Stochastic approach to the molecular counting problem in superresolution microscopy.

Superresolution imaging methods--now widely used to characterize biological structures below the diffraction limit--are poised to reveal in quantitative detail the stoichiometry of protein complexes in living cells. In practice, the photophysical properties of the fluorophores used as tags in superresolution methods have posed a severe theoretical challenge toward achieving this goal. Here we develop a stochastic approach to enumerate fluorophores in a diffraction-limited area measured by superresolution microscopy. The method is a generalization of aggregated Markov methods developed in the ion channel literature for studying gating dynamics. We show that the method accurately and precisely enumerates fluorophores in simulated data while simultaneously determining the kinetic rates that govern the stochastic photophysics of the fluorophores to improve the prediction's accuracy. This stochastic method overcomes several critical limitations of temporal thresholding methods.

General mechanism of two-state protein folding kinetics.

We describe here a general model of the kinetic mechanism of protein folding. In the Foldon Funnel Model, proteins fold in units of secondary structures, which form sequentially along the folding pathway, stabilized by tertiary interactions. The model predicts that the free energy landscape has a volcano shape, rather than a simple funnel, that folding is two-state (single-exponential) when secondary structures are intrinsically unstable, and that each structure along the folding path is a transition state for the previous structure. It shows how sequential pathways are consistent with multiple stochastic routes on funnel landscapes, and it gives good agreement with the 9 order of magnitude dependence of folding rates on protein size for a set of 93 proteins, at the same time it is consistent with the near independence of folding equilibrium constant on size. This model gives estimates of folding rates of proteomes, leading to a median folding time in Escherichia coli of about 5 s.

Examinations of tRNA Range of Motion Using Simulations of Cryo-EM Microscopy and X-Ray Data.

We examined tRNA flexibility using a combination of steered and unbiased molecular dynamics simulations. Using Maxwell's demon algorithm, molecular dynamics was used to steer X-ray structure data toward that from an alternative state obtained from cryogenic-electron microscopy density maps. Thus, we were able to fit X-ray structures of tRNA onto cryogenic-electron microscopy density maps for hybrid states of tRNA. Additionally, we employed both Maxwell's demon molecular dynamics simulations and unbiased simulation methods to identify possible ribosome-tRNA contact areas where the ribosome may discriminate tRNAs during translation. Herein, we collected >500 ns of simulation data to assess the global range of motion for tRNAs. Biased simulations can be used to steer between known conformational stop points, while unbiased simulations allow for a general testing of conformational space previously unexplored. The unbiased molecular dynamics data describes the global conformational changes of tRNA on a sub-microsecond time scale for comparison with steered data. Additionally, the unbiased molecular dynamics data was used to identify putative contacts between tRNA and the ribosome during the accommodation step of translation. We found that the primary contact regions were H71 and H92 of the 50S subunit and ribosomal proteins L14 and L16.

The role of DNA twist in the packaging of viral genomes.

We performed molecular dynamics simulations of the genome packaging of bacteriophage P4 using two coarse-grained models of DNA. The first model, 1DNA6 (one pseudo-atom per six DNA basepairs), represents DNA as a string of beads, for which DNA torsions are undefined. The second model, 3DNA6 (three pseudo-atoms per six DNA basepairs), represents DNA as a series of base planes with torsions defined by the angles between successive planes. Bacteriophage P4 was packaged with 1DNA6, 3DNA6 in a torsionally relaxed state, and 3DNA6 in a torsionally strained state. We observed good agreement between the packed conformation of 1DNA6 and the packed conformations of 3DNA6. The free energies of packaging were in agreement, as well. Our results suggest that DNA torsions can be omitted from coarse-grained bacteriophage packaging simulations without significantly altering the DNA conformations or free energies of packaging that the simulations predict.