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

Dynamic Sub-10-nm Nanostructured Ultrathin Films of Sugar–Polyolefin Conjugates Thermoresponsive at Physiological Temperatures

Spin-casting of a cellobiose-atactic polypropene (CB-aPP) conjugate (<b>1</b>) from a 0.1% (w/w) <i>n</i>-butanol/hexane solution onto highly oriented pyrolytic graphite (HOPG) and carbon-coated Si(100) spontaneously produced microphase-separated sub-10-nm nanostructured ultrathin films in the form of alternating CB and aPP lamellar domains (<i>d</i> = 6.60 ± 0.68 nm) that are oriented perpendicular to the substrate surface. Thermal annealing at modest temperatures (e.g., 50–100 °C), and as low as the physiologically relevant temperature of 38 °C, serves to drive a structural transition that yields a parallel stacked bilayer assembly as the thermodynamically favored nanostructure. These results establish the advantage of low molecular weight, narrow polydispersity, and amorphous, low <i>T</i>_g, poly­(α-olefinate)­s (xPAOs) as a new class of hydrophobic building block for amphiphilic materials, and sugar–PAO conjugates in particular, for the development of stimuli-responsive, nanostructured materials for technological applications at physiological temperatures

Dinuclear Bis-Propagators for the Stereoselective Living Coordinative Chain Transfer Polymerization of Propene

Modulation of steric interactions remote from the active sites within a series of dinuclear bis-propagators derived from racemic <b>2</b>–<b>4</b> was used to attenuate the rate of reversible chain transfer between active transition-metal centers and excess equivalents of inactive main-group-metal alkyl species relative to chain growth propagation, as a strategy for achieving the stereoselective living coordinative chain transfer polymerization of propene to provide isotactic stereoblock polypropene. Under identical conditions, the corresponding mononuclear propagator derived from racemic <b>1</b> produced only atactic polypropene

Representative time traces of H-DNA at [Na⁺] = 100 mM and their analysis.

<p>(A) (i) Fluorescence signal and (ii) their FRET state. (iii) Internal states estimated for <i>K</i> = 1, 2, …, 5. Right panel shows <i>G</i>(<i>K</i>) (blue circle) where <i>K</i>_<i>obs</i> specifies the number of detected internal states in individual traces (blue). (B, C, D) Other representative time traces and their <i>G</i>(<i>K</i>) obtained under the same experimental condition.</p

Validation of VB-DCMM on synthetic data.

<p>(A) (i) A time trace of internal state generated with <i>γ</i>^(1)→(2)Δ<i>t</i> = γ^(2)→(1)Δ<i>t</i> = 0.001. (ii) An observable time trace generated based on the trace of internal state in (i) by using internal state-dependent parameters , , . (iii) An synthetic FRET data with Gaussian noise overlaid on the trace in (ii). (iv) Noised filtered FRET state by HMM (blue line). (v) Traces of internal state with different <i>K</i>, estimated using VB-DCMM on the noise-filtered FRET trace from (iv) (black line is the true internal state trace while red, orange, and blue are internal state estimated from the model with <i>K</i> = 1, 2, and 3, respectively. The indices of internal state were determined by comparing <b><i>B</i></b>^(<i>μ</i>) estimated for each internal state with <b><i>B</i></b>^{(<i>μ</i>),true} which is used to generate the synthetic data). (B) Estimated lower bound of the evidence function <i>F</i>(<i>K</i>) of DCMM models with <i>K</i> = 1, 2, and 3. (C) Accuracy of detecting internal states. The overlap function <i>χ</i> calculated for 100 synthetic FRET traces generated under the identical condition used for generating the trace of internal state shown in (A).</p

Duplex-triplex transitions of H-DNA with dynamic disorder.

<p>(A) Illustration of H-DNA dynamics. The sequences in blue and black form duplex via Watson-Crick base pairing; the sequences in red extended from 3’-end region of the black sequence can pair with the sequences in blue via Hoogsteen base pairs to form the triplex helix. (B) A time trace of H-DNA displaying dynamic disorder. (Top) The fluorescence signals from Cy3 (green) and Cy5 (red) dyes. (Bottom) FRET signal (gray) was calculated using the signals from Cy3 and Cy5. Blue line is the noise-filtered FRET signal obtained using HMM. The low-FRET (~0.1) and high-FRET state (~0.9) correspond to the duplex and triplex states, respectively. The dynamic pattern of the time trace changes occasionally from one time interval to another. For example, the transitions from low to high FRET state around 70 s are much slower compared with those around 140 s. (C) The model for H-DNA dynamics with dynamic disorder. Hierarchical transitions, (1) transitions within <i>x</i>(<i>t</i>) = <i>i</i>, and (2) interconversion between <i>x</i>(<i>t</i>) = <i>i</i> and <i>x</i>(<i>t</i>′) = <i>j</i> (<i>i</i> ≠ <i>j</i>), can be described using Double Chain Markov Model (DCMM). (D) Graphical representation of DCMM. <i>x</i>(<i>t</i>), <i>o</i>(<i>t</i>), and <i>o_n</i>(<i>t</i>) represent internal state, noise-filtered observable (blue line in (B)), and the original observable at time t (gray line in (B)), respectively. The black arrows signify how each state is determined by others. For example, the state of observable at time <i>t</i>, <i>o</i>(<i>t</i>) is determined by the previous observable state at time <i>t</i> − 1, o(<i>t</i> − 1), and the state of the previous internal state, <i>x</i>(<i>t</i> − 1).</p

A rugged energy-landscape with hierarchical structure and an emergence of multiple time scales of transitions.

<p><i>τ</i>_<i>int</i> is the transition time between different superbasins of attraction whereas <i>τ</i>_<i>conf</i> is the time scale of conformational dynamics of molecule <i>within</i> each basin. Due to large difference in kinetic barriers (), <i>τ</i>_<i>int</i> ≫ <i>τ</i>_<i>conf</i>.</p

Accuracy of VB-DCMM in detecting internal states under various conditions of and <i>γ</i>^(1)↔(2) with <i>T</i>_<i>obs</i>/Δ<i>t</i> = 8800.

<p>(A) The color bar denotes the accuracy of analysis in terms of 〈<i>χ</i>〉 under varying with <i>K</i> = 2, , , and <i>γ</i>^(1)→(2)Δ<i>t</i> = <i>γ</i>^(2)→(1)Δ<i>t</i> = 0.001. (B) 〈<i>χ</i>〉 under varying <i>γ</i>^(1)→(2) and <i>γ</i>^(2)→(1) with <i>K</i> = 2, . 〈<i>χ</i>〉 was calculated by averaging over the results from analysis of 100 traces in each condition. The panels on the right show the relation between the value of 〈<i>χ</i>〉 and pairs of <i>D</i>_int and <i>D</i>_conf values which are evaluated at varying kinetic parameters. Results from the analysis over the data with the same parameters but different length of time trace (or different number of data points <i>T</i>_<i>obs</i>/Δ<i>t</i> = 2200, 4400) are provided in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005286#pcbi.1005286.s005" target="_blank">S4 Fig</a>.</p

Average accuracy of internal state detection as a function of <i>D</i>_conf, and <i>D</i>_int.

<p>To construct this diagram, we employed various synthetic data in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005286#pcbi.1005286.g004" target="_blank">Fig 4</a> (circle, two internal states (<i>K</i> = 2), two FRET states (<i>N</i> = 2)), <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005286#pcbi.1005286.s006" target="_blank">S5 Fig</a> (left triangle, <i>K</i> = 3, <i>N</i> = 2), and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005286#pcbi.1005286.s007" target="_blank">S6 Fig</a> (hexagon, <i>K</i> = 2, <i>N</i> = 3). The right triangle symbol denotes the result from the similar analysis shown in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005286#pcbi.1005286.s006" target="_blank">S5 Fig</a> with <i>K</i> = 3 but with smaller relative differences in the transition rates, <i>k</i>’s. Pentagon represents the result obtained with <i>K</i> = 4 and <i>N</i> = 2. (A) Color code denotes the accuracy of internal states predictions in terms of 〈<i>χ</i>〉, averaged over 100 traces for each condition. (B) The dashed lines corresponding to Δ = <i>D</i>_conf + 0.8<i>D</i>_int = 4, 5, … 9 are overlaid on the 2-D scatter plot of 〈<i>χ</i>〉(<i>D</i>_conf, <i>D</i>_int) calculated in (A).</p

Dynamic Anchoring of the 3′-End of the Guide Strand Controls the Target Dissociation of Argonaute–Guide Complex

Argonaute (Ago) is the catalytic core of small RNA-based gene regulation. Despite plenty of mechanistic studies on Ago, the dynamical aspects and the mechanistic determinants of target mRNA binding and dissociation of Ago–guide strand remain unclear. Here, by using single-molecule fluorescence resonance energy transfer (FRET) assays and <i>Thermus thermophilus</i> Ago (<i>Tt</i>Ago), we reveal that the 3′-end of the guide strand dynamically anchors at and releases from the PAZ domain of Ago, and that the 3′-end anchoring of the guide strand greatly accelerates the target dissociation by destabilizing the guide–target duplex. Our results indicate that the target binding/dissociation of Ago–guide is executed through the dynamic interplays among Ago, guide, and target