Searching the optimal folding routes of a Complex Lasso protein

ABSTRACTUnderstanding how polypeptides can efficiently and reproducibly attain a self-entangled conformation is a compelling biophysical challenge, which might shed new light on our general knowledge of protein folding. Complex Lassos, namely self-entangled protein structures characterized by a covalent loop sealed by a cysteine bridge, represent an ideal test system in the framework of entangled folding. Indeed, as cysteine bridges form in oxidizing conditions, they can be used as on/off switches of the structure topology, to investigate the role played by the backbone entanglement in the process.In the present work we have used molecular dynamics to simulate the folding of a complex lasso glycoprotein, Granulocyte-macrophage colony-stimulating factor, modeling both reducing and oxidizing conditions. Together with a well-established Go-like description, we have employed the elastic folder model, a Coarse-Grained, minimalistic representation of the polypeptide chain, driven by a structure-based angular potential. The purpose of this study is to assess the kinetically optimal pathways, in relation to the formation of the native topology. To this end we have implemented an evolutionary strategy that tunes the elastic folder model potentials to maximize the folding probability within the early stages of the dynamics. The resulting protein model is capable of folding with high success rate, avoiding the kinetic traps that hamper the efficient folding in the other tested models. Employing specifically designed topological descriptors, we could observe that the selected folding routes avoid the topological bottleneck by locking the cysteine bridge after the topology is formed.These results provide valuable insights on the selection of mechanisms in self-entangled protein folding while, at the same time, the proposed methodology can complement the usage of established minimalistic models, and draw useful guidelines for more detailed simulations.

Boundary Galerkin Method of a Skew-Derivative Problem in the Exterior of an Open Arc Based on Chebyshev Polynomials

A problem modeling Hall effect in a semiconductor film from an electrode of arbitrary shape is considered, which is a skew-derivative problem. Boundary Galerkin method for solving the problem in Sobolev spaces is developed firstly. The solution is represented in the form of the combined angular potential and single-layer potential. The final integral equations do not contain hypersingular integrals. Uniqueness and existence of the solution to the equations are proved. The weakly singular and Cauchy singular integral arising in these equations can be computed directly by truncated series of Chebyshev polynomials with their weighting function without approximation. The numerical simulation showing the high accuracy of the scheme is presented.

Theoretical study of the X2B1, A2A1, 2B2 valence-shell and the first πu23s-type doublet and quartet Rydberg states of NH2

The angular potential energy curves of the X2B1, A2A1, B2B2 valence-shell and 4Σg−, 2Σg− (22B1), 2Δg (22A1, 32B1), and 2Σg+ Rydberg states arising from πu2 3s configurations are calculated by configuration interaction techniques. The data obtained reproduce very satisfactorily all X2B1 and A2A1 characteristics deduced from experiments; they support the previous theoretical prediction of a small-angle 2B2 state but find a very low |Re′e′′|2 value for the 2B2–A2A1 transition. The 4Σg− as well as three of the above four doublet Rydberg multiplets are found to prefer linear (or nearly linear) geometry and larger NH separations (in the symmetric structure) than NH2 in its ground state. A relatively large electronic transition moment for combination with both X2B1 and A2A1 is calculated for the lowest Rydberg multiplet which lies roughly 5.3 eV above the A2A1 state, while the intensity of transitions of the higher 3s states is found to be considerably smaller. Finally it is pointed out that the former Rydberg transition fits in well with recent emission experiments in this wavelength region recently reported by Herzberg.