring cells were shown to be protein. Four protein components of type IV pilin were identified. In addition, the lectin staining showed that the adhesion threads were covered with galactose containing glycoconjugates. The threads were not exposed on planktic cells indicating their primary role in adhesion and in biofilm formation. I investigated by quantitative real-time PCR the presence of D. geothermalis in biofilms, deposits, process waters and paper end products from 24 paper and board mills. The primers designed for doing this were targeted to the 16S rRNA gene of D. geothermalis. We found D. geothermalis DNA from 9 machines, in total 16 samples of the 120 mill samples searched for. The total bacterial content varied in those samples between 107 to 3 ×1010 16S rRNA gene copies g-1. The proportion of D. geothermalis in those same samples was minor, 0.03 1.3 % of the total bacterial content. Nevertheless D. geothermalis may endanger paper quality as its DNA was shown in an end product. As an antifouling method towards biofilms we studied the electrochemical polarization. Two novel instruments were designed for this work. The double biofilm analyzer was designed for search for a polarization program that would eradicate D. geothermalis biofilm or from stainless steel under conditions simulating paper mill environment. The Radbox instrument was designed to study the generation of reactive oxygen species during the polarization that was effective in antifouling of D. geothermalis. We found that cathodic character and a pulsed mode of polarization were required to achieve detaching D. geothermalis biofilm from stainless steel. We also found that the efficiency of polarization was good on submerged, and poor on splash area biofilms. By adding oxidative biocides, bromochloro-5,5-dimethylhydantoin, 2,2-dibromo-2-cyanodiacetamide or peracetic acid gave additive value with polarization, being active on splash area biofilms. We showed that the cathodically weighted pulsed polarization that was active in removing D. geothermalis was also effective in generation of reactive oxygen species. It is possible that the antifouling effect relied on the generation of ROS on the polarized steel surfaces. Antifouling method successful towards D. geothermalis that is a tenacious biofouler and possesses a high tolerance to oxidative stressors could be functional also towards other biofoulers and applicable in wet industrial processes elsewhere.

Pricing Index Options with Stochastic Volatility

The objective of this paper is to investigate the pricing accuracy under stochastic volatility where the volatility follows a square root process. The theoretical prices are compared with market price data (the German DAX index options market) by using two different techniques of parameter estimation, the method of moments and implicit estimation by inversion. Standard Black & Scholes pricing is used as a benchmark. The results indicate that the stochastic volatility model with parameters estimated by inversion using the available prices on the preceding day, is the most accurate pricing method of the three in this study and can be considered satisfactory. However, as the same model with parameters estimated using a rolling window (the method of moments) proved to be inferior to the benchmark, the importance of stable and correct estimation of the parameters is evident.

Bacteria colonizing paper machines

Bacteria growing in paper machines can cause several problems. Biofilms detaching from paper machine surfaces may lead to holes and spots in the end product or even break the paper web leading to expensive delays in production. Heat stable endospores will remain viable through the drying section of paper machine, increasing the microbial contamination of paper and board. Of the bacterial species regularly found in the end products, Bacillus cereus is the only one classified as a pathogen. Certain B. cereus strains produce cereulide, the toxin that causes vomiting disease in food poisonings connected to B. cereus. The first aim of this thesis was to identify harmful bacterial species colonizing paper machines and to assess the role of bacteria in the formation of end product defects. We developed quantitative PCR methods for detecting Meiothermus spp. and Pseudoxanthomonas taiwanensis. Using these methods I showed that Meiothermus spp. and Psx. taiwanensis are major biofoulers in paper machines. I was the first to be able to show the connection between end product defects and biofilms in the wet-end of paper machines. I isolated 48 strains of primary-biofilm forming bacteria from paper machines. Based on one of them, strain K4.1T, I described a novel bacterial genus Deinobacterium with Deinobacterium chartae as the type species. I measured the transfer of Bacillus cereus spores from packaging paper into food. To do this, we constructed a green fluorescent protein (GFP) labelled derivative of Bacillus thuringiensis and prepared paper containing spores of this strain. Chocolate and rice were the recipient foods when transfer of the labelled spores from the packaging paper to food was examined. I showed that only minority of the Bacillus cereus spores transferred into food from packaging paper and that this amount is very low compared to the amount of B. cereus naturally occurring in foods. Thus the microbiological risk caused by packaging papers is very low. Until now, the biological function of cereulide for the producer cell has remained unknown. I showed that B. cereus can use cereulide to take up K+ from environment where K+ is scarce: cereulide binds K+ ions outside the cell with high affinity and transports these ions across cell membrane into the cytoplasm. Externally added cereulide increased the growth rate of cereulide producing strains in medium where potassium was growth limiting. In addition, cereulide producing strains outcompeted cereulide non-producing B. cereus in potassium deficient environment, but not when the potassium concentration was high. I also showed that cereulide enhances biofilm formation of B. cereus.