Carmeline J. Dsilva

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.

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.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.

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. Summary: Learning algorithms allow developmental dynamics to be reconstructed through the automatic registration and ordering of fixed images of developing tissues.

Data-Driven Reduction for a Class of Multiscale Fast-Slow Stochastic Dynamical Systems

Multi-time-scale stochastic dynamical systems are ubiquitous in science and engineering, and the reduction of such systems and their models to only their slow components is often essential for scientific computation and further analysis. Rather than being available in the form of an explicit analytical model, often such systems can only be observed as a data set which embodies dynamics on several time scales. We focus on applying and adapting data-mining and manifold learning techniques to detect the slow components in a class of such multiscale data. Traditional data-mining methods are based on metrics (and thus, geometries) which are not informed of the multiscale nature of the underlying system dynamics; such methods cannot successfully recover the slow variables. Here, we present an approach which utilizes both the local geometry and the local noise dynamics within the data set through a metric which is both insensitive to the fast variables and more general than simple statistical averaging. Our anal...

State reduction in molecular simulations

Abstract Model reduction is an important systems task with a long history in traditional chemical engineering modeling. We discuss its interplay with modern data-mining tools (such as Local Feature Analysis and Diffusion Maps) through illustrative examples, and comment on important open issues regarding applications to large systems arising in molecular/atomistic simulations.

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.