The effects of L‐ to D‐isomerization and C‐terminus deamidation on the secondary structure of antimicrobial peptide Anoplin in aqueous and membrane mimicking environment

UV resonance Raman spectra of the antimicrobial peptide (AMP) Anoplin (L ‐Anoplin‐NH₂) and two of its derivatives (enantiomer D ‐Anoplin‐NH₂ and C‐terminus deamidated L ‐Anoplin‐OH) were measured in aqueous buffer solution and in membrane‐mimetic environments including 2,2,2‐trifluoro ethanol (TFE), zwitterionic lipid dipalmitoylglycerophosphocholine (DPPC) and anionic lipid dipalmitoylglycerophosphoglycerol (DPPG) vesicle solutions. All three peptides were found to adopt random‐coil/β turn‐like conformation in aqueous solution over the temperature range of 1–60 °C. The conformation was found to become more α‐helical in membrane‐mimetic solutions such as TFE and DPPG but not in DPPC for all Anoplin derivatives. The data demonstrate that Anoplin preferentially binds to the anionic over the zwitterionic model cell membranes. Results also showed that deamidation does not change the conformation of L ‐Ano‐NH₂ very significantly, but does alter membrane rupturing and antimicrobial activities thus confirming that it is the physicochemical properties rather than the peptide conformation that define the mechanism of AMP action. Copyright © 2010 John Wiley & Sons, Ltd.     

The second law of thermodynamics under unitary evolution and external operations

The von Neumann entropy cannot represent the thermodynamic entropy of equilibrium pure states in isolated quantum systems. The diagonal entropy, which is the Shannon entropy in the energy eigenbasis at each instant of time, is a natural generalization of the von Neumann entropy and applicable to equilibrium pure states. We show that the diagonal entropy is consistent with the second law of thermodynamics upon arbitrary external unitary operations. In terms of the diagonal entropy, thermodynamic irreversibility follows from the facts that quantum trajectories under unitary evolution are restricted by the Hamiltonian dynamics and that the external operation is performed without reference to the microscopic state of the system.     

Universal high-frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineering

We give a general overview of the high-frequency regime in periodically driven systems and identify three distinct classes of driving protocols in which the infinite-frequency Floquet Hamiltonian is not equal to the time-averaged Hamiltonian. These classes cover systems, such as the Kapitza pendulum, the Harper–Hofstadter model of neutral atoms in a magnetic field, the Haldane Floquet Chern insulator and others. In all setups considered, we discuss both the infinite-frequency limit and the leading finite-frequency corrections to the Floquet Hamiltonian. We provide a short overview of Floquet theory focusing on the gauge structure associated with the choice of stroboscopic frame and the differences between stroboscopic and non-stroboscopic dynamics. In the latter case, one has to work with dressed operators representing observables and a dressed density matrix. We also comment on the application of Floquet Theory to systems described by static Hamiltonians with well-separated energy scales and, in particular, discuss parallels between the inverse-frequency expansion and the Schrieffer–Wolff transformation extending the latter to driven systems.     

Explicit mass renormalization and consistent derivation of radiative response of classical electron

The radiative response of the classical electron is commonly described by the Lorentz–Abraham–Dirac (LAD) equation. Dirac’s derivation of this equation is based on energy and momentum conservation laws and on regularization of the field singularities and infinite energies of the point charge by subtraction of certain quantities: “We... shall try to get over difficulties associated with the infinite energy of the process by a process of direct omission or subtraction of unwanted terms”. To substantiate Dirac’s approach and clarify the mass renormalization, we introduce the point charge as a limit of extended charges contracting to a point; the fulfillment of conservation laws follows from the relativistic covariant Lagrangian formulation of the problem. We derive the relativistic point charge dynamics described by the LAD equation from the extended charge dynamics in a localization limit by a method which can be viewed as a refinement of Dirac’s approach in the spirit of Ehrenfest theorem. The model exhibits the mass renormalization as the cancellation of Coulomb energy with the Poincaré cohesive energy. The value of the renormalized mass is not postulated as an arbitrary constant, but is explicitly calculated. The analysis demonstrates that the local energy–momentum conservation laws yield dynamics of a point charge which involves three constants: mass, charge and radiative response coefficient θ$\theta$. The value of θ$\theta$ depends on the composition of the adjacent potential which generates Poincaré forces. The classical value of the radiative response coefficient is singled out by the global requirement that the adjacent potential does not affect the radiated energy balance and affects only the local energy balance involved in the renormalization.     

Constructing fixed rank optimal estimators with method of best recurrent approximations

We propose a new approach which generalizes and improves principal component analysis (PCA) and its recent advances. The approach is based on the following underlying ideas. PCA can be reformulated as a technique which provides the best linear estimator of the fixed rank for random vectors. By the proposed method, the vector estimate is presented in a special quadratic form aimed to improve the error of estimation compared with customary linear estimates. The vector is first pre-estimated from the special iterative procedure such that each iterative loop consists of a solution of the unconstrained nonlinear best approximation problem. Then, the final vector estimate is obtained from a solution of the constrained best approximation problem with the quadratic approximant. We show that the combination of these techniques allows us to provide a new nonlinear estimator with a significantly better performance compared with that of PCA and its known modifications.     

Single freezing and triple melting of micrometre-scaled (NH4)2SO4/H2O droplets

Atmospheric aerosol droplets containing NH(4)(+) and SO(4)(2-) ions are precursors of cirrus ice clouds. However, the low-temperature phase transformation of such droplets is not understood yet. Here we show for the first time that micrometre-scaled (NH(4))(2)SO(4)/H(2)O droplets produce one freezing event but three melting events which are the melting of (i) pure ice, (ii) eutectic ice/(NH(4))(2)SO(4), and (iii) eutectic ice/(NH(4))(3)H(SO(4))(2). We also find that the melting of ice/(NH(4))(3)H(SO(4))(2) consists of two eutectic melting events, presumably ice/letovicite-II and ice/letovicite-III.     

DN‐Scattering of a plane wave by wedges

We continue our study of a nonstationary scattering by wedges. In this paper we consider nonstationary scattering of plane waves by a ‘hard–soft’ wedge. We prove the uniqueness and existence of a solution to the corresponding DN‐Cauchy problem in appropriate functional spaces. We also give the explicit form of the solution and prove the Limiting Amplitude Principle. Copyright © 2011 John Wiley & Sons, Ltd.     

Projection Method for Cauchy Problem for an Operator-Differential Equation

In the current paper, we study a projection method for a Cauchy problem for an operator-differential equation with a leading self-adjoint operator A(t) and a subordinate linear operator K(t) in a Hilbert space. The projection subspaces are linear spans of eigenvectors of an operator similar to A(t). It is assumed that the operators A(t) and K(t) are sufficiently smooth. Error estimates for the approximate solutions and their derivatives are obtained. The application of the developed method for solving the initial boundary value problems is given.