Stories from different worlds in the universe of complex systems: A journey through microstructural dynamics and emergent behaviours in the human heart and financial markets

A physical system is said to be complex if it exhibits unpredictable structures, patterns or regularities emerging from microstructural dynamics involving a large number of components. The study of complex systems, known as complexity science, is maturing into an independent and multidisciplinary area of research seeking to understand microscopic interactions and macroscopic emergence across a broad spectrum systems, such as the human brain and the economy, by combining specific modelling techniques, data analytics, statistics and computer simulations. In this dissertation we examine two different complex systems, the human heart and financial markets, and present various research projects addressing specific problems in these areas. Cardiac fibrillation is a diffuse pathology in which the periodic planar electrical conduction across the cardiac tissue is disrupted and replaced by fast and disorganised electrical waves. In spite of a century-long history of research, numerous debates and disputes on the mechanisms of cardiac fibrillation are still unresolved while the outcomes of clinical treatments remain far from satisfactory. In this dissertation we use cellular automata and mean-field models to qualitatively replicate the onset and maintenance of cardiac fibrillation from the interactions among neighboring cells and the underlying topology of the cardiac tissue. We use these models to study the transition from paroxysmal to persistent atrial fibrillation, the mechanisms through which the gap-junction enhancer drug Rotigaptide terminates cardiac fibrillation and how focal and circuital drivers of fibrillation may co-exist as projections of transmural electrical activities. Financial markets are hubs in which heterogeneous participants, such as humans and algorithms, adopt different strategic behaviors to exchange financial assets. In recent decades the widespread adoption of algorithmic trading, the electronification of financial transactions, the increased competition among trading venues and the use of sophisticated financial instruments drove the transformation of financial markets into a global and interconnected complex system. In this thesis we introduce agent-based and state-space models to describe specific microstructural dynamics in the stock and foreign exchange markets. We use these models to replicate the emergence of cross-currency correlations from the interactions between heterogeneous participants in the currency market and to disentangle the relationships between price fluctuations, market liquidity and demand/supply imbalances in the stock market.Open Acces

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

Out-of-plane graphene materials for enhanced cell-chip coupling

Bioelectronic devices interact directly with biological systems to monitor cellular electrical activity and promote cell reaction to electrical stimulation. The capabilities of such devices, in terms of recording and stimulation, are affected by the effective cell-platform coupling. Therefore, during the last years, the development of engineered 2.5-3D micro and nanostructures has improved the effectiveness of biosensors using protruding structures to achieve a more intimate contact between cells and substrates. The vertical structures, due to their surface curvature, can actively modulate the cell-material interaction and the coupling conditions by regulating peculiar cellular processes at the interface such as membrane bending, ruffling, which ultimately reduce the distance between the electroactive materials and the biological components. In parallel, the rising of carbon-based materials (i.e., graphene) for bioelectronics has gained attention during the last years because of their outstanding chemical properties which allow improved cell-device interfacing. Given this scenario, 3D out-of-the-plane graphene structures has been designed and grown on planar platforms, exploiting the electrical, mechanical and optical features of this promising material. 3D fuzzy graphene (3DFG) and two nanowire-templated arrangements (NT-3DFG collapsed and non-collapsed) were realized to ultimately increase the dimensionality at the interface with cells through nanoscale features and wire-based architectures. Here we report a comprehensive study of the electrogenic cells-material interface by using fluorescence and electron microscopy for characterizing cell-graphene materials interactions at micro and nanoscale. First, we investigated the biocompatibility and the adhesion effect (cell stretching and outgrowth) of the diverse graphene-based pseudo-3D surfaces coupled to cardiomyocytes-like cells and primary cortical neuronal cells. Then, we examined the membrane deformation and the actual cell-device coupling via scanning electron microscopy/focused ion beam sectioning. We found out an enhanced cells adhesion on the substrates, suggesting that out-of-the-plane platform could improve the coupling between cells and sensors not only for electrophysiology application but also to modulate cellular functionalities and outgrowth

Ultra-sensitive bioelectronic transducers for extracellular electrophysiological studies

Extracellular electrical activity of cells is commonly recorded using microelectrode arrays (MEA) with planar electrodes. MEA technology has been optimized to record signals generated by excitable cells such as neurons. These cells produce spikes referred to as action potentials. However, all cells produce membrane potentials. In contrast to action potentials, electrical signals produced by non-excitable or non-electrogenic cells, do not exhibit spikes, rather smooth potentials that can change over periods of several minutes with amplitudes of only a few microvolts. These bioelectric signals serve functional roles in signalling pathways that control cell proliferation, differentiation and migration. Measuring and understanding these signals is of high priority in developmental biology, regenerative medicine and cancer research. The objective of this thesis is to fabricate and characterise bioelectronic transducers to measure in vitro the bioelectrical activity of non-electrogenic cells. Since these signals are in the order of few microvolts the electrodes must have an unrivaled low detection limit in the order of hundreds of nanovolts. To meet this challenge a methodology to analyze how bioelectrical signals are coupled into sensing surfaces was developed. The methodology relies on a description of the sensing interface by an equivalent circuit. Procedures for circuit parameter extraction are presented. Relation between circuit parameters, material properties and geometrical design was established. This knowledge was used to establish guidelines for device optimization. The methodology was first used to interpret recordings using gold electrodes, later it as extended to conducting polymers surfaces (PEDOT:PSS ) and finally to graphene electrolyte-gated transistors. The results of this thesis have contributed to the advance of the knowledge in bioelectronic transducers in the following aspects: (i) Detection of signals produced by an important class of neural cells, astrocyte and glioma that thus far had remained inaccessible using conventional extracellular electrodes. (ii) Development of an electrophysiological quantitative method for in vitro monitoring of cancer cell migration and cell-to-cell connections. (iii)An understanding of the limitations of electrolyte-gated transistors to record high frequency signals.A atividade elétrica extracelular das células é geralmente medida usando matrizes de micro-elétrodos (MEA) planares. A tecnologia MEA foi otimizada para medir sinais gerados por células excitáveis, como os neurónios. Essas células produzem sinais conhecidos como potenciais de ação. No entanto, todas as células produzem potenciais de membrana. Em contraste com os potenciais de ação, os sinais elétricos gerados por células não excitáveis ou não eletrogénicas, não são “spikes”, mas sinais que variam lentamente e que podem mudar ao longo de períodos de vários minutos com amplitudes de apenas alguns microvolts. Estes sinais desempenham funções importantes nos mecanismos de sinalização que controlam a proliferação, a diferenciação e a migração celular. Medir e entender esses sinais é importante na biologia do desenvolvimento, na medicina regenerativa e no desenvolvimento de novas terapias para combater células cancerosas. O objetivo desta tese é fabricar e caracterizar transdutores para medir in vitro a atividade de células não eletrogénicas. Como esses sinais são da ordem de alguns microvolts, os elétrodos devem ter um limite de detecção na ordem de centenas de nanovolts. Para enfrentar este desafio, foi desenvolvida uma metodologia para analisar a forma como os sinais se acoplam à superfície do sensor. A metodologia baseia-se na descrição da interface de detecção por um circuito eléctrico equivalente. Procedimentos para extração dos parâmetros de circuito e a relação com as propriedades do material e o desenho geométrico foi estabelecida. Este conhecimento foi usado para estabelecer diretrizes para otimização dos transdutores. Em primeiro lugar a metodologia foi usada para interpretar as medidas de sinais usando elétrodos de ouro, posteriormente estendida para analisar superfícies de polímeros condutores (PEDOT: PSS) e, finalmente, para compreender o funcionamento de transístores. Os resultados desta tese contribuíram para o avanço do conhecimento em transdutores bioeletrónicos nos seguintes aspectos: (i) Detecção de sinais produzidos por uma importante classe de células neurais, astrócitos e gliomas, que tem permanecido inacessíveis usando elétrodos extracelulares. (ii) Desenvolvimento de um método eletrofisiológico para medir a migração de células cancerosas e o estabelecimento de conexões entre células. (ii) Estudo das limitações dos transístores para medir sinais eletrofisiológicos rápidos.The work developed in this thesis was carried out within the framework of the project entitled: “Implantable Organic Devices for Advanced Therapies (INNOVATE)”, ref. PTDC/EEI-AUT/5442/2014, financed by Fundação para a Ciência e Tecnologia (FCT).This project was carried out at the laboratories of the “ Instituto de Telecomunicações (IT) UID/Multi/04326/2013” at the University of the Algarve. The PhD study period received full scholarship under European EM program, “Erasmus Mundus Action 2 (EMA2)” coordinated by University of Warsaw