Mechanical Transition from α‑Helical Coiled Coils to β‑Sheets in Fibrin(ogen)

We characterized the α-to-β transition in α-helical coiled-coil connectors of the human fibrin­(ogen) molecule using biomolecular simulations of their forced elongation and theoretical modeling. The force (<i>F</i>)–extension (<i>X</i>) profiles show three distinct regimes: (1) the elastic regime, in which the coiled coils act as entropic springs (<i>F</i> < 100–125 pN; <i>X</i> < 7–8 nm); (2) the constant-force plastic regime, characterized by a force-plateau (<i>F</i> ≈ 150 pN; <i>X</i> ≈ 10–35 nm); and (3) the nonlinear regime (<i>F > </i>175–200 pN; <i>X</i> > 40–50 nm). In the plastic regime, the three-stranded α-helices undergo a noncooperative phase transition to form parallel three-stranded β-sheets. The critical extension of the α-helices is 0.25 nm, and the energy difference between the α-helices and β-sheets is 4.9 kcal/mol per helical pitch. The soft α-to-β phase transition in coiled coils might be a universal mechanism underlying mechanical properties of filamentous α-helical proteins

Dynamic evolution of mechanical degrees of freedom and survival probability for CCMV shell.

<p>Panel (a) exemplifies the dynamics of Hertzian deformation <i>x</i>_<i>H</i> and beam-bending deformation <i>x</i>_<i>b</i> vs. <i>X</i> in the Hertzian regime I and in the transition regime II. Model calculations are performed using parameter values obtained from the fit of theoretical <i>FX</i>-curves to the simulated average <i>FX</i>-spectra for CCMV nanoindentation along the 2-fold symmetry axis (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004729#pcbi.1004729.t001" target="_blank">Table 1</a>). The solid curves correspond to the exact method of parameter estimation; the dashed and dashed-dotted curves are for the (piece-wise) approximate method of estimation. Snapshots exemplify the local flattening of CCMV structure under the tip for <i>X</i> = 1 nm and 5 nm deformation. Panel (b) displays the results of overlap function <i>χ</i>-based estimation of the survival probability <i>s</i>(<i>X</i>) from simulations of CCMV nanoindentation (<i>ν</i>_<i>f</i> = 1.0 <i>μ</i>m/s, <i>R</i>_<i>tip</i> = 20 nm, and <i>κ</i> = 0.05 N/m; <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004729#pcbi.1004729.s007" target="_blank">S3a Fig</a>) along the 2-fold (red), quasi-3-fold (blue), and quasi-2-fold symmetry axes (green). The theoretical profiles of <i>s</i>(<i>X</i>) (solid curves; see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004729#pcbi.1004729.e055" target="_blank">Eq (16)</a>) are compared with the simulated profiles of <i>χ</i>(<i>X</i>) (data points; see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004729#pcbi.1004729.e053" target="_blank">Eq (15)</a>). The model parameters are summarized in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004729#pcbi.1004729.t001" target="_blank">Table 1</a>. The values of are obtained using Lagrange multipliers and the approximate method of parameter estimation (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004729#sec010" target="_blank">Discussion</a>).</p

Deformation and collapse of biological particles—CCMV, TrV, and AdV.

<p>Accumulated are the Young’s moduli for Hertzian <i>E</i>_<i>H</i> and bending <i>E</i>_<i>b</i> deformations, the beam strength and the cooperativity parameter <i>m</i>. The first (second) entries correspond to the exact (approximate) methods of parameter estimation. The model predictions for <i>F</i>^<i>col</i> are compared with the peak forces (in parenthesis) from the spectra (Figs <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004729#pcbi.1004729.g004" target="_blank">4</a> and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004729#pcbi.1004729.g005" target="_blank">5</a>). For TrV and AdV particles, the shell thickness was estimated as described in the <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004729#pcbi.1004729.s003" target="_blank">S3 Text</a>.</p

Stress distribution on CCMV shell surface.

<p>Map of the Cauchy stress tensor projections along the direction of out-of-plane bending deformation (left) and tangential in-plane stretching (right) for different deformation <i>X</i> of the CCMV shell and corresponding indentation force <i>F</i> (indentation along the 2-fold symmetry axis with <i>R</i>_<i>tip</i> = 20 nm and <i>ν</i>_<i>f</i> = 1.0 <i>μ</i>m/s). For each amino acid residue (<i>C</i>_<i>α</i>-particle), the stress components are averaged over amino acids within a sphere of radius <i>R</i>_<i>C</i> = 15 Å (color denotation is presented in the graph). Also shown are formation and subsequent evolution of microscopic cracks in the side portion (particle barrel) of CCMV structure (shown in red circle/ellipse).</p

Types of mechanical excitations exemplified using the CCMV shell.

<p>(a)-(c) Hertzian deformation <i>x</i>_<i>H</i> with normal displacements <i>u</i>_<i>tip</i> and <i>u</i>_<i>par</i> (scheme on (a)) under the influence of force (vertical arrow). Dashed contour lines show the tip and particle in their undeformed states. Structures in (b)—the native (left) and partially deformed (right) states show an amplitude of <i>x</i>_<i>H</i> ≈ 3 nm. (c) CCMV shell profile showing parts of the structure with high potential energy (>3 kcal/mol per residue; red) and low potential energy (blue). (d)-(f) Bending deformation. The side portion of the structure (barrel) is partitioned into curved beams (top-side view on (d)). Structures in (e)—the partially deformed (left) and pre-collapse (middle and right) states reveal the amplitude of <i>x</i>_<i>b</i> ≈ 4.3 nm. (f) CCMV shell profile under Hertzian and bending deformations showing the potential energy distribution.</p

Mechanistic Basis for the Binding of RGD- and AGDV-Peptides to the Platelet Integrin αIIbβ3

Binding of soluble fibrinogen to the activated conformation of the integrin αIIbβ3 is required for platelet aggregation and is mediated exclusively by the C-terminal AGDV-containing dodecapeptide (γC-12) sequence of the fibrinogen γ chain. However, peptides containing the Arg-Gly-Asp (RGD) sequences located in two places in the fibrinogen Aα chain inhibit soluble fibrinogen binding to αIIbβ3 and make substantial contributions to αIIbβ3 binding when fibrinogen is immobilized and when it is converted to fibrin. Here, we employed optical trap-based nanomechanical measurements and computational molecular modeling to determine the kinetics, energetics, and structural details of cyclic RGDFK (cRGDFK) and γC-12 binding to αIIbβ3. Docking analysis revealed that NMR-determined solution structures of cRGDFK and γC-12 bind to both the open and closed αIIbβ3 conformers at the interface between the αIIb β-propeller domain and the β3 βI domain. The nanomechanical measurements revealed that cRGDFK binds to αIIbβ3 at least as tightly as γC-12. A subsequent analysis of molecular force profiles and the number of peptide−αIIbβ3 binding contacts revealed that both peptides form stable bimolecular complexes with αIIbβ3 that dissociate in the 60–120 pN range. The Gibbs free energy profiles of the αIIbβ3–peptide complexes revealed that the overall stability of the αIIbβ3-cRGDFK complex was comparable with that of the αIIbβ3−γC-12 complex. Thus, these results provide a mechanistic explanation for previous observations that RGD- and AGDV-containing peptides are both potent inhibitors of the αIIbβ3–fibrinogen interactions and are consistent with the observation that RGD motifs, in addition to AGDV, support interaction of αIIbβ3 with immobilized fibrinogen and fibrin

Tubulin Bond Energies and Microtubule Biomechanics Determined from Nanoindentation <i>in Silico</i>

Microtubules, the primary components of the chromosome segregation machinery, are stabilized by longitudinal and lateral noncovalent bonds between the tubulin subunits. However, the thermodynamics of these bonds and the microtubule physicochemical properties are poorly understood. Here, we explore the biomechanics of microtubule polymers using multiscale computational modeling and nanoindentations <i>in silico</i> of a contiguous microtubule fragment. A close match between the simulated and experimental force–deformation spectra enabled us to correlate the microtubule biomechanics with dynamic structural transitions at the nanoscale. Our mechanical testing revealed that the compressed MT behaves as a system of rigid elements interconnected through a network of lateral and longitudinal elastic bonds. The initial regime of continuous elastic deformation of the microtubule is followed by the transition regime, during which the microtubule lattice undergoes discrete structural changes, which include first the reversible dissociation of lateral bonds followed by irreversible dissociation of the longitudinal bonds. We have determined the free energies of dissociation of the lateral (6.9 ± 0.4 kcal/mol) and longitudinal (14.9 ± 1.5 kcal/mol) tubulin–tubulin bonds. These values in conjunction with the large flexural rigidity of tubulin protofilaments obtained (18,000–26,000 pN·nm²) support the idea that the disassembling microtubule is capable of generating a large mechanical force to move chromosomes during cell division. Our computational modeling offers a comprehensive quantitative platform to link molecular tubulin characteristics with the physiological behavior of microtubules. The developed <i>in silico</i> nanoindentation method provides a powerful tool for the exploration of biomechanical properties of other cytoskeletal and multiprotein assemblies

Botulinum neurotoxin: unique folding of enzyme domain of the most-poisonous poison

<div><p>Botulinum neurotoxin (BoNT), the most toxic substance known to mankind, is the first example of the fully active molten globule state. To understand its folding mechanism, we performed urea denaturation experiments and theoretical modeling using BoNT serotype A (BoNT/A). We found that the extent of BoNT/A denaturation from the native state (<i>N</i>) shows a nonmonotonic dependence on urea concentration indicating a unique multistep denaturation process, <i>N</i> → <i>I</i>₁<i>I</i>₂<i>U</i>, with two intermediate states <i>I</i>₁ and <i>I</i>₂. BoNT/A loses almost all its secondary structure in 3.75 M urea (<i>I</i>₁), yet it displays a native-like secondary structure in 5 M urea (<i>I</i>₂). This agrees with the results of theoretical modeling, which helped to determine the molecular basis of unique behavior of BoNT/A in solution. Except for <i>I</i>₂, all the states revert back to full enzymatic activity for SNAP-25 including the unfolded state <i>U</i> stable in 7 M urea. Our results stress the importance of structural flexibility in the toxin’s mechanism of survival and action, an unmatched evolutionary trait from billion-year-old bacteria, which also correlates with the long-lasting enzymatic activity of BoNT inside neuronal cells. BoNT/A provides a rich model to explore protein folding in relation to functional activity.</p></div

Tubulin Bond Energies and Microtubule Biomechanics Determined from Nanoindentation <i>in Silico</i>

Microtubules, the primary components of the chromosome segregation machinery, are stabilized by longitudinal and lateral noncovalent bonds between the tubulin subunits. However, the thermodynamics of these bonds and the microtubule physicochemical properties are poorly understood. Here, we explore the biomechanics of microtubule polymers using multiscale computational modeling and nanoindentations <i>in silico</i> of a contiguous microtubule fragment. A close match between the simulated and experimental force–deformation spectra enabled us to correlate the microtubule biomechanics with dynamic structural transitions at the nanoscale. Our mechanical testing revealed that the compressed MT behaves as a system of rigid elements interconnected through a network of lateral and longitudinal elastic bonds. The initial regime of continuous elastic deformation of the microtubule is followed by the transition regime, during which the microtubule lattice undergoes discrete structural changes, which include first the reversible dissociation of lateral bonds followed by irreversible dissociation of the longitudinal bonds. We have determined the free energies of dissociation of the lateral (6.9 ± 0.4 kcal/mol) and longitudinal (14.9 ± 1.5 kcal/mol) tubulin–tubulin bonds. These values in conjunction with the large flexural rigidity of tubulin protofilaments obtained (18,000–26,000 pN·nm²) support the idea that the disassembling microtubule is capable of generating a large mechanical force to move chromosomes during cell division. Our computational modeling offers a comprehensive quantitative platform to link molecular tubulin characteristics with the physiological behavior of microtubules. The developed <i>in silico</i> nanoindentation method provides a powerful tool for the exploration of biomechanical properties of other cytoskeletal and multiprotein assemblies