Long-term observation of fluorescence of free single molecules to explore protein-folding energy landscapes

A method was developed to detect fluorescence intensity signals from single molecules diffusing freely in a capillary cell. A unique optical system based on a spherical mirror was designed to enable quantitative detection of the fluorescence intensity. Furthermore, "flow-and-stop" control of the sample can extend the observation time of single molecules to several seconds, which is more than 1000 times longer than the observation time available using a typical confocal method. We used this method to scrutinize the fluorescence time series of the labeled cytochrome c in the unfolded state. Time series analyses of the trajectories based on local equilibrium state analysis revealed dynamically differing substates on a millisecond time scale. This system presents a new avenue for experimental characterization of the protein-folding energy landscape.     

Stability analysis of multiple nonequilibrium fixed points in self-consistent electron transport calculations

We present a method to perform stability analysis of nonequilibrium fixed points appearing in self-consistent electron transport calculations. The nonequilibrium fixed points are given by the self-consistent solution of stationary, nonlinear kinetic equation for single-particle density matrix. We obtain the stability matrix by linearizing the kinetic equation around the fixed points and analyze the real part of its spectrum to assess the asymptotic time behavior of the fixed points. We derive expressions for the stability matrices within Hartree-Fock and linear response adiabatic time-dependent density functional theory. The stability analysis of multiple fixed points is performed within the nonequilibrium Hartree-Fock approximation for the electron transport through a molecule with a spin-degenerate single level with local Coulomb interaction.     

Characterizing Single‐Molecule FRET Dynamics with Probability Distribution Analysis

Probability distribution analysis (PDA) is a recently developed statistical tool for predicting the shapes of single‐molecule fluorescence resonance energy transfer (smFRET) histograms, which allows the identification of single or multiple static molecular species within a single histogram. We used a generalized PDA method to predict the shapes of FRET histograms for molecules interconverting dynamically between multiple states. This method is tested on a series of model systems, including both static DNA fragments and dynamic DNA hairpins. By fitting the shape of this expected distribution to experimental data, the timescale of hairpin conformational fluctuations can be recovered, in good agreement with earlier published results obtained using different techniques. This method is also applied to studying the conformational fluctuations in the unliganded Klenow fragment (KF) of Escherichia coli DNA polymerase I, which allows both confirmation of the consistency of a simple, two‐state kinetic model with the observed smFRET distribution of unliganded KF and extraction of a millisecond fluctuation timescale, in good agreement with rates reported elsewhere. We expect this method to be useful in extracting rates from processes exhibiting dynamic FRET, and in hypothesis‐testing models of conformational dynamics against experimental data.     

Energy Landscape of Aptamer/Protein Complexes Studied by Single‐Molecule Force Spectroscopy

Aptamers are single‐stranded nucleic acid molecules selected in vitro to bind to a variety of target molecules. Aptamers bound to proteins are emerging as a new class of molecules that rival commonly used antibodies in both therapeutic and diagnostic applications. With the increasing application of aptamers as molecular probes for protein recognition, it is important to understand the molecular mechanism of aptamer–protein interaction. Recently, we developed a method of using atomic force microscopy (AFM) to study the single‐molecule rupture force of aptamer/protein complexes. In this work, we investigate further the unbinding dynamics of aptamer/protein complexes and their dissociation‐energy landscape by AFM. The dependence of single‐molecule force on the AFM loading rate was plotted for three aptamer/protein complexes and their dissociation rate constants, and other parameters characterizing their dissociation pathways were obtained. Furthermore, the single‐molecule force spectra of three aptamer/protein complexes were compared to those of the corresponding antibody/protein complexes in the same loading‐rate range. The results revealed two activation barriers and one intermediate state in the unbinding process of aptamer/protein complexes, which is different from the energy landscape of antibody/protein complexes. The results provide new information for the study of aptamer–protein interaction at the molecular level.     

Parallel, linear-scaling building-block and embedding method based on localized orbitals and orbital-specific basis sets

We present a linear scaling method for the energy minimization step of semiempirical and first-principles Hartree-Fock and Kohn-Sham calculations. It is based on the self-consistent calculation of the optimum localized orbitals of any localization method of choice and on the use of orbital-specific basis sets. The full set of localized orbitals of a large molecule is seen as an orbital mosaic where each tessera is made of only a few of them. The orbital tesserae are computed out of a set of embedded cluster pseudoeigenvalue coupled equations which are solved in a building-block self-consistent fashion. In each iteration, the embedded cluster equations are solved independently of each other and, as a result, the method is parallel at a high level of the calculation. In addition to full system calculations, the method enables to perform simpler, much less demanding embedded cluster calculations, where only a fraction of the localized molecular orbitals are variational while the rest is frozen, taking advantage of the transferability of the localized orbitals of a given localization method between similar molecules. Monitoring single point energy calculations of large poly(ethylene oxide) molecules and three dimensional carbon monoxide clusters using an extended Huckel Hamiltonian are presented.     

Single molecule probing of the glass transition phenomenon: simulations of several types of probes

Molecular dynamics simulations of a system of short bead-spring chains containing an additional dumbbell are presented and analyzed. This system represents a coarse-grained model for a melt of short, flexible polymers containing fluorescent probe molecules at very dilute concentration. It is shown that such a system is very well suited to study aspects of the glass transition of the undercooled polymer melt via single molecule spectroscopy, which are not easily accessed by other methods. Such aspects include data which can be extracted from a study of fluctuations along a trajectory of the single molecule, probing the rugged energy landscape of the glass-forming liquid and transitions from one metabasin of this energy landscape to the next one. Such an information can be inferred from "distance maps" constructed from trajectories characterizing the translational and orientational motion of the probe. At the same time, determining autocorrelation functions along such trajectories, it is shown for several types of probes (differing in their size and/or mass within reasonable limits) that this time-averaged information of the probe is fully compatible with ensemble averaged information on the relaxation of the glass-forming matrix, accessible from bulk measurements. The analyzed quantities include the fluorescence lifetime, linear dichroism, and also various orientational correlation functions of the probe, in order to provide guidance to experimental work. Similar to earlier findings from simulations of bulk molecular fluids, deviations from the Stokes-Einstein and Stokes-Einstein-Debye relations are observed.     

Reorientation and translation of individual dye molecules in a polymer matrix

The orientational and translational motion of individual dye molecules embedded in a polymer matrix is studied in the temperature regime above the glass transition. The rotational diffusion close to the glass transition is heterogeneous on the single molecule level and few sudden changes in the reorientational speed of single molecules are found. The exchange between these reorientational speeds is found to be one order of magnitude slower than the reorientational time constant of the molecules. Translational motion can be clearly identified at about 1.2 T_g. However, the translational diffusion shows no signs of heterogeneity on the timescale of our experiments, from which we conclude, that the timescale of the exchange process between microenvironments has become too fast or that no heterogeneity exists at the temperatures above 1.2 T_g.     

Relaxation of highly vibrationally excited molecules

The rate constant for V-V relaxation of diatomic homonuclear molecules is determined from collisions of unexcited molecules with molecules near the dissociation threshold. It is shown that a quasi-resonant transition through several levels dominates in this process so that the energy difference between the initial and final states of the excited molecule is approximately equal to the transition energy from the zero level to the first one. The relaxation kinetics of excited molecules is studied. Absorption of IR radiation by polyatomic molecules is discussed taking into account collisions. A criterion for the negligibility of energy loss is obtained, and the dissociation rate of molecules under the action of IR laser irradiation found. The computational results are compared with experimental data. A self-consistent procedure is formulated for a gas irradiated by a quasi-continuously operating IR laser, in order to determine simultaneously the dissociation rate, dissipation energy flux and temperature. The existence of an optimum radiation region for dissociation is found.     

Unexpected Photoluminescence of Fluorinated Naphthalene Diimides

Two new amino core‐substituted naphthalene diimides (cNDIs) bearing fluorinated side chains have been synthesised. Steady‐state and time‐resolved fluorescence spectroscopy reveals unprecedented optical properties for the cNDIs with high quantum yields of ～0.8 and fluorescence lifetimes of ～13 ns in a range of solvents. These properties are apparent at the level of single molecules, where the compounds also show exceptional photostability under pulsed‐laser excitation. Photon emission is remarkably consistent with very few long timescale (millisecond or longer) interruptions with molecules regularly undergoing >10⁷ cycles of excitation and emission. Intermittencies owing to triplet‐state formation occur on a sub‐millisecond timescale with a low yield of 1–2 %, indicating that the presence of the fluorine atoms does not lead to a significant triplet yield through the heavy‐atom effect. These properties make the compounds excellent candidates for single‐molecule labelling applications.     

Searching and optimizing structure ensembles for complex flexible sugars

NMR restrictions are suitable to specify the geometry of a molecule when a single well-defined global free energy minimum exists that is significantly lower than other local minima. Carbohydrates are quite flexible, and therefore, NMR observables do not always correlate with a single conformer but instead with an ensemble of low free energy conformers that can be accessed by thermal fluctuations. In this communication, we describe a novel procedure to identify and weight the contribution to the ensemble of local minima conformers based on comparison to residual dipolar couplings (RDCs) or other NMR observables, such as scalar couplings. A genetic algorithm is implemented to globally minimize the R factor comparing calculated RDCs to experiment. This is done by optimizing the weights of different conformers derived from the exhaustive local minima conformational search program, fast sugar structure prediction software (FSPS). We apply this framework to six human milk sugars, LND-1, LNF-1, LNF-2, LNF-3, LNnT, and LNT, and are able to determine corresponding population weights for the ensemble of conformers. Interestingly, our results indicate that in all cases the RDCs can be well represented by only a few most important conformers. This confirms that several, but not all of the glycosidic linkages in histo-blood group "epitopes" are quite rigid.     

Generalized energy-based fragmentation approach for computing the ground-state energies and properties of large molecules

We present a generalized energy-based fragmentation (GEBF) approach for approximately predicting the ground-state energies and molecular properties of large molecules, especially those charged and polar molecules. In this approach, the total energy (or properties) of a large molecule can be approximately obtained from energy (or properties) calculations on various small subsystems, each of which is constructed to contain a certain fragment and its local surroundings within a given distance. In the quantum chemistry calculation of a given subsystem, those distant atoms (outside this subsystem) are modeled as background point charges at the corresponding nuclear centers. This treatment allows long-range electrostatic interaction and polarization effects between distant fragments to be taken into account approximately, which are very important for polar and charged molecules. We also propose a new fragmentation scheme for constructing subsystems. Our test calculations at the Hartree-Fock and second-order M?ller-Plesser perturbation theory levels demonstrate that the approach could yield satisfactory ground-state energies, the dipole moments, and static polarizabilities for polar and charged molecules such as water clusters and proteins.     

Reactions associated with ionization in water: a direct ab initio dynamics study of ionization in (H2O)17

Quasiclassical ab initio simulations of the ionization dynamics in a (H(2)O)(17) cluster, the first water cluster that includes a fourfold coordinated (internally solvated) water molecule, have been carried out to obtain a detailed picture of the elementary processes and energy redistribution induced by ionization in a model of aqueous water. General features observable from the simulations are the following: (i) well within 100 fs following the ionization, one or more proton transfers are seen to take place from the "ionized molecule" to neighboring molecules and beyond, forming a hydronium ion and a hydroxyl radical; (ii) two water molecules close to the ionized water molecule play an important role in the reaction, in what we term a "reactive trimer." The reaction time is gated by the encounter of the ionized water molecule with these two neighboring molecules, and this occurs anytime between 10 and 50 fs after the ionization. The distances of approach between the ionized molecule and the neighboring molecules indeed display best the time characteristics of the transfer of a proton, and thus of the formation of a hydronium ion and a OH radical. These findings are consistent with those for smaller cyclic clusters, albeit the dynamics of the proton transfer displays more varieties in the larger cluster than in the small cyclic clusters. We used a partitioning scheme for the kinetic energy in the (H(2)O)(17) system that distinguishes between the reactive trimer and the surrounding "medium." The analysis of the simulations indicates that the kinetic energy of the surrounding medium increases markedly right after the event of ionization, a manifestation of the local heating of the medium. The increase in kinetic energy is consistent with a reorganization of the surrounding medium, electrostatically forced in a very short time by the water cation and in a longer time by the formation of the hydronium ion.     

Computational experiments on the intramolecular energy flow in macromolecules

The microscopic details of the flow of energy in a single chain of polyethylene containing 300 atoms is discussed. The intramolecular dynamics of the polyethylene molecule is studied as a function of CH stretch excitation, temperature, and pressure. The rate of energy flow from CH stretching modes is found to be very rapid and irreversible, occurring on a timescale of less than 0.5 ps at low temperatures, and increases with temperature. A general characteristic two-phase energy flow behavior is observed, where there is initially a very rapid flow (due to the decay of the initial excitation) followed by a slower flow (due to energy redistribution throughout the system). The mechanism for the initial facile energy flow is shown to involve strong resonant pathways. In particular, a CH stretch/HCH bend Fermi (1:2) resonance is shown to dominate the short-time dynamics and facilitates the overall process of energy redistribution. The increase in the rate of energy flow as a function of the backbone temperature is found to be due to the increase in the density of the bath states for energy redistribution which subsequently results in the formation of new low-order resonant interactions (1:1, etc). The long-time dynamics, associated to complete redistribution of the initial CH stretch energy with all of the 894 available vibrational modes, occurs within a time of 2 ps. This timescale corresponds to the time for intramolecular redistribution. A comparison of the intramolecular redistribution time to that of intermolecular redistribution (redistribution in the condensed or solid phase as opposed to a single chain) is also made. A preliminary study of energy flow in a crystal of polyethylene (system containing 19 polyethylene chains) shows that the energy flow exhibits two very different time behaviors. The first is for the intramolecular redistribution as in the single chain study and the second is for intermolecular (chain-to-chain) redistribution. The timescale for intermolecular redistribution is found to be on the order of 0.2 ns at room temperature and pressure, about two orders of magitude larger than the intramolecular timescale.     

Orbital-dependent correlation energy in density-functional theory based on a second-order perturbation approach: success and failure

We have developed a second-order perturbation theory (PT) energy functional within density-functional theory (DFT). Based on PT with the Kohn-Sham (KS) determinant as a reference, this new ab initio exchange-correlation functional includes an exact exchange (EXX) energy in the first order and a correlation energy including all single and double excitations from the KS reference in the second order. The explicit dependence of the exchange and correlation energy on the KS orbitals in the functional fits well into our direct minimization approach for the optimized effective potential, which is a very efficient method to perform fully self-consistent calculations for any orbital-dependent functionals. To investigate the quality of the correlation functional, we have applied the method to selected atoms and molecules. For two-electron atoms and small molecules described with small basis sets, this new method provides excellent results, improving both second-order Moller-Plesset expression and any conventional DFT results significantly. For larger systems, however, it performs poorly, converging to very low unphysical total energies. The failure of PT based energy functionals is analyzed, and its origin is traced back to near degeneracy problems due to the orbital- and eigenvalue-dependent algebraic structure of the correlation functional. The failure emerges in the self-consistent approach but not in perturbative post-EXX calculations, emphasizing the crucial importance of self-consistency in testing new orbital-dependent energy functionals.     

在分子中单电子受到的作用势的理论研究

分子的所有性质都是由分子内的电子和原子核的相互作用及其运动所决定的 .这种相互作用 ,在讨论各种问题中 ,可以用各种各样的作用势来描写 [1～ 9] .分子静电势为分子间的相互作用研究 ,尤其是药物和受体相互作用的研究 ,提供一种非常有用的手段 [1,2 ] .在 Hartree- Fock[3 ,4 ] 方程中的势能项是某个分子轨道上 1个电子所受到的所有原子核和其余电子的作用势 . Slater[5,6] 提出了平均作用势 .Kohn- Sham[7]把单电子轨道引进密度泛函理论中 ,建立了 Kohn- Sham单电子运动方程 .KS轨道上1个电子所受的有效定域势场为该电子与其余电子…     

Strain in strain-free benzenoid hydrocarbons: the case of fibonacenes

In a recent paper (Radenkovic et al. Chem Phys Lett 625:69–72, 2015), a new method for quantifying the strain energy in benzenoid molecules, resulting from the repulsion between the bay H-atoms was elaborated. In this work, we present a modified procedure, capable of estimating the strain energy in a single-step calculation. Strain energies were obtained at the B3LYP/def2-TZVP level of density functional theory. It was found that in benzenoid molecules with a single bay region, the strain energy is essentially constant, equal to around 7.3 kJ/mol. On the other hand, in the case of the first four members of the fibonacene series, the strain energy is found to be linearly proportional to the number of bay regions.     

Application of the spline-function method to determination of potential constants for diatomic molecules

We describe a new technique for calculating force constants for diatomic molecules, making significnat use of approximate information on derivatives of the function of the total energy of the molecule given in tables. The proposed procedure is applied to determine the potential constants for the LiH molecule.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 21, No. 1, pp. 98–101, January–February, 1985.     

Application of a two-length-scale field theory to the solvation of neutral and charged molecules

We develop a continuous self-consistent theory of solute-water interactions that allows determination of the hydrophobic layer around a solute molecule of any geometry, with an explicit account of solvent structure described by its correlation function. We compute the mean solvent density profile n(r) surrounding the solute molecule as well as its solvation free energy deltaG. We compare the two-length-scale field theory to the numerical data of Monte Carlo simulations found in the literature for spherical molecules and discuss the possibility of self-consistent adjustment of the free parameters of the theory. In the framework of this approach, we compute the solvation free energies of alkane molecules and the free energy of interaction of two spheres of radius R separated by the distance D. We describe the general setting of the self-consistent account of electrostatic interactions in the framework of our model where the water is considered not as a continuous medium but as a gas of dipoles. We analyze the limiting cases where the proposed theory coincides with the electrostatics of a continuous medium.     

Charge transfer between a molecule and an infinite electron reservoir in the MO scheme

A quantitative reference for comparing molecules (and sites of molecules) likely to exchange electrons with a molecular or crystalline partner can be obtained by coupling such molecules to a model electron reservoir with a continuous energy spectrum. In this study the required procedure is defined and mathematically formulated, within the standard orbital scheme. The reservoir is modeled as an infinite linear chain of atoms with one atomic orbital whose coupling is larger than the largest half-bandwidth of the molecules to be compared, coupled by a suitable bond parameter to a specific site of the molecule. The resulting level broadening and local density of states (DOS) are determined using Dyson's equation to get a tractable expansion of the Green function of the molecule-reservoir system. An example of application and a brief discussion of the dependence of the results on the type of Hamiltonian utilized are given. © 1996 John Wiley & Sons, Inc.