Spectral bifurcations in dispersive wave turbulence

Dispersive wave turbulence is studied numerically for a class of one-dimensional nonlinear wave equations. Both deterministic and random (white noise in time) forcings are studied. Four distinct stable spectra are observed—the direct and inverse cascades of weak turbulence (WT) theory, thermal equilibrium, and a fourth spectrum (MMT; Majda, McLaughlin, Tabak). Each spectrum can describe long-time behavior, and each can be only metastable (with quite diverse lifetimes)—depending on details of nonlinearity, forcing, and dissipation. Cases of a long-live MMT transient state dcaying to a state with WT spectra, and vice-versa, are displayed. In the case of freely decaying turbulence, without forcing, both cascades of weak turbulence are observed. These WT states constitute the clearest and most striking numerical observations of WT spectra to date—over four decades of energy, and three decades of spatial, scales. Numerical experiments that study details of the composition, coexistence, and transition between spectra are then discussed, including: (i) for deterministic forcing, sharp distinctions between focusing and defocusing nonlinearities, including the role of long wavelength instabilities, localized coherent structures, and chaotic behavior; (ii) the role of energy growth in time to monitor the selection of MMT or WT spectra; (iii) a second manifestation of the MMT spectrum as it describes a self-similar evolution of the wave, without temporal averaging; (iv) coherent structures and the evolution of the direct and inverse cascades; and (v) nonlocality (in k-space) in the transferral process.

Kinetic equilibrium of forces and molecular events in muscle contraction

In biomolecular systems, the mechanical transfer of free energy occurs with both high efficiency and high speed. It is shown here that such a transfer can be achieved only if the participating free-energy-storing elements exhibit opposing relationships between their content of free energy and the force they exert in the transfer direction. A kinetic equilibrium of forces (KEF) results, in which the transfer of free energy is mediated essentially by thermal molecular motion. On the basis of present evidence, KEF is used as a guiding principle in developing a mechanical model of the crossbridge cycle in muscle contraction. The model allows the basic features of molecular events to be visualized in terms of plausible structures. Real understanding of the process will require identification of the elements that perform the functions described here. Besides chemomechanical energy transduction, KEF may have a role in other biomolecular processes in which free energy is transferred mechanically over large distances.

Brain-wave representation of words by superposition of a few sine waves

Data from three previous experiments were analyzed to test the hypothesis that brain waves of spoken or written words can be represented by the superposition of a few sine waves. First, we averaged the data over trials and a set of subjects, and, in one case, over experimental conditions as well. Next we applied a Fourier transform to the averaged data and selected those frequencies with high energy, in no case more than nine in number. The superpositions of these selected sine waves were taken as prototypes. The averaged unfiltered data were the test samples. The prototypes were used to classify the test samples according to a least-squares criterion of fit. The results were seven of seven correct classifications for the first experiment using only three frequencies, six of eight for the second experiment using nine frequencies, and eight of eight for the third experiment using five frequencies.

The role of structure, energy landscape, dynamics, and allostery in the enzymatic function of myoglobin

The grail of protein science is the connection between structure and function. For myoglobin (Mb) this goal is close. Described as only a passive dioxygen storage protein in texts, we argue here that Mb is actually an allosteric enzyme that can catalyze reactions among small molecules. Studies of the structural, spectroscopic, and kinetic properties of Mb lead to a model that relates structure, energy landscape, dynamics, and function. Mb functions as a miniature chemical reactor, concentrating and orienting diatomic molecules such as NO, CO, O2, and H2O2 in highly conserved internal cavities. Reactions can be controlled because Mb exists in distinct taxonomic substates with different catalytic properties and connectivities of internal cavities.

Top-down free-energy minimization on protein potential energy landscapes

The hierarchical properties of potential energy landscapes have been used to gain insight into thermodynamic and kinetic properties of protein ensembles. It also may be possible to use them to direct computational searches for thermodynamically stable macroscopic states, i.e., computational protein folding. To this end, we have developed a top-down search procedure in which conformation space is recursively dissected according to the intrinsic hierarchical structure of a landscape's effective-energy barriers. This procedure generates an inverted tree similar to the disconnectivity graphs generated by local minima-clustering methods, but it fundamentally differs in the manner in which the portion of the tree that is to be computationally explored is selected. A key ingredient is a branch-selection algorithm that takes advantage of statistically predictive properties of the landscape to guide searches down the tree branches that are most likely to lead to the physically relevant macroscopic states. Using the computational folding of a β-hairpin-forming peptide as an example, we show that such predictive properties indeed exist and can be used for structure prediction by free-energy global minimization.

Kinetic coupling between electron and proton transfer in cytochrome c oxidase: simultaneous measurements of conductance and absorbance changes.

Bovine heart cytochrome c oxidase is an electron-current driven proton pump. To investigate the mechanism by which this pump operates it is important to study individual electron- and proton-transfer reactions in the enzyme, and key reactions in which they are kinetically and thermodynamically coupled. In this work, we have simultaneously measured absorbance changes associated with electron-transfer reactions and conductance changes associated with protonation reactions following pulsed illumination of the photolabile complex of partly reduced bovine cytochrome c oxidase and carbon monoxide. Following CO dissociation, several kinetic phases in the absorbance changes were observed with time constants ranging from approximately 3 microseconds to several milliseconds, reflecting internal electron-transfer reactions within the enzyme. The data show that the rate of one of these electron-transfer reactions, from cytochrome a3 to a on a millisecond time scale, is controlled by a proton-transfer reaction. These results are discussed in terms of a model in which cytochrome a3 interacts electrostatically with a protonatable group, L, in the vicinity of the binuclear center, in equilibrium with the bulk through a proton-conducting pathway, which determines the rate of proton transfer (and indirectly also of electron transfer). The interaction energy of cytochrome a3 with L was determined independently from the pH dependence of the extent of the millisecond-electron transfer and the number of protons released, as determined from the conductance measurements. The magnitude of the interaction energy, 70 meV (1 eV = 1.602 x 10(-19) J), is consistent with a distance of 5-10 A between cytochrome a3 and L. Based on the recently determined high-resolution x-ray structures of bovine and a bacterial cytochrome c oxidase, possible candidates for L and a physiological role for L are discussed.

Unraveling principles of lead discovery: from unfrustrated energy landscapes to novel molecular anchors.

The search for novel leads is a critical step in the drug discovery process. Computational approaches to identify new lead molecules have focused on discovering complete ligands by evaluating the binding affinity of a large number of candidates, a task of considerable complexity. A new computational method is introduced in this work based on the premise that the primary molecular recognition event in the protein binding site may be accomplished by small core fragments that serve as molecular anchors, providing a structurally stable platform that can be subsequently tailored into complete ligands. To fulfill its role, we show that an effective molecular anchor must meet both the thermodynamic requirement of relative energetic stability of a single binding mode and its consistent kinetic accessibility, which may be measured by the structural consensus of multiple docking simulations. From a large number of candidates, this technique is able to identify known core fragments responsible for primary recognition by the FK506 binding protein (FKBP-12), along with a diverse repertoire of novel molecular cores. By contrast, absolute energetic criteria for selecting molecular anchors are found to be promiscuous. A relationship between a minimum frustration principle of binding energy landscapes and receptor-specific molecular anchors in their role as "recognition nuclei" is established, thereby unraveling a mechanism of lead discovery and providing a practical route to receptor-biased computational combinatorial chemistry.

Kinetic traps in lysozyme folding.

Folding of lysozyme from hen egg white was investigated by using interrupted refolding experiments. This method makes use of a high energy barrier between the native state and transient folding intermediates, and, in contrast to conventional optical techniques, it enables one to specifically monitor the amount of native molecules during protein folding. The results show that under strongly native conditions lysozyme can refold on parallel pathways. The major part of the lysozyme molecules (86%) refold on a slow kinetic pathway with well-populated partially folded states. Additionally, 14% of the molecules fold faster. The rate constant of formation of native molecules on the fast pathway corresponds well to the rate constant expected for folding to occur by a two-state process without any detectable intermediates. The results suggest that formation of the native state for the major fraction of lysozyme molecules is retarded compared with the direct folding process. Partially structured intermediates that transiently populate seem to be kinetically trapped in a conformation that can only slowly reach the native structure.