The shape and function of plant cells are often highly interdependent. The puzzle-shaped cells that appear in the epidermis of many plants are a striking example of a complex cell shape, however their functional benefit has remained elusive. We propose that these intricate forms provide an effective strategy to reduce mechanical stress in the cell wall of the epidermis. When tissue-level growth is isotropic, we hypothesize that lobes emerge at the cellular level to prevent formation of large isodiametric cells that would bulge under the stress produced by turgor pressure. Data from various plant organs and species support the relationship between lobes and growth isotropy, which we test with mutants where growth direction is perturbed. Using simulation models we show that a mechanism actively regulating cellular stress plausibly reproduces the development of epidermal cell shape. Together, our results suggest that mechanical stress is a key driver of cell-shape morphogenesis.

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.

Organ size and shape are precisely regulated to ensure proper function. The four sepals in each Arabidopsis thaliana flower must maintain the same size throughout their growth to enclose and protect the developing bud. Here we show that DEVELOPMENT RELATED MYB-LIKE1 (DRMY1) is required for both timing of organ initiation and proper growth, leading to robust sepal size in Arabidopsis. Within each drmy1 flower, the initiation of some sepals is variably delayed. Late-initiating sepals in drmy1 mutants remain smaller throughout development resulting in variability in sepal size. DRMY1 focuses the spatiotemporal signaling patterns of the plant hormones auxin and cytokinin, which jointly control the timing of sepal initiation. Our findings demonstrate that timing of organ initiation together with growth and maturation contribute to robust organ size.