Electrolyte disorders in the human ventricle. A simulation study.

Ventricular cells are immersed in a bath of electrolytes and these ions are essential for a healthy heart and a regular rhythm. Maintaining physiological concentration of them is fundamental for reducing arrhythmias and risk of sudden cardiac death, especially in haemodialysis patients and in the heart diseases treatments. Models of electrically activity of the heart based on mathematical formulation are a part of the efforts to improve the understanding and prediction of heart behaviour. Modern models incorporate the extensive and ever increasing amounts of experimental data in incorporating biophysically detailed mechanisms to allow the detailed study of molecular and subcellular mechanisms of heart disease. The goal of this project was to simulate the effects of changes in potassium and calcium concentrations in the extracellular space between experimental data and and a description incorpored into two modern biophysically detailed models (Grandi et al. Model; O’Hara Rudy Model). Moreover the task was to analyze the changes in the ventricular electrical activity, in particular by studying the modifications on the simulated electrocardiographic signal. We used the cellular information obtained by the heart models in order to build a 1D tissue description. The fibre is composed by 165 cells, it is divided in four groups to differentiate the cell types that compound human ventricular tissue. The main results are the following: Grandi et al. (GBP) model is not even able to reproduce the correct action potential profile in hyperkalemia. Data from hospitalized patients indicates that the action potential duration (APD) should be shorter than physiological state but in this model we have the opposite. From the potassium point of view the results obtained by using O’Hara model (ORD) are in agreement with experimental data for the single cell action potential in hypokalemia and hyperkalemia, most of the currents follow the data from literature. In the 1D simulations we were able to reproduce ECGs signal in most the potassium concentrations we selected for this study and we collected data that can help physician in understanding what happens in ventricular cells during electrolyte disorder. However the model fails in the conduction of the stimulus under hyperkalemic conditions. The model emphasized the ECG modifications when the K+ is slightly more than physiological value. In the calcium setting using the ORD model we found an APD shortening in hypocalcaemia and an APD lengthening in hypercalcaemia, i.e. the opposite to experimental observation. This wrong behaviour is kept in one dimensional simulations bringing a longer QT interval in the ECG under higher [Ca2+]o conditions and vice versa. In conclusion it has highlighted that the actual ventricular models present in literature, even if they are useful in the original form, they need an improvement in the sensitivity of these two important electrolytes. We suggest an use of the GBP model with modifications introduced by Carro et al. who understood that the failure of this model is related to the Shannon et al. model (a rabbit model) from which the GBP model was built. The ORD model should be modified in the Ca2+ - dependent IcaL and in the influence of the Iks in the action potential for letting it him produce a correct action potential under different calcium concentrations. In the 1D tissue maybe a heterogeneity setting of intra and extracellular conductances for the different cell types should improve a reproduction of the ECG signal.

Multicelled Behaviour in E. coli: Design and experimental characterization of an engineered library of hybrid promoters.

Synthetic biology has recently had a great development, many papers have been published and many applications have been presented, spanning from the production of biopharmacheuticals to the synthesis of bioenergetic substrates or industrial catalysts. But, despite these advances, most of the applications are quite simple and don’t fully exploit the potential of this discipline. This limitation in complexity has many causes, like the incomplete characterization of some components, or the intrinsic variability of the biological systems, but one of the most important reasons is the incapability of the cell to sustain the additional metabolic burden introduced by a complex circuit. The objective of the project, of which this work is part, is trying to solve this problem through the engineering of a multicellular behaviour in prokaryotic cells. This system will introduce a cooperative behaviour that will allow to implement complex functionalities, that can’t be obtained with a single cell. In particular the goal is to implement the Leader Election, this procedure has been firstly devised in the field of distributed computing, to identify the process that allow to identify a single process as organizer and coordinator of a series of tasks assigned to the whole population. The election of the Leader greatly simplifies the computation providing a centralized control. Further- more this system may even be useful to evolutionary studies that aims to explain how complex organisms evolved from unicellular systems. The work presented here describes, in particular, the design and the experimental characterization of a component of the circuit that solves the Leader Election problem. This module, composed of an hybrid promoter and a gene, is activated in the non-leader cells after receiving the signal that a leader is present in the colony. The most important element, in this case, is the hybrid promoter, it has been realized in different versions, applying the heuristic rules stated in [22], and their activity has been experimentally tested. The objective of the experimental characterization was to test the response of the genetic circuit to the introduction, in the cellular environment, of particular molecules, inducers, that can be considered inputs of the system. The desired behaviour is similar to the one of a logic AND gate in which the exit, represented by the luminous signal produced by a fluorescent protein, is one only in presence of both inducers. The robustness and the stability of this behaviour have been tested by changing the concentration of the input signals and building dose response curves. From these data it is possible to conclude that the analysed constructs have an AND-like behaviour over a wide range of inducers’ concentrations, even if it is possible to identify many differences in the expression profiles of the different constructs. This variability accounts for the fact that the input and the output signals are continuous, and so their binary representation isn’t able to capture the complexity of the behaviour. The module of the circuit that has been considered in this analysis has a fundamental role in the realization of the intercellular communication system that is necessary for the cooperative behaviour to take place. For this reason, the second phase of the characterization has been focused on the analysis of the signal transmission. In particular, the interaction between this element and the one that is responsible for emitting the chemical signal has been tested. The desired behaviour is still similar to a logic AND, since, even in this case, the exit signal is determined by the hybrid promoter activity. The experimental results have demonstrated that the systems behave correctly, even if there is still a substantial variability between them. The dose response curves highlighted that stricter constrains on the inducers concentrations need to be imposed in order to obtain a clear separation between the two levels of expression. In the conclusive chapter the DNA sequences of the hybrid promoters are analysed, trying to identify the regulatory elements that are most important for the determination of the gene expression. Given the available data it wasn’t possible to draw definitive conclusions. In the end, few considerations on promoter engineering and complex circuits realization are presented. This section aims to briefly recall some of the problems outlined in the introduction and provide a few possible solutions.

Analisi della propagazione elettrica nel tessuto cardiaco mediante simulazione numerica implementata su GPU

Il segnale elettrico si propaga nel tessuto cardiaco attraverso gap-junctions che si trovano tra i miociti cardiaci e in ciascuno di essi si avvia un processo chiamato potenziale d'azione (PA). In questa tesi prenderò in considerazione il modello Luo-Rudy 1991 e il difetto oggetto di studio sono le Early Afterdepolarizations (EADs). Si analizzerà la propagazione del potenziale d’azione in un cavo di 300 cellule. Dopo alcune simulazioni preliminari è emersa l’utilità di trovare una soluzione che permettesse di ridurre i tempi di calcolo, il modello è stato quindi implementato in CUDA. Il lavoro è stato sviluppato nei seguenti step: 1) l’impiego dell’ambiente di calcolo MATLAB per implementare il modello, descrivendo ogni cellula attraverso il modello Luo-Rudy 1991 e l’interazione elettrica inter-cellulare, considerando un cavo di 300 cellule; 2) individuazione dei parametri che, adeguatamente modificati, sono in grado di indurre EADs a livello single cell; 3) implementazione del modello in CUDA, creando uno strumento che potrà essere utilizzato per aumentare notevolmente il numero delle simulazioni nell’unità di tempo; 4) messa a punto di un criterio per valutare in modo conciso la bontà (safety factor) della relazione source-sink. L’utilità di un simile criterio è quella di valutare, sia nel caso di propagazione di AP che in quello di eventuale propagazione di EADs, la propensione alla propagazione in un tessuto. Il primo capitolo descriverà il potenziale d’azione, il modello usato e la teoria del cavo. Il secondo capitolo discuterà l’implementazione del modello usato, descriverà CUDA e come il modello sia stato implementato. Il terzo capitolo riguarderà i primi risultati ottenuti dalle simulazioni e come la variazione dei parametri influisce sulla forma delle EADs. L’ultimo capitolo approfondirà i requisiti necessari per far avvenire una propagazione in un cavo.