Using Stochastic Differential Equations to Model Gap-Junction Gating Dynamics in Cardiac Myocytes

The cell-to-cell propagation of the cardiac action potential allows for the electro-mechanical coupling of cells, which promotes the coordinated contraction of cardiac tissue, often referred to as the heartbeat. The main structures that promote electrical coupling between adjacent cardiac cells are pore-like proteins called gap junctions that line the membranes of such cells, allowing a channel for electrically charged ions to travel between cells. It is known that the conformational, and hence conducting, properties of gap-junction channels change as a function of local gap-junctional voltage and local ionic concentrations and are stochastic in nature. Many previous models of gap junctions have made a constant-resistance approximation or used an ODE model relating gating state to a local voltage. In this thesis, we extend a previous ODE model of gap-junction gating state by Henriquez et al. and formulate it as a system of stochastic differential equations (SDEs) by deriving the expected change vector and covariance matrix of the model and integrating the covariance with respect to a stochastic process, the Wiener Process. In doing so, we construct the first SDE-based model of gap-junction gating dynamics. This SDE description of the electrical coupling between cardiac cells is integrated into a 1D cable model where intracellular current dynamics are described using the Luo-Rudy 1 formulation. Monte Carlo simulations are performed on the resulting model in order to gather data used to construct distributions of several model responses of interest, including conduction block, conduction velocity, gap-junction current and gap-junction conductance. We find a smoothing effect occurs as the number of gap junctions considered increases, but at small numbers of gap junctions, such as those observed in many diseased states, stochastic effects can be pronounced. In such decoupled regimes, stochastic effects are found to have a large effect on the occurrence of conduction block, the cessation of action potential propagation at some tissue location, and are found to increase the variance in conduction velocity from cell to cell. The waiting time between when two consecutive gap junctions reach their maximum current was found to conform to a gamma distribution, with shape and scale parameters a function of the number of gap junctions. As the number of gap junctions increases, the spread of the waiting time distributions decreases. Gap-junctional conductance was modeled as a time-dependent Gaussian distribution, with a temporal variance decreasing as a function of the elapsed time after depolarization. In the case of conduction block, we show that an emulator function can be constructed to estimate the probability of occurrence, thereby reducing the need for a large number of computationally intensive Monte Carlo simulations. Along with probabilistically describing the stochastic gap- junction model, these distributions can be leveraged in larger-scale tissue-level simulations to incorporate stochastic gap-junction gating at a reduced computational cost

From multiscale biophysics to digital twins of tissues and organs: future opportunities for in silico pharmacology

With many advancements in in silico biology in recent years, the paramount challenge is to translate the accumulated knowledge into exciting industry partnerships and clinical applications. Achieving models that characterize the link of molecular interactions to the activity and structure of a whole organ are termed multiscale biophysics. Historically, the pharmaceutical industry has worked well with in silico models by leveraging their prediction capabilities for drug testing. However, the needed higher fidelity and higher resolution of models for efficient prediction of pharmacological phenomenon dictates that in silico approaches must account for the verifiable multiscale biophysical phenomena, as a spatial and temporal dimension variation for different processes and models. The collection of different multiscale models for different tissues and organs can compose digital twin solutions towards becoming a service for researchers, clinicians, and drug developers. Our paper has two main goals: 1) To clarify to what extent detailed single- and multiscale modeling has been accomplished thus far, we provide a review on this topic focusing on the biophysics of epithelial, cardiac, and brain tissues; 2) To discuss the present and future role of multiscale biophysics in in silico pharmacology as a digital twin solution by defining a roadmap from simple biophysical models to powerful prediction tools. Digital twins have the potential to pave the way for extensive clinical and pharmaceutical usage of multiscale models and our paper shows the basic fundamentals and opportunities towards their accurate development enabling the quantum leaps of future precise and personalized medical software.Comment: 30 pages, 10 figures, 1 tabl

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

Reconstruction of cell surface densities of ion pumps, exchangers, and channels from mRNA expression, conductance kinetics, whole-cell calcium, and current-clamp voltage recordings, with an application to human uterine smooth muscle cells

Uterine smooth muscle cells remain quiescent throughout most of gestation, only generating spontaneous action potentials immediately prior to, and during, labor. This study presents a method that combines transcriptomics with biophysical recordings to characterise the conductance repertoire of these cells, the ‘conductance repertoire’ being the total complement of ion channels and transporters expressed by an electrically active cell. Transcriptomic analysis provides a set of potential electrogenic entities, of which the conductance repertoire is a subset. Each entity within the conductance repertoire was modeled independently and its gating parameter values were fixed using the available biophysical data. The only remaining free parameters were the surface densities for each entity. We characterise the space of combinations of surface densities (density vectors) consistent with experimentally observed membrane potential and calcium waveforms. This yields insights on the functional redundancy of the system as well as its behavioral versatility. Our approach couples high-throughput transcriptomic data with physiological behaviors in health and disease, and provides a formal method to link genotype to phenotype in excitable systems. We accurately predict current densities and chart functional redundancy. For example, we find that to evoke the observed voltage waveform, the BK channel is functionally redundant whereas hERG is essential. Furthermore, our analysis suggests that activation of calcium-activated chloride conductances by intracellular calcium release is the key factor underlying spontaneous depolarisations

Stochastic hybrid systems in cellular neuroscience

We review recent work on the theory and applications of stochastic hybrid systems in cellular neuroscience. A stochastic hybrid system or piecewise deterministic Markov process involves the coupling between a piecewise deterministic differential equation and a time-homogeneous Markov chain on some discrete space. The latter typically represents some random switching process. We begin by summarizing the basic theory of stochastic hybrid systems, including various approximation schemes in the fast switching (weak noise) limit. In subsequent sections, we consider various applications of stochastic hybrid systems, including stochastic ion channels and membrane voltage fluctuations, stochastic gap junctions and diffusion in randomly switching environments, and intracellular transport in axons and dendrites. Finally, we describe recent work on phase reduction methods for stochastic hybrid limit cycle oscillators

Structure of Native Lens Connexin 46/50 Intercellular Channels by Cryo-EM

Gap junctions establish direct pathways for cell-to-cell communication through the assembly of twelve connexin subunits that form intercellular channels connecting neighbouring cells. Co-assembly of different connexin isoforms produces channels with unique properties and enables communication across cell types. Here we used single-particle cryo-electron microscopy to investigate the structural basis of connexin co-assembly in native lens gap junction channels composed of connexin 46 and connexin 50 (Cx46/50). We provide the first comparative analysis to connexin 26 (Cx26), which—together with computational studies—elucidates key energetic features governing gap junction permselectivity. Cx46/50 adopts an open-state conformation that is distinct from the Cx26 crystal structure, yet it appears to be stabilized by a conserved set of hydrophobic anchoring residues. ‘Hot spots’ of genetic mutations linked to hereditary cataract formation map to the core structural–functional elements identified in Cx46/50, suggesting explanations for many of the disease-causing effects