Three mathematical models for bucking-to-order

Abstract

Nuclear Matrix in Apoptotic Cell Death and Cell Proliferation. The role of Nuclear Mitotic Apparatus (NuMA) Protein

The nucleus is a membrane enclosed organelle containing most of the genetic information of the cell in the form of chromatin. The nucleus, which can be divided into many sub-organelles such as the nucleoli, the Cajal bodies and the nuclear lamina, is the site for several essential cellular functions such as the DNA replication and its regulation and most of the RNA synthesis and processing. The nucleus is often affected in disease: the size and the shape of the nucleus, the chromatin distribution and the size of the nucleoli have remained the basis for the grading of several cancers. The maintenance of the vertebrate body shape depends on the skeleton. Similarly, in a smaller context, the shape of the cell and the nucleus are mainly regulated by the cytoskeletal and nucleoskeletal elements. The nuclear matrix, which by definition is a detergent, DNase and salt resistant proteinaceous nuclear structure, has been suggested to form the nucleoskeleton responsible for the nuclear integrity. Nuclear mitotic apparatus protein, NuMA, a component of the nuclear matrix, is better known for its mitotic spindle organizing function. NuMA is one of the nuclear matrix proteins suggested to participate in the maintenance of the nuclear integrity during interphase but its interphase function has not been solved to date. This thesis study concentrated on the role of NuMA and the nuclear matrix as structural and functional components of the interphase nucleus. The first two studies clarified the essential role of caspase-3 in the disintegration of the nuclear structures during apoptosis. The second study also showed NuMA and chromatin to co-elute from cells in significant amounts and the apoptotic cleavage of NuMA was clarified to have an important role in the dissociation of NuMA from the chromatin. The third study concentrated on the interphase function of NuMA showing NuMA depletion to result in cell cycle arrest and the cytoplasmic relocalization of NuMA interaction partner GAS41. We suggest that the relocalization of the transcription factor GAS41 may mediate the cell cycle arrest. Thus, this study has given new aspects in the interactions of NuMA, chromatin and the nuclear matrix.

Some advances in mathematical models for preference relations

Preference relations, and their modeling, have played a crucial role in both social sciences and applied mathematics. A special category of preference relations is represented by cardinal preference relations, which are nothing other than relations which can also take into account the degree of relation. Preference relations play a pivotal role in most of multi criteria decision making methods and in the operational research. This thesis aims at showing some recent advances in their methodology. Actually, there are a number of open issues in this field and the contributions presented in this thesis can be grouped accordingly. The first issue regards the estimation of a weight vector given a preference relation. A new and efficient algorithm for estimating the priority vector of a reciprocal relation, i.e. a special type of preference relation, is going to be presented. The same section contains the proof that twenty methods already proposed in literature lead to unsatisfactory results as they employ a conflicting constraint in their optimization model. The second area of interest concerns consistency evaluation and it is possibly the kernel of the thesis. This thesis contains the proofs that some indices are equivalent and that therefore, some seemingly different formulae, end up leading to the very same result. Moreover, some numerical simulations are presented. The section ends with some consideration of a new method for fairly evaluating consistency. The third matter regards incomplete relations and how to estimate missing comparisons. This section reports a numerical study of the methods already proposed in literature and analyzes their behavior in different situations. The fourth, and last, topic, proposes a way to deal with group decision making by means of connecting preference relations with social network analysis.

Role and Function of c-Jun Protein Complex in Cancer Cell Behavior

Transcription factors play a crucial role in the regulation of cell behavior by modulating gene expression profiles. Previous studies have described a dual role for the AP-1 family transcription factor c-Jun in the regulation of cellular fate. In various cell types weak and transient activations of c-Jun N-terminal kinase (JNK) and c-Jun appear to contribute to proliferation and survival, whereas strong and prolonged activation of JNK and c-Jun result in apoptosis. These opposite roles played by c-Jun are cell type specific and the molecular mechanisms defining these antonymous c-Jun-mediated responses remain incompletely understood. c-Jun activity in transformed cells is regulated by signalling cascades downstream of oncoproteins such as Ras and Raf. In addition, the pro-proliferative role and the survival promoting function for c-Jun has been described in various cancer models. Furthermore, c-Jun was described to be overexpressed in different cancer types. However, the molecular mechanisms by which c-Jun exerts these oncogenic functions are not all clearly established. Therefore it is of primary interest to further identify molecular mechanisms and functions for c-Jun in cancer. Regulation of gene expression is tightly dependent on accurate protein-protein interactions. Therefore, co-factors for c-Jun may define the functions for c-Jun in cancer. Identification of protein-protein interactions promoting cancer may provide novel possibilities for cancer treatment. In this study, we show that DNA topoisomerase I (TopoI) is a transcriptional co-factor for c-Jun. Moreover, c-Jun and TopoI together promote expression of epidermal growth factor receptor (EGFR) in cancer cells. We also show that the clinically used TopoI inhibitor topotecan reduces EGFR expression. Importantly, the effect of TopoI on EGFR transcription was shown to depend on c-Jun as Jun-/- cells or cells treated with JNK inhibitor SP600125 are resistant to topotecan treatment both in regulation of EGFR expression and cell proliferation. Moreover, c-Jun regulates the nucleolar localization and the function of the ribonucleic acid (RNA) helicase DDX21, a previously identified member of c-Jun protein complex. In addition, c-Jun stimulates rRNA processing by supporting DDX21 rRNA binding. Finally, this study characterizes a DDX21 dependent expression of cyclin dependent kinase (Cdk) 6, a correlation of DDX21 expression with prostate cancer progression and a substrate binding dependency of DDX21 nucleolar localization in prostate cancer cells. Taken together, the results of this study validate the c-Jun-TopoI interaction and precise the c-Jun-DDX21 interaction. Moreover, these results show the importance for protein-protein interaction in the regulation of their cellular functions in cancer cell behavior. Finally, the results presented here disclose new exciting therapeutic opportunities for cancer treatment.

Superoxide dismutase 3-mediated cell survival and proliferation

This dissertation studies the signaling events mediated by the extracellular superoxide dismutase (SOD3). SOD3 is an antioxidant enzyme which converts the harmful superoxide into hydrogen peroxide. Overproduction of these reactive oxygen species (ROS) in the cellular environment as a result of tissue injury or impaired antioxidant defense system has detrimental effects on tissue integrity and function. However, especially hydrogen peroxide is also an important signaling agent. Ischemic injury in muscle causes acute oxidative stress and inflammation. We investigated the ability of SOD3 to attenuate ischemia induced inflammation and to promote recovery of skeletal muscle tissue. We found that SOD3 can downregulate the expression of several inflammatory cytokines and cell adhesion molecules thus preventing the accumulation of oxidant-producing inflammatory cells. Secondly, SOD3 was able to promote long-term activation of the mitogenic Erk pathway, but increased only briefly the activity of pro-survival Akt pathway at an early stage of ischemic inflammation, thus reducing apoptosis. SOD3 is a prominent antioxidant in the thyroid gland where oxidative stress is constantly present. We investigated the role of SOD3 in normal thyroid follicular cells and the changes in its expression in various hyperproliferative disorders. We first showed that SOD3 is TSH-responsive which indicated its participation in thyroid function. Its principal function seems to be in follicular cell proliferation since knockdown cells were deficient in proliferation. Additionally, it was overexpressed in goiter tissue. However, SOD3 was consistently downregulated in thyroid cancer cell lines and tissues. In conclusion, SOD3 is involved in tissue maintenance, cell proliferation and inflammatory cell migration. Its mechanisms of action are the activation of known proliferation/survival pathways, inhibition of apoptosis and regulation of adhesion molecule expression.

Regulation of cell fate by c-FLIP phosphorylation

Programmed cell death is an important physiological cellular process that maintains homeostasis and protects multicellular organisms from diseases. Apoptosis is the principal mode of cell death, which eliminates unwanted cells and an enormous effort has been made to understand the molecular mechanisms of the signaling pathway and its regulatory systems. Irregular apoptosis often has life-threatening consequences to humans, including cancer, autoimmune diseases and degenerative diseases. In cancer for example, cell death is an attractive target to eradicate uncontrollably proliferating cells that have disregard pro-apoptotic signaling. Targeted therapeutic approaches are not as effective as once expected, since now we know that the cell death pathways are not sole entities in cells, but are highly associated with various cellular processes. Proteins that regulate apoptosis can also control non-apoptotic signaling pathways. For example, c-FLIP is a protein that can either inhibit or promote caspase-8 activation, which is required to induce apoptosis. Not only has c-FLIP opposing effects on initiating apoptosis, but it also regulates various pro-survival signaling pathways in the cell. It is well known that protein expression level is a determinant of how c-FLIP can regulate different signaling pathways, but other regulatory mechanisms potentially affecting the role of c-FLIP are less well understood. This work addresses novel insights into the mechanisms of c-FLIP post-translational modifications and their functional consequences. We have identified that phosphorylation is an important inception for subcellular localization of c-FLIP, thereby dictating which apoptotic and non-apoptotic signaling pathways c-FLIP could regulate to promote cell survival. Furthermore, we have constructed mathematical models to unite independent studies to establish more systematic c-FLIP signaling pathways to understand the dynamics of extrinsically-induced apoptosis.

Monte Carlo Methods in Parameter Estimation of Nonlinear Models

Yksi keskeisimmistä tehtävistä matemaattisten mallien tilastollisessa analyysissä on mallien tuntemattomien parametrien estimointi. Tässä diplomityössä ollaan kiinnostuneita tuntemattomien parametrien jakaumista ja niiden muodostamiseen sopivista numeerisista menetelmistä, etenkin tapauksissa, joissa malli on epälineaarinen parametrien suhteen. Erilaisten numeeristen menetelmien osalta pääpaino on Markovin ketju Monte Carlo -menetelmissä (MCMC). Nämä laskentaintensiiviset menetelmät ovat viime aikoina kasvattaneet suosiotaan lähinnä kasvaneen laskentatehon vuoksi. Sekä Markovin ketjujen että Monte Carlo -simuloinnin teoriaa on esitelty työssä siinä määrin, että menetelmien toimivuus saadaan perusteltua. Viime aikoina kehitetyistä menetelmistä tarkastellaan etenkin adaptiivisia MCMC menetelmiä. Työn lähestymistapa on käytännönläheinen ja erilaisia MCMC -menetelmien toteutukseen liittyviä asioita korostetaan. Työn empiirisessä osuudessa tarkastellaan viiden esimerkkimallin tuntemattomien parametrien jakaumaa käyttäen hyväksi teoriaosassa esitettyjä menetelmiä. Mallit kuvaavat kemiallisia reaktioita ja kuvataan tavallisina differentiaaliyhtälöryhminä. Mallit on kerätty kemisteiltä Lappeenrannan teknillisestä yliopistosta ja Åbo Akademista, Turusta.

Ion-exchange resins as stationary phase in reactive chromatography

Dynamic behavior of bothisothermal and non-isothermal single-column chromatographic reactors with an ion-exchange resin as the stationary phase was investigated. The reactor performance was interpreted by using results obtained when studying the effect of the resin properties on the equilibrium and kinetic phenomena occurring simultaneously in the reactor. Mathematical models were derived for each phenomenon and combined to simulate the chromatographic reactor. The phenomena studied includes phase equilibria in multicomponent liquid mixture¿ion-exchange resin systems, chemicalequilibrium in the presence of a resin catalyst, diffusion of liquids in gel-type and macroporous resins, and chemical reaction kinetics. Above all, attention was paid to the swelling behavior of the resins and how it affects the kinetic phenomena. Several poly(styrene-co-divinylbenzene) resins with different cross-link densities and internal porosities were used. Esterification of acetic acid with ethanol to produce ethyl acetate and water was used as a model reaction system. Choosing an ion-exchange resin with a low cross-link density is beneficial inthe case of the present reaction system: the amount of ethyl acetate as well the ethyl acetate to water mole ratio in the effluent stream increase with decreasing cross-link density. The enhanced performance of the reactor is mainly attributed to increasing reaction rate, which in turn originates from the phase equilibrium behavior of the system. Also mass transfer considerations favor the use ofresins with low cross-link density. The diffusion coefficients of liquids in the gel-type ion-exchange resins were found to fall rapidly when the extent of swelling became low. Glass transition of the polymer was not found to significantlyretard the diffusion in sulfonated PS¿DVB ion-exchange resins. It was also shown that non-isothermal operation of a chromatographic reactor could be used to significantly enhance the reactor performance. In the case of the exothermic modelreaction system and a near-adiabatic column, a positive thermal wave (higher temperature than in the initial state) was found to travel together with the reactive front. This further increased the conversion of the reactants. Diffusion-induced volume changes of the ion-exchange resins were studied in a flow-through cell. It was shown that describing the swelling and shrinking kinetics of the particles calls for a mass transfer model that explicitly includes the limited expansibility of the polymer network. A good description of the process was obtained by combining the generalized Maxwell-Stefan approach and an activity model that was derived from the thermodynamics of polymer solutions and gels. The swelling pressure in the resin phase was evaluated by using a non-Gaussian expression forthe polymer chain length distribution. Dimensional changes of the resin particles necessitate the use of non-standard mathematical tools for dynamic simulations. A transformed coordinate system, where the mass of the polymer was used as a spatial variable, was applied when simulating the chromatographic reactor columns as well as the swelling and shrinking kinetics of the resin particles. Shrinking of the particles in a column leads to formation of dead volume on top of the resin bed. In ordinary Eulerian coordinates, this results in a moving discontinuity that in turn causes numerical difficulties in the solution of the PDE system. The motion of the discontinuity was eliminated by spanning two calculation grids in the column that overlapped at the top of the resin bed. The reactive and non-reactive phase equilibrium data were correlated with a model derived from thethermodynamics of polymer solution and gels. The thermodynamic approach used inthis work is best suited at high degrees of swelling because the polymer matrixmay be in the glassy state when the extent of swelling is low.

Negative Regulation of Receptor Tyrosine Kinases by T-cell Protein Tyrosine Phosphatase

Protein tyrosine phosphorylation controls a wide array of cellular responses such as growth, migration, proliferation, differentiation, metabolism and cytoskeletal organisation. Tyrosine phosphorylation is a dynamic process involving the competing activities of protein tyrosine kinases and protein tyrosine phosphatases. The protein tyrosine kinases are further divided into non-receptor- and receptor tyrosine kinases. The latter are transmembrane glycoproteins activated by the binding of specific ligands, mostly growth factors, to their extracellular domain, transmitting different signals to the cell. Growth factor receptors such as the epidermal growth factor receptor, vascular endothelial growth factor receptor 2 and platelet-derived growth factor receptor β, belong to the receptor tyrosine kinases, the signalling of which is often disturbed in various diseases, including cancer. This has led to the development of receptor tyrosine kinase antagonists for use as anti-cancer drugs. As the receptor tyrosine kinases, also the protein tyrosine phosphatases can be divided into receptor- and non-receptor types. The protein tyrosine phosphatases have attained much less attention than the receptor tyrosine kinases partly because they were identified later. However, accumulating evidence shows that the protein tyrosine phosphatases have important roles as specific and active regulators of tyrosine phosphorylation in cells and of physiological processes. Consequently, the protein tyrosine phosphatases are receiving arising interest as novel drug targets. The aim of this work was to elucidate the negative regulation of receptor tyrosine kinases by one non-receptor protein tyrosine phosphatase, T-cell protein tyrosine phosphatase TCPTP. The results show that TCPTP activated by cell adhesion receptor integrin α1 functions as a negative regulator of the epidermal growth factor receptor. It was also found that TCPTP affects vascular endothelial growth factor receptor 2 signalling and angiogenesis. Lastly, a High-throughput screen with 64,280 compounds was performed to identify novel TCPTP activators, resulting in identification of one small molecule compound capable of exerting similar effects on TCPTP signalling as integrin α1. This compound is shown to downregulate signalling of epidermal growth factor receptor and platelet-derived growth factor receptor β, as well as to inhibit cell proliferation and angiogenesis. Our results suggest that a suitable small-molecule TCPTP activator could be utilized in the development of novel anti-cancer drugs.

A comparison of electricity spot prices simulation using ARMA-GARCH and mean-reverting models

The aim of this work is to compare two families of mathematical models for their respective capability to capture the statistical properties of real electricity spot market time series. The first model family is ARMA-GARCH models and the second model family is mean-reverting Ornstein-Uhlenbeck models. These two models have been applied to two price series of Nordic Nord Pool spot market for electricity namely to the System prices and to the DenmarkW prices. The parameters of both models were calibrated from the real time series. After carrying out simulation with optimal models from both families we conclude that neither ARMA-GARCH models, nor conventional mean-reverting Ornstein-Uhlenbeck models, even when calibrated optimally with real electricity spot market price or return series, capture the statistical characteristics of the real series. But in the case of less spiky behavior (System prices), the mean-reverting Ornstein-Uhlenbeck model could be seen to partially succeeded in this task.

Parallel-Operating Three-Phase Voltage Source Inverters – Circulating CurrentModeling, Analysis and Mitigation

The maximum realizable power throughput of power electronic converters may be limited or constrained by technical or economical considerations. One solution to this problemis to connect several power converter units in parallel. The parallel connection can be used to increase the current carrying capacity of the overall system beyond the ratings of individual power converter units. Thus, it is possible to use several lower-power converter units, produced in large quantities, as building blocks to construct high-power converters in a modular manner. High-power converters realized by using parallel connection are needed for example in multimegawatt wind power generation systems. Parallel connection of power converter units is also required in emerging applications such as photovoltaic and fuel cell power conversion. The parallel operation of power converter units is not, however, problem free. This is because parallel-operating units are subject to overcurrent stresses, which are caused by unequal load current sharing or currents that flow between the units. Commonly, the term ’circulatingcurrent’ is used to describe both the unequal load current sharing and the currents flowing between the units. Circulating currents, again, are caused by component tolerances and asynchronous operation of the parallel units. Parallel-operating units are also subject to stresses caused by unequal thermal stress distribution. Both of these problemscan, nevertheless, be handled with a proper circulating current control. To design an effective circulating current control system, we need information about circulating current dynamics. The dynamics of the circulating currents can be investigated by developing appropriate mathematical models. In this dissertation, circulating current models aredeveloped for two different types of parallel two-level three-phase inverter configurations. Themodels, which are developed for an arbitrary number of parallel units, provide a framework for analyzing circulating current generation mechanisms and developing circulating current control systems. In addition to developing circulating current models, modulation of parallel inverters is considered. It is illustrated that depending on the parallel inverter configuration and the modulation method applied, common-mode circulating currents may be excited as a consequence of the differential-mode circulating current control. To prevent the common-mode circulating currents that are caused by the modulation, a dual modulator method is introduced. The dual modulator basically consists of two independently operating modulators, the outputs of which eventually constitute the switching commands of the inverter. The two independently operating modulators are referred to as primary and secondary modulators. In its intended usage, the same voltage vector is fed to the primary modulators of each parallel unit, and the inputs of the secondary modulators are obtained from the circulating current controllers. To ensure that voltage commands obtained from the circulating current controllers are realizable, it must be guaranteed that the inverter is not driven into saturation by the primary modulator. The inverter saturation can be prevented by limiting the inputs of the primary and secondary modulators. Because of this, also a limitation algorithm is proposed. The operation of both the proposed dual modulator and the limitation algorithm is verified experimentally.

Identification of Epigenetic Targets in Prostate Cancer for Therapeutic Development

Recurrent castration resistant prostate cancer remains a challenge for cancer therapies and novel treatment options in addition to current anti-androgen and mitosis inhibitors are needed. Aberrations in epigenetic enzymes and chromatin binding proteins have been linked to prostate cancer and they may form a novel class of drug targets in the future. In this thesis we systematically evaluated the epigenenome as a prostate cancer drug target. We functionally silenced 615 known and putative epigenetically active protein coding genes in prostate cancer cell lines using high throughput RNAi screening and evaluated the effects on cell proliferation, androgen receptor (AR) expression and histone patterns. Histone deacetylases (HDACs) were found to regulate AR expression. Furthermore, HDAC inhibitors reduced AR signaling and inhibited synergistically with androgen deprivation prostate cancer cell proliferation. In particular, TMPRSS2- EGR fusion gene positive prostate cancer cell lines were sensitive to combined HDAC and AR inhibition, which may partly be related to the dependency of a fusion gene induced epigenetic pathway. Histone demethylases (HDMs) were identified to regulate prostate cancer cell line proliferation. We discovered a novel histone JmjC-domain histone demethylase PHF8 to be highly expressed in high grade prostate cancers and mediate cell proliferation, migration and invasion in in vitro models. Additionally, we explored novel HDM inhibitor chemical structures using virtual screening methods. The structures best fitting to the active pocket of KDM4A were tested for enzyme inhibition and prostate cancer cell proliferation activity in vitro. In conclusion, our results show that prostate cancer may efficiently be targeted with combined AR and HDAC inhibition which is also currently being tested in clinical trials. HDMs were identified as another feasible novel drug target class. Future studies in representative animal models and development of specific inhibitors may reveal HDMs full potential in prostate cancer therapy

Linguistic models for decision support

Linguistic modelling is a rather new branch of mathematics that is still undergoing rapid development. It is closely related to fuzzy set theory and fuzzy logic, but knowledge and experience from other fields of mathematics, as well as other fields of science including linguistics and behavioral sciences, is also necessary to build appropriate mathematical models. This topic has received considerable attention as it provides tools for mathematical representation of the most common means of human communication - natural language. Adding a natural language level to mathematical models can provide an interface between the mathematical representation of the modelled system and the user of the model - one that is sufficiently easy to use and understand, but yet conveys all the information necessary to avoid misinterpretations. It is, however, not a trivial task and the link between the linguistic and computational level of such models has to be established and maintained properly during the whole modelling process. In this thesis, we focus on the relationship between the linguistic and the mathematical level of decision support models. We discuss several important issues concerning the mathematical representation of meaning of linguistic expressions, their transformation into the language of mathematics and the retranslation of mathematical outputs back into natural language. In the first part of the thesis, our view of the linguistic modelling for decision support is presented and the main guidelines for building linguistic models for real-life decision support that are the basis of our modeling methodology are outlined. From the theoretical point of view, the issues of representation of meaning of linguistic terms, computations with these representations and the retranslation process back into the linguistic level (linguistic approximation) are studied in this part of the thesis. We focus on the reasonability of operations with the meanings of linguistic terms, the correspondence of the linguistic and mathematical level of the models and on proper presentation of appropriate outputs. We also discuss several issues concerning the ethical aspects of decision support - particularly the loss of meaning due to the transformation of mathematical outputs into natural language and the issue or responsibility for the final decisions. In the second part several case studies of real-life problems are presented. These provide background and necessary context and motivation for the mathematical results and models presented in this part. A linguistic decision support model for disaster management is presented here – formulated as a fuzzy linear programming problem and a heuristic solution to it is proposed. Uncertainty of outputs, expert knowledge concerning disaster response practice and the necessity of obtaining outputs that are easy to interpret (and available in very short time) are reflected in the design of the model. Saaty’s analytic hierarchy process (AHP) is considered in two case studies - first in the context of the evaluation of works of art, where a weak consistency condition is introduced and an adaptation of AHP for large matrices of preference intensities is presented. The second AHP case-study deals with the fuzzified version of AHP and its use for evaluation purposes – particularly the integration of peer-review into the evaluation of R&D outputs is considered. In the context of HR management, we present a fuzzy rule based evaluation model (academic faculty evaluation is considered) constructed to provide outputs that do not require linguistic approximation and are easily transformed into graphical information. This is achieved by designing a specific form of fuzzy inference. Finally the last case study is from the area of humanities - psychological diagnostics is considered and a linguistic fuzzy model for the interpretation of outputs of multidimensional questionnaires is suggested. The issue of the quality of data in mathematical classification models is also studied here. A modification of the receiver operating characteristics (ROC) method is presented to reflect variable quality of data instances in the validation set during classifier performance assessment. Twelve publications on which the author participated are appended as a third part of this thesis. These summarize the mathematical results and provide a closer insight into the issues of the practicalapplications that are considered in the second part of the thesis.

Mathematical modeling and optimal control of malaria

Malaria continues to infect millions and kill hundreds of thousands of people worldwide each year, despite over a century of research and attempts to control and eliminate this infectious disease. Challenges such as the development and spread of drug resistant malaria parasites, insecticide resistance to mosquitoes, climate change, the presence of individuals with subpatent malaria infections which normally are asymptomatic and behavioral plasticity in the mosquito hinder the prospects of malaria control and elimination. In this thesis, mathematical models of malaria transmission and control that address the role of drug resistance, immunity, iron supplementation and anemia, immigration and visitation, and the presence of asymptomatic carriers in malaria transmission are developed. A within-host mathematical model of severe Plasmodium falciparum malaria is also developed. First, a deterministic mathematical model for transmission of antimalarial drug resistance parasites with superinfection is developed and analyzed. The possibility of increase in the risk of superinfection due to iron supplementation and fortification in malaria endemic areas is discussed. The model results calls upon stakeholders to weigh the pros and cons of iron supplementation to individuals living in malaria endemic regions. Second, a deterministic model of transmission of drug resistant malaria parasites, including the inflow of infective immigrants, is presented and analyzed. The optimal control theory is applied to this model to study the impact of various malaria and vector control strategies, such as screening of immigrants, treatment of drug-sensitive infections, treatment of drug-resistant infections, and the use of insecticide-treated bed nets and indoor spraying of mosquitoes. The results of the model emphasize the importance of using a combination of all four controls tools for effective malaria intervention. Next, a two-age-class mathematical model for malaria transmission with asymptomatic carriers is developed and analyzed. In development of this model, four possible control measures are analyzed: the use of long-lasting treated mosquito nets, indoor residual spraying, screening and treatment of symptomatic, and screening and treatment of asymptomatic individuals. The numerical results show that a disease-free equilibrium can be attained if all four control measures are used. A common pitfall for most epidemiological models is the absence of real data; model-based conclusions have to be drawn based on uncertain parameter values. In this thesis, an approach to study the robustness of optimal control solutions under such parameter uncertainty is presented. Numerical analysis of the optimal control problem in the presence of parameter uncertainty demonstrate the robustness of the optimal control approach that: when a comprehensive control strategy is used the main conclusions of the optimal control remain unchanged, even if inevitable variability remains in the control profiles. The results provide a promising framework for the design of cost-effective strategies for disease control with multiple interventions, even under considerable uncertainty of model parameters. Finally, a separate work modeling the within-host Plasmodium falciparum infection in humans is presented. The developed model allows re-infection of already-infected red blood cells. The model hypothesizes that in severe malaria due to parasite quest for survival and rapid multiplication, the Plasmodium falciparum can be absorbed in the already-infected red blood cells which accelerates the rupture rate and consequently cause anemia. Analysis of the model and parameter identifiability using Markov chain Monte Carlo methods is presented.

To Divide or Not to Divide; MicroRNAs and Small Compounds as Modulators of Mitosis

Mitosis is under the stringent quality control of the spindle assembly checkpoint (SAC). However, in cancer cells this control can fail, leading to excessive cellular proliferation and ultimately to the formation of a tumor. Novel cancer cell selective therapies are needed to stop the uncontrolled cell proliferation and tumor growth. The aim of the research presented in this thesis was to identify microRNAs (miRNAs) that could play a role in cancer cell proliferation as well as low molecular weight (LMW) compounds that could interfere with cell division. The findings could be used to develop better cancer diagnostics and therapies in the future. First, a high-throughput screen (HTS) was performed to identify LMW compounds that possess a similar chemical interaction field as rigosertib, an anti-cancer compound undergoing clinical trials. A compound termed Centmitor-1 was discovered that phenocopied the cellular impact of rigosertib by affecting the microtubule dynamics. Next, another HTS aimed at identifying compounds that would target the Hec1 protein, which mediates the interaction between spindle microtubules and chromosomes. Perturbation of this connection should prevent cell division and induce cell death. A compound termed VTT-006 was discovered that abrogated mitosis in several cell line models and exhibited binding to Hec1 in vitro. Lastly, using a cell-based HTS two miRNAs were identified that affected cancer cell proliferation via Aurora B kinase, which is an important mitotic regulator. MiR-378a-5p was found to indirectly suppress the production of the kinase whereas let-7b showed direct binding to the 3’UTR of Aurora B mRNA and repressed its translation. The miRNA-mediated perturbation of Aurora B induced defects in mitosis leading to abnormal chromosome segregation and induction of aneuploidy. The results of this thesis provide new information on miRNA signaling in cancer, which could be utilized for diagnostic purposes. Moreover, the thesis introduces two small compounds that may benefit future drug research.