Membrane induced dynamic filament bundling.

<p>(a) Contour lengths of growing filaments vs. simulation time. <i>N</i>_fil = 10 semiflexible filaments (<i>L</i>_p = 15<i>μ</i>m) are initialized at random positions 50nm below and perpendicular to the membrane. Initially, a collection of nearby filaments (red) begin to bundle where filament density is high. Remote filaments (colors other than red) then bend and subsequently join the bundle in a cascade of dynamic transitions (black box). Insets: Snapshots at intermediate simulation times (cf. <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004982#pcbi.1004982.s004" target="_blank">S3 Movie</a>). (b) Left inset: An individual filament with a fixed base at <i>L</i>₀ = 60nm below the membrane and at relative angle <i>θ</i> = 45° grows against the membrane. Rare polymerization events lead to a bent filament state growing tangentially to the membrane (cf. <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004982#pcbi.1004982.s005" target="_blank">S4 Movie</a>). Main figure: First passage time distribution <i>p</i>(<i>τ</i>_FP) to reach the bent and growing filament state. GCMC simulation results (black bars) are compared to the master equation <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004982#pcbi.1004982.e008" target="_blank">Eq (5)</a> (red solid line). Vertical dashed lines indicate mean first passage times (MFPT). Right inset: Probability <i>P</i>_bend(<i>n</i> → <i>n</i> + 1) that a gap of sufficient size is available to add a monomer to a filament of contour length <i>nδ</i>_fil. (c) Heat map of the MFPT for the filament bending transition vs. the initial angle and distance of the filament relative to the membrane. Color scale is logarithmic, and cooler colors indicate longer waiting times. Top inset: Each individual dynamic filament bending transition I→II can be understood as a single filament interacting with a predeformed membrane.</p

Patterns without Patches: Hierarchical Self-Assembly of Complex Structures from Simple Building Blocks

Nanoparticles with “sticky patches” have long been proposed as building blocks for the self-assembly of complex structures. The synthetic realizability of such patchy particles, however, greatly lags behind predictions of patterns they could form. Using computer simulations, we show that structures of the same genre can be obtained from a solution of simple isotropic spheres, with control only over their sizes and a small number of binding affinities. In a first step, finite clusters of well-defined structure and composition emerge from natural dynamics with high yield. In effect a kind of patchy particle, these clusters can further assemble into a variety of complex superstructures, including filamentous networks, ordered sheets, and highly porous crystals

Immobile membrane nodes screen membrane mediated attractions between filaments.

<p>(a) & (b) Two simulated tubes at equal height, generated by simulations with the same initial filament conditions and parameters, differing only by the presence in (b) of one additional immobilized membrane node at the center. Bundle formation is delayed and fewer filaments join the bundle in (b) compared to (a) (cf. <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004982#pcbi.1004982.s002" target="_blank">S1</a> & <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004982#pcbi.1004982.s003" target="_blank">S2</a> Movies). Insets: Top view of the simulation snapshot indicating immobile nodes (black circles) and initial positions of tube filaments (red crosses) and as yet unbundled filaments (green crosses). (c) Fraction of 50 simulation trajectories with and without the central frozen node that yield a membrane tube before time <i>t</i>, plotted as a function of <i>t</i>. At any given time, fewer of the constrained trajectories (dashed line) formed tubes than in the unconstrained case (solid line).</p

GCMC simulation of a triangulated membrane patch.

<p>(a) Sketch of the simulation setup. The area of a small fluctuating membrane patch is coupled grand canonically to an implicit lipid reservoir at constant surface tension, mimicking the large excess of vesicle area in typical experiments. (b) The control parameter fugacity <i>z</i> can be mapped to surface tension <i>γ</i> in simulation (black crosses) and fitted using <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004982#pcbi.1004982.e002" target="_blank">Eq (2)</a> (red line). Simulation snapshots are shown for fugacities, <i>z</i> = 13 and <i>z</i> = 29. Inset sketch: GCMC node removal and insertion moves. (c) Membrane force-extension curves (black) compared to zero-temperature calculations at <i>κ</i> = 20<i>k</i>_B<i>T</i> and <i>γ</i> = {0.005;0.01;0.02}<i>k</i>_B<i>T</i>nm⁻² (red solid lines from bottom to top, respectively). Asymptotic pulling force, (red dashed lines). Simulation snapshots are shown at tube extensions <i>L</i> around 72nm, 188nm, and 540nm, with <i>γ</i> = 0.01<i>k</i>_B<i>T</i>nm⁻². (d) Effective polymerization rate <i>k</i>_on(<i>n</i>)/<i>k</i>_on,0 (black solid) of a single rigid filament comprising <i>n</i> monomers compared to the expected near-equilibrium behavior (red dashed), for <i>κ</i> = 20<i>k</i>_B<i>T</i> and <i>γ</i> = {0.005;0.01}<i>k</i>_B<i>T</i>nm⁻² (upper and lower curves, respectively). Snapshots are shown for <i>γ</i> = 0.01<i>k</i>_B<i>T</i>nm⁻².</p

Ligand-Mediated Interactions between Nanoscale Surfaces Depend Sensitively and Nonlinearly on Temperature, Facet Dimensions, and Ligand Coverage

Nanoparticles are often covered in ligand monolayers, which can undergo a temperature-dependent order–disorder transition that switches the particle–particle interaction from repulsive to attractive in solution. In this work, we examine how changes in the ligand surface coverage and facet dimensions affect the ordering of ligands, the arrangement of nearby solvent molecules, and the interaction between ligand monolayers on different particles. In particular, we consider the case of strongly bound octadecyl ligands on the (100) facet of CdS in the presence of an explicit <i>n</i>-hexane solvent. Depending on the facet dimensions and surface coverage, we observe three distinct ordered states that differ in how the ligands are packed together, and which affect the thickness of the ligand shell and the structure of the ligand–solvent interface. The temperature dependence of the order–disorder transition also broadens and shifts to lower temperature in a nonlinear manner as the nanoscale is approached from above. We find that ligands on nanoscale facets can behave very similarly to those on macroscopic surfaces in solution, and that some facet dimensions affect the ligand alignment more strongly than others. As the ligands order, the interaction between opposing monolayers becomes attractive, even well below full surface coverage. The strength of attraction per unit surface area is strongly affected by ligand coverage, but only weakly by facet width. Conversely, we find that bringing two monolayers together just above the order–disorder transition temperature can induce ordering and attraction

Mutual information of residue pairs in calmodulin.

<p>The mutual information, , associated with side-chain fluctuations of residue pairs in calmodulin. Plots (b)–(f) display the mutual information signal∶noise ratio, (upper left triangles) and the excess mutual information (lower right triangles), as indicated in (a). The - and -axes run over labels, and respectively, of residues in the amino acid sequence, excluding those lacking rotameric freedom in our model. Scale bars for the signal∶noise ratio and the excess mutual information are presented on the top and bottom left, respectively. Results are shown for the following combinations of interactions: (b) repulsive sterics (S), (c) implicit solvent (IS) (d) Lennard-Jones (LJ) interaction comprising repulsive sterics and van der Waals attractions, (e) hydrogen bonding and salt-bridges (HBSB), and (f) the full potential (LJ+HBSB+IS). Residue 30K, which we scrutinize in detail later (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002168#pcbi-1002168-g005" target="_blank">Fig. 5</a>), is highlighted in (f) for reference.</p

Structural representations of extended crystalline calmodulin.

<p>The crystal structure (a) and contact map (b) of calcium-bound calmodulin (3cln <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002168#pcbi.1002168-Babu1" target="_blank">[39]</a>). The calcium ions are shown in yellow, and several residues are labeled in both panels for reference. The distance between each pair of atoms is indicated by color (see scale bar) in (b), where - and -axes run over residue labels. The residue labeling corresponds to the full sequence, however residues that do not possess torsional degrees of freedom in our model (A, G, P, and all residues bound to the calcium ions) are excluded from the contact map.</p

Mutual information by residue type.

<p>The average excess mutual information per interaction, , for all twenty amino acids. In each case data was pooled from all applicable pairs of fluctuating residues within a set of twelve small globular proteins (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002168#s4" target="_blank">Methods</a>).</p

Correlation between residue 30 and other residues in calmodulin.

<p>The extent of correlation between residue 30 (shown in black and circled) and all other side-chains in calmodulin (3cln <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002168#pcbi.1002168-Babu1" target="_blank">[39]</a>) is shown here. In (a) each residue is colored according to the magnitude of its excess mutual information with 30K (see left scale bar and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002168#pcbi-1002168-g003" target="_blank">Fig. 3</a>). Coloring in (b) indicates the change in each residue's side chain entropy effected by the mutation K30G. Here, red represents increased entropy and blue decreased entropy (see right scale bar). See <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002168#s4" target="_blank">Methods</a> for details.</p

Single-residue perturbations in barstar.

<p>Changes in the Gibbs entropy of each residue in barstar (1a19 <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002168#pcbi.1002168-Ratnaparkhi1" target="_blank">[47]</a>) that resulted from perturbations to single side-chains. Residues whose entropy changes by a significant amount, according to Student's t-test at the 90% level, are shown in color. Red indicates increased entropy, blue indicates decreased entropy (see scale bar). Although side-chains are depicted in their crystallographic arrangements for graphical simplicity, note that is a measure of the extent of fluctuations among a wide variety of distinct packings. For the results presented in panel (a), I86 (shown in black and circled) was mutated to G. For those of panel (b) E46 (shown in black and circled) was constrained to its crystallographic configuration.</p