Growth couples temporal and spatial fluctuations of tissue properties during morphogenesis.

Living tissues display fluctuations - random spatial and temporal variations of tissue properties around their reference values - at multiple scales. It is believed that such fluctuations may enable tissues to sense their state or their size. Recent theoretical studies developed specific models of fluctuations in growing tissues and predicted that fluctuations of growth show long-range correlations. Here we elaborated upon these predictions and we tested them using experimental data. We first introduced a minimal model for the fluctuations of any quantity that has some level of temporal persistence or memory, such as concentration of a molecule, local growth rate, or mechanical properties. We found that long-range correlations are generic, applying to to any such quantity, and that growth couples temporal and spatial fluctuations. We then analysed growth data from sepals of the model plant Arabidopsis and we quantified spatial and temporal fluctuations of cell growth using the previously developed Cellular Fourier Transform. Growth appears to have long-range correlations. We compared different genotypes and growth conditions: mutants with altered response to mechanical stress have lower temporal correlations and longer-range spatial correlations than wild-type plants. Finally, we used a theoretical prediction to collapse experimental data from all conditions and developmental stages, validating the notion that temporal and spatial fluctuations are coupled by growth. Altogether, our work reveals kinematic constraints on spatiotemporal fluctuations that have an impact on the robustness of morphogenesis.

Robust organ size in Arabidopsis is primarily governed by cell growth rather than cell division patterns.

Organ sizes and shapes are highly reproducible, or robust, within a species and individuals. Arabidopsis thaliana sepals, which are the leaf-like organs that enclose flower buds, have consistent size and shape, which indicates robust development. Counterintuitively, variability in cell growth rate over time and between cells facilitates robust development because cumulative cell growth averages to a uniform rate. Here we investigate how sepal morphogenesis is robust to changes in cell division but not robust to changes in cell growth variability. We live image and quantitatively compare the development of sepals with increased or decreased cell division rate (lgo mutant and LGO overexpression, respectively), a mutant with altered cell growth variability (ftsh4), and double mutants combining these. We find that robustness is preserved when cell division rate changes because there is no change in the spatial pattern of growth. Meanwhile when robustness is lost in ftsh4 mutants, cell growth accumulates unevenly, and cells have disorganized growth directions. Thus, we demonstrate in vivo that both cell growth rate and direction average in robust development, preserving robustness despite changes in cell division.

Rotary properties of hybrid F1-ATPases consisting of subunits from different species.

F1-ATPase (F1) is an ATP-driven rotary motor protein ubiquitously found in many species as the catalytic portion of FoF1-ATP synthase. Despite the highly conserved amino acid sequence of the catalytic core subunits: α and ß, F1 shows diversity in the maximum catalytic turnover rate Vmax and the number of rotary steps per turn. To study the design principle of F1, we prepared eight hybrid F1s composed of subunits from two of three genuine F1s: thermophilic Bacillus PS3 (TF1), bovine mitochondria (bMF1), and Paracoccus denitrificans (PdF1), differing in the Vmax and the number of rotary steps. The Vmax of the hybrids can be well fitted by a quadratic model highlighting the dominant roles of ß and the couplings between α-ß. Although there exist no simple rules on which subunit dominantly determines the number of steps, our findings show that the stepping behavior is characterized by the combination of all subunits.

Shape-aware stochastic neighbor embedding for robust data visualisations.

BACKGROUND: The t-distributed Stochastic Neighbor Embedding (t-SNE) algorithm has emerged as one of the leading methods for visualising high-dimensional (HD) data in a wide variety of fields, especially for revealing cluster structure in HD single-cell transcriptomics data. However, t-SNE often fails to correctly represent hierarchical relationships between clusters and creates spurious patterns in the embedding. In this work we generalised t-SNE using shape-aware graph distances to mitigate some of the limitations of the t-SNE. Although many methods have been recently proposed to circumvent the shortcomings of t-SNE, notably Uniform manifold approximation (UMAP) and Potential of heat diffusion for affinity-based transition embedding (PHATE), we see a clear advantage of the proposed graph-based method. RESULTS: The superior performance of the proposed method is first demonstrated on simulated data, where a significant improvement compared to t-SNE, UMAP and PHATE, based on quantitative validation indices, is observed when visualising imbalanced, nonlinear, continuous and hierarchically structured data. Thereafter the ability of the proposed method compared to the competing methods to create faithfully low-dimensional embeddings is shown on two real-world data sets, the single-cell transcriptomics data and the MNIST image data. In addition, the only hyper-parameter of the method can be automatically chosen in a data-driven way, which is consistently optimal across all test cases in this study. CONCLUSIONS: In this work we show that the proposed shape-aware stochastic neighbor embedding method creates low-dimensional visualisations that robustly and accurately reveal key structures of high-dimensional data.

Shepherd: accurate clustering for correcting DNA barcode errors.

MOTIVATION: DNA barcodes are short, random nucleotide sequences introduced into cell populations to track the relative counts of hundreds of thousands of individual lineages over time. Lineage tracking is widely applied, e.g. to understand evolutionary dynamics in microbial populations and the progression of breast cancer in humans. Barcode sequences are unknown upon insertion and must be identified using next-generation sequencing technology, which is error prone. In this study, we frame the barcode error correction task as a clustering problem with the aim to identify true barcode sequences from noisy sequencing data. We present Shepherd, a novel clustering method that is based on an indexing system of barcode sequences using k-mers, and a Bayesian statistical test incorporating a substitution error rate to distinguish true from error sequences. RESULTS: When benchmarking with synthetic data, Shepherd provides barcode count estimates that are significantly more accurate than state-of-the-art methods, producing 10-150 times fewer spurious lineages. For empirical data, Shepherd produces results that are consistent with the improvements seen on synthetic data. These improvements enable higher resolution lineage tracking and more accurate estimates of biologically relevant quantities, e.g. the detection of small effect mutations. AVAILABILITY AND IMPLEMENTATION: A Python implementation of Shepherd is freely available at: https://www.github.com/Nik-Tavakolian/Shepherd. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Robust organ size requires robust timing of initiation orchestrated by focused auxin and cytokinin signalling.

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 continuously enclose and protect the developing bud. Here we show that DEVELOPMENT RELATED MYB-LIKE 1 (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 signalling 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.

Efficiencies of molecular motors: a comprehensible overview.

Many biological molecular motors can operate specifically and robustly at the highly fluctuating nano-scale. How these molecules achieve such remarkable functions is an intriguing question that requires various notions and quantifications of efficiency associated with the operations and energy transduction of these nano-machines. Here we give a short review of some important concepts of motor efficiencies, including the thermodynamic, Stokes, and generalized and transport efficiencies, as well as some implications provided by the thermodynamic uncertainty relations recently developed in nonequilibrium physics.

Rotary catalysis of bovine mitochondrial F1-ATPase studied by single-molecule experiments.

The reaction scheme of rotary catalysis and the torque generation mechanism of bovine mitochondrial F1 (bMF1) were studied in single-molecule experiments. Under ATP-saturated concentrations, high-speed imaging of a single 40-nm gold bead attached to the γ subunit of bMF1 showed 2 types of intervening pauses during the rotation that were discriminated by short dwell and long dwell. Using ATPγS as a slowly hydrolyzing ATP derivative as well as using a functional mutant ßE188D with slowed ATP hydrolysis, the 2 pausing events were distinctively identified. Buffer-exchange experiments with a nonhydrolyzable analog (AMP-PNP) revealed that the long dwell corresponds to the catalytic dwell, that is, the waiting state for hydrolysis, while it remains elusive which catalytic state short pause represents. The angular position of catalytic dwell was determined to be at +80° from the ATP-binding angle, mostly consistent with other F1s. The position of short dwell was found at 50 to 60° from catalytic dwell, that is, +10 to 20° from the ATP-binding angle. This is a distinct difference from human mitochondrial F1, which also shows intervening dwell that probably corresponds to the short dwell of bMF1, at +65° from the binding pause. Furthermore, we conducted "stall-and-release" experiments with magnetic tweezers to reveal how the binding affinity and hydrolysis equilibrium are modulated by the γ rotation. Similar to thermophilic F1, bMF1 showed a strong exponential increase in ATP affinity, while the hydrolysis equilibrium did not change significantly. This indicates that the ATP binding process generates larger torque than the hydrolysis process.

Heterogeneity and Robustness in Plant Morphogenesis: From Cells to Organs.

Development is remarkably reproducible, producing organs with the same size, shape, and function repeatedly from individual to individual. For example, every flower on the Antirrhinum stalk has the same snapping dragon mouth. This reproducibility has allowed taxonomists to classify plants and animals according to their morphology. Yet these reproducible organs are composed of highly variable cells. For example, neighboring cells grow at different rates in Arabidopsis leaves, sepals, and shoot apical meristems. This cellular variability occurs in normal, wild-type organisms, indicating that cellular heterogeneity (or diversity in a characteristic such as growth rate) is either actively maintained or, at a minimum, not entirely suppressed. In fact, cellular heterogeneity can contribute to producing invariant organs. Here, we focus on how plant organs are reproducibly created during development from these highly variable cells.

Why plants make puzzle cells, and how their shape emerges.

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.

Effects of non-equilibrium angle fluctuation on F1-ATPase kinetics induced by temperature increase.

F1-ATPase (F1) is an efficient rotary protein motor, whose reactivity is modulated by the rotary angle to utilize thermal fluctuation. In order to elucidate how its kinetics are affected by the change in the fluctuation, we have extended the reaction-diffusion formalism [R. Watanabe et al., Biophys. J., 2013, 105, 2385] applicable to a wider range of temperatures based on experimental data analysis of F1 derived from thermophilic Bacillus under high ATP concentration conditions. Our simulation shows that the rotary angle distribution manifests a stronger non-equilibrium feature as the temperature increases, because ATP hydrolysis and Pi release are more accelerated compared with the timescale of rotary angle relaxation. This effect causes the rate coefficient obtained from dwell time fitting to deviate from the Arrhenius relation in Pi release, which has been assumed in the previous activation thermodynamic quantities estimation using linear Arrhenius fitting. Larger negative correlation is also found between hydrolysis and Pi release waiting time in a catalytic dwell with the increase in temperature. This loss of independence between the two successive reactions at the catalytic dwell sheds doubt on the conventional dwell time fitting to obtain rate coefficients with a double exponential function at temperatures higher than 65 °C, which is close to the physiological temperature of the thermophilic Bacillus.

Clones of cells switch from reduction to enhancement of size variability in Arabidopsis sepals.

Organs form with remarkably consistent sizes and shapes during development, whereas a high variability in growth is observed at the cell level. Given this contrast, it is unclear how such consistency in organ scale can emerge from cellular behavior. Here, we examine an intermediate scale, the growth of clones of cells in Arabidopsis sepals. Each clone consists of the progeny of a single progenitor cell. At early stages, we find that clones derived from a small progenitor cell grow faster than those derived from a large progenitor cell. This results in a reduction in clone size variability, a phenomenon we refer to as size uniformization. By contrast, at later stages of clone growth, clones change their growth pattern to enhance size variability, when clones derived from larger progenitor cells grow faster than those derived from smaller progenitor cells. Finally, we find that, at early stages, fast growing clones exhibit greater cell growth heterogeneity. Thus, cellular variability in growth might contribute to a decrease in the variability of clones throughout the sepal.

Mechanical Shielding of Rapidly Growing Cells Buffers Growth Heterogeneity and Contributes to Organ Shape Reproducibility.

A landmark of developmental biology is the production of reproducible shapes, through stereotyped morphogenetic events. At the cell level, growth is often highly heterogeneous, allowing shape diversity to arise. Yet, how can reproducible shapes emerge from such growth heterogeneity? Is growth heterogeneity filtered out? Here, we focus on rapidly growing trichome cells in the Arabidopsis sepal, a reproducible floral organ. We show via computational modeling that rapidly growing cells may distort organ shape. However, the cortical microtubule alignment along growth-derived maximal tensile stress in adjacent cells would mechanically isolate rapidly growing cells and limit their impact on organ shape. In vivo, we observed such microtubule response to stress and consistently found no significant effect of trichome number on sepal shape in wild-type and lines with trichome number defects. Conversely, modulating the microtubule response to stress in katanin and spiral2 mutant made sepal shape dependent on trichome number, suggesting that, while mechanical signals are propagated around rapidly growing cells, the resistance to stress in adjacent cells mechanically isolates rapidly growing cells, thus contributing to organ shape reproducibility.

Variable Cell Growth Yields Reproducible OrganDevelopment through Spatiotemporal Averaging.

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.

Extracting Subcellular Fibrillar Alignment with Error Estimation: Application to Microtubules.

The order and orientation of cortical microtubule (CMT) arrays and their dynamics play an essential role in plant morphogenesis. To extract detailed CMT alignment structures in an objective, local, and accurate way, we propose an error-based extraction method that applies to general fluorescence intensity data on three-dimensional cell surfaces. Building on previous techniques to quantify alignments, our method can determine the statistical error for specific local regions, or the minimal scales of local regions for a desired accuracy goal. After validating our method with synthetic images with known alignments, we demonstrate the ability of our method to quantify subcellular CMT alignments on images with microtubules marked with green fluorescent protein in various cell types. Our method could also be applied to detect alignment structures in other fibrillar elements, such as actin filaments, cellulose, and collagen.

ATP hydrolysis assists phosphate release and promotes reaction ordering in F1-ATPase.

F1-ATPase (F1) is a rotary motor protein that can efficiently convert chemical energy to mechanical work of rotation via fine coordination of its conformational motions and reaction sequences. Compared with reactant binding and product release, the ATP hydrolysis has relatively little contributions to the torque and chemical energy generation. To scrutinize possible roles of ATP hydrolysis, we investigate the detailed statistics of the catalytic dwells from high-speed single wild-type F1 observations. Here we report a small rotation during the catalytic dwell triggered by the ATP hydrolysis that is indiscernible in previous studies. Moreover, we find in freely rotating F1 that ATP hydrolysis is followed by the release of inorganic phosphate with low synthesis rates. Finally, we propose functional roles of the ATP hydrolysis as a key to kinetically unlock the subsequent phosphate release and promote the correct reaction ordering.

Error-based extraction of states and energy landscapes from experimental single-molecule time-series.

Characterization of states, the essential components of the underlying energy landscapes, is one of the most intriguing subjects in single-molecule (SM) experiments due to the existence of noise inherent to the measurements. Here we present a method to extract the underlying state sequences from experimental SM time-series. Taking into account empirical error and the finite sampling of the time-series, the method extracts a steady-state network which provides an approximation of the underlying effective free energy landscape. The core of the method is the application of rate-distortion theory from information theory, allowing the individual data points to be assigned to multiple states simultaneously. We demonstrate the method's proficiency in its application to simulated trajectories as well as to experimental SM fluorescence resonance energy transfer (FRET) trajectories obtained from isolated agonist binding domains of the AMPA receptor, an ionotropic glutamate receptor that is prevalent in the central nervous system.

Fast Step Transition and State Identification (STaSI) for Discrete Single-Molecule Data Analysis.

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.

Local-heterogeneous responses and transient dynamics of cage breaking and formation in colloidal fluids.

Quantifying the interactions in dense colloidal fluids requires a properly designed order parameter. We present a modified bond-orientational order parameter, ψ̄6, to avoid problems of the original definition of bond-orientational order parameter. The original bond-orientational order parameter can change discontinuously in time but our modified order parameter is free from the discontinuity and, thus, it is a suitable measure to quantify the dynamics of the bond-orientational ordering of the local surroundings. Here we analyze ψ̄6 in a dense driven monodisperse quasi-two-dimensional colloidal fluids where a single particle is optically trapped at the center. The perturbation by the trapped and driven particle alters the structure and dynamics of the neighboring particles. This perturbation disturbs the flow and causes spatial and temporal distortion of the bond-orientational configuration surrounding each particle. We investigate spatio-temporal behavior of ψ̄6 by a Wavelet transform that provides a time-frequency representation of the time series of ψ̄6. It is found that particles that have high power in frequencies corresponding to the inverse of the timescale of perturbation undergo distortions of their packing configurations that result in cage breaking and formation dynamics. To gain insight into the dynamic structure of cage breaking and formation of bond-orientational ordering, we compare the cage breaking and formation dynamics with the underlying dynamical structure identified by Lagrangian Coherent Structures (LCSs) estimated from the finite-time Lyapunov exponent (FTLE) field. The LCSs are moving separatrices that effectively divide the flow into distinct regions with different dynamical behavior. It is shown that the spatial distribution of the FTLE field and the power of particles in the wavelet transform have positive correlation, implying that LCSs provide a dynamic structure that dominates the dynamics of cage breaking and formation of the colloidal fluids.