A model for short alpha-neurotoxin bound to nicotinic acetylcholine receptor from Torpedo californica: comparison with long-chain alpha-neurotoxins and alpha-conotoxins

Short-chain alpha-neurotoxins from snakes are highly selective antagonists of the muscle-type nicotinic acetylcholine receptors (nAChR). Although their spatial structures are known and abundant information on topology of binding to nAChR is obtained by labeling and mutagenesis studies, the accurate structure of the complex is not yet known. Here, we present a model for a short alpha-neurotoxin, neurotoxin II from Naja oxiana (NTII), bound to Torpedo californica nAChR. It was built by comparative modeling, docking and molecular dynamics using 1H NMR structure of NTII, cross-linking and mutagenesis data, cryoelectron microscopy structure of Torpedo marmorata nAChR [Unwin, N., 2005. Refined structure of the nicotinic acetylcholine receptor at 4A resolution. J. Mol. Biol. 346, 967-989] and X-ray structures of acetylcholine-binding protein (AChBP) with agonists [Celie, P.H., van Rossum-Fikkert, S.E., van Dijk, W.J., Brejc, K., Smit, A.B., Sixma, T.K., 2004. Nicotine and carbamylcholine binding to nicotinic acetylcholine receptors as studied in AChBP crystal structures. Neuron 41 (6), 907-914] and antagonists: alpha-cobratoxin, a long-chain alpha-neurotoxin [Bourne, Y., Talley, T.T., Hansen, S.B., Taylor, P., Marchot, P., 2005. Crystal structure of Cbtx-AChBP complex reveals essential interactions between snake alpha-neurotoxins and nicotinic receptors. EMBO J. 24 (8), 1512-1522] and alpha-conotoxin [Celie, P.H., Kasheverov, I.E., Mordvintsev, D.Y., Hogg, R.C., van Nierop, P., van Elk, R., van Rossum-Fikkert, S.E., Zhmak, M.N., Bertrand, D., Tsetlin, V., Sixma, T.K., Smit, A.B., 2005. Crystal structure of nicotinic acetylcholine receptor homolog AChBP in complex with an alpha-conotoxin PnIA variant. Nat. Struct. Mol. Biol. 12 (7), 582-588]. In complex with the receptor, NTII was located at about 30 A from the membrane surface, the tip of its loop II plunges into the ligand-binding pocket between the alpha/gamma or alpha/delta nAChR subunits, while the loops I and III contact nAChR by their tips only in a 'surface-touch' manner. The toxin structure undergoes some changes during the final complex formation (for 1.45 rmsd in 15-25 ps according to AMBER'99 molecular dynamics simulation), which correlates with NMR data. The data on the mobility and accessibility of spin- and fluorescence labels in free and bound NTII were used in MD simulations. The binding process is dependent on spontaneous outward movement of the C-loop earlier found in the AChBP complexes with alpha-cobratoxin and alpha-conotoxin. Among common features in binding of short- and long alpha-neurotoxins is the rearrangement of aromatic residues in the binding pocket not observed for alpha-conotoxin binding. Being in general very similar, the binding modes of short- and long alpha-neurotoxins differ in the ways of loop II entry into nAChR.     

Conditions for the production of a single conducting nanostructure by electroforming

The process of electroforming (the production of a carboniferous conducting medium when the current flows through an organic material under a high electric field) in open sandwichlike structures with an insulating gap several tens of nanometers in width is considered. It is shown experimentally that there are factors that both favor (external ballast resistor) and prevent (local spreading resistance and the presence of the initial conductivity in the insulating gap) the production of a single conducting element between the electrodes. A simple model of the process in terms of the equivalent electric circuit is proposed. The model helps to find the trade-off between these factors and to construct an I-V diagram, which exhibits a region within which a single conducting nanostructure can be electroformed. An expression that relates the minimum permissible resistance of the nanostructure to its geometric parameters is derived.     

Study of the aerodynamic stability of a blunt cone with a side flap in a hypersonic flow

The stationary and time-dependent aerodynamic coefficients of a slender blunt cone with a flap located near the base section of the model are experimentally investigated. The freestream parameters (M_∞ = 6, Re _L = 0.88 × 10⁷, and γ = 1.4) ensured a turbulent regime of flow over the conical surface and the flap. At high angles of attack (α ～ 10°) laminar-turbulent transition is observable in the separation zone on the leeward side of the body. Emphasis is placed on the determination of the trimming angles of attack for different positions of the center of rotation and the static and dynamic stability coefficients (the model oscillation damping coefficient).     

Steered molecular dynamics simulations of cobra cytotoxin interaction with zwitterionic lipid bilayer: no penetration of loop tips into membranes

Cobra cytotoxins, small proteins of three-fingered toxin family, unspecifically damage membranes in different cells and artificial vesicles. However, the molecular mechanism of this damage is not yet completely understood. We used steered molecular dynamics simulations to study the interaction of cardiotoxin A3 from Naja atra cobra venom with hydrated 1-palmitoyl-2-oleoyl-1-sn-3-phosphatidylcholine (POPC) bilayer. The studied system included one cytotoxin molecule, 64 lipid molecules (32 molecules in each monolayer) and 2500 water molecules. It was found that the toxin interacted with zwitterionic bilayer formed by POPC. During first nanosecond of simulation the toxin molecule was oriented toward membrane surface by loops' basement including cytotoxin regions Cys14-Asn19 and Cys38-Ser46. This orientation was stable enough and was not changed during next 6 ns of simulation. The obtained data suggest that cytotoxin molecule cannot penetrate into membrane composed of zwitterionic lipids without some auxiliary interaction.     

Duality, triality and complementary extremum principles in non-convex parametric variational problems with applications

This paper presents a reasonably complete duality theory anda nonlinear dual transformation method for solving the fullynonlinear, non-convex parametric variational problem inf{W(u- µ) - F(u)}, and associated nonlinear boundary valueproblems, where is a nonlinear operator, W is either convexor concave functional of p = u, and µ is a given parameter.Detailed mathematical proofs are provided for the complementaryextremum principles proposed recently in finite deformationtheory. A method for obtaining truly dual variational principles(without a dual gap and involving the dual variable p* of uonly) in n-dimensional problems is proposed. It is proved thatfor convex W(p), the critical point of the associated LagrangianL_µ(u, p*) is a saddle point if and only if the so-calledcomplementary gap function is positive. In this case, the systemhas only one dual problem. However, if this gap function isnegative, the critical point of the Lagrangian is a so-calledsuper-critical point, which is equivalent to the Auchmuty'sanomalous critical point in geometrically linear systems. Wediscover that, in this case, the system may have more than oneprimal-dual set of problems. The critical point of the Lagrangianeither minimizes or maximizes both primal and dual problems.An interesting triality theorem in non-convex systems is proved,which contains a minimax complementary principle and a pairof minimum and maximum complementary principles. Applicationsin finite deformation theory are illustrated. An open problemleft by Hellinger and Reissner is solved completely and a purecomplementary energy principle is constructed. It is provedthat the dual Euler-Lagrange equation is an algebraic equation,and hence, a general analytic solution for non-convex variational-boundaryvalue problems is obtained. The connection between nonlineardifferential equations and algebraic geometry is revealed.     

Calculation of the Flow Pattern and the Heat Fluxes in the Interaction of a Shock Wave with a Cylinder in a Supersonic Flow

The problem of determining the mechanical and thermal action on a cylinder in a supersonic flow with account for the interference between an incident shock and the detached bow shock has been studied extensively, both experimentally and theoretically, in the last few decades [1–12]. A fairly complete survey can be found in monograph [12]. The interest in the problem is mainly due to the fact that in this case the so-called fourth type of shock interaction can occur, leading to a sharp local increase in the mechanical and thermal loads. As for the problem of the interference flow past a cylinder itself, it can serve as a model problem for testing techniques of calculating the separation flow past the controls of hypersonic flight vehicles.In this paper, we attempt to demonstrate the possibility of using a fairly simple approach to the calculation of the above-mentioned flows, including those with a separation zone. The approach is based on a combination of numerical simulation within the framework of the inviscid gas model and subsequent calculation of the heat transfer parameters and does not require an excessive amount of computing power.     

Conductivity of nano-MIM diodes with a carbonaceous active medium in a model including percolation effects

A model proposed previously for processes in nano-MIM (metal-insulator-metal) diodes with a carbonaceous active medium is developed and refined. The inclusion of percolation effects in the insulating gap yields qualitatively new results and provides better agreement between the calculations and experimental data for physically reasonable values of all the parameters. An analysis of the model has made it possible to distinguish two different elements in the mechanism upon which it is based, which are important for understanding the essence of the processes that take place in electroformed nano-MIM diodes with a carbonaceous active medium: an internal negative feedback in the structure and modulation of the parameters of the cathode potential barrier. These elements show up in different ways in the observed characteristics of MIM structures. Zh. Tekh. Fiz. 69, 66–73 (November 1999)     

Benchmark calculations of some molecular properties of O2, CN and other selected small radicals using the ROHF-CCSD(T) method

The capability of the ROHF-CCSD(T) method in obtaining accurate molecular properties in a defined and controlled way is analysed. Electron affinity, polarizability, and hyperpolarizability of the oxygen molecule in its ground state, electron affinity, electric dipole moment of the CN radical, and some other molecules serve as model cases for obtaining the ‘right result for the right reason’. Most calculated CCSD(T) data were extrapolated to the complete basis set (CBS) limit in order to minimize the basis set dependence of results. Some problems, specific to open shell systems include effects due to the spin adaptation, and details in the selection of the reference orbitals and related selection of denominators in non-iterative triples and other subtleties, which can affect the accuracy of the final ROHF-CCSD(T) results, are investigated.     

Electroforming as a self-organizing process of a nanometer gap in a carbonaceous medium

Analysis of the existing experimental data and proposed mechanisms and models for processes occurring in the electroforming of metal-insulator-metal (MIM) structures leads to the conclusion that the electroforming process includes the following two stages: the formation of a carbonaceous conducting medium of organic molecules as a result of the passage of current in the insulating gap, and the self-organization of the a nanometer gap in the conducting carbonaceous medium through bifurcation when the temperature of this medium locally exceeds a certain critical value on account of self-heating. It can be asserted that the nanogap is a dissipative structure which arises by virtue of the thermal instability of the carbonaceous medium when a stream of electrons is passed through it and the presence of a high electric field and which is stable on account the substantial nonlinearity of processes occuring in it which are involved in the feedback mechanism. It is shown that the initial conductivity of the structure which is necessary for carrying out electroforming can arise on account of the nanometer width of the insulating gap, and this is demonstrated experimentally on a so-called “open sandwich” MIM structure. Zh. Tekh. Fiz. 67, 39–44 (November 1997)