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Self-assembly is usually considered a parallel process while self-folding and origami are usually considered to be serial processes. We believe that these distinctions do not hold in actual experiments. Based upon our experience with 4D printing, we have developed three additional hybrid classes: (1) templated-assisted (tethered) self-assembly: e.g., when RNA is bound to viral capsomeres, the subunits are constricted in their interactions to have aspects of self-folding as well; (2) self-folding can depend upon interactions with the environment; for example, a protein synthesized on a ribosome will fold as soon as peptides enter the intracellular environment in a serial process whereas if denatured complete proteins are put into solution, parallel folding can occur simultaneously; and, (3) in turbulent environments, chaotic conditions continuously alternate processes. We have examined the 43,380 Dürer nets of dodecahedra and 43,380 Dürer nets of icosahedra and their corresponding duals: Schlegel diagrams. In order to better understand models of self-assembly of viral capsids, we have used both geometric (radius of gyration, convex hulls, angles) and topological (vertex connections, leaves, spanning trees, cutting trees, and degree distributions) perspectives to develop design principles for 4D printing experiments. Which configurations fold most rapidly? Which configurations lead to complete polyhedra most of the time? By using Hamiltonian circuits of the vertices of Dürer nets and Eulerian paths of cutting trees of polyhedra unto Schlegel diagrams, we have been able to develop a systematic sampling procedure to explore the 86,760 configurations, models of a T1 viral capsid with 60 subunits and to test alternatives with 4D printing experiments, use of Magforms^TM, and origami models to demonstrate via movies the five processes described above. Full article

Sortase A (SrtA) of Staphylococcus aureus is a well-defined molecular target to combat the virulence of these clinically important bacteria. However up to now no efficient drugs or even clinical candidates are known, hence the search for such drugs is still relevant and necessary. SrtA is a complex target, so many straight-forward techniques for modeling using the structure-based drug design (SBDD) fail to produce the results they used to bring for other, simpler, targets. In this work we conduct theoretical studies of the binding/activity of Leu-Pro-Arg-Asp-Ala (LPRDA) polypeptide, which was recently shown to possess antivirulence activity against S. aureus. Our investigation was aimed at establishing a framework for the estimation of the key interactions and subsequent modification of LPRDA, targeted at non-peptide molecules, with better drug-like properties than the original polypeptide. Firstly, the available PDB structures are critically analyzed and the criteria to evaluate the quality of the ligand–SrtA complex geometry are proposed. Secondly, the docking protocol was investigated to establish its applicability to the LPRDA–SrtA complex prediction. Thirdly, the molecular dynamics studies were carried out to refine the geometries and estimate the stability of the complexes, predicted by docking. The main finding is that the previously reported partially chaotic movement of the β6/β7 and β7/β8 loops of SrtA (being the intrinsically disordered parts related to the SrtA binding site) is exaggerated when SrtA is complexed with LPRDA, which in turn reveals all the signs of the flexible and structurally disordered molecule. As a result, a wealth of plausible LPRDA–SrtA complex conformations are hard to distinguish using simple modeling means, such as docking. The use of more elaborate modeling approaches may help to model the system reliably but at the cost of computational efficiency. Full article

The transition from the quantum to the classical world is not yet understood. Here, we take a new approach. Central to this is the understanding that measurement and actualization cannot occur except on some specific basis. However, we have no established theory for the emergence of a specific basis. Our framework entails the following: (i) Sets of N entangled quantum variables can mutually actualize one another. (ii) Such actualization must occur in only one of the 2^N possible bases. (iii) Mutual actualization progressively breaks symmetry among the 2^N bases. (iv) An emerging “amplitude” for any basis can be amplified by further measurements in that basis, and it can decay between measurements. (v) The emergence of any basis is driven by mutual measurements among the N variables and decoherence with the environment. Quantum Zeno interactions among the N variables mediates the mutual measurements. (vi) As the number of variables, N, increases, the number of Quantum Zeno mediated measurements among the N variables increases. We note that decoherence alone does not yield a specific basis. (vii) Quantum ordered, quantum critical, and quantum chaotic peptides that decohere at nanosecond versus femtosecond time scales can be used as test objects. (viii) By varying the number of amino acids, N, and the use of quantum ordered, critical, or chaotic peptides, the ratio of decoherence to Quantum Zeno effects can be tuned. This enables new means to probe the emergence of one among a set of initially entangled bases via weak measurements after preparing the system in a mixed basis condition. (ix) Use of the three stable isotopes of carbon, oxygen, and nitrogen and the five stable isotopes of sulfur allows any ten atoms in the test protein to be discriminably labeled and the basis of emergence for those labeled atoms can be detected by weak measurements. We present an initial mathematical framework for this theory, and we propose experiments. Full article