Colored Motifs Reveal Computational Building Blocks in the C. elegans Brain

Background: Complex networks can often be decomposed into less complex sub-networks whose structures can give hints about the functional organization of the network as a whole. However, these structural motifs can only tell one part of the functional story because in this analysis each node and edge is treated on an equal footing. In real networks, two motifs that are topologically identical but whose nodes perform very different functions will play very different roles in the network. Methodology/Principal Findings: Here, we combine structural information derived from the topology of the neuronal network of the nematode C. elegans with information about the biological function of these nodes, thus coloring nodes by function. We discover that particular colorations of motifs are significantly more abundant in the worm brain than expected by chance, and have particular computational functions that emphasize the feed-forward structure of information processing in the network, while evading feedback loops. Interneurons are strongly over-represented among the common motifs, supporting the notion that these motifs process and transduce the information from the sensor neurons towards the muscles. Some of the most common motifs identified in the search for significant colored motifs play a crucial role in the system of neurons controlling the worm's locomotion. Conclusions/Significance: The analysis of complex networks in terms of colored motifs combines two independent data sets to generate insight about these networks that cannot be obtained with either data set alone. The method is general and should allow a decomposition of any complex networks into its functional (rather than topological) motifs as long as both wiring and functional information is available

Spatial Extent of Charge Repulsion Regulates Assembly Pathways for Lysozyme Amyloid Fibrils

Formation of large protein fibrils with a characteristic cross β-sheet architecture is the key indicator for a wide variety of systemic and neurodegenerative amyloid diseases. Recent experiments have strongly implicated oligomeric intermediates, transiently formed during fibril assembly, as critical contributors to cellular toxicity in amyloid diseases. At the same time, amyloid fibril assembly can proceed along different assembly pathways that might or might not involve such oligomeric intermediates. Elucidating the mechanisms that determine whether fibril formation proceeds along non-oligomeric or oligomeric pathways, therefore, is important not just for understanding amyloid fibril assembly at the molecular level but also for developing new targets for intervening with fibril formation. We have investigated fibril formation by hen egg white lysozyme, an enzyme for which human variants underlie non-neuropathic amyloidosis. Using a combination of static and dynamic light scattering, atomic force microscopy and circular dichroism, we find that amyloidogenic lysozyme monomers switch between three different assembly pathways: from monomeric to oligomeric fibril assembly and, eventually, disordered precipitation as the ionic strength of the solution increases. Fibril assembly only occurred under conditions of net repulsion among the amyloidogenic monomers while net attraction caused precipitation. The transition from monomeric to oligomeric fibril assembly, in turn, occurred as salt-mediated charge screening reduced repulsion among individual charged residues on the same monomer. We suggest a model of amyloid fibril formation in which repulsive charge interactions are a prerequisite for ordered fibril assembly. Furthermore, the spatial extent of non-specific charge screening selects between monomeric and oligomeric assembly pathways by affecting which subset of denatured states can form suitable intermolecular bonds and by altering the energetic and entropic requirements for the initial intermediates emerging along the monomeric vs. oligomeric assembly path

Net Interactions among Native and Denatured Lysozyme Monomers.

<p>(<b>A</b>) Debye plot of the static light scattering intensity (KC/R) <i>vs.</i> lysozyme concentration C at T = 20°C. The positive slope of these curves indicates that the interactions among the lysozyme monomers are predominately repulsive. This repulsion becomes screened out once NaCl concentrations reach about 400 mM. (<b>B</b>) Plot of the static interaction parameter k_s (which is proportional to the slope of KCp/R <i>vs.</i> Cp) <i>vs.</i> salt concentration for the Data in A. The dotted line is a guide to the eye indicating how repulsion decreases with increasing salt concentration. The two dashed vertical lines mark the switch of lysozyme aggregation from monomeric (MF) to oligomeric fibril (OF) assembly and, eventually, precipitate formation (P). (<b>C</b>) Change in net interactions as lysozyme monomers undergo thermal denaturation in the presence of 50 mM (○) and 200 mM (▪) NaCl. The vertical dashed line indicates the onset of thermal denaturation at 50°C. Note that, the prevailing intermolecular interactions remain repulsive (positive K_s values) even after thermal denaturation. At the same time, denaturation at 50 mM NaCl makes lysozyme slightly more repulsive while the monomers become less repulsive following denaturation at 200 mM NaCl.</p

Precipitate Formation of Amyloidogenic Lysozyme.

<p>(<b>A</b>) AFM image of precipitates and their corresponding height distributions observed shortly after the onset of aggregation. (<b>B</b>) DLS aggregate peaks of lysozyme in 400 mM NaCl before and right after partial denaturation of lysozyme (see vertical dashed line). (<b>C</b>) Congo Red spectra of native lysozyme (—) and lysozyme precipitates (▪) are indistinguishable. In contrast, mature fibrils grown at lower salt concentrations (open circles) induce the red shift and shoulder characteristic for binding to amyloid fibrils.</p

Monomeric vs. Oligomeric Assembly Pathways for Lysozyme Amyloid Fibrils.

<p>(<b>A</b>) <i>In situ</i> particle size distributions at different stages of growth and corresponding temporal evolution of the detected aggregate peaks during lysozyme fibril growth at 50 mM NaCl (left two panels) <i>vs.</i> 175 mM NaCl (right two panels), as obtained from dynamic light scattering measurements. The temporal evolution of the aggregate peak radii (1A panel 3&4) highlights the dramatic difference in lag periods (see vertical dashed line) and distinctly different nucleation signatures: Low-salt samples always yielded two peaks while only a single peak nucleated at elevated salt concentrations (<b>B</b>) Morphology of growth intermediates in the presence of 50 mM NaCl (top row) <i>vs.</i> 175 mM NaCl (bottom row), as observed with atomic force microscopy. The vertical dashed line separates samples taken before and after the nucleation event detected by DLS. The false color scale indicates the height of the different aggregates in nm. The scale bars represent 50 nm, except for the 200 nm scale bars in the last image in either series. AFM images and aggregate dimensions for the 175 mM data are adapted from our earlier work (Hill et al, 2009). They are representative of the behavior observed throughout the "intermediate" salt concentrations (150 mM to 350 mM) associated with the oligomeric assembly regime. (<b>C</b>) Cross sectional areas for the various aggregates in (B) measured with calibrated AFM tips. Note the distinctly different cross sections for aggregates along the two different assembly pathways. <i><u>Top</u></i>: Cross-sectional areas of monomers, monomeric filaments and mature lysozyme fibrils grown at 50 mM NaCl. At low salt, no globular oligomeric species are detected. The cross sections for monomers and monomeric filaments are identical then increase by a factor of three for mature fibrils. <i><u>Bottom</u></i>: At intermediate salt concentrations, ellipsoidal oligomers are formed well before the nucleation event seen in DLS. These oligomers have a volume close to eight monomers (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0018171#pone-0018171-t001" target="_blank">Table 1</a>). The filaments emerging after nucleation have a cross section identical to that of the ellipsoidal oligomers. Late stage mature fibrils, in turn, had cross sectional areas close to two oligomeric filaments.</p

Effects of Salt-mediated Charge Screening on Denatured Monomers.

<p>The schematic indicates how the spatial extent (Debye screening length λ_D) of salt-mediated charge screening changes the character of the net interactions among denatured monomers and favors the formation of different aggregate geometries. The black curvy line represents the protein backbone while the blue perimeter symbolizes the short-range attractive protein interactions (hydrophobic, dipole-dipole, hydrogen bonding). Individual charged residues are represented by small positive spheres, and the extent of charge screening mediated by the salt ions is indicated as a red cloud surrounding the charge residues. At low salt concentrations, (monomeric assembly pathway) individual charges on the same monomer strongly repel each other and those on neighboring monomers. Only those few conformations of denatured monomers that can form intermolecular bonds similar to those in the native monomer are aggregation competent. In addition, charge repulsion among monomers will favor extended, polymeric structures for intermediates since that will separate the monomer charges from each other while preserving sufficient intermolecular contacts. When salt screening reduces λ_D below the separation of charged residues (oligomeric assembly pathway) along the monomer backbone, charge repulsion within a given monomer and, concurrently, among several aggregated monomers is significantly reduced. This favors the formation of more compact (oligomeric) aggregate assemblies and requires fewer monomers to share their hydrophobic cores to overcome the residual charge repulsion and loss in configurational entropy. Finally, when λ_D becomes comparable in range to the attractive interactions, the charge restrictions on "suitable" aggregate morphologies and favorable monomer conformation fall by the wayside and the denatured monomers precipitate randomly out of solution.</p