Energetic Costs, Precision, and Transport Efficiency of Molecular Motors

An efficient molecular motor would deliver cargo to the target site at a high speed and in a punctual manner while consuming a minimal amount of energy. According to a recently formulated thermodynamic principle, referred to as the <i>thermodynamic uncertainty relation</i>, the travel distance of a motor and its variance are, however, constrained by the free energy being consumed. Here we use the principle underlying the uncertainty relation to quantify the <i>transport efficiency</i> of molecular motors for varying ATP concentration ([ATP]) and applied load (<i>f</i>). Our analyses of experimental data find that transport efficiencies of the motors studied here are semioptimized under the cellular condition. The efficiency is significantly deteriorated for a kinesin-1 mutant that has a longer neck-linker, which underscores the importance of molecular structure. It is remarkable to recognize that, among many possible directions for optimization, biological motors have evolved to optimize the transport efficiency in particular

Ripping RNA by Force Using Gaussian Network Models

Using force as a probe to map the folding landscapes of RNA molecules has become a reality thanks to major advances in single molecule pulling experiments. Although the unfolding pathways under tension are complicated to predict, studies in the context of proteins have shown that topology is the major determinant of the unfolding landscapes. By building on this finding we study the responses of RNA molecules to force by adapting Gaussian network model (GNM) that represents RNAs using a bead–spring network with isotropic interactions. Cross-correlation matrices of residue fluctuations, which are analytically calculated using GNM even upon application of mechanical force, show distinct allosteric communication as RNAs rupture. The model is used to calculate the force–extension curves at full thermodynamic equilibrium, and the corresponding unfolding pathways of four RNA molecules subject to a quasi-statically increased force. Our study finds that the analysis using GNM captures qualitatively the unfolding pathway of <i>T</i>. ribozyme elucidated by the optical tweezers measurement. However, the simple model cannot capture features, such as bifurcation in the unfolding pathways or the ion effects, in the forced-unfolding of RNAs

Urea-Induced Denaturation of PreQ₁‑Riboswitch

Urea, a polar molecule with a large dipole moment, not only destabilizes folded RNA structures but can also enhance the folding rates of large ribozymes. Unlike the mechanism of urea-induced unfolding of proteins, which is well understood, the action of urea on RNA has barely been explored. We performed extensive all-atom molecular dynamics simulations to determine the molecular underpinnings of urea-induced RNA denaturation. Urea displays its denaturing power in both secondary and tertiary motifs of the riboswitch structure. Our simulations reveal that the denaturation of RNA structures is mainly driven by the hydrogen-bonding and stacking interactions of urea with the bases. Through detailed studies of the simulation trajectories, we found that geminate pairs between urea and bases due to hydrogen bonds and stacks persist only ∼0.1–1 ns, which suggests that the urea–base interaction is highly dynamic. Most importantly, the early stage of base-pair disruption is triggered by penetration of water molecules into the hydrophobic domain between the RNA bases. The infiltration of water into the narrow space between base pairs is critical in increasing the accessibility of urea to transiently disrupted bases, thus allowing urea to displace inter-base hydrogen bonds. This mechanismwater-induced disruption of base pairs resulting in the formation of a “wet” destabilized RNA followed by solvation by ureais the exact opposite of the two-stage denaturation of proteins by urea. In the latter case, initial urea penetration creates a dry globule, which is subsequently solvated by water, leading to global protein unfolding. Our work shows that the ability to interact with both water and polar or nonpolar components of nucleotides makes urea a powerful chemical denaturant for nucleic acids

Microstates observed during the MD simulation and their occupancies.

<p>For each microstate, the switches in the ON state (<i>s</i>_<i>i</i> = 1) are marked with colored boxes.</p

Ultrasensitivity of Water Exchange Kinetics to the Size of Metal Ion

Metal ions play a vital role in many biological processes. An important factor in these processes is the dynamics of exchange between ion bound-water molecules and the bulk. Although structural and dynamical properties of labile waters bound to metal ions, such as Na⁺ and Ca²⁺, can be elucidated using molecular dynamics simulations, direct evaluation of rates of exchange of waters rigidly bound to high charge density Mg²⁺, has been elusive. Here, we report a universal relationship, allowing us to determine the water exchange time on metal ions as a function of valence and hydration radius. The proposed relationship, which covers times spanning 14 orders of magnitude, highlights the ultrasensitivity of water lifetime to the ion size, as exemplified by divalent ions, Ca²⁺ (∼100 ps) and Mg²⁺ (∼1.5 μs). We show that even when structures, characterized by radial distributions are similar, a small difference in hydration radius leads to a qualitatively different (associative or dissociative) mechanism of water exchange. Our work provides a theoretical basis for determination of hydration radius, which is critical for accurately modeling the water dynamics around multivalent ions, and hence in describing all electrostatically driven events such as ribozyme folding and catalysis

Ten binary switches.

<p>The time traces of the apo, antagonist-bound, and agonist-bound forms are colored by black, blue, and red, respectively, and their histograms are shown on the right side of the panels. From 4 to 10, the values separating the on and off states are marked in red circles.</p

Cross-correlations among binary switches.

<p>(a) Cross-correlation matrices between the changes in 10 ON/OFF switches for three distinct receptor states calculated by using <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004044#pcbi.1004044.g003" target="_blank">Fig. 3</a>. The symbols “P” in the matrix elements are for the postive correlatin (<i>C</i>_<i>ij</i> > 0.25); “N” is for the negative correlation (<i>C</i>_<i>ij</i> < −0.25). (b) Diagram of the cross-correlation between the switches. TM1 to TM7 helices are displayed in gray circles, and the ten switches are specified with the boxes. The positive and negative correlations are depicted using red and blue lines, respectively. (c) Coordination of the antagonist and agonist to 7 (W246). W246 and the bound ligands are depicted in the left and right figures. The graph in the middle shows the distances between the center of mass of the W246 (indole 6-ring) and the center of mass of the furan ring (ZM-241385, blue) and ethyl group (UK-432097, red).</p

Agonist inserted to apo form.

<p>(a) Time traces from the case 1 to case 4. In the cases 1 and 2, the agonist was inserted into the apo form when the ionic-lock was intact; whereas in the cases 3 and 4, the agonist was inserted when the ionic-lock was disrupted. (b) Average values of switch from 1 to 10 for the case 1 through 4. (c) Population of microstates sampled after the insertion of agonist. (d) Hamming distance and complexity calculated for cases 1–4. (e) The stars are the locations of the cases from 1 to 4, calculated in terms of Hamming distance relative to the apo, antagonist, and agonist forms.</p

Correlation between symmetric-asymmetric transition and fluctuation at NT binding region.

<p>(a) Head-stalk contact region and NT binding pocket in Ncd motor are marked on the Ncd structure. (b) Disruption of the head-stalk contact induces disruption of NT binding pocket. Shaded in grey are the anti-correlated signals between the number of head-stalk contacts and the RMSD of NT binding pocket. (c) Different elements of NT binding pocket region in Ncd motor are marked: P-loop (orange), switch I (red) and switch II (yellow). Structural differences of these motifs are compared between the two states. For symmetric state, we use blue color for all elements. Switch I region reveals maximum deformation. (d) RMSD distribution of P-loop, switch I and switch II are shown for both the states. Note the noticeable difference for switch I region.</p

5 to 10 defined from the rotameric switches in TM4, TM5, TM6, and TM7.

<p>Rotameric states of (a) W129, (b) Y197, (c) CWxP motif, and (d) NPxxY motif are compared for the apo (white), antagonist-bound (cyan), and agonist-bound (pink) forms. (e) Helix bending in TM7. The helix bending angle (bendix) of TM7 was calculated using bendix program [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004044#pcbi.1004044.ref045" target="_blank">45</a>]. The helix is displayed as a cylinder marked with the heatmap ranging from 0^<i>o</i> to 20^<i>o</i>. The scatter plot on right side depicts the relationship between H-bond of N280-S281 and the bending angle of the TM7 helix (apo: black, antagonist-bound: blue, agonist-bound states: red). The average bending angles are annotated with the symbols, X.</p