We quantitatively analyzed particle tracking data on insulin granules expressing fluorescent fusion proteins in MIN6 cells to better understand the motions contributing to intracellular transport and, more generally, the means for characterizing systems far from equilibrium. Care was taken to ensure that the statistics reflected intrinsic features of the individual granules rather than details of the measurement and overall cell state. We find anomalous diffusion. Interpreting such data conventionally requires assuming that a process is either ergodic with particles working against fluctuating obstacles (fractional Brownian motion) or nonergodic with a broad distribution of dwell times for traps (continuous-time random walk). However, we find that statistical tests based on these two models give conflicting results. We resolve this issue by introducing a subordinated scheme in which particles in cages with random dwell times undergo correlated motions owing to interactions with a fluctuating environment. We relate this picture to the underlying microtubule structure by imaging in the presence of vinblastine. Our results provide a simple physical picture for how diverse pools of insulin granules and, in turn, biphasic secretion could arise.

Significance: Growth and division of individual cells are the fundamental events underlying many biological processes, including the development of organisms, the growth of tumors, and pathogen–host interactions. Quantitative studies of bacteria can provide insights into single-cell growth and division but are challenging owing to the intrinsic noise in these processes. Now, by using a unique combination of measurement and analysis technologies, together with mathematical modeling, we discover quantitative features that are conserved across physiological conditions. These universal behaviors reflect the physical principle that a single timescale governs noisy bacterial growth and division despite the complexity of underlying molecular mechanisms.

Fitting the image of a single molecule to the point spread function of an optical system greatly improves the precision with which single molecules can be located. Centroid localization with nanometer precision has been achieved when a sufficient number of photons are collected. However, if multiple single molecules reside within a diffraction-limited spot, this localization approach does not work. This paper demonstrates nanometer-localized multiple single-molecule (NALMS) fluorescence microscopy by using both centroid localization and photobleaching of the single fluorophores. Short duplex DNA strands are used as nanoscale “rulers” to validate the NALMS microscopy approach. Nanometer accuracy is demonstrated for two to five single molecules within a diffraction-limited area. NALMS microscopy will greatly facilitate single-molecule study of biological systems because it covers the gap between fluorescence resonance energy transfer-based (100 nm) measurements of the distance between two fluorophores. Application of NALMS microscopy to DNA mapping with <10-nm (i.e., 30-base) resolution is demonstrated.

Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. The model makes minimal assumptions, and we describe how more complex reaction networks can reduce to such a cycle. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth.

The equilibrium folding of the catalytic domain of Bacillus subtilis RNase P RNA is investigated by single-molecule fluorescence resonance energy transfer (FRET). Previous ensemble studies of this 255-nucleotide ribozyme described the equilibrium folding with two transitions, U-to-I _eq -to-N, and focused on the I _eq -to-N transition. The present study focuses on the U-to-I _eq transition. Comparative ensemble measurements of the ribozyme construct labeled with fluorescein at the 5′ end and Cy3 at the 3′ end show that modifications required for labeling do not interfere with folding and help to define the Mg ²⁺ concentration range for the U-to-I _eq transition. Histogram analysis of the Mg ²⁺ -dependent single-molecule FRET efficiency reveals two previously undetermined folding intermediates. The single-molecule FRET trajectories exhibit non-two-state and nonergodic behaviors at intermediate Mg ²⁺ concentrations on the time scale of seconds. The trajectories at intermediate Mg ²⁺ concentrations are classified into five classes based on three FRET levels and their dynamics of interconversion within the measured time range. This heterogeneity, together with the observation of “nonsudden jump” FRET transitions, indicates that the early folding steps of this ribozyme involve a series of intermediates with different degrees of kinetic isolation and that folding occurs under kinetic control and involves many “local” conformational switches. A free energy contour is constructed to illustrate the complex folding surface.

Optical matter can be created using the intensity gradient and electrodynamic (e.g., optical binding) forces that nano- and microparticles experience in focused optical beams. Here we show that the force associated with phase gradient is also important. In fact, in optical line traps the phase gradient force is crucial in determining the structure and stability of optical matter arrays consisting of Ag nanoparticles (NPs). NP lattices can be repeatedly assembled and disassembled simply by changing the sign of the phase gradient. The phase gradient creates a compressive force (and thus a stress) in the optically bound Ag NP lattices, causing structural transitions (a stress response) from 1D “chains” to 2D lattices, and even to amorphous structures. The structural transitions and dynamics of driven transport are well described by electrodynamics simulations and modeling using a drift-diffusion Langevin equation.