Symmetry in chemistry from the hydrogen atom to proteins

The last 2 decades have seen discoveries in highly excited states of atoms and molecules of phenomena that are qualitatively different from the “planetary” model of the atom, and the near-rigid model of molecules, characteristic of these systems in their low-energy states. A unified view is emerging in terms of approximate dynamical symmetry principles. Highly excited states of two-electron atoms display “molecular” behavior of a nonrigid linear structure undergoing collective rotation and vibration. Highly excited states of molecules described in the “standard molecular model” display normal mode couplings, which induce bifurcations on the route to molecular chaos. New approaches such as rigid–nonrigid correlation, vibrons, and quantum groups suggest a unified view of collective electronic motion in atoms and nuclear motion in molecules.

Single-pair fluorescence resonance energy transfer on freely diffusing molecules: Observation of Förster distance dependence and subpopulations

Photon bursts from single diffusing donor-acceptor labeled macromolecules were used to measure intramolecular distances and identify subpopulations of freely diffusing macromolecules in a heterogeneous ensemble. By using DNA as a rigid spacer, a series of constructs with varying intramolecular donor-acceptor spacings were used to measure the mean and distribution width of fluorescence resonance energy transfer (FRET) efficiencies as a function of distance. The mean single-pair FRET efficiencies qualitatively follow the distance dependence predicted by Förster theory. Possible contributions to the widths of the FRET efficiency distributions are discussed, and potential applications in the study of biopolymer conformational dynamics are suggested. The ability to measure intramolecular (and intermolecular) distances for single molecules implies the ability to distinguish and monitor subpopulations of molecules in a mixture with different distances or conformational states. This is demonstrated by monitoring substrate and product subpopulations before and after a restriction endonuclease cleavage reaction. Distance measurements at single-molecule resolution also should facilitate the study of complex reactions such as biopolymer folding. To this end, the denaturation of a DNA hairpin was examined by using single-pair FRET.

Equilibrium distributions of topological states in circular DNA: Interplay of supercoiling and knotting

Two variables define the topological state of closed double-stranded DNA: the knot type, K, and ΔLk, the linking number difference from relaxed DNA. The equilibrium distribution of probabilities of these states, P(ΔLk, K), is related to two conditional distributions: P(ΔLk|K), the distribution of ΔLk for a particular K, and P(K|ΔLk) and also to two simple distributions: P(ΔLk), the distribution of ΔLk irrespective of K, and P(K). We explored the relationships between these distributions. P(ΔLk, K), P(ΔLk), and P(K|ΔLk) were calculated from the simulated distributions of P(ΔLk|K) and of P(K). The calculated distributions agreed with previous experimental and theoretical results and greatly advanced on them. Our major focus was on P(K|ΔLk), the distribution of knot types for a particular value of ΔLk, which had not been evaluated previously. We found that unknotted circular DNA is not the most probable state beyond small values of ΔLk. Highly chiral knotted DNA has a lower free energy because it has less torsional deformation. Surprisingly, even at |ΔLk| > 12, only one or two knot types dominate the P(K|ΔLk) distribution despite the huge number of knots of comparable complexity. A large fraction of the knots found belong to the small family of torus knots. The relationship between supercoiling and knotting in vivo is discussed.

Spectral diffusion and the energy landscape of a protein

We present a novel type of spectral diffusion experiment in the millikelvin range to characterize the energy landscape of a protein as compared with that of a glass. We measure the time evolution of spectral holes for more than 300 hr after well-defined initial nonequilibrium conditions. We show that the model of noninteracting two-level systems can describe spectral diffusion in the glass, but fails for the protein. Our results further demonstrate that randomness in the energy landscape of a protein shows features of organization. There are “deep minimum” states separated by barriers, the heights of which we are able to estimate. The energy landscape of a glass is featureless by comparison.

Dynamics and folding of single two-stranded coiled-coil peptides studied by fluorescent energy transfer confocal microscopy

We report single-molecule measurements on the folding and unfolding conformational equilibrium distributions and dynamics of a disulfide crosslinked version of the two-stranded coiled coil from GCN4. The peptide has a fluorescent donor and acceptor at the N termini of its two chains and a Cys disulfide near its C terminus. Thus, folding brings the two N termini of the two chains close together, resulting in an enhancement of fluorescent resonant energy transfer. End-to-end distance distributions have thus been characterized under conditions where the peptide is nearly fully folded (0 M urea), unfolded (7.4 M urea), and in dynamic exchange between folded and unfolded states (3.0 M urea). The distributions have been compared for the peptide freely diffusing in solution and deposited onto aminopropyl silanized glass. As the urea concentration is increased, the mean end-to-end distance shifts to longer distances both in free solution and on the modified surface. The widths of these distributions indicate that the molecules are undergoing millisecond conformational fluctuations. Under all three conditions, these fluctuations gave nonexponential correlations on 1- to 100-ms time scale. A component of the correlation decay that was sensitive to the concentration of urea corresponded to that measured by bulk relaxation kinetics. The trajectories provided effective intramolecular diffusion coefficients as a function of the end-to-end distances for the folded and unfolded states. Single-molecule folding studies provide information concerning the distributions of conformational states in the folded, unfolded, and dynamically interconverting states.

The vibrational energy flow transition in organic molecules: Theory meets experiment

Most large dynamical systems are thought to have ergodic dynamics, whereas small systems may not have free interchange of energy between degrees of freedom. This assumption is made in many areas of chemistry and physics, ranging from nuclei to reacting molecules and on to quantum dots. We examine the transition to facile vibrational energy flow in a large set of organic molecules as molecular size is increased. Both analytical and computational results based on local random matrix models describe the transition to unrestricted vibrational energy flow in these molecules. In particular, the models connect the number of states participating in intramolecular energy flow to simple molecular properties such as the molecular size and the distribution of vibrational frequencies. The transition itself is governed by a local anharmonic coupling strength and a local state density. The theoretical results for the transition characteristics compare well with those implied by experimental measurements using IR fluorescence spectroscopy of dilution factors reported by Stewart and McDonald [Stewart, G. M. & McDonald, J. D. (1983) J. Chem. Phys. 78, 3907–3915].

Solvent effects on the energy landscapes and folding kinetics of polyalanine

The effect of a solvation on the thermodynamics and kinetics of polyalanine (Ala12) is explored on the basis of its energy landscapes in vacuum and in an aqueous solution. Both energy landscapes are characterized by two basins, one associated with α-helical structures and the other with coil and β-structures of the peptide. In both environments, the basin that corresponds to the α-helical structure is considerably narrower than the basin corresponding to the β-state, reflecting their different contributions to the entropy of the peptide. In vacuum, the α-helical state of Ala12 constitutes the native state, in agreement with common helical propensity scales, whereas in the aqueous medium, the α-helical state is destabilized, and the β-state becomes the native state. Thus solvation has a dramatic effect on the energy landscape of this peptide, resulting in an inverted stability of the two states. Different folding and unfolding time scales for Ala12 in hydrophilic and hydrophobic chemical environments are caused by the higher entropy of the native state in water relative to vacuum. The concept of a helical propensity has to be extended to incorporate environmental solvent effects.

An unusual pathway of excitation energy deactivation in carotenoids: Singlet-to-triplet conversion on an ultrafast timescale in a photosynthetic antenna

Carotenoids are important biomolecules that are ubiquitous in nature and find widespread application in medicine. In photosynthesis, they have a large role in light harvesting (LH) and photoprotection. They exert their LH function by donating their excited singlet state to nearby (bacterio)chlorophyll molecules. In photosynthetic bacteria, the efficiency of this energy transfer process can be as low as 30%. Here, we present evidence that an unusual pathway of excited state relaxation in carotenoids underlies this poor LH function, by which carotenoid triplet states are generated directly from carotenoid singlet states. This pathway, operative on a femtosecond and picosecond timescale, involves an intermediate state, which we identify as a new, hitherto uncharacterized carotenoid singlet excited state. In LH complex-bound carotenoids, this state is the precursor on the reaction pathway to the triplet state, whereas in extracted carotenoids in solution, this state returns to the singlet ground state without forming any triplets. We discuss the possible identity of this excited state and argue that fission of the singlet state into a pair of triplet states on individual carotenoid molecules constitutes the mechanism by which the triplets are generated. This is, to our knowledge, the first ever direct observation of a singlet-to-triplet conversion process on an ultrafast timescale in a photosynthetic antenna.

Logic gates using high Rydberg states

Connected logic gates can be operated on the levels of one molecule by making use of the special properties of high Rydberg states. Explicit experimental results for the NO molecule are provided as an example. A number of other options, including that of several gates concatenated so as to operate as a full adder, are discussed. Specific properties of high Rydberg states that are used are: their autoionization is delayed so that they can be distinguished from direct multiphoton ionization, during their long life such states also can decay by energy transfer to the molecular core in a way that can be controlled by the judicious application of very weak external electrical fields, and the Rydberg states can be detected by the application of an ionizing electrical field. The combination of two (or three) color photons with and without external weak fields allows the construction of quite elaborate logic circuit diagrams and shows that taking advantage of the different intramolecular dynamics of levels that differ by their excitation enables the compounding of logic operations on one molecular frame.

Chemically distinct transition states govern rapid dissociation of single L-selectin bonds under force

Carbohydrate–protein bonds interrupt the rapid flow of leukocytes in the circulation by initiation of rolling and tethering at vessel walls. The cell surface carbohydrate ligands are glycosylated proteins like the mucin P-selectin glycoprotein ligand-1 (PSGL-1), which bind ubiquitously to the family of E-, P-, and L-selectin proteins in membranes of leukocytes and endothelium. The current view is that carbohydrate–selectin bonds dissociate a few times per second, and the unbinding rate increases weakly with force. However, such studies have provided little insight into how numerous hydrogen bonds, a Ca2+ metal ion bond, and other interactions contribute to the mechanical strength of these attachments. Decorating a force probe with very dilute ligands and controlling touch to achieve rare single-bond events, we have varied the unbinding rates of carbohydrate–selectin bonds by detachment with ramps of force/time from 10 to 100,000 pN/sec. Testing PSGL-1, its outer 19 aa (19FT), and sialyl LewisX (sLeX) against L-selectin in vitro on glass microspheres and in situ on neutrophils, we found that the unbinding rates followed the same dependence on force and increased by nearly 1,000-fold as rupture forces rose from a few to ≈200 pN. Plotted on a logarithmic scale of loading rate, the rupture forces reveal two prominent energy barriers along the unbinding pathway. Strengths above 75 pN arise from rapid detachment (<0.01 sec) impeded by an inner barrier that requires a Ca2+ bond between a single sLeX and the lectin domain. Strengths below 75 pN occur under slow detachment (>0.01 sec) impeded by the outer barrier, which appears to involve an array of weak (putatively hydrogen) bonds.

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.

Dynamical hierarchy in transition states: Why and how does a system climb over the mountain?

How a reacting system climbs through a transition state during the course of a reaction has been an intriguing subject for decades. Here we present and quantify a technique to identify and characterize local invariances about the transition state of an N-particle Hamiltonian system, using Lie canonical perturbation theory combined with microcanonical molecular dynamics simulation. We show that at least three distinct energy regimes of dynamical behavior occur in the region of the transition state, distinguished by the extent of their local dynamical invariance and regularity. Isomerization of a six-atom Lennard–Jones cluster illustrates this: up to energies high enough to make the system manifestly chaotic, approximate invariants of motion associated with a reaction coordinate in phase space imply a many-body dividing hypersurface in phase space that is free of recrossings even in a sea of chaos. The method makes it possible to visualize the stable and unstable invariant manifolds leading to and from the transition state, i.e., the reaction path in phase space, and how this regularity turns to chaos with increasing total energy of the system. This, in turn, illuminates a new type of phase space bottleneck in the region of a transition state that emerges as the total energy and mode coupling increase, which keeps a reacting system increasingly trapped in that region.

Ultra-fast excited state dynamics in green fluorescent protein: multiple states and proton transfer.

The green fluorescent protein (GFP) of the jellyfish Aequorea Victoria has attracted widespread interest since the discovery that its chromophore is generated by the autocatalytic, posttranslational cyclization and oxidation of a hexapeptide unit. This permits fusion of the DNA sequence of GFP with that of any protein whose expression or transport can then be readily monitored by sensitive fluorescence methods without the need to add exogenous fluorescent dyes. The excited state dynamics of GFP were studied following photo-excitation of each of its two strong absorption bands in the visible using fluorescence upconversion spectroscopy (about 100 fs time resolution). It is shown that excitation of the higher energy feature leads very rapidly to a form of the lower energy species, and that the excited state interconversion rate can be markedly slowed by replacing exchangeable protons with deuterons. This observation and others lead to a model in which the two visible absorption bands correspond to GFP in two ground-state conformations. These conformations can be slowly interconverted in the ground state, but the process is much faster in the excited state. The observed isotope effect suggests that the initial excited state process involves a proton transfer reaction that is followed by additional structural changes. These observations may help to rationalize and motivate mutations that alter the absorption properties and improve the photo stability of GFP.

Bond orientational order, molecular motion, and free energy of high-density DNA mesophases.

By equilibrating condensed DNA arrays against reservoirs of known osmotic stress and examining them with several structural probes, it has been possible to achieve a detailed thermodynamic and structural characterization of the change between two distinct regions on the liquid-crystalline phase diagram: (i) a higher density hexagonally packed region with long-range bond orientational order in the plane perpendicular to the average molecular direction and (ii) a lower density cholesteric region with fluid-like positional order. X-ray scattering on highly ordered DNA arrays at high density and with the helical axis oriented parallel to the incoming beam showed a sixfold azimuthal modulation of the first-order diffraction peak that reflects the macroscopic bond-orientational order. Transition to the less-dense cholesteric phase through osmotically controlled swelling shows the loss of this bond orientational order, which had been expected from the change in optical birefringence patterns and which is consistent with a rapid onset of molecular positional disorder. This change in order was previously inferred from intermolecular force measurements and is now confirmed by 31P NMR. Controlled reversible swelling and compaction under osmotic stress, spanning a range of densities between approximately 120 mg/ml to approximately 600 mg/ml, allow measurement of the free-energy changes throughout each phase and at the phase transition, essential information for theories of liquid-crystalline states.