Nano Pétanques – A Snippet
by Christoph
Figure 1. Structure of the bacteriophage T4 capsid. A Cryo-EM reconstruction; the square block shows in the enlarged view gp23 (yellow), gp24 (purple), Hoc (red) and Soc (white); B Structure of phage RB49 Soc; C Structural model showing one gp23 hexamer (blue) surrounded by six Soc trimers (red). Neighboring gp23 hexamers are shown in green, black and magenta; D Structure of gp24; E Structural model of gp24 pentameric vertex. Source
"The power of evolution is revealed through the diversity of life." Aha! It was solemnly declared by the Nobel Prize committee in their statement announcing last year's chemistry prizes for "the directed evolution of enzymes [and] phage display of peptides and antibodies". Royal academies – national or other academies likewise – tend to add luster to the often horribly arduous efforts of scientists with dramatic formulations. I'd like to tone it down a bit, and suggest that the laureates and their numerous collaborators cleverly applied evolution's "tinkering" approach of genetic change and selection (as François Jacob called it, see also here in STC) to evolve novel enzyme-substrate and protein-protein interactions. Phage display is a particularly intriguing and powerful technique with numerous applications in research and medicine (and worth a separate post). So far, however, phage display is limited to evolving pairwise interactions of proteins with other proteins or nucleic acids, for example antigen-antibody interactions. I'm not aware of studies aimed at evolving three-dimensional macromolecular structures like, for example, virus capsids. Today, we know the "rules of the game" quite well when it comes to three-dimensional protein complexes such as virus capsids (in prokaryotese: phage heads) that assemble from a handful of subunits (Figure 1). Much of this knowledge about the "rules" comes from mutants with defects in coat/head proteins and in vitro assembly studies (Dale Kaiser was among the pioneers in 1973). And lastly, for a number of viruses and phages we have an understanding of their fine structure in the nanometer range (see here for an example). But we don't have a good sense of how evolution "shaped" a probably rather fluffy ancestral T4 gp23 protein stepwise by trial and error to finally make it interaction-proficient in a way that lets it oligomerize into icosahedral shells. Where do the instructions "go make icosahedrons" come from?
Junwei Wang and his colleagues, all physicists at the Faculty of Engineering at Erlangen University, Germany, certainly didn't waste more than a single thought on virus capsids when they designed their particular game of pétanque. Rather, they set out to study spontaneous cluster formation by polysterene particles. The particles had uniform surfaces and negligible interactions (attraction/repulsion), making this a very simple system. Yet, the clusters they obtained were remarkably well-ordered, shedding light into the "rules" of cluster formation.
Figure 2. Library of magic number colloidal clusters and comparison to model. A rich variety of magic number colloidal clusters (MCCs) are observed with increasing number of particles. a–c MCCs without anti-Mackay shells (m0 type) correspond to truncated Mackay icosahedra. d–f MCCs with one anti-Mackay shell ((m+1)1 type) are characterized by a two particle wide rectangular region and a varying number of Mackay shells. g–i Similarly, two anti-Mackay shell clusters ((m+2)2 type) feature a width of the rectangular region of three particles. j–l MCCs with a fixed total number of 13 shells but a varying number of anti-Mackay shells (13a type). In each example, SEM images (left) are compared to the corresponding model (right). Scale bars, 1 μm. Frontpage: Low-magnification scanning electron microscopy (SEM) image showing the uniformity in size and structure of the prepared clusters. Icosahedral clusters dominate at slow evaporation. Scale bar, 2 μm. Source
Experimentally, they studied cluster formation at different polystyrene particle concentration in a microfluidic device (see here). The particles were uniformly 244 nm in diameter and stabilized by carboxylate surface groups. They reduced the water content by evaporation at various rates. They found that the volume fraction of the particles gradually increased towards a solidified cluster. At the lowest evaporation rate, the dominant species of the observed clusters (up to 75%) evolved from buckled to spherical to icosahedral symmetry with increasing assembly time. Only very slow evaporation provided sufficient time for the particles to arrange into icosahedral clusters.
Wang et al. knew from diverse systems that clusters of metal atoms, virus capsid proteins, noble gases, and nucleons have properties that depend sensitively on the number of constituent particles. Certain numbers of constituent particles were termed 'magic' because they lead to clusters with closed shells and exceptional stability. So far, magic number clusters had been exclusively found with attractive interactions between particles (among atoms, interactions among proteins). They now show that also colloidal particles with negligible interactions in an emulsion droplet spontaneously organize into a series of clusters with precisely defined shell structures, that is, magic number clusters (Figure 2). Their free-energy calculations suggest that particle clusters with magic numbers possess higher thermodynamic stability than those off magic numbers. And they found by modeling that a complex kinetic pathway is responsible for the efficiency of this system in finding its minimum free energy configuration. In a nutshell: icosahedron formation by particles is an emergent property during cluster formation, driven by thermodynamics rather than the quality of interactions among the particles but strongly dependent on their concentration.
You probably saw it already in Figure 2, but if not, please note that the boules studied by Wang et al. are completely filled. This spontaneous arrangement of the particles into icosahedrons gives no immediate clue as to how phage capsid proteins assemble into empty icosahedral phage heads, which are subsequently "stuffed" with phage DNA (here is an EM picture of DNA "stuffed" into a phage head). Is it sufficient that in an evolving phage head protein numerous weak, unspecific interaction sites are turned stepwise into a small set of specific interaction sites without loosing along the way the inherent proficiency to assemble into icosahedrons? We don't know yet. Yet, no one would leave a pétanque tournament after the first mène (round) as it is not possible to gather 13 points for winning a game that easily.
