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.

Models of Dispersal and Diversification

Ecology and evolutionary biology is the study of life on this planet. One of the many methods applied to answering the great diversity of questions regarding the lives and characteristics of individual organisms, is the utilization of mathematical models. Such models are used in a wide variety of ways. Some help us to reason, functioning as aids to, or substitutes for, our own fallible logic, thus making argumentation and thinking clearer. Models which help our reasoning can lead to conceptual clarification; by expressing ideas in algebraic terms, the relationship between different concepts become clearer. Other mathematical models are used to better understand yet more complicated models, or to develop mathematical tools for their analysis. Though helping us to reason and being used as tools in the craftmanship of science, many models do not tell us much about the real biological phenomena we are, at least initially, interested in. The main reason for this is that any mathematical model is a simplification of the real world, reducing the complexity and variety of interactions and idiosynchracies of individual organisms. What such models can tell us, however, both is and has been very valuable throughout the history of ecology and evolution. Minimally, a model simplifying the complex world can tell us that in principle, the patterns produced in a model could also be produced in the real world. We can never know how different a simplified mathematical representation is from the real world, but the similarity models do strive for, gives us confidence that their results could apply. This thesis deals with a variety of different models, used for different purposes. One model deals with how one can measure and analyse invasions; the expanding phase of invasive species. Earlier analyses claims to have shown that such invasions can be a regulated phenomena, that higher invasion speeds at a given point in time will lead to a reduction in speed. Two simple mathematical models show that analysis on this particular measure of invasion speed need not be evidence of regulation. In the context of dispersal evolution, two models acting as proof-of-principle are presented. Parent-offspring conflict emerges when there are different evolutionary optima for adaptive behavior for parents and offspring. We show that the evolution of dispersal distances can entail such a conflict, and that under parental control of dispersal (as, for example, in higher plants) wider dispersal kernels are optimal. We also show that dispersal homeostasis can be optimal; in a setting where dispersal decisions (to leave or stay in a natal patch) are made, strategies that divide their seeds or eggs into fractions that disperse or not, as opposed to randomized for each seed, can prevail. We also present a model of the evolution of bet-hedging strategies; evolutionary adaptations that occur despite their fitness, on average, being lower than a competing strategy. Such strategies can win in the long run because they have a reduced variance in fitness coupled with a reduction in mean fitness, and fitness is of a multiplicative nature across generations, and therefore sensitive to variability. This model is used for conceptual clarification; by developing a population genetical model with uncertain fitness and expressing genotypic variance in fitness as a product between individual level variance and correlations between individuals of a genotype. We arrive at expressions that intuitively reflect two of the main categorizations of bet-hedging strategies; conservative vs diversifying and within- vs between-generation bet hedging. In addition, this model shows that these divisions in fact are false dichotomies.

Society by Numbers : Studies on Model-Based Explanations in the Social Sciences

The aim of this dissertation is to provide conceptual tools for the social scientist for clarifying, evaluating and comparing explanations of social phenomena based on formal mathematical models. The focus is on relatively simple theoretical models and simulations, not statistical models. These studies apply a theory of explanation according to which explanation is about tracing objective relations of dependence, knowledge of which enables answers to contrastive why and how-questions. This theory is developed further by delineating criteria for evaluating competing explanations and by applying the theory to social scientific modelling practices and to the key concepts of equilibrium and mechanism. The dissertation is comprised of an introductory essay and six published original research articles. The main theses about model-based explanations in the social sciences argued for in the articles are the following. 1) The concept of explanatory power, often used to argue for the superiority of one explanation over another, compasses five dimensions which are partially independent and involve some systematic trade-offs. 2) All equilibrium explanations do not causally explain the obtaining of the end equilibrium state with the multiple possible initial states. Instead, they often constitutively explain the macro property of the system with the micro properties of the parts (together with their organization). 3) There is an important ambivalence in the concept mechanism used in many model-based explanations and this difference corresponds to a difference between two alternative research heuristics. 4) Whether unrealistic assumptions in a model (such as a rational choice model) are detrimental to an explanation provided by the model depends on whether the representation of the explanatory dependency in the model is itself dependent on the particular unrealistic assumptions. Thus evaluating whether a literally false assumption in a model is problematic requires specifying exactly what is supposed to be explained and by what. 5) The question of whether an explanatory relationship depends on particular false assumptions can be explored with the process of derivational robustness analysis and the importance of robustness analysis accounts for some of the puzzling features of the tradition of model-building in economics. 6) The fact that economists have been relatively reluctant to use true agent-based simulations to formulate explanations can partially be explained by the specific ideal of scientific understanding implicit in the practise of orthodox economics.

Serum uric acid and metabolic risk factors in three ethnic groups: Asian Indians and Creoles in Mauritius and Chinese in Qingdao, China

In humans with a loss of uricase the final oxidation product of purine catabolism is uric acid (UA). The prevalence of hyperuricemia has been increasing around the world accompanied by a rapid increase in obesity and diabetes. Since hyperuricemia was first described as being associated with hyperglycemia and hypertension by Kylin in 1923, there has been a growing interest in the association between elevated UA and other metabolic abnormalities of hyperglycemia, abdominal obesity, dyslipidemia, and hypertension. The direction of causality between hyperuricemia and metabolic disorders, however, is unceartain. The association of UA with metabolic abnormalities still needs to be delineated in population samples. Our overall aims were to study the prevalence of hyperuricemia and the metabolic factors clustering with hyperuricemia, to explore the dynamical changes in blood UA levels with the deterioration in glucose metabolism and to estimate the predictive capability of UA in the development of diabetes. Four population-based surveys for diabetes and other non-communicable diseases were conducted in 1987, 1992, and 1998 in Mauritius, and in 2001-2002 in Qingdao, China. The Qingdao study comprised 1 288 Chinese men and 2 344 women between 20-74, and the Mauritius study consisted of 3 784 Mauritian Indian and Mauritian Creole men and 4 442 women between 25-74. In Mauritius, re-exams were made in 1992 and/or 1998 for 1 941 men (1 409 Indians and 532 Creoles) and 2 318 non pregnant women (1 645 Indians and 673 Creoles), free of diabetes, cardiovascular diseases, and gout at baseline examinations in 1987 or 1992, using the same study protocol. The questionnaire was designed to collect demographic details, physical examinations and standard 75g oral glucose tolerance tests were performed in all cohorts. Fasting blood UA and lipid profiles were also determined. The age-standardized prevalence in Chinese living in Qingdao was 25.3% for hyperuricemia (defined as fasting serum UA > 420 μmol/l in men and > 360 μmol/l in women) and 0.36% for gout in adults between 20-74. Hyperuricemia was more prevalent in men than in women. One standard deviation increase in UA concentration was associated with the clustering of metabolic risk factors for both men and women in three ethnic groups. Waist circumference, body mass index, and serum triglycerides appeared to be independently associated with hyperuricemia in both sexes and in all ethnic groups except in Chinese women, in whom triglycerides, high-density lipoprotein cholesterol, and total cholesterol were associated with hyperuricemia. Serum UA increased with increasing fasting plasma glucose levels up to a value of 7.0 mmol/l, but significantly decreased thereafter in mainland Chinese. An inverse relationship occurred between 2-h plasma glucose and serum UA when 2-h plasma glucose higher than 8.0 mmol/l. In the prospective study in Mauritius, 337 (17.4%) men and 379 (16.4%) women developed diabetes during the follow-up. Elevated UA levels at baseline increased 1.14-fold in risk of incident diabetes in Indian men and 1.37-fold in Creole men, but no significant risk was observed in women. In conclusion, the prevalence of hyperuricemia was high in Chinese in Qingdao, blood UA was associated with the clustering of metabolic risk factors in Mauritian Indian, Mauritian Creole, and Chinese living in Qingdao, and a high baseline UA level independently predicted the development of diabetes in Mauritian men. The clinical use of UA as a marker of hyperglycemia and other metabolic disorders needs to be further studied. Keywords: Uric acid, Hyperuricemia, Risk factors, Type 2 Diabetes, Incidence, Mauritius, Chinese

The social patterning of health, smoking and drinking in Estonia, Latvia, Lithuania and Finland in 1994-2004

The Baltic countries share public health problems typical of most Eastern European transition economies: morbidity and mortality from non-communicable diseases is higher than in Western European countries. This situation has many similarities compared to a neighbouring country, Finland during the late 1960s. There are reasons to expect that health disadvantage may be increasing among the less advantaged population groups in the Baltic countries. The evidence on social differences in health in the Baltic countries is, however, scattered to studies using different methodologies making comparisons difficult. This study aims to bridge the evidence gap by providing comparable standardized cross-sectional and time trend analyses to the social patterning of variation in health and two key health behaviours i.e. smoking and drinking in Estonia, Latvia, Lithuania and Finland in 1994-2004 representing Eastern European transition countries and a stable Western European country. The data consisted of similar cross-sectional postal surveys conducted in 1994, 1996, 1998, 2000, 2002 and 2004 on adult populations (aged 20 64 years) in Estonia (n=9049), Latvia (n=7685), Lithuania (n=11634) and Finland (n=18821) in connection with the Finbalt Health Monitor project. The main statistical method was logistic regression analysis. Perceived health was found to be worse among both men and women in the Baltic countries than in Finland. Poor health was associated with older age and lower education in all countries studied. Urbanization and marital status were not consistently related to health. The existing educational inequalities in health remained generally stable over time from 1994 to 2004. In the Baltic countries, however, improvement in perceived health was mainly found among the better educated men and women. Daily smoking was associated with young age, lower education and psychological distress in all countries. Among women smoking was also associated with urbanisation in all countries except Estonia. Among Lithuanian women, the educational gradient in smoking was weakest, and the overall prevalence of smoking increased over time. Drinking was generally associated with young age among men and women, and with education among women. Better educated women were more often frequent drinkers and less educated binge drinkers. The exception was that in Latvian men and women both frequent drinking and binge drinking were associated with low education. In conclusion, the Baltic countries are likely to resemble Western European countries rather than other transition societies. While health inequalities did not markedly change, substantial inequalities do remain, and there were indications of favourable developments mainly among the better educated. Pressures towards increasing health inequalities may therefore be visible in the future, which would be in accordance with the results on smoking and drinking in this study.

Effects of environmental variation on ecological and evolutionary dynamics

Environmental variation is a fact of life for all the species on earth: for any population of any particular species, the local environmental conditions are liable to vary in both time and space. In today's world, anthropogenic activity is causing habitat loss and fragmentation for many species, which may profoundly alter the characteristics of environmental variation in remaining habitat. Previous research indicates that, as habitat is lost, the spatial configuration of remaining habitat will increasingly affect the dynamics by which populations are governed. Through the use of mathematical models, this thesis asks how environmental variation interacts with species properties to influence population dynamics, local adaptation, and dispersal evolution. More specifically, we couple continuous-time continuous-space stochastic population dynamic models to landscape models. We manipulate environmental variation via parameters such as mean patch size, patch density, and patch longevity. Among other findings, we show that a mixture of high and low quality habitat is commonly better for a population than uniformly mediocre habitat. This conclusion is justified by purely ecological arguments, yet the positive effects of landscape heterogeneity may be enhanced further by local adaptation, and by the evolution of short-ranged dispersal. The predicted evolutionary responses to environmental variation are complex, however, since they involve numerous conflicting factors. We discuss why the species that have high levels of local adaptation within their ranges may not be the same species that benefit from local adaptation during range expansion. We show how habitat loss can lead to either increased or decreased selection for dispersal depending on the type of habitat and the manner in which it is lost. To study the models, we develop a recent analytical method, Perturbation expansion, to enable the incorporation of environmental variation. Within this context, we use two methods to address evolutionary dynamics: Adaptive dynamics, which assumes mutations occur infrequently so that the ecological and evolutionary timescales can be separated, and via Genotype distributions, which assume mutations are more frequent. The two approaches generally lead to similar predictions yet, exceptionally, we show how the evolutionary response of dispersal behaviour to habitat turnover may qualitatively depend on the mutation rate.

Association between molecular variation in the phosphoglucose isomerase (Pgi) locus and migration propensity in the Glanville fritillary butterfly

Habitat fragmentation produces patches of suitable habitat surrounded by unfavourable matrix habitat. A species may persist in such a fragmented landscape in an equilibrium between the extinctions and recolonizations of local populations, thus forming a metapopulation. Migration between local populations is necessary for the long-term persistence of a metapopulation. The Glanville fritillary butterfly (Melitaea cinxia) forms a metapopulation in the Åland islands in Finland. There is migration between the populations, the extent of which is affected by several environmental factors and variation in the phenotype of individual butterflies. Different allelic forms of the glycolytic enzyme phosphoglucose isomerase (Pgi) has been identified as a possible genetic factor influencing flight performance and migration rate in this species. The frequency of a certain Pgi allele, Pgi-f, follows the same pattern in relation to population age and connectivity as migration propensity. Furthermore, variation in flight metabolic performance, which is likely to affect migration propensity, has been linked to genetic variation in Pgi or a closely linked locus. The aim of this study was to investigate the association between Pgi genotype and the migration propensity in the Glanville fritillary both at the individual and population levels using a statistical modelling approach. A mark-release-recapture (MRR) study was conducted in a habitat patch network of M. cinxia in Åland to collect data on the movements of individual butterflies. Larval samples from the study area were also collected for population level examinations. Each butterfly and larva was genotyped at the Pgi locus. The MRR data was parameterised with two mathematical models of migration: the Virtual Migration Model (VM) and the spatially explicit diffusion model. VM model predicted and observed numbers of emigrants from populations with high and low frequencies of Pgi-f were compared. Posterior predictive data sets were simulated based on the parameters of the diffusion model. Lack-of-fit of observed values to the model predicted values of several descriptors of movements were detected, and the effect of Pgi genotype on the deviations was assessed by randomizations including the genotype information. This study revealed a possible difference in the effect of Pgi genotype on migration propensity between the two sexes in the Glanville fritillary. The females with and males without the Pgi-f allele moved more between habitat patches, which is probably related to differences in the function of flight in the two sexes. Females may use their high flight capacity to migrate between habitat patches to find suitable oviposition sites, whereas males may use it to acquire mates by keeping a territory and fighting off other intruding males, possibly causing them to emigrate. The results were consistent across different movement descriptors and at the individual and population levels. The effect of Pgi is likely to be dependent on the structure of the landscape and the prevailing environmental conditions.