Quantifying heterogeneity and conformational dynamics from single molecule FRET of diffusing molecules: recurrence analysis of single particles (RASP)

Single molecule F?rster resonance energy transfer (FRET) experiments are a versatile method for investigating the conformational distributions and dynamics of biological macromolecules. In a common type of experiment, the fluorescence bursts from individual molecules freely diffusing in solution are detected as they pass through the observation volume of a confocal microscope. Correlation analysis of the fluorescence bursts shows that under typical experimental conditions, for time scales up to several tens of milliseconds, the probability for a molecule to return to the confocal volume is greater than the probability of a new molecule being detected. Here we present RASP (recurrence analysis of single particles), a method that is based on this recurrence behavior and allows us to significantly extend the information that can be extracted from single molecule FRET experiments. The number and peak shapes of subpopulations within the sample can be identified essentially in a model-free way by constructing recurrence FRET efficiency histograms. These are obtained by first selecting photon bursts from a small transfer efficiency range (initial bursts), and then building the FRET efficiency histogram only from bursts detected within a short time (the recurrence interval) after the initial bursts. Systematic variation of the recurrence interval allows the kinetics of interconversion between subpopulations to be determined on time scales from ~50 μs up to ~100 ms from equilibrium measurements. We demonstrate the applicability of the method on measurements of several peptides and proteins with different degrees of conformational heterogeneity and folding dynamics. The concepts presented here can be extended to other observables available from single molecule fluorescence experiments.     

Substrate-mediated intermolecular interactions: a quantitative single molecule analysis

Long-range intermolecular interactions mediated by the surface are believed to be responsible for many effects in surface science, including molecular ordering, formation of nanostructures, and aligning reactive intermediates in catalysis. Here, we use scanning tunneling microscopy to probe the weak substrate-mediated interactions in benzene overlayers on Au{111} at 4 K. Using an automated procedure to monitor single molecule motion, we are able to quantify the substrate-mediated interaction strength. We explain quantitatively both the kinetics of the benzene motion and the thermodynamics that determine the packing structures benzene adopts in this system in light of these substrate-mediated interactions.     

Ab initio conformational analysis of cyclooctane molecule

The potential energy surface (PES) for the cyclooctane molecule was comprehensively investigated at the Hartree–Fock (HF) level of theory employing the 3–21G, 6–31G, and 6–31G* basis sets. Six distinct true minimum energy structures (named B, BB, BC, CROWN, TBC, and TCC₁), characterized through harmonic frequency analysis, were located on the multidimensional PES. Two transition state structures were also located on the PES for the cyclooctane molecule. Electron correlation effects were accounted for using the Møller–Plesset second-order perturbation theory (MP2) approach. The predicted global minimum energy structure on the ab initio PES for the cyclooctane molecule is the BC conformer. A gas phase electron diffraction study at 300 K suggested a conformational mixture while an NMR study in solution at 161.5 K predicted the BC conformer as the predominant form. The equilibrium constants reported in the present study, which were evaluated from the ab initio calculated total Gibbs free energy change values, were in good agreement with both experimental investigations. The ab initio results showed that the low temperature condition significantly favored the BC conformer while above room temperature both BC and CROWN structures can coexist. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 524–534, 1998     

Synthesis and conformational analysis of a ribo-type cyclohexenyl nucleoside

A straightforward approach to a novel class of ribo-type cyclohexenyl nucleosides is described. An electron-demand Diels-Alder reaction forms the key-step of the chosen synthetic pathway. Although the difference is small, conformational analysis using NMR shows that this nucleoside analogue adopts preferentially an 2H3 conformation (S-type), while the "deoxy" cyclohexenyl analogue has a preference for a C3' endo conformation (N-type). Analyses of the conformational equilibrium reveal that, in the given experimental conditions, the difference between adenosine and its cyclohexenyl congener resides in their different DeltaG values; furthermore, in adenosine, the conformational preference is of enthalpic origin, whereas in the cyclohexenyl congener, the conformational preference is of entropic origin.     

Synthesis and conformational analysis of efrapeptins

The efrapeptin family of peptide antibiotics produced by the fungus Tolypocladium niveum, and the neo‐efrapeptins from the fungus Geotrichum candidumare inhibitors of F₁‐ATPase with promising antitumor, antimalaria, and insecticidal activity. They are rich in C^α‐dialkyl amino acids (Aib, Iva, Acc) and contain one β‐alanine and several pipecolic acid residues. The C‐terminus bears an unusual heterocyclic cationic cap. The efrapeptins C–G and three analogues of efrapeptin C were synthesized using α‐azido carboxylic acids as masked amino acid derivatives. All compounds display inhibitory activity toward F₁‐ATPase. The conformation in solution of the peptides was investigated with electronic CD spectroscopy, FT‐IR spectroscopy, and VCD spectroscopy. All efrapeptins and most efrapeptin analogues were shown to adopt helical conformations in solution. In the case of efrapeptin C, VCD spectra proved that a 3₁₀‐helix prevails. In addition, efrapeptin C was conformationally studied in detail with NMR and molecular modeling. Besides NOE distance restraints, residual dipolar couplings (RDC) observed upon partial alignment with stretched PDMS gels were used for the conformational analysis and confirmed the 3₁₀‐helical conformation.     

Synthesis and conformational analysis of 1,3-azasilinanes

1-Isopropyl-3-methyl-3-phenyl-1,3-azasilinane 1 and 1-isopropyl-3,3-dimethyl-1,3-azasilinane 2 were synthesized and a detailed analysis of their NMR spectra, conformational equilibria and ring inversion processes is presented. Low temperature ¹H/¹³C NMR spectroscopy, iteration of the ¹H NMR spectra and quantum chemical calculations showed slight predominance of the Ph_eqMe_ax over the Ph_axMe_eq conformer of 1 at low temperature. The barrier for the chair to chair interconversion of both compounds was measured to be 8.25 kcal/mol.     

Synthesis and conformational analysis of redox-active ferrocenyl-calixarenes

A novel synthetic approach toward redox-active calixarene-based receptors is described wherein ferrocene fragments have been introduced at the lower rim through anion-binding urea or amide connections. A thorough ¹H NMR investigation on a series of calixarene-ferrocene receptors was performed in order to estimate their hydrogen bonding-driven self-association properties and improve our understanding of the correlation between molecular structures and redox properties.     

Synthesis and conformational analysis of small peptides containing 6-endo-BT(t)L scaffolds as reverse turn mimetics

Two new dipeptide isosteres derived from L-leucine and meso-tartaric acid derivatives, named 6-endo-BTL and 6-endo-BtL, were inserted in a small peptide by means of SPPS, and the conformational features of the resulting peptides 3 and 4 were studied by NMR, IR, and molecular modeling techniques. The presence of a reverse turn conformation was observed in all the structures, suggesting the key role of the scaffolds as reverse turn promoters. Peptides 3 and 4 did not adopt a preferred conformation as indicated by the presence of equilibria between open turn and intramolecular hydrogen-bonded structures. 6-endo-BTL-peptide 3 showed a 3:1 mixture of conformers. The major conformer adopted mainly an open turn structure in equilibrium with hydrogen-bonded structures. The minor conformer displayed a better organized structure with a 14-membered ring hydrogen-bond typical of a beta-hairpin-like structure, in equilibrium with a gamma-turn, too. 6-endo-BtL-peptide 4 showed a unique conformer, and did not adopt as good a conformation as 3, due to the bulky equatorial substituent at C-2. Thus, marked structural differences between peptides containing 6-endo-BTL and 6-endo-BtL scaffolds as reverse turn inducers exist.     

Synthesis and conformational analysis of phosphine selenides

Methods of preparation of complex phosphine selenide via the original Trofimov–Gusarova reaction are described. The results of the products conformational analysis by means of a set of physical methods (IR spectroscopy, dipole moments, and quantum chemical calculation) are presented.     

Electronic states of pyrene single crystal and of its single molecule inserted in a molecular vessel of cyclodextrin

Highly purified single crystals of pyrene were made by a gas phase crystal growth method from 180 times of zone-refined pyrene. The absorption spectra of the single crystal have been transformed from the reflection spectra between 2.5 and at 2, and room temperature. The dry powder of β-cyclodextrin including pyrene single molecule were prepared in vacuum to investigate the electronic states of the isolated molecule. The absorption spectra of the single molecule show similar spectra to those of the single crystal. The pyrene molecule keeps its electronic character even in the single crystal.     

Density functional theory-based conformational analysis of a phospholipid molecule (dimyristoyl phosphatidylcholine)

The conformational space of the dimyristoyl phosphatidylcholine (DMPC) molecule has been studied using density functional theory (DFT), augmented with a damped empirical dispersion energy term (DFT-D). Fourteen ground-state isomers have been found with total energies within less than 1 kcal/mol. Despite differences in combinations of their torsion angles, all these conformers share a common geometric profile, which includes a balance of attractive, repulsive, and constraint forces between and within specific groups of atoms. The definition of this profile fits with most of the structural characteristics deduced from measured NMR properties of DMPC solutions. The calculated vibrational spectrum of the molecule is in good agreement with experimental data obtained for DMPC bilayers. These results support the idea that DMPC molecules preserve their individual molecular structures in the various assemblies.     

DNA-psoralen interaction: a single molecule experiment

By attaching one end of a single lambda-DNA molecule to a microscope coverslip and the other end to a polystyrene microsphere trapped by an optical tweezers, we can study the entropic elasticity of the lambda-DNA by measuring force versus extension as we stretch the molecule. This powerful method permits single molecule studies. We are particularly interested in the effects of the photosensitive drug psoralen on the elasticity of the DNA molecule. We have illuminated the sample with different light sources, studying how the different wavelengths affect the psoralen-DNA linkage. To do this, we measure the persistence length of individual DNA-psoralen complexes.     

Automated conformational analysis and structure generation: algorithms for molecular perception

Many methodologies for performing automated conformational analysis require some means of "perceiving" a molecule to determine features of interest. Algorithms for finding rings, bond orders, and stereocenters and detecting the presence of substructural fragments have been developed. These algorithms are described, emphasizing their importance in conformational analysis.     

Synthesis, molecular structure, conformational analysis, and chemical properties of silicon-containing derivatives of quinolizidine

A silicon analog of quinolizidine 3,3,7,7-tetramethylhexahydro-1H-[1,4,2]oxazasilino[4,5-d][1,4,2]oxazasilin-9a-yl)methanol 3 was synthesized. X-ray diffraction analysis confirmed the trans configuration and low temperature NMR spectroscopy both the flexibility (barrier of interconversion 5.8 kcal mol(-1)) and the conformational equilibrium (chair-chair and chair-twist conformers) of the compound. The relative stability of the different isomers/conformers of 3 was calculated also at the MP2/6-311G(d,p) level of theory. Intra- and intermolecular hydrogen bonding in 3 and the appropriate equilibrium between free and self-associated molecules was studied in solvents of different polarity. Both the N-methyl quaternary ammonium salt and the O-trimethylsilyl derivative of 3 could be obtained and their structure determined.     

Quantum-mechanical and molecular mechanics conformational analysis of 1,5-cyclooctadiene

The 1,5-cyclooctadiene (COD) molecule can easily form complexes with transition metals with the molecular structure of various of these complexes being proposed with the aid of X-ray diffraction methods. The fact that the complexes exhibit weak metal-COD bonds makes it very important in inorganic synthesis and catalysis. In this work the potential energy surface (PES) for the COD molecule was comprehensively investigated: first with molecular mechanics (using the MM3 force field); and, in a second stage, at the ab initio Hartree-Fock level of theory employing the 3-21G^*, 6-31G, and 6-31G^* basis sets and also including electron correlation effects at the Moller-Plesset second-order perturbation theory level. This work revealed that there are three distinct conformers of the COD molecule with the predicted lowest energy conformation being in agreement with the proposed structure based on experimental electron diffraction data. © 1997 by John Wiley & Sons, Inc.     

Mechano-chemical coupling of molecular motors revealed by single molecule measurements

Single molecule measurements have allowed series of kinetic events of biomolecules to be monitored without interruption. The stepwise movement of molecular motors was measured and analyzed in relation to the hydrolysis reaction of ATP. In the case of kinesin, forward and backward steps occurred stochastically at the same chemical state. The directional movement was explained by the asymmetric potential created by the interaction between kinesin and microtubules. Similarly thermal Brownian movement of myosin during the hydrolysis of single ATP molecules was biased through an asymmetric potential, resulting in directional movement. Thus, single molecule measurements have provided new approaches to analyze the function of molecular motors which often consist of several different events.     

A theoretical approach to molecular conformational analysis

The application of ab initio molecular orbital theory to the study of molecular conformational analysis is discussed. Examples presented include methyl rotational barriers, internal rotation in 1,2-dihalogenoethanes, $\text{cis-trans}$ isomerism in 1,2-dihalogenoethylenes, rotational barriers in substituted acetones and conformational preferences in substituted hydrazines.