Kinetics and thermodynamics of the rate-limiting conformational change in the actomyosin V mechanochemical cycle

Switch-2 determines Mg2+ADP-release kinetics and fine-tunes the duty ratio of Dictyostelium class-1 myosins

Though myosins share a structurally conserved motor domain, single amino acid variations of active site elements, including the P-loop, switch-1 and switch-2, which act as nucleotide sensors, can substantially determine the kinetic signature of a myosin, i.e., to either perform fast movement or enable long-range transport and tension generation. Switch-2 essentially contributes to the ATP hydrolysis reaction and determines product release. With few exceptions, class-1 myosin harbor a tyrosine in the switch-2 consensus sequence DIYGFE, at a position where class-2 myosins and a selection of myosins from other classes have a substitution. Here, we addressed the role of the tyrosine in switch-2 of class-1 myosins as potential determinant of the duty ratio. We generated constitutively active motor domain constructs of two class-1 myosins from the social amoeba Dictyostelium discoideum, namely, Myo1E, a high duty ratio myosin and Myo1B, a low duty ratio myosin. In Myo1E we introduced mutation Y388F and in Myo1B mutation F387Y. The detailed functional characterization by steady-state and transient kinetic experiments, combined with in vitro motility and landing assays revealed an almost reciprocal relationship of a number of critical kinetic parameters and equilibrium constants between wild-type and mutants that dictate the lifetime of the strongly actin-attached states of myosin. The Y-to-F mutation increased the duty ratio of Moy1B by almost one order of magnitude, while the introduction of the phenylalanine in switch-2 of Myo1E transformed the myosin into a low duty ratio motor. These data together with structural considerations propose a role of switch-2 in fine-tuning ADP release through a mechanism, where the class-specific tyrosine together with surrounding residues contributes to the coordination of Mg2+ and ADP. Our results highlight the importance of conserved switch-2 residues in class-1 myosins for efficient chemo-mechanical coupling, revealing that switch-2 is important to adjust the duty ratio of the amoeboid class-1 myosins for performing movement, transport or gating functions.

Cell-cell interactions and fluctuations in the direction of motility promote directed migration of osteoblasts in direct current electrotaxis

Under both physiological (development, regeneration) and pathological conditions (cancer metastasis), cells migrate while sensing environmental cues in the form of mechanical, chemical or electrical stimuli. In the case of bone tissue, osteoblast migration is essential in bone regeneration. Although it is known that osteoblasts respond to exogenous electric fields, the underlying mechanism of electrotactic collective movement of human osteoblasts is unclear. Here, we present a computational model that describes the osteoblast cell migration in a direct current electric field as the motion of a collection of active self-propelled particles and takes into account fluctuations in the direction of single-cell migration, finite-range cell-cell interactions, and the interaction of a cell with the external electric field. By comparing this model with in vitro experiments in which human primary osteoblasts are exposed to a direct current electric field of different field strengths, we show that cell-cell interactions and fluctuations in the migration direction promote anode-directed collective migration of osteoblasts.

Cardiomyopathy mutations impact the actin-activated power stroke of human cardiac myosin

Cardiac muscle contraction is driven by the molecular motor myosin, which uses the energy from ATP hydrolysis to generate a power stroke when interacting with actin filaments, although it is unclear how this mechanism is impaired by mutations in myosin that can lead to heart failure. We have applied a fluorescence resonance energy transfer (FRET) strategy to investigate structural changes in the lever arm domain of human β-cardiac myosin subfragment 1 (M2β-S1). We exchanged the human ventricular regulatory light chain labeled at a single cysteine (V105C) with Alexa 488 onto M2β-S1, which served as a donor for Cy3ATP bound to the active site. We monitored the FRET signal during the actin-activated product release steps using transient kinetic measurements. We propose that the fast phase measured with our FRET probes represents the macroscopic rate constant associated with actin-activated rotation of the lever arm during the power stroke in M2β-S1. Our results demonstrated M2β-S1 has a slower actin-activated power stroke compared with fast skeletal muscle myosin and myosin V. Measurements at different temperatures comparing the rate constants of the actin-activated power stroke and phosphate release are consistent with a model in which the power stroke occurs before phosphate release and the two steps are tightly coupled. We suggest that the actin-activated power stroke is highly reversible but followed by a highly irreversible phosphate release step in the absence of load and free phosphate. We demonstrated that hypertrophic cardiomyopathy (R723G)- and dilated cardiomyopathy (F764L)-associated mutations both reduced actin activation of the power stroke in M2β-S1. We also demonstrate that both mutations alter in vitro actin gliding in the presence and absence of load. Thus, examining the structural kinetics of the power stroke in M2β-S1 has revealed critical mutation-associated defects in the myosin ATPase pathway, suggesting these measurements will be extremely important for establishing structure-based mechanisms of contractile dysfunction.

High-Speed Atomic Force Microscopy to Study Myosin Motility

High-speed atomic force microscopy (HS-AFM) is a unique tool that enables imaging of protein molecules during their functional activity at sub-100 ms temporal and submolecular spatial resolution. HS-AFM is suited for the study of highly dynamic proteins, including myosin motors. HS-AFM images of myosin V walking on actin filaments provide irrefutable evidence for the swinging lever arm motion propelling the molecule forward. Moreover, molecular behaviors that have not been noticed before are also displayed on the AFM movies. This chapter describes the principle, underlying techniques and performance of HS-AFM, filmed images of myosin V, and mechanistic insights into myosin motility provided from the filmed images.

Human Osteoblast Migration in DC Electrical Fields Depends on Store Operated Ca2+-Release and Is Correlated to Upregulation of Stretch-Activated TRPM7 Channels

Fracture healing and bone regeneration, particularly in the elderly, remains a challenge. There is an ongoing search for methods to activate osteoblasts, and the application of electrical fields is an attractive approach in this context. Although it is known that such electromagnetic fields lead to osteoblast migration and foster mesenchymal osteogenic differentiation, so far the mechanisms of osteoblast activation remain unclear. Possible mechanisms could rely on changes in Ca²⁺-influx via ion channels, as these are known to modulate osteoblast activity, e.g., via voltage-sensitive, stretch-sensitive, transient-receptor-potential (TRP) channels, or store-operated release. In the present in vitro study, we explored whether electrical fields are able to modulate the expression of voltage-sensitive calcium channels as well as TRP channels in primary human osteoblast cell lines. We show migration speed is significantly increased in stimulated osteoblasts (6.4 ± 2.1 μm/h stimulated, 3.6 ± 1.1 μm/h control), and directed toward the anode. However, within a range of 154–445 V/m, field strength did not correlate with migration velocity. Neither was there a correlation between electric field and voltage-gated calcium channel (Ca_v3.2 and Ca_v1.4) expression. However, the expression of TRPM7 significantly correlated positively to electric field strength. TRPM7 channel blockade using NS8593, in turn, did not significantly alter migration speed, nor did blockade of Ca_v3.2 and Ca_v1.4 channels using Ni⁺ or verapamil, respectively, while a general Ca²⁺-influx block using Mg²⁺ accelerated migration. Stimulating store-operated Ca²⁺-release significantly reduced migration speed, while blocking IP3 had only a minor effect (at low and high concentrations of 2-APB, respectively). We conclude that (i) store operated channels negatively modulate migration speed and that (ii) the upregulation of TRPM7 might constitute a compensatory mechanism-which might explain how increasing expression levels at increasing field strengths result in constant migration speeds.

Converter domain mutations in myosin alter structural kinetics and motor function

Myosins are molecular motors that use a conserved ATPase cycle to generate force. We investigated two mutations in the converter domain of myosin V (R712G and F750L) to examine how altering specific structural transitions in the motor ATPase cycle can impair myosin mechanochemistry. The corresponding mutations in the human β-cardiac myosin gene are associated with hypertrophic and dilated cardiomyopathy, respectively. Despite similar steady-state actin-activated ATPase and unloaded in vitro motility-sliding velocities, both R712G and F750L were less able to overcome frictional loads measured in the loaded motility assay. Transient kinetic analysis and stopped-flow FRET demonstrated that the R712G mutation slowed the maximum ATP hydrolysis and recovery-stroke rate constants, whereas the F750L mutation enhanced these steps. In both mutants, the fast and slow power-stroke as well as actin-activated phosphate release rate constants were not significantly different from WT. Time-resolved FRET experiments revealed that R712G and F750L populate the pre- and post-power-stroke states with similar FRET distance and distance distribution profiles. The R712G mutant increased the mole fraction in the post-power-stroke conformation in the strong actin-binding states, whereas the F750L decreased this population in the actomyosin ADP state. We conclude that mutations in key allosteric pathways can shift the equilibrium and/or alter the activation energy associated with key structural transitions without altering the overall conformation of the pre- and post-power-stroke states. Thus, therapies designed to alter the transition between structural states may be able to rescue the impaired motor function induced by disease mutations.

JED: a Java Essential Dynamics Program for comparative analysis of protein trajectories

BACKGROUND

Essential Dynamics (ED) is a common application of principal component analysis (PCA) to extract biologically relevant motions from atomic trajectories of proteins. Covariance and correlation based PCA are two common approaches to determine PCA modes (eigenvectors) and their eigenvalues. Protein dynamics can be characterized in terms of Cartesian coordinates or internal distance pairs. In understanding protein dynamics, a comparison of trajectories taken from a set of proteins for similarity assessment provides insight into conserved mechanisms. Comprehensive software is needed to facilitate comparative-analysis with user-friendly features that are rooted in best practices from multivariate statistics.

RESULTS

We developed a Java based Essential Dynamics toolkit called JED to compare the ED from multiple protein trajectories. Trajectories from different simulations and different proteins can be pooled for comparative studies. JED implements Cartesian-based coordinates (cPCA) and internal distance pair coordinates (dpPCA) as options to construct covariance (Q) or correlation (R) matrices. Statistical methods are implemented for treating outliers, benchmarking sampling adequacy, characterizing the precision of Q and R, and reporting partial correlations. JED output results as text files that include transformed coordinates for aligned structures, several metrics that quantify protein mobility, PCA modes with their eigenvalues, and displacement vector (DV) projections onto the top principal modes. Pymol scripts together with PDB files allow movies of individual Q- and R-cPCA modes to be visualized, and the essential dynamics occurring within user-selected time scales. Subspaces defined by the top eigenvectors are compared using several statistical metrics to quantify similarity/overlap of high dimensional vector spaces. Free energy landscapes can be generated for both cPCA and dpPCA.

CONCLUSIONS

JED offers a convenient toolkit that encourages best practices in applying multivariate statistics methods to perform comparative studies of essential dynamics over multiple proteins. For each protein, Cartesian coordinates or internal distance pairs can be employed over the entire structure or user-selected parts to quantify similarity/differences in mobility and correlations in dynamics to develop insight into protein structure/function relationships.

Direct measurements of the coordination of lever arm swing and the catalytic cycle in myosin V

Myosins use a conserved structural mechanism to convert the energy from ATP hydrolysis into a large swing of the force-generating lever arm. The precise timing of the lever arm movement with respect to the steps in the actomyosin ATPase cycle has not been determined. We have developed a FRET system in myosin V that uses three donor-acceptor pairs to examine the kinetics of lever arm swing during the recovery and power stroke phases of the ATPase cycle. During the recovery stroke the lever arm swing is tightly coupled to priming the active site for ATP hydrolysis. The lever arm swing during the power stroke occurs in two steps, a fast step that occurs before phosphate release and a slow step that occurs before ADP release. Time-resolved FRET demonstrates a 20-Å change in distance between the pre- and postpower stroke states and shows that the lever arm is more dynamic in the postpower stroke state. Our results suggest myosin binding to actin in the ADP.Pi complex triggers a rapid power stroke that gates the release of phosphate, whereas a second slower power stroke may be important for mediating strain sensitivity.

Kinetics of fast changing intramolecular distance distributions obtained by combined analysis of FRET efficiency kinetics and time-resolved FRET equilibrium measurements

Detailed studies of the mechanisms of macromolecular conformational transitions such as protein folding are enhanced by analysis of changes of distributions for intramolecular distances during the transitions. Time-resolved Förster resonance energy transfer (FRET) measurements yield such data, but the more readily available kinetics of mean FRET efficiency changes cannot be analyzed in terms of changes in distances because of the sixth-power dependence on the mean distance. To enhance the information obtained from mean FRET efficiency kinetics, we combined the analyses of FRET efficiency kinetics and equilibrium trFRET experiments. The joint analysis enabled determination of transient distance distributions along the folding reaction both in cases where a two-state transition is valid and in some cases consisting of a three-state scenario. The procedure and its limits were tested by simulations. Experimental data obtained from stopped-flow measurements of the refolding of Escherichia coli adenylate kinase were analyzed. The distance distributions between three double-labeled mutants, in the collapsed transient state, were determined and compared to those obtained experimentally using the double-kinetics technique. The proposed method effectively provides information on distance distributions of kinetically accessed intermediates of fast conformational transitions induced by common relaxation methods.

Magnesium modulates actin binding and ADP release in myosin motors

We examined the magnesium dependence of five class II myosins, including fast skeletal muscle myosin, smooth muscle myosin, β-cardiac myosin (CMIIB), Dictyostelium myosin II (DdMII), and nonmuscle myosin IIA, as well as myosin V. We found that the myosins examined are inhibited in a Mg(2+)-dependent manner (0.3-9.0 mm free Mg(2+)) in both ATPase and motility assays, under conditions in which the ionic strength was held constant. We found that the ADP release rate constant is reduced by Mg(2+) in myosin V, smooth muscle myosin, nonmuscle myosin IIA, CMIIB, and DdMII, although the ADP affinity is fairly insensitive to Mg(2+) in fast skeletal muscle myosin, CMIIB, and DdMII. Single tryptophan probes in the switch I (Trp-239) and switch II (Trp-501) region of DdMII demonstrate these conserved regions of the active site are sensitive to Mg(2+) coordination. Cardiac muscle fiber mechanic studies demonstrate cross-bridge attachment time is increased at higher Mg(2+) concentrations, demonstrating that the ADP release rate constant is slowed by Mg(2+) in the context of an activated muscle fiber. Direct measurements of phosphate release in myosin V demonstrate that Mg(2+) reduces actin affinity in the M·ADP·Pi state, although it does not change the rate of phosphate release. Therefore, the Mg(2+) inhibition of the actin-activated ATPase activity observed in class II myosins is likely the result of Mg(2+)-dependent alterations in actin binding. Overall, our results suggest that Mg(2+) reduces the ADP release rate constant and rate of attachment to actin in both high and low duty ratio myosins.

The path to visualization of walking myosin V by high-speed atomic force microscopy

The quest for understanding the mechanism of myosin-based motility started with studies on muscle contraction. From numerous studies, the basic frameworks for this mechanism were constructed and brilliant hypotheses were put forward. However, the argument about the most crucial issue of how the actin-myosin interaction generates contractile force and shortening has not been definitive. To increase the "directness of measurement", in vitro motility assays and single-molecule optical techniques were created and used. Consequently, detailed knowledge of the motility of muscle myosin evolved, which resulted in provoking more arguments to a higher level. In parallel with technical progress, advances in cell biology led to the discovery of many classes of myosins. Myosin V was discovered to be a processive motor, unlike myosin II. The processivity reduced experimental difficulties because it allowed continuous tracing of the motor action of single myosin V molecules. Extensive studies of myosin V were expected to resolve arguments and build a consensus but did not necessarily do so. The directness of measurement was further enhanced by the recent advent of high-speed atomic force microscopy capable of directly visualizing biological molecules in action at high spatiotemporal resolution. This microscopy clearly visualized myosin V molecules walking on actin filaments and at last provided irrefutable evidence for the swinging lever-arm motion propelling the molecules. However, a peculiar foot stomp behavior also appeared in the AFM movie, raising new questions of the chemo-mechanical coupling in this motor and myosin motors in general. This article reviews these changes in the research of myosin motility and proposes new ideas to resolve the newly raised questions.

Principal component analysis: a method for determining the essential dynamics of proteins

It has become commonplace to employ principal component analysis to reveal the most important motions in proteins. This method is more commonly known by its acronym, PCA. While most popular molecular dynamics packages inevitably provide PCA tools to analyze protein trajectories, researchers often make inferences of their results without having insight into how to make interpretations, and they are often unaware of limitations and generalizations of such analysis. Here we review best practices for applying standard PCA, describe useful variants, discuss why one may wish to make comparison studies, and describe a set of metrics that make comparisons possible. In practice, one will be forced to make inferences about the essential dynamics of a protein without having the desired amount of samples. Therefore, considerable time is spent on describing how to judge the significance of results, highlighting pitfalls. The topic of PCA is reviewed from the perspective of many practical considerations, and useful recipes are provided.

Magnesium impacts myosin V motor activity by altering key conformational changes in the mechanochemical cycle

We investigated how magnesium (Mg) impacts key conformational changes during the ADP binding/release steps in myosin V and how these alterations impact the actomyosin mechanochemical cycle. The conformation of the nucleotide binding pocket was examined with our established FRET system in which myosin V labeled with FlAsH in the upper 50 kDa domain participates in energy transfer with mant labeled nucleotides. We examined the maximum actin-activated ATPase activity of MV FlAsH at a range of free Mg concentrations (0.1-9 mM) and found that the highest activity occurs at low Mg (0.1-0.3 mM), while there is a 50-60% reduction in activity at high Mg (3-9 mM). The motor activity examined with the in vitro motility assay followed a similar Mg-dependence, and the trend was similar with dimeric myosin V. Transient kinetic FRET studies of mantdADP binding/release from actomyosin V FlAsH demonstrate that the transition between the weak and strong actomyosin.ADP states is coupled to movement of the upper 50 kDa domain and is dependent on Mg with the strong state stabilized by Mg. We find that the kinetics of the upper 50 kDa conformational change monitored by FRET correlates well with the ATPase and motility results over a wide range of Mg concentrations. Our results suggest the conformation of the upper 50 kDa domain is highly dynamic in the Mg free actomyosin.ADP state, which is in agreement with ADP binding being entropy driven in the absence of Mg. Overall, our results demonstrate that Mg is a key factor in coupling the nucleotide- and actin-binding regions. In addition, Mg concentrations in the physiological range can alter the structural transition that limits ADP dissociation from actomyosin V, which explains the impact of Mg on actin-activated ATPase activity and in vitro motility.

Global fit analysis of myosin-5b motility reveals thermodynamics of Mg2+-sensitive acto-myosin-ADP states

Kinetic and thermodynamic studies of the mechanochemical cycle of myosin motors are essential for understanding the mechanism of energy conversion. Here, we report our investigation of temperature and free Mg²⁺-ion dependencies of sliding velocities of a high duty ratio class-5 myosin motor, myosin-5b from D. discoideum using in vitro motility assays. Previous studies have shown that the sliding velocity of class-5 myosins obeys modulation by free Mg²⁺-ions. Free Mg²⁺-ions affect ADP release kinetics and the dwell time of actin-attached states. The latter determines the maximal velocity of actin translocation in the sliding filament assay. We measured the temperature dependence of sliding velocity in the range from 5 to 55°C at two limiting free Mg²⁺-ion concentrations. Arrhenius plots demonstrated non-linear behavior. Based on this observation we propose a kinetic model, which explains both sensitivity towards free Mg²⁺-ions and non-linearity of the temperature dependence of sliding velocity. According to this model, velocity is represented as a simple analytical function of temperature and free Mg²⁺-ion concentrations. This function has been applied to global non-linear fit analysis of three data sets including temperature and magnesium (at 20°C) dependence of sliding velocity. As a result we obtain thermodynamic parameters (ΔH_Mg and ΔS_Mg) of a fast equilibrium between magnesium free (AM·D) and magnesium bound acto-myosin-ADP (AM· Mg²⁺D) states and the corresponding enthalpic barriers associated with ADP release (ΔH₁^‡ and ΔH₂^‡). The herein presented integrative approach of data analysis based on global fitting can be applied to the remaining steps of the acto-myosin ATPase cycle facilitating the determination of energetic parameters and thermodynamics of acto-myosin interactions.

A subdomain interaction at the base of the lever allosterically tunes the mechanochemical mechanism of myosin 5a

The motor domain of myosin is the core element performing mechanochemical energy transduction. This domain contains the actin and ATP binding sites and the base of the force-transducing lever. Coordinated subdomain movements within the motor are essential in linking the ATPase chemical cycle to translocation along actin filaments. A dynamic subdomain interface located at the base of the lever was previously shown to exert an allosteric influence on ATP hydrolysis in the non-processive myosin 2 motor. By solution kinetic, spectroscopic and ensemble and single-molecule motility experiments, we determined the role of a class-specific adaptation of this interface in the mechanochemical mechanism of myosin 5a, a processive intracellular transporter. We found that the introduction of a myosin 2-specific repulsive interaction into myosin 5a via the I67K mutation perturbs the strong-binding interaction of myosin 5a with actin, influences the mechanism of ATP binding and facilitates ATP hydrolysis. At the same time, the mutation abolishes the actin-induced activation of ADP release and, in turn, slows down processive motility, especially when myosin experiences mechanical drag exerted by the action of multiple motor molecules bound to the same actin filament. The results highlight that subtle structural adaptations of the common structural scaffold of the myosin motor enable specific allosteric tuning of motor activity shaped by widely differing physiological demands.

Nanoscopic surfactant behavior of the porin MspA in aqueous media

The mycobacterial porin MspA is one of the most stable channel proteins known to date. MspA forms vesicles at low concentrations in aqueous buffers. Evidence from dynamic light scattering, transmission electron microscopy and zeta-potential measurements by electrophoretic light scattering indicate that MspA behaves like a nanoscale surfactant. The extreme thermostability of MspA allows these investigations to be carried out at temperatures as high as 343 K, at which most other proteins would quickly denature. The principles of vesicle formation of MspA as a function of temperature and the underlying thermodynamic factors are discussed here. The results obtained provide crucial evidence in support of the hypothesis that, during vesicle formation, nanoscopic surfactant molecules, such as MspA, deviate from the principles underlined in classical surface chemistry.

Temperature dependent measurements reveal similarities between muscle and non-muscle myosin motility

We examined the temperature dependence of muscle and non-muscle myosin (heavy meromyosin, HMM) with in vitro motility and actin-activated ATPase assays. Our results indicate that myosin V (MV) has a temperature dependence that is similar in both ATPase and motility assays. We demonstrate that skeletal muscle myosin (SK), smooth muscle myosin (SM), and non-muscle myosin IIA (NM) have different temperature dependence in ATPase compared to in vitro motility assays. In the class II myosins we examined (SK, SM, and NM) the rate-limiting step in ATPase assays is thought to be attachment to actin or phosphate release, while for in vitro motility assays it is controversial. In MV the rate-limiting step for both in vitro motility and ATPase assays is known to be ADP release. Consequently, in MV the temperature dependence of the ADP release rate constant is similar to the temperature dependence of in vitro motility. Interestingly, the temperature dependence of the ADP release rate constant of SM and NM was shifted toward the in vitro motility temperature dependence. Our results suggest that the rate-limiting step in SK, SM, and NM may shift from attachment-limited in solution to detachment limited in the in vitro motility assay. Internal strain within the myosin molecule or by neighboring myosin motors may slow ADP release which becomes rate-limiting in the in vitro motility assay. Within this small subset of myosins examined, the in vitro sliding velocity correlates reasonably well with actin-activated ATPase activity, which was suggested by the original study by Barany (J Gen Physiol 50:197-218, 1967).

Switch II mutants reveal coupling between the nucleotide- and actin-binding regions in myosin V

Conserved active-site elements in myosins and other P-loop NTPases play critical roles in nucleotide binding and hydrolysis; however, the mechanisms of allosteric communication among these mechanoenzymes remain unresolved. In this work we introduced the E442A mutation, which abrogates a salt-bridge between switch I and switch II, and the G440A mutation, which abolishes a main-chain hydrogen bond associated with the interaction of switch II with the γ phosphate of ATP, into myosin V. We used fluorescence resonance energy transfer between mant-labeled nucleotides or IAEDANS-labeled actin and FlAsH-labeled myosin V to examine the conformation of the nucleotide- and actin-binding regions, respectively. We demonstrate that in the absence of actin, both the G440A and E442A mutants bind ATP with similar affinity and result in only minor alterations in the conformation of the nucleotide-binding pocket (NBP). In the presence of ADP and actin, both switch II mutants disrupt the formation of a closed NBP actomyosin.ADP state. The G440A mutant also prevents ATP-induced opening of the actin-binding cleft. Our results indicate that the switch II region is critical for stabilizing the closed NBP conformation in the presence of actin, and is essential for communication between the active site and actin-binding region.

Mesoscopic analysis of motion and conformation of cross-bridges

The orientation of a cross-bridge is widely used as a parameter in determining the state of muscle. The conventional measurements of orientation, such as that made by wide-field fluorescence microscopy, electron paramagnetic resonance (EPR) or X-ray diffraction or scattering, report the average orientation of 10¹²-10⁹ myosin cross-bridges. Under conditions where all the cross-bridges are immobile and assume the same orientation, for example in normal skeletal muscle in rigor, it is possible to determine the average orientation from such global measurements. But in actively contracting muscle, where a parameter indicating orientation fluctuates in time, the measurements of the average value provide no information about cross-bridge kinetics. To avoid problems associated with averaging information from trillions of cross-bridges, it is necessary to decrease the number of observed cross-bridges to a mesoscopic value (i.e. the value affected by fluctuations around the average). In such mesoscopic regimes, the averaging of the signal is minimal and dynamic behavior can be examined in great detail. Examples of mesoscopic analysis on skeletal and cardiac muscle are provided.

Characterizing protein motions from structure

To clarify the extent structure plays in determining protein dynamics, a comparative study is made using three models that characterize native state dynamics of single domain proteins starting from known structures taken from four distinct SCOP classifications. A geometrical simulation using the framework rigidity optimized dynamics algorithm (FRODA) based on rigid cluster decomposition is compared to the commonly employed elastic network model (specifically the Anisotropic Network Model ANM) and molecular dynamics (MD) simulation. The essential dynamics are quantified by a mode subspace constructed from ANM and a principal component analysis (PCA) on FRODA and MD trajectories. Aggregate conformational ensembles are constructed to provide a basis for quantitative comparisons between FRODA runs using different parameter settings to critically assess how the predictions of essential dynamics depend on a priori arbitrary user-defined distance constraint rules. We established a range of physicality for these parameters. Surprisingly, FRODA maintains greater intra-consistent results than obtained from MD trajectories, comparable to ANM. Additionally, a mode subspace is constructed from PCA on an exemplar set of myoglobin structures from the Protein Data Bank. Significant overlap across the three model subspaces and the experimentally derived subspace is found. While FRODA provides the most robust sampling and characterization of the native basin, all three models give similar dynamical information of a native state, further demonstrating that structure is the key determinant of dynamics.