A universal chemical potential for sulfur vapours

The unusual chemistry of sulfur is illustrated by the tendency for catenation. Sulfur forms a range of open and closed S$_n$ species in the gas phase, which has led to speculation on the composition of sulfur vapours as a function of temperature and pressure for over a century. Unlike elemental gases such as O$_2$ and N$_2$, there is no widely accepted thermodynamic potential for sulfur. Here we combine a first-principles global structure search for the low energy clusters from S$_2$ to S$_8$ with a thermodynamic model for the mixed-allotrope system, including the Gibbs free energy for all gas-phase sulfur on an atomic basis. A strongly pressure-dependent transition from a mixture dominant in S$_2$ to S$_8$ is identified. A universal chemical potential function, $\mu_{\mathrm{S}}(T,P)$, is proposed with wide utility in modelling sulfurisation processes including the formation of metal chalcogenide semiconductors.Comment: 12 pages, 9 figures. Supporting code and data is available at https://github.com/WMD-Bath/sulfur-model [snapshot DOI: 10.5281/zenodo.28536]. Further data will be available from DOI:10.6084/m9.figshare.1513736 and DOI:10.6084/m9.figshare.1513833 following peer-revie

Designability of lattice model heteropolymers

Protein folds are highly designable, in the sense that many sequences fold to the same conformation. In the present work we derive an expression for the designability in a 20 letter lattice model of proteins which, relying only on the Central Limit Theorem, has a generality which goes beyond the simple model used in its derivation. This expression displays an exponential dependence on the energy of the optimal sequence folding on the given conformation measured with respect to the lowest energy of the conformational dissimilar structures, energy difference which constitutes the only parameter controlling designability. Accordingly, the designability of a native conformation is intimately connected to the stability of the sequences folding to them.Comment: in press on Phys. Rev.

Mapping of mutation-sensitive sites in protein-like chains

In this work we have studied, with the help of a simple on-lattice model, the distribution pattern of sites sensitive to point mutations ('hot' sites) in protein-like chains. It has been found that this pattern depends on the regularity of the matrix that rules the interaction between different kinds of residues. If the interaction matrix is dominated by the hydrophobic effect (Miyazawa Jernigan like matrix), this distribution is very simple - all the 'hot' sites can be found at the positions with maximum number of closest nearest neighbors (bulk). If random or nonlinear corrections are added to such an interaction matrix the distribution pattern changes. The rising of collective effects allows the 'hot' sites to be found in places with smaller number of nearest neighbors (surface) while the general trend of the 'hot' sites to fall into a bulk part of a conformation still holds.Comment: 15 pages, 6 figure

Proofs of some Propositions of the semi-Intuitionistic Logic with Strong Negation

We offer the proofs that complete our article introducing the propositional calculus called semi-intuitionistic logic with strong negation.Comment: Contains proofs omitted, because of their extention, from an article published in Studia Logic

The Emergence of Scaling in Sequence-based Physical Models of Protein Evolution

It has recently been discovered that many biological systems, when represented as graphs, exhibit a scale-free topology. One such system is the set of structural relationships among protein domains. The scale-free nature of this and other systems has previously been explained using network growth models that, while motivated by biological processes, do not explicitly consider the underlying physics or biology. In the present work we explore a sequence-based model for the evolution protein structures and demonstrate that this model is able to recapitulate the scale-free nature observed in graphs of real protein structures. We find that this model also reproduces other statistical feature of the protein domain graph. This represents, to our knowledge, the first such microscopic, physics-based evolutionary model for a scale-free network of biological importance and as such has strong implications for our understanding of the evolution of protein structures and of other biological networks.Comment: 20 pages (including figures), 4 figures, to be submitted to PNA

What thermodynamic features characterize good and bad folders? Results from a simplified off-lattice protein model

The thermodynamics of the small SH3 protein domain is studied by means of a simplified model where each bead-like amino acid interacts with the others through a contact potential controlled by a 20x20 random matrix. Good folding sequences, characterized by a low native energy, display three main thermodynamical phases, namely a coil-like phase, an unfolded globule and a folded phase (plus other two phases, namely frozen and random coil, populated only at extremes temperatures). Interestingly, the unfolded globule has some regions already structured. Poorly designed sequences, on the other hand, display a wide transition from the random coil to a frozen state. The comparison with the analytic theory of heteropolymers is discussed

Role of bulk and of interface contacts in the behaviour of model dimeric proteins

Some dimeric proteins first fold and then dimerize (three--state dimers) while others first dimerize and then fold (two--state dimers). Within the framework of a minimal lattice model, we can distinguish between sequences obeying to one or to the other mechanism on the basis of the partition of the ground state energy between bulk than for interface contacts. The topology of contacts is very different for the bulk than for the interface: while the bulk displays a rich network of interactions, the dimer interface is built up a set of essentially independent contacts. Consequently, the two sets of interactions play very different roles both in the the folding and in the evolutionary history of the protein. Three--state dimers, where a large fraction of the energy is concentrated in few contacts buried in the bulk, and where the relative contact energy of interface contacts is considerably smaller than that associated with bulk contacts, fold according to a hierarchycal pathway controlled by local elementary structures, as also happens in the folding of single--domain monomeric proteins. On the other hand, two--state dimers display a relative contact energy of interface contacts which is larger than the corresponding quantity associated with the bulk. In this case, the assembly of the interface stabilizes the system and lead the two chains to fold. The specific properties of three--state dimers acquired through evolution are expected to be more robust than those of two--state dimers, a fact which has consequences on proteins connected with viral diseases