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Single-molecule fluorescence trajectories for investigating molecular transport in thin silica sol-gel films.

Single-molecule fluorescence tracking has been used to examine diffusion of small molecules in sol-gel films in order to identify spatial heterogeneity in the structure and molecular diffusivities for different regions of the film. Fluorescence intensity profiles from single molecules are fit to a two-dimensional Gaussian function to determine their x,y positions with subpixel resolution. Scatter plots and histograms of molecular step sizes indicate that the trajectories conform to the predictions of a two-dimensional random walk. The mean-square step size is shown to be an unbiased estimate of the variance of the step-size probability distribution and a valid statistic for determining the diffusion coefficient from a molecular trajectory. The diffusion coefficients measured for different molecules are subjected to an F test, which showed that the sol-gel film exhibits spatial variation in the diffusion coefficient on a micrometer-length scale. The spatial variation in diffusivities is a measure of structural heterogeneity of these films.

Journal Article↗

Ligand-free and -bound structures of the binding protein (LivJ) of the Escherichia coli ABC leucine/isoleucine/valine transport system: trajectory and dynamics of the interdomain rotation and ligand specificity.

The leucine/isoleucine/valine-binding protein (LIVBP or LivJ) serves as the primary high-affinity receptor of the Escherichia coli ABC-type transporter for the three aliphatic amino acids. The first structure of LIVBP determined previously without bound ligand showed a molecule comprised of two domains which are far apart and bisected by a wide open, solvent-accessible cleft. Here we report the crystal structures of another ligand-free state and three complexes with the aliphatic amino acids. In the present ligand-free structure, the two domains are farther apart. In the three very similar complex structures, the two domains are in close proximity, and each desolvated ligand is completely engulfed in the cleft and bound by both domains. The two different ligand-free structures, combined with those of the very similar ligand-bound structures, indicate the trajectory and backbone torsion angle changes of the hinges that accompany domain closure and play crucial functional roles. The amino acids are bound by polar and nonpolar interactions, occurring predominantly in one domain. Consistent with the protein specificity, the aliphatic side chains of the ligands lie in a hydrophobic pocket fully formed following domain or cleft closure. Comparison of the structures of LIVBP with several different binding proteins indicates no correlations between the magnitudes of the hinge-bending angles and the protein masses, the ligand sizes, or the number of segments connecting the two domains. Results of normal-mode analysis and molecular dynamics simulations are consistent with the trajectory and intrinsic flexibility of the interdomain hinges and the dominance of one domain in ligand binding in the open state.

ATP-Binding Cassette Transporters↗

Initial trajectory of carbon monoxide after photodissociation from myoglobin at cryogenic temperatures.

Migration of the CO ligand following photolysis of carbonmonoxy myoglobin (MbCO) in single crystals has been investigated by time-resolved X-ray diffraction at 40K. After short illumination by weak visible light at a photolysis rate of approximately 1 s-1, the photodissociated CO molecule is found about 1 A from its bound location. After continuous illumination over several hours, the CO molecule migrates to a more distant site in the distal pocket, about 2.5 A from its bound location. Migration of the ligand under continuous illumination accounts for different locations of the photodissociated CO molecule previously reported in three cryocrystallographic studies [Teng, T.-Y., et al. (1994) Nat. Struct. Biol. 1, 701-705; Schlichting, I., et al. (1994) Nature 371, 808-812; Hartmann, H., et al. (1996) Proc.Natl.Acad. Sci. U.S.A. 93, 7013-7016]. Due to the different photolysis protocols employed in these studies, each reveals a different part of the trajectory of the photodissociated CO molecule. When the different experimental parts of the trajectory at 40 K are pieced together and combined with our nanosecond time-resolved studies at room temperature [Srajer, V., et al. (1996) Science 274, 1726-1729], excellent agreement is obtained with recent theoretical predictions of the CO probability distribution in the ligand pocket [Vitkup, D., et al. (1997) Nat. Struct. Biol. 4, 202-208]. The heme relaxation that accompanies ligand photolysis is incomplete, about 30% of that associated with the conversion of MbCO to deoxy-Mb at room temperature, and independent of the duration of illumination. Other tertiary structural changes in the globin are also greatly diminished. The globin structure is therefore very rigid at cryogenic temperatures, and structural relaxation is greatly hindered, consistent with numerous spectroscopic measurements.

Carbon Monoxide↗

Byte structure variable length coding (BS-VLC): a new specific algorithm applied in the compression of trajectories generated by molecular dynamics

Molecular dynamics is a well-known technique very much used in the study of biomolecular systems. The trajectory files produced by molecular dynamics simulations are extensive, and the classical lossless algorithms give poor efficiencies in their compression. In this work, a new specific algorithm, named byte structure variable length coding (BS-VLC), is introduced. Trajectory files, obtained by molecular dynamics applied to trypsin and a trypsin:pancreatic trypsin inhibitor complex, were compressed using four classical lossless algorithms (Huffman, adaptive Huffman, LZW, and LZ77) as well as the BS-VLC algorithm. The results obtained show that BS-VLC nearly triplicates the compression efficiency of the best classical lossless algorithm, preserving a near lossless behavior. Compression efficiencies close to 50% can be obtained with a high degree of precision, and the maximum efficiency possible (75%), within this algorithm, can be performed with good precision.

Journal Article↗

Reconciling trajectory ensemble receptor model results with emissions.

Several approaches have been developed that use ensembles of air parcel back trajectories to identify likely source regions for contaminants observed at a downwind receptor site. Although the results of these models have appeared to provide results that agree with known sources, there have not been efforts to make direct comparisons between the results of such analyses with emissions inventories. In this paper, the results of residence time analysis (RTA) of data from Underhill, VT and from Brigantine, NJ are compared to the average estimated emissions of coal- and oil-fired power plants. Excellent correspondence was found between the areas of highest probability identified in the trajectory ensemble analyses and the averaged emission intensities.

Air Movements↗

Comparison between back-trajectory based modeling and Lagrangian backward dispersion modeling for locating sources of reactive gaseous mercury.

Reactive gaseous mercury (RGM) was measured using an annular denuder coated with potassium chloride at three rural sites (Potsdam, Stockton, and Sterling) in New York State from April 2002 to April 2003. Concentrations of RGM ranged from 0.1 to 84.6 pg m(-3) with large spatial and temporal variation. Potential source contribution function (PSCF), a common receptor modeling tool, was used with these measurements, and source-receptor relationships were calculated using back-dispersion and deposition as well as back-trajectories. Modeling results were compared with the RGM emissions inventory, and Spearman rank-order correlation coefficients were calculated. PSCF results incorporating backward dispersion and deposition were better correlated with the emissions inventory than PSCF based on back-trajectories alone. This difference was determined to be mainly due to the inclusion of dispersion rather than deposition. The main sources of RGM were suggested to be coal-fired power plants in New York and Pennsylvania, the large copper smelter in Quebec, and the taconite mining areas around the Great Lakes.

Air Movements↗

Carbene formation in its lower singlet state from photoexcited 3H-diazirine or diazomethane. A combined CASPT2 and ab initio direct dynamics trajectory study.

The potential energy surfaces of the ground and valence excited states of both 3H-diazirine and diazomethane have been studied computationally by mean of the CASSCF method in conjunction with the cc-pVTZ basis set. The energies of the critical points found on such surfaces have been recomputed at the CASPT2/cc-pVTZ level. Additionally, ab initio direct dynamic trajectory calculations have been carried out on the S(1) and S(2) surfaces, starting each trajectory run at the region dominated by the conformational molecular rearrangement of diazomethane. It is found that both isomers are interconnected along a C(s)() reaction coordinate on each potential surface. Radiationless deactivation of the corresponding S(1) state of each isomer occurs through the same point on the surface, an S(1)/S(0) conical intersection. Thereafter, the system has enough energy to surmount the barrier which leads to dissociation products (CH(2) + N(2)) on S(0) state. Therefore, photoexcitation to S(1) state of either diazirine of diazomethane produces methylene in its lower singlet state on a very short time scale (ca. 100 fs). Furthermore, both isomers can generate excited singlet carbene when they are excited onto the S(2) surface; in this case, they lose the activation energy passing through another common S(2)/S(1) conical intersection and then proceed to dissociation into carbene and N(2) on the S(1) surface. For the special case of methylene, it rapidly experiences deexcitation to S(0) state.

Journal Article↗

Fluorophore-quencher distance correlation functions from single-molecule photon arrival trajectories.

We generalize and simplify the method of Yang and Xie (J. Chem. Phys. 2002, 117, 10965) to obtain distance correlation functions from photon arrival trajectories of single fluorophores whose lifetime, [k(r)](-1), depends on the distance to a quencher. It is assumed that this distance does not change during the fluorescence lifetime. The experimental trajectory is first transformed by replacing the delay time (i.e., the interval between the photon arrival and the nearest laser pulse) by a certain function of this delay time. This function is the inverse Laplace transform of r(k), which is the solution of k(r) = 1. The correlation function of the transformed data then directly gives the distance correlation function. Illustrative examples include Förster energy transfer and quenching due to electron transfer.

Diffusion↗

Quasi-classical trajectory simulations of intramolecular vibrational energy redistribution in HONO2 and DONO2.

By use of an analytic potential energy surface developed in this work for nitric acid, the quasi-classical trajectory method was used to simulate intramolecular vibrational energy redistribution (IVR). A method was developed for monitoring the average vibrational energy in the OH (or OD) mode that uses the mean-square displacement of the bond length calculated during the trajectories. This method is effective for both rotating and nonrotating molecules. The calculated IVR time constant for HONO(2) decreases exponentially with increasing excitation energy, is almost independent of rotational temperature, and is in excellent agreement with the experimental determination (Bingemann, D.; Gorman, M. P.; King, A. M.; Crim, F. F. J. Chem.Phys. 1997, 107, 661). In DONO(2), the IVR time constants show more complicated behavior with increasing excitation energy, apparently due to 2:1 Fermi-resonance coupling with lower frequency modes. This effect should be measurable in experiments.

Journal Article↗

Quasiclassical trajectory simulations of OH(v) + NO2 --> HONO2* --> OH(v') + NO2: capture and vibrational deactivation rate constants.

Quasiclassical trajectory calculations are used to investigate the dynamics of the OH(v) + NO(2) --> HONO(2) --> OH(v') + NO(2) recombination/dissociation reaction on an analytic potential energy surface (PES) that gives good agreement with the known structure and vibrational frequencies of nitric acid. The calculated recombination rate constants depend only weakly on temperature and on the initial vibrational energy level of OH(v). The magnitude of the recombination rate constant is sensitive to the potential function describing the newly formed bond and to the switching functions in the PES that attenuate inter-mode interactions at long range. The lifetime of the nascent excited HONO(2) depends strongly not only on its internal energy but also on the identity of the initial state, in disagreement with statistical theory. This disagreement is probably due to the effects of slow intramolecular vibrational energy redistribution (IVR) from the initially excited OH stretching mode. The vibrational energy distribution of product OH(v') radicals is different from statistical distributions, a result consistent with the effects of slow IVR. Nonetheless, the trajectory results predict that vibrational deactivation of OH(v) via the HONO(2) transient complex is approximately 90% efficient, almost independent of initial OH(v) vibrational level, in qualitative agreement with recent experiments. Tests are also carried out using the HONO(2) PES, but assuming the weaker O-O bond strength found in HOONO (peroxynitrous acid). In this case, the predicted vibrational deactivation efficiencies are significantly lower and depend strongly on the initial vibrational state of OH(v), in disagreement with experiments. This disagreement suggests that the actual HOONO PES may contain more inter-mode coupling than found in the present model PES, which is based on HONO(2). For nitric acid, the measured vibrational deactivation rate constant is a useful proxy for the recombination rate, but IVR randomization of energy is not complete, suggesting that the efficacy of the proxy method must be evaluated on a case-by-case basis.

Journal Article↗

Quasi-classical trajectory calculations analyzing the role of bending mode excitations of methane in the Cl + CH4 reaction.

The effects of the methane torsional (nu(2)), umbrella (nu(4)), and the combination nu(2)+nu(4) bending mode excitations on the reactivity and dynamics of the gas-phase Cl + CH(4) --> HCl + CH(3) reaction were analyzed. Quasi-classical trajectory (QCT) calculations, including corrections to avoid zero-point energy leakage along the trajectories, were used on an analytical potential energy surface previously developed by our group. With respect to the reactivity, we found that excitation of either bending mode independently gave similar increases in the reactivity, while the increase observed upon excitation of both modes was larger than the sum of the effect of exciting them independently. Both results agree with recent experimental measures. With respect to the dynamics (rotovibrational and angular distributions of the products), the two bending modes and their combination gave very similar pictures, reproducing the experimental behavior. The satisfactory agreement obtained with a great variety of experimental data (always qualitatively acceptable and sometimes even quantitatively) of the present QCT study lends confidence to the potential energy surface constructed by our group.

Journal Article↗

Quasi-classical trajectory calculations analyzing the reactivity and dynamics of asymmetric stretch mode excitations of methane in the H + CH4 reaction.

An exhaustive dynamics study was performed at two collision energies, 1.52 and 2.20 eV, analyzing the effects of the asymmetric (nu3) stretch mode excitation in the reactivity and dynamics of the gas-phase H + CH4 reaction. Quasi-classical trajectory (QCT) calculations, including corrections to avoid zero-point energy leakage along the trajectories, were performed on an analytical potential energy surface previously developed by our group. First, strong coupling between different vibrational modes in the entry channel was observed, indicating that energy can flow between these modes, and therefore that they do not preserve their adiabatic character along the reaction path; i.e., the reaction is nonadiabatic. Second, we found that the reactant vibrational excitation has a significant influence on the vibrational and rotational product distributions. With respect to the vibrational distribution, our results confirm the purely qualitative experimental evidence, although the theoretical results presented here are also quantitative. The rotational distributions are predictive, because no experimental data have been reported. Third, with respect to the reactivity, we found that the nu3 mode excitation by one quantum is more reactive than the ground state by a factor of about 2, independently of the collision energy, and in agreement with the experimental measurement of 3.0 +/- 1.5. Fourth, the state-to-state angular distributions of the products reproduce the experimental behavior at 1.52 eV, where the CH3 products scatter sideways and backward. At 2.20 eV this experimental information is not available, and therefore the results reported here are again predictive. The satisfactory reproduction of a great variety of experimental data by the present QCT study lends confidence to the potential energy surface constructed by our group and to those results whose accuracy cannot be checked by comparison with experiment.

Journal Article↗

Optic nerve regeneration after intravitreal peripheral nerve implants: trajectories of axons regrowing through the optic chiasm into the optic tracts.

We have studied axon regeneration through the optic chiasm of adult rats 30 days after prechiasmatic intracranial optic nerve crush and serial intravitreal sciatic nerve grafting on day 0 and 14 post-lesion. The experiments comprised three groups of treated rats and three groups of controls. All treated animals received intravitreal grafts either into the left eye after both left sided (unilateral) and bilateral optic nerve transection, or into both eyes after bilateral optic nerve transection. Control eyes were all sham grafted on day 0 and 14 post-lesion, and the optic nerves either unlesioned, or crushed unilaterally or bilaterally. No regeneration through the chiasm was seen in any of the lesioned control optic nerves. In all experimental groups, large numbers of axons regenerated across the optic nerve lesions ipsilateral to the grafted eyes, traversed the short distal segment of the optic nerve and invaded the chiasm without deflection. Regeneration was correlated with the absence of the mesodermal components in the scar. In all cases, axon regrowth through the chiasm appeared to establish a major crossed and a minor uncrossed projection into both optic tracts, with some aberrant growth into the contralateral optic nerve. Axons preferentially regenerated within the degenerating trajectories from their own eye, through fragmented myelin and axonal debris, and reactive astrocytes, oligodendrocytes, microglia and macrophages. In bilaterally lesioned animals, no regeneration was detected in the optic nerve of the unimplanted eye. Although astrocytes became reactive and their processes proliferated, the architecture of their intrafascicular processes was little perturbed after optic nerve transection within either the distal optic nerve segment or the chiasm. The re-establishment of a comparatively normal pattern of passage through the chiasm by regenerating axons in the adult might therefore be organised by this relatively immutable scaffold of astrocyte processes. Binocular interactions between regenerating axons from both nerves (after bilateral optic nerve transection and intravitreal grafting), and between regenerating axons and the intact transchiasmatic projections from the unlesioned eye (after unilateral optic nerve lesions and after ipsilateral grafting) may not be important in establishing the divergent trajectories, since regenerating axons behave similarly in the presence and absence of an intact projection from the other eye.

Age Factors↗

Twelve-month outcome of nonmelancholic depressive subjects: refinement of subgroups by examination of trajectories.

We previously studied a sample of patients with nonmelancholic depression and attempted to subtype their depression on the basis of etiological factors and current clinical features, analyzed individually and together. We now examine the validity of the three contrasting analytic approaches by examining outcome trajectories in a prospective study. At follow-up we reinterviewed 67% of our initially assessed nonmelancholic subjects, with progress over the 12-month interval assessed across a range of outcome parameters. The "anxious depressed" groups identified across all three differing analytic strategies consistently had the poorest 12-month outcome. However, varying definitions of this group influenced quite differing trajectories, with the worst outcome being for those defined on the basis of clinical features. Study results strongly suggest that patients presenting with a nonmelancholic depressive disorder and who acknowledge a significant number of concurrent anxiety symptoms are likely to have a distinctly poor medium-term outcome. Thus, clinical definition does have predictive utility in such a group.

Affect↗

Functional development of the mammary gland: use of expression profiling and trajectory clustering to reveal changes in gene expression during pregnancy, lactation, and involution.

To characterize the molecular mechanisms by which progesterone withdrawal initiates milk secretion, we examined global gene expression during pregnancy and lactation in mice, focusing on the period around parturition. Trajectory clustering was used to profile the expression of 1358 genes that changed significantly between pregnancy day 12 and lactation day 9. Predominantly downward trajectories included stromal and proteasomal genes and genes for the enzymes of fatty acid degradation. Milk protein gene expression increased throughout pregnancy, whereas the expression of genes for lipid synthesis increased sharply at the onset of lactation. Examination of regulatory genes with profiles similar or complementary to those of lipid synthesis genes led to a model in which progesterone stimulates synthesis of TGF-beta, Wnt 5b, and IGFBP-5 during pregnancy. These factors are suggested to repress secretion by interfering with PRL and IGF-1 signaling. With progesterone withdrawal, PRL and IGF-1 signaling are activated, in turn activating Akt/PKB and the SREBPs, leading to increased lipid synthesis.

Animals↗

Patterns and correlates of binge drinking trajectories from early adolescence to young adulthood.

Latent growth mixture modeling was used to identify developmental trajectories (described in terms of demographics, exposure and resistance to a pro-drug environment, and deviant behavior) of binge drinking among 5,694 individuals who completed 6 surveys from ages 13 to 23 years: nonbingers (32%); moderate stables (37%), who had consistently low levels of bingeing; steady increasers (16%), who increased from the lowest to highest level of bingeing; adolescent bingers (9%), whose early rise in bingeing was followed by a decrease to a moderate level; and early highs (6%), who decreased from the highest level of bingeing to a moderate level. Results show considerable diversity in binge drinking patterns and the correlates of bingeing across trajectory classes.

Adolescent↗

Judgments of natural and anomalous trajectories in the presence and absence of motion.

Recent studies have shown that many people demonstrate erroneous beliefs about motion when asked to predict the trajectories of objects. The present experiments examine whether people can select as correct natural trajectories over anomalous ones when presented with the actual on-going event (motion condition) or static representations of the event (no-motion condition). McCloskey's curved tube problem was used as the event. Results indicate that adults benefit from the motion information in these stimuli, choosing the correct path more often in the motion condition. Men performed better than women in both conditions; this gender effect could not be attributed to formal instruction in physics. Only in the no-motion condition did any men prefer a path which reflected an impetus model of motion. Some women chose a curvilinear path in the motion condition, and in the no-motion condition the curvilinear path was their most often selected alternative. Fifth-grade children demonstrated no effect for gender and their path preferences resembled those of adult males. Children's responses failed to demonstrate a preference for those curvilinear paths which reflect an impetus-based approach to the problem. Adults' performance in the no-motion condition was not enhanced by instructions to employ mental imagery of the event.

Adult↗

Reactive personality-environment transactions and adult developmental trajectories.

The possibility, which is based on the concept of reactive personality-environment transactions, that individuals learn different things from the same experience as a function of personality differences may help explain individual differences in adult developmental trajectories. In an analogue, longitudinal design, business students were taught about stock market investing, and they engaged in 5 practice investment sessions. Although all participants earned the same returns on their investments, they varied in the expectancies they formed about stock investing as a function of their personality status. As anticipated, behavioral inhibition (heightened sensitivity to punishment) facilitated formation of negative investing expectancies and antagonized formation of positive investing expectancies, and behavioral activation (heightened sensitivity to reward) facilitated formation of positive investing expectancies and antagonized formation of negative investing expectancies. Differential learning in a task that approximated skill acquisition for a developmental transition implies that personality may help shape individual developmental trajectories in the adult years.

Adolescent↗