Predicting fully-developed channel flow with zero-equation model

A new zero-equation model (ZEM) is devised with an eddy-viscosity formulation using a stress length variable which the structural ensemble dynamics (SED) theory predicts. The ZEM is distinguished by obvious physical parameters, quantifying the underlying flow domain with a universal multi-layer structure. The SED theory is also utilized to formulate an anisotropic Bradshaw stress-intensity factor, parameterized with an eddy-to-laminar viscosity ratio. Bradshaw’s structure function is employed to evaluate the kinetic energy of turbulence k and turbulent dissipation rate epsilon . The proposed ZEM is intrinsically plausible, having a dramatic impact on the prediction of wall-bounded turbulence.

Effects of cryo-EM cooling on structural ensembles

Structure determination by cryo electron microscopy (cryo-EM) provides information on structural heterogeneity and ensembles at atomic resolution. To obtain cryo-EM images of macromolecules, the samples are first rapidly cooled down to cryogenic temperatures. To what extent the structural ensemble is perturbed by the cooling is currently unknown. Here, to quantify the effects of cooling, we combined continuum model calculations of the temperature drop, molecular dynamics simulations of a ribosome complex before and during cooling with kinetic models. Our results suggest that three effects markedly contribute to the narrowing of the structural ensembles: thermal contraction, reduced thermal motion within local potential wells, and the equilibration into lower free-energy conformations by overcoming separating free-energy barriers. During cooling, barrier heights below 10 kJ/mol were found to be overcome resulting in reduction of B-factors in the ensemble imaged by cryo-EM. Our approach now enables the quantification of the heterogeneity of room-temperature ensembles from cryo-EM structures.

Atomic-Resolution Prediction of Degrader-mediated Ternary Complex Structures by Combining Molecular Simulations with Hydrogen Deuterium Exchange

Targeted protein degradation (TPD) has recently emerged as a powerful approach for removing (rather than inhibiting) proteins implicated in diseases. A key step in TPD is the formation of an induced proximity complex where a degrader molecule recruits an E3 ligase to the protein of interest (POI), facilitating the transfer of ubiquitin to the POI and initiating the proteasomal degradation process. Here, we address three critical aspects of the TPD process using atomistic simulations: 1) formation of the ternary complex induced by a degrader molecule, 2) conformational heterogeneity of the ternary complex, and 3) degradation efficiency via the full Cullin Ring Ligase (CRL) macromolecular assembly. The novel approach described here combines experimental biophysical data with molecular dynamics (MD) simulations to accurately predict ternary complex structures at atomic resolution. We integrate hydrogen-deuterium exchange mass spectrometry (HDX-MS, which measures the solvent exposure of protein residues) directly into the MD simulation algorithm to improve the efficiency and accuracy of the ternary structure predictions of the bromodomain of the cancer target SMARCA2 with the E3 ligase VHL, as mediated by three different degrader molecules. The simulations accurately reproduce X-ray crystal structures--including a new structure that we determined in this work (PDB ID: 7S4E)--with root mean square deviations (RMSD) of 1.1 to 1.6 Å. The simulations also reveal a structural ensemble of low-energy conformations of the ternary complex. Snapshots from these simulations are used as seeds for additional simulations, where we perform 5.7 milliseconds of aggregate simulation time using Folding@home, the world's largest distributed supercomputer. The detailed free energy surface captures the crystal structure conformation within the low-energy basin and is consistent with solution-phase experimental data (HDX-MS and SAXS). Finally, we graft a structural ensemble of the ternary complexes onto the full CRL and perform enhanced sampling simulations. Our results suggest that differences in degradation efficiency may be related to the proximity distribution of lysine residues on the POI relative to the E2-loaded ubiquitin. We make source code and the simulation and experimental datasets from this work publicly available for researchers to further advance the field of induced proximity modulation.

Rosetta:MSF:NN: Boosting performance of multi-state computational protein design with a neural network

Rational protein design aims at the targeted modification of existing proteins. To reach this goal, software suites like Rosetta propose sequences to introduce the desired properties. Challenging design problems necessitate the representation of a protein by means of a structural ensemble. Thus, Rosetta multi-state design (MSD) protocols have been developed wherein each state represents one protein conformation. Computational demands of MSD protocols are high, because for each of the candidate sequences a costly three-dimensional (3D) model has to be created and assessed for all states. Each of these scores contributes one data point to a complex, design-specific energy landscape. As neural networks (NN) proved well-suited to learn such solution spaces, we integrated one into the framework Rosetta:MSF instead of the so far used genetic algorithm with the aim to reduce computational costs. As its predecessor, Rosetta:MSF:NN administers a set of candidate sequences and their scores and scans sequence space iteratively. During each iteration, the union of all candidate sequences and their Rosetta scores are used to re-train NNs that possess a design-specific architecture. The enormous speed of the NNs allows an extensive assessment of alternative sequences, which are ranked on the scores predicted by the NN. Costly 3D models are computed only for a small fraction of best-scoring sequences; these and the corresponding 3D-based scores replace half of the candidate sequences during each iteration. The analysis of two sets of candidate sequences generated for a specific design problem by means of a genetic algorithm confirmed that the NN predicted 3D-based scores quite well; the Pearson correlation coefficient was at least 0.95. Applying Rosetta:MSF:NN:enzdes to a benchmark consisting of 16 ligand-binding problems showed that this protocol converges ten-times faster than the genetic algorithm and finds sequences with comparable scores.

Automatic Bayesian Weighting for SAXS Data

Small-angle X-ray scattering (SAXS) experiments are important in structural biology because they are solution methods, and do not require crystallization of protein complexes. Structure determination from SAXS data, however, poses some difficulties. Computation of a SAXS profile from a protein model is expensive in CPU time. Hence, rather than directly refining against the data, most computational methods generate a large number of conformers and then filter the structures based on how well they satisfy the SAXS data. To address this issue in an efficient manner, we propose here a Bayesian model for SAXS data and use it to directly drive a Monte Carlo simulation. We show that the automatic weighting of SAXS data is the key to finding optimal structures efficiently. Another key problem with obtaining structures from SAXS data is that proteins are often flexible and the data represents an average over a structural ensemble. To address this issue, we first characterize the stability of the best model with extensive molecular dynamics simulations. We analyse the resulting trajectories further to characterize a dynamic structural ensemble satisfying the SAXS data. The combination of methods is applied to a tandem of domains from the protein PTPN4, which are connected by an unstructured linker. We show that the SAXS data contain information that supports and extends other experimental findings. We also show that the conformation obtained by the Bayesian analysis is stable, but that a minor conformation is present. We propose a mechanism in which the linker may maintain PTPN4 in an inhibited enzymatic state.

Theoretical and computational modeling of naturally and artificially modified RNA nucleotides

Ribonucleic acid (RNA) is a polymeric nucleic acid that is crucial for cellular function, regulating gene expression and encoding/decoding protein/DNA molecules. Recent discoveries of diverse functionality in non-coding RNAs have led to unprecedented demand for RNA 3D structure determination. With current technology, general, accurate prediction of 3D structures for large RNAs from the sequence remains computationally intractable. One of the principal challenges arises from the conformational flexibility of RNA, especially in loop/junction regions, which results in a rugged energy landscape. Several strategies exist to overcome this challenge, including incorporation of efficient experimental information and coarse-grained (CG) modeling to improve computational sampling of the structural ensemble. A second challenge is the inclusion of naturally modified derivatives of canonical RNA nucleotides in structure analysis. Most RNA prediction strategies rely upon the canonical nucleotides (adenine (A), uracil (U), guanine (G), and cytosine (C)), ignoring the effects of modified nucleotides on the structure and system dynamics. In general, RNA molecules contain rigid and flexible structural elements, which can be probed using efficient selective 2'-hydroxyl analyzed by primer extension (SHAPE) experiments. SHAPE experiments selectively modify flexible RNA nucleotides and can be processed to produce a characteristic reactivity profile for an RNA molecule that contains structural information. Incorporation of efficient experimental information, such as SHAPE, in predicting RNA 3D structure is highly desirable for overcoming the current knowledge gap between RNA sequence and 3D structure. In the first project, we introduce a physics-based model, the 3D structure-SHAPE relationship (3DSSR) model, to predict the SHAPE reactivity from the structure and show how this model may be used to sieve SHAPE-compatible structures from a pool of low-energy decoys and refine our predictions. In the second project, we compare 3DSSR performance to that of a convolutional neural network (CNN) trained on the SHAPE data and RNA structures, showing that 3DSSR outperforms the CNN given the limited data available. In the third project, we further improve the 3DSSR model, gaining deeper insights into the SHAPE reaction and biases. In the fourth project, we explore the theory underpinning the iterative simulated CG RNA folding model (IsRNA). In establishing the underlying mechanics driving the success of the model, we were able to clarify and improve the parameterization method while expanding the model interpretation, which should broaden application of the method to other biopolymers, such as protein. We found that the parameterization method follows statistical mechanics principles but also has a Bayesian interpretation. Further, we found that the parameterization process can benefit from application of the principle of maximum entropy, which improves simulation and parameterization efficiency. In the fifth project, we investigate the impact of nucleotide modification on the structure and configurational ensemble of RNA molecules using free energy calculations. By applying modifications to a common RNA hairpin, we estimate the impact on the stability of the structural ensemble, identifying specific interactions that drive changes to the potential of mean force (PMF) and showing the context and modification-dependence of the variable alterations to the structure stability.