Mathematical models for the study of electromechanical and mechanoelectrical coupling in the myocardium

Mathematical models have been developed to describe interactions of electrical, mechanical and chemical processes in cardiomyocytes. The models simulate wide range of experimental data on excitation-contraction coupling and, more importantly, on mechanoelectric feedback in heart muscle. The model results clearly show that mechano-dependence of intracellular calcium handling due to cooperative effects of contractile proteins activation plays a key role in cardiac mechanoelectric coupling. At the same time, mechanosensitive currents can also contribute to action potential responses to mechanical perturbations. Using this model to study the heterogeneous myocardium we have shown that temporal and functional electromechanical heterogeneity of coupled cardiomyocytes can essentially determine the myocardium contractility. Optimization of the electromechanical function of contractile system emerges from the fine coordination between the activation sequence of cardiomyocytes, their local electromechanical properties and the mechanical interaction during contraction.     

Electromechanical models of the ventricles

Computational modeling has traditionally played an important role in dissecting the mechanisms for cardiac dysfunction. Ventricular electromechanical models, likely the most sophisticated virtual organs to date, integrate detailed information across the spatial scales of cardiac electrophysiology and mechanics and are capable of capturing the emergent behavior and the interaction between electrical activation and mechanical contraction of the heart. The goal of this review is to provide an overview of the latest advancements in multiscale electromechanical modeling of the ventricles. We first detail the general framework of multiscale ventricular electromechanical modeling and describe the state of the art in computational techniques and experimental validation approaches. The powerful utility of ventricular electromechanical models in providing a better understanding of cardiac function is then demonstrated by reviewing the latest insights obtained by these models, focusing primarily on the mechanisms by which mechanoelectric coupling contributes to ventricular arrythmogenesis, the relationship between electrical activation and mechanical contraction in the normal heart, and the mechanisms of mechanical dyssynchrony and resynchronization in the failing heart. Computational modeling of cardiac electromechanics will continue to complement basic science research and clinical cardiology and holds promise to become an important clinical tool aiding the diagnosis and treatment of cardiac disease.     

Detection of a novel sense-antisense RNA-hybrid structure by RACE experiments on endogenous troponin I antisense RNA

Conformational changes in the troponin/tropomyosin complex significantly alter the mechanical properties of cardiac muscle. Phosphorylation of cardiac troponin I, part of the troponin/tropomyosin complex, reduces calcium affinity, which leads to increased relaxation of cardiac muscle. Because cardiac troponin I plays a central role in tuning the heart to different work demands, detailed knowledge of troponin I protein regulation is required. Our group previously detected naturally occurring antisense RNA for troponin I in human and rat hearts, and here, attempt to unravel the structure of rat cardiac troponin I antisense RNA. We performed rapid amplification of cDNA ends (RACE) experiments and discovered antisense sequences identical to a copy of the sense mRNA, which led us to conclude that the antisense RNA must be transcribed from troponin I mRNA in the cytoplasm. Moreover, we isolated RNA structures comprising sense and antisense sequences in one continuous molecule. As we found no homolog structures described in the literature, we called this "hybrid RNA." Because a duplex formation was demonstrated previously we concluded that hybrid RNA is a consequence of a tight interaction between sense and antisense troponin I RNA in vivo, which we discuss in the article.     

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.     

A physical model of ATP-induced actin-myosin movement in vitro.

The nature of the mechanism limiting the velocity of ATP-induced unidirectional movements of actin-myosin filaments in vitro is considered. In the sliding process two types of "cyclic" interactions between myosin heads and actin are involved, i.e., productive and nonproductive. In the productive interaction, myosin heads split ATP and generate a force which produces sliding between actin and myosin. In the nonproductive interaction "cycle," on the other hand, myosin heads rapidly attach to and detach from actin "reversibly," i.e., without splitting ATP or generating an active force. Such a nonproductive interaction "cycle" causes irreversible dissipation of sliding energy into heat, because the myosin cross-bridges during this interaction are passive elastic structures. This consideration has led us to postulate that such cross-bridges, in effect, exert viscous-like frictional drag on moving elements. Energetic considerations suggest that this frictional drag is much greater than the hydrodynamic viscous drag. We present a model in which the sliding velocity is limited by the balance between the force generated by myosin cross-bridges in the productive interaction and the frictional drag exerted by other myosin cross-bridges in the nonproductive interaction. The model is consistent with experimental findings of in vitro sliding, including the dependence of velocity on ATP concentration, as well as the sliding velocity of co-polymers of skeletal muscle myosin and phosphorylated and unphosphorylated smooth muscle myosins.     

Models of cardiac electromechanics based on individual hearts imaging data Image-based electromechanical models of the heart

Current multi-scale computational models of ventricular electromechanics describe the full process of cardiac contraction on both the micro- and macro- scales including: the depolarization of cardiac cells, the release of calcium from intracellular stores, tension generation by cardiac myofilaments, and mechanical contraction of the whole heart. Such models are used to reveal basic mechanisms of cardiac contraction as well as the mechanisms of cardiac dysfunction in disease conditions. In this paper, we present a methodology to construct finite element electromechanical models of ventricular contraction with anatomically accurate ventricular geometry based on magnetic resonance and diffusion tensor magnetic resonance imaging of the heart. The electromechanical model couples detailed representations of the cardiac cell membrane, cardiac myofilament dynamics, electrical impulse propagation, ventricular contraction, and circulation to simulate the electrical and mechanical activity of the ventricles. The utility of the model is demonstrated in an example simulation of contraction during sinus rhythm using a model of the normal canine ventricles.     

Mechanical properties and fiber type composition of chronically inactive muscles

A role for neuromuscular activity in the maintenance of skeletal muscle properties has been well established. However, the role of activity-independent factors is more difficult to evaluate. We have used the spinal cord isolation model to study the effects of chronic inactivity on the mechanical properties of the hindlimb musculature in cats and rats. This model maintains the connectivity between the motoneurons and the muscle fibers they innervate, but the muscle unit is electrically "silent". Consequently, the measured muscle properties are activity-independent and thus the advantage of using this model is that it provides a baseline level (zero activity) from which regulatory factors that affect muscle cell homeostasis can be defined. In the present paper, we will present a brief review of our findings using the spinal cord isolation model related to muscle mechanical and fiber type properties.     

Validation of a musculo-skeletal model of the mandible and its application to mandibular distraction osteogenesis

Mandibular distraction osteogenesis will lead to a change in muscle coordination and load transfer to the temporomandibular joints (TMJ). The objective of this work is to present and validate a rigid-body musculo-skeletal model of the mandible based on inverse dynamics for calculation of the muscle activations, muscle forces and TMJ reaction forces for different types of clenching tasks and dynamic tasks. This approach is validated on a symmetric mandible model and an application will be presented where the TMJ reaction forces during unilateral clenching are estimated for a virtual distraction patient with a shortened left ramus. The mandible model consists of 2 rigid segments and has 4 degrees-of-freedom. The model was equipped with 24 hill-type musculotendon actuators. During the validation experiment one subject was asked to do several tasks while measuring EMG activity, bite force and kinematics. The bite force and kinematics were used as input for the simulations of the same tasks after which the estimated muscle activities were compared with the measured muscle activities. This resulted in an average correlation coefficient of 0.580 and an average of the Mean Absolute Error of 0.109. The virtual distraction model showed a large difference in the TMJ reaction forces between left and right compared with the symmetric model for the same loading case. The present work is a step in the direction of building patient-specific mandible models, which can assess the mechanical effects on the TMJ before mandibular distraction osteogenesis surgery.     

An integrated electromechanical-growth heart model for simulating cardiac therapies

An emerging class of models has been developed in recent years to predict cardiac growth and remodeling (G&R). We recently developed a cardiac G&R constitutive model that predicts remodeling in response to elevated hemodynamics loading, and a subsequent reversal of the remodeling process when the loading is reduced. Here, we describe the integration of this G&R model to an existing strongly coupled electromechanical model of the heart. A separation of timescale between growth deformation and elastic deformation was invoked in this integrated electromechanical-growth heart model. To test our model, we applied the G&R scheme to simulate the effects of myocardial infarction in a realistic left ventricular (LV) geometry using the finite element method. We also simulate the effects of a novel therapy that is based on alteration of the infarct mechanical properties. We show that our proposed model is able to predict key features that are consistent with experiments. Specifically, we show that the presence of a non-contractile infarct leads to a dilation of the left ventricle that results in a rightward shift of the pressure volume loop. Our model also predicts that G&R is attenuated by a reduction in LV dilation when the infarct stiffness is increased.     

Sequence-specific targeting of RNA with an oligonucleotide-neomycin conjugate

The synthesis of neomycin covalently attached at the C5-position of 2'-deoxyuridine is reported. The synthesis outlined allows for incorporation of an aminoglycoside (neomycin) at any given site in an oligonucleotide (ODN) where a thymidine (or uridine) is present. Incorporation of this modified base into an oligonucleotide, which is complementary to a seven-bases-long alpha-sarcin loop RNA sequence, leads to enhanced duplex hybridization. The increase in Tm for this duplex (DeltaTm = 6 degrees C) suggests a favorable interaction of neomycin within the duplex groove. CD spectroscopy shows that the modified duplex adopts an A-type confirmation. ITC measurements indicate the additive effects of ODN and neomycin binding to the RNA target (Ka = 4.5 x 107 M-1). The enhanced stability of the hybrid duplex from this neomycin-ODN conjugate originates primarily from the enthalpic contribution of neomycin {DeltaDeltaHobs = -7.21 kcal/mol (DeltaHneomycin conjugated - DeltaH nonconjugated)} binding to the hybrid duplex. The short linker length allows for selective stabilization of the hybrid duplex over the hybrid triplex. The results described here open up new avenues in the design and synthesis of nucleo-aminoglycoside-conjugates (N-Ag-C) where the inclusion of any number of aminoglycoside (neomycin) molecules per oligonucleotide can be accomplished.     

DO SUTURE ZONES EXIST?

Remington (1968) argued that 13 suture zones exist in North America. Remington defined a suture zone as, "a band of geographic overlap between major biotic assemblages, including some pairs of species or semispecies which hybridize in the zone" (p. 322). Although initially controversial, the idea that suture zones exist has picked up momentum over the past decade, due largely to the phylogeographic work of Hewitt, Avise, and their colleagues. Nevertheless, the reality of suture zones has not yet been subjected to rigorous analysis using statistical and geographic information system (GIS) approaches. To test for the existence of Remington's suture zones, we first identified 117 terrestrial hybrid zones in Canada and the United States through a literature search for the key words "cline," "contact zone," "hybrid zone," and "hybridization" in articles published between 1970 and 2002. The 117 hybrid zones were mapped using a GIS approach and compared with a digitized version of Remington's original suture zone map. Overall, there does appear to be an association between hybrid zones and suture zones, but this association is largely attributable to clustering of hybrid zones in only two of the 13 suture zones recognized by Remington. The results suggest that evolutionary biologists should retain some skepticism toward Remington's suture zones.     

Characterization of structural features important for T7 RNAP elongation complex stability reveals competing complex conformations and a role for the non-template strand in RNA displacement.

We have characterized the roles of the phage T7 RNA polymerase (RNAP) thumb subdomain and the RNA binding activity of the N-terminal domain in elongation complex (EC) stability by evaluating how disrupting these structures affects the dissociation rates of halted ECs. Our results reveal distinct roles for these elements in EC stabilization. On supercoiled or partially single-stranded templates the enzyme with a deletion of the thumb subdomain is exceptionally unstable. However, on linear duplex templates the polymerase which has been proteolytically cleaved within the N-terminal domain is the most unstable. The differences in the effects of these RNAP modifications on the stability of ECs on the different templates appear to be due to differences in EC structure: on the linear duplex templates the RNA is properly displaced from the DNA, but on the supercoiled or partially single-stranded templates an extended RNA:DNA hybrid makes a larger contribution to the conformational state of the EC. The halted EC can therefore exist either in a conformation in which the RNA is displaced from the DNA and forms an interaction with the RNAP, or in a conformation in which a more extended RNA:DNA hybrid is present and the RNA:RNAP interaction is less extensive. The partitioning between these competing conformations appears to be a function of the energetics of template reannealing and the relative strengths of the RNA:RNAP interaction and the RNA:DNA hybrid.     

It's all in the timing: Modeling isovolumic contraction through development and disease with a dynamic dual electromechanical bioreactor system

This commentary discusses the rationale behind our recently reported work entitled “Mimicking isovolumic contraction with combined electromechanical stimulation improves the development of engineered cardiac constructs,” introduces new data supporting our hypothesis, and discusses future applications of our bioreactor system. The ability to stimulate engineered cardiac tissue in a bioreactor system that combines both electrical and mechanical stimulation offers a unique opportunity to simulate the appropriate dynamics between stretch and contraction and model isovolumic contraction in vitro. Our previous study demonstrated that combined electromechanical stimulation that simulated the timing of isovolumic contraction in healthy tissue improved force generation via increased contractile and calcium handling protein expression and improved hypertrophic pathway activation. In new data presented here, we further demonstrate that modification of the timing between electrical and mechanical stimulation to mimic a non-physiological process negatively impacts the functionality of the engineered constructs. We close by exploring the various disease states that have altered timing between the electrical and mechanical stimulation signals as potential future directions for the use of this system.     

Three-dimensional finite element modeling of skeletal muscle using a two-domain approach: linked fiber-matrix mesh model

In previous applications of the finite element method in modeling mechanical behavior of skeletal muscle, the passive and active properties of muscle tissue were lumped in one finite element. Although this approach yields increased understanding of effects of force transmission, it does not support an assessment of the interaction between the intracellular structures and extracellular matrix. In the present study, skeletal muscle is considered in two domains: (1) the intracellular domain and (2) extracellular matrix domain. The two domains are represented by two separate meshes that are linked elastically to account for the trans-sarcolemmal attachments of the muscle fibers' cytoskeleton and extracellular matrix. With this approach a finite element skeletal muscle model is developed, which allows force transmission between these domains with the possibility of investigating their interaction as well as the role of the trans-sarcolemmal systems. The model is applied to show the significance of myofascial force transmission by investigating possible mechanical consequences due to any missing link within the trans-sarcolemmal connections such as found in muscular dystrophies. This is realized by making the links between the two meshes highly compliant at selected intramuscular locations. The results indicate the role of extracellular matrix for a muscle in sustaining its physiological condition. It is shown that if there is an inadequate linking to the extracellular matrix, the myofibers become deformed beyond physiological limits due to the lacking of mechanical support and impairment of a pathway of force transmission by the extracellular matrix. This leads to calculation of a drop of muscle force and if the impairment is located more towards the center of the muscle model, its effects are more pronounced. These results indicate the significance of non-myotendinous force transmission pathways.     

Pharmacophore-based discovery of triaryl-substituted imidazole as new telomeric G-quadruplex ligand

Discovery of potent and selective ligands for telomeric G-quadruplex DNA is a challenging work. Through a combination approach of pharmacophore model construction, model validation, database virtual screening, chemical synthesis and interaction evaluation, we discovered and confirmed triaryl-substituted imidazole TSIZ01 to be a new telomeric G-quadruplex ligand with potent binding and stabilizing activity to G-quadruplex DNA, as well as a 8.7-fold selectivity towards telomeric G-quadruplex DNA over duplex DNA.     

Model for T-antigen-dependent melting of the simian virus 40 core origin based on studies of the interaction of the beta-hairpin with DNA

The interaction of simian virus 40 (SV40) T antigen (T-ag) with the viral origin has served as a model for studies of site-specific recognition of a eukaryotic replication origin and the mechanism of DNA unwinding. These studies have revealed that a motif termed the "beta-hairpin" is necessary for assembly of T-ag on the SV40 origin. Herein it is demonstrated that residues at the tip of the "beta-hairpin" are needed to melt the origin-flanking regions and that the T-ag helicase domain selectively assembles around one of the newly generated single strands in a manner that accounts for its 3'-to-5' helicase activity. Furthermore, T-ags mutated at the tip of the "beta-hairpin" are defective for oligomerization on duplex DNA; however, they can assemble on hybrid duplex DNA or single-stranded DNA (ssDNA) substrates provided the strand containing the 3' extension is present. Collectively, these experiments indicate that residues at the tip of the beta-hairpin generate ssDNA in the core origin and that the ssDNA is essential for subsequent oligomerization events.     

The Motif of Human Cardiac Myosin-binding Protein C Is Required for Its Ca2+-dependent Interaction with Calmodulin

The N-terminal modules of cardiac myosin-binding protein C (cMyBP-C) play a regulatory role in mediating interactions between myosin and actin during heart muscle contraction. The so-called "motif," located between the second and third immunoglobulin modules of the cardiac isoform, is believed to modulate contractility via an "on-off" phosphorylation-dependent tether to myosin ΔS2. Here we report a novel Ca(2+)-dependent interaction between the motif and calmodulin (CaM) based on the results of a combined fluorescence, NMR, and light and x-ray scattering study. We show that constructs of cMyBP-C containing the motif bind to Ca(2+)/CaM with a moderate affinity (K(D) ～10 μm), which is similar to the affinity previously determined for myosin ΔS2. However, unlike the interaction with myosin ΔS2, the Ca(2+)/CaM interaction is unaffected by substitution with a triphosphorylated motif mimic. Further, Ca(2+)/CaM interacts with the highly conserved residues (Glu(319)-Lys(341)) toward the C-terminal end of the motif. Consistent with the Ca(2+) dependence, the binding of CaM to the motif is mediated via the hydrophobic clefts within the N- and C-lobes that are known to become more exposed upon Ca(2+) binding. Overall, Ca(2+)/CaM engages with the motif in an extended clamp configuration as opposed to the collapsed binding mode often observed in other CaM-protein interactions. Our results suggest that CaM may act as a structural conduit that links cMyBP-C with Ca(2+) signaling pathways to help coordinate phosphorylation events and synchronize the multiple interactions between cMyBP-C, myosin, and actin during the heart muscle contraction.