Modelling pathological effects in intracellular calcium dynamics leading to atrial fibrillation

The heart beating is produced by the synchronization of the cardiac cells' contraction. A dysregulation in this mechanism may produce episodes of abnormal heart contraction. The origin of these abnormalities often lies at the subcellular level where calcium is the most important ion that controls the cell contraction. The regulation of calcium concentration is determined by the ryanodine receptors (RyR), the calcium channels that connect the cytosol and the sarcoplasmic reticulum. RyRs open and close stochastically with calcium-dependent rates. The fundamental calcium release event is known as calcium spark, which refers to a local release of calcium through one or more RyRs. Thus, a deep knowledge on both the spatio-temporal characteristics of the calcium patterns and the role of the RyRs is crucial to understand the transition between healthy to unhealthy cells. The aim of this Thesis has been to figure out these changes at the submicron scale, which may induce the transition to Atrial Fibrillation (AF) in advanced stages. To address this issue, I have developed, and validated, a subcellular mathematical model of an atrial myocyte which includes the electro-physiological currents as well as the fundamental intracellular structures. The high resolution of the model has allowed me to study the spatio-temporal calcium features that arise from both the cell stimulation and the resting conditions. Simulations show the relevance of the assembly of RyRs into clusters, leading to the formation of macro-sparks for heterogeneous distributions. These macro-sparks may produce ectopic beats under pathophysiological conditions. The incorporation of RyR-modulators into the model produces a nonuniform spatial distribution of calcium sparks, a situation observed during AF. In this sense, calsequestrin (CSQ) has emerged as a key calcium buffer that modifies the calcium handling. The lack of CSQ produces an increase in the spark frequency and, during calcium overload, it also promotes the appearance of global calcium oscillations. Finally, I have also characterized the effect of detubulation, a common issue in cells with AF and heart failure. Thus, the present work represents a step forward in the understanding of the mechanisms leading to AF, with the development of computational models that, in the future, can be used to complement in vitro or in vivo studies, helping find therapeutic targets for this disease

Computational Model of Calcium Signaling in Cardiac Atrial Cells at the Submicron Scale

In cardiac cells, calcium is the mediator of excitation-contraction coupling. Dysfunctions in calcium handling have been identified as the origin of some cardiac arrhythmias. In the particular case of atrial myocytes, recent available experimental data has found links between these dysfunctions and structural changes in the calcium handling machinery (ryanodine cluster size and distribution, t-tubular network, etc). To address this issue, we have developed a computational model of an atrial myocyte that takes into account the detailed intracellular structure. The homogenized macroscopic behavior is described with a two-concentration field model, using effective diffusion coefficients of calcium in the sarcoplasmic reticulum (SR) and in the cytoplasm. The model reproduces the right calcium transients and dependence with pacing frequency. Under basal conditions, the calcium rise is mostly restricted to the periphery of the cell, with a large concentration ratio between the periphery and the interior. We have then studied the dependence of the speed of the calcium wave on cytosolic and SR diffusion coefficients, finding an almost linear relation with the former, in agreement with a diffusive and fire mechanism of propagation, and little dependence on the latter. Finally, we have studied the effect of a change in RyR cluster microstructure. We find that, under resting conditions, the spark frequency decreases slightly with RyR cluster spatial dispersion, but markedly increases when the RyRs are distributed in clusters of larger size, stressing the importance of RyR cluster organization to understand atrial arrhythmias, as recent experimental results suggest (Macquaide et al., 2015).Peer ReviewedPostprint (published version

Influence of the tubular network on the characteristics of calcium transients in cardiac myocytes

Transverse and axial tubules (TATS) are an essential ingredient of the excitation-contraction machinery that allow the effective coupling of L-type Calcium Channels (LCC) and ryanodine receptors (RyR2). They form a regular network in ventricular cells, while their presence in atrial myocytes is variable regionally and among animal species We have studied the effect of variations in the TAT network using a bidomain computational model of an atrial myocyte with variable density of tubules. At each z-line the t-tubule length is obtained from an exponential distribution, with a given mean penetration length. This gives rise to a distribution of t-tubules in the cell that is characterized by the fractional area (F.A.) occupied by the t-tubules. To obtain consistent results, we average over different realizations of the same mean penetration length. To this, in some simulations we add the effect of a network of axial tubules. Then we study global properties of calcium signaling, as well as regional heterogeneities and local properties of sparks and RyR2 openings. In agreement with recent experiments in detubulated ventricular and atrial cells, we find that detubulation reduces the calcium transient and synchronization in release. However, it does not affect sarcoplasmic reticulum (SR) load, so the decrease in SR calcium release is due to regional differences in Ca2+ release, that is restricted to the cell periphery in detubulated cells. Despite the decrease in release, the release gain is larger in detubulated cells, due to recruitment of orphaned RyR2s, i.e, those that are not confronting a cluster of LCCs. This probably provides a safeguard mechanism, allowing physiological values to be maintained upon small changes in the t-tubule density. Finally, we do not find any relevant change in spark properties between tubulated and detubulated cells, suggesting that the differences found in experiments could be due to differential properties of the RyR2s in the membrane and in the t-tubules, not incorporated in the present model. This work will help understand the effect of detubulation, that has been shown to occur in disease conditions such as heart failure (HF) in ventricular cells, or atrial fibrillation (AF) in atrial cells.Postprint (published version

Analysis and prediction of COVID-19 for EU-EFTA-UK and other countries

The present report aims to provide a comprehensive picture of the pandemic situation of COVID‐19 in the EU countries, and to be able to foresee the situation in the next coming days. We employ an empirical model, verified with the evolution of the number of confirmed cases in previous countries where the epidemic is close to conclude, including all provinces of China. The model does not pretend to interpret the causes of the evolution of the cases but to permit the evaluation of the quality of control measures made in each state and a short-term prediction of trends. Note, however, that the effects of the measures’ control that start on a given day are not observed until approximately 7-10 days later. The model and predictions are based on two parameters that are daily fitted to available data: a: the velocity at which spreading specific rate slows down; the higher the value, the better the control. K: the final number of expected cumulated cases, which cannot be evaluated at the initial stages because growth is still exponential. We show an individual report with 8 graphs and a table with the short-term predictions for different countries and regions. We are adjusting the model to countries and regions with at least 4 days with more than 100 confirmed cases and a current load over 200 cases. The predicted period of a country depends on the number of datapoints over this 100 cases threshold, and is of 5 days for those that have reported more than 100 cumulated cases for 10 consecutive days or more. For short-term predictions, we assign higher weight to last 3 points in the fittings, so that changes are rapidly captured by the model. The whole methodology employed in the inform is explained in the last pages of this document. In addition to the individual reports, the reader will find an initial dashboard with a brief analysis of the situation in EU-EFTA-UK countries, some summary figures and tables as well as long-term predictions for some of them, when possible. These long-term predictions are evaluated without different weights to datapoints. We also discuss a specific issue every day.These reports are funded by the European Commission (DG CONNECT, LC-01485746) PJC and MC received funding from “la Caixa” Foundation (ID 100010434), under agreement LCF/PR/GN17/50300003; CP, DL, SA, MC, received funding from Ministerio de Ciencia, Innovación y Universidades and FEDER, with the project PGC2018-095456-B-I00Postprint (author's final draft

Analysis and prediction of COVID-19 for EU-EFTA-UK and other countries

The present report aims to provide a comprehensive picture of the pandemic situation of COVID-19 in the EU countries, and to be able to foresee the situation in the next coming days. We employ an empirical model, verified with the evolution of the number of confirmed cases in previous countries where the epidemic is close to conclude, including all provinces of China. The model does not pretend to interpret the causes of the evolution of the cases but to permit the evaluation of the quality of control measures made in each state and a short-term prediction of trends. Note, however, that the effects of the measures’ control that start on a given day are not observed until approximately 7-10 days later. The model and predictions are based on two parameters that are daily fitted to available data: a: the velocity at which spreading specific rate slows down; the higher the value, the better the control. K: the final number of expected cumulated cases, which cannot be evaluated at the initial stages because growth is still exponential. We show an individual report with 8 graphs and a table with the short-term predictions for different countries and regions. We are adjusting the model to countries and regions with at least 4 days with more than 100 confirmed cases and a current load over 200 cases. The predicted period of a country depends on the number of datapoints over this 100 cases threshold, and is of 5 days for those that have reported more than 100 cumulated cases for 10 consecutive days or more. For short-term predictions, we assign higher weight to last 3 points in the fittings, so that changes are rapidly captured by the model. The whole methodology employed in the inform is explained in the last pages of this document. In addition to the individual reports, the reader will find an initial dashboard with a brief analysis of the situation in EU-EFTA-UK countries, some summary figures and tables as well as long-term predictions for some of them, when possible. These long-term predictions are evaluated without different weights to datapoints. We also discuss a specific issue every day.These reports are funded by the European Commission (DG CONNECT, LC-01485746) PJC and MC received funding from “la Caixa” Foundation (ID 100010434), under agreement LCF/PR/GN17/50300003; CP, DL, SA, MC, received funding from Ministerio de Ciencia, Innovación y Universidades and FEDER, with the project PGC2018-095456-B-I00Postprint (published version

Analysis and prediction of COVID-19 for EU-EFTA-UK and other countries

The present report aims to provide a comprehensive picture of the pandemic situation of COVID-19 in the EU countries, and to be able to foresee the situation in the next coming days. We employ an empirical model, verified with the evolution of the number of confirmed cases in previous countries where the epidemic is close to conclude, including all provinces of China. The model does not pretend to interpret the causes of the evolution of the cases but to permit the evaluation of the quality of control measures made in each state and a short-term prediction of trends. Note, however, that the effects of the measures’ control that start on a given day are not observed until approximately 7-10 days later. The model and predictions are based on two parameters that are daily fitted to available data: ¿ a: the velocity at which spreading specific rate slows down; the higher the value, the better the control. ¿ K: the final number of expected cumulated cases, which cannot be evaluated at the initial stages because growth is still exponential. We show an individual report with 8 graphs and a table with the short-term predictions for different countries and regions. We are adjusting the model to countries and regions with at least 4 days with more than 100 confirmed cases and a current load over 200 cases. The predicted period of a country depends on the number of datapoints over this 100 cases threshold, and is of 5 days for those that have reported more than 100 cumulated cases for 10 consecutive days or more. For short-term predictions, we assign higher weight to last 3 points in the fittings, so that changes are rapidly captured by the model. The whole methodology employed in the inform is explained in the last pages of this document. In addition to the individual reports, the reader will find an initial dashboard with a brief analysis of the situation in EU-EFTA-UK countries, some summary figures and tables as well as long-term predictions for some of them, when possible. These long-term predictions are evaluated without different weights to datapoints. We also discuss a specific issue every day.These reports are funded by the European Commission (DG CONNECT, LC-01485746) PJC and MC received funding from “la Caixa” Foundation (ID 100010434), under agreement LCF/PR/GN17/50300003; CP, DL, SA, MC, received funding from Ministerio de Ciencia, Innovación y Universidades and FEDER, with the project PGC2018-095456-B-I00Postprint (published version

Analysis and prediction of COVID-19 for EU-EFTA-UK and other countries

The present report aims to provide a comprehensive picture of the pandemic situation of COVID-19 in the EU countries, and to be able to foresee the situation in the next coming days. We employ an empirical model, verified with the evolution of the number of confirmed cases in previous countries where the epidemic is close to conclude, including all provinces of China. The model does not pretend to interpret the causes of the evolution of the cases but to permit the evaluation of the quality of control measures made in each state and a short-term prediction of trends. Note, however, that the effects of the measures’ control that start on a given day are not observed until approximately 7-10 days later. The model and predictions are based on two parameters that are daily fitted to available data: a: the velocity at which spreading specific rate slows down; the higher the value, the better the control. K: the final number of expected cumulated cases, which cannot be evaluated at the initial stages because growth is still exponential. We show an individual report with 8 graphs and a table with the short-term predictions for different countries and regions. We are adjusting the model to countries and regions with at least 4 days with more than 100 confirmed cases and a current load over 200 cases. The predicted period of a country depends on the number of datapoints over this 100 cases threshold, and is of 5 days for those that have reported more than 100 cumulated cases for 10 consecutive days or more. For short-term predictions, we assign higher weight to last 3 points in the fittings, so that changes are rapidly captured by the model. The whole methodology employed in the inform is explained in the last pages of this document. In addition to the individual reports, the reader will find an initial dashboard with a brief analysis of the situation in EU-EFTA-UK countries, some summary figures and tables as well as long-term predictions for some of them, when possible. These long-term predictions are evaluated without different weights to datapoints. We also discuss a specific issue every day.These reports are funded by the European Commission (DG CONNECT, LC-01485746) PJC and MC received funding from “la Caixa” Foundation (ID 100010434), under agreement LCF/PR/GN17/50300003; CP, DL, SA, MC, received funding from Ministerio de Ciencia, Innovación y Universidades and FEDER, with the project PGC2018-095456-B-I00Postprint (published version

Analysis and prediction of COVID-19 for EU-EFTA-UK and other countries

The present report aims to provide a comprehensive picture of the pandemic situation of COVID-19 in the EU countries, and to be able to foresee the situation in the next coming days. We employ an empirical model, verified with the evolution of the number of confirmed cases in previous countries where the epidemic is close to conclude, including all provinces of China. The model does not pretend to interpret the causes of the evolution of the cases but to permit the evaluation of the quality of control measures made in each state and a short-term prediction of trends. Note, however, that the effects of the measures’ control that start on a given day are not observed until approximately 7-10 days later. The model and predictions are based on two parameters that are daily fitted to available data: ¿ a: the velocity at which spreading specific rate slows down; the higher the value, the better the control. ¿ K: the final number of expected cumulated cases, which cannot be evaluated at the initial stages because growth is still exponential. We show an individual report with 8 graphs and a table with the short-term predictions for different countries and regions. We are adjusting the model to countries and regions with at least 4 days with more than 100 confirmed cases and a current load over 200 cases. The predicted period of a country depends on the number of datapoints over this 100 cases threshold, and is of 5 days for those that have reported more than 100 cumulated cases for 10 consecutive days or more. For short-term predictions, we assign higher weight to last 3 points in the fittings, so that changes are rapidly captured by the model. The whole methodology employed in the inform is explained in the last pages of this document. In addition to the individual reports, the reader will find an initial dashboard with a brief analysis of the situation in EU-EFTA-UK countries, some summary figures and tables as well as long-term predictions for some of them, when possible. These long-term predictions are evaluated without different weights to datapoints. We also discuss a specific issue every day.These reports are funded by the European Commission (DG CONNECT, LC-01485746) PJC and MC received funding from “la Caixa” Foundation (ID 100010434), under agreement LCF/PR/GN17/50300003; CP, DL, SA, MC, received funding from Ministerio de Ciencia, Innovación y Universidades and FEDER, with the project PGC2018-095456-B-I00Postprint (published version

Analysis and prediction of COVID-19 for EU-EFTA-UK and other countries

The present report aims to provide a comprehensive picture of the pandemic situation of COVID-19 in the EU countries, and to be able to foresee the situation in the next coming days. We employ an empirical model, verified with the evolution of the number of confirmed cases in previous countries where the epidemic is close to conclude, including all provinces of China. The model does not pretend to interpret the causes of the evolution of the cases but to permit the evaluation of the quality of control measures made in each state and a short-term prediction of trends. Note, however, that the effects of the measures’ control that start on a given day are not observed until approximately 7-10 days later. The model and predictions are based on two parameters that are daily fitted to available data: ¿ a: the velocity at which spreading specific rate slows down; the higher the value, the better the control. ¿ K: the final number of expected cumulated cases, which cannot be evaluated at the initial stages because growth is still exponential. We show an individual report with 8 graphs and a table with the short-term predictions for different countries and regions. We are adjusting the model to countries and regions with at least 4 days with more than 100 confirmed cases and a current load over 200 cases. The predicted period of a country depends on the number of datapoints over this 100 cases threshold, and is of 5 days for those that have reported more than 100 cumulated cases for 10 consecutive days or more. For short-term predictions, we assign higher weight to last 3 points in the fittings, so that changes are rapidly captured by the model. The whole methodology employed in the inform is explained in the last pages of this document. In addition to the individual reports, the reader will find an initial dashboard with a brief analysis of the situation in EU-EFTA-UK countries, some summary figures and tables as well as long-term predictions for some of them, when possible. These long-term predictions are evaluated without different weights to datapoints. We also discuss a specific issue every day.These reports are funded by the European Commission (DG CONNECT, LC-01485746) PJC and MC received funding from “la Caixa” Foundation (ID 100010434), under agreement LCF/PR/GN17/50300003; CP, DL, SA, MC, received funding from Ministerio de Ciencia, Innovación y Universidades and FEDER, with the project PGC2018-095456-B-I00Postprint (published version

Analysis and prediction of COVID-19 for EU-EFTA-UK and other countries

The present report aims to provide a comprehensive picture of the pandemic situation of COVID-19 in the EU countries, and to be able to foresee the situation in the next coming days. We employ an empirical model, verified with the evolution of the number of confirmed cases in previous countries where the epidemic is close to conclude, including all provinces of China. The model does not pretend to interpret the causes of the evolution of the cases but to permit the evaluation of the quality of control measures made in each state and a short-term prediction of trends. Note, however, that the effects of the measures’ control that start on a given day are not observed until approximately 7-10 days later. The model and predictions are based on two parameters that are daily fitted to available data: ¿ a: the velocity at which spreading specific rate slows down; the higher the value, the better the control. ¿ K: the final number of expected cumulated cases, which cannot be evaluated at the initial stages because growth is still exponential. We show an individual report with 8 graphs and a table with the short-term predictions for different countries and regions. We are adjusting the model to countries and regions with at least 4 days with more than 100 confirmed cases and a current load over 200 cases. The predicted period of a country depends on the number of datapoints over this 100 cases threshold, and is of 5 days for those that have reported more than 100 cumulated cases for 10 consecutive days or more. For short-term predictions, we assign higher weight to last 3 points in the fittings, so that changes are rapidly captured by the model. The whole methodology employed in the inform is explained in the last pages of this document. In addition to the individual reports, the reader will find an initial dashboard with a brief analysis of the situation in EU-EFTA-UK countries, some summary figures and tables as well as long-term predictions for some of them, when possible. These long-term predictions are evaluated without different weights to datapoints. We also discuss a specific issue every day.These reports are funded by the European Commission (DG CONNECT, LC-01485746) PJC and MC received funding from “la Caixa” Foundation (ID 100010434), under agreement LCF/PR/GN17/50300003; CP, DL, SA, MC, received funding from Ministerio de Ciencia, Innovación y Universidades and FEDER, with the project PGC2018-095456-B-I00Postprint (published version