Markov models for the evolution of duplicate genes, and microsatellites

Duplicate genes and microsatellites are two key sequences in the study of evolutionary genomics. Gene duplication has been identified as a central process driving functional change in genomes, since it creates functional redundancy in the genome and allows for subsequent mutation to occur in the absence of selective pressure. Microsatellites are rapidly evolving sequences which can be studied over much smaller timescales than most other sequences, and are thus key to the study of population demographics and forensic science. In this thesis we construct mathematical models for the evolution of duplicate genes, and microsatellites, respectively. We analyse the models in order to make scientific predictions, and derive the following novel results. We introduce and analyse a modified hazard function, which we use to investigate the preservation of gene duplicates. Further, we construct individual-level models, and present a framework for the extension to population-level models. Also, we construct mappings from mechanistically-motivated intuitive models for gene duplicate evolution, to less intuitive models, which have smaller state spaces and hence are more computationally tractable. Throughout this analysis, we make scientific predictions based on the properties of the models. We find that the pattern of gene duplicate preservation is more consistent with subfunctionalization than with neofunctionalization. This result is of particular scientific interest, since it is the opposite conclusion of earlier work in the gene duplication literature. ${Duplicate}$ ${genes}$ Several biological models exist for the evolution of a pair of duplicate genes after a duplication event, and it is believed that gene duplicates can evolve in different ways, according to one process, or a mix of processes. Subfunctionalization is a process under which the two duplicates can be preserved by dividing up the functions of the original gene between them. Here, we find that subfunctionalization is highly consistent with the pattern of gene duplicate preservation, in contrast to previous analysis in the literature. Another process important to gene duplicate evolution is neofunctionalization, under which both duplicates can be preserved when one copy mutates so as to produce some new beneficial function. Our analysis of neofunctionalization suggests that this process is not a significant contributor to the preservation of duplicates over the timescales during which regulatory subfunctionalization is resolved. Instead, it is likely that neofunctionalization occurs subsequent to previous subfunctionalization, which acts to preserve copies over the longer time frames required for rare beneficial mutations to have any significant probability of occurring. Analysis of genomic data using sub- and neofunctionalization models has thus far been relatively coarse-grained, with mathematical treatments usually focusing on the phenomenological features of gene duplicate evolution. In contrast, we develop mechanistically motivated Markov models, and fit directly to duplicate preservation data. We introduce a modified-cause-specific hazard function to analyse the preservation of gene duplicates. In the context of gene duplication, we refer to this as the pseudogenization rate, owing to the biological interpretation. We analyse the properties of the modified-cause-specific hazard rate in detail, including limit analysis of the general case, and discuss the shape properties of the specific case of the pseudogenization rate. Further, we extend our model for the evolution of a pair of gene duplicates to model a population of duplicate pairs, by modelling the birth of such pairs as a homogeneous Poisson process. We show that the age distribution of preserved duplicates follows an inhomogenous Poisson distribution, with its rate function depending on the individuallevel model. We then fit this distribution to count-data of surviving duplicates in the genomes of four animal species. Additionally, we extend the individual-level model to a model that includes the process of neofunctionalization, and next, to a model of subfunctionalization for families of gene duplicates. Finally, we map these intuitive models, to less intuitive but more computationally tractable models, and discuss a number of related computational considerations. ${Microsatellites}$ Microsatellites are repetitive regions of DNA where a short motif is repeated many times. Mutations in the number of repeat units occur frequently compared to point mutations and thus provide a useful source of genetic variation for studying recent events. Empirical studies have suggested that the rate of length-changing mutations due to slipped-strand mispairing may depend on the purity of the repeat units, i.e. how well they each match the motif. However, most studies that use microsatellite data are based on models that only track the number of repeat units. In order to address this gap, we introduce a series of models on a two-dimensional state-space (which are level-dependent quasi-birth-and-death processes) that track the length of the sequence as the level variable, and the number of interruptions (purity) as the phase variable. Our models account for the biological process of point mutation, and its observed effect on the rate of slipped-strand mispairing. We find that modelling microsatellite purity leads to some complications due to the nature of available data. In terms of the initial model, we discover what constitutes a state-dependent bias in the reporting of repeat sequences by Tandem Repeats Finder (or any similar software used to search whole-genomes for microsatellite sequences). Consequently, we construct a modified model such that all states fall into one of two categories - 'observable states', against which the reporting algorithm is unbiased, and 'unobservable states', which are never reported. We consider two approaches for treating the unobservable states, first to condition on the process being in the observable states, second to treat unobservable states as absorbing. Our initial analysis and underlying biological intuition suggest that transitions from the unobservable to observable states are very rare, and thus we ultimately treat the unobservable states as absorbing. Additionally, we extend the individual-level model to a population-level model by modelling the birth of microsatellites as a homogeneous Poisson process. We then derive the transient distribution of such model in terms of the individual-level process. This distribution has appropriate relative clock via the inclusion of point mutation. We fit this transient distribution to whole-genome derived sequence data, however we encounter some dificulties in the optimisation owing to the presence of many local optima. The standard approach for microsatellite models is to make the assumption that the empirical distribution is at equilibrium, and then to fit the stationary distribution to data. The key exception to this is the step-wise mutation model, which predicts infinite growth of the repeat number. Here we fit the above-mentioned transient distribution, and thus do not assume that the empirical distribution is at equilibrium. In contrast to the step-wise mutation model, our model does not predict infinite sequence lengths in the long run

Study on the Urban Structure and the Building Activitiesin Fukui City

This paper aims to clarify the actual conditions of building activities，and the rel ations between the urban structure and the building activities，in Fukui city. The conclusions are as follows; 1. The mean floor space of building stock in 1986 is 3486.5 ㎡ per hectare and recently 108.0 ㎡ are added to its volume each year. 2. The amount of the construction activities in view point of floor space is recently about 171.8㎡ per hectare. 3. Recently，the newly building operation is produced about 0.49case per hectare，and the enlargement and remodeling of building is 0.17

Study on Origins and Meanings of the City Beautiful Movement in America

The City Beautiful Movement, from about 1900 to 1910，has exerted the great influence on the design，planning，and management of many American cities. Its effects are still observed in，for example，wide tree-lined boulevards，ornamental parks，monumental neoclassic buildings，and street embellishments，etc. However，many critics hitherto have been under the misunderstanding that the City Beautiful Movement was derived from the 1893 Chicago Fair and had been subjected to the infiuence of the grand manner city planning only. In this paper，the fresh interpretations are tried to put the City Beautiful Movement and to clarify the correct meanings and origins of the movement in place of the traditional notions. Three concepts are presented in this paper. These are municipal art movement， civic improvement and outdoor art movement. Each movement had been formed from the historical roots predating the 1893 Chicago Fair and had obtained the original results. The formative years of the City Beautiful were from 1897 to 1902. In this period，th ese three movements had spread out into many cities and in each city，their leaders found that they were bound together by the common interests in city beauty. In this way， these three movements were united to the City Beautiful Movement

Endogenous reference RNAs for microRNA quantitation in formalin-fixed, paraffin-embedded lymph node tissue

Lymph node metastasis is one of the most important factors for tumor dissemination. Quantifying microRNA (miRNA) expression using real-time PCR in formalin-fixed, paraffin-embedded (FFPE) lymph node can provide valuable information regarding the biological research for cancer metastasis. However, a universal endogenous reference gene has not been identified in FFPE lymph node. This study aimed to identify suitable endogenous reference genes for miRNA expression analysis in FFPE lymph node. FFPE lymph nodes were obtained from 41 metastatic cancer and from 16 non-cancerous tissues. We selected 10 miRNAs as endogenous reference gene candidates using the global mean method. The stability of candidate genes was assessed by the following four statistical tools: BestKeeper, geNorm, NormFinder, and the comparative ΔCt method. miR-103a was the most stable gene among candidate genes. However, the use of a single miR-103a was not recommended because its stability value exceeded the reference value. Thus, we combined stable genes and investigated the stability and the effect of gene normalization. The combination of miR-24, miR-103a, and let-7a was identified as one of the most stable sets of endogenous reference genes for normalization in FFPE lymph node. This study may provide a basis for miRNA expression analysis in FFPE lymph node tissue

Evaluation of Treatment Response in Prostate Cancer and Renal Cell Carcinoma Patients Using 11C-choline PET/CT Findings

We investigated the effectiveness of 11C-choline-positron emission tomography/computed tomography (PET/CT) for evaluating treatment response in patients with prostate cancer or renal cell carcinoma. We performed 34 11C-choline PET/CT scans before/after a combined total of 17 courses of treatment in 6 patients with prostate cancer and 2 with renal cell carcinoma. The 17 treatments including hormonal therapy, radiotherapy, chemotherapy, radium-223, molecular target therapy, radiofrequency ablation, transcatheter arterial embolization, and cancer immunotherapy yielded 1 (5.9%) complete metabolic response (CMR), 3 (17.6%) partial metabolic responses (PMRs), 2 (11.8%) stable metabolic diseases (SMDs), and 11 (64.7%) progressive metabolic diseases (PMDs). Target lesions were observed in bone (n=14), lymph nodes (n=5), lung (n=2), prostate (n=2), and pleura (n=1), with CMR in 4, PMR in 10, SMD in 8 and PMD in 2 lesions. SUVmax values of the target lesions before and after treatment were 7.87±2.67 and 5.29±3.98, respectively, for a mean reduction of −35.4±43.6%. The response for the 8 prostate cancer-treatment courses was PMD, which correlated well with changes in serum prostatic specific antigen (PSA) (7 of 8 cases showed increased PSA). 11C-choline-PET/CT may be an effective tool for detecting viable residual tumors and evaluating treatment response in prostate cancer and renal cell carcinoma patients

High-resolution photoelectron spectroscopy study of Kondo metals : SmSn3 and Sm0.9La0.1Sn3

We performed a high-resolution photoelectron spectroscopy study on the Kondo metals SmSn3 and Sm0.9La0.1Sn3. The experimental results are compared with calculations of density of state performed within the local density approximation plus the dynamical mean-field theory. The theory is found to reproduce the experimental valence-band spectra well. In both SmSn3 and Sm0.9La0.1Sn3 the bulk Sm valence is nearly trivalent, with a small fraction of divalent component. Resonant photoelectron spectroscopy indicates a decrease in the Kondo effect in the diluted system Sm0.9La0.1Sn3