Multiscale modeling of twitch contractions in cardiac trabeculae

© 2021 Mijailovich et al. Understanding the dynamics of a cardiac muscle twitch contraction is complex because it requires a detailed understanding of the kinetic processes of the Ca2+ transient, thin-filament activation, and the myosin-actin cross-bridge chemomechanical cycle. Each of these steps has been well defined individually, but understanding how all three of the processes operate in combination is a far more complex problem. Computational modeling has the potential to provide detailed insight into each of these processes, how the dynamics of each process affect the complexity of contractile behavior, and how perturbations such as mutations in sarcomere proteins affect the complex interactions of all of these processes. The mechanisms involved in relaxation of tension during a cardiac twitch have been particularly difficult to discern due to nonhomogeneous sarcomere lengthening during relaxation. Here we use the multiscale MUSICO platform to model rat trabecular twitches. Validation of computational models is dependent on being able to simulate different experimental datasets, but there has been a paucity of data that can provide all of the required parameters in a single experiment, such as simultaneous measurements of force, intracellular Ca2+ transients, and sarcomere length dynamics. In this study, we used data from different studies collected under similar experimental conditions to provide information for all the required parameters. Our simulations established that twitches either in an isometric sarcomere or in fixed-length, multiple-sarcomere trabeculae replicate the experimental observations if models incorporate a length-tension relationship for the nonlinear series elasticity of muscle preparations and a scheme for thick-filament regulation. The thick-filament regulation assumes an off state in which myosin heads are parked onto the thick-filament backbone and are unable to interact with actin, a state analogous to the super-relaxed state. Including these two mechanisms provided simulations that accurately predict twitch contractions over a range of different conditions

Coupling biochemistry and mechanics in cell adhesion: a model for inhomogeneous stress fiber contraction

Biochemistry and mechanics are closely coupled in cell adhesion. At sites of cell-matrix adhesion, mechanical force triggers signaling through the Rho-pathway, which leads to structural reinforcement and increased contractility in the actin cytoskeleton. The resulting force acts back to the sites of adhesion, resulting in a positive feedback loop for mature adhesion. Here we model this biochemical-mechanical feedback loop for the special case when the actin cytoskeleton is organized in stress fibers, which are contractile bundles of actin filaments. Activation of myosin II molecular motors through the Rho-pathway is described by a system of reaction-diffusion equations, which are coupled into a viscoelastic model for a contractile actin bundle. We find strong spatial gradients in the activation of contractility and in the corresponding deformation pattern of the stress fiber, in good agreement with experimental findings.Comment: Revtex, 35 pages, 13 Postscript figures included, in press with New Journal of Physics, Special Issue on The Physics of the Cytoskeleto

Interactions between Connected Half-Sarcomeres Produce Emergent Mechanical Behavior in a Mathematical Model of Muscle

Most reductionist theories of muscle attribute a fiber's mechanical properties to the scaled behavior of a single half-sarcomere. Mathematical models of this type can explain many of the known mechanical properties of muscle but have to incorporate a passive mechanical component that becomes ∼300% stiffer in activating conditions to reproduce the force response elicited by stretching a fast mammalian muscle fiber. The available experimental data suggests that titin filaments, which are the mostly likely source of the passive component, become at most ∼30% stiffer in saturating Ca2+ solutions. The work described in this manuscript used computer modeling to test an alternative systems theory that attributes the stretch response of a mammalian fiber to the composite behavior of a collection of half-sarcomeres. The principal finding was that the stretch response of a chemically permeabilized rabbit psoas fiber could be reproduced with a framework consisting of 300 half-sarcomeres arranged in 6 parallel myofibrils without requiring titin filaments to stiffen in activating solutions. Ablation of inter-myofibrillar links in the computer simulations lowered isometric force values and lowered energy absorption during a stretch. This computed behavior mimics effects previously observed in experiments using muscles from desmin-deficient mice in which the connections between Z-disks in adjacent myofibrils are presumably compromised. The current simulations suggest that muscle fibers exhibit emergent properties that reflect interactions between half-sarcomeres and are not properties of a single half-sarcomere in isolation. It is therefore likely that full quantitative understanding of a fiber's mechanical properties requires detailed analysis of a complete fiber system and cannot be achieved by focusing solely on the properties of a single half-sarcomere

Soft Substrates Promote Homogeneous Self-Renewal of Embryonic Stem Cells via Downregulating Cell-Matrix Tractions

Maintaining undifferentiated mouse embryonic stem cell (mESC) culture has been a major challenge as mESCs cultured in Leukemia Inhibitory Factor (LIF) conditions exhibit spontaneous differentiation, fluctuating expression of pluripotency genes, and genes of specialized cells. Here we show that, in sharp contrast to the mESCs seeded on the conventional rigid substrates, the mESCs cultured on the soft substrates that match the intrinsic stiffness of the mESCs and in the absence of exogenous LIF for 5 days, surprisingly still generated homogeneous undifferentiated colonies, maintained high levels of Oct3/4, Nanog, and Alkaline Phosphatase (AP) activities, and formed embryoid bodies and teratomas efficiently. A different line of mESCs, cultured on the soft substrates without exogenous LIF, maintained the capacity of generating homogeneous undifferentiated colonies with relatively high levels of Oct3/4 and AP activities, up to at least 15 passages, suggesting that this soft substrate approach applies to long term culture of different mESC lines. mESC colonies on these soft substrates without LIF generated low cell-matrix tractions and low stiffness. Both tractions and stiffness of the colonies increased with substrate stiffness, accompanied by downregulation of Oct3/4 expression. Our findings demonstrate that mESC self-renewal and pluripotency can be maintained homogeneously on soft substrates via the biophysical mechanism of facilitating generation of low cell-matrix tractions

Reinforcement versus Fluidization in Cytoskeletal Mechanoresponsiveness

Every adherent eukaryotic cell exerts appreciable traction forces upon its substrate. Moreover, every resident cell within the heart, great vessels, bladder, gut or lung routinely experiences large periodic stretches. As an acute response to such stretches the cytoskeleton can stiffen, increase traction forces and reinforce, as reported by some, or can soften and fluidize, as reported more recently by our laboratory, but in any given circumstance it remains unknown which response might prevail or why. Using a novel nanotechnology, we show here that in loading conditions expected in most physiological circumstances the localized reinforcement response fails to scale up to the level of homogeneous cell stretch; fluidization trumps reinforcement. Whereas the reinforcement response is known to be mediated by upstream mechanosensing and downstream signaling, results presented here show the fluidization response to be altogether novel: it is a direct physical effect of mechanical force acting upon a structural lattice that is soft and fragile. Cytoskeletal softness and fragility, we argue, is consistent with early evolutionary adaptations of the eukaryotic cell to material properties of a soft inert microenvironment

On the theory of muscle contraction: filament extensibility and the development of isometric force and stiffness.

The newly discovered extensibility of actin and myosin filaments challenges the foundation of the theory of muscle mechanics. We have reformulated A. F. Huxley's sliding filament theory to explicitly take into account filament extensibility. During isometric force development, growing cross-bridge tractions transfer loads locally between filaments, causing them to extend and, therefore, to slide locally relative to one another. Even slight filament extensibility implies that 1) relative displacement between the two must be nonuniform along the region of filament overlap, 2) cross-bridge strain must vary systematically along the overlap region, and importantly, 3) the local shortening velocities, even at constant overall sarcomere length, reduce force below the level that would have developed if the filaments had been inextensible. The analysis shows that an extensible filament system with only two states (attached and detached) displays three important characteristics: 1) muscle stiffness leads force during force development; 2) cross-bridge stiffness is significantly higher than previously assessed by inextensible filament models; and 3) stiffness is prominently dissociated from the number of attached cross-bridges during force development. The analysis also implies that the local behavior of one myosin head must depend on the state of neighboring attachment sites. This coupling occurs exclusively through local sliding velocities, which can be significant, even during isometric force development. The resulting mechanical cooperativity is grounded in fiber mechanics and follows inevitably from filament extensibility