Recent advances in quantitative single-cell analysis revealed large diversity in gene expression levels between individual cells, which could affect the physiology and/or fate of each cell. In contrast, for most metabolites, the concentrations were only measureable as ensemble averages of many cells. In living cells, adenosine triphosphate (ATP) is a critically important metabolite that powers many intracellular reactions. Quantitative measurement of the absolute ATP concentration in individual cells has not been achieved because of the lack of reliable methods. In this study, we developed a new genetically-encoded ratiometric fluorescent ATP indicator “QUEEN”, which is composed of a single circularly-permuted fluorescent protein and a bacterial ATP binding protein. Unlike previous FRET-based indicators, QUEEN was apparently insensitive to bacteria growth rate changes. Importantly, intracellular ATP concentrations of numbers of bacterial cells calculated from QUEEN fluorescence were almost equal to those from firefly luciferase assay. Thus, QUEEN is suitable for quantifying the absolute ATP concentration inside bacteria cells. Finally, we found that, even for a genetically-identical Escherichia coli cell population, absolute concentrations of intracellular ATP were significantly diverse between individual cells from the same culture, by imaging QUEEN signals from single cells.

Organ sizes and shapes are strikingly reproducible, despite the variable growth and division of individual cells within them. To reveal which mechanisms enable this precision, we designed a screen for disrupted sepal size and shape uniformity in Arabidopsis and identified mutations in the mitochondrial i-AAA protease FtsH4. Counterintuitively, through live imaging we observed that variability of neighboring cell growth was reduced in ftsh4 sepals. We found that regular organ shape results from spatiotemporal averaging of the cellular variability in wild-type sepals, which is disrupted in the less-variable cells of ftsh4 mutants. We also found that abnormal, increased accumulation of reactive oxygen species (ROS) in ftsh4 mutants disrupts organ size consistency. In wild-type sepals, ROS accumulate in maturing cells and limit organ growth, suggesting that ROS are endogenous signals promoting termination of growth. Our results demonstrate that spatiotemporal averaging of cellular variability is required for precision in organ size.

Conformational dynamics of proteins can be interpreted as itinerant motions as the protein traverses from one state to another on a complex network in conformational space or, more generally, in state space. Here we present a scheme to extract a multiscale state space network (SSN) from a single-molecule time series. Analysis by this method enables us to lift degeneracy-different physical states having the same value for a measured observable-as much as possible. A state or node in the network is defined not by the value of the observable at each time but by a set of subsequences of the observable over time. The length of the subsequence can tell us the extent to which the memory of the system is able to predict the next state. As an illustration, we investigate the conformational fluctutation dynamics probed by single-molecule electron transfer (ET), detected on a photon-by-photon basis. We show that the topographical features of the SSNs depend on the time scale of observation; the longer the time scale, the simpler the underlying SSN becomes, leading to a transition of the dynamics from anomalous diffusion to normal Brownian diffusion.single-molecule experiment ͉ anomalous diffusion ͉ time series analysis O ptical single-molecule spectroscopy has provided unique insights into both the distribution of molecular properties and their dynamic behavior, which are inaccessible using ensemble-averaged measurements (1-5). In principle, the complexity observed in the dynamics and kinetics of a protein originates in the underlying multidimensional energy landscape (6-12). The dynamics can be understood as the protein traversing from one state (node) to another along a complex network in conformational space or, more generally, in state space. The network properties of biological systems can provide a new perspective for addressing the nature of their hierarchical organization in multidimensional state space (10,11,13,14), enabling us to ask such questions as: Is there any distinctive network topology that is characteristic for the native basin into which a protein folds? Are there any common network features that biological systems may have evolved by adapting to the changes in the environment? Motivated by questions of this nature, we address how one can extract the state space network (SSN) of multiscale biological systems explicitly from a single-molecule time series, free from a priori assumptions on the underlying physical model or rules. These theoretical studies underscore the difficulties in establishing a minimal physical model for the origin of complexity in the kinetics or dynamics of biomolecules. Instead of postulating or constructing a physical model to characterize experimental results, we take a different approach to "let the system speak for itself'' through the single-molecule time series. Such unbiased solutions, which are data-driven instead of model-driven, have been provided in the context of single-molecule FRET experiments (24) and emission intermittency, demonstrated in resolving quantum dot bl...

We introduce a step transition and state identification (STaSI) method for piecewise constant single-molecule data with a newly derived minimum description length equation as the objective function. We detect the step transitions using the Student’s t test and group the segments into states by hierarchical clustering. The optimum number of states is determined based on the minimum description length equation. This method provides comprehensive, objective analysis of multiple traces requiring few user inputs about the underlying physical models and is faster and more precise in determining the number of states than established and cutting-edge methods for single-molecule data analysis. Perhaps most importantly, the method does not require either time-tagged photon counting or photon counting in general and thus can be applied to a broad range of experimental setups and analytes.

We scrutinize the saddle crossings of a simple cluster of six atoms to show (a) that it is possible to choose a coordinate system in which the transmission coefficient for the classical reaction path is unity at all energies up to a moderately high energy, above which the transition state is chaotic; (b) that at energies just more than sufficient to allow passage across the saddle, all or almost all the degrees of freedom of the system are essentially regular in the region of the transition state; and (c) that the degree of freedom associated with the reaction coordinate remains essentially regular through the region of the transition state, even to moderately high energies. Microcanonical molecular dynamics simulation of Ar6 bound by pairwise Lennard-Jones potentials reveals the mechanics of passage. We use Lie canonical perturbation theory to construct the nonlinear transformation to a hyperbolic coordinate system which reveals these regularities. This transform “rotates away” the recrossings and nonregular behavior, especially of the motion along the reaction coordinate, leaving a coordinate and a corresponding dividing surface in phase space which minimize recrossings and mode–mode mixing in the transition state region. The action associated with the reactive mode tends to be an approximate invariant of motion through the saddle crossings throughout a relatively wide range of energy. Only at very low energies just above the saddle could any other approximate invariants of motion be found for the other, nonreactive modes. No such local invariants appeared at energies at which the modes are all chaotic and coupled to one another.