Better understanding of protein folding process can provide physical insights on the function of proteins and makes it possible to benefit from genetic information accumulated so far. Protein folding process normally takes place in less than seconds but even seconds are beyond reach of current computational power for simulations on a system of all-atom detail. Hence, to model and explore protein folding process it is crucial to construct a proper model that can adequately describe the physical process and mechanism for the relevant time scale. We discuss the reduced off-lattice model that can express <em>&alpha;</em>-helix and <em>&beta;</em>-hairpin conformations defined solely by a given sequence in order to investigate a protein folding mechanism of conformations such as a <em>&beta;</em>-hairpin and also to investigate conformational conversions in proteins. The first two chapters introduce and review essential concepts in protein folding modelling physical interaction in proteins, various simple models, and also review computational methods, in particular, the Metropolis Monte Carlo method, its dynamic interpretation and thermodynamic Monte Carlo algorithms. Chapter 3 describes the minimalist model that represents both <em>&alpha;</em>-helix and <em>&beta;</em>-sheet conformations using simple potentials. The native conformation can be specified by the sequence without particular conformational biases to a reference state. In Chapter 4, the model is used to investigate the folding mechanism of <em>&beta;</em>-hairpins exhaustively using the dynamic Monte Carlo and a thermodynamic Monte Carlo method an effcient combination of the multicanonical Monte Carlo and the weighted histogram analysis method. We show that the major folding pathways and folding rate depend on the location of a hydrophobic. The conformational conversions between <em>&alpha;</em>-helix and <em>&beta;</em>-sheet conformations are examined in Chapter 5 and 6. First, the conformational conversion due to mutation in a non-hydrophobic system and then the conformational conversion due to mutation with a hydrophobic pair at a different position at various temperatures are examined.

Better understanding of protein folding process can provide physical insights on the function of proteins and makes it possible to benefit from genetic information accumulated so far. Protein folding process normally takes place in less than seconds but even seconds are beyond reach of current computational power for simulations on a system of all-atom detail. Hence, to model and explore protein folding process it is crucial to construct a proper model that can adequately describe the physical process and mechanism for the relevant time scale. We discuss the reduced off-lattice model that can express <em>&alpha;</em>-helix and <em>&beta;</em>-hairpin conformations defined solely by a given sequence in order to investigate a protein folding mechanism of conformations such as a <em>&beta;</em>-hairpin and also to investigate conformational conversions in proteins. The first two chapters introduce and review essential concepts in protein folding modelling physical interaction in proteins, various simple models, and also review computational methods, in particular, the Metropolis Monte Carlo method, its dynamic interpretation and thermodynamic Monte Carlo algorithms. Chapter 3 describes the minimalist model that represents both <em>&alpha;</em>-helix and <em>&beta;</em>-sheet conformations using simple potentials. The native conformation can be specified by the sequence without particular conformational biases to a reference state. In Chapter 4, the model is used to investigate the folding mechanism of <em>&beta;</em>-hairpins exhaustively using the dynamic Monte Carlo and a thermodynamic Monte Carlo method an effcient combination of the multicanonical Monte Carlo and the weighted histogram analysis method. We show that the major folding pathways and folding rate depend on the location of a hydrophobic. The conformational conversions between <em>&alpha;</em>-helix and <em>&beta;</em>-sheet conformations are examined in Chapter 5 and 6. First, the conformational conversion due to mutation in a non-hydrophobic system and then the conformational conversion due to mutation with a hydrophobic pair at a different position at various temperatures are examined.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20753号 / 理博第4329号 / 新制||理||1622(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)教授 森脇 淳, 教授 雪江 明彦, 教授 並河 良典 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

Background: Canine hypothyroidism is thought to cause abnormalities in glucose homeostasis, but the effect on glucose tolerance and insulin sensitivity has not been determined to date. Hypothesis/Objectives: The purpose of the study was to investigate whether hypothyroidism has an effect on glucose tolerance and insulin sensitivity in dogs. We hypothesized that hypothyroidism causes insulin resistance. Animals: Sixteen euthyroid bitches were randomly selected and allocated into two groups. In 8 dogs, hypothyroidism was induced by administration of 1 mCi/kg I-131. Experiments were performed on non-anesthetized, fasted dogs in anestrous approximately 12 months after hypothyroidism was induced. Methods: The insulin-modified frequently sampled intravenous glucose tolerance test (FSIGT) and minimal model analysis were used to determine basal insulin and glucose concentrations, acute insulin response to glucose (AIRg), insulin sensitivity (SI), glucose effectiveness (SG) and the disposition index (DI). Results: In the hypothyroid group, basal glucose concentrations were mildly decreased (P = 0.0079), whereas basal insulin was increased (P = 0.019). Insulin sensitivity was reduced in the hypothyroid group (P<0.001), whereas AIRg was higher (P=0.01). Other parameters were not different between groups. Conclusions/Clinical Importance: Hypothyroidism negatively affects glucose homeostasis by inducing insulin resistance. In hypothyroid dogs, the disposition index (insulin sensitivity x insulin secretion) remained unchanged due to a compensatory increase in insulin secretion, thereby maintaining glucose tolerance. In cases with impaired insulin secretion, such as canine diabetes mellitus, concurrent hypothyroidism can have important clinical implications in the successful management of the disease. / Master of Science

Model generation and minimal model generation are useful for tasks such as model checking, query answering and for debugging of logical specifications. Due to this variety of applications, several minimality criteria and model generation methods for classical logics have been studied. Minimal model generation for modal logics how ever did not receive the same attention from the research community. This thesis aims to fill this gap by investigating minimality criteria and designing minimal model generation procedures for all the sublogics of the multi-modal logic S5(m) and their extensions with universal modalities. All the procedures are minimal model sound and complete, in the sense that they generate all and only minimal models. The starting point of the investigation is the definition of a Herbrand semantics for modal logics on which a syntactic minimality criterion is devised. The syntactic nature of the minimality criterion allows for an efficient minimal model generation procedure, but, on the other hand, the resulting minimal models can be redundant or semantically non minimal with respect to each other. To overcome the syntactic limitations of the first minimality criterion, the thesis moves from minimal modal Herbrand models to semantic minimality criteria based on subset-simulation. At first, theoretical procedures for the generation of models minimal modulo subset-simulation are presented. These procedures for the generation of models minimal modulo subset-simulation are minimal model sound and complete, but they might not terminate. The minimality criterion and the procedures are then refined in such a way that termination can be ensured while preserving minimal model soundness and completeness.

Insulin sensitivity decreases during pregnancy, presumably an adaptation ensuring sufficient glucose supply to feto-placental tissues. Feeds high in non-structural carbohydrates are also linked to diminished insulin sensitivity in horses. Because the equine fetus is highly glucose reliant, maternal glucose and insulin dynamics during pregnancy may have implications for optimal fetal development in horses. Mismanagement of maternal nutrition during gestation could predispose the offspring to metabolic disorders (e.g. insulin resistance) later in life. In horses, insulin resistance is associated with increased risk for development of laminitis. These studies measured insulin sensitivity and glucose dynamics in pregnant and non-pregnant mares fed high sugar and starch (SS) or high fat and fiber (FF) feeds, as well as neonatal foals born from pregnant mares fed SS and FF feed. Insulin modified frequently sampled intravenous glucose tolerance tests (FSIGT) were applied to pregnant Thoroughbred mares (n = 22) at 28 ± 3 wks (Period 1) and 47 wks (Period 2) gestation, as well as non-pregnant mares (n=10) measured simultaneously. Following the first FSIGT mares were fed SS or FF feed for the remainder of the study. After 11 wks adaptation to feeding, a subset of mares were evaluated with hourly blood samples for 24 h to assess glycemic and insulinemic response to three times daily feeding while on pasture. Neonatal foal FSIGTs (n=20) were conducted at 5 ± 1 d of age. The minimal model of glucose and insulin dynamics was used to determine insulin sensitivity (SI), glucose effectiveness (Sg), acute insulin response to glucose (AIRg) and disposition index (DI). Pregnant mares during Period 1 exhibited lowered SI, Sg and elevated AIRg relative to non-pregnant mares. Pregnant mares demonstrated greater glycemic and insulinemic responses to feeding of both SS and FF meals than non-pregnant mares consuming the same feeds. Also, SS feed elicited greater glycemic and insulinemic areas under the curve following feeding than FF feed in pregnant mares. These data support that pregnancy in mares in associated with lowered SI by 28 wks gestation and that altered SI, Sg and AIRg are associated with different responses to consuming SS and FF feeds. Foals exhibited high basal glucose, basal insulin, SI and Sg relative to mature horses, indicating a large capacity for glucose uptake with or without insulin. Basal glucose concentrations were higher and basal insulin concentrations tended to be higher in SS than FF foals (P = 0.016 and P = 0.071, respectively). Glucose and insulin dynamics in late gestation mares and neonatal foals exemplify the adaptive nature of energy metabolism in horses. Furthermore, dietary energy composition affects glucose and insulin responses to feeding in late gestation mares, which in turn was associated with different basal blood concentrations of these variables in the resulting neonatal foals. / Master of Science

Diets rich in hydrolyzable carbohydrates induce a hyperglycemic/insulinemic response and may increase the incidence of metabolic disorders associated with some types of laminitis, exertional rhabdomyolysis and osteochondrosis in horses. This study applied the minimal model of glucose and insulin dynamics to determine the effect of diet on metabolites and hormones that regulate glucose metabolism in young horses. Twelve Thoroughbred foals were raised on pasture and supplemented twice daily with a feed high in either sugar and starch (SS) or fat and fiber (FF). As weanlings (age 199 ± 19 d, weight 274 ± 18 kg), the subjects underwent a modified frequent sampling intravenous glucose tolerance test during which they remained in stalls and had access to grass hay and water ad libitum. Samples were colleted at -60, -45, 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 16, 19, 22, 23, 24, 25, 27, 30, 35, 40, 50, 60 , 70 , 80, 90, 100, 120, 150, 180, 210, 240, 270, 300, 330 and 360 min with a glucose bolus of 300 mg/kg BW at 0 min and an insulin bolus of 1.5 mU/kg BW at 20 min. Plasma was analyzed for glucose, insulin, growth hormone (GH) and insulin-like growth factor-I (IGF-I) concentrations. Insulin sensitivity, glucose effectiveness, acute insulin response to glucose and disposition index were derived using Minmod Millennium and WinSAAM software. Diet groups were compared using the non-parametric Kruskal-Wallis test or the sign test. Time interactions were compared using a mixed model with repeated effects. Rank-ordered linear regression was used for correlations. Basal glucose did not differ between groups (P = 0.75). There was nearly a trend towards higher basal (P = 0.11), and median insulin was higher in the sugar and starch foals at all 36 sample points (P = 0.030). The basal glucose:basal insulin ratio for the sugar and starch supplemented foals was lower than for fat and fiber foals (P = 0.025). Insulin sensitivity (SI) was lower in foals fed sugar and starch than foals fed fat and fiber (P = 0.007). Acute insulin response to glucose was directly correlated to weight (r = 0.78; P = 0.003) and inversely correlated with SI (r = -0.55; P = 0.067). The glucose:insulin ratio was directly correlated to SI (r = 0.92; P < 0.001). Growth hormone concentrations were increased from basal from 19 to 180 min after the glucose dose (P < 0.05). Basal IGF-I was higher (P = 0.006) in the SS group compared to the FF group. Concentrations of total IGF-I increased with time (P = 0.002) in the SS group. The change in IGF-I concentration from baseline to the end of the study was positively correlated (r = 0.72; P = 0.008) to the area under the insulin curve from 0 to 80 min. Basal IGF-I was inversely correlated to SI (r = 0.71; P = 0.015). These results show that the metabolic response to a diet high in hydrolyzable carbohydrates differs from the response to a fat and fiber meal resembling forage. Weanlings adapted to meals high in glucose equivalents have higher insulin and IGF-I secretion as compared to foals adapted to a fat and fiber feed, possibly contributing to lower insulin sensitivity observed in these foals. Such deviations may contribute to metabolic dysfunction and osteochondrosis in horses fed grain diets. / Master of Science

Glucose is a fundamental energy source, the utilization and regulation of which impacts exercise performance and health. These studies have used modeling techniques to evaluate glucose kinetics and dynamics in equids and developed tests to evaluate the status of glucose metabolism. In Part I, 12 exercise-trained Arabians underwent insulin-modified FSIGT (with minimal model analysis) and single-injection glucose tracer (with compartmental analysis) studies at rest and during exercise to evaluate the effects of exercise on glucose kinetics and dynamics. These geldings were maintained on pasture, but adapted for 4 months to twice-daily feeding of feeds rich in sugar and starch (SS, n=6: NSC 45%, Fat 3%, NDF 24%) or fat and fiber (FF, n=6:NSC 13%, Fat 11%, NDF 45% ). Exercise increased insulin sensitivity (P = 0.070) and glucose transport (P < 0.038). Although variables were not different between FF and SS horses at rest, during exercise SS horses tended to have lower (P = 0.085) insulin sensitivity and increased (P = 0.043) glucose utilization compared to FF horses. In Part II, satisfactory proxies for minimal model parameters were developed to facilitate the evaluation of insulin sensitivity in larger populations. These proxies were applied to a population of 163 ponies and used to characterize metabolic differences between ponies predisposed to pasture laminitis (PL) from ponies not predisposed (NL). A subset of 14 ponies (7 PL, 7 NL) also underwent the FSIGT for minimal model analysis. Ponies predisposed to laminitis were found to have lower insulin sensitivity (P < 0.007) and higher insulin secretory response (P < 0.045) by both the minimal model and proxies, and higher (P < 0.001) circulating triglycerides and body condition score. Cut-point analysis for these variables was used to define a pre-laminitic metabolic syndrome with total predictive power of 78% to identifity ponies at risk for developing pasture laminitis. Increased insulin resistance and prevalence of lamintis were associated with increased non-structural carbohydrates in spring pasture. These studies demonstrate the importance of glucose regulation for exercise and animal health. When glucose regulation is altered in the case of insulin resistance, performance could be impacted and diseases such as laminitis may occur. Insulin resistance may be moderated by exercise or by avoiding sugar and starch in feeds and pasture. / Ph. D.

Diese Arbeit untersucht verschiedene Fragen hinsichtlich der birationalen Geometrie der Modulräume $\Mbar_g$ und $\Mbar_{g,n}$, mit besonderem Augenmerk auf der Berechnung effektiver Divisorklassen. In Kapitel 2 definieren wir für jedes $n$-Tupel ganzer Zahlen $\d$, die sich zu $g-1$ summieren, einen geometrisch bedeutsamen Divisor auf $\Mbar_{g,n}$, der durch Zurückziehen des Thetadivisors einer universellen Jacobi-Varietät mittels einer Abel-Jacobi-Abbildung erhalten wird. Er ist eine Verallgemeinerung verschiedener in der Literatur verwendeten Arten von Divisoren. Wir berechnen die Klasse dieses Divisors und zeigen, dass er für bestimmte $\d$ irreduzibel und extremal im effektiven Kegel von $\Mbar_{g,n}$ ist. Kapitel 3 beschäftigt sich mit einem birationalen Modell $X_6$ von $\Mbar_6$, das durch quadrische Hyperebenenschnitte auf der del-Pezzo-Fläche vom Grad $5$ erhalten wird. Wir berechnen die Klasse des großen Divisors, der die birationale Abbildung $\Mbar_6 \dashrightarrow X_6$ induziert, und erhalten so eine obere Schranke an die bewegliche Steigung von $\Mbar_6$. Wir zeigen, dass $X_6$ der letzte nicht-triviale Raum im log-minimalen Modellprogramm für $\Mbar_6$ ist. Weiterhin geben wir einige Resultate bezüglich der Unirationalität der Weierstraßorte auf $\Mbar_{g,1}$. Für $g = 6$ hängen diese mit der del-Pezzo-Konstruktion zusammen, die benutzt wurde, um das Modell $X_6$ zu konstruieren. Kapitel 4 konzentriert sich auf den Fall $g = 0$. Castravet and Tevelev führten auf $\Mbar_{0,n}$ kombinatorisch definierte Hyperbaumdivisoren ein, die für $n = 6$ zusammen mit den Randdivisoren den effektiven Kegel erzeugen. Wir berechnen die Klasse des Hyperbaumdivisors auf $\Mbar_{0,7}$, der bis auf Permutation der markierten Punkte eindeutig ist. Wir geben eine geometrische Charakterisierung für ihn an, die zu der von Keel und Vermeire für den Fall $n = 6$ gegebenen analog ist. / This thesis investigates various questions concerning the birational geometry of the moduli spaces $\Mbar_g$ and $\Mbar_{g,n}$, with a focus on the computation of effective divisor classes. In Chapter 2 we define, for any $n$-tuple $\d$ of integers summing up to $g-1$, a geometrically meaningful divisor on $\Mbar_{g,n}$ that is essentially the pullback of the theta divisor on a universal Jacobian variety under an Abel-Jacobi map. It is a generalization of various kinds of divisors used in the literature, for example by Logan to show that $\Mbar_{g,n}$ is of general type for all $g \geq 4$ as soon as $n$ is big enough. We compute the class of this divisor and show that for certain choices of $\d$ it is irreducible and extremal in the effective cone of $\Mbar_{g,n}$. Chapter 3 deals with a birational model $X_6$ of $\Mbar_6$ that is obtained by taking quadric hyperplane sections of the degree $5$ del Pezzo surface. We compute the class of the big divisor inducing the birational map $\Mbar_6 \dashrightarrow X_6$ and use it to derive an upper bound on the moving slope of $\Mbar_6$. Furthermore we show that $X_6$ is the final non-trivial space in the log minimal model program for $\Mbar_6$. We also give a few results on the unirationality of Weierstraß loci on $\Mbar_{g,1}$, which for $g = 6$ are related to the del Pezzo construction used to construct the model $X_6$. Finally, Chapter 4 focuses on the case $g = 0$. Castravet and Tevelev introduced combinatorially defined hypertree divisors on $\Mbar_{0,n}$ that for $n = 6$ generate the effective cone together with boundary divisors. We compute the class of the hypertree divisor on $\Mbar_{0,7}$, which is unique up to permutation of the marked points. We also give a geometric characterization of it that is analogous to the one given by Keel and Vermeire in the $n = 6$ case.

A refinement of a minimal model for protein folding originally proposed by Imamura is presented. The representation of the alpha-helix has been improved by adding in explicit modelling of the entire peptide unit. A four-helix bundle consisting of four alpha-helices and three loop regions is generated with the parallel tempering Monte Carlo scheme. Six native states are found for the given sequence, four U-bundle and two Z-bundle states. All six states have energies of E approx -218ε and all appear equally likely to occur in simulation. The highest probability of folding a native state is found to be at a hydrophobic strength of Ch = 0.8 which agrees with the value of Ch = 0.7 used by Imamura in his studies of alpha to beta structural conversions. Two folding stages are observed in the temperature spectrum dependent on the magnitude of the hydrophobic strength parameter. The two stages observed as temperature decreases are 1) the hydrophobic energy causes the random coil to collapse into a compact globule 2) the secondary structure starts forming below a temperature of about T = 0.52ε/kB. The temperature of the first stage, which corresponds to the characteristic collapse temperature Tθ, is highly dependent on the hydrophobic strength. The temperature of the second stage is constant with respect to hydrophobic strength. Attempts to measure the characteristic folding temperature, Tf , from the structural overlap function proved to be difficult due mostly to the presence of six minima and the complications that arose in the parallel tempering Monte Carlo scheme. However, a rough estimate of Tf is obtained at each hydrophobic strength from a native state density analysis. Tf is found to be significantly lower than Tθ.