A thermodynamic framework for modelling membrane transporters

Membrane transporters contribute to the regulation of the internal environment of cells by translocating substrates across cell membranes. Like all physical systems, the behaviour of membrane transporters is constrained by the laws of thermodynamics. However, many mathematical models of transporters, especially those incorporated into whole-cell models, are not thermodynamically consistent, leading to unrealistic behaviour. In this paper we use a physics-based modelling framework, in which the transfer of energy is explicitly accounted for, to develop thermodynamically consistent models of transporters. We then apply this methodology to model two specific transporters: the cardiac sarcoplasmic/endoplasmic Ca$^{2+}$ ATPase (SERCA) and the cardiac Na$^+$/K$^+$ ATPase

Cellular Classes in the Human Brain Revealed In Vivo by Heartbeat-Related Modulation of the Extracellular Action Potential Waveform

Determining cell types is critical for understanding neural circuits but remains elusive in the living human brain. Current approaches discriminate units into putative cell classes using features of the extracellular action potential (EAP); in absence of ground truth data, this remains a problematic procedure. We find that EAPs in deep structures of the brain exhibit robust and systematic variability during the cardiac cycle. These cardiac-related features refine neural classification. We use these features to link bio-realistic models generated from in vitro human whole-cell recordings of morphologically classified neurons to in vivo recordings. We differentiate aspiny inhibitory and spiny excitatory human hippocampal neurons and, in a second stage, demonstrate that cardiac-motion features reveal two types of spiny neurons with distinct intrinsic electrophysiological properties and phase-locking characteristics to endogenous oscillations. This multi-modal approach markedly improves cell classification in humans, offers interpretable cell classes, and is applicable to other brain areas and species

Analysis of parametric biological models with non-linear dynamics

In this paper we present recent results on parametric analysis of biological models. The underlying method is based on the algorithms for computing trajectory sets of hybrid systems with polynomial dynamics. The method is then applied to two case studies of biological systems: one is a cardiac cell model for studying the conditions for cardiac abnormalities, and the second is a model of insect nest-site choice.Comment: In Proceedings HSB 2012, arXiv:1208.315

Modelling the effect of gap junctions on tissue-level cardiac electrophysiology

When modelling tissue-level cardiac electrophysiology, continuum approximations to the discrete cell-level equations are used to maintain computational tractability. One of the most commonly used models is represented by the bidomain equations, the derivation of which relies on a homogenisation technique to construct a suitable approximation to the discrete model. This derivation does not explicitly account for the presence of gap junctions connecting one cell to another. It has been seen experimentally [Rohr, Cardiovasc. Res. 2004] that these gap junctions have a marked effect on the propagation of the action potential, specifically as the upstroke of the wave passes through the gap junction. In this paper we explicitly include gap junctions in a both a 2D discrete model of cardiac electrophysiology, and the corresponding continuum model, on a simplified cell geometry. Using these models we compare the results of simulations using both continuum and discrete systems. We see that the form of the action potential as it passes through gap junctions cannot be replicated using a continuum model, and that the underlying propagation speed of the action potential ceases to match up between models when gap junctions are introduced. In addition, the results of the discrete simulations match the characteristics of those shown in Rohr 2004. From this, we suggest that a hybrid model -- a discrete system following the upstroke of the action potential, and a continuum system elsewhere -- may give a more accurate description of cardiac electrophysiology.Comment: In Proceedings HSB 2012, arXiv:1208.315

Cardiac cell modelling: Observations from the heart of the cardiac physiome project

In this manuscript we review the state of cardiac cell modelling in the context of international initiatives such as the IUPS Physiome and Virtual Physiological Human Projects, which aim to integrate computational models across scales and physics. In particular we focus on the relationship between experimental data and model parameterisation across a range of model types and cellular physiological systems. Finally, in the context of parameter identification and model reuse within the Cardiac Physiome, we suggest some future priority areas for this field

A study of early afterdepolarizations in a model for human ventricular tissue

Sudden cardiac death is often caused by cardiac arrhythmias. Recently, special attention has been given to a certain arrhythmogenic condition, the long-QT syndrome, which occurs as a result of genetic mutations or drug toxicity. The underlying mechanisms of arrhythmias, caused by the long-QT syndrome, are not fully understood. However, arrhythmias are often connected to special excitations of cardiac cells, called early afterdepolarizations (EADs), which are depolarizations during the repolarizing phase of the action potential. So far, EADs have been studied mainly in isolated cardiac cells. However, the question on how EADs at the single-cell level can result in fibrillation at the tissue level, especially in human cell models, has not been widely studied yet. In this paper, we study wave patterns that result from single-cell EAD dynamics in a mathematical model for human ventricular cardiac tissue. We induce EADs by modeling experimental conditions which have been shown to evoke EADs at a single-cell level: by an increase of L-type Ca currents and a decrease of the delayed rectifier potassium currents. We show that, at the tissue level and depending on these parameters, three types of abnormal wave patterns emerge. We classify them into two types of spiral fibrillation and one type of oscillatory dynamics. Moreover, we find that the emergent wave patterns can be driven by calcium or sodium currents and we find phase waves in the oscillatory excitation regime. From our simulations we predict that arrhythmias caused by EADs can occur during normal wave propagation and do not require tissue heterogeneities. Experimental verification of our results is possible for experiments at the cell-culture level, where EADs can be induced by an increase of the L-type calcium conductance and by the application of I blockers, and the properties of the emergent patterns can be studied by optical mapping of the voltage and calcium

Genetically engineered cardiac pacemaker: stem cells transfected with HCN2 gene and myocytes - a model

Artificial biological pacemakers were developed and tested in canine ventricles. Next steps will require obtaining oscillations sensitive to external regulations, and robust with respect to long term drifts of expression levels of pacemaker currents and gap junctions. We introduce mathematical models intended to be used in parallel with the experiments. The models describe human mesenchymal stem cells ({\it hMSC}) transfected with HCN2 genes and connected to myocytes. They are intended to mimic experiments with oscillation induction in a cell pair, in cell culture and in the cardiac tissue. We give examples of oscillations in a cell pair, in a 1 dim cell culture, and oscillation dependence on number of pacemaker channels per cell and number of gap junctions. The models permit to mimic experiments with levels of gene expressions not achieved yet, and to predict if the work to achieve this levels will significantly increase the quality of oscillations. This give arguments for selecting the directions of the experimental work

Cardiosphere-derived cells suppress allogeneic lymphocytes by production of PGE2 acting via the EP4 receptor

derived cells (CDCs) are a cardiac progenitor cell population, which have been shown to possess cardiac regenerative properties and can improve heart function in a variety of cardiac diseases. Studies in large animal models have predominantly focussed on using autologous cells for safety, however allogeneic cell banks would allow for a practical, cost-effective and efficient use in a clinical setting. The aim of this work was to determine the immunomodulatory status of these cells using CDCs and lymphocytes from 5 dogs. CDCs expressed MHC I but not MHC II molecules and in mixed lymphocyte reactions demonstrated a lack of lymphocyte proliferation in response to MHC-mismatched CDCs. Furthermore, MHC-mismatched CDCs suppressed lymphocyte proliferation and activation in response to Concanavalin A. Transwell experiments demonstrated that this was predominantly due to direct cell-cell contact in addition to soluble mediators whereby CDCs produced high levels of PGE2 under inflammatory conditions. This led to down-regulation of CD25 expression on lymphocytes via the EP4 receptor. Blocking prostaglandin synthesis restored both, proliferation and activation (measured via CD25 expression) of stimulated lymphocytes. We demonstrated for the first time in a large animal model that CDCs inhibit proliferation in allo-reactive lymphocytes and have potent immunosuppressive activity mediated via PGE2