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

Coupled Systems of Differential-Algebraic and Kinetic Equations with Application to the Mathematical Modelling of Muscle Tissue

We consider a coupled system composed of a linear differential-algebraic equation (DAE) and a linear large-scale system of ordinary differential equations where the latter stands for the dynamics of numerous identical particles. Replacing the discrete particles by a kinetic equation for a particle density, we obtain in the mean-field limit the new class of partially kinetic systems. We investigate the influence of constraints on the kinetic theory of those systems and present necessary adjustments. We adapt the mean-field limit to the DAE model and show that index reduction and the mean-field limit commute. As a main result, we prove Dobrushin's stability estimate for linear systems. The estimate implies convergence of the mean-field limit and provides a rigorous link between the particle dynamics and their kinetic description. Our research is inspired by mathematical models for muscle tissue where the macroscopic behaviour is governed by the equations of continuum mechanics, often discretised by the finite element method, and the microscopic muscle contraction process is described by Huxley's sliding filament theory. The latter represents a kinetic equation that characterises the state of the actin-myosin bindings in the muscle filaments. Linear partially kinetic systems are a simplified version of such models, with focus on the constraints.Comment: 32 pages, 18 figure

Light smoking at base-line predicts a higher mortality risk to women than to men; evidence from a cohort with long follow-up

BACKGROUND: There is conflicting evidence as to whether smoking is more harmful to women than to men. The UK Cotton Workers’ Cohort was recruited in the 1960s and contained a high proportion of men and women smokers who were well matched in terms of age, job and length of time in job. The cohort has been followed up for 42 years. METHODS: Mortality in the cohort was analysed using an individual relative survival method and Cox regression. Whether smoking, ascertained at baseline in the 1960s, was more hazardous to women than to men was examined by estimating the relative risk ratio women to men, smokers to never smoked, for light (1–14), medium (15–24), heavy (25+ cigarettes per day) and former smoking. RESULTS: For all-cause mortality relative risk ratios were 1.35 for light smoking at baseline (95% CI 1.07-1.70), 1.15 for medium smoking (95% CI 0.89-1.49) and 1.00 for heavy smoking (95% CI 0.63-1.61). Relative risk ratios for light smoking at baseline for circulatory system disease was 1.42 (95% CI 1.01 to 1.98) and for respiratory disease was 1.89 (95% CI 0.99 to 3.63). Heights of participants provided no explanation for the gender difference. CONCLUSIONS: Light smoking at baseline was shown to be significantly more hazardous to women than to men but the effect decreased as consumption increased indicating a dose response relationship. Heavy smoking was equally hazardous to both genders. This result may help explain the conflicting evidence seen elsewhere. However gender differences in smoking cessation may provide an alternative explanation

An analysis of the temperature dependence of force, during steady shortening at different velocities, in (mammalian) fast muscle fibres

We examined, over a wide range of temperatures (10–35°C), the isometric tension and tension during ramp shortening at different velocities (0.2–4 L0/s) in tetanized intact fibre bundles from a rat fast (flexor hallucis brevis) muscle; fibre length (L0) was 2.2 mm and sarcomere length ~2.5 μm. During a ramp shortening, the tension change showed an initial inflection of small amplitude (P1), followed by a larger exponential decline towards an approximate steady level; the tension continued to decline slowly afterwards and the approximate steady tension at a given velocity was estimated as the tension (P2) at the point of intersection between two linear slopes, as previously described (Roots et al. 2007). At a given temperature, the tension P2 declined to a lower level and at a faster rate (from an exponential curve fit) as the shortening velocity was increased; the temperature sensitivity of the rate of tension decline during ramp shortening at different velocities was low (Q10 0.9–1.5). The isometric tension and the P2 tension at a given shortening velocity increased with warming so that the relation between tension and (reciprocal) temperature was sigmoidal in both. In isometric muscle, the temperature T0.5 for half-maximal tension was ~10°C, activation enthalpy change (∆H) was ~100 kJ mol−1 and entropy change (∆S) ~350 J mol−1 K−1. In shortening, these were increased with increase of velocity so that at a shortening velocity (~4 L0/s) producing maximal power at 35°C, T0.5 was ~28°C, ∆H was ~200 kJ mol−1 and ∆S ~ 700 J mol−1 K−1; the same trends were seen in the tension data from isotonic release experiments on intact muscle and in ramp shortening experiments on maximally Ca-activated skinned fibres. In general, our findings show that the sigmoidal relation between force and temperature can be extended from isometric to shortening muscle; the implications of the findings are discussed in relation to the crossbridge cycle. The data indicate that the endothermic, entropy driven process that underlies crossbridge force generation in isometric muscle (Zhao and Kawai 1994; Davis, 1998) is even more pronounced in shortening muscle, i.e. when doing external work

Axial and Radial Forces of Cross-Bridges Depend on Lattice Spacing

Nearly all mechanochemical models of the cross-bridge treat myosin as a simple linear spring arranged parallel to the contractile filaments. These single-spring models cannot account for the radial force that muscle generates (orthogonal to the long axis of the myofilaments) or the effects of changes in filament lattice spacing. We describe a more complex myosin cross-bridge model that uses multiple springs to replicate myosin's force-generating power stroke and account for the effects of lattice spacing and radial force. The four springs which comprise this model (the 4sXB) correspond to the mechanically relevant portions of myosin's structure. As occurs in vivo, the 4sXB's state-transition kinetics and force-production dynamics vary with lattice spacing. Additionally, we describe a simpler two-spring cross-bridge (2sXB) model which produces results similar to those of the 4sXB model. Unlike the 4sXB model, the 2sXB model requires no iterative techniques, making it more computationally efficient. The rate at which both multi-spring cross-bridges bind and generate force decreases as lattice spacing grows. The axial force generated by each cross-bridge as it undergoes a power stroke increases as lattice spacing grows. The radial force that a cross-bridge produces as it undergoes a power stroke varies from expansive to compressive as lattice spacing increases. Importantly, these results mirror those for intact, contracting muscle force production

Factors affecting phage D29 infection: a tool to investigate different growth states of mycobacteria

Bacteriophages D29 and TM4 are able to infect a wide range of mycobacteria, including pathogenic and non pathogenic species. Successful phage infection of both fast- and slow-growing mycobacteria can be rapidly detected using the phage amplification assay. Using this method, the effect of oxygen limitation during culture of mycobacteria on the success of phage infection was studied. Both D29 and TM4 were able to infect cultures of M. smegmatis and Mycobacterium avium subspecies paratuberculosis (MAP) grown in liquid with aeration. However when cultures were grown under oxygen limiting conditions, only TM4 could productively infect the cells. Cell attachment assays showed that D29 could bind to the cells surface but did not complete the lytic cycle. The ability of D29 to productively infect the cells was rapidly recovered (within 1 day) when the cultures were returned to an aerobic environment and this recovery required de novo RNA synthesis. These results indicated that under oxygen limiting conditions the cells are entering a growth state which inhibits phage D29 replication, and this change in host cell biology which can be detected by using both phage D29 and TM4 in the phage amplification assay

Prime movers : mechanochemistry of mitotic kinesins

Mitotic spindles are self-organizing protein machines that harness teams of multiple force generators to drive chromosome segregation. Kinesins are key members of these force-generating teams. Different kinesins walk directionally along dynamic microtubules, anchor, crosslink, align and sort microtubules into polarized bundles, and influence microtubule dynamics by interacting with microtubule tips. The mechanochemical mechanisms of these kinesins are specialized to enable each type to make a specific contribution to spindle self-organization and chromosome segregation