Ion mechanisms of the mechanoelectrical feedback in myocardial cells

This article is dedicated to the mechanism of mechano-electric feedback in heart. The evidence is briefly discussed on organ, tissue, cell and in details on cell membrane levels in case of application of one of applied mechanical stimulus to cardiomyocytes. Stretch of the hole heart or its tissue fragment causes quick starting repolarization of action potentials (AP)/monophasic action potentials (MAP), shift of AP/MAP plato to higher negative zone, appearance of peaks of stretch-induced depolarization (SID) on final phase of AP/MAP repolarization level, which are overgrowing into extra AP/extra MAP. Mechanical events (changes in length and force of contractions) change electrical processes by means of direct influence on cell membrane via stretch activated channels (SAC). Cardiomyocytes, isolated from animal atrium and animal and human ventricular are responsible for the stretch of depolarized membrane, prolongation of AP and appearance of extra AP (extra systoles). Analysis of experiments, conducted following the patch clamp method in whole cell configuration, shows that the main cause of that mechanical events is SAC current--ISAC. During negative potential ISAC is determined by incoming into the cell sodium ions and is negative. Negative ISAC is changing final phase of AP/MAP repolarization and causes SID, which is overgrowing into extra AP (extra systoles), in case that SID exceeds threshold. Fast AP repolarization and AP plato shift into higher negative zone is related to positive ISAC (living potassium ions through SAC), activation of IK and reduction of ISAC. Activation of ISAC and arrhythmia induction require lower mechanical stimulus for hypertrophied cardiomyocytes, in comparisment to healthy ones. Hypertrophy of cardiomyocytes can lead to expression of SAC therefore increasing channel density and ISAC maximum amplitude. In this article is discussing data, acquired by means of direct measurement of conduction of single SAC on the background of mechanical stimulation of the cardiomyocytes membrane. It contains characteristics of the estimated SACs. It is shown that blocking of conduction of ions through SAC prevents mechanically induced arrhythmia in healthy and hypertrophied cardiomyocytes, which transforms the problem of mechano-electric feedback in heart from purely fundamental into clinical one.     

Hyaluronic acid salt — a mechanoelectrical transducer

Hyaluronic acid transduces a very gentle pressure into an electrical potential. Such pressure, depending on its direction, changes the optical rotary dispersion properties of the salt, either increasing the rotation in the direction already shown by the unpressured salt or changing and increasing the rotation in the opposite direction. These findings have implications for understanding the funtion of the cochlear and vestibular fluids, renal function, and the approximation to frictionless motion of normal joints.     

Reversible mechanosensitive ion pumping as a part of mechanoelectrical transduction.

To explain the ability of some mechanosensitive cells to reverse the process of mechanotransduction and to generate mechanical oscillations and emit sound, a piezo-conformational coupling model (PCC model) is proposed. The model includes a transport protein which changes either its volume (PV-coupling) or its area in the membrane (gamma A-coupling) when undergoing conformational transitions. Such a protein can interact with an oscillating pressure to pump ions and create a transmembrane gradient if the affinities of the protein for ions are different at the two sides of membrane. The frequency and concentration windows for mechanical energy transduction were determined. Under optimal conditions, the efficiency of energy transduction can approach the theoretical maximum of 100%. If the concentration gradient exceeds the static head value (quasi-equilibrium which can be built up and maintained by this transport system), the energy transduction reverses and the transporter becomes a generator of mechanical oscillations at the expense of a concentration gradient. Estimation of thermodynamic parameters of the pump shows that the PV-coupling model would require large pressure oscillations to work while the gamma A-coupling model could work in physiological conditions. The gamma A-coupling mechanism may be used by cells for two purposes. In the reverse mode, it can be a force generator for various applications. In the direct mode, it may serve bioenergetic purposes by harvesting the energy of mechanical oscillations and storing it in the form of a concentration gradient.(ABSTRACT TRUNCATED AT 250 WORDS)     

Computer modeling of ventricular fibrillation

Electrical activity of a heart in ventricular fibrillation was modeled as a sum of independent pulse streams with various amplitude-frequency and phase characteristics. Results of computer experiments were compared with those of real physiological experiments on rabbits. Identification of the model was carried out by means of the least-squares procedure. The offered technique allows a computer model investigation of internal structure of irregularities of ventricular fibrillation.     

Computer modeling of ventricular fibrillation

Electrical activity of a heart in ventricular fibrillation was modeled as a sum of independent pulse streams with various amplitude-frequency and phase characteristics. Results of computer experiments were compared with those of real physiological experiments on rabbits. Identification of the model was carried out by means of the least-squares procedure. The offered technique allows a computer model investigation of internal structure of irregularities of ventricular fibrillation.     

Computational modeling of morphogenesis regulated by mechanical feedback

Mechanical forces cause changes in form during embryogenesis and likely play a role in regulating these changes. This paper explores the idea that changes in homeostatic tissue stress (target stress), possibly modulated by genes, drive some morphogenetic processes. Computational models are presented to illustrate how regional variations in target stress can cause a range of complex behaviors involving the bending of epithelia. These models include growth and cytoskeletal contraction regulated by stress-based mechanical feedback. All simulations were carried out using the commercial finite element code ABAQUS, with growth and contraction included by modifying the zero-stress state in the material constitutive relations. Results presented for bending of bilayered beams and invagination of cylindrical and spherical shells provide insight into some of the mechanical aspects that must be considered in studying morphogenetic mechanisms.     

Action potential conduction between a ventricular cell model and an isolated ventricular cell.

We used the Luo and Rudy (LR) mathematical model of the guinea pig ventricular cell coupled to experimentally recorded guinea pig ventricular cells to investigate the effects of geometrical asymmetry on action potential propagation. The overall correspondence of the LR cell model with the recorded real cell action potentials was quite good, and the strength-duration curves for the real cells and for the LR model cell were in general correspondence. The experimental protocol allowed us to modify the effective size of either the simulation model or the real cell. 1) When we normalized real cell size to LR model cell size, required conductance for propagation between model cell and real cell was greater than that found for conduction between two LR model cells (5.4 nS), with a greater disparity when we stimulated the LR model cell (8.3 +/- 0.6 nS) than when we stimulated the real cell (7.0 +/- 0.2 nS). 2) Electrical loading of the action potential waveform was greater for real cell than for LR model cell even when real cell size was normalized to be equal to that of LR model cell. 3) When the size of the follower cell was doubled, required conductance for propagation was dramatically increased; but this increase was greatest for conduction from real cell to LR model cell, less for conduction from LR model cell to real cell, and least for conduction from LR model cell to LR model cell. The introduction of this "model clamp" technique allows testing of proposed membrane models of cardiac cells in terms of their source-sink behavior under conditions of extreme coupling by examining the symmetry of conduction of a cell pair composed of a model cell and a real cardiac cell. We have focused our experimental work with this technique on situations of extreme uncoupling that can lead to conduction block. In addition, the analysis of the geometrical factors that determine success or failure of conduction is important in the understanding of the process of discontinuous conduction, which occurs in myocardial infarction.     

Simulation of mechanoelectrical coupling in cardiomyocytes under normal and abnormal conditions

Mathematical models of the electromechanical function of cardiomyocytes and muscle duplexes, the simplest mechanically inhomogeneous myocardial systems, are developed. Using these models, the contribution of mechanoelectrical feedbacks to the contractive activity of the myocardium in normal and abnormal conditions is studied. In particular, the influence of the mechanical conditions of contraction on the shape and duration of the action potentials is reproduced and interpreted. In this context, different types of mechanical heterogeneity of the myocardium are analyzed. It is established that this heterogeneity can play a positive or negative role depending on the distribution of heterogeneous properties and on the order the elements of the system are activated. Using the same models, the contribution of mechanical factors to arrhythmogenesis under calcium overload of cardiomyocytes due to the weakening of the sodium-potassium pump is studied. Methods for correction of the contractive activity of cardiomyocytes in the case of such abnormalities are outlined.     

Compliance of the hair bundle associated with gating of mechanoelectrical transduction channels in the bullfrog's saccular hair cell

Mechanical stimuli are thought to open the transduction channels of a hair cell by tensing elastic components, the gating springs, that pull directly on the channels. To test this model, we measured the stiffness of hair bundles during mechanical stimulation. A bundle's compliance increased by about 40% at the position where half of the channels opened. This we attribute to conformational changes of transduction channels as they open and close. The magnitude and displacement dependence of the gating compliance provide quantitative information about the molecular basis of mechanoelectrical transduction: the force required to open each channel, the number of transduction channels per hair cell, the stiffness of a gating spring, and the swing of a channel's gate as it opens.     

Multi-scale modeling of a wound-healing cell migration assay

A continuum model and a discrete model are developed to capture the population-scale and cell-scale behavior in a wound-healing cell migration assay created from a scrape wound in a confluent cell monolayer. During wound closure, the cell population forms a sustained traveling wave, with close contact between cells behind the wavefront. Cells exhibit contact inhibition of migration and contact-limited proliferation. The continuum model includes the two dominant mechanisms and characteristics of cell migration and proliferation, using a cell diffusivity function that decreases with cell density and a logistic proliferative growth term. The discrete model arises naturally from the continuum model. Individual cells are simulated as continuous-time random walkers with nearest-neighbor transitions, together with a birth/death process. The migration and proliferation parameters are determined by analysing individual mice 3T3 fibroblast cell trajectories obtained during the development of a confluent cell monolayer and in a wound healing assay. The population-scale model successfully predicts the shape and speed of the traveling wave, while the discrete model is also successful in capturing the contact inhibition of migration effects.     

Effect of cytoskeletal elastic properties on the mechanoelectrical transduction in excitable cells

This paper addresses the possible mechanism of stretch on cell electrochemical potential change, based on the physicochemical properties of cytoskeletal network. Synthetic polyelectrolyte gel was used as an experimental model of the cytoskeleton. Gel samples with different density of network cross linking were studied. Triangular axial deformations of samples were applied. Simultaneously, the electrochemical (Donnan) potential of the gel was measured between a micropipette electrode pinned into the swollen gel, and a reference electrode in the outer solution. We found that axial deformation shifts the gel potential toward depolarization. The extent of gel depolarization showed a close negative correlation with the Young modulus of the gel. We suggest that the underlying mechanism is likely to be a universal process of counterion adsorption on charged polymer filaments due to the decrease of distance between polymer filaments owing to gel elongation.     

Mechanical feedback in morphogenesis and cell differentiation

Studies of mechanical stresses and mechanical feedback at the cell level are reviewed. It is shown that cells and embryonic tissues respond to external mechanical stresses and can generate such stresses themselves. Regular feedback loops between external (passive) and internal (active) mechanical stresses have been established. They are essential for cell survival, determination of the direction of their differentiation, and selforganization of morphogenetic processes. Relevant experimental data are presented, and models of mechanical feedback loops are discussed.     

Autoproteolysis and feedback in a protease cascade directing Drosophila dorsal-ventral cell fate

Three serine protease zymogens, Gastrulation defective (GD), Snake (Snk) and Easter (Ea), and a nerve growth factor-like growth factor ligand precursor, Spaetzle, are required for specification of dorsal- ventral cell fate during Drosophila embryogenesis. The proteases have been proposed to function in a sequential activation cascade within the extracellular compartment called the perivitelline space. We examined biochemical interactions between these four proteins using a heterologous co-expression system. The results indicate that the three proteases do function in a sequential activation cascade, that GD becomes active and initiates the cascade and that interaction between GD and Snk is sufficient for GD to cleave itself autoproteolytically. The proteolytically active form of Ea cleaves GD at a different position, revealing biochemical feedback in the pathway. Both GD and Snk bind to heparin-Sepharose, providing a link between the pipe-defined ventral prepattern and the protease cascade. Our results suggest a model of the cascade in which initiation is by relief from inhibition, and spatial regulation of activity is due to interaction with sulfated proteoglycans.     

Computational modeling of amylin-induced calcium dysregulation in rat ventricular cardiomyocytes

Hyperamylinemia is a condition that accompanies obesity and precedes type II diabetes, and it is characterized by above-normal blood levels of amylin, the pancreas-derived peptide. Human amylin oligomerizes easily and can deposit in the pancreas [1], brain [2], and heart [3], where they have been associated with calcium dysregulation. In the heart, accumulating evidence suggests that human amylin oligomers form moderately cation-selective [[4], [5]] channels that embed in the cell sarcolemma (SL). The oligomers increase membrane conductance in a concentration-dependent manner [5], which is correlated with elevated cytosolic Ca²⁺. These findings motivate our core hypothesis that non-selective inward Ca²⁺ conduction afforded by human amylin oligomers increase cytosolic and sarcoplasmic reticulum (SR) Ca²⁺ load, which thereby magnifies intracellular Ca²⁺ transients. Questions remain however regarding the mechanism of amylin-induced Ca²⁺ dysregulation, including whether enhanced SL Ca²⁺ influx is sufficient to elevate cytosolic Ca²⁺ load [6], and if so, how might amplified Ca²⁺ transients perturb Ca²⁺-dependent cardiac pathways. To investigate these questions, we modified a computational model of cardiomyocytes Ca²⁺ signaling to reflect experimentally-measured changes in SL membrane permeation and decreased sarcoplasmic/endoplasmic reticulum calcium ATPase (SERCA) function stemming from acute and transgenic human amylin peptide exposure. With this model, we confirmed the hypothesis that increasing SL permeation alone was sufficient to enhance Ca²⁺ transient amplitudes. Our model indicated that amplified cytosolic transients are driven by increased Ca²⁺ loading of the SR and that greater fractional release may contribute to the Ca²⁺-dependent activation of calmodulin, which could prime the activation of myocyte remodeling pathways. Importantly, elevated Ca²⁺ in the SR and dyadic space collectively drive greater fractional SR Ca²⁺ release for human amylin expressing rats (HIP) and acute amylin-exposed rats (+Amylin) mice, which contributes to the inotropic rise in cytosolic Ca²⁺ transients. These findings suggest that increased membrane permeation induced by oligomeratization of amylin peptide in cell sarcolemma contributes to Ca²⁺ dysregulation in pre-diabetes.     

Mathematical modeling of ventricular disturbances following atrial fibrillation

The present study presents the results of mathematical and computer modeling of atrial fibrillation and ventricular disturbances following atrial fibrillation. The model is based on the assumption, that electric impulsation arriving on the atrioventricular node during atrial fibrillation is sum N of independent pulse streams with various amplitude-frequency and phase characteristics. With this model it becomes possible to investigate the dependence of nonlinear dynamics of PP and RR intervals on amplitude-frequency and phase characteristics pulse streams. Results of computer experiments are compared with real physiological experiments on rabbits. Identification of model was carried out by means of least-squares procedure.     

一套研究机械电反馈的心室压力钳系统

在心脏机械电反馈的研究中准确控制机械刺激是非常重要的。本研究室构建了一套适用于离体家兔心脏的心室压力钳系统。该系统通过计算机控制压力钳,不仅能模拟正常生理条件下左心室的压力波形,还能在心室活动周期的特定时相、以适当波形对心室施加机械刺激。该系统集心脏灌流与起搏、表面心电图记录、单相动作电位记录、心室压力钳制与测定等多种功能于一体,特别适用于器官水平上观察机械电反馈现象并探讨其机制。     

UML as a cell and biochemistry modeling language

The systems biology community is building increasingly complex models and simulations of cells and other biological entities, and are beginning to look at alternatives to traditional representations such as those provided by ordinary differential equations (ODE). The lessons learned over the years by the software development community in designing and building increasingly complex telecommunication and other commercial real-time reactive systems, can be advantageously applied to the problems of modeling in the biology domain. Making use of the object-oriented (OO) paradigm, the unified modeling language (UML) and Real-Time Object-Oriented Modeling (ROOM) visual formalisms, and the Rational Rose RealTime (RRT) visual modeling tool, we describe a multi-step process we have used to construct top–down models of cells and cell aggregates. The simple example model described in this paper includes membranes with lipid bilayers, multiple compartments including a variable number of mitochondria, substrate molecules, enzymes with reaction rules, and metabolic pathways. We demonstrate the relevance of abstraction, reuse, objects, classes, component and inheritance hierarchies, multiplicity, visual modeling, and other current software development best practices. We show how it is possible to start with a direct diagrammatic representation of a biological structure such as a cell, using terminology familiar to biologists, and by following a process of gradually adding more and more detail, arrive at a system with structure and behavior of arbitrary complexity that can run and be observed on a computer. We discuss our CellAK (Cell Assembly Kit) approach in terms of features found in SBML, CellML, E-CELL, Gepasi, Jarnac, StochSim, Virtual Cell, and membrane computing systems.     

Mathematical modeling of ventricular disturbances following atrial fibrillation

The present study presents the results of mathematical and computer modeling of atrial fibrillation and ventricular disturbances following atrial fibrillation. The model is based on the assumption that electric impulsation arriving on the atrioventricular node during atrial fibrillation is sum of N independent pulse streams with various amplitude-frequency and phase characteristics. With this model it becomes possible to investigate the dependence of nonlinear dynamics of PP and RR intervals on amplitude-frequency and phase characteristics pulse streams. Results of computer experiments are compared with real physiological experiments on rabbits. Identification of model was carried out by means of least-squares procedure.