Optimal sequencing budget allocation for trajectory reconstruction of single cells.

BACKGROUND: Charting cellular trajectories over gene expression is key to understanding dynamic cellular processes and their underlying mechanisms. While advances in single-cell RNA-sequencing technologies and computational methods have pushed forward the recovery of such trajectories, trajectory inference remains a challenge due to the noisy, sparse, and high-dimensional nature of single-cell data. This challenge can be alleviated by increasing either the number of cells sampled along the trajectory (breadth) or the sequencing depth, i.e. the number of reads captured per cell (depth). Generally, these two factors are coupled due to an inherent breadth-depth tradeoff that arises when the sequencing budget is constrained due to financial or technical limitations. RESULTS: Here we study the optimal allocation of a fixed sequencing budget to optimize the recovery of trajectory attributes. Empirical results reveal that reconstruction accuracy of internal cell structure in expression space scales with the logarithm of either the breadth or depth of sequencing. We additionally observe a power law relationship between the optimal number of sampled cells and the corresponding sequencing budget. For linear trajectories, non-monotonicity in trajectory reconstruction across the breadth-depth tradeoff can impact downstream inference, such as expression pattern analysis along the trajectory. We demonstrate these results for five single-cell RNA-sequencing datasets encompassing differentiation of embryonic stem cells, pancreatic beta cells, hepatoblast and multipotent hematopoietic cells, as well as induced reprogramming of embryonic fibroblasts into neurons. By addressing the challenges of single-cell data, our study offers insights into maximizing the efficiency of cellular trajectory analysis through strategic allocation of sequencing resources.

Static adhesion hysteresis in elastic structures.

Adhesive interactions between elastic structures such as graphene sheets, carbon nanotubes, and microtubules have been shown to exhibit hysteresis due to irrecoverable energy loss associated with bond breakage, even in static (rate-independent) experiments. To understand this phenomenon, we start with a minimal theory for the peeling of a thin sheet from a substrate, coupling the local event of bond breaking to the nonlocal elastic relaxation of the sheet and show that this can drive static adhesion hysteresis over a bonding/debonding cycle. Using this model we quantify hysteresis in terms of the adhesion and elasticity parameters of the system. This allows us to derive a scaling relation that preserves hysteresis at different levels of granularity while resolving a seeming paradox of lattice trapping in the continuum limit of a discrete fracture process. Finally, to verify our theory, we use new experiments to demonstrate and measure adhesion hysteresis in bundled microtubules.

Mechanical basis for fibrillar bundle morphology.

Understanding the morphology of self-assembled fibrillar bundles and aggregates is relevant to a range of problems in molecular biology, supramolecular chemistry and materials science. Here, we propose a coarse-grained approach that averages over specific molecular details and yields an effective mechanical theory for the spatial complexity of self-assembling fibrillar structures that arises due to the competing effects of (the bending and twisting) elasticity of individual filaments and the adhesive interactions between them. We show that our theoretical framework accounting for this allows us to capture a number of diverse fibril morphologies observed in natural and synthetic systems, ranging from Filopodia to multi-walled carbon nanotubes, and leads to a phase diagram of possible fibril shapes. We also show how the extreme sensitivity of these morphologies can lead to spatially chaotic structures. Together, these results suggest a common mechanical basis for mesoscale fibril morphology as a function of the nanoscale mechanical properties of its filamentous constituents.

An allometric prior enhances acoustic niche partitioning signal.

The acoustic niche hypothesis suggests that vocal signals of sympatric animal species are structured so as to minimize acoustic interference and facilitate communication. Accordingly, each species attempts to establish its own acoustic bandwidth so that intra-species signals are not masked. Detecting a non-random partitioning of the frequency spectrum among sympatric species could constitute evidence for the existence of acoustic avoidance behaviour. However, results from previous studies have been mixed or inconclusive, possibly as a consequence of overlooking the importance of physiological and ecological constraints. Here we introduce an improved test that incorporates prior information on body mass to account for the allometric correlation between mass (size) and vocalization frequency. By correcting for the bias induced by this correlation, the new test uncovers evidence of acoustic niche partitioning as a function of frequency in several tropical bird communities that would not be detected under a more standard test. Separately, we introduce a spatial version of the acoustic partitioning test which, in theory, could prove effective when data are collected from multiple sites located in close spatial proximity.

Microtubules soften due to cross-sectional flattening.

We use optical trapping to continuously bend an isolated microtubule while simultaneously measuring the applied force and the resulting filament strain, thus allowing us to determine its elastic properties over a wide range of applied strains. We find that, while in the low-strain regime, microtubules may be quantitatively described in terms of the classical Euler-Bernoulli elastic filament, above a critical strain they deviate from this simple elastic model, showing a softening response with increasingdeformations. A three-dimensional thin-shell model, in which the increased mechanical compliance is caused by flattening and eventual buckling of the filament cross-section, captures this softening effect in the high strain regime and yields quantitative values of the effective mechanical properties of microtubules. Our results demonstrate that properties of microtubules are highly dependent on the magnitude of the applied strain and offer a new interpretation for the large variety in microtubule mechanical data measured by different methods.