Showing papers by "Paul C. Whitford published in 2019"

Diffusion of tRNA inside the ribosome is position-dependent.

Abstract: In recent years, there has been a growing interest to quantify the energy landscape that governs ribosome dynamics. However, in order to quantitatively integrate theoretical predictions and experimental measurements, it is essential that one has a detailed understanding of the associated diffusive properties. Here, all-atom explicit-solvent simulations (50 μs of aggregate sampling) predict that the diffusion coefficient of a tRNA molecule will depend on its position within the ribosome. Specifically, during aa-tRNA accommodation (i.e., the process by which tRNA enters the ribosome), the apparent diffusion coefficient decreases by approximately an order of magnitude. By comparing these to values obtained with an energetically “smooth” model, we show that the observed nonuniform behavior likely arises from electrostatic and solvation interactions between the tRNA and ribosome. These calculations also reveal the hierarchical character of ribosomal energetics, where steric interactions induce a large-scale free-energy barrier, and short-scale roughness determines the rate of diffusive movement across the landscape.In recent years, there has been a growing interest to quantify the energy landscape that governs ribosome dynamics. However, in order to quantitatively integrate theoretical predictions and experimental measurements, it is essential that one has a detailed understanding of the associated diffusive properties. Here, all-atom explicit-solvent simulations (50 μs of aggregate sampling) predict that the diffusion coefficient of a tRNA molecule will depend on its position within the ribosome. Specifically, during aa-tRNA accommodation (i.e., the process by which tRNA enters the ribosome), the apparent diffusion coefficient decreases by approximately an order of magnitude. By comparing these to values obtained with an energetically “smooth” model, we show that the observed nonuniform behavior likely arises from electrostatic and solvation interactions between the tRNA and ribosome. These calculations also reveal the hierarchical character of ribosomal energetics, where steric interactions induce a large-scale fr...

Drift-diffusion (DrDiff) framework determines kinetics and thermodynamics of two-state folding trajectory and tunes diffusion models.

Abstract: The stochastic drift-diffusion (DrDiff) theory is an approach used to characterize the dynamical properties of simulation data. With new features in transition times analyses, the framework characterized the thermodynamic free-energy profile [F(Q)], the folding time (τf), and transition path time (τTP) by determining the coordinate-dependent drift-velocity [v(Q)] and diffusion [D(Q)] coefficients from trajectory time traces. In order to explore the DrDiff approach and to tune it with two other methods (Bayesian analysis and fep1D algorithm), a numerical integration of the Langevin equation with known D(Q) and F(Q) was performed and the inputted coefficients were recovered with success by the diffusion models. DrDiff was also applied to investigate the prion protein (PrP) kinetics and thermodynamics by analyzing folding/unfolding simulations. The protein structure-based model, the well-known Go¯-model, was employed in a coarse-grained Cα level to generate long constant-temperature time series. PrP was chosen due to recent experimental single-molecule studies in D and τTP that stressed the importance and the difficulty of probing these quantities and the rare transition state events related to prion misfolding and aggregation. The PrP thermodynamic double-well F(Q) profile, the "X" shape of τf(T), and the linear shape of τTP(T) were predicted with v(Q) and D(Q) obtained by the DrDiff algorithm. With the advance of single-molecule techniques, the DrDiff framework might be a useful ally for determining kinetic and thermodynamic properties by analyzing time observables of biomolecular systems. The code is freely available at https://github.com/ronaldolab/DrDiff.

Dissecting the Energetics of Subunit Rotation in the Ribosome.

Abstract: The accurate expression of proteins requires the ribosome to efficiently undergo elaborate conformational rearrangements. The most dramatic of these motions is subunit rotation, which is necessary for tRNA molecules to transition between ribosomal binding sites. While rigid-body descriptions provide a qualitative picture of the process, obtaining quantitative mechanistic insights requires one to account for the relationship between molecular flexibility and collective dynamics. Using simulated rotation events, we assess the quality of experimentally accessible measures for describing the collective displacement of the ∼4000-residue small subunit. For this, we ask whether each coordinate is able to identify the underlying free-energy barrier and transition state ensemble (TSE). We find that intuitive structurally motivated coordinates (e.g., rotation angle, interprotein distances) can distinguish between the endpoints, though they are poor indicators of barrier-crossing events, and they underestimate the free-energy barrier. In contrast, coordinates based on intersubunit bridges can identify the TSE. We additionally verify that the committor probability for the putative TSE configurations is 0.5, a hallmark feature of any transition state. In terms of structural properties, these calculations implicate a transition state in which flexibility allows for asynchronous rearrangements of the bridges, as the ribosome adopts a partially rotated orientation. This provides a theoretical foundation, upon which experimental techniques may precisely quantify the energy landscape of the ribosome.

Distinguishing Biomolecular Pathways and Metastable States.

Abstract: Protein folding occurs in a high dimensional phase space, and the representation of the associated energy landscape is nontrivial. A widely applied approach to studying folding landscapes is to describe the dynamics along a small number of reaction coordinates. However, other strategies involve more elaborate analysis of the complex phase space. There have been many attempts to obtain a more detailed representation of all available conformations for a given system. In this work, we address this problem using a metric based on internal distances between amino acids to describe the differences between any two conformations. Using an effective projection method, we are able to go beyond the typical one-dimensional representation and provide intuitive two dimensional visualizations of the landscape. We refer to this method as the energy landscape visualization method (ELViM). We have applied this methodology using a Cα structure-based model to study the folding of two well-known proteins: SH3 domain and prote...

Using SMOG 2 to Simulate Complex Biomolecular Assemblies.

Abstract: Over the last 20 years, the application of structure-based (Gō-like) models has ranged from protein folding with coarse-grained models to all-atom representations of large-scale molecular assemblies. While there are many variants that may be employed, the common feature of these models is that some (or all) of the stabilizing energetic interactions are defined based on the knowledge of a particular experimentally obtained conformation. With the generality of this approach, there was a need for a versatile computational platform for designing and implementing this class of models. To this end, the SMOG 2 software package provides an easy-to-use interface, where the user has full control of the model parameters. This software allows the user to edit XML-formatted files in order to provide definitions of new structure-based models. SMOG 2 reads these "template" files and maps the interactions onto specific structures, which are provided in PDB format. The force field files produced by SMOG 2 may then be used to perform simulations with a variety of popular molecular dynamics suites. In this chapter, we describe some of the key features of the SMOG 2 package, while providing examples and strategies for applying these techniques to complex (often large-scale) molecular assemblies, such as the ribosome.

Dissecting the energetics of subunit rotation in the ribosome

Abstract: The accurate expression of proteins requires the ribosome to efficiently undergo elaborate conformational rearrangements. The most dramatic of these motions is subunit rotation, which is necessary for tRNA molecules to transition between ribosomal binding sites. While rigid-body descriptions provide a qualitative picture of the process, obtaining quantitative mechanistic insights requires one to account for the relationship between molecular flexibility and collective dynamics. Using simulated rotation events, we assess the quality of experimentally-accessible measures for describing the collective displacement of the ~ 4000-residue small subunit. For this, we ask whether each coordinate is able to identify the underlying free-energy barrier and transition state ensemble (TSE). We find that intuitive structurally-motivated coordinates (e.g. rotation angle, inter-protein distances) can distinguish between the endpoints, though they are poor indicators of barrier-crossing events, and they underestimate the free-energy barrier. In contrast, coordinates based on inter-subunit bridges can identify the TSE. We additionally verify that the committor probability for the putative TSE configurations is 0.5, a hallmark feature of any transition state. In terms of structural properties, these calculations implicate a transition state in which flexibility allows for asynchronous rearrangements of the bridges as the ribosome adopts a partially-rotated orientation. These calculations provide a theoretical foundation, upon which experimental techniques may precisely quantify the energy landscape of the ribosome.