A-Site Residues Move Independently from P-Site Residues in all-Atom Molecular Dynamics Simulations of the 70S Bacterial Ribosome

The ribosome is a large macromolecular machine, and correlated motion between residues is necessary for coordinating function across multiple protein and RNA chains. We ran two all-atom, explicit solvent molecular dynamics simulations of the bacterial ribosome and calculated correlated motion between residue pairs by using mutual information. Because of the short timescales of our simulation (ns), we expect that dynamics are largely local fluctuations around the crystal structure. We hypothesize that residues that show coupled dynamics are functionally related, even on longer timescales. We validate our model by showing that crystallographic B-factors correlate well with the entropy calculated as part of our mutual information calculations. We reveal that A-site residues move relatively independently from P-site residues, effectively insulating A-site functions from P-site functions during translation

MI_norm in the catalytic site, the peptidyltransferase center (PTC), reveals a coupled P-region that moves independently from an A-region.

<p>MI_norm between all residues in the PTC for the trajectory of the ribosome alone (A) and the ribosome with mRNA and tRNA (B). 23S residues 2056–2063, 2250–2254, 2447–2454, and 2492–2507* have coupled dynamics in both trajectories (P-region, colored red in (C) and (D)). This group of residues moves relatively independently from the second group of atoms, 23S residues 2552–2556, 2573, 2582–2591 and 2601–2614 (A-region, colored orange in (C)). These two groups correspond to the two symmetry-related regions of the PTC <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0029377#pone.0029377-Belousoff1" target="_blank">[21]</a>. Two main differences are apparent in the dynamics with (A) and without (B) mRNA and tRNA: 1. dynamics in the A-loop become coupled in the presence of tRNA, and 2. residues 2610–2614 (colored yellow in (D)) become more coupled to the P-region. *<i>E.coli</i> numbering throughout.</p

The top ten highest MI triplets for U519 (2A, red) and C487 (2B, yellow) form a connected series across the protein structure (standard <i>E.coli</i> numbering).

<p>Both U519 and C487 form base pairs with other 23S nucleotides, and thus all interactions are via backbone atoms. Many of the amino acids in the high MI clusters are at the edges of secondary structure elements. Other nucleotides did not have high MI triplets clustered in 3D space.</p

K-means clustering of large subunit residues into three clusters based on mutual information in dynamics.

<p>(A) Mutual information between all residue pairs in the large subunit. Residues are ordered according to cluster. Cluster 1 residues (colored red in (B)) move relatively independently from the rest of the subunit (low MI_norm). Cluster 2 (color orange in (B)) and cluster 3 (colored yellow in (B)) residues show coupled motion between residues in the same cluster (high MI). Residues in cluster 2 and cluster 3 are more coupled to each other than they are to cluster 1. (B) Residues in each cluster are shown on the crystal structure of the large subunit. Cluster 1 residues (colored red) are the three protuberances that mark the tRNA translocation path and the residues that interact with the small subunit. Cluster 1 includes the A-loop residues that bind to A-site tRNA. Cluster 2 (colored orange) and cluster 3 (colored yellow) residues make up of the center of the subunit, including residues that surround the peptide exit tunnel. Cluster 2 residues include the P-loop residues that bind to P-site tRNA. Data based on the trajectory of the ribosome alone.</p

Residue distributions for the most proximal high MI triplet with U519, U519/R18/D22, a typical high MI proximal triplet.

<p>A pyrimidine (RNA is C or U) results in a tight distribution in which R18 is an Arg (R) and D22 is an Asp (D). A purine (RNA is A or G), slightly smaller than pyrimidines, results in a more diverse distribution in which R18 is most commonly an Asn (N) or Arg (R) and D22 is more widely distributed.</p

Likelihood of contact between triplets (orange *, red o) and pairs (blue □, green ∇) of residue positions vs. the coevolution rank.

<p>High MI triplets are likely to be in contact for triplets of residue positions (similar to coevolution seen in protein position pairs <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030022#pone.0030022-Dunn1" target="_blank">[5]</a>), but doublets are not. For example, 40% of the top 5 highest ranking MI triplets are in contact, while only 20% of the top 5 highest ranking MI doublets are in contact. MI between RNA and polar amino acids, more likely to lie on the surface on the protein and therefore interact with RNA, enhances the trend (o triplets, ∇ doublets). High MI triplets between polar amino acids and RNA are most likely to be in contact. In comparison, random coevolution between pairs of amino acids is expected to have a contact frequency of 8% <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030022#pone.0030022-Dunn1" target="_blank">[5]</a>.</p

Experimental positional flexibility (crystallographic B-factors, closed circles and left axes in (A, B)) correlates with computational positional flexibility.

<p>(A) B-factors for C4′ atoms of each residue (closed circles) are compared with entropy in DMA (open circles) for the 16S RNA chain, the largest RNA chain in the small subunit. The correlation coefficient is 0.7. (B) B-factors for C4′ atoms of each residue (closed circles) are compared with the root mean squared fluctuation (RMSF, open circles) for the 16S RNA chain. The correlation coefficient is 0.5. B-factors are taken from pdb ID 2J02 <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0029377#pone.0029377-Selmer1" target="_blank">[20]</a>. Computational data is from the 53 ns trajectory of the ribosome alone.</p

MI_norm between tRNA and residues in the large subunit.

<p>High MI_norm is indicated in red, and low MI_norm is indicated in blue. The PTC is depicted as spheres. (A) A-site tRNA dynamics are correlated to residues in the GTPase association center. (B) P-site tRNA dynamics are correlated to residues in the central protuberance, the P-site region of the PTC, and the peptide exit tunnel. (C) E-site tRNA dynamics have the least correlated dynamics to the active site. Residues in the large subunit that are most correlated to E-site tRNA are in the L1 stalk, central protuberance and along the peptide exit tunnel.</p

MI_norm in the dynamics between all pairs of residues in a 53 ns MD trajectory of the ribosome alone (A), and a 32 ns MD trajectory of the ribosome with mRNA and tRNA (B).

<p>High MI_norm indicates that two residues have coupled dynamics (red), and low MI_norm indicates that two residues move relatively independently from one another (blue). There is more coupling within a subunit than between, and within protein chains than within RNA chains. To increase the color contrast the MI_norm values along the diagonal (representing the MI between a residue and itself, by definition the highest MI for that residue) have been removed.</p

A Universal Lower-Bound Technique for the Size of Decision Trees and Two-Level AND/OR Circuits

A universal lower-bound technique for the size and other implementation characteristics of an arbitrary Boolean function as a decision tree and as a two-level AND/OR circuit is derived. The technique is based on the power spectrum coefficients of the n-dimensional Fourier transform of the function. The bounds vary from constant to exponential and are tight in many cases. Several examples are presented. 1 Introduction The two-level AND/OR implementation of a Boolean function f (also called sum of products, conjunctive normal form, or single-output PLA) is a logic circuit in which all the input variables or their complements are connected to AND gates; the outputs of all these AND gates are connected to a single OR gate whose output is the value of f . A decision tree is a rooted binary tree where each internal node (including the root) is labeled by a variable, and each leaf and each edge is labeled by a Boolean value (0 or 1). One of the two edges emanating from each internal node is..