18 research outputs found

    Calculation of the Free Energy and Cooperativity of Protein Folding

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    Calculation of the free energy of protein folding and delineation of its pre-organization are of foremost importance for understanding, predicting and designing biological macromolecules. Here, we introduce an energy smoothing variant of parallel tempering replica exchange Monte Carlo (REMS) that allows for efficient configurational sampling of flexible solutes under the conditions of molecular hydration. Its usage to calculate the thermal stability of a model globular protein, Trp cage TC5b, achieves excellent agreement with experimental measurements. We find that the stability of TC5b is attained through the coupled formation of local and non-local interactions. Remarkably, many of these structures persist at high temperature, concomitant with the origin of native-like configurations and mesostates in an otherwise macroscopically disordered unfolded state. Graph manifold learning reveals that the conversion of these mesostates to the native state is structurally heterogeneous, and that the cooperativity of their formation is encoded largely by the unfolded state ensemble. In all, these studies establish the extent of thermodynamic and structural pre-organization of folding of this model globular protein, and achieve the calculation of macromolecular stability ab initio, as required for ab initio structure prediction, genome annotation, and drug design

    Structural Repertoire of HIV-1-Neutralizing Antibodies Targeting the CD4 Supersite in 14 Donors

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    The site on the HIV-1 gp120 glycoprotein that binds the CD4 receptor is recognized by broadly reactive antibodies, several of which neutralize over 90% of HIV-1 strains. To understand how antibodies achieve such neutralization, we isolated CD4-binding-site (CD4bs) antibodies and analyzed 16 co-crystal structures –8 determined here– of CD4bs antibodies from 14 donors. The 16 antibodies segregated by recognition mode and developmental ontogeny into two types: CDR H3-dominated and VH-gene-restricted. Both could achieve greater than 80% neutralization breadth, and both could develop in the same donor. Although paratope chemistries differed, all 16 gp120-CD4bs antibody complexes showed geometric similarity, with antibody-neutralization breadth correlating with antibody-angle of approach relative to the most effective antibody of each type. The repertoire for effective recognition of the CD4 supersite thus comprises antibodies with distinct paratopes arrayed about two optimal geometric orientations, one achieved by CDR H3 ontogenies and the other achieved by VH-gene-restricted ontogenies

    Thermal stability of TC5b.

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    <p>A. Fraction of formed α-helix L<sup>2</sup>YIQWLK<sup>8</sup> (dashed black), β-turn S<sup>14</sup> (solid green), and polyprolyl helix P<sup>18</sup> (dotted blue), as defined using self-consistent clustering and enumeration of their backbone dihedral angles. Note that P<sup>18</sup> remains unchanged in its backbone conformation due to its definition in CHARMM. Individual α-helical residues have varying thermal stability, with the more N-terminal ones being less stable, consistent with the existence of α-helical fraying. B. Fraction of formed α-helical salt/secondary bridge Q<sup>5</sup>∶K<sup>8</sup> (solid red), α-helical hydrogen bond Y<sup>3</sup>∶L<sup>7</sup> (dotted red), β-turn/tertiary salt bridge D<sup>9</sup>∶R<sup>16</sup> (solid blue), β-turn hydrogen bond D<sup>9</sup>∶S<sup>14</sup> (dashed green), tertiary hydrophobic core W<sup>6</sup>∶P<sup>19</sup> and Y<sup>3</sup>∶P<sup>19</sup> (solid and dashed black), and secondary hydrophobic core Y<sup>3</sup>∶W<sup>6</sup> (dashed red), as defined by using self-consistent clustering and enumeration of their distances. Note that the α-helical salt/secondary bridge is only partially formed at low temperature, even though the rest of the structure is nearly fully folded by other measures. Similarly, the secondary hydrophobic core Y<sup>3</sup>∶W<sup>6</sup> persists even at high temperature, where the rest of the protein is largely unfolded by other measures. Importantly, substantial amount of residual native structure persists at high temperature. C. Fraction of formed mean α-helical structure (dashed black), mean β-turn structure (solid green), mean tertiary structure (solid black) in the REMS calculated ensembles, and native fraction measured experimentally using chemical shift dispersion (squares), as adapted from the first study of TC5b <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0000446#pone.0000446-Neidigh1" target="_blank">[28]</a>.</p

    Manifold of unfolded mesostates.

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    <p>Mapping of the unfolded state ensemble, as calculated using the 363 K replica, onto the two top coordinates of its locally linear embedding space (open black circles), and the two top coordinates of its principal component projection (solid green circles). Principle component analysis fails to discern mesostate structure of the unfolded state ensemble, with the entire ensemble located near the origin of the PCA projection. On the other hand, displacement along the manifold from the origin of the LLE map coincides with the formation of native-like mesostates, containing: 1) α-helical/secondary salt bridge (red), 2) β-turn/tertiary salt bridge (blue), 3) α-helix and α-helical hydrophobic core, and 4) nearly native configurations with both the α-helix and the tertiary hydrophobic core.</p

    Sampling and efficiency of REMS simulations of TC5b in explicit water.

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    <p>A. Mean probabilities 〈<i>P</i>〉 of MC exchange between adjoining replicas <i>x<sub>n</sub></i> and <i>x<sub>m</sub></i> as a function of temperature, demonstrating that usage of REMS leads to efficient replica exchange. B. Exchanges of replicas in the temperature space, tracking the initial lowest (red dashed) and highest (blue solid) containing the predominantly native and unfolded states, respectively, as they diffuse in temperature space in the course of the simulation. C. Divergence of the normalized difference (<i>Δ</i>) of fraction of formed hydrophobic core W<sup>6</sup>∶P<sup>19</sup> (closed squares), hydrophobic core Y<sup>3</sup>∶W<sup>6</sup> (open circles), salt bridge D<sup>9</sup>∶R<sup>16</sup> (closed stars), α-helical Y3∶L7 (solid circles) and the β-turn D9∶S14 (open squares) hydrogen bonds between initial and final structures as a function of replica exchange for the 363 K replica. These measure were chosen because their non-local nature should be most sensitive to initial configuration memory effects. The total length of REMS simulation exceeds the apparent computational time constant of self-diffusion by nearly three orders of magnitude.</p

    Equilibration and calibration of REMS simulations of TC5b in explicit water.

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    <p>A. Instantaneous potential energy (<i>U</i>) as a function of MD time during evolution of the 273 K replica in the canonical <i>NVT</i> ensemble prior to initiating REMS, demonstrating its equilibration, as reflected in the energetic stability during the last 50 ps. B. Instantaneous potential energy (<i>U</i>) as a function of MD time upon replica exchange from 276 to 273 K, demonstrating thermalization in less than 2 ps. C. Average potential energy 〈<i>U</i>〉 of 273 K replica as a function of energy smoothing time (<i>ts</i>). As <i>ts</i> approaches 2000 fs, the standard deviation of <<i>U></i> approaches the fluctuation of the energy distribution in that time domain. At <i>ts</i>  =  200 fs, energy-smoothed 〈<i>U</i>〉 of REMS is statistically indistinguishable from the instantaneous <i>U</i> used during conventional REM; double-sided <i>p</i> = 0.73. Bars represent ±1σ.</p

    Folding reaction manifold.

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    <p>Mapping of TC5b's folding ensemble at the midpoint of its thermal transition, as calculated using the 310 K replica, onto the top three coordinates of its LLE manifold. Displacement along the <i>M<sub>1</sub></i> coordinate of the manifold coincides with the transformation of the 5) nearly native and 6) partially unfolded mesostates that lack the tertiary hydrophobic core and the native β-turn, but retain a frayed α-helix and the tertiary salt bridge. Displacement along the <i>M<sub>2</sub></i> coordinate coincides in part with the transformation of the α-helix from mesostate 7) that possesses a near native β-turn and hydrophobic cores and a non-α-helical but compact N-terminus, and mesostate 8) that lacks the native hydrophobic cores and has a non-native β-turn centered at K<sup>8</sup> that is part of the N-terminal α-helix in the NMR structure. Displacement along the <i>M<sub>3</sub></i> coordinate coincides with the transformation of the β-turn, including mesostates 9) that have a near native β-turn and tertiary salt bridge but have an unfolded α-helix and hydrophobic cores, and 10) possess a near native topology and α-helix but lack a native β-turn.</p
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