Matching Mechanics and Energetics of Muscle Contraction Suggests Unconventional Chemomechanical Coupling during the Actin-Myosin Interaction.

The mechanical performances of the vertebrate skeletal muscle during isometric and isotonic contractions are interfaced with the corresponding energy consumptions to define the coupling between mechanical and biochemical steps in the myosin-actin energy transduction cycle. The analysis is extended to a simplified synthetic nanomachine in which eight HMM molecules purified from fast mammalian skeletal muscle are brought to interact with an actin filament in the presence of 2 mM ATP, to assess the emergent properties of a minimum number of motors working in ensemble without the effects of both the higher hierarchical levels of striated muscle organization and other sarcomeric, regulatory and cytoskeleton proteins. A three-state model of myosin-actin interaction is able to predict the known relationships between energetics and transient and steady-state mechanical properties of fast skeletal muscle either in vivo or in vitro only under the assumption that during shortening a myosin motor can interact with two actin sites during one ATP hydrolysis cycle. Implementation of the molecular details of the model should be achieved by exploiting kinetic and structural constraints present in the transients elicited by stepwise perturbations in length or force superimposed on the isometric contraction.

Muscle myosin performance measured with a synthetic nanomachine reveals a class-specific Ca2+ -sensitivity of the frog myosin II isoform.

KEY POINTS: A nanomachine made of an ensemble of seven heavy-meromyosin (HMM) fragments of muscle myosin interacting with an actin filament is able to mimic the half-sarcomere generating steady force and constant-velocity shortening. To preserve Ca2+ as a free parameter, the Ca2+ -insensitive gelsolin fragment TL40 is used to attach the correctly oriented actin filament to the laser-trapped bead acting as a force transducer. The new method reveals that the performance of the nanomachine powered by myosin from frog hind-limb muscles depends on [Ca2+ ], an effect mediated by a Ca2+ -binding site in the regulatory light chain of HMM. The Ca2+ -sensitivity is class-specific because the performance of the nanomachine powered by mammalian skeletal muscle myosin is Ca2+ independent. A model simulation is able to interface the nanomachine performance with that of the muscle of origin and provides a molecular explanation of the functional diversity of muscles with different orthologue isoforms of myosin. ABSTRACT: An ensemble of seven heavy-meromyosin (HMM) fragments of myosin-II purified from the hindlimb muscles of the frog (Rana esculenta) is used to drive a synthetic nanomachine that pulls an actin filament in the absence of confounding effects of other sarcomeric proteins. In the present version of the nanomachine the +end of the actin filament is attached to the laser trapped bead via the Ca2+ -insensitive gelsolin fragment TL40, making [Ca2+ ] a free parameter. Frog myosin performance in 2 mm ATP is affected by Ca2+ : in 0.1 mm Ca2+ , the isometric steady force (F0 , 15.25 pN) is increased by 50% (P = 0.004) with respect to that in Ca2+ -free solution, the maximum shortening velocity (V0 , 4.6 µm s-1 ) is reduced by 27% (P = 0.46) and the maximum power (Pmax , 7.6 aW) is increased by 21% (P = 0.17). V0 reduction is not significant for the paucity of data at low force, although it is solidified by a similar decrease (33%, P < 0.0001) in the velocity of actin sliding as indicated by an in vitro motility assay (Vf ). The rate of ATP-hydrolysis in solution (φ) exhibits a similar calcium dependence. Ca2+ titration curves for Vf and φ give Kd values of ∼30 µm. All the above mechanical and kinetic parameters are independent of Ca2+ when HMM from rabbit psoas myosin is used, indicating that the Ca2+ -sensitivity is a class-specific property of muscle myosin. A unique multiscale model allows interfacing of the nanomachine performance to that of the muscle of origin and identifies the kinetic steps responsible for the Ca2+ -sensitivity of frog myosin.

A Myosin II-Based Nanomachine Devised for the Study of Ca2+-Dependent Mechanisms of Muscle Regulation.

The emergent properties of the array arrangement of the molecular motor myosin II in the sarcomere of the striated muscle, the generation of steady force and shortening, can be studied in vitro with a synthetic nanomachine made of an ensemble of eight heavy-meromyosin (HMM) fragments of myosin from rabbit psoas muscle, carried on a piezoelectric nanopositioner and brought to interact with a properly oriented actin filament attached via gelsolin (a Ca2+-regulated actin binding protein) to a bead trapped by dual laser optical tweezers. However, the application of the original version of the nanomachine to investigate the Ca2+-dependent regulation mechanisms of the other sarcomeric (regulatory or cytoskeleton) proteins, adding them one at a time, was prevented by the impossibility to preserve [Ca2+] as a free parameter. Here, the nanomachine is implemented by assembling the bead-attached actin filament with the Ca2+-insensitive gelsolin fragment TL40. The performance of the nanomachine is determined both in the absence and in the presence of Ca2+ (0.1 mM, the concentration required for actin attachment to the bead with gelsolin). The nanomachine exhibits a maximum power output of 5.4 aW, independently of [Ca2+], opening the possibility for future studies of the Ca2+-dependent function/dysfunction of regulatory and cytoskeletal proteins.

A myosin II nanomachine mimicking the striated muscle.

The contraction of striated muscle (skeletal and cardiac muscle) is generated by ATP-dependent interactions between the molecular motor myosin II and the actin filament. The myosin motors are mechanically coupled along the thick filament in a geometry not achievable by single-molecule experiments. Here we show that a synthetic one-dimensional nanomachine, comprising fewer than ten myosin II dimers purified from rabbit psoas, performs isometric and isotonic contractions at 2 mM ATP, delivering a maximum power of 5 aW. The results are explained with a kinetic model fitted to the performance of mammalian skeletal muscle, showing that the condition for the motor coordination that maximises the efficiency in striated muscle is a minimum of 32 myosin heads sharing a common mechanical ground. The nanomachine offers a powerful tool for investigating muscle contractile-protein physiology, pathology and pharmacology without the potentially disturbing effects of the cytoskeletal-and regulatory-protein environment.

Transient kinetics measured with force steps discriminate between double-stranded DNA elongation and melting and define the reaction energetics.

Under a tension of ∼65 pN, double-stranded DNA undergoes an overstretching transition from its basic (B-form) conformation to a 1.7 times longer conformation whose nature is only recently starting to be understood. Here we provide a structural and thermodynamic characterization of the transition by recording the length transient following force steps imposed on the λ-phage DNA with different melting degrees and temperatures (10-25°C). The shortening transient following a 20-35 pN force drop from the overstretching force shows a sequence of fast shortenings of double-stranded extended (S-form) segments and pauses owing to reannealing of melted segments. The lengthening transients following a 2-35 pN stretch to the overstretching force show the kinetics of a two-state reaction and indicate that the whole 70% extension is a B-S transition that precedes and is independent of melting. The temperature dependence of the lengthening transient shows that the entropic contribution to the B-S transition is one-third of the entropy change of thermal melting, reinforcing the evidence for a double-stranded S-form that maintains a significant fraction of the interstrand bonds. The cooperativity of the unitary elongation (22 bp) is independent of temperature, suggesting that structural factors, such as the nucleic acid sequence, control the transition.

PicoNewton-millisecond force steps reveal the transition kinetics and mechanism of the double-stranded DNA elongation.

We study the kinetics of the overstretching transition in λ-phage double-stranded (ds) DNA from the basic conformation (B state) to the 1.7-times longer and partially unwound conformation (S state), using the dual-laser optical tweezers under force-clamp conditions at 25°C. The unprecedented resolution of our piezo servo-system, which can impose millisecond force steps of 0.5-2 pN, reveals the exponential character of the elongation kinetics and allows us to test the two-state nature of the B-S transition mechanism. By analyzing the load-dependence of the rate constant of the elongation, we find that the elementary elongation step is 5.85 nm, indicating a cooperativity of ~25 basepairs. This mechanism increases the free energy for the elementary reaction to ~94 k(B)T, accounting for the stability of the basic conformation of DNA, and explains why ds-DNA can remain in equilibrium as it overstretches.

Stochastic dynamics of model proteins on a directed graph.

A method for reconstructing the potential energy landscape of simple polypeptidic chains is described. We show how to obtain a faithful representation of the energy landscape in terms of a suitable directed graph. Topological and dynamical indicators of the graph are shown to yield an effective estimate of the time scales associated with both folding and equilibration processes. This conclusion is drawn by comparing molecular dynamics simulations at constant temperature with the dynamics on the graph, defined as a temperature-dependent Markov process. The main advantage of the graph representation is that its dynamics can be naturally renormalized by collecting nodes into "hubs" while redefining their connectivity. We show that the dynamical properties at large time scales are preserved by the renormalization procedure. Moreover, we obtain clear indications that the heteropolymers exhibit common topological properties, at variance with the homopolymer, whose peculiar graph structure stems from its spatial homogeneity. In order to distinguish between "fast" and "slow" folders, one has to look at the kinetic properties of the corresponding directed graphs. In particular, we find that the average time needed to the fast folder for reaching its native configuration is two orders of magnitude smaller than its equilibration time while for the bad folder these time scales are comparable.

Graph theoretical analysis of the energy landscape of model polymers.

In systems characterized by a rough potential-energy landscape, local energetic minima and saddles define a network of metastable states whose topology strongly influences the dynamics. Changes in temperature, causing the merging and splitting of metastable states, have nontrivial effects on such networks and must be taken into account. We do this by means of a recently proposed renormalization procedure. This method is applied to analyze the topology of the network of metastable states for different polypeptidic sequences in a minimalistic polymer model. A smaller spectral dimension emerges as a hallmark of stability of the global energy minimum and highlights a nonobvious link between dynamic and thermodynamic properties.

A dynamical study of antibody-antigen encounter reactions.

The effects of internal dynamics in diffusion-driven encounters between macro-molecules represent a problem of broad relevance in molecular biology. In this view, we investigate a typical antigen-antibody reaction chain, based on a coarse-grained mechanical model parameterized directly upon results from single-molecule experiments. We demonstrate that the internal dynamics is a crucial factor in the encounter process. To describe our numerical results, we formulate a simple, intuitive theoretical framework, and we develop it analytically. This enables us to show that the inner dynamics of antibody molecules results in a cooperative behavior of their individual sub-units. Along the same lines, we also investigate the case of double binding to multi-valent antigens. Our results quantify the enhancement of avidity afforded by the double binding in excellent agreement with the available experimental data.

Exploring the energy landscape of model proteins: a metric criterion for the determination of dynamical connectivity.

A method to reconstruct the energy landscape of small peptides is presented with reference to a two-dimensional off-lattice model. The starting point is a statistical analysis of the configurational distances between generic minima and directly connected pairs (DCP). As the mutual distance of DCP is typically much smaller than that of generic pairs, a metric criterion can be established to identify the great majority of DCP. Advantages and limits of this approach are thoroughly analyzed for three different heteropolymeric chains. A funnel-like structure of the energy landscape is found in all of the three cases, but the escape rates clearly reveal that the native configuration is more easily accessible (and is significantly more stable) for the sequence that is expected to behave as a real protein.

Topological properties of the energy landscape of small peptides.

In several works it has been shown that the interplay between short range and long range interactions, mimicking the hydrophobic effect, leads to the formation of the typical secondary structures in proteins, alpha-helices and beta-sheets. In this work we study in detail how the general properties of the energy landscape emerge in a model that presents both components. In this regard it proves useful a sort of perturbative approach. In our model many features of the energy landscape in absence of long range interaction can be determined analytically. The comparison between the energy landscape of this reduced model to that of the complete model gives interesting insight on the role of long range interactions.

Thermally activated processes in polymer dynamics.

Jumps between neighboring minima in the energy landscape of both homopolymeric and heteropolymeric chains are numerically investigated by determining the average escape time from different valleys. The numerical results are compared to the theoretical expression derived by Langer [J.S. Langer, Ann. Phys. (N.Y.) 54, 258 (1969)] with reference to a 2N-dimensional space. Our simulations indicate that the dynamics within the native valley is well described by a sequence of thermally activated process up to temperatures well above the folding temperature. At larger temperatures, systematic deviations from the Langer's estimate are instead observed. Several sources for such discrepancies are thoroughly discussed.