F-1-ATPase (F-1) 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: alpha and beta, F-1 shows diversity in the maximum catalytic turnover rate V-max and the number of rotary steps per turn. To study the design principle of F-1, we prepared eight hybrid F(1)s composed of subunits from two of three genuine (F)1s: thermophilic Bacillus PS3 (TF1), bovine mitochondria (bMF(1)), and Paracoccus denitrificans (PdF1), differing in the V-max and the number of rotary steps. The V-max of the hybrids can be well fitted by a quadratic model highlighting the dominant roles of 0 and the couplings between alpha-beta. 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.

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.

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.

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.

The shape of plant organs shows low variability. Sepals of the same age look the same. Here the authors identify one transcription factor (DRMY1) crucial for sepal size reproducibility, and its effect on initiation timing and growth of the organ. 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.

The reaction scheme of rotary catalysis and the torque generation mechanism of bovine mitochondrial F-1 (bMF(1)) were studied in single-molecule experiments. Under ATP-saturated concentrations, high-speed imaging of a single 40-nm gold bead attached to the gamma subunit of bMF(1) showed 2 types of intervening pauses during the rotation that were discriminated by short dwell and long dwell. Using ATP gamma S as a slowly hydrolyzing ATP derivative as well as using a functional mutant beta E188D 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 degrees from the ATP-binding angle, mostly consistent with other F(1)s. The position of short dwell was found at 50 to 60 degrees from catalytic dwell, that is, +10 to 20 degrees from the ATP-binding angle. This is a distinct difference from human mitochondrial F-1, which also shows intervening dwell that probably corresponds to the short dwell of bMF(1), at +65 degrees 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 gamma rotation. Similar to thermophilic F-1, bMF(1) 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.

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.

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.

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.

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.