Rates for Actin [1], [3] and Microtubules (MT) [1], [4], [19].

<p>Rates for Actin <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0114014#pone.0114014-Howard1" target="_blank">[1]</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0114014#pone.0114014-Pollard1" target="_blank">[3]</a> and Microtubules (MT) <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0114014#pone.0114014-Howard1" target="_blank">[1]</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0114014#pone.0114014-Desai1" target="_blank">[4]</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0114014#pone.0114014-Mitchison1" target="_blank">[19]</a>.</p

Average cap size as a function of scaled force for microtubules, and for filament numbers (red), and (green).

<p>The system is in the bounded phase for forces greater than the stall forces. The GTP concentration is , and other parameters are specified in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0114014#pone-0114014-t001" target="_blank">Table 1</a>. The Y-axis is in log scale.</p

Defining a Physical Basis for Diversity in Protein Self-Assemblies Using a Minimal Model

Self-assembly of proteins into ordered, fibrillar structures is a commonly observed theme in biology. It has been observed that diverse set of proteins (e.g., alpha-synuclein, insulin, TATA-box binding protein, Sup35, p53), independent of their sequence, native structure, or function could self-assemble into highly ordered structures known as amyloids. What are the crucial features underlying amyloidogenesis that make it so generic? Using coarse-grained simulations of peptide self-assembly, we argue that variation in two physical parametersbending stiffness of the polypeptide and strength of intermolecular interactionscan give rise to many of the structural features typically associated with amyloid self-assembly. We show that the interplay between these two factors gives rise to a rich phase diagram displaying high diversity in aggregated states. For certain parameters, we find a bimodal distribution for the order parameter implying the coexistence of ordered and disordered aggregates. Our findings may explain the experimentally observed variability including the “off-pathway” aggregated structures. Further, we demonstrate that sequence-dependence and protein-specific signatures could be mapped to our coarse-grained framework to study self-assembly behavior of realistic systems such as the STVIIE peptide and Aβ42. The work also provides certain guiding principles that could be used to design novel peptides with desired self-assembly properties, by tuning a few physical parameters

Average cap size as a function of for (a) actin filaments and (b) microtubules, and for filament numbers (red), (green) and (blue).

<p>The concentrations are for actin, and for microtubule. Y-axes are in log scale. Note that the single filament stall forces are 0.68 pN for actin and 0.97 pN for microtubule.</p

Average collapse times <i>T</i>_coll as a function of scaled force with increasing number of filaments (<b><i>N</i></b>), for (a) actin filaments and (b) microtubules.

<p>Blue and red curves are with hydrolysis () and without hydrolysis () respectively. The curves are plotted by scaling the force-axis with corresponding single-filament stall forces. For , the numerically obtained values of single-filament stall forces are pN for actin, and pN for microtubule. While, for , the corresponding single-filament stall forces are obtained from the formula (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0114014#pone.0114014-vanDoorn1" target="_blank">[27]</a>) – these are pN for actin, and pN for microtubule. Parameters are taken from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0114014#pone-0114014-t001" target="_blank">Table 1</a>. The ATP/GTP concentrations are for actin, and for microtubules.</p

Negative effective dynamic mass-density and stiffness: Micro-architecture and phononic transport in periodic composites

We report the results of the calculation of negative effective density and negative effective compliance for a layered composite. We show that the frequency-dependent effective properties remain positive for cases which lack the possibility of localized resonances (a 2-phase composite) whereas they may become negative for cases where there exists a possibility of local resonance below the length-scale of the wavelength (a 3-phase composite). We also show that the introduction of damping in the system considerably affects the effective properties in the frequency region close to the resonance. It is envisaged that this demonstration of doubly negative material characteristics for 1-D wave propagation would pave the way for the design and synthesis of doubly negative material response for full 3-D elastic wave propagation

Unzippering and shrinkage of MT.

<p>(A) Unzippering velocities <i>v</i>_<i>AB</i>, <i>v</i>_<i>AC</i>, and effective shrinkage velocity (<i>v</i>₋) compared to experimentally measured MT shrinkage velocity (horizontal line). The timescale corresponding to the blue points, <i>τ</i>_<i>AC</i> = 250nm/<i>v</i>_<i>AC</i> is shown along the right hand side ordinate (<i>Y</i>₂ axis). The vertical bars represent standard error. (Inset): Average lifetime of unzippered PFs (<i>T</i>_<i>u</i>, squares) and the number of unzippering events per second (<i>N</i>_<i>u</i>, circles). (B) and (C): Examples of typical time-trajectories from the Langevin simulation for Δ<i>E</i> = 1.2<i>k</i>_B<i>T</i> and Δ<i>E</i> = 1.4<i>k</i>_B<i>T</i>, respectively; here <i>R</i>_<i>x</i>(<i>t</i>) is the tip position of the unzippered PF (green), <i>bN</i>_<i>d</i>(<i>t</i>) is the length change due to dissociation of the subunits (blue), and ℒ(<i>t</i>) is the observable MT length (red). (B) Unzippering of the protofilament (see <i>R</i>_<i>x</i>(<i>t</i>)) is the dominant mechanism in the change in observed length when </p><p></p><p><mo>Δ</mo><mi>E</mi></p><p><mo><</mo><mo>≈</mo></p><mn>1.2</mn><p><mi>k</mi>B</p><mi>T</mi><p></p><p></p>. (C) The dissociation of subunits becomes the dominant mechanism of length change in MT when <p></p><p><mo>Δ</mo><mi>E</mi></p><p><mo>></mo><mo>≈</mo></p><mn>1.4</mn><p><mi>k</mi>B</p><mi>T</mi><p></p><p></p>. Here, one can see that unzippering of protofilament leads to partially peeled-off states where one can simultaneously observe subunit dissociation and existence of ram’s horns—see inset in (c), where we have zoomed into a small time window of the main figure. (D) Effect of force (per protofilament) on the shrinkage velocity of MT.<p></p

The diffusion constant of the wall position as a function of scaled force for (a) actin filaments and (b) microtubules, with filament number (red), (green) and (blue).

<p>Concentrations are for actin and for microtubule (for other parameters see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0114014#pone-0114014-t001" target="_blank">Table 1</a>). In (a), the arrows correspond to the force values at which we shall investigate the cap dynamics of the filaments in the next section (see Fig. 9).</p

A time trace of the wall position <i>x</i>(<i>t</i>) for two microtubules (<i>N</i> = 2) in the bounded phase, showing “collective catastrophe”, at a concentration <i>c</i> = 100<i>µ</i>M , and at a force <i>f</i> = 36.8 pN (<i>c_crit</i> = 8.67<i>µ</i>M, and pN in this case).

<p>Other parameters are taken from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0114014#pone-0114014-t001" target="_blank">Table 1</a>. The regions shaded grey correspond to the catastrophes, and provide the collapse time intervals whose average is <i>T</i>_coll.</p

Distributions of cap sizes, at different forces for (a) single actin (), and (b) two actin filaments (), for a concentration .

<p>Y-axes are in log scale.</p