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.

Questions to Artificial Nature: A Philosophical Study of Interdisciplinary Models and their Functions in Scientific Practice

This thesis presents an interdisciplinary analysis of how models and simulations function in the production of scientific knowledge. The work is informed by three scholarly traditions: studies on models and simulations in philosophy of science, so-called micro-sociological laboratory studies within science and technology studies, and cultural-historical activity theory. Methodologically, I adopt a naturalist epistemology and combine philosophical analysis with a qualitative, empirical case study of infectious-disease modelling. This study has a dual perspective throughout the analysis: it specifies the modelling practices and examines the models as objects of research. The research questions addressed in this study are: 1) How are models constructed and what functions do they have in the production of scientific knowledge? 2) What is interdisciplinarity in model construction? 3) How do models become a general research tool and why is this process problematic? The core argument is that the mediating models as investigative instruments (cf. Morgan and Morrison 1999) take questions as a starting point, and hence their construction is intentionally guided. This argument applies the interrogative model of inquiry (e.g., Sintonen 2005; Hintikka 1981), which conceives of all knowledge acquisition as process of seeking answers to questions. The first question addresses simulation models as Artificial Nature, which is manipulated in order to answer questions that initiated the model building. This account develops further the "epistemology of simulation" (cf. Winsberg 2003) by showing the interrelatedness of researchers and their objects in the process of modelling. The second question clarifies why interdisciplinary research collaboration is demanding and difficult to maintain. The nature of the impediments to disciplinary interaction are examined by introducing the idea of object-oriented interdisciplinarity, which provides an analytical framework to study the changes in the degree of interdisciplinarity, the tools and research practices developed to support the collaboration, and the mode of collaboration in relation to the historically mutable object of research. As my interest is in the models as interdisciplinary objects, the third research problem seeks to answer my question of how we might characterise these objects, what is typical for them, and what kind of changes happen in the process of modelling. Here I examine the tension between specified, question-oriented models and more general models, and suggest that the specified models form a group of their own. I call these Tailor-made models, in opposition to the process of building a simulation platform that aims at generalisability and utility for health-policy. This tension also underlines the challenge of applying research results (or methods and tools) to discuss and solve problems in decision-making processes.

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.

Tumour markers as prognostic factors of survival of gastric cancer patients

The incidence of gastric cancer in the last decades has declined rapidly in the industrialised countries. Worldwide, however, gastric cancer is still the second most common cause of cancer death. Although surgery is currently the most effective treatment, the rapid progress in adjuvant chemotherapy and radiation therapy requires a re-evaluation of prognosis assessment. The TNM staging system of the UICC is ubiquitously used; it groups patients by decreasing survival times from stage I to stage IV based on the spread of disease, i.e. depth of tumour penetration (T), extent of spread to lymph nodes (N), and the presence or absence of distant (M) metastases. This is by far the most consistent prognostic classification system today. However, even within the stage groups there are patients that follow a varying course of disease. Our knowledge of the molecular differences between tumours of the same stage and morphology has been accumulating over the years and methods for a more accurate assessment of the phenotype of neoplasias are of value when evaluating the prognosis of individual patients with gastric cancer. In this study, the immunohistochemical expression of tumour markers involved in different phases in tumourigenesis was examined. The aim was to find new markers which could provide prognostic information in addition to what is provided by the TNM variables. A total of 337 specimens from the primary tumour of patients who underwent surgery for gastric cancer were collected and the immunohistochemical expression of seven different biomarkers was analysed. DNA ploidy and S-phase fraction (SPF) was assessed by flow cytometry. Finally, all biomarkers and clinicopathological prognostic factors were combined and evaluated by a multivariate Cox regression model to elucidate which specific factors provide independent prognostic information. By univariate survival analysis the following variables were significant prognostic factors: epithelial and stromal syndecan-1 expression, stromal tenascin-C expression, expression of tumour-associated trypsin inhibitor (TATI) in cancer cells, nuclear p53 expression, nuclear p21 expression, DNA ploidy, and SPF. By multivariate survival analysis adjusted for all available clinicopathological and biomolecular variables, p53 expression, p21 expression, and DNA ploidy emerged as independent prognostic biomarkers, together with penetration depth of the tumour, presence of nodal metastases, surgical cure of the cancer, and age of the patient at the time of diagnosis.

Studies on Binary Time Series Models with Applications to Empirical Macroeconomics and Finance

This thesis studies binary time series models and their applications in empirical macroeconomics and finance. In addition to previously suggested models, new dynamic extensions are proposed to the static probit model commonly used in the previous literature. In particular, we are interested in probit models with an autoregressive model structure. In Chapter 2, the main objective is to compare the predictive performance of the static and dynamic probit models in forecasting the U.S. and German business cycle recession periods. Financial variables, such as interest rates and stock market returns, are used as predictive variables. The empirical results suggest that the recession periods are predictable and dynamic probit models, especially models with the autoregressive structure, outperform the static model. Chapter 3 proposes a Lagrange Multiplier (LM) test for the usefulness of the autoregressive structure of the probit model. The finite sample properties of the LM test are considered with simulation experiments. Results indicate that the two alternative LM test statistics have reasonable size and power in large samples. In small samples, a parametric bootstrap method is suggested to obtain approximately correct size. In Chapter 4, the predictive power of dynamic probit models in predicting the direction of stock market returns are examined. The novel idea is to use recession forecast (see Chapter 2) as a predictor of the stock return sign. The evidence suggests that the signs of the U.S. excess stock returns over the risk-free return are predictable both in and out of sample. The new "error correction" probit model yields the best forecasts and it also outperforms other predictive models, such as ARMAX models, in terms of statistical and economic goodness-of-fit measures. Chapter 5 generalizes the analysis of univariate models considered in Chapters 2 4 to the case of a bivariate model. A new bivariate autoregressive probit model is applied to predict the current state of the U.S. business cycle and growth rate cycle periods. Evidence of predictability of both cycle indicators is obtained and the bivariate model is found to outperform the univariate models in terms of predictive power.

Prognostic significance of cyclooxygenase-2 and associated molecules in gastric cancer

Background and aims: Low stage and curative surgery are established factors for improved survival in gastric cancer. However, not all low-stage patients have a good prognosis. Cyclooxygenase-2 (COX-2) is known to associate with reduced survival in several cancers, and has been shown to play an important role in gastric carcinogenesis. Since new and better prognostic markers are needed for gastric cancer, we studied the prognostic significance of COX-2 and of markers that associate with COX-2 expression. We also studied markers reflecting proliferation and apoptosis, and evaluated their association with COX-2. Our purpose was to construct an accurate prognostic model by combining tissue markers and clinicopathogical factors. Materials and methods: Of 342 consecutive patients who underwent surgery for gastric cancer at Meilahti Hospital, Helsinki University Central Hospital, 337 were included in this study. Low stages I to II were represented by 141 (42%) patients, and high stages III to IV by 196 (58%). Curative surgery was performed on 176 (52%) patients. Survival data were obtained from the national registers. Slides from archive tissue blocks were prepared for immunohistochemistry by use of COX-2, human antigen R (HuR), cyclin A, matrix metalloproteinases 2 and 9 (MMP-2, MMP-9), and Ki-67 antibodies. Immunostainings were scored by microscopy, and scores were entered into a database. Associations of tumor markers with clinicopathological factors were calculated, as well as associations with p53, p21, and results of flow cytometry from earlier studies. Survival analysis was performed by the Kaplan-Meier method, and Cox multivariate models were reconstructed. Cell culture experiments were performed to explore the effect of small interfering (si)RNA of HuR on COX-2 expression in a TMK-1 gastric cancer cell line. Results: Overall 5-year survival was 35.1%. Study I showed that COX-2 was an independent prognostic factor, and that the prognostic impact of COX-2 was more pronounced in low-stage patients. Cytoplasmic HuR expression also associated with reduced survival in gastric cancer patients in a non-independent manner. Cell culture experiments showed that HuR can regulate COX-2 expression in TMK-1 cells in vitro, with an association also between COX-2 and HuR tissue expression in a clinical material. In Study II, cyclin A was an independent prognostic factor and was associated with HuR expression in the gastric cancer material. The results of Study III showed that epithelial MMP-2 associated with survival in univariate, but not in multivariate analysis. However, MMP-9 showed no prognostic value. MMP-2 expression was associated with COX-2 expression. In Study IV, the prognostic power of COX-2 was compared with that of all tested markers associated with survival in Studies I to III, as well as with p21, p53, and flow cytometry results. COX-2 and p53 were independent prognostic factors, and COX-2 expression was associated with that of p53 and Ki-67 and also with aneuploidy. Conclusions: COX-2 is an independent prognostic factor in gastric cancer, and its prognostic power emerges especially in low stage cancer. COX-2 is regulated by HuR, and is associated with factors reflecting invasion, proliferation, and apoptosis. In an extended multivariate model, COX-2 retained its position as an independent prognosticator. COX-2 can be considered a promising new prognostic marker in gastric cancer.

Relative Contribution of Cell Proliferation and Microvascularity to Metastasis in Malignant Uveal Melanoma

Uveal melanoma (UM) is the second most common primary intraocular cancer worldwide. It is a relatively rare cancer, but still the second most common type of primary malignant melanoma in humans. UM is a slowly growing tumor, and gives rise to distant metastasis mainly to the liver via the bloodstream. About 40% of patients with UM die of metastatic disease within 10 years of diagnosis, irrespective of the type of treatment. During the last decade, two main lines of research have aimed to achieve enhanced understanding of the metastasis process and accurate prognosis of patients with UM. One emphasizes the characteristics of tumor cells, particularly their nucleoli, and markers of proliferation, and the other the characteristics of tumor blood vessels. Of several morphometric measurements, the mean diameter of the ten largest nucleoli (MLN) has become the most widely applied. A large MLN has consistently been associated with high likelihood of dying from UM. Blood vessels are of paramount importance in metastasis of UM. Different extravascular matrix patterns can be seen in UM, like loops and networks. This presence is associated with death from metastatic melanoma. However, the density of microvessels is also of prognostic importance. This study was undertaken to help understanding some histopathological factors which might contribute to developing metastasis in UM patients. Factors which could be related to tumor progression to metastasis disease, namely nucleolar size, MLN, microvascular density (MVD), cell proliferation, and The Insulin-like Growth Factor 1 Receptor(IGF-1R), were investigated. The primary aim of this thesis was to study the relationship between prognostic factors such as tumor cell nucleolar size, proliferation, extravascular matrix patterns, and dissemination of UM, and to assess to what extent there is a relationship to metastasis. The secondary goal was to develop a multivariate model which includes MLN and cell proliferation in addition to MVD, and which would fit better with population-based, melanoma-related survival data than previous models. I studied 167 patients with UM, who developed metastasis even after a very long time following removal of the eye, metastatic disease was the main cause of death, as documented in the Finnish Cancer Registry and on death certificates. Using an independent population-based data set, it was confirmed that MLN and extravascular matrix loops and networks were unrelated, independent predictors of survival in UM. Also, it has been found that multivariate models including MVD in addition to MLN fitted significantly better with survival data than models which excluded MVD. This supports the idea that both the characteristics of the blood vessels and the cells are important, and the future direction would be to look for the gene expression profile, whether it is associated more with MVD or MLN. The former relates to the host response to the tumor and may not be as tightly associated with the gene expression profile, yet most likely involved in the process of hematogenous metastasis. Because fresh tumor material is needed for reliable genetic analysis, such analysis could not be performed Although noninvasive detection of certain extravascular matrix patterns is now technically possible,in managing patients with UM, this study and tumor genetics suggest that such noninvasive methods will not fully capture the process of clinical metastasis. Progress in resection and biopsy techniques is likely in the near future to result in fresh material for the ophthalmic pathologist to correlate angiographic data, histopathological characteristics such as MLN, and genetic data. This study supported the theory that tumors containing epithelioid cells grow faster and have poorer prognosis when studied by cell proliferation in UM based on Ki-67 immunoreactivity. Cell proliferation index fitted best with the survival data when combined with MVD, MLN, and presence of epithelioid cells. Analogous with the finding that high MVD in primary UM is associated with shorter time to metastasis than low MVD, high MVD in hepatic metastasis tends to be associated with shorter survival after diagnosis of metastasis. Because the liver is the main organ for metastasis from UM, growth factors largely produced in the liver hepatocyte growth factor, epidermal growth factor and insulin-like growth factor-1 (IGF-1) together with their receptors may have a role in the homing and survival of metastatic cells. Therefore the association between immunoreactivity for IGF-1R in primary UM and metastatic death was studied. It was found that immunoreactivity for IGF-IR did not independently predict metastasis from primary UM in my series.

Analysis and evaluation of public forest policies.

XVIII IUFRO World Congress, Ljubljana 1986.