Synthesizing developmental trajectories

Dynamics of Drosophila endoderm specification

To understand developmental patterning of an organism, it is necessary to accurately measure how the state of a gene regulatory network is changing over time. One way of extracting dynamics of a network involves simultaneously imaging several reporters within fixed tissue. Reconstructing dynamics from such data requires staging many samples over time and often leads to low temporal resolution. Time-lapse microscopy of fluorescent transcriptional reporters has revolutionized studies of biological dynamics at the single-cell level. However, this method is limited by the number of reporters that can be imaged at one time. We present a computational method for addressing this problem and demonstrate its application by modeling the gene regulatory network underlying Drosophila posterior patterning and reconstructing its developmental dynamics.

During early Drosophila embryogenesis, a network of gene regulatory interactions orchestrates terminal patterning, playing a critical role in the subsequent formation of the gut. We utilized CRISPR gene editing at endogenous loci to create live reporters of transcription and light-sheet microscopy to monitor the individual components of the posterior gut patterning network across 90 min prior to gastrulation. We developed a computational approach for fusing imaging datasets of the individual components into a common multivariable trajectory. Data fusion revealed low intrinsic dimensionality of posterior patterning and cell fate specification in wild-type embryos. The simple structure that we uncovered allowed us to construct a model of interactions within the posterior patterning regulatory network and make testable predictions about its dynamics at the protein level. The presented data fusion strategy is a step toward establishing a unified framework that would explore how stochastic spatiotemporal signals give rise to highly reproducible morphogenetic outcomes.

The many bits of positional information

Half a century after Lewis Wolpert's seminal conceptual advance on how cellular fates distribute in space, we provide a brief historical perspective on how the concept of positional information emerged and influenced the field of developmental biology and beyond. We focus on a modern interpretation of this concept in terms of information theory, largely centered on its application to cell specification in the early Drosophila embryo. We argue that a true physical variable (position) is encoded in local concentrations of patterning molecules, that this mapping is stochastic, and that the processes by which positions and corresponding cell fates are determined based on these concentrations need to take such stochasticity into account. With this approach, we shift the focus from biological mechanisms, molecules, genes and pathways to quantitative systems-level questions: where does positional information reside, how it is transformed and accessed during development, and what fundamental limits it is subject to?

What machine learning can do for developmental biology

Developmental biology has grown into a data intensive science with the development of high-throughput imaging and multi-omics approaches. Machine learning is a versatile set of techniques that can help make sense of these large datasets with minimal human intervention, through tasks such as image segmentation, super-resolution microscopy and cell clustering. In this Spotlight, I introduce the key concepts, advantages and limitations of machine learning, and discuss how these methods are being applied to problems in developmental biology. Specifically, I focus on how machine learning is improving microscopy and single-cell 'omics' techniques and data analysis. Finally, I provide an outlook for the futures of these fields and suggest ways to foster new interdisciplinary developments.

Cryo-EM reconstruction of continuous heterogeneity by Laplacian spectral volumes

Single-particle electron cryomicroscopy is an essential tool for high-resolution 3D reconstruction of proteins and other biological macromolecules. An important challenge in cryo-EM is the reconstruction of non-rigid molecules with parts that move and deform. Traditional reconstruction methods fail in these cases, resulting in smeared reconstructions of the moving parts. This poses a major obstacle for structural biologists, who need high-resolution reconstructions of entire macromolecules, moving parts included. To address this challenge, we present a new method for the reconstruction of macromolecules exhibiting continuous heterogeneity. The proposed method uses projection images from multiple viewing directions to construct a graph Laplacian through which the manifold of three-dimensional conformations is analyzed. The 3D molecular structures are then expanded in a basis of Laplacian eigenvectors, using a novel generalized tomographic reconstruction algorithm to compute the expansion coefficients. These coefficients, which we name spectral volumes, provide a high-resolution visualization of the molecular dynamics. We provide a theoretical analysis and evaluate the method empirically on several simulated data sets.

Linking Gaussian process regression with data-driven manifold embeddings for nonlinear data fusion

In statistical modelling with Gaussian process regression, it has been shown that combining (few) high-fidelity data with (many) low-fidelity data can enhance prediction accuracy, compared to prediction based on the few high-fidelity data only. Such information fusion techniques for multi-fidelity data commonly approach the high-fidelity model f h(t) as a function of two variables (t, s), and then use f l(t) as the s data. More generally, the high-fidelity model can be written as a function of several variables (t, s 1, s 2….); the low-fidelity model f l and, say, some of its derivatives can then be substituted for these variables. In this paper, we will explore mathematical algorithms for multi-fidelity information fusion that use such an approach towards improving the representation of the high-fidelity function with only a few training data points. Given that f h may not be a simple function-and sometimes not even a function-of f l, we demonstrate that using additional functions of t, such as derivatives or shifts of f l, can drastically improve the approximation of f h through Gaussian processes. We also point out a connection with 'embedology' techniques from topology and dynamical systems. Our illustrative examples range from instructive caricatures to computational biology models, such as Hodgkin-Huxley neural oscillations.

Quantitative analysis of cell shape and the cytoskeleton in developmental biology

Computational approaches that enable quantification of microscopy data have revolutionized the field of developmental biology. Due to its inherent complexity, elucidating mechanisms of development requires sophisticated analysis of the structure, shape, and kinetics of cellular processes. This need has prompted the creation of numerous techniques to visualize, quantify, and merge microscopy data. These approaches have defined the order and structure of developmental events, thus, providing insight into the mechanisms that drive them. This review describes current computational approaches that are being used to answer developmental questions related to morphogenesis and describe how these approaches have impacted the field. Our intent is not to comprehensively review techniques, but to highlight examples of how different approaches have impacted our understanding of development. Specifically, we focus on methods to quantify cell shape and cytoskeleton structure and dynamics in developing tissues. Finally, we speculate on where the future of computational analysis in developmental biology might be headed. This article is categorized under: Technologies > Analysis of Cell, Tissue, and Animal Phenotypes Early Embryonic Development > Gastrulation and Neurulation Early Embryonic Development > Development to the Basic Body Plan.