Relationship between Vitamin D Receptor gene polymorphisms and the components of metabolic syndrome

Abstract Background The Vitamin D Receptor gene (VDR) is expressed in many tissues and modulates the expression of several other genes. The purpose of this study was to investigate the association between metabolic syndrome (MetSyn) with the presence of VDR 2228570 C > T and VDR 1544410 A > G polymorphisms in Brazilian adults. Methods Two hundred forty three (243) individuals were included in a cross-sectional study. MetSyn was classified using the criteria proposed by National Cholesterol Educational Program - Adult Treatment Panel III. Insulin resistance and β cell secretion were estimated by the mathematical models of HOMA IR and β, respectively. The VDR 2228570 C > T and VDR 1544410 A > G polymorphisms were detected by enzymatic digestion and confirmed by allele specific PCR or amplification of refractory mutation. Results Individuals with MetSyn and heterozygosis for VDR 2228570 C > T have higher concentrations of iPTH and HOMA β than those without this polymorphism, and subjects with recessive homozygosis for the same polymorphisms presented higher insulin resistance than those with the heterozygous genotype. There is no association among VDR 1544410 A > G and components of MetSyn, HOMA IR and β, serum vitamin D (25(OH)D3) and intact parathormone (iPTH) levels in patients with MetSyn. A significant lower concentration of 25(OH)D3 was observed only in individuals without MetSyn in the VDR 1544410 A > G genotype. Additionally, individuals without MetSyn and heterozygosis for VDR 2228570 C > T presented higher concentration of triglycerides and lower HDL than those without this polymorphism. Conclusions Using two common VDR polymorphism data suggests they may influence insulin secretion, insulin resistance an serum HDL-cholesterol in our highly heterogeneous population. Whether VDR polymorphism may influence the severity of MetSyn component disorder, warrants examination in larger cohorts used for genome-wide association studies.

Performance estimation for concretes made with recycled aggregates of construction and demolition waste of some Brazilian cities

The aim of this paper is to verify the influence of composition variability of recycled aggregates (RA) of construction and demolition wastes (CDW) on the performance of concretes. Performance was evaluated building mathematical models for compressive strength, modulus of elasticity and drying shrinkage. To obtain such models, an experimental program comprising 50 concrete mixtures was carried out. Specimens were casted, tested and results for compressive strength, modulus of elasticity and drying shrinkage were statistically analyzed. Models inputs are CDW composition observed at seven Brazilian cities. Results confirm that using RA from CDW for concrete building is quite feasible, independently of its composition, once compressive strength and modulus of elasticity still reached considerable values. We concluded the variability presented by recycled aggregates of CDW does not compromise their use for concrete building. However, this information must be used with caution, and experimental tests should always be performed to certify concrete properties.

Multimodality and flexibility of stochastic gene expression

We consider a general class of mathematical models for stochastic gene expression where the transcription rate is allowed to depend on a promoter state variable that can take an arbitrary (finite) number of values. We provide the solution of the master equations in the stationary limit, based on a factorization of the stochastic transition matrix that separates timescales and relative interaction strengths, and we express its entries in terms of parameters that have a natural physical and/or biological interpretation. The solution illustrates the capacity of multiple states promoters to generate multimodal distributions of gene products, without the need for feedback. Furthermore, using the example of a three states promoter operating at low, high, and intermediate expression levels, we show that using multiple states operons will typically lead to a significant reduction of noise in the system. The underlying mechanism is that a three-states promoter can change its level of expression from low to high by passing through an intermediate state with a much smaller increase of fluctuations than by means of a direct transition.

Computational analyses on the structure-function relation in ion channels

Ion channels are protein molecules, embedded in the lipid bilayer of the cell membranes. They act as powerful sensing elements switching chemicalphysical stimuli into ion-fluxes. At a glance, ion channels are water-filled pores, which can open and close in response to different stimuli (gating), and one once open select the permeating ion species (selectivity). They play a crucial role in several physiological functions, like nerve transmission, muscular contraction, and secretion. Besides, ion channels can be used in technological applications for different purpose (sensing of organic molecules, DNA sequencing). As a result, there is remarkable interest in understanding the molecular determinants of the channel functioning. Nowadays, both the functional and the structural characteristics of ion channels can be experimentally solved. The purpose of this thesis was to investigate the structure-function relation in ion channels, by computational techniques. Most of the analyses focused on the mechanisms of ion conduction, and the numerical methodologies to compute the channel conductance. The standard techniques for atomistic simulation of complex molecular systems (Molecular Dynamics) cannot be routinely used to calculate ion fluxes in membrane channels, because of the high computational resources needed. The main step forward of the PhD research activity was the development of a computational algorithm for the calculation of ion fluxes in protein channels. The algorithm - based on the electrodiffusion theory - is computational inexpensive, and was used for an extensive analysis on the molecular determinants of the channel conductance. The first record of ion-fluxes through a single protein channel dates back to 1976, and since then measuring the single channel conductance has become a standard experimental procedure. Chapter 1 introduces ion channels, and the experimental techniques used to measure the channel currents. The abundance of functional data (channel currents) does not match with an equal abundance of structural data. The bacterial potassium channel KcsA was the first selective ion channels to be experimentally solved (1998), and after KcsA the structures of four different potassium channels were revealed. These experimental data inspired a new era in ion channel modeling. Once the atomic structures of channels are known, it is possible to define mathematical models based on physical descriptions of the molecular systems. These physically based models can provide an atomic description of ion channel functioning, and predict the effect of structural changes. Chapter 2 introduces the computation methods used throughout the thesis to model ion channels functioning at the atomic level. In Chapter 3 and Chapter 4 the ion conduction through potassium channels is analyzed, by an approach based on the Poisson-Nernst-Planck electrodiffusion theory. In the electrodiffusion theory ion conduction is modeled by the drift-diffusion equations, thus describing the ion distributions by continuum functions. The numerical solver of the Poisson- Nernst-Planck equations was tested in the KcsA potassium channel (Chapter 3), and then used to analyze how the atomic structure of the intracellular vestibule of potassium channels affects the conductance (Chapter 4). As a major result, a correlation between the channel conductance and the potassium concentration in the intracellular vestibule emerged. The atomic structure of the channel modulates the potassium concentration in the vestibule, thus its conductance. This mechanism explains the phenotype of the BK potassium channels, a sub-family of potassium channels with high single channel conductance. The functional role of the intracellular vestibule is also the subject of Chapter 5, where the affinity of the potassium channels hEag1 (involved in tumour-cell proliferation) and hErg (important in the cardiac cycle) for several pharmaceutical drugs was compared. Both experimental measurements and molecular modeling were used in order to identify differences in the blocking mechanism of the two channels, which could be exploited in the synthesis of selective blockers. The experimental data pointed out the different role of residue mutations in the blockage of hEag1 and hErg, and the molecular modeling provided a possible explanation based on different binding sites in the intracellular vestibule. Modeling ion channels at the molecular levels relates the functioning of a channel to its atomic structure (Chapters 3-5), and can also be useful to predict the structure of ion channels (Chapter 6-7). In Chapter 6 the structure of the KcsA potassium channel depleted from potassium ions is analyzed by molecular dynamics simulations. Recently, a surprisingly high osmotic permeability of the KcsA channel was experimentally measured. All the available crystallographic structure of KcsA refers to a channel occupied by potassium ions. To conduct water molecules potassium ions must be expelled from KcsA. The structure of the potassium-depleted KcsA channel and the mechanism of water permeation are still unknown, and have been investigated by numerical simulations. Molecular dynamics of KcsA identified a possible atomic structure of the potassium-depleted KcsA channel, and a mechanism for water permeation. The depletion from potassium ions is an extreme situation for potassium channels, unlikely in physiological conditions. However, the simulation of such an extreme condition could help to identify the structural conformations, so the functional states, accessible to potassium ion channels. The last chapter of the thesis deals with the atomic structure of the !- Hemolysin channel. !-Hemolysin is the major determinant of the Staphylococcus Aureus toxicity, and is also the prototype channel for a possible usage in technological applications. The atomic structure of !- Hemolysin was revealed by X-Ray crystallography, but several experimental evidences suggest the presence of an alternative atomic structure. This alternative structure was predicted, combining experimental measurements of single channel currents and numerical simulations. This thesis is organized in two parts, in the first part an overview on ion channels and on the numerical methods adopted throughout the thesis is provided, while the second part describes the research projects tackled in the course of the PhD programme. The aim of the research activity was to relate the functional characteristics of ion channels to their atomic structure. In presenting the different research projects, the role of numerical simulations to analyze the structure-function relation in ion channels is highlighted.

Relationships between running economy and mechanics in middle-distance runners

Running economy (RE), i.e. the oxygen consumption at a given submaximal speed, is an important determinant of endurance running performance. So far, investigators have widely attempted to individuate the factors affecting RE in competitive athletes, focusing mainly on the relationships between RE and running biomechanics. However, the current results are inconsistent and a clear mechanical profile of an economic runner has not been yet established. The present work aimed to better understand how the running technique influences RE in sub-elite middle-distance runners by investigating the biomechanical parameters acting on RE and the underlying mechanisms. Special emphasis was given to accounting for intra-individual variability in RE at different speeds and to assessing track running rather than treadmill running. In Study One, a factor analysis was used to reduce the 30 considered mechanical parameters to few global descriptors of the running mechanics. Then, a biomechanical comparison between economic and non economic runners and a multiple regression analysis (with RE as criterion variable and mechanical indices as independent variables) were performed. It was found that a better RE was associated to higher knee and ankle flexion in the support phase, and that the combination of seven individuated mechanical measures explains ∼72% of the variability in RE. In Study Two, a mathematical model predicting RE a priori from the rate of force production, originally developed and used in the field of comparative biology, was adapted and tested in competitive athletes. The model showed a very good fit (R2=0.86). In conclusion, the results of this dissertation suggest that the very complex interrelationships among the mechanical parameters affecting RE may be successfully dealt with through multivariate statistical analyses and the application of theoretical mathematical models. Thanks to these results, coaches are provided with useful tools to assess the biomechanical profile of their athletes. Thus, individual weaknesses in the running technique may be identified and removed, with the ultimate goal to improve RE.

Design of wireless sensor networks for fluid dynamic applications

In fluid dynamics research, pressure measurements are of great importance to define the flow field acting on aerodynamic surfaces. In fact the experimental approach is fundamental to avoid the complexity of the mathematical models for predicting the fluid phenomena. It’s important to note that, using in-situ sensor to monitor pressure on large domains with highly unsteady flows, several problems are encountered working with the classical techniques due to the transducer cost, the intrusiveness, the time response and the operating range. An interesting approach for satisfying the previously reported sensor requirements is to implement a sensor network capable of acquiring pressure data on aerodynamic surface using a wireless communication system able to collect the pressure data with the lowest environmental–invasion level possible. In this thesis a wireless sensor network for fluid fields pressure has been designed, built and tested. To develop the system, a capacitive pressure sensor, based on polymeric membrane, and read out circuitry, based on microcontroller, have been designed, built and tested. The wireless communication has been performed using the Zensys Z-WAVE platform, and network and data management have been implemented. Finally, the full embedded system with antenna has been created. As a proof of concept, the monitoring of pressure on the top of the mainsail in a sailboat has been chosen as working example.

A new approach for the dynamic modelling of the human knee

Mathematical models of the knee joint are important tools which have both theoretical and practical applications. They are used by researchers to fully understand the stabilizing role of the components of the joint, by engineers as an aid for prosthetic design, by surgeons during the planning of an operation or during the operation itself, and by orthopedists for diagnosis and rehabilitation purposes. The principal aims of knee models are to reproduce the restraining function of each structure of the joint and to replicate the relative motion of the bones which constitute the joint itself. It is clear that the first point is functional to the second one. However, the standard procedures for the dynamic modelling of the knee tend to be more focused on the second aspect: the motion of the joint is correctly replicated, but the stabilizing role of the articular components is somehow lost. A first contribution of this dissertation is the definition of a novel approach — called sequential approach — for the dynamic modelling of the knee. The procedure makes it possible to develop more and more sophisticated models of the joint by a succession of steps, starting from a first simple model of its passive motion. The fundamental characteristic of the proposed procedure is that the results obtained at each step do not worsen those already obtained at previous steps, thus preserving the restraining function of the knee structures. The models which stem from the first two steps of the sequential approach are then presented. The result of the first step is a model of the passive motion of the knee, comprehensive of the patello-femoral joint. Kinematical and anatomical considerations lead to define a one degree of freedom rigid link mechanism, whose members represent determinate components of the joint. The result of the second step is a stiffness model of the knee. This model is obtained from the first one, by following the rules of the proposed procedure. Both models have been identified from experimental data by means of an optimization procedure. The simulated motions of the models then have been compared to the experimental ones. Both models accurately reproduce the motion of the joint under the corresponding loading conditions. Moreover, the sequential approach makes sure the results obtained at the first step are not worsened at the second step: the stiffness model can also reproduce the passive motion of the knee with the same accuracy than the previous simpler model. The procedure proved to be successful and thus promising for the definition of more complex models which could also involve the effect of muscular forces.

Transportation theory and planning

The aim of this research is to analyze the transport system and its subcomponents in order to highlight which are the design tools for physical and/or organizational projects related to transport supply systems. A characteristic of the transport systems is that the change of their structures can recoil on several entities, groups of entities, which constitute the community. The construction of a new infrastructure can modify both the transport service characteristic for all the user of the entire network; for example, the construction of a transportation infrastructure can change not only the transport service characteristics for the users of the entire network in which it is part of, but also it produces economical, social, and environmental effects. Therefore, the interventions or the improvements choices must be performed using a rational decision making approach. This approach requires that these choices are taken through the quantitative evaluation of the different effects caused by the different intervention plans. This approach becomes even more necessary when the decisions are taken in behalf of the community. Then, in order to understand how to develop a planning process in Transportation I will firstly analyze the transport system and the mathematical models used to describe it: these models provide us significant indicators which can be used to evaluate the effects of possible interventions. In conclusion, I will move on the topics related to the transport planning, analyzing the planning process, and the variables that have to be considered to perform a feasibility analysis or to compare different alternatives. In conclusion I will perform a preliminary analysis of a new transit system which is planned to be developed in New York City.

Sorveglianza dell'influenza aviare: studio di un sistema di rilevazione precoce della circolazione virale in popolazioni di volatili selvatici

The emergency of infection by highly pathogenic avian influenza virus (HPAI) subtype H5N1 has focused the attention of the world scientific community, requiring the prompt provision of effective control systems for early detection of the circulation of low pathogenic influenza H5 viruses (LPAI) in populations of wild birds to prevent outbreaks of highly pathogenic (HPAI) in populations of domestic birds with possible transmission to humans. The project stems from the aim to provide, through a preliminary analysis of data obtained from surveillance in Italy and Europe, a preliminary study about the virus detection rates and the development of mathematical models, an objective assessment of the effectiveness of avian influenza surveillance systems in wild bird populations, and to point out guidelines to support the planning process of the sampling activities. The results obtained from the statistical processing quantify the sampling effort in terms of time and sample size required, and simulating different epidemiological scenarios identify active surveillance as the most suitable for endemic LPAI infection monitoring in wild waterfowl, and passive surveillance as the only really effective tool in early detecting HPAI H5N1 circulation in wild populations. Given the lack of relevant information on H5N1 epidemiology, and the actual finantial and logistic constraints, an approach that makes use of statistical tools to evaluate and predict monitoring activities effectiveness proves to be of primary importance to direct decision-making and make the best use of available resources.

Sviluppo di modelli motore e veicolo per l'analisi di strategie di controllo in applicazioni Software e Hardware In the Loop

This work describes the development of a simulation tool which allows the simulation of the Internal Combustion Engine (ICE), the transmission and the vehicle dynamics. It is a control oriented simulation tool, designed in order to perform both off-line (Software In the Loop) and on-line (Hardware In the Loop) simulation. In the first case the simulation tool can be used in order to optimize Engine Control Unit strategies (as far as regard, for example, the fuel consumption or the performance of the engine), while in the second case it can be used in order to test the control system. In recent years the use of HIL simulations has proved to be very useful in developing and testing of control systems. Hardware In the Loop simulation is a technology where the actual vehicles, engines or other components are replaced by a real time simulation, based on a mathematical model and running in a real time processor. The processor reads ECU (Engine Control Unit) output signals which would normally feed the actuators and, by using mathematical models, provides the signals which would be produced by the actual sensors. The simulation tool, fully designed within Simulink, includes the possibility to simulate the only engine, the transmission and vehicle dynamics and the engine along with the vehicle and transmission dynamics, allowing in this case to evaluate the performance and the operating conditions of the Internal Combustion Engine, once it is installed on a given vehicle. Furthermore the simulation tool includes different level of complexity, since it is possible to use, for example, either a zero-dimensional or a one-dimensional model of the intake system (in this case only for off-line application, because of the higher computational effort). Given these preliminary remarks, an important goal of this work is the development of a simulation environment that can be easily adapted to different engine types (single- or multi-cylinder, four-stroke or two-stroke, diesel or gasoline) and transmission architecture without reprogramming. Also, the same simulation tool can be rapidly configured both for off-line and real-time application. The Matlab-Simulink environment has been adopted to achieve such objectives, since its graphical programming interface allows building flexible and reconfigurable models, and real-time simulation is possible with standard, off-the-shelf software and hardware platforms (such as dSPACE systems).

Development of synthetic molecular circuits for the control of cell systems

Synthetic biology is a young field of applicative research aiming to design and build up artificial biological devices, useful for human applications. How synthetic biology emerged in past years and how the development of the Registry of Standard Biological Parts aimed to introduce one practical starting solution to apply the basics of engineering to molecular biology is presented in chapter 1 in the thesis The same chapter recalls how biological parts can make up a genetic program, the molecular cloning tecnique useful for this purpose, and an overview of the mathematical modeling adopted to describe gene circuit behavior. Although the design of gene circuits has become feasible the increasing complexity of gene networks asks for a rational approach to design gene circuits. A bottom-up approach was proposed, suggesting that the behavior of a complicated system can be predicted from the features of its parts. The option to use modular parts in large-scale networks will be facilitated by a detailed and shared characterization of their functional properties. Such a prediction, requires well-characterized mathematical models of the parts and of how they behave when assembled together. In chapter 2, the feasibility of the bottom-up approach in the design of a synthetic program in Escherichia coli bacterial cells is described. The rational design of gene networks is however far from being established. The synthetic biology approach can used the mathematical formalism to identify biological information not assessable with experimental measurements. In this context, chapter 3 describes the design of a synthetic sensor for identifying molecules of interest inside eukaryotic cells. The Registry of Standard parts collects standard and modular biological parts. To spread the use of BioBricks the iGEM competition was started. The ICM Laboratory, where Francesca Ceroni completed her Ph.D, partecipated with teams of students and Chapter 4 summarizes the projects developed.

Epidemiologia delle strongilosi dell'asino: quali applicazioni per il controllo delle infezioni da elminti?

Strongylosis in equids, despite being very common, have never been studied from a strictly ecological point of view. Mathematical models are important ecological tools used to study the temporal dynamics of parasite populations, and are useful to study the effect of different biological parameters, as well as to analyse the outcome produced by perturbations such as anthelmintic treatments. This work describes the study of the temporal dynamics of strongyles infection in an organic donkey population, performed using coprological quantitative analysis and donkeys’ age as a proxy of the time of infection. Force of infection was then estimated for Strongylus vulgaris and small strongyles and the results used as the basis for the development of mathematical models. In particular, the comparison of models output and field data made it possible to estimate the transmission coefficient  and to consequently calculate the basic reproduction number R0 and the threshold host density. Small strongyles model includes hypobiosis and, more interestingly as never found in literature, a density-dependent development rate of hypobiotic larvae in adult parasites in order to simulate a negative feedback between larvae emergence from hypobiosis and adult parasite abundance. Simulations of pharmacological and environmental treatments showed that parasite eradication was possible for S. vulgaris only, while small strongyles, due to hypobiosis and density-dependent development rate of their hypobiotic larvae, are very difficult to control and impossible to eradicate. In addition, density-dependence in larval development has been demonstrated to act as a key factor in improving parasite population survival and abundance even in absence of human intervention.

New mechanisms for modelling the motion of the human ankle complex

The relevance of human joint models was shown in the literature. In particular, the great importance of models for the joint passive motion simulation (i.e. motion under virtually unloaded conditions) was outlined. They clarify the role played by the principal anatomical structures of the articulation, enhancing the comprehension of surgical treatments, and in particular the design of total ankle replacement and ligament reconstruction. Equivalent rigid link mechanisms proved to be an efficient tool for an accurate simulation of the joint passive motion. This thesis focuses on the ankle complex (i.e. the anatomical structure composed of the tibiotalar and the subtalar joints), which has a considerable role in human locomotion. The lack of interpreting models of this articulation and the poor results of total ankle replacement arthroplasty have strongly suggested devising new mathematical models capable of reproducing the restraining function of each structure of the joint and of replicating the relative motion of the bones which constitute the joint itself. In this contest, novel equivalent mechanisms are proposed for modelling the ankle passive motion. Their geometry is based on the joint’s anatomical structures. In particular, the role of the main ligaments of the articulation is investigated under passive conditions by means of nine 5-5 fully parallel mechanisms. Based on this investigation, a one-DOF spatial mechanism is developed for modelling the passive motion of the lower leg. The model considers many passive structures constituting the articulation, overcoming the limitations of previous models which took into account few anatomical elements of the ankle complex. All the models have been identified from experimental data by means of optimization procedure. Then, the simulated motions have been compared to the experimental one, in order to show the efficiency of the approach and thus to deduce the role of each anatomical structure in the ankle kinematic behavior.

Entwicklungen zur Absolutquantifizierung der Lungenperfusion mittels kontrastmittelverstärkter Magnetresonanztomographie

Die regionale Bestimmung der Durchblutung (Perfusion) ermöglicht differenzierte Aussagen über den Gesundheitszustand und die Funktionalität der Lunge. Durch neue Messverfahren ermöglicht die Magnetresonanztomographie (MRT) eine nicht-invasive und strahlungsfreie Untersuchung der Perfusion. Obwohl die Machbarkeit qualitativer MRT-Durchblutungsmessungen bereits gezeigt wurde, fehlt bisher eine validierte quantitative Methode. Ziel dieser Arbeit war eine Optimierung der bestehenden Messprotokolle und mathematischen Modelle zur Absolutquantifizierung der Lungenperfusion mit Magnetresonanztomographie. Weiterhin sollte die Methodik durch Vergleich mit einem etablierten Referenzverfahren validiert werden. Durch Simulationen und Phantommessungen konnten optimale MRT-Messparameter und ein standardisiertes Protokoll festgelegt werden. Des Weiteren wurde eine verallgemeinerte Bestimmung der Kontrastmittelkonzentration aus den gemessenen Signalintensitäten vorgestellt, diskutiert und durch Probandenmessungen validiert. Auf der Basis dieser Entwicklungen wurde die MRT-Durchblutungsmessung der Lunge tierexperimentell mit der Positronenemissionstomographie (PET) intraindividuell verglichen und validiert. Die Ergebnisse zeigten nur kleine Abweichungen und eine statistisch hochsignifikante, stark lineare Korrelation. Zusammenfassend war es durch die Entwicklungen der vorgestellten Arbeit möglich, die kontrastmittelgestützte MRT-Durchblutungsmessung der Lunge zu optimieren und erstmals zu validieren.

Computational Modeling of Cardiac Excitation-Contraction Coupling in Physiological and Pathological Conditions

The cardiomyocyte is a complex biological system where many mechanisms interact non-linearly to regulate the coupling between electrical excitation and mechanical contraction. For this reason, the development of mathematical models is fundamental in the field of cardiac electrophysiology, where the use of computational tools has become complementary to the classical experimentation. My doctoral research has been focusing on the development of such models for investigating the regulation of ventricular excitation-contraction coupling at the single cell level. In particular, the following researches are presented in this thesis: 1) Study of the unexpected deleterious effect of a Na channel blocker on a long QT syndrome type 3 patient. Experimental results were used to tune a Na current model that recapitulates the effect of the mutation and the treatment, in order to investigate how these influence the human action potential. Our research suggested that the analysis of the clinical phenotype is not sufficient for recommending drugs to patients carrying mutations with undefined electrophysiological properties. 2) Development of a model of L-type Ca channel inactivation in rabbit myocytes to faithfully reproduce the relative roles of voltage- and Ca-dependent inactivation. The model was applied to the analysis of Ca current inactivation kinetics during normal and abnormal repolarization, and predicts arrhythmogenic activity when inhibiting Ca-dependent inactivation, which is the predominant mechanism in physiological conditions. 3) Analysis of the arrhythmogenic consequences of the crosstalk between β-adrenergic and Ca-calmodulin dependent protein kinase signaling pathways. The descriptions of the two regulatory mechanisms, both enhanced in heart failure, were integrated into a novel murine action potential model to investigate how they concur to the development of cardiac arrhythmias. These studies show how mathematical modeling is suitable to provide new insights into the mechanisms underlying cardiac excitation-contraction coupling and arrhythmogenesis.