Cognate (blue), near-cognate (purple), and non-cognate tRNAs (white).

<p>for all sense codons in <i>E. coli</i> following the definitions of “cognate” and “near-cognate” as given in [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0134994#pone.0134994.ref037" target="_blank">37</a>] and [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0134994#pone.0134994.ref038" target="_blank">38</a>], respectively.</p

Protein Synthesis in <i>E. coli</i>: Dependence of Codon-Specific Elongation on tRNA Concentration and Codon Usage

<div><p>To synthesize a protein, a ribosome moves along a messenger RNA (mRNA), reads it codon by codon, and takes up the corresponding ternary complexes which consist of aminoacylated transfer RNAs (aa-tRNAs), elongation factor Tu (EF-Tu), and GTP. During this process of translation elongation, the ribosome proceeds with a codon-specific rate. Here, we present a general theoretical framework to calculate codon-specific elongation rates and error frequencies based on tRNA concentrations and codon usages. Our theory takes three important aspects of <i>in-vivo</i> translation elongation into account. First, non-cognate, near-cognate and cognate ternary complexes compete for the binding sites on the ribosomes. Second, the corresponding binding rates are determined by the concentrations of free ternary complexes, which must be distinguished from the total tRNA concentrations as measured <i>in vivo</i>. Third, for each tRNA species, the difference between total tRNA and ternary complex concentration depends on the codon usages of the corresponding cognate and near-cognate codons. Furthermore, we apply our theory to two alternative pathways for tRNA release from the ribosomal E site and show how the mechanism of tRNA release influences the concentrations of free ternary complexes and thus the codon-specific elongation rates. Using a recently introduced method to determine kinetic rates of <i>in-vivo</i> translation from <i>in-vitro</i> data, we compute elongation rates for all codons in <i>Escherichia coli</i>. We show that for some tRNA species only a few tRNA molecules are part of ternary complexes and, thus, available for the translating ribosomes. In addition, we find that codon-specific elongation rates strongly depend on the overall codon usage in the cell, which could be altered experimentally by overexpression of individual genes.</p></div

Dwell Time Distributions of the Molecular Motor Myosin V

<div><p>The dwell times between two successive steps of the two-headed molecular motor myosin V are governed by non-exponential distributions. These distributions have been determined experimentally for various control parameters such as nucleotide concentrations and external load force. First, we use a simplified network representation to determine the dwell time distributions of myosin V, with the associated dynamics described by a Markov process on networks with absorbing boundaries. Our approach provides a direct relation between the motor’s chemical kinetics and its stepping properties. In the absence of an external load, the theoretical distributions quantitatively agree with experimental findings for various nucleotide concentrations. Second, using a more complex branched network, which includes ADP release from the leading head, we are able to elucidate the motor’s gating effect. This effect is caused by an asymmetry in the chemical properties of the leading and the trailing head of the motor molecule. In the case of an external load acting on the motor, the corresponding dwell time distributions reveal details about the motor’s backsteps.</p> </div

(a) Typical stepping trajectory, i.e., spatial displacement as a function of time and (b) dwell time distribution of myosin V, adapted from [4].

<p>(a) In single-molecule experiments with a feedback loop, the data are monitored under constant external load. Hence, the distance between the bead monitoring the motor’s motion (upper gray trajectory, with the thin black line showing a filtered curve) and the trap center (black trajectory) remains constant. (b) Dwell time distribution of myosin V for saturating [ATP]. The solid line is a fit from Ref. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0055366#pone.0055366-Rief1" target="_blank">[4]</a> that involves two exponential functions with decay rates 150/s and 12.5/s.</p

(a) Root mean square deviation RMSD between the experimental data (green bars in Fig. 3 (c, d)) and the simulated dwell time distributions for the three-cycle network as a function of the gating parameter for [ATP] = 10 (crosses) and [ATP] = 2 (circles).

<p>A lower deviation indicates an improved agreement between the experimental values and the distributions that result from the three-cycle network. For both concentrations, the RMSD decreases with increasing , until it saturates for , as indicated by the dashed line. The fluctuations for large values of arise from the variance in the simulations. The solid lines serve as a guide to the eye. (b) In case of a variable ATP binding rate , the agreement between the simulated dwell time distributions (symbols) and the experimental data (green bars) is further improved. The agreement is optimal for (red crosses), and is significantly improved in contrast to the distribution based on the experimental value of (red circles). The inset shows the RMSD as a function of , illustrating the minimal deviation for </p

Motor velocity as a function of external load for the network formed by the cycle (lines) compared to experimental data (symbols) for varying [ATP].

<p>In the experiments, the concentrations of ADP and P are believed to be rather small. In the calculations, we consider the limit of [ADP] = [P] = 0.</p

Translation elongation cycle.

<p>The ribosome has three tRNA binding sites, the A, P, and E site. A ribosome that has just arrived at a new (green) codon of an mRNA (state “0”) has an empty A site, whereas the P site is occupied by a tRNA (here shown as small gray sphere) that is cognate or near-cognate to the preceding codon. Elongation factor EF-Tu (blue spheres), aa-tRNAs (green, orange, and purple small spheres), and GTP molecules (not shown) form ternary complexes. Free cognate, near-cognate and non-cognate ternary complexes bind to the ribosome with rates depending on their respective concentrations (green, orange, and purple arrows from state “0” to states “1”, “6”, and “11”, respectively). Since the initial binding is not codon-specific, all kinds of ternary complexes unbind again from the ribosome with the same dissociation rate. Alternatively, a cognate or near-cognate ternary complex can be recognized by the ribosome (dotted arrows from states “1” and “6” to states “4” and “9”, respectively) before the ternary complex is either completely released (arrows from states “4” and “9” to state “0”), brought back to the initial binding state (dotted arrows from states “4” and “9’ to states “1” and “6”, respectively), or its aa-tRNA is accommodated in the ribosomal A site (arrows from states “4” and ”9” to states “5” and “10”, respectively). Along with aa-tRNA accommodation, EF-Tu leaves the ribosome. The new A-site tRNA is then further processed and shifted to the P site, while the ribosome translocates to the next (purple) codon. The former P-site tRNA is now in the E site. Depending on the assumed pathway of tRNA release, the E-site tRNA either dissociates very rapidly from the ribosome (2-1-2 pathway), or stays until the next aa-tRNA has been accommodated in the ribosomal A site (2-3-2 pathway). The numerals correspond to the ribosomal states of the codon-specific Markov process introduced below.</p

Cooperative Slowdown of Water Rotation near Densely Charged Ions Is Intense but Short-Ranged

We investigate the reorientation dynamics of water at 300 K in solutions of magnesium sulfate and cesium chloride from classical atomistic molecular dynamics simulations using the “simple water model with four sites and negative Drude polarizability” (SWM4-NDP) and accompanying ion models; for SO₄^2–, we derive SWM4-NDP-compatible parameters. Results indicate that pairs of ions have a cooperative effect on water rotation but do not support the model based on experiment whereby ion cooperativity increases the number of very slow water molecules well beyond the ions’ first hydration shell. Instead, we find that cooperative slowdown beyond the first hydration shell is weak. Intense cooperative slowdown is limited to the first hydration shells, the magnitude of the slowdown being stronger for the multivalent ions. Cooperative effects for different salts differ in both the magnitude of rotational slowdown and the spatial range of the affected water subpopulations

Changing the codon usage of AAA for fixed ratios of the codon usages for all other codons.

<p>(A) The concentration of free Lys-tRNA^Lys ternary complexes decreases when the codon usage of one of its cognate codons, AAA, increases. (B) Elongation rates of codons AAA (solid line) and AAG (dashed line), both of which are cognate to tRNA^Lys. The solid and dashed lines coincide almost perfectly. (C) Near-cognate missense error frequencies for both codons (AAA: solid; AAG: dashed). Results are shown for both the 2-1-2 pathway (blue) and the 2-3-2 pathway (orange) of E-site tRNA release. The vertical dashed lines (black) indicate the wild type value 0.0467 of AAA codon usage, see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0134994#pone.0134994.s008" target="_blank">S7 Table</a> in the Supporting Information.</p