"Many cellular processes are carried out by molecular ‘machines’—assemblies of multiple differentiated proteins that physically interact to execute biological functions1, 2, 3, 4, 5, 6, 7, 8. Despite much speculation, strong evidence of the mechanisms by which these assemblies evolved is lacking. Here we use ancestral gene resurrection9, 10, 11 and manipulative genetic experiments to determine how the complexity of an essential molecular machine—the hexameric transmembrane ring of the eukaryotic V-ATPase proton pump—increased hundreds of millions of years ago. We show that the ring of Fungi, which is composed of three paralogous proteins, evolved from a more ancient two-paralogue complex because of a gene duplication that was followed by loss in each daughter copy of specific interfaces by which it interacts with other ring proteins. These losses were complementary, so both copies became obligate components with restricted spatial roles in the complex. Reintroducing a single historical mutation from each paralogue lineage into the resurrected ancestral proteins is sufficient to recapitulate their asymmetric degeneration and trigger the requirement for the more elaborate three-component ring. Our experiments show that increased complexity in an essential molecular machine evolved because of simple, high-probability evolutionary processes, without the apparent evolution of novel functions. They point to a plausible mechanism for the evolution of complexity in other multi-paralogue protein complexes."

Nested sampling is a Bayesian sampling technique developed to explore probability distributions lo- calised in an exponentially small area of the parameter space. The algorithm provides both posterior samples and an estimate of the evidence (marginal likelihood) of the model. The nested sampling algo- rithm also provides an efficient way to calculate free energies and the expectation value of thermodynamic observables at any temperature, through a simple post-processing of the output. Previous applications of the algorithm have yielded large efficiency gains over other sampling techniques, including parallel tempering (replica exchange). In this paper we describe a parallel implementation of the nested sampling algorithm and its application to the problem of protein folding in a Go-type force field of empirical potentials that were designed to stabilize secondary structure elements in room-temperature simulations. We demonstrate the method by conducting folding simulations on a number of small proteins which are commonly used for testing protein folding procedures: protein G, the SH3 domain of Src tyrosine kinase and chymotrypsin inhibitor 2. A topological analysis of the posterior samples is performed to produce energy landscape charts, which give a high level description of the potential energy surface for the protein folding simulations. These charts provide qualitative insights into both the folding process and the nature of the model and force field used.

"… We examine here how the algorithm of phyllotaxis could contribute to the analysis of the structure of collagen fibrils. Such an algorithm indeed leads to organizations giving to each element of the assembly the most homogeneous and isotropic dense environment in a situation of cylindrical symmetry. The scattered intensity expected from a phyllotactic distribution of triple helices in collagen fibrils well agrees with the major features observed along the equatorial direction of their X ray patterns. Following this approach, the aggregation of triple helices in fibrils should be considered within the frame of soft condensed matter studies rather than that of molecular crystal studies."

Bond motifs.