Spontaneous and propagated contractions in rat cardiac trabeculae

Sarcomere length measurement by microscopic and laser diffraction techniques in trabeculae of rat heart, superfused with Krebs-Henseleit solution at 21 degrees C, showed spontaneous local sarcomere shortening after electrically stimulated twitches. The contractions originated in a region of several hundred micrometers throughout the width of the muscle close to the end of the preparation that was damaged by dissection. The contractions propagated at a constant velocity along the trabeculae. The velocity of propagation increased from 0 to 10 mm/s in proportion to the number of stimuli (3-30) in a train of electrically evoked twitches at 2 Hz and at an external calcium ion concentration ([Ca++]o) of 1.5 mM. At a constant number of stimuli (n), the velocity of propagation increased from 0 to 15 mm/s with [Ca++]o increasing from 1 to 7 mM. In addition, increase of n and [Ca++]o led to an increase of the extent of local sarcomere shortening during the spontaneous contractions, and the occurrence of multiple contractions. Spontaneous contractions with much internal shortening and a high velocity of propagation frequently induced spontaneous synchronized contractions and eventually arrhythmias. Propagation of spontaneous contractions at low and variable velocity is consistent with the hypothesis that calcium leakage into damaged cells causes spontaneous calcium release from the overloaded sarcoplasmic reticulum in the damaged cells. This process propagates as a result of diffusion of calcium into adjacent cells, which triggers calcium release from their sarcoplasmic reticulum. We postulate that the propagation velocity depends on the intracellular calcium ion concentration, with increases with n and [Ca++]o.     

Spontaneous contractions in rat cardiac trabeculae. Trigger mechanism and propagation velocity

It has previously been observed that spontaneous contractions start in a region of damage of isolated right ventricular trabeculae of rat, propagate along the muscle, and induce triggered arrhythmias (Mulder, B.J.M., P.P. de Tombe, and H.E.D.J. ter Keurs. 1989. J. Gen. Physiol. 93:943-961). The present study was designed to analyze the mechanisms that lead to triggered propagated contractions (TPCs). TPCs were elicited in 29 trabeculae by stimulation with trains (2 Hz; 15-s intervals) at varied number of stimuli (n), lowered temperature (19-21 degrees C), and varied [Ca++]o (1.5-4 mM) in the superfusate. Length (SL) and shortening of sarcomeres in the muscle were measured at two sites using laser diffraction techniques; twitch force (Ft) was measured with a silicon strain gauge. Time between the last stimulus in the train and the onset of sarcomere shortening due to a TPC at a site close to the damaged end region (latency) and propagation velocity of the contraction (Vprop) were correlated with Ft. For 10 trabeculae, TPCs were calculated to start in the end region itself 586 +/- 28 ms (mean +/- 1 SEM) after the last stimulus of a train (n = 15; [Ca++]o: 1.5 mM), i.e., at the end of or after the rapid release of the damaged end during twitch relaxation. When Ft was increased by increasing either SL prior to stimulation or the afterload during twitches, methods that do not affect intracellular calcium levels, latency decreased, but Vprop remained constant. No TPC occurred when Ft was less than 20% of maximal Ft. Both increasing [Ca++]o and n increased Ft to a maximum, increased Vprop progressively (maximum Vprop, 17 mm/s), but decreased latency. These observations suggest that initiation of TPCs depends on the force developed by the preceding twitch, and therefore on the degree of stretch and subsequent rapid release of damaged areas in the myocardium, while Vprop along the trabeculae is determined by intracellular calcium concentration.     

Interfilament spacing is preserved during sarcomere length isometric contractions in rat cardiac trabeculae

It is generally assumed that the myofilament lattice in intact (i.e., nonskinned) striated muscle obeys constant volume. However, whether such is the case during the myocardial contraction is unknown. Accordingly, we measured interfilament spacing by x-ray diffraction in ultra-thin isolated rat right ventricular trabeculae during a short 10 ms shuttered exposure either just before electrical stimulation (diastole), or at the peak of the contraction (systole); sarcomere length (SL) was held constant throughout the contraction using an iterative feedback control system. SL was thus varied in a series of SL-clamped contractions; the relationship between SL and interfilament spacing was not different between diastole and systole within 1%; this was true also over a wide range of inotropic states induced by varied [Ca(2+)](o). We conclude that the cardiac myofilament lattice maintains constant volume, and thus constant interfilament spacing, during contraction.     

Stretch and quick release of rat cardiac trabeculae accelerates Ca2+ waves and triggered propagated contractions

Rapid shortening of active cardiac muscle [quick release (QR)] dissociates Ca2+ from myofilaments. We studied, using muscle stretches and QR, whether Ca2+ dissociation affects triggered propagated contractions (TPCs) and Ca2+ waves. The intracellular Ca2+ concentration was measured by a SIT camera in right ventricular trabeculae dissected from rat hearts loaded with fura 2 salt, force was measured by a silicon strain gauge, and sarcomere length was measured by laser diffraction while a servomotor controlled muscle length. TPCs (n = 27) were induced at 28 degrees C by stimulus trains (7.5 s at 2.65 +/- 0.13 Hz) at an extracellular Ca2+ concentration ([Ca2+]o) = 2.0 mM or with 10 microM Gd3+ at [Ca2+]o = 5.2 +/- 0.73 mM. QR during twitch relaxation after a 10% stretch for 100-200 ms reduced both the time between the last stimulus and the peak TPC (PeakTPC) and the time between the last stimulus and peak Ca2+ wave (PeakCW) and increased PeakTPC and PeakCW (n = 13) as well as the propagation velocity (Vprop; n = 8). Active force during stretch also increased Vprop (r = 0.84, n = 12, P < 0.01), but Gd3+ had no effect (n = 5). These results suggest that Ca2+ dissociation by QR during relaxation accelerates the initiation and propagation of Ca2+ waves.     

Multiscale agent-based cancer modeling

Agent-based modeling (ABM) is an in silico technique that is being used in a variety of research areas such as in social sciences, economics and increasingly in biomedicine as an interdisciplinary tool to study the dynamics of complex systems. Here, we describe its applicability to integrative tumor biology research by introducing a multi-scale tumor modeling platform that understands brain cancer as a complex dynamic biosystem. We summarize significant findings of this work, and discuss both challenges and future directions for ABM in the field of cancer research.     

Multiscale modeling of nucleosome dynamics

Nucleosomes form the fundamental building blocks of chromatin. Subtle modifications of the constituent histone tails mediate chromatin stability and regulate gene expression. For this reason, it is important to understand structural dynamics of nucleosomes at atomic levels. We report a novel multiscale model of the fundamental chromatin unit, a nucleosome, using a simplified model for rapid discrete molecular dynamics simulations and an all-atom model for detailed structural investigation. Using a simplified structural model, we perform equilibrium simulations of a single nucleosome at various temperatures. We further reconstruct all-atom nucleosome structures from simulation trajectories. We find that histone tails bind to nucleosomal DNA via strong salt-bridge interactions over a wide range of temperatures, suggesting a mechanism of chromatin structural organization whereby histone tails regulate inter- and intranucleosomal assemblies via binding with nucleosomal DNA. We identify specific regions of the histone core H2A/H2B-H4/H3-H3/H4-H2B/H2A, termed “cold sites”, which retain a significant fraction of contacts with adjoining residues throughout the simulation, indicating their functional role in nucleosome organization. Cold sites are clustered around H3-H3, H2A-H4 and H4-H2A interhistone interfaces, indicating the necessity of these contacts for nucleosome stability. Essential dynamics analysis of simulation trajectories shows that bending across the H3-H3 is a prominent mode of intranucleosomal dynamics. We postulate that effects of salts on mononucleosomes can be modeled in discrete molecular dynamics by modulating histone-DNA interaction potentials. Local fluctuations in nucleosomal DNA vary significantly along the DNA sequence, suggesting that only a fraction of histone-DNA contacts make strong interactions dominating mononucleosomal dynamics. Our findings suggest that histone tails have a direct functional role in stabilizing higher-order chromatin structure, mediated by salt-bridge interactions with adjacent DNA.     

Multiscale modeling of macromolecular biosystems

In this article, we review the recent progress in multiresolution modeling of structure and dynamics of protein, RNA and their complexes. Many approaches using both physics-based and knowledge-based potentials have been developed at multiple granularities to model both protein and RNA. Coarse graining can be achieved not only in the length, but also in the time domain using discrete time and discrete state kinetic network models. Models with different resolutions can be combined either in a sequential or parallel fashion. Similarly, the modeling of assemblies is also often achieved using multiple granularities. The progress shows that a multiresolution approach has considerable potential to continue extending the length and time scales of macromolecular modeling.     

The collagenous microstructure of cardiac ventricular trabeculae carneae

Cardiac ventricular trabeculae are widely used in the study of cardiac muscle function, primarily because their myocytes are axially-aligned. However, their collagen content has not been rigorously determined. In particular, it is unknown whether the content of collagen differs between specimens originating from the left (LV) and right (RV) ventricles and whether, indeed, either corresponds to the collagen content of the ventricular walls themselves. In order to redress this deficit of knowledge, we have used the techniques of fluorescence confocal microscopy and environmental scanning electron microscopy to quantify the proportion of perimysial collagen comprising the cross-sectional area of trabeculae carneae. In trabeculae from both the RV and LV of adult rat hearts, collagen may occupy as little as 1% or as much as 100% of the cross-section. For specimens of dimensions typically used experimentally, there was no difference in average collagen content (6.03 ± 5.14%, n = 33) of preparations from the two ventricles.     

Multiscale modeling of calcium cycling in cardiac ventricular myocyte: macroscopic consequences of microscopic dyadic function

In cardiac ventricular myocytes, calcium (Ca) release occurs at distinct structures (dyads) along t-tubules, where L-type Ca channels (LCCs) appose sarcoplasmic reticulum (SR) Ca release channels (RyR2s). We developed a model of the cardiac ventricular myocyte that simulates local stochastic Ca release processes. At the local Ca release level, the model reproduces Ca spark properties. At the whole-cell level, the model reproduces the action potential, Ca currents, and Ca transients. Changes in microscopic dyadic properties (e.g., during detubulation in heart failure) affect whole-cell behavior in complex ways, which we investigated by simulating changes in the dyadic volume and number of LCCs/RyR2s in the dyad, and effects of calsequestrin (CSQN) as a Ca buffer (CSQN buffer) or a luminal Ca sensor (CSQN regulator). We obtained the following results: 1), Increased dyadic volume and reduced LCCs/RyR2s decrease excitation-contraction coupling gain and cause asynchrony of SR Ca release, and interdyad coupling partially compensates for the reduced synchrony. 2), Impaired CSQN buffer depresses Ca transients without affecting the synchrony of SR Ca release. 3), When CSQN regulator function is impaired, interdyad coupling augments diastolic Ca release activity to form Ca waves and long-lasting Ca release events.     

Variability in the interpolated twitch torque for maximal and submaximal voluntary contractions.

The superimposed twitch technique is frequently used to study the degree of motor unit activation during voluntary effort. This technique is one of the preferred methods to determine the activation deficit (AD) in normal, athletic, and patient populations. One of the limitations of the superimposed twitch technique is its variability under given contractile conditions. The objective of this research was to determine the source(s) of variability in the superimposed twitch force (STF) for repeat measurements. We hypothesized that the variability in the AD measurements may be caused by the timing of the twitch force relative to the onset of muscle activation, by force transients during the twitch application, by small variations in the actual force from the nominal target force, and by variations in the resting twitch force. Twenty-eight healthy subjects participated in this study. Sixteen of these subjects participated in a protocol involving contractions at 50% of their maximal voluntary contraction (MVC) effort, whereas the remaining 12 participated in a protocol involving contractions at 100% of their MVC. Doublet-twitch stimuli were superimposed onto the 50 and 100% effort knee extensor muscle contractions, and the resting twitch forces, voluntary knee extensor forces, and STFs were then measured. The mean resting twitch forces obtained before and after 8 s of 50% of MVC were the same. Similarly, the mean STFs determined at 1, 3, 5, and 7 s into the 50% MVC were the same. The variations in twitch force were significantly smaller after accounting for the actual force at twitch application than those calculated from the prescribed forces during the 50% MVC protocol (P < 0.05). Furthermore, the AD and the actual force showed statistically significant negative correlations for the 50% MVC tests. The interpolated twitch torque determined for the maximal effort contractions ranged from 1 to 70%. In contrast to the protocol at 50% of MVC, negative correlations were only observed in 5 of the 12 subjects during the 100% effort contractions. These results suggest that small variations in the actual force from the target force can account for the majority of the variations in the STFs for submaximal but not maximal effort contractions. For the maximal effort contractions, large variations in the STF exist due to undetermined causes.     

Effect of transient stretch on intracellular Ca2+ during triggered propagated contractions in intact trabeculae

Transient stretch of cardiac muscle during a twitch contraction may dissociate Ca2+ from myofilaments into the cytosol at the moment of quick release of the muscle. We studied the effect of stretch and quick release of trabeculae on changes in intracellular Ca2+ ([Ca2+]i) during triggered propagated contractions (TPCs). Trabeculae were dissected from the right ventricle of 9 rat hearts. [Ca2+]i was measured using electrophoretically injected fura-2. Force was measured using a silicon strain gauge and sarcomere length was measured using laser diffraction techniques. Reproducible TPCs (n = 13) were induced by trains of electrical stimuli (378 +/- 19 ms interval) for 7.5 s at [Ca2+]o of 2.0 mM (27.9 +/- 0.2 degrees C). The latency of the TPC force and the underlying increase in [Ca2+]i was calculated from the time (TimeF) between the last stimulus and the peak of TPC force (PeakF), or the time (TimeCa) between the last stimulus and the peak of the increase in [Ca2+]i during the TPCs (PeakCa). As a result of a 10% increase in muscle length for 150-200 ms during the last stimulated twitches, TimeF and TimeCa decreased and PeakF and PeakCa increased significantly (n = 13). In addition, transient stretch sometimes induced a twitch contraction subsequent to the accelerated TPC and its underlying increase in [Ca2+]i. These results suggest that Ca2+ binding and dissociation from the myofilaments by the stretch and quick release of muscle may modulate the TPC force and the underlying increases in [Ca2+]i and play an important role in the induction of arrhythmias.     

Multiscale modeling of growth plate cartilage mechanobiology

Biomechanics and Modeling in Mechanobiology - Growth plate chondrocytes are responsible for bone growth through proliferation and differentiation. However, the way they experience physiological...     

Multiscale modeling of lipids and lipid bilayers

A multiscale modeling approach is applied for simulations of lipids and lipid assemblies on mesoscale. First, molecular dynamics simulation of initially disordered system of lipid molecules in water within all-atomic model was carried out. On the next stage, structural data obtained from the molecular dynamics (MD) simulation were used to build a coarse-grained (ten sites) lipid model, with effective interaction potentials computed by the inverse Monte Carlo method. Finally, several simulations of the coarse-grained model on longer length- and time-scale were performed, both within Monte Carlo and molecular dynamics simulations: a periodical sample of lipid molecules ordered in bilayer, a free sheet of such bilayer without periodic boundary conditions, formation of vesicle from a plain membrane, process of self-assembly of lipids randomly dispersed in volume. It was shown that the coarse-grained model, developed exclusively from all-atomic simulation data, reproduces well all the basic features of lipids in water solution.     

Analysis of the mechanisms of mitochondrial NADH regulation in cardiac trabeculae.

We have previously shown that increased cardiac work initially caused a rapid Ca(2+)-independent fall of mitochondrial [NADH] ([NADH](m)) to a minimum level, and this was followed by a slow Ca(2+)-dependent recovery toward control level (Brandes and Bers, Biophys. J. 71:1024-1035, 1996; Brandes and Bers, Circ. Res. 80:82-87, 1997). The purpose of this study is to improve our understanding of the factors that control [NADH](m) during increased work. [NADH](m) was monitored using fluorescence spectroscopy in intact rat trabeculae isolated from the right ventricular wall. Work was increased by increasing sarcomere length, pacing frequency, external [Ca(2+)], or by decreased temperature. The results were: 1) The initial fall of [NADH](m) during increased pacing frequency depends independently on increased myofilament work and on increased Ca(2+)-transport ATPase activity. 2) The [NADH](m) recovery process depends on average cytosolic [Ca(2+)] (Av[Ca(2+)](c)), but not on absolute work level. 3) The initial fall of [NADH](m) and the [NADH](m) recovery are similar whether increased work is associated with low frequency and high Ca(2+)-transient amplitude or vice versa (at the same myofilament work level and Av[Ca(2+)](c)). 4) The mechanisms associated with the smaller fall and recovery of [NADH](m) at 37 degrees C versus 27 degrees C, may be explained by lowered Av[Ca(2+)](c) and myofilament work. The NADH control mechanisms that operate at lower temperature are thus qualitatively similar at more physiological temperatures.     

Measurement of myofilament calcium sensitivity at physiological temperature in intact cardiac trabeculae

Cardiac contraction-relaxation coupling is determined by both the free intracellular calcium concentration ([Ca2+]i) and myofilament properties. We set out to develop a technique where we could assess these parameters (twitch and steady-state force [Ca2+]i) under near physiological conditions. Bis-fura-2 was iontophorically introduced into ultrathin rat trabeculae preparations to monitor the [Ca2+]i, and steady-state contractures were achieved by using a modified Krebs-Henseleit solution containing high K+. During K+ contractures, the very slow changes in [Ca2+]i and force development were in equilibrium and allowed for the construction of a steady-state, force-[Ca2+]i relationship. Twitch contractions before and after this myofilament calcium sensitivity assessment were unaltered, and this protocol could be repeated several times. For the first time, this novel protocol allows us to measure myofilament calcium sensitivity under physiological temperature. Not only do the data so obtained allow us to assess myofilament calcium sensitivity, the data also will allow us, in the same preparation under nearly identical conditions, to compare the dynamic to the steady-state, force-calcium relationship. To test whether the steady-state relationship between force and calcium in our novel protocol reproduces expected changes, we determined this relationship in the presence of isoproterenol and under acidosis and alkalosis. As expected, beta-adrenergic stimulation resulted in an increase of calcium amplitude and twitch force and a desensitization of the myofilaments as indicated by a rightward shift of the obtained steady-state, force-calcium relationship. An increase in pH shifted the curve leftward, whereas a decrease in pH resulted in the expected rightward shift.     

Multiscale modeling and mechanics of filamentous actin cytoskeleton

The adaptive structure and functional changes of the actin cytoskeleton are induced by its mechanical behavior at various temporal and spatial scales. In particular, the mechanical behaviors at different scales play important roles in the mechanical functions of various cells, and these multiscale phenomena require clarification. To establish a milestone toward achieving multiscale modeling and simulation, this paper reviews mathematical analyses and simulation methods applied to the mechanics of the filamentous actin cytoskeleton. The actin cytoskeleton demonstrates characteristic behaviors at every temporal and spatial scale, and mathematical models and simulation methods can be applied to each level of actin cytoskeletal structure ranging from the molecular to the network level. This paper considers studies on mathematical models and simulation methods based on the molecular dynamics, coarse-graining, and continuum dynamics approaches. Every temporal and spatial scale of actin cytoskeletal structure is considered, and it is expected that discrete and continuum dynamics ranging from functional expression at the molecular level to macroscopic functional expression at the whole cell level will be developed and applied to multiscale modeling and simulation.     

Multiscale dynamic modeling and simulation of a biorefinery

A biorefinery comprises a variety of process steps to synthesize products from sustainable natural resources. Dynamic plant-wide simulation enhances the process understanding, leads to improved cost efficiency and enables model-based operation and control. It is thereby important for an increased competitiveness to conventional processes. To this end, we developed a Modelica library with replaceable building blocks that allow dynamic modeling of an entire biorefinery. For the microbial conversion step, we built on the dynamic flux balance analysis (DFBA) approach to formulate process models for the simulation of cellular metabolism under changing environmental conditions. The resulting system of differential-algebraic equations with embedded optimization criteria (DAEO) is solved by a tailor-made toolbox. In summary, our modeling framework comprises three major pillars: A Modelica library of dynamic unit operations, an easy-to-use interface to formulate DFBA process models and a DAEO toolbox that allows simulation with standard environments based on the Modelica modeling language. A biorefinery model for dynamic simulation of the OrganoCat pretreatment process and microbial conversion of the resulting feedstock by Corynebacterium glutamicum serves as case study to demonstrate its practical relevance.     

Gender comparison of contractile performance and beta-adrenergic response in isolated rat cardiac trabeculae

It is known that gender can affect susceptibility to development of various cardiomyopathies. However, it is unclear whether basic mechanical contractile function of the myocardium differs between genders, whether they respond differently to stressors, or both. To test for a possible gender factor, contractile parameters of healthy, isolated myocardium were investigated under near physiological conditions. Right ventricular ultra-thin trabeculae from young adult LBN-f1 rats were electrically stimulated to isometrically contract at 37°C. No differences were found in developed force or kinetic parameters. In each muscle, the force-frequency relationship was measured at 4, 6, and 8 Hz, encompassing most of the in vivo range. Again, no differences were observed in force-frequency behavior; developed force rose from 21.6 ± 4.0 at 4 Hz to 30.3 ± 5.8 mN/mm² at 8 Hz in females and from 23.4 ± 3.4 to 29.8 ± 3.4 mN/mm² in males. The response to β-adrenergic stimulation was similar; at 1 μM isoproterenol, developed force increased to 34.5 ± 6.2 mN/mm² in females and 32.3 ± 3.2 mN/mm² in males (female vs. male, not significant). We conclude that basic mechanical performance of healthy isolated myocardium under physiological conditions is not different between males and females, and a different response to stress must underlie gender-based differences in cardiac performance.