A statistical mechanics investigation of sarcomere and titin organisation in cardiac myocytes and disease evolution
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2024-07-18
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doctoral thesis
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Abstract
A fundamental examination of sarcomere function in cardiac myocytes serves as a focal point for this computational modelling exploration, where thermodynamic considerations of fundamental sub-cellular components guide predictions of sarcomere maturation.
A steady-state framework predicting sarcomere organisation is developed in a three-state model of actin-myosin organisation of sarcomeres, stress fibres, and unbound cytoskeletal proteins, where global conservation of these cytoskeletal proteins is considered. Contributions of internal energies, strain energies and work associated with deformation, as well as entropic considerations, inform thermodynamically motivated sub-cellular formation of sarcomeres in myofibrils and stress fibre (SF) organisation. A non-local finite element model of the cell allows us to interpret sarcomere organisation within modelled cardiac myocytes, where we implement a statistical mechanics framework for cell homeostasis through a bespoke nested sampling methodology to generate a population of cells. We refer to this population as the homeostatic ensemble, where we maximise morphological entropy of cells subject to the constraint that the ensemble average free-energy is equal to the homeostatic free energy associated with a suspended cell. A modelling study investigates the response of human induced pluripotent stem cell (HiPSC) cardiac myocytes on confined aspect ratio micropatterned patches with substrates of equivalent stiffness to the native myocardium. Free energy considerations of cytoskeletal actin-myosin organisation, passive energies associated with deformation of the cell cytoplasm and membrane, and deformation of the attached substrate, inform homeostasis of modelled cardiac myocytes. Predicted patterns of sarcomere alignment and sarcomere density are shown to be in agreement with reported experimental data. This computational framework uncovers that Gibbs free energy decreases with increasing sarcomere density, which drives an increase in sarcomere length and the elongation of cells into high aspect-ratio spread-states. Constrained cell spreading on high aspect-ratio rectangular micropatterned patches is shown to facilitate strong sarcomere formation. In contrast, constrained spreading on square micropatterned patches results in low sarcomere formation.
Titin is a protein which guides sarcomere formation in muscular cells. A wealth of experimental evidence supports the fact that titin plays a role in sarcomere formation and active contractility in cardiac myocytes. However, the underlying mechanisms are poorly understood, and no computational myofibril model to-date has incorporated a description of titin biomechanical behaviour. We develop a novel theoretical model to predict the force-deformation response of the sub structural immunoglobulin (Ig) domains of titin. Chemical potentials and consideration of thermodynamic equilibrium govern the folding and unfolding of Ig domains. Our model is shown to correctly predict complex patterns of active unfolding and extension in response to applied loading, providing accurate predictions of previously reported experimentally measured force-displacement data and Ig folding and unfolding data. Our model reveals that application of a mechanical load to an Ig chain results in an imbalance between chemical potentials of folded and unfolded Ig domains, inducing transient unfolding of Ig domains in order to restore thermodynamic equilibrium. This novel titin model provides a deeper understanding of the underlying thermodynamic principles governing the folding and unfolding of Ig domains, and can be directly incorporated into a dynamic model of sarcomerogenesis in cardiac myocytes.
In the field of tissue culture engineering, cyclic loading regimes are often applied to HiPSC cardiac myocytes, as it is experimentally observed to induce sarcomerogenesis. To investigate this phenomenon, our thermodynamically motivated framework for sarcomere organisation under steady-state conditions is extended to a transient framework, predicting actin-myosin organisation in response to dynamic loading. The biomechanical contributions of titin is included within the implemented energetic contributions of sarcomeres, using our developed framework for Ig domain unfolding. Our model predicts that biaxial cyclic deformation of cells results in increased sarcomere concentration, with a corresponding decrease in SFs. Our model predicts that if the maximum cyclic strain magnitude is increased (ranging from 5% up to 20%), the formation of sarcomeres is increased, with an associated increase in cell contractility. These model predictions are in strong agreement with previously reported experimental measurements of sarcomere formation and cell contractility as a function of applied cyclic strain magnitude. Our model uncovers the thermodynamic drivers of sarcomere formation, based on changes in chemical potential of sarcomeres, SFs, and unbound proteins during dynamic loading. Our model also elucidates the thermodynamic mechanism by which unfolding and folding of Ig domains in titin affects sarcomere formation.
In the final technical chapter of this thesis, we develop transient models of immune cell behaviour and virus replication following SARS-CoV-2 infection. We then extend our nested sampling statistical mechanics methodologies to investigate the dynamics of viral spread in a population with heterogeneous immunity, by developing a modified heterogeneous SEIR framework based on our dynamic immune cell model. We develop an immunological model to simulate a multi-layered response to viral infection. A series of kinetic equations is developed to describe the increase in viral titre following initial infection of respiratory tract cells. This induces an innate and targeted immune response, including the generation of IgA and IgG antibodies, in addition to T cells. Model outputs include: (i) duration of pre-symptomatic infectiousness; (ii) evolving viral load; (iii) duration of infectiousness; (iv) number of infected cells; (v) time-dependent concentration of antibodies and memory B cells; (v) time-dependent concentration of T cells and memory T cells. The distribution of heterogeneous immune responses in a population is simulated by incorporating the following considerations: (i) age dependent strength of innate immunity; (ii) heterogeneous distribution of memory B cells and memory T cells due to prior infection. The computed distribution heterogeneous immunity is input into a modified SEIR framework, whereby the computed viral load determines the level of infectiousness, while the computed number of infected cells determines if transmission is classified as symptomatic or asymptomatic. Our immunological model is also use to determine the following key features of the SARS-CoV-2 pandemic: (i) increased viral load due to enhanced cell invasion of alpha- and delta-variants; (ii) efficacy of vaccines as a function of the rate of cell invasion by a variant. This novel framework is used to simulate the spread of SARS-CoV-2 in several European countries. A nested sampling approach is implemented to determine the mean and standard deviation of model parameters, based on reported age-stratified hospitalisations and fatalities. Computed partition functions reveal strong evidence for our novel heterogeneous immunity model compared to a standard homogeneous SEIR model.
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University Of Galway
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Attribution-NonCommercial-NoDerivatives 4.0 International