Quasiparticle dispersion in Bi2Sr2CaCu2O8 is investigated with improved angular resolution as a function of temperature and doping. Unlike the linear dispersion predicted by the band calculation, the data show a sharp break in dispersion at 50+/-15 meV binding energy where the velocity changes by a factor of 2 or more. This change provides an energy scale in the quasiparticle self-energy. This break in dispersion is evident at and away from the d-wave node line, but the magnitude of the dispersion change decreases with temperature and with increasing doping.

By representing the high-resolution crystal structures of a number of enzymes using the elastic network model, it has been shown that only a few low-frequency normal modes are needed to describe the large-scale domain movements that are triggered by ligand binding. Here we explore a link between the nearly invariant nature of the modes that describe functional dynamics at the mesoscopic level and the large evolutionary sequence variations at the residue level. By using a structural perturbation method (SPM), which probes the residue-specific response to perturbations (or mutations), we identify a sparse network of strongly conserved residues that transmit allosteric signals in three structurally unrelated biological nanomachines, namely, DNA polymerase, myosin motor, and the Escherichia coli chaperonin. Based on the response of every mode to perturbations, which are generated by interchanging specific sequence pairs in a multiple sequence alignment, we show that the functionally relevant low-frequency modes are most robust to sequence variations. Our work shows that robustness of dynamical modes at the mesoscopic level is encoded in the structure through a sparse network of residues that transmit allosteric signals.DNA polymerase ͉ myosin ͉ GroEL ͉ elastic network model ͉ robustness A common theme in the function of many biological nanomachines is that they undergo large-scale domain movements in response to binding of ligands or other biomolecules. DNA polymerases are well studied examples in which such large conformational changes have been described using crystal structures and biophysical studies (1, 2). The global structure of polymerases is described by using the hand metaphor (3). The first step in the function involves the binding of the duplex DNA to the unliganded polymerases, which triggers the closing of the thumb domain around the DNA. Subsequent binding of dNTP to the binary complex results in the rotation of the fingers from the open conformation to the closed state. Similarly, large-scale conformational changes, induced by ATP binding and hydrolysis, are involved in the directed movements of myosins on actin filaments (4). In another class of nanomachines, binding of ATP to the equatorial domain of the Escherichia coli chaperonin GroEL results in a downward movement of the intermediate domain, which results in the locking of the ATP-binding sites (5). Upon binding of GroES, the apical domain swings upward and simultaneously twists, thus doubling the volume of the cavity as compared with the unliganded state. Such large-scale conformational changes are linked to the function of GroEL (6).To obtain insights into these universally prevalent motions, normal modes analysis (NMA) of the elastic network model (ENM) representations of large protein complexes have been used to describe ligand-induced conformational changes. A number of studies on vastly different enzymes have shown that the domain movements are dominated by one or a few normal modes (7-17). To understand how the allosteric transitions are...

In this work, we report on a study of the structure-function relationships for three families of motor proteins, including kinesins, myosins, and F1-ATPases, by using a version of the simple elastic-network model of large-scale protein motions originally proposed by Tirion [Tirion, M. (1996) Phys. Rev. Lett. 77, 1905Lett. 77, -1908. We find a surprising dichotomy between kinesins and the other motor proteins (myosins and F1-ATPase). For the latter, there exist one or two dominant lowest-frequency modes (one for myosin, two for F1-ATPase) obtained from normal-mode analysis of the elastic-network model, which overlap remarkably well with the measured conformational changes derived from pairs of solved crystal structures in different states. Furthermore, we find that the computed global conformational changes induced by the measured deformation of the nucleotide-binding pocket also overlap well with the measured conformational changes, which is consistent with the ''nucleotide-binding-induced power-stroke'' scenario. In contrast, for kinesins, this simplicity breaks down. Multiple modes are needed to generate the measured conformational changes, and the computed displacements induced by deforming the nucleotide-binding pocket also overlap poorly with the measured conformational changes, and are insufficient to explain the large-scale motion of the relay helix and the linker region. This finding may suggest the presence of two different mechanisms for myosins and kinesins, despite their strong evolutionary ties and structural similarities. T he mechanism by which molecular motor proteins convert energy from ATP hydrolysis into mechanical work is currently an active area of research (1). The coupling of the ATP hydrolysis cycle to force generation and the determinants of motor polarity are actively being investigated by using biochemical, biophysical, and molecular approaches.The availability of crystal structures of myosins in different nucleotide-binding states has been helpful in furthering the understanding of the working mechanism of myosin. A purely mechanical power-stroke scenario has been proposed to explain the observed conformational changes and their coupling to the binding and hydrolysis of the nucleotide. In this class of models (1, 2), the motor contains an elastic element, a spring that becomes strained as a result of the transitions between chemical states of the nucleotide: the relief of this internal strain is the driving force for the forward movement.In the case of kinesin, the picture is more elusive, mostly due to the lack of solved structures in the ATP-binding state. Two main scenarios exist. The first is based on the mechanical power stroke that amplifies the small changes in the nucleotide and microtubule-binding sites to generate large-scale motion in the linker (1) (similar to the power-stroke scenario for myosins). The second one is based on the model of a biased Brownian ratchet where a nondeterministic random walk in a biased potential forms the basis of the mechanochemical conversion ...

The open/closed transition in polymerases is a crucial event in DNA replication and transcription. We hypothesize that the residues that transmit the signal for the open/closed transition are also strongly conserved. To identify the dynamically relevant residues, we use an elastic network model of polymerases and probe the residue-specific response to a local perturbation. In a variety of DNA/RNA polymerases, a network of residues spanning the fingers and palm domains is involved in the open/closed transition. The similarity in the network of residues responsible for large-scale domain movements supports the notion of a common induced-fit mechanism in the polymerase families for the formation of a closed ternary complex. Multiple sequence alignment shows that many of these residues are also strongly conserved. Residues with the largest sensitivity to local perturbations include those that are not so obviously involved in the polymerase catalysis. Our results suggest that mutations of the mechanical "hot spots" can compromise the efficiency of the enzyme.

We develop a mixed elastic network model (MENM) to study large-scale conformational transitions of proteins between two (or more) known structures. Elastic network potentials for the beginning and end states of a transition are combined, in effect, by adding their respective partition functions. The resulting effective MENM energy function smoothly interpolates between the original surfaces, and retains the beginning and end structures as local minima. Saddle points, transition paths, potentials of mean force, and partition functions can be found efficiently by largely analytic methods. To characterize the protein motions during a conformational transition, we follow "transition paths" on the MENM surface that connect the beginning and end structures and are invariant to parameterizations of the model and the mathematical form of the mixing scheme. As illustrations of the general formalism, we study large-scale conformation changes of the motor proteins KIF1A kinesin and myosin II. We generate possible transition paths for these two proteins that reveal details of their conformational motions. The MENM formalism is computationally efficient and generally applicable even for large protein systems that undergo highly collective structural changes.

The Escherichia coli chaperonin GroEL, which helps proteins to fold, consists of two heptameric rings stacked back-to-back. During the reaction cycle GroEL undergoes a series of allosteric transitions triggered by ligand (substrate protein, ATP, and the cochaperonin GroES) binding. Based on an elastic network model of the bullet-shaped double-ring chaperonin GroEL-(ADP)(7)-GroES structure (R''T state), we perform a normal mode analysis to explore the energetically favorable collective motions encoded in the R''T structure. By comparing each normal mode with the observed conformational changes in the R''T --> TR'' transition, a single dominant normal mode provides a simple description of this highly intricate allosteric transition. A detailed analysis of this relatively high-frequency mode describes the structural and dynamic changes that underlie the positive intra-ring and negative inter-ring cooperativity. The dynamics embedded in the dominant mode entails highly concerted structural motions with approximate preservation of sevenfold symmetry within each ring and negatively correlated ones between the two rings. The dominant normal mode (in comparison with the other modes) is robust to parametric perturbations caused by sequence variations, which validates its functional importance. Response of the dominant mode to local changes that mimic mutations using the structural perturbation method technique leads to a wiring diagram that identifies a network of key residues that regulate the allosteric transitions. Many of these residues are located in intersubunit interfaces, and may therefore play a critical role in transmitting allosteric signals between subunits.

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Based on the elastic network model, we develop a new analysis for protein complexes, which probes the local dynamics of a subsystem that is elastically coupled to a fluctuating environment. This method is applied to a comparative dynamical analysis of the nucleotide-binding pocket of two motor proteins-myosins and kinesins. In myosins, the observed structural changes in the nucleotide-pocket from the transition state to the rigorlike state are dominated by the lowest normal mode that involves significant movements in both switch I and switch II; in kinesins, the measured conformational changes in the nucleotide-pocket are also dominated by the lowest mode, which, however, only involves large movement in switch I. We then compute the global structural changes induced by the nucleotide-pocket deformations as described by the dominant pocket-mode, which yield encouraging results: in myosins, multiple hinge motions involving the opening/closing of the cleft between the upper and lower 50 -kDa subdomains and the swinging movement of the converter are induced, which are dominated by precisely the same global mode that has been recently identified by us as important to the dynamical correlations among the nucleotide-pocket, the actin-binding site, and the converter; in kinesins, the induced global conformational changes are well described by a highly collective global mode which hints for a dynamical pathway spanning from the nucleotide-pocket to the neck-linker via the H6 helix.