Search

Deep convolutional neural networks (DCNNs) are routinely used for image segmentation of biomedical data sets to obtain quantitative measurements of cellular structures like tissues. These cellular structures often contain gaps in their boundaries, leading to poor segmentation performance when using DCNNs like the U-Net. The gaps can usually be corrected by post-hoc computer vision (CV) steps, which are specific to the data set and require a disproportionate amount of work. As DCNNs are Universal Function Approximators, it is conceivable that the corrections should be obsolete by selecting the appropriate architecture for the DCNN. In this article, we present a novel theoretical framework for the gap-filling problem in DCNNs that allows the selection of architecture to circumvent the CV steps. Combining information-theoretic measures of the data set with a fundamental property of DCNNs, the size of their receptive field, allows us to formulate statements about the solvability of the gap-filling problem independent of the specifics of model training. In particular, we obtain mathematical proof showing that the maximum proficiency of filling a gap by a DCNN is achieved if its receptive field is larger than the gap length. We then demonstrate the consequence of this result using numerical experiments on a synthetic and real data set and compare the gap-filling ability of the ubiquitous U-Net architecture with variable depths. Our code is available at https://github.com/ai-biology/dcnn-gap-filling.

G-protein-coupled receptors (GPCRs) are key signaling proteins that mostly function as monomers, but for several receptors constitutive dimer formation has been described and in some cases is essential for function. Using single-molecule microscopy combined with super-resolution techniques on intact cells, we describe here a dynamic monomer–dimer equilibrium of µ-opioid receptors (µORs), where dimer formation is driven by specific agonists. The agonist DAMGO, but not morphine, induces dimer formation in a process that correlates both temporally and in its agonist- and phosphorylation-dependence with β-arrestin2 binding to the receptors. This dimerization is independent from, but may precede, µOR internalization. These data suggest a new level of GPCR regulation that links dimer formation to specific agonists and their downstream signals.

In the low copy number regime, the dynamics of chemically reacting systems is accurately modeled as a continuous-time Markov chain and the associated probability density obeys the chemical master equation. Parameter inference in such models is very challenging for various reasons: large levels of noise implies that large amount of data is required for identification, the presence of transient phases may shadow subsets of the parameters, and accurate likelihood estimation requires the solutions to master equations. The latter is itself a computational very challenging problem and although many approximate computational methods have been proposed previously, the final implied accuracy in estimated rate parameters is difficult to assess.

Osteoarthritis of the knee is a common degenerative disease during aging. It is typically caused by articular cartilage degeneration. Cartilage, which is located between bone surfaces, is a viscoelastic material aiming to absorb, redirect and transmit mechanical forces during movement. Without the cartilages’ buffering capacity, bones come into direct contact inducing severe pain up to the stage where affected individuals loose mobility. The mechanisms of cartilage remodeling are poorly understood, and there is currently no effective method to reconstitute damaged cartilage. Cartilage consists of extracellular matrix (ECM) and a low density of cells (chondrocytes), which generate matrix proteins. The composition of the matrix gives the cartilage specific viscoelastic properties, which are sensed by chondrocytes feeding back on ECM remodeling. The aim of this study is to build a mathematical model that couples mechanical ECM properties with chondrocyte phenotype in the upkeep of cartilage homeostasis. We model the viscoelastic properties of the cartilage in terms of a linear Kelvin-Voigt model, where the dampening ratio feeds back on the phenotypic switching behaviour in chondrocytes. The chondrocytes, depending on their phenotypic state, may either produce proteoglycans or collagens or both, which alters the viscoelastic properties of the cartilage. We formulate a coupled system of equations integrating mechano-sensitive phenotypic switching behaviour of chondrocytes with respect to ECM remodelling. We define cartilage homeostasis as the fixed point of the derived systems of equations. Using this framework we can reproduce the long term changes in cartilage composition during aging.

Single-cell RNA sequencing (scRNA-seq) has become ubiquitous in biology. Recently, there has been a push for using scRNA-seq snapshot data to infer the underlying gene regulatory networks (GRNs) steering cellular function. To date, this aspiration remains unrealized due to technical and computational challenges. In this work we focus on the latter, which is under-represented in the literature. We took a systemic approach by subdividing the GRN inference into three fundamental components: data pre-processing, feature extraction, and inference. We observed that the regulatory signature is captured in the statistical moments of scRNA-seq data and requires computationally intensive minimization solvers to extract it. Furthermore, current data pre-processing might not conserve these statistical moments. Although our moment-based approach is a didactic tool for understanding the different compartments of GRN inference, this line of thinking—finding computationally feasible multi-dimensional statistics of data—is imperative for designing GRN inference methods.