A quantitative map of nuclear pore assembly reveals two distinct mechanisms.

Understanding how the nuclear pore complex (NPC) is assembled is of fundamental importance to grasp the mechanisms behind its essential function and understand its role during the evolution of eukaryotes1-4. There are at least two NPC assembly pathways-one during the exit from mitosis and one during nuclear growth in interphase-but we currently lack a quantitative map of these events. Here we use fluorescence correlation spectroscopy calibrated live imaging of endogenously fluorescently tagged nucleoporins to map the changes in the composition and stoichiometry of seven major modules of the human NPC during its assembly in single dividing cells. This systematic quantitative map reveals that the two assembly pathways have distinct molecular mechanisms, in which the order of addition of two large structural components, the central ring complex and nuclear filaments are inverted. The dynamic stoichiometry data was integrated to create a spatiotemporal model of the NPC assembly pathway and predict the structures of postmitotic NPC assembly intermediates.

Using multiscale preconditioning to accelerate the convergence of iterative molecular calculations.

Iterative procedures for optimizing properties of molecular models often converge slowly owing to the computational cost of accurately representing features of interest. Here, we introduce a preconditioning scheme that allows one to use a less expensive model to guide exploration of the energy landscape of a more expensive model and thus speed the discovery of locally stable states of the latter. We illustrate our approach in the contexts of energy minimization and the string method for finding transition pathways. The relation of the method to other multilevel simulation techniques and possible extensions are discussed.

Integrative spatiotemporal modeling of biomolecular processes: application to the assembly of the Nuclear Pore Complex.

Dynamic processes involving biomolecules are essential for the function of the cell. Here, we introduce an integrative method for computing models of these processes based on multiple heterogeneous sources of information, including time-resolved experimental data and physical models of dynamic processes. We first compute integrative structure models at fixed time points and then optimally select and connect these snapshots into a series of trajectories that optimize the likelihood of both the snapshots and transitions between them. The method is demonstrated by application to the assembly process of the human Nuclear Pore Complex in the context of the reforming nuclear envelope during mitotic cell division, based on live-cell correlated electron tomography, bulk fluorescence correlation spectroscopy-calibrated quantitative live imaging, and a structural model of the fully-assembled Nuclear Pore Complex. Modeling of the assembly process improves the model precision over static integrative structure modeling alone. The method is applicable to a wide range of time-dependent systems in cell biology, and is available to the broader scientific community through an implementation in the open source Integrative Modeling Platform software.

Trajectory stratification of stochastic dynamics.

We present a general mathematical framework for trajectory stratification for simulating rare events. Trajectory stratification involves decomposing trajectories of the underlying process into fragments limited to restricted regions of state space (strata), computing averages over the distributions of the trajectory fragments within the strata with minimal communication between them, and combining those averages with appropriate weights to yield averages with respect to the original underlying process. Our framework reveals the full generality and flexibility of trajectory stratification, and it illuminates a common mathematical structure shared by existing algorithms for sampling rare events. We demonstrate the power of the framework by defining strata in terms of both points in time and path-dependent variables for efficiently estimating averages that were not previously tractable.

Refining Disordered Peptide Ensembles with Computational Amide I Spectroscopy: Application to Elastin-Like Peptides.

The characterization of intrinsically disordered protein (IDP) ensembles is complicated both by inherent heterogeneity and by the fact that many common experimental techniques function poorly when applied to IDPs. For this reason, the development of alternative structural tools for probing IDP ensembles has attracted considerable attention. Here we describe our recent work in developing experimental and computational tools for characterizing IDP ensembles using Amide I (backbone carbonyl stretch) vibrational spectroscopy. In this approach, the infrared (IR) absorption frequencies of isotope-labeled amide bonds probe their local electrostatic environments and structures. Empirical frequency maps allow us to use this spectroscopic data as a direct experimental test of atomistic structural models. We apply these methods to a family of short elastin-like peptides (ELPs), fragments of the elastin protein based around the Pro-Gly turn motif characteristic of the elastomeric segments of the full protein. Using a maximum entropy analysis that applies constraints from experimental spectra to weighting predicted spectra from molecular dynamics (MD) ensembles, we find that peptides with Ala or Val side chains preceding the Pro-Gly turn unit exhibit a stronger tendency toward extended structures than do Gly-Pro-Gly motifs, suggesting an important role for steric interactions in tuning the molecular properties of elastin.