Molecular Dynamics Simulations Illuminate the Role of Counterion Condensation in the Electrophoretic Transport of Homogalacturonans

Homogalacturonans (HGs) are polysaccharide copolymers of galacturonic acid and its methylesterified counterpart. The inter- and intramolecular distributions of the methylesterifed residues are vital behavior-determining characteristics of a sample’s structure, and much experimental effort has been directed to their measurement. While many techniques are able to measure the sample-averaged degree of methylesterification (DM), the measurement of inter- and intramolecular charge distributions are challenging. Here, molecular dynamics (MD) simulations are used to calculate the electrophoretic mobilities of HGs that have different amounts and distributions of charges placed along the backbone. The simulations are shown to capture experimental results well, even for low-DM samples that possess high charge densities. In addition, they illuminate the role that local counterion condensation can play in the determination of the electrophoretic mobility of heterogeneous blocky polyelectrolytes that cannot be adequately described by a single chain-averaged charge spacing

The <i>Ec</i>-PME protein.

<p>(A) Representation of the Ec-PME binding groove in an Ec-PME-HG decasaccharide complex. PME secondary structure is represented in cartoon and its surface is shown in white. The catalytic triad is represented in blue and coincides with the +1 subsite along the binding cleft. The HG decasaccharide is represented in cyan for carbon and red for oxygen atoms. (B) Electrostatic potential calculated for Ec-PME. The protein surface is colored in blue (positive) and red (negative) in the range between +3 k_bT and −3 k_bT (left panel). The negative patch observable in the active site is shown in close up (right panel) and is generated by the carboxylate groups of Asp178 and Asp199 that actively participate in the substrate catalysis and form an oxyanion. The oligosaccharide is shown, for clarity, in ball-and-stick representation and colored by atom type. Monosaccharide residues docked in the +1 and +2 subsites are labelled.</p

Schematic representation of the potential energy changes during <i>Ec</i>-PME processive catalysis.

<p>Calculated electrostatic binding energy of <i>Ec</i>-PME in complex to the HXM decasaccharide compared with the potential of a hypothetical molecular motor. The solid lines refer to regions of the potential sampled by molecular dynamics while the dashed line describes the final docking of the whole oligomer with the restoration of the alternating monosaccharide residue orientations and the next de-methylesterification reaction (not sampled in molecular mechanics studies). Relative potential units are reported in kJ mol⁻¹ (black) and <i>k</i>_b<i>T</i> (red).</p

Cα-Cα distances between the residues Arg267 and Asp143 (red) and Trp317 and Lys223 (black) located at the opposite ends of the <i>Ec</i>-PME binding groove.

<p>The graph shows the distances for the simulation where a full sliding of the oligosaccharide along the binding groove is reported. In such a case, correlated motions of the two flanking regions (see also <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0087581#pone-0087581-g003" target="_blank">figure 3</a>) are observed along the binding groove and contribute to the docking of a fresh methylesterified monosaccharide residue into the active site of the protein.</p

Electrostatic binding energy profile of the sliding motions of HG decasaccharide in complex with <i>Ec</i>-PME.

<p>Calculated electrostatic binding energy of <i>Ec</i>-PME in complex to the HXM decasaccharide as a function of the time (A) and movement along the binding groove of the monosaccharide residue docked in the +2 subsite (B). The circled numbers indicate different phases observable during the simulation: 0) start of the simulation; 1) end of rotation of the monosaccharide subunits docked in the subsites +1 and +2 about the glycosidic linkage, 2) stationary thermal fluctuations; 3) siting of the monosaccharide residue previously in the subsite +2 into the catalytic pocket (subsite +1) 4) continued Brownian sliding of the decasaccharide along the binding groove.</p

Time-evolution of the electrostatic profile for <i>Ec</i>-PME.

<p>The <i>Ec</i>-PME surface is colored by the calculated electrostatic potential of the protein in complex to the HXM decasaccharide (shown in ball-and-stick representation). The figures represent the conformations of protein and oligosaccharide before and after the catalysis, when rotation of monosaccharide subunits around the glycosidic bond and sliding of the oligosaccharide along the binding groove occur. Patches of positive electrostatic potential patches on the protein surface are represented in blue, negative patches are reported in red and neutral patches are in white. The surface is colored between −3 k_bT (red) and +3 k_bT (blue). The monosaccharide residue docked, at the start of the simulation, in subsite +2 is circled in yellow.</p

Rotation along the glycosidic bond and sliding of the substrate are the key events for the processive action of <i>Ec</i>-PME.

<p>Time-evolution of the conformational variations occurring for the catalytic triad of <i>Ec</i>-PME and two monosaccharide residues of the HXM decasaccharide, labelled by the subsite in which they were originally docked (+1 or +2). 0–10 ns: concerted approximately 180° rotation of monosaccharide residues at subsites +1 and +2. 10–30 ns: Brownian fluctuations of this disaccharide moiety and active-site side chains. 30–50 ns: movement of disaccharide moiety relative to protein bringing, a fresh carboxymethyl group (that began in subsite +2 and is still labelled as such) into the active site at +1. Carbon atoms are colored cyan, oxygen atoms are colored red and nitrogen atoms are colored in blue. Black and red arrows show the carboxylate and carboxy-methylesterified groups of the monosaccharides initially docked in the +1 and +2 subsites respectively. The green arrow in the 40 ns window signals the movement of the monosaccharide that began in the +2 subsiste into the active site (+1 subsite). Note the similarity between the final position (50 ns) occupied by the sugar ring that began in subsite +2 and the initial position (0 ns) of the residue that started in subsite +1.</p

Representation of the interactions in the −2 subsite during the sliding of the decasaccharide along the binding groove of <i>Ec</i>-PME.

<p>At the start of the simulation (crystal structure coordinates) the monosaccharide residue docked in the −2 subsite establishes hydrogen bonds between Thr109 and Ala110 backbone nitrogens (A). After the rotation of the monosaccharide residues about the glycosidic bond and the sliding of the polysaccharide along the groove, the monosaccharide residue previously docked in the subsite −1 establishes contacts with Thr109 and Ala110 in the −2 subsite. The same two sugar moieties are circled in yellow and blue respectively in both (A) and (B) to highlight changes occurring in their interactions with the protein. PME secondary structure is shown in cartoon form and colored in grey. The active site (+1 subsite) region is colored in green. Thr109, Ala110 and the HG decasaccharide are represented with cyan for carbon and red for oxygen atoms.</p

Correlated motions of the regions flanking the enzyme-substrate binding interface are crucial for the sliding of the polysaccharide along the binding cleft.

<p>Porcupine plots of the <i>Ec</i>-PME backbone in complex with the HXM decasaccharide (oligosaccharide not shown for simplicity) in the time windows 15 ns to 30 ns (A) and 30 ns to 50 ns (B). The enzyme binding-groove is indicated by the black ellipse. The represented motions account for more than 80% of the total correlated motions of the enzyme as reported for the first 8 eigenvectors along the trace of the matrix. Arrows point in the direction of the motion with length and color representing the total displacement along the sampled window. Color bars quantify the displacement in Ångstroms.</p

An example of the hydrolysis reaction catalyzed by pectin methylesterase (PME).

<p>A homogalacturonan trimer, with conventional atom-labelling scheme, undergoes de-methylesterification of the middle subunit.</p