Temporal ordering and registration of images in studies of developmental dynamics.

Progress of development is commonly reconstructed from imaging snapshots of chemical or mechanical processes in fixed tissues. As a first step in these reconstructions, snapshots must be spatially registered and ordered in time. Currently, image registration and ordering are often done manually, requiring a significant amount of expertise with a specific system. However, as the sizes of imaging data sets grow, these tasks become increasingly difficult, especially when the images are noisy and the developmental changes being examined are subtle. To address these challenges, we present an automated approach to simultaneously register and temporally order imaging data sets. The approach is based on vector diffusion maps, a manifold learning technique that does not require a priori knowledge of image features or a parametric model of the developmental dynamics. We illustrate this approach by registering and ordering data from imaging studies of pattern formation and morphogenesis in three model systems. We also provide software to aid in the application of our methodology to other experimental data sets.

Systematic characterization of protein folding pathways using diffusion maps: application to Trp-cage miniprotein.

Understanding the mechanisms by which proteins fold from disordered amino-acid chains to spatially ordered structures remains an area of active inquiry. Molecular simulations can provide atomistic details of the folding dynamics which complement experimental findings. Conventional order parameters, such as root-mean-square deviation and radius of gyration, provide structural information but fail to capture the underlying dynamics of the protein folding process. It is therefore advantageous to adopt a method that can systematically analyze simulation data to extract relevant structural as well as dynamical information. The nonlinear dimensionality reduction technique known as diffusion maps automatically embeds the high-dimensional folding trajectories in a lower-dimensional space from which one can more easily visualize folding pathways, assuming the data lie approximately on a lower-dimensional manifold. The eigenvectors that parametrize the low-dimensional space, furthermore, are determined systematically, rather than chosen heuristically, as is done with phenomenological order parameters. We demonstrate that diffusion maps can effectively characterize the folding process of a Trp-cage miniprotein. By embedding molecular dynamics simulation trajectories of Trp-cage folding in diffusion maps space, we identify two folding pathways and intermediate structures that are consistent with the previous studies, demonstrating that this technique can be employed as an effective way of analyzing and constructing protein folding pathways from molecular simulations.

Nonlinear intrinsic variables and state reconstruction in multiscale simulations.

Finding informative low-dimensional descriptions of high-dimensional simulation data (like the ones arising in molecular dynamics or kinetic Monte Carlo simulations of physical and chemical processes) is crucial to understanding physical phenomena, and can also dramatically assist in accelerating the simulations themselves. In this paper, we discuss and illustrate the use of nonlinear intrinsic variables (NIV) in the mining of high-dimensional multiscale simulation data. In particular, we focus on the way NIV allows us to functionally merge different simulation ensembles, and different partial observations of these ensembles, as well as to infer variables not explicitly measured. The approach relies on certain simple features of the underlying process variability to filter out measurement noise and systematically recover a unique reference coordinate frame. We illustrate the approach through two distinct sets of atomistic simulations: a stochastic simulation of an enzyme reaction network exhibiting both fast and slow time scales, and a molecular dynamics simulation of alanine dipeptide in explicit water.

Data Mining for Parameters Affecting Polymorph Selection in Contorted Hexabenzocoronene Derivatives.

The macroscopic properties of molecular materials can be drastically influenced by their solid-state packing arrangements, of which there can be many (e.g., polymorphism). Strategies to controllably and predictively access select polymorphs are thus highly desired, but computationally predicting the conditions necessary to access a given polymorph is challenging with the current state of the art. Using derivatives of contorted hexabenzocoronene, cHBC, we employed data mining, rather than first-principles approaches, to find relationships between the crystallizing molecule, postdeposition solvent-vapor annealing conditions that induce polymorphic transformation, and the resulting polymorphs. This analysis yields a correlative function that can be used to successfully predict the appearance of either one of two polymorphs in thin films of cHBC derivatives. Within the postdeposition processing phase space of cHBC derivatives, we have demonstrated an approach to generate guidelines to select crystallization conditions to bias polymorph access. We believe this approach can be applied more broadly to accelerate the predictions of processing conditions to access desired molecular polymorphs, making progress toward one of the grand challenges identified by the Materials Genome Initiative.

Reconstructing ERK Signaling in the Drosophila Embryo from Fixed Images.

The early Drosophila embryo provides unique opportunities for quantitative studies of ERK signaling. This system is characterized by simple anatomy, the ease of obtaining large numbers of staged embryos, and the availability of powerful tools for genetic manipulation of the ERK pathway. Here, we describe how these experimental advantages can be combined with recently developed microfluidic devices for high throughput imaging of ERK activation dynamics. We focus on the stage during the third hour of development, when ERK activation is essential for patterning of the future nerve cord. Our approach starts with an ensemble of fixed embryos stained with an antibody that recognizes the active, dually phosphorylated form of ERK. Each embryo in this ensemble provides a snapshot of the spatial and temporal pattern of ERK activation during development. We then quantitatively estimate the ages of fixed embryos using a model that links their morphology and developmental time. This model is learned based on live imaging of cellularization and gastrulation, two highly stereotyped morphogenetic processes at this stage of embryogenesis. Applying this approach, we can characterize ERK signaling at high spatial and temporal resolution. Our methodology can be readily extended to studies of ERK regulation and function in multiple mutant backgrounds, providing a versatile assay for quantitative studies of developmental ERK signaling.

Dynamics of Inductive ERK Signaling in the Drosophila Embryo.

Transient activation of the highly conserved extracellular-signal-regulated kinase (ERK) establishes precise patterns of cell fates in developing tissues. Quantitative parameters of these transients are essentially unknown, but a growing number of studies suggest that changes in these parameters can lead to a broad spectrum of developmental abnormalities. We provide a detailed quantitative picture of an ERK-dependent inductive signaling event in the early Drosophila embryo, an experimental system that offers unique opportunities for high-throughput studies of developmental signaling. Our analysis reveals a spatiotemporal pulse of ERK activation that is consistent with a model in which transient production of a short-ranged ligand feeds into a simple signal interpretation system. The pulse of ERK signaling acts as a switch in controlling the expression of the ERK target gene. The quantitative approach that led to this model, based on the integration of data from fixed embryos and live imaging, can be extended to other developmental systems patterned by transient inductive signals.