Molecular mechanisms of muscle contraction: A historical perspective.

Studies of muscle structure and function can be traced to at least 2,000 years ago. However, the modern era of muscle contraction mechanisms started in the 1950s with the classic works by AF Huxley and HE Huxley, both born in the United Kingdom, but not related and working independently. HE Huxley was the first to suggest that muscle contraction occurred through the sliding of two sets of filamentous structures (actin or thin filaments and myosin or thick filaments). AF Huxley then developed a biologically inspired mathematical model suggesting a possible molecular mechanism of how this sliding of actin and myosin might take place. This model then evolved from a two-state to a multi-state model of myosin-actin interactions, and from one that suggested a linear motor causing the sliding to a rotating motor. This model, the cross-bridge model of muscle contraction, is still widely used in biomechanics, and even the more sophisticated cross-bridge models of today still contain many of the features originally proposed by AF Huxley. In 2002, we discovered a hitherto unknown property of muscle contraction that suggested the involvement of passive structures in active force production, the so-called passive force enhancement. It was quickly revealed that this passive force enhancement was caused by the filamentous protein titin, and the three-filament (actin, myosin, and titin) sarcomere model of muscle contraction evolved. There are many suggestions of how these three proteins interact to cause contraction and produce active force, and one such suggestion is described here, but the molecular details of this proposed mechanism still need careful evaluation.

Double ionophore application in cases with previous failed/low fertilization or poor embryo development.

RESEARCH QUESTION: Does a double ionophore application improve the outcome of cycles in which single ionophore application was unsuccessful? DESIGN: This retrospective intervention study (duration 4.5 years) included 79 patients with suspected chronic failed oocyte activation (<30% fertilizations) and/or poor embryo development (developmental arrest, 24 h developmental delay, blastulation rate <15%) in both preceding cycles, the first without ionophore and the second with single ionophore treatment. Within the study period, all patients with failed ionophore treatments (single applications of ready-to-use calcimycin for 15 min) were offered an adapted protocol in the subsequent cycle (study cycle) in which the same ionophore was applied twice (separated by 30 min). Tests for paired data (control and study cycle) were used to reduce the effect of confounders. RESULTS: The overall fertilization rate did not differ between the study and control cycles. Cleavage (P = 0.020) and blastocyst formation (P = 0.018) rates improved significantly in the study cycles. Implantation (P = 0.001), biochemical (P < 0.001) and clinical pregnancy (P < 0.001) rates were also significantly higher in the study cycles. The study cycles resulted in 29 live births and all 32 babies born were healthy. CONCLUSIONS: This study suggests that double ionophore application may improve blastocyst formation and clinical pregnancy rates in cases of failed single ionophore treatment, irrespective of whether the ionophore was used to overcome fertilization failure or poor embryo development. Fertilization rate was only increased in cases with a history of fertilization failure. Because single ionophore treatment was used in only one previous cycle it cannot be ruled out that some improvement in clinical outcomes would also have been achieved by using single instead of double ionophore treatment again in the subsequent attempt.

Mathematical Models of Parathyroid Gland Biology: Complexity and Clinical Use.

Altered parathyroid gland biology is a major driver of chronic kidney disease-mineral bone disorder (CKD-MBD) in patients with chronic kidney disease. CKD-MBD is associated with a high risk of vascular calcification and cardiovascular events. A hallmark of CKD-MBD is secondary hyperparathyroidism with increased parathyroid hormone (PTH) synthesis and release and reduced expression of calcium-sensing receptors on the surface of parathyroid cells and eventually hyperplasia of parathyroid gland cells. The KDIGO guidelines strongly recommend the control of PTH in hemodialysis patients. Due to the complexity of parathyroid gland biology, mathematical models have been employed to study the interaction of PTH regulators and PTH plasma concentrations. Here, we present an overview of various model approaches and discuss the impact of different model structures and complexities on the clinical use of these models.

Electromyographic and Systemic Physiological Thresholds in Single-Joint Elbow Flexion Movements.

PURPOSE: Reported relationships between electromyographic (EMG) thresholds and systemic thresholds based on lactate, ventilation, or heart rate are contradictory. This might be related to the complexity of the investigated whole-body movements involving many muscles with different activation patterns. Therefore, the aim of the study was to investigate these relationships during an incremental single-joint exercise. METHODS: Eighteen male subjects (29.7 [4.4] y) performed single-arm elbow flexions on a biceps curl machine with loads increasing every minute until exhaustion. EMG signals of the main elbow flexors (short and long head of the biceps brachii, flexor carpi radialis, and brachioradialis) as well as gas exchange variables, blood lactate concentration, and heart rate were measured, and 2 turn points based on a 3-phase model of metabolism were determined for each variable. RESULTS: The first and second turn points for EMG were determined at 32.0% to 33.1% and 64.4% to 66.5% of maximal achieved performance (maximum weight), respectively. Systemic turn points were determined at 33.3% to 34.4% and 65.9% to 66.7% of maximum weight and were not significantly different from EMG turn points. Furthermore, systemic and EMG turn points showed a strong or very strong relationship at the first (ρ = .54-.93, P < .05) and second turn point (ρ = .76-.93, P < .01). CONCLUSIONS: A close relationship between EMG and systemic turn points could be confirmed for the applied movement of a small muscle group. The determination of local single muscle thresholds using EMG provides additional muscle-specific information about performance-limiting properties of muscles involved in endurance-type incremental exercise.

Personalized Prediction of Short- and Long-Term PTH Changes in Maintenance Hemodialysis Patients.

Background: Personalized management of secondary hyperparathyroidism is a critical part of hemodialysis patient care. We used a mathematical model of parathyroid gland (PTG) biology to predict (1) short-term peridialytic intact PTH (iPTH) changes in response to diffusive calcium (Ca) fluxes and (2) to predict long-term iPTH levels. Methods: We dialyzed 26 maintenance hemodialysis patients on a single occasion with a dialysate Ca concentration of 1.75 mmol/l to attain a positive dialysate-to-blood ionized Ca (iCa) gradient and thus diffusive Ca loading. Intradialytic iCa kinetics, peridialytic iPTH change, and dialysate-sided iCa mass balance (iCaMB) were assessed. Patient-specific PTG model parameters were estimated using clinical, medication, and laboratory data. We then used the personalized PTG model to predict peridialytic and long-term (6-months) iPTH levels. Results: At dialysis start, the median dialysate-to-blood iCa gradient was 0.3 mmol/l (IQR 0.11). The intradialytic iCa gain was 488 mg (IQR 268). Median iPTH decrease was 75% (IQR 15) from pre-dialysis 277 to post-dialysis 51 pg/ml. Neither iCa gradient nor iCaMB were significantly associated with peridialytic iPTH changes. The personalized PTG model accurately predicted both short-term, treatment-level peridialytic iPTH changes (r = 0.984, p < 0.001, n = 26) and patient-level 6-months iPTH levels (r = 0.848, p < 0.001, n = 13). Conclusions: This is the first report showing that both short-term and long-term iPTH dynamics can be predicted using a personalized mathematical model of PTG biology. Prospective studies are warranted to explore further model applications, such as patient-level prediction of iPTH response to PTH-lowering treatment.

A mathematical model of the four cardinal acid-base disorders.

Precise maintenance of acid-base homeostasis is fundamental for optimal functioning of physiological and cellular processes. The presence of an acid-base disturbance can affect clinical outcomes and is usually caused by an underlying disease. It is, therefore, important to assess the acid-base status of patients, and the extent to which various therapeutic treatments are effective in controlling these acid-base alterations. In this paper, we develop a dynamic model of the physiological regulation of an HCO3-/CO2 buffering system, an abundant and powerful buffering system, using Henderson-Hasselbalch kinetics. We simulate the normal physiological state and four cardinal acidbase disorders: Metabolic acidosis and alkalosis and respiratory acidosis and alkalosis. We show that the model accurately predicts serum pH over a range of clinical conditions. In addition to qualitative validation, we compare the in silico results with clinical data on acid-base homeostasis and alterations, finding clear relationships between primary acid-base disturbances and the secondary adaptive compensatory responses. We also show that the predicted primary disturbances accurately resemble clinically observed compensatory responses. Furthermore, via sensitivity analysis, key parameters were identified which could be the most effective in regulating systemic pH in healthy individuals, and those with chronic kidney disease and distal and proximal renal tubular acidosis. The model presented here may provide pathophysiologic insights and can serve as a tool to assess the safety and efficacy of different therapeutic interventions to control or correct acid-base disorders.

A Multi-Compartment Model Capturing the Pharmacokinetics of the Calcimimetic Cinacalcet.

BACKGROUND/AIMS: Chronic kidney disease-mineral bone disorder is a major complication affecting the vast majority of chronic kidney disease patients. A hallmark of the disorder is an altered parathyroid gland biology resulting in secondary hyperparathyroidism. This condition is widely treated by calcimimetics like cinacalcet which act by allosteric activation of the calcium sensing receptor. METHODS: Here, we present a linear multi-compartment model based on physiological principles such as first-pass metabolism and protein binding, which captures all relevant pharmacokinetic parameters of cinacalcet. RESULTS: Due to the linear structure of the model, simulations are numerically stable and allow fast and accurate short or long-term predictions of cinacalcet concentrations in the body. CONCLUSION: The model compartments are physiological meaningful and can be easily adjusted to various conditions like impaired hepatic clearance or different drug administration regimens. Moreover, the model can be easily adapted to specific patient groups.

A mathematical model of parathyroid gland biology.

Altered parathyroid gland biology in patients with chronic kidney disease (CKD) is a major contributor to chronic kidney disease-mineral bone disorder (CKD-MBD). This disorder is associated with an increased risk of bone disorders, vascular calcification, and cardiovascular events. Parathyroid hormone (PTH) secretion is primarily regulated by the ionized calcium concentration as well as the phosphate concentration in the extracellular fluid and vitamin D. The metabolic disturbances in patients with CKD lead to alterations in the parathyroid gland biology. A hallmark of CKD is secondary hyperparathyroidism, characterized by an increased production and release of PTH, reduced expression of calcium-sensing and vitamin D receptors on the surface of parathyroid cells, and hyperplasia and hypertrophy of these cells. These alterations happen on different timescales and influence each other, thereby triggering a cascade of negative and positive feedback loops in a highly complex manner. Due to this complexity, mathematical models are a useful tool to break down the patterns of the multidimensional cascade of processes enabling the detailed study of subsystems. Here, we introduce a comprehensive mathematical model that includes the major adaptive mechanisms governing the production, secretion, and degradation of PTH in patients with CKD on hemodialysis. Combined with models for medications targeting the parathyroid gland, it provides a ready-to-use tool to explore treatment strategies. While the model is of particular interest for use in hemodialysis patients with secondary hyperparathyroidism, it has the potential to be applicable to other clinical scenarios such as primary hyperparathyroidism or hypo- and hypercalcemia.

Titin-mediated thick filament activation stabilizes myofibrils on the descending limb of their force-length relationship.

PURPOSE: The aim of this study was to extend current half-sarcomere models by involving a recently found force-mediated activation of the thick filament and analyze the effect of this mechanosensing regulation on the length stability of half-sarcomeres arranged in series. METHODS: We included a super-relaxed state of myosin motors and its force-dependent activation in a conventional cross-bridge model. We simulated active stretches of a sarcomere consisting of 2 non-uniform half-sarcomeres on the descending limb of the force-length relationship. RESULTS: The mechanosensing model predicts that, in a passive sarcomere on the descending limb of the force-length relationship, the longer half-sarcomere has a higher fraction of myosin motors in the on-state than the shorter half-sarcomere. The difference in the number of myosin motors in the on-state ensures that upon calcium-mediated thin filament activation, the force-dependent thick filament activation keeps differences in active force within 20% during an active stretch. In the classical cross-bridge model, the corresponding difference exceeds 80%, leading to great length instabilities. CONCLUSION: Our simulations suggest that, in contrast to the classical cross-bridge model, the mechanosensing regulation is able to stabilize a system of non-uniform half-sarcomeres arranged in series on the descending limb of the force-length relationship.

Differences in titin segmental elongation between passive and active stretch in skeletal muscle.

Since the 1950s, muscle contraction has been explained using a two-filament system in which actin and myosin exclusively dictate active force in muscle sarcomeres. Decades later, a third filament called titin was discovered. This titin filament has recently been identified as an important regulator of active force, but has yet to be incorporated into contemporary theories of muscle contraction. When sarcomeres are actively stretched, a substantial and rapid increase in force occurs, which has been suggested to arise in part from titin-actin binding that is absent in passively stretched sarcomeres. However, there is currently no direct evidence for such binding within muscle sarcomeres. Therefore, we aimed to determine whether titin binds to actin in actively but not in passively stretched sarcomeres by observing length changes of proximal and distal titin segments in the presence and absence of calcium. We labeled I-band titin with fluorescent F146 antibody in rabbit psoas myofibrils and tracked segmental elongations during passive (no calcium) and active (high calcium) stretch. Without calcium, proximal and distal segments of titin elongated as expected based on their free spring properties. In contrast, active stretch differed statistically from passive stretch, demonstrating that calcium activation increases titin segment stiffness, but not in an actin-dependent manner. The consistent elongation of the proximal segment was contrary to what was expected if titin's proximal segment was attached to actin. This rapid calcium-dependent change in titin stiffness likely contributes to active muscle force regulation in addition to actin and myosin.

An in silico method to predict net calcium transfer during hemodialysis.

International guidelines for chronic hemodialysis patients suggest a dialysate calcium concentration between 1.25 and 1.5 mmol/L. However, it is not certain if these dialysate calcium levels result in net calcium transfer into the patient. With ubiquitous prevalence of vascular calcification in hemodialysis patients, it is pertinent to model the mass balance of calcium during dialysis. To this end, we developed a two compartmental patient model and spatiotemporal representation of dialyzer model to investigate and quantify the calcium mass balance during dialysis. The model accounts for calcium-albumin binding and varying protein concentration; the latter accounts for the Gibbs-Donnan effect. The model simulations suggest that despite a lower dialysate calcium concentration of 1.25 mmol/L, some of our patients may be loaded with calcium during dialysis. This net calcium flux from dialysate to blood side may be a potential contributor to vascular calcification, a primary cause of cardiovascular mortality in hemodialysis patients.

Computing Average Passive Forces in Sarcomeres in Length-Ramp Simulations.

Passive forces in sarcomeres are mainly related to the giant protein titin. Titin's extensible region consists of spring-like elements acting in series. In skeletal muscles these elements are the PEVK segment, two distinct immunoglobulin (Ig) domain regions (proximal and distal), and a N2A portion. While distal Ig domains are thought to form inextensible end filaments in intact sarcomeres, proximal Ig domains unfold in a force- and time-dependent manner. In length-ramp experiments of single titin strands, sequential unfolding of Ig domains leads to a typical saw-tooth pattern in force-elongation curves which can be simulated by Monte Carlo simulations. In sarcomeres, where more than a thousand titin strands are arranged in parallel, numerous Monte Carlo simulations are required to estimate the resultant force of all titin filaments based on the non-uniform titin elongations. To simplify calculations, the stochastic model of passive forces is often replaced by linear or non-linear deterministic and phenomenological functions. However, new theories of muscle contraction are based on the hypothesized binding of titin to the actin filament upon activation, and thereby on a prominent role of the structural properties of titin. Therefore, these theories necessitate a detailed analysis of titin forces in length-ramp experiments. In our study we present a simple and efficient alternative to Monte Carlo simulations. Based on a structural titin model, we calculate the exact probability distributions of unfolded Ig domains under length-ramp conditions needed for rigorous analysis of expected forces, distribution of unfolding forces, etc. Due to the generality of our model, the approach is applicable to a wide range of stochastic protein unfolding problems.

Quantitative and qualitative trophectoderm grading allows for prediction of live birth and gender.

PURPOSE: Prolonged in vitro culture is thought to affect pre- and postnatal development of the embryo. This prospective study was set up to determine whether quality/size of inner cell mass (ICM) (from which the fetus ultimately develops) and trophectoderm (TE) (from which the placenta ultimately develops) is reflected in birth and placental weight, healthy live-birth rate, and gender after fresh and frozen single blastocyst transfer. METHODS: In 225 patients, qualitative scoring of blastocysts was done according to the criteria expansion, ICM, and TE appearance. In parallel, all three parameters were quantified semi-automatically. RESULTS: TE quality and cell number were the only parameters that predicted treatment outcome. In detail, pregnancies that continued on to a live birth could be distinguished from those pregnancies that aborted on the basis of TE grade and cell number. Male blastocysts had a 2.53 higher chance of showing TE of quality A compared to female ones. There was no correlation between the appearance of both cell lineages and birth or placental weight, respectively. CONCLUSIONS: The presented correlation of TE with outcome indicates that TE scoring could replace ICM scoring in terms of priority. This would automatically require a rethinking process in terms of blastocyst selection and cryopreservation strategy.

A novel three-filament model of force generation in eccentric contraction of skeletal muscles.

We propose and examine a three filament model of skeletal muscle force generation, thereby extending classical cross-bridge models by involving titin-actin interaction upon active force production. In regions with optimal actin-myosin overlap, the model does not alter energy and force predictions of cross-bridge models for isometric contractions. However, in contrast to cross-bridge models, the three filament model accurately predicts history-dependent force generation in half sarcomeres for eccentric and concentric contractions, and predicts the activation-dependent forces for stretches beyond actin-myosin filament overlap.

Viability of cumulus cells is associated with basal AMH levels in assisted reproduction.

OBJECTIVE(S): An interesting non-invasive approach to select embryos for transfer is analyzing the health state of somatic granulosa cells surrounding the oocyte addressing their mutual dependence. This prospective study was set up to analyse whether the DNA integrity of cumulus cells correlates with preimplantation development and basal AMH levels. STUDY DESIGN: Therefore, 56 patients who gave written consent were enrolled. Sequential denudation of the cumulus-oocyte-complexes was performed in order to separate corona radiata from outer cumulus cells. DNA integrity of both cell types was analysed using a modified chromatin dispersion test. RESULTS: The percentage of viable corona radiata cells per patient showed a linear correlation to blastulation (P<0.05). These innermost cells showed significantly lower rates of strand breaks (P<0.01) as compared to outer cumulus cells. Age-corrected AMH was significantly associated with the DNA integrity of outer cumulus cells (P<0.05). CONCLUSION(S): For the first time it could be shown that in fact clinical embryologists deal with two different entities of cumulus cells, inner and outer ones. It seems that any protective mechanism of the female gamete follows an outward gradient, so that negative effects, e.g. apoptosis, may impair outer cumulus cells first. Age-corrected AMH reflects quality of these outer cumulus cells. KEYWORDS: AMH; Corona radiata cells; DNA fragmentation; Outer cumulus cells; SCD test.

Titin force is enhanced in actively stretched skeletal muscle.

The sliding filament theory of muscle contraction is widely accepted as the means by which muscles generate force during activation. Within the constraints of this theory, isometric, steady-state force produced during muscle activation is proportional to the amount of filament overlap. Previous studies from our laboratory demonstrated enhanced titin-based force in myofibrils that were actively stretched to lengths which exceeded filament overlap. This observation cannot be explained by the sliding filament theory. The aim of the present study was to further investigate the enhanced state of titin during active stretch. Specifically, we confirm that this enhanced state of force is observed in a mouse model and quantify the contribution of calcium to this force. Titin-based force was increased by up to four times that of passive force during active stretch of isolated myofibrils. Enhanced titin-based force has now been demonstrated in two distinct animal models, suggesting that modulation of titin-based force during active stretch is an inherent property of skeletal muscle. Our results also demonstrated that 15% of the enhanced state of titin can be attributed to direct calcium effects on the protein, presumably a stiffening of the protein upon calcium binding to the E-rich region of the PEVK segment and selected Ig domain segments. We suggest that the remaining unexplained 85% of this extra force results from titin binding to the thin filament. With this enhanced force confirmed in the mouse model, future studies will aim to elucidate the proposed titin-thin filament interaction in actively stretched sarcomeres.

Changes in fascicle lengths and pennation angles do not contribute to residual force enhancement/depression in voluntary contractions.

Force enhancement following muscle stretching and force depression following muscle shortening are well-accepted properties of skeletal muscle contraction. However, the factors contributing to force enhancement/depression remain a matter of debate. In addition to factors on the fiber or sarcomere level, fiber length and angle of pennation affect the force during voluntary isometric contractions in whole muscles. Therefore, we hypothesized that differences in fiber lengths and angles of pennation between force-enhanced/depressed and reference states may contribute to force enhancement/depression during voluntary contractions. The purpose of this study was to test this hypothesis. Twelve subjects participated in this study, and force enhancement/depression was measured in human tibialis anterior. Fiber lengths and angles of pennation were quantified using ultrasound imaging. Neither fiber lengths nor angles of pennation were found to differ between the isometric reference contractions and any of the force-enhanced or force-depressed conditions. Therefore, we rejected our hypothesis and concluded that differences in fiber lengths or angles of pennation do not contribute to the observed force enhancement/depression in human tibialis anterior, and speculate that this result is likely true for other muscles too.

Velocity-dependent cost function for the prediction of force sharing among synergistic muscles in a one degree of freedom model.

Prediction of accurate and meaningful force sharing among synergistic muscles is a major problem in biomechanics research. Given a resultant joint moment, a unique set of muscle forces can be obtained from this mathematically redundant system using nonlinear optimization. The classical cost functions for optimization involve a normalization of the muscle forces to the absolute force capacity of the target muscles, usually by the cross-sectional area or the maximal isometric force. In a one degree of freedom model this leads to a functional relationship between moment arms and the predicted muscle forces, such that for constant moment arms, or constant ratios of moment arms, agonistic muscle forces increase or decrease in unison. Experimental studies have shown however that the relationship between muscle forces is highly task-dependent often causing forces to increase in one muscle while decreasing in a functional agonist, likely because of the contractile conditions and contractile properties of the involved muscles. We therefore, suggest a modified cost function that accounts for the instantaneous contraction velocity of the muscles and its effect on the instantaneous maximal force. With this novel objective function, a task-dependent prediction of muscle force distribution is obtained that allows, even in a one degree of freedom system, the prediction of force sharing loops, and simultaneously increasing and decreasing forces for agonist pairs of muscles.