The cardiac muscle duplex as a method to study myocardial heterogeneity.

This paper reviews the development and application of paired muscle preparations, called duplex, for the investigation of mechanisms and consequences of intra-myocardial electro-mechanical heterogeneity. We illustrate the utility of the underlying combined experimental and computational approach for conceptual development and integration of basic science insight with clinically relevant settings, using previously published and new data. Directions for further study are identified.

Effects of cardiac myosin binding protein-C on the regulation of interaction of cardiac myosin with thin filament in an in vitro motility assay.

Modulatory role of whole cardiac myosin binding protein-C (сMyBP-C) in regulation of cardiac muscle contractility was studied in the in vitro motility assay with rabbit cardiac myosin as a motor protein. The effects of cMyBP-C on the interaction of cardiac myosin with regulated thin filament were tested in both in vitro motility and ATPase assays. We demonstrate that the addition of cMyBP-C increases calcium regulated Mg-ATPase activity of cardiac myosin at submaximal calcium. The Hill coefficient for 'pCa-velocity' relation in the in vitro motility assay decreased and the calcium sensitivity increased when сMyBP-C was added. Results of our experiments testifies in favor of the hypothesis that сMyBP-C slows down cross-bridge kinetics when binding to actin.

Study of the interaction between rabbit cardiac contractile and regulatory proteins. An in vitro motility assay.

A series of experiments was performed in an in vitro motility assay with reconstructed thin filaments to obtain pCa-force relationships for cardiac isomyosins V1 and V3. Two concentrations of each isomyosin (200 and 300 microg/ml) on the surface of a flow cell were tested. Isometric force was estimated as the amount of actin-binding protein, alpha-actinin, stopping thin filament movement. It was found that the amount of alpha-actinin stopping the movement at saturating calcium concentration for V3 was twice higher than for V1 at both concentrations of isoforms. Hill coefficients of cooperativity (h) were determined for pCa-force relationships. The value of h did not differ significantly for isoforms at 300 microg/ml of protein (h was 1.56 for V1 and 1.54 for V3). However, the Hill coefficient was higher for V3 isoform at 200 microg/ml (h = 2.00 and 1.76 for V3 and V1, respectively). Importantly, the Hill coefficient increased for both isoenzymes when their concentrations were decreased. The connection between Hill coefficient and cooperative interactions between cardiac contractile and regulatory proteins is analyzed in detail.

Activation sequence as a key factor in spatio-temporal optimization of myocardial function.

Using one-dimensional models of myocardial tissue, implemented as chains of virtual ventricular muscle segments that are kinematically connected in series, we studied the role of the excitation sequence in spatio-temporal organization of cardiac function. Each model element was represented by a well-verified mathematical model of cardiac electro-mechanical activity. We found that homogeneous chains, consisting of identical elements, respond to non-simultaneous stimulation by generation of complex spatio-temporal heterogeneities in element deformation. These are accompanied by the establishment of marked gradients in local electro-mechanical properties of the elements (heterogeneity in action potential duration, Ca2+ transient characteristics and sarcoplasmic reticulum Ca2+ loading). In heterogeneous chains, composed of elements simulating fast and slow contracting cardiomyocytes from different transmural layers, we found that only activation sequences where stimulation of the slower elements preceded that of faster ones gave rise to optimization of the system's electro-mechanical function, which was confirmed experimentally. Based on the results obtained, we hypothesize that the sequence of activation of cardiomyocytes in different ventricular layers is one of the key factors of spatio-temporal organization of myocardium. Moreover, activation sequence and regional differences in intrinsic electro-mechanical properties of cardiac muscle must be matched in order to optimize myocardial function.

Mechano-electric interactions in heterogeneous myocardium: development of fundamental experimental and theoretical models.

The heart is structurally and functionally a highly non-homogenous organ, yet its main function as a pump can only be achieved by the co-ordinated contraction of millions of ventricular cells. This apparent contradiction gives rise to the hypothesis that 'well-organised' inhomogeneity may be a pre-requisite for normal cardiac function. Here, we present a set of novel experimental and theoretical tools for the study of this concept. Heterogeneity, in its most condensed form, can be simulated using two individually controlled, mechanically interacting elements (duplex). We have developed and characterised three different types of duplexes: (i) biological duplex, consisting of two individually perfused biological samples (like thin papillary muscles or a trabeculae), (ii) virtual duplex, made-up of two interacting mathematical models of cardiac muscle, and (iii) hybrid duplex, containing a biological sample that interacts in real-time with a virtual muscle. In all three duplex types, in-series or in-parallel mechanical interaction of elements can be studied during externally isotonic, externally isometric, and auxotonic modes of contraction and relaxation. Duplex models, therefore, mimic (patho-)physiological mechano-electric interactions in heterogeneous myocardium at the multicellular level, and in an environment that allows one to control mechanical, electrical and pharmacological parameters. Results obtained using the duplex method show that: (i) contractile elements in heterogeneous myocardium are not 'independent' generators of tension/shortening, as their ino- and lusitropic characteristics change dynamically during mechanical interaction-potentially matching microscopic contractility to macroscopic demand, (ii) mechanical heterogeneity contributes differently to action potential duration (APD) changes, depending on whether mechanical coupling of elements is in-parallel or in-series, which may play a role in mechanical tuning of distant tissue regions, (iii) electro-mechanical activity of mechanically interacting contractile elements is affected by their activation sequence, which may optimise myocardial performance by smoothing intrinsic differences in APD. In conclusion, we present a novel set of tools for the experimental and theoretical investigation of cardiac mechano-electric interactions in healthy and/or diseased heterogeneous myocardium, which allows for the testing of previously inaccessible concepts.

Effects of mechanical interaction between two rabbit cardiac muscles connected in parallel.

The hypothesis that myocardium mechanical inhomogeneity produces a substantial effect on mechanical function was tested. Muscle inhomogeneity was studied in isolated papillary muscles or trabeculae excised from rabbit right ventricle and connected in a parallel duplex. Each muscle was placed in a separate perfusion bath. One end of each muscle was fastened to an individual force transducer and the other to the common lever of a servomotor. This arrangement allowed both muscles, being excited independently, to pull jointly a load applied to the lever. Separate electrodes for each perfusion bath allowed to stimulate muscles with a time delay. Tension developed in the individual muscles and their interaction were studied. Developed tension was critically dependent on the timing and sequence of excitation. Using mathematical modeling, patterns of tension distribution experimentally observed in parallel duplexes were simulated. These results suggest that changes both in Ca(2+) transients and in the time course of Ca(2+)-troponin complexion due to the duplexed muscles interaction offset the effect of mechanical inhomogeneity.

Mathematical modeling of the effect of the sarcoplasmic reticulum calcium pump function on load dependent myocardial relaxation.

Earlier, we developed a mathematical model of myocardial contraction-relaxation cycle regulation. A great number of mechanical experiments was simulated in the model, the phenomenon of load dependent relaxation (LDR) included. In the present work we used the same model to analyze experimental data revealing that high temperature leads to reduction of LDR. We simulated three main factors arising due to high temperature, which a priori may cause LDR reduction: increasing the cross-bridges cycling rate, decreasing the duration of the Ca transient ascending limb, and increasing Ca pumping rate. Indeed, these factors together result in LDR reduction; i.e., the model correctly simulates the effect of high temperature on LDR in general. At the same time, the sensitivity of LDR to the third factor is much higher than to the first and the second ones; i.e., increasing the rate of Ca pumping is sufficient to induce the observed effect in the framework of the model. This seems to contrast with the result of our previous study dealing with the simulation of LDR disappearance due to increasing Ca pumping rate as it happens during relatively severe cardiac hypertrophy. However, the model analysis shows that the specific mechanism underlying the change in Ca pumping rate in either case is extremely important for the effect on LDR. Particularly, the model predicts that LDR will reduce if this rate increases due to enhanced ATP hydrolysis rate by the Ca pump; and vice versa, if this rate increases due to decreasing retroinhibition of the pump ATPase, it may result in LDR increase. Probably, but the first mechanism is operational due to high temperature and makes LDR to reduce, whereas slowing down Ca pumping due to increasing retroinhibition results in LDR disappearance during severe cardiac hypertrophy.

Mathematical modelling of the contribution of mechanical inhomogeneity in the myocardium to contractile function.

Earlier we developed a mathematical model of the cardiac muscle that allowed for inactivation through the effects of cooperativity of contractile proteins. In the present work we used the model to analyze the mechanical function of an inhomogeneous myocardium. To simulate the latter we chose, as the simplest sytstem, a duplex in which muscles with different mechanical properties were connected in series and in parallel. Numerical experiments showed that the basic effect due to the inhomogeneity consists in the non-additivity of the mechanical characteristics of the muscle, e.g., of the relationship between end-systolic length and end-systolic force (Les - Pes). As a rule, non-additivity consists in a negative inotropic effect. The analysis showed that the cause of non-additivity is redistribution of loads between muscles (in a parallel duplex), redistribution of lengths (in a serial duplex), changes in the rate of contraction of each muscle compared to contraction that when working separately, shifts in time to Les. Also, the model predicts that additional inactivation of contractile proteins in a muscle within a duplex against isolation is the substantial mechanism of enhanced non-additivity. Among the factors of inhomogeneity studied the basic determinants are difference in amplitudes between isometric tensions developed by each muscle in isolation and the asynchronism in the development of these tensions.

Mathematical modeling of relations between the kinetics of free intracellular calcium and mechanical function of myocardium.

The paper describes a mathematical model of cardiac muscle contraction based on the assumption of two types of co-operativity which control the formation of calcium-troponin complexes and on a simplified scheme of free intracellular calcium kinetics. Calcium transients are shown to be different in isotonic and isometric conditions, being dependent on initial muscle length as well. Numerical experiments and analysis of the model suggest that calcium uptake by the sarcoplasmic reticulum slows down with an increase in the intracellular concentration of free calcium. This suggestion enables the model to explain the disappearance of load-dependent relaxation observed experimentally at cardiac hypertrophy.

Cooperative effects due to calcium binding by troponin and their consequences for contraction and relaxation of cardiac muscle under various conditions of mechanical loading.

A mathematical model for the regulation of mechanical activity in cardiac muscle has been developed based on a three-element rheological model of this muscle. The contractile element has been modeled taking into account the results of extensive mechanical tests that involved the recording of length-force and force-velocity relations and muscle responses to short-time deformations during various phases of the contraction-relaxation cycle. The best agreement between the experimental and the mathematical modeling results was obtained when a postulate stating two types of cooperativity to regulate the calcium binding by troponin was introduced into the model. Cooperativity of the first type is due to the dependence of the affinity of troponin C for Ca2+ on the concentration of myosin crossbridges in the vicinity of a given troponin C. Cooperativity of the second type assumes an increase in the affinity of a given troponin C for Ca2+ when the latter is bound by molecules neighboring troponin.

Heart muscle: mathematical modelling of the mechanical activity and modelling of mechanochemical uncoupling.

A mechanical model of heart muscle is proposed which includes rheological equations and equations for Ca-troponin interaction, for the dependences of the number of myosin cross-bridges on the length of sarcomere and on the speed of motion. The main assumption of the model is the dependence of the troponin affinity to calcium ions on the number of myosin cross-bridges attached. The model successfully imitates isometric and isotonic contractions, the "length-force" relationships, load-dependent relaxation, and the group of mechanical phenomena known as mechanochemical uncoupling.