Advanced Mathematical Modelling of Pancreatic β-Cells

Insulin-secreting pancreatic $\beta$-cells are responsible for maintaining the whole body glucose homeostasis. Dysfunction or loss of $\beta$-cell mass results in impaired insulin secretion and, in some cases, diabetes. Many of the factors that influence $\beta$-cell function or insulin exocytosis, however, are not fully understood. To support the investigation, mathematical models have been developed and used to design experiments. In this dissertation, we present the Integrated Oscillator Model (IOM) that is one of the mathematical models used for the investigation of the mechanism behind the bursting activity that underlies intracellular Ca$^{2+}$ oscillations and pulsatile insulin secretion. The IOM describes the interaction of the cellular electrical activity and intracellular Ca$^{2+}$ with glucose metabolism via numerous feedforward and feedback pathways. These interactions, in turn, produce metabolic oscillations with a sawtooth or pulsatile time course, reflecting different oscillation mechanisms. We determine conditions favorable to each type of oscillations, and show that the model accounts for key experimental findings of $\beta$-cell activity. We propose several extensions of the model to include all the main elements involved in the insulin secretion. The latest and most sophisticated model describes the complex metabolism in the mitochondria and the several biological processes in the insulin exocytosis cascade. The model, also, captures the changes in the $\beta$-cell activity and the resulting amount of secreted insulin in response to different concentrations of glucose in the blood. The model predictions, in agreement with findings reported in the experimental literature, show an increase of insulin secretion when the glucose level is high and a basal-low insulin concentration when the glucose level decreases. Finally, we use the new model to simulate the interaction among $\beta$-cells (through gap junction) within the same islet. The simulations show that the electrical coupling is sufficient to synchronize the $\beta$-cells within an islet. We also show that the amplitude of the oscillations in the insulin secretion rate is bigger when the $\beta$-cells synchronize. This suggests a more efficient secretion of insulin in the bloodstream when the cells burst in unison, as it has been observed experimentally

Transitions between bursting modes in the integrated oscillator model for pancreatic β-cells

Insulin-secreting $\beta$-cells of pancreatic islets of Langerhans produce bursts of electrical impulses, resulting in intracellular Ca$^{2+}$ oscillations and pulsatile insulin secretion. The mechanism for this bursting activity has been the focus of mathematical modeling for more than three decades, and as new data are acquired old models are modified and new models are developed. Comprehensive models must now account for the various modes of bursting observed in islet $\beta$-cells, which include fast bursting, slow bursting, and compound bursting. One such model is the Integrated Oscillator Model (IOM), in which $\beta$-cell electrical activity, intracellular Ca$^{2+}$ , and glucose metabolism interact via numerous feedforward and feedback pathways. These interactions can produce metabolic oscillations with a sawtooth time course or a pulsatile time course, reflecting very different oscillation mechanisms. In this report, we determine conditions favorable to one form of oscillations or the other, and examine the transitions between modes of bursting and the relationship of the transitions to the patterns of metabolic oscillations. Importantly, this work clarifies what can be expected in experimental measurements of $\beta$-cell oscillatory activity, and suggests pathways through which oscillations of one type can be converted to oscillations of another type.R. Bertram was supported by grant number DMS-1612193 from the National Science Foundatio

Two different quasiparticle scattering rates in vortex line liquid phase of layered d-wave superconductors

We carry out a quantum mechanical analysis of the behavior of nodal quasiparticles in the vortex line liquid phase of planar d-wave superconductors. Applying a novel path integral technique we calculate a number of experimentally relevant observables and demonstrate that in the low-field regime the quasiparticle scattering rates deduced from photoemission and thermal transport data can be markedly different from that extracted from tunneling, specific heat, superfluid stiffness or spin-lattice relaxation time.Comment: Latex, 4 pages, no figure

Vacuum Polarization and the Electric Charge of the Positron

We show that higher-order vacuum polarization would contribute a measureable net charge to atoms, if the charges of electrons and positrons do not balance precisely. We obtain the limit $|Q_e+Q_{\bar e}| < 10^{-18} e$ for the sum of the charges of electron and positron. This also constitutes a new bound on certain violations of PCT invariance.Comment: 9 pages, 1 figure attached as PostScript file, DUKE-TH-92-38. Revised versio

Dissecting the contribution of Staphylococcus aureus α-phenol-soluble modulins to biofilm amyloid structure

The opportunistic pathogen Staphylococcus aureus is recognized as one of the most frequent causes of biofilm-associated infections. The recently discovered phenol soluble modulins (PSMs) are small α-helical amphipathic peptides that act as the main molecular effectors of staphylococcal biofilm maturation, promoting the formation of an extracellular fibril structure with amyloid-like properties. Here, we combine computational, biophysical and in cell analysis to address the specific contribution of individual PSMs to biofilm structure. We demonstrate that despite their highly similar sequence and structure, contrary to what it was previously thought, not all PSMs participate in amyloid fibril formation. A balance of hydrophobic/hydrophilic forces and helical propensity seems to define the aggregation propensity of PSMs and control their assembly and function. This knowledge would allow to target specifically the amyloid properties of these peptides. In this way, we show that Epigallocatechin-3-gallate (EGCG), the principal polyphenol in green tea, prevents the assembly of amyloidogenic PSMs and disentangles their preformed amyloid fibrils

Patient-specific computational modeling of Cortical Spreading Depression via Diffusion Tensor Imaging

Cortical Spreading Depression (CSD), a depolarization wave originat- ing in the visual cortex and traveling towards the frontal lobe, is com- monly accepted as a correlate of migraine visual aura. As of today, little is known about the mechanisms that can trigger or stop such phenomenon. However, the complex and highly individual characteristics of the brain cortex suggest that the geometry might have a significant impact in sup- porting or contrasting the propagation of CSD. Accurate patient-specific computational models are fundamental to cope with the high variability in cortical geometries among individuals, but also with the conduction anisotropy induced in a given cortex by the complex neuronal organisa- tion in the grey matter. In this paper we integrate a distributed model for extracellular potassium concentration with patient-specific diffusivity tensors derived locally from Diffusion Tensor Imaging data.This work was supported by the Bizkaia Talent and European Commission through COFUND under the grant BRAhMS - Brain Aura Mathematical Sim- ulation (AYD-000-285), by the Basque Government through the BERC 2014- 2017 program, and by the Spanish Ministry of Economics and Competitiveness MINECO through the BCAM Severo Ochoa excellence accreditation SEV-2013- 0323 and the Spanish "Plan Estatal de Investigación, Desarrollo e Innovación Orientada a los Retos de la Sociedad" under Grant BELEMET - Brain ELEctro- METabolic modeling and numerical approximation (MTM2015-69992-R). JMC acknowledges financial support from Ikerbasque: The Basque Foundation for Science and Euskampus at UPV/EHU

Stationary states in Langevin dynamics under asymmetric L\'evy noises

Properties of systems driven by white non-Gaussian noises can be very different from these systems driven by the white Gaussian noise. We investigate stationary probability densities for systems driven by $\alpha$-stable L\'evy type noises, which provide natural extension to the Gaussian noise having however a new property mainly a possibility of being asymmetric. Stationary probability densities are examined for a particle moving in parabolic, quartic and in generic double well potential models subjected to the action of $\alpha$-stable noises. Relevant solutions are constructed by methods of stochastic dynamics. In situations where analytical results are known they are compared with numerical results. Furthermore, the problem of estimation of the parameters of stationary densities is investigated.Comment: 9 pages, 9 figures, 3 table

Estimation of age-specific rates of reactivation and immune boosting of the varicella zoster virus

Studies into the impact of vaccination against the varicella zoster virus (VZV) have increasingly focused on herpes zoster (HZ), which is believed to be increasing in vaccinated populations with decreasing infection pressure. This idea can be traced back to Hope-Simpson's hypothesis, in which a person's immune status determines the likelihood that he/she will develop HZ. Immunity decreases over time, and can be boosted by contact with a person experiencing varicella (exogenous boosting) or by a reactivation attempt of the virus (endogenous boosting). Here we use transmission models to estimate age-specific rates of reactivation and immune boosting, exogenous as well as endogenous, using zoster incidence data from the Netherlands (2002–2011, n = 7026). The boosting and reactivation rates are estimated with splines, enabling these quantities to be optimally informed by the data. The analyses show that models with high levels of exogenous boosting and estimated or zero endogenous boosting, constant rate of loss of immunity, and reactivation rate increasing with age (to more than 5% per year in the elderly) give the best fit to the data. Estimates of the rates of immune boosting and reactivation are strongly correlated. This has important implications as these parameters determine the fraction of the population with waned immunity. We conclude that independent evidence on rates of immune boosting and reactivation in persons with waned immunity are needed to robustly predict the impact of varicella vaccination on the incidence of HZ.PIENTER2 serological stud