Force-dependent recruitment from myosin OFF-state increases end-systolic pressure-volume relationship in left ventricle

Mathematical modeling of active contraction of the human cardiac myocyte: A review

Background and objective

In this present research paper, a mathematical model has been developed to study myocyte contraction in the human cardiac muscle, using the Land model. Different parts of the human heart with a focus on the composition of the myocyte cells have been explored numerically to enabling us to determine the interaction of various parameters in the heart muscle. The main objective of the work is to direct the study of the Land model, which has been exploited to simulate the contraction of real human myocytes.

Methods

Mathematical models has been developed based on the Hill model and Huxley model. Myocyte contraction for different scenarios, such as in isometric tension and isotonic tension have been studied.

Results

It is found that increase in stretch, the peak active tension increases, in line with well-established length-dependent tension generation. Five parameters are selected: [Ca2+]T50, Tref, TRPN50, β0, and β1, which have been varied in between the range of -50%-100%, to examine the isometric effects of each parameter on the behavior of the tension developed in the intact myocyte cells, with the most sensitive parameter being [Ca2+]T50.

Conclusion

In conclusion, it is found that the Land model provides a good platform for the analysis of the active contraction of the human cardiac myocyte.

Cardiac efficiency and Starling's Law of the Heart

The formulation by Starling of The Law of the Heart states that 'the [mechanical] energy of contraction, however measured, is a function of the length of the muscle fibre'. Starling later also stated that 'the oxygen consumption of the isolated heart … is determined by its diastolic volume, and therefore by the initial length of its muscular fibres'. This phrasing has motivated us to extend Starling's Law of the Heart to include consideration of the efficiency of contraction. In this study, we assessed both mechanical efficiency and crossbridge efficiency by studying the heat output of isolated rat ventricular trabeculae performing force-length work-loops over ranges of preload and afterload. The combination of preload and afterload allowed us, using our modelling frameworks for the end-systolic zone and the heat-force zone, to simulate cases by recreating physiologically feasible loading conditions. We found that across all cases examined, both work output and change of enthalpy increased with initial muscle length; hence it can only be that the former increases more than the latter to yield increased mechanical efficiency. In contrast, crossbridge efficiency increased with initial muscle length in cases where the extent of muscle shortening varied greatly with preload. We conclude that the efficiency of cardiac contraction increases with increasing initial muscle length and preload. An implication of our conclusion is that the length-dependent activation mechanism underlying the cellular basis of Starling's Law of the Heart is an energetically favourable process that increases the efficiency of cardiac contraction. KEY POINTS: Ernest Starling in 1914 formulated the Law of the Heart to describe the mechanical property of cardiac muscle whereby force of contraction increases with muscle length. He subsequently, in 1927, showed that the oxygen consumption of the heart is also a function of the length of the muscle fibre, but left the field unclear as to whether cardiac efficiency follows the same dependence. A century later, the field has gained an improved understanding of the factors, including the distinct effects of preload and afterload, that affect cardiac efficiency. This understanding presents an opportunity for us to investigate the elusive length-dependence of cardiac efficiency. We found that, by simulating physiologically feasible loading conditions using a mechano-energetics framework, cardiac efficiency increased with initial muscle length. A broader physiological importance of our findings is that the underlying cellular basis of Starling's Law of the Heart is an energetically favourable process that yields increased efficiency.

Multiscale simulations of left ventricular growth and remodeling

Cardiomyocytes can adapt their size, shape, and orientation in response to altered biomechanical or biochemical stimuli. The process by which the heart undergoes structural changes-affecting both geometry and material properties-in response to altered ventricular loading, altered hormonal levels, or mutant sarcomeric proteins is broadly known as cardiac growth and remodeling (G&R). Although it is likely that cardiac G&R initially occurs as an adaptive response of the heart to the underlying stimuli, prolonged pathological changes can lead to increased risk of atrial fibrillation, heart failure, and sudden death. During the past few decades, computational models have been extensively used to investigate the mechanisms of cardiac G&R, as a complement to experimental measurements. These models have provided an opportunity to quantitatively study the relationships between the underlying stimuli (primarily mechanical) and the adverse outcomes of cardiac G&R, i.e., alterations in ventricular size and function. State-of-the-art computational models have shown promise in predicting the progression of cardiac G&R. However, there are still limitations that need to be addressed in future works to advance the field. In this review, we first outline the current state of computational models of cardiac growth and myofiber remodeling. Then, we discuss the potential limitations of current models of cardiac G&R that need to be addressed before they can be utilized in clinical care. Finally, we briefly discuss the next feasible steps and future directions that could advance the field of cardiac G&R.

Hypertrophic cardiomyopathy β-cardiac myosin mutation (P710R) leads to hypercontractility by disrupting super relaxed state

Hypertrophic cardiomyopathy (HCM) is the most common inherited form of heart disease, associated with over 1,000 mutations, many in β-cardiac myosin (MYH7). Molecular studies of myosin with different HCM mutations have revealed a diversity of effects on ATPase and load-sensitive rate of detachment from actin. It has been difficult to predict how such diverse molecular effects combine to influence forces at the cellular level and further influence cellular phenotypes. This study focused on the P710R mutation that dramatically decreased in vitro motility velocity and actin-activated ATPase, in contrast to other MYH7 mutations. Optical trap measurements of single myosin molecules revealed that this mutation reduced the step size of the myosin motor and the load sensitivity of the actin detachment rate. Conversely, this mutation destabilized the super relaxed state in longer, two-headed myosin constructs, freeing more heads to generate force. Micropatterned human induced pluripotent derived stem cell (hiPSC)-cardiomyocytes CRISPR-edited with the P710R mutation produced significantly increased force (measured by traction force microscopy) compared with isogenic control cells. The P710R mutation also caused cardiomyocyte hypertrophy and cytoskeletal remodeling as measured by immunostaining and electron microscopy. Cellular hypertrophy was prevented in the P710R cells by inhibition of ERK or Akt. Finally, we used a computational model that integrated the measured molecular changes to predict the measured traction forces. These results confirm a key role for regulation of the super relaxed state in driving hypercontractility in HCM with the P710R mutation and demonstrate the value of a multiscale approach in revealing key mechanisms of disease.

Hypertrophic cardiomyopathy β-cardiac myosin mutation (P710R) leads to hypercontractility by disrupting super relaxed state

Hypertrophic cardiomyopathy (HCM) is the most common inherited form of heart disease, associated with over 1,000 mutations, many in β-cardiac myosin (MYH7). Molecular studies of myosin with different HCM mutations have revealed a diversity of effects on ATPase and load-sensitive rate of detachment from actin. It has been difficult to predict how such diverse molecular effects combine to influence forces at the cellular level and further influence cellular phenotypes. This study focused on the P710R mutation that dramatically decreased in vitro motility velocity and actin-activated ATPase, in contrast to other MYH7 mutations. Optical trap measurements of single myosin molecules revealed that this mutation reduced the step size of the myosin motor and the load sensitivity of the actin detachment rate. Conversely, this mutation destabilized the super relaxed state in longer, two-headed myosin constructs, freeing more heads to generate force. Micropatterned human induced pluripotent derived stem cell (hiPSC)-cardiomyocytes CRISPR-edited with the P710R mutation produced significantly increased force (measured by traction force microscopy) compared with isogenic control cells. The P710R mutation also caused cardiomyocyte hypertrophy and cytoskeletal remodeling as measured by immunostaining and electron microscopy. Cellular hypertrophy was prevented in the P710R cells by inhibition of ERK or Akt. Finally, we used a computational model that integrated the measured molecular changes to predict the measured traction forces. These results confirm a key role for regulation of the super relaxed state in driving hypercontractility in HCM with the P710R mutation and demonstrate the value of a multiscale approach in revealing key mechanisms of disease.

The Sliding Filament Theory Since Andrew Huxley: Multiscale and Multidisciplinary Muscle Research

Two groundbreaking papers published in 1954 laid out the theory of the mechanism of muscle contraction based on force-generating interactions between myofilaments in the sarcomere that cause filaments to slide past one another during muscle contraction. The succeeding decades of research in muscle physiology have revealed a unifying interest: to understand the multiscale processes-from atom to organ-that govern muscle function. Such an understanding would have profound consequences for a vast array of applications, from developing new biomimetic technologies to treating heart disease. However, connecting structural and functional properties that are relevant at one spatiotemporal scale to those that are relevant at other scales remains a great challenge. Through a lens of multiscale dynamics, we review in this article current and historical research in muscle physiology sparked by the sliding filament theory.

Diverse and complex muscle spindle afferent firing properties emerge from multiscale muscle mechanics

Despite decades of research, we lack a mechanistic framework capable of predicting how movement-related signals are transformed into the diversity of muscle spindle afferent firing patterns observed experimentally, particularly in naturalistic behaviors. Here, a biophysical model demonstrates that well-known firing characteristics of mammalian muscle spindle Ia afferents - including movement history dependence, and nonlinear scaling with muscle stretch velocity - emerge from first principles of muscle contractile mechanics. Further, mechanical interactions of the muscle spindle with muscle-tendon dynamics reveal how motor commands to the muscle (alpha drive) versus muscle spindle (gamma drive) can cause highly variable and complex activity during active muscle contraction and muscle stretch that defy simple explanation. Depending on the neuromechanical conditions, the muscle spindle model output appears to 'encode' aspects of muscle force, yank, length, stiffness, velocity, and/or acceleration, providing an extendable, multiscale, biophysical framework for understanding and predicting proprioceptive sensory signals in health and disease.

Multiscale Modeling of Cardiovascular Function Predicts That the End-Systolic Pressure Volume Relationship Can Be Targeted via Multiple Therapeutic Strategies

Most patients who develop heart failure are unable to elevate their cardiac output on demand due to impaired contractility and/or reduced ventricular filling. Despite decades of research, few effective therapies for heart failure have been developed. In part, this may reflect the difficulty of predicting how perturbations to molecular-level mechanisms that are induced by drugs will scale up to modulate system-level properties such as blood pressure. Computer modeling might help with this process and thereby accelerate the development of better therapies for heart failure. This manuscript presents a new multiscale model that uses a single contractile element to drive an idealized ventricle that pumps blood around a closed circulation. The contractile element was formed by linking an existing model of dynamically coupled myofilaments with a well-established model of myocyte electrophysiology. The resulting framework spans from molecular-level events (including opening of ion channels and transitions between different myosin states) to properties such as ejection fraction that can be measured in patients. Initial calculations showed that the model reproduces many aspects of normal cardiovascular physiology including, for example, pressure-volume loops. Subsequent sensitivity tests then quantified how each model parameter influenced a range of system level properties. The first key finding was that the End Systolic Pressure Volume Relationship, a classic index of cardiac contractility, was ∼50% more sensitive to parameter changes than any other system-level property. The second important result was that parameters that primarily affect ventricular filling, such as passive stiffness and Ca²⁺ reuptake via sarco/endoplasmic reticulum Ca²⁺-ATPase (SERCA), also have a major impact on systolic properties including stroke work, myosin ATPase, and maximum ventricular pressure. These results reinforce the impact of diastolic function on ventricular performance and identify the End Systolic Pressure Volume Relationship as a particularly sensitive system-level property that can be targeted using multiple therapeutic strategies.