Distances as degrees of freedom

Tertiary contact distance information of varying resolution for large biological molecules abounds in the literature. The results provided herein develop a framework by which information of this type can be used to reduce the allowable configuration space of a macromolecule. The approach combines graph theory and distance geometry. Large molecules are represented as simple, undirected graphs, with atoms, or groups, as vertices, and distances between them as edges. It is shown that determination of the exact structure of a molecule in three dimensions only requires the specification of all the distances in a single tetrahedron, and four distances to every other atom. This is 4N-10 distances which is a subset of the total N(N-1)/2 unique distances in a molecule consisting of N atoms. This requirement for only 4N-10 distances has serious implications for distance geometry implementations in which all N(N-1)/2 distances are specified by bounded random numbers. Such distance matrices represent overspecified systems which when solved lead to non-obvious distribution of any error caused by inherent contradictions in the input data. It is also shown that numerous valid subsets of 4N-10 distances can be constructed. It is thus possible to tailor a subset of distances using all known distances as degrees of freedom, and thereby reduce the configuration space of the molecule. Simple algebraic relationships are derived that relate sets of distances, and complicated rotations are avoided. These relationships are used to construct minimum, complete sets of distances necessary to specify the exact structure of the entire molecule in three dimensions from incomplete distance information, and to identify sets of inconsistent distances. The method is illustrated for the flexible structural types present in large ribosomal RNAs: 1.) A five-membered ring; 2.) a chemically bonded chain with its ends in contact (i.e., a hairpin loop); 3.) the spatial orientation of two separate molecules, and; 4.) an RNA helix that can have variation in individual base pairs, giving rise to global deviation from standardized helical forms.     

Stochastic properties of actomyosin motor

The epoch-making techniques for manipulating a single myosin molecule have recently been developed, and the unitary mechanical reactions of a single actomyosin, muscle motor molecule, are directly measured. The data show that the unitary mechanical step during sliding along an actin filament of approximately 5.5 nm, but groups of two to five rapid steps in succession produce displacements of approximately 11-30 nm. The instances of multiple stepping are produced by single myosin heads during one biochemical cycle of ATP hydrolysis. Thus, the coupling between ATP hydrolysis cycle and mechanical step is variable, i.e. loose-coupling. Such a unique operation of actomyosin molecules is different from that of man-made machines, and most likely explains the flexible and effective mechanisms of molecular machines in the biosystems.     

Essential degrees of freedom of proteins

Analysis of extended molecular dynamics (MD) simulations of several proteins in aquous solutions reveals that it is possible to separate the configurational space into two subspaces: (1) an essential subspace containing only a few degrees of freedom in which anharmonic motion occurs that comprises most of the positional fluctuations; and (2) the remaining space in which the motion has a narrow Gaussian distribution and which can be considered as physically constrained.     

Single actomyosin motor interactions in skeletal muscle

We present a study of intramuscular motion during contraction of skeletal muscle myofibrils. Myofibrillar actin was labeled with fluorescent dye so that the ratio of fluorescently labeled to unlabeled protein was 1:10⁵. Such sparse labeling assured that there was on average only one actin-marker present in the focus at a given time. From the intensity signal in the two orthogonal detection channels, significant fluctuations, similar to fluorescent burst in diffusion-based single-molecule detection schemes, were identified via a threshold algorithm and analyzed with respect to their intensity and polarization. When only rigor complexes were formed, the fluctuations of polarized intensity were characterized by unimodal Gaussian photon distributions. During contraction, in contrast, bimodal Gaussian photon distributions were observed above the rigor background threshold. This suggests that the bimodal Gaussian photon distributions represent pre- and post-power stroke conformations. Clusters of polarized photons indicated an anisotropy decay of single actomyosin motors of ~ 9 s during muscle contraction.     

Actin cross-linking and inhibition of the actomyosin motor.

Intrastrand cross-linking of actin filaments by ANP, N-(4-azido-2-nitrophenyl) putrescine, between Gln-41 in subdomain 2 and Cys-374 at the C-terminus, was shown to inhibit force generation with myosin in the in vitro motility assays [Kim et al. (1998) Biochemistry 37, 17801-17809]. To clarify the immobilization of which of these two sites inhibits the actomyosin motor, the properties of actins with partially overlapping cross-linked sites were examined. pPDM (N,N'-p-phenylenedimaleimide) and ABP [N-(4-azidobenzoyl) putrescine] were used to obtain actin filaments cross-linked ( approximately 50%) between Cys-374 and Lys-191 (interstrand) and Gln-41 and Lys-113 (intrastrand), respectively. ANP, ABP, and pPDM cross-linked filaments showed similar inhibition of their sliding speeds and force generation with myosin ( approximately 25%) in the in vitro motility assays. In analogy to ANP cross-linking of actin, pPDM and ABP cross-linkings did not change the strong S1 binding to actin and the V(max) and K(m) parameters of actomyosin ATPase. The similar effects of these three cross-linkings reveal the tight coupling between structural elements of the subdomain 2/subdomain 1 interface and show the importance of its dynamic flexibility to force generation with myosin. The possibility that actin cross-linkings inhibit rate-limiting steps in motion and force generation during myosin cross-bridge cycle was tested in stopped-flow experiments. Measurements of the rates of mantADP release from actoS1 and ATP-induced dissociation of actoS1 did not reveal any differences between un-cross-linked and ANP cross-linked actin in these complexes. These findings are discussed in terms of the uncoupling between force generation and other aspects of actomyosin interactions due to a constrained dynamic flexibility of the subdomain 2/subdomain 1 interface in cross-linked actin filaments.     

Trimethylamine N-oxide suppresses the activity of the actomyosin motor

Background

During actomyosin interactions, the transduction of energy from ATP hydrolysis to motility seems to occur with the modulation of hydration. Trimethylamine N-oxide (TMAO) perturbs the surface of proteins by altering hydrogen bonding in a manner opposite to that of urea. Hence, we focus on the effects of TMAO on the motility and ATPase activation of actomyosin complexes.

Methods

Actin and heavy meromyosin (HMM) were prepared from rabbit skeletal muscle. Structural changes in HMM were detected using fluorescence and circular dichroism spectroscopy. The sliding velocity of rhodamine-phalloidin-bound actin filaments on HMM was measured using an in vitro motility assay. ATPase activity was measured using a malachite green method.

Results

Although TMAO, unlike urea, stabilized the HMM structure, both the sliding velocity and ATPase activity of acto-HMM were considerably decreased with increasing TMAO concentrations from 0–1.0 M. Whereas urea-induced decreases in the structural stability of HMM were recovered by TMAO, TMAO further decreased the urea-induced decrease in ATPase activation. Urea and TMAO were found to have counteractive effects on motility at concentrations of 0.6 M and 0.2 M, respectively.

Conclusions

The excessive stabilization of the HMM structure by TMAO may suppress its activities; however, the counteractive effects of urea and TMAO on actomyosin motor activity is distinct from their effects on HMM stability.

General significance

The present results provide insight into not only the water-related properties of proteins, but also the physiological significance of TMAO and urea osmolytes in the muscular proteins of water-stressed animals.     

Link between the enzymatic kinetics and mechanical behavior in an actomyosin motor

We have attempted to link the solution actomyosin ATPase with the mechanical properties of in vitro actin filament sliding over heavy meromyosin. To accomplish this we perturbed the system by altering the substrate with various NTPs and divalent cations, and by altering ionic strength. A wide variety of enzymatic and mechanical measurements were made under very similar solution conditions. Excellent correlations between the mechanical and enzymatic quantities were revealed. Analysis of these correlations based on a force-balance model led us to two fundamental equations, which can be described approximately as follows: the maximum sliding velocity is proportional to square root of V(max)K(m)(A), where K(m)(A) is the actin concentration at which the substrate turnover rate is half of its maximum (V(max)). The active force generated by a cross-bridge under no external load or under a small external load is proportional to square root of V(max)/K(m)(A). The equations successfully accounted for the correlations observed in the present study and observations in other laboratories.     

pH-dependence of kinetic parameters in the superprecipitation reaction and ATPase activity of myometrial actomyosin

The investigation of pH-dependence of superprecipitation reaction and ATPase activity of myometrium actomyosin in the interval of pH 5.5-8.0 has detected cupola-shaped curves with maximal activity of both processes by pH 6.5. On the basis of calculating the constants of ionization it was supposed that in the case of actomyosin ATPase imidazole groups of two histidins had an essential role in reaction of ATP hydrolysis and in superprecipitation process--imidazol group of histidine and carboxyl group of asparagin acid. The investigation of [ATP]- and [Mg2+]-dependence of superprecipitation reaction by pH 6.0, 6.5 and 7.0 has demonstrated different pH-sensitiveness of Michaelis constants and maximal speeds relatively Mg2+ and ATP for both processes. It was shown that pH-optimum of ATPase activity of myometrium actomyosin coincided with maximal affinity of actomyosin with ATP and Mg2+ while as for superprecipitation reaction the correlation between value of process by certain pH and affinity with ATP and Mg2+ was not detected.     

The sticking region in three chest-press exercises with increasing degrees of freedom

ABSTRACT: Van den Tillaar, R, and S?terbakken, A. The sticking region in three chest-press exercises with increasing degrees of freedom. J Strength Cond Res 26(11): 2962-2969, 2012-The purpose was to investigate the effect of 3 chest-press exercises with different degrees of freedom upon the sticking region and muscle activity in maximal attempts. It was hypothesized that, with increasing degrees of freedom, the sticking region (the weakest region during the lift) would be longer because the muscles need to use a part of their ability to control these increasing degrees of freedom during the exercise. Furthermore, the prime movers would have the same muscle activity, but the biceps muscle activity would increase when the degrees of freedom increases because of the enhanced control of the upward movement. Eleven male subjects (age 22.6 ± 1.7 years, body mass 78.6 ± 8.0 kg, stature 1.80 ± 0.07 m) with at least 1 year of bench press training experience participated in this study. Every subject was tested in 1 repetition maximum (1RM) in the 3 chest-press exercises. During the attempts, kinematics and muscle activity were recorded and analyzed in 4 different regions (downward, presticking, sticking, and poststicking). The participants achieved the highest 1RM strength using the free barbell (106.4 ± 15.5 kg), followed by the Smith machine (103.6 ± 14.8 kg) and dumbbells (89.5 ± 13.7 kg). Furthermore, muscle activity differences (electromyographic) between the 3 different exercises and the muscle activation between the 4 different regions were found. The length of the different lifting regions together with muscle activity was different between the exercises. However, the differences found did not follow the line of increasing degrees of freedom that would result in a longer sticking region. Therefore, it is possible to choose to train a particular chest press exercise with the purpose of training a particular muscle more than the others.     

Design and functional analysis of actomyosin motor domain chimera proteins

To gain more structural and functional information on the actomyosin complexes, we have engineered chimera proteins carrying the entire Dictyostelium actin in the loop 2 sequence of the motor domain of Dictyostelium myosin II. Although the chimera proteins were unable to polymerize by themselves, addition of skeletal actin promoted polymerization. Electron microscopic observation demonstrated that the chimera proteins were incorporated into actin filaments, when copolymerized with skeletal actin. Copolymerization with skeletal actin greatly enhanced the MgATPase, while the chimera proteins without added skeletal actin hydrolyzed ATP at a very low rate. These results indicate that the actin part and the motor domain part of the chimera proteins are correctly folded, but the chimera proteins are structurally stressed so that efficient polymerization is inhibited.     

Electric dipole theory and thermodynamics of actomyosin molecular motor in muscle contraction

Movements in muscles are generated by the myosins which interact with the actin filaments. In this paper we present an electric theory to describe how the chemical energy is first stored in electrostatic form in the myosin system and how it is then released and transformed into work. Due to the longitudinal polarized molecular structure with the negative phosphate group tail, the ATP molecule possesses a large electric dipole moment (p(0)), which makes it an ideal energy source for the electric dipole motor of the actomyosin system. The myosin head contains a large number of strongly restrained water molecules, which makes the ATP-driven electric dipole motor possible. The strongly restrained water molecules can store the chemical energy released by ATP binding and hydrolysis processes in the electric form due to their myosin structure fixed electric dipole moments (p(i)). The decrease in the electric energy is transformed into mechanical work by the rotational movement of the myosin head, which follows from the interaction of the dipoles p(i) with the potential field V(0) of ATP and with the potential field Psi of the actin. The electrical meaning of the hydrolysis reaction is to reduce the dipole moment p(0)-the remaining dipole moment of the adenosine diphosphate (ADP) is appropriately smaller to return the low negative value of the electric energy nearly back to its initial value, enabling the removal of ADP from the myosin head so that the cycling process can be repeated. We derive for the electric energy of the myosin system a general equation, which contains the potential field V(0) with the dipole moment p(0), the dipole moments p(i) and the potential field psi. Using the previously published experimental data for the electric dipole of ATP (p(0) congruent with 230 debye) and for the amount of strongly restrained water molecules (N congruent with 720) in the myosin subfragment (S1), we show that the Gibbs free energy changes of the ATP binding and hydrolysis reaction steps can be converted into the form of electric energy. The mechanical action between myosin and actin is investigated by the principle of virtual work. An electric torque always appears, i.e. a moment of electric forces between dipoles p(0) and p(i)(/M/ > or = 16 pN nm) that causes the myosin head to function like a scissors-shaped electric dipole motor. The theory as a whole is illustrated by several numerical examples and the results are compared with experimental results.     

A light weight compliant hand mechanism with high degrees of freedom

This paper presents the design and prototyping of an inherently compliant lightweight hand mechanism. The hand mechanism itself has 15 degrees of freedom and five fingers. Although the degrees of freedom in each finger are coupled, reducing the number of independent degrees of freedom to 5, the 15 degrees of freedom of the hand could potentially be individually actuated. Each joint consists of a novel flexing mechanism that is based on the loading of a compression spring in the axial and transverse direction via a cable and conduit system. Currently, a bench top version of the prototype is being developed; the three joints of each finger are coupled together to simplify the control system. The current control scheme under investigation simulates a control scheme where myoelectric signals in the wrist flexor and extensor muscles are converted in to x and y coordinates on a control scheme chart. Static load-deformation analysis of finger segments is studied based on a 3-dimensional model without taking the stiffener into account, and the experiment validates the simulation.     

Assessment of the accuracy of a human arm model with seven degrees of freedom

We are proposing a human arm model that consists of three rigid segments with seven degrees of freedom. The shoulder joint was modeled as a ball-and-socket joint and the elbow and wrist joints were modelled as skew-oblique joints. Optimal parameters for this model were calculated on the base of in vivo recordings with a spatial tracking system. The criterion of optimality was defined as the minimum of the mean-square deviation between the experimentally obtained sensor positions and orientations and their positions and orientations calculated by solving the direct kinematics problem. The minimal value of the direct kinematics error was found to be 0.5-0.6cm for sensor positions and 5-7 degrees for sensor orientations. We are proposing that these values serve as the assessment for the accuracy of the arm model.