Charge dependent behavior of PNA/DNA/PNA triplexes in the gas phase

Intact noncovalent complexes were studied in the gas phase using negative ion nano-ESI mass spectrometry. Among various noncovalent systems studied in the gas phase, the interaction of DNA strands with peptide nucleic acids (PNAs) presents a strong interest as biologically relevant systems. PNAs originally described by Nielsen are used as DNA mimics as possible medical agents by imprisoning DNA single strands into stable noncovalent complexes. Two types of PNAs were investigated in the PNA/DNA multiplex: the original Nielsen's PNA and a modified backbone PNA by the introduction of syn- and anti-(aminoethyl)thiazolidine rings. We first investigated the stoichiometry of PNA/DNA multiplexes formed in solution and observed them in the gas phase via qualitative kinetics of complementary strand associations. It resulted in observing PNA2/DNA triplexes (ts) as the multiply deprotonated species, most stable in both the solution and gas phase. Second, charge-dependant decompositions of these species were undertaken under low-energy collision conditions. It appears that covalent bond cleavages (base releasing or skeleton cleavage) occur from lower ts charge states rather than ts unzipping, which takes place from higher charge states. This behavior can be explained by considering the presence of zwitterions depending on the charge state. They result in strong salt-bridge interactions between the positively charged PNA side chain and the negatively charged DNA backbone. We propose a general model to clearly display the involved patterns in the noncovalent triplex decompositions. Third, the relative stability of three PNA2/DNA complexes was scrutinized in the gas phase by acquiring the breakdown curves of their ts(6-) form, corresponding to the ts unzipping. The chemical structures of the studied PNAs were chosen in order to evidence the possible influence of backbone stereochemistry on the rigidity of PNA2/DNA complexes. It provided significantly different stabilities via V(m) measurements. The relative gas-phase stability order obtained was compared to that found in solution by Chassaing et al., and shows qualitative agreement.     

Syntheses and structures of lithiated sulfones Li[CR(R′)SO2Ph] - C versus O bound lithium. [{Li{CH(Me)SO2Ph}(thf)}∞] - The structure of a C-bound derivative

Sulfones RCH(R′)SO₂Ph were reacted with n-BuLi in thf/n-hexane (R/R′ = H/Me, Me/Et, H/CH₂Ph) and toluene/n-hexane (R/R′ = Me/Ph) yielding under deprotonation Li[CR(R′)SO₂Ph] which reacted with Me₃SiCl and n-Bu₃SnCl forming the requisite trimethylsilyl and tri(n-butyl)tin substituted derivatives . Performing the reactions of RCH(R′)SO₂Ph with n-BuLi in n-hexane (instead of thf/n-hexane) and toluene/n-hexane, respectively, resulted in the precipitation of the organo lithium compounds Li[CR(R′)SO₂Ph] (1-4) which were isolated as strongly moisture-sensitive yellow powders in essentially quantitative yields. Their identities were confirmed by ¹H and ¹³C NMR spectroscopic measurements in thf-d₈. Solutions of each 1, 3, and 4 in thf/n-hexane and thf/n-pentane afforded crystals of each [{Li{CH(Me)SO₂Ph}(thf)}_∞] (1a), [{Li{CH(CH₂Ph)SO₂Ph}(thf)}_∞] (3a), and [{Li{CMe(Ph)SO₂Ph}(thf)₂}₂] (4a), respectively, whose structures were determined by single-crystal X-ray crystallography. The compounds 1a and 3a crystallize in 1D polymeric ladder-like structures. The strands of 1a are built-up by eight-membered Li₂C₂S₂O₂ rings having direct Li-C bonding interactions (Li-C 2.215(5) Å). The donor set of Li is completed by three oxygen atoms, one from the thf ligand and two from SO₂ groups of neighboring Li{CH(Me)SO₂Ph}(thf) entities. The strands of 3a are built-up of alternating Li₂S₂O₄ eight- and Li₂O₂ four-membered rings. Each lithium atom is coordinated to three oxygen atoms, two from O₂S(Ph)CHCH₂Ph groups and one from thf oxygen atom. There is no Li-C bonding. Compound 4a crystallizes in dimers consisting of eight-membered Li₂S₂O₄ rings in which the two lithium atoms are bridged by two O₂S(Ph)CHMePh groups. The coordination sphere of lithium is completed by two oxygen atoms of the thf ligands.     

Two-parameter p, q-variation Paths and Integrations of Local Times

In this paper, we prove two main results. The first one is to give a new condition for the existence of two-parameter -variation path integrals. Our condition of locally bounded -variation is more natural and easy to verify than those of Young. This result can be easily generalized to multi-parameter case. The second result is to define the integral of local time pathwise and then give generalized It’s formula when is only of bounded -variation in . In the case that is of locally bounded variation in , the integral is the Lebesgue–Stieltjes integral and was used by Elworthy, Truman and Zhao. When is of only locally -variation, where , , and , the integral is a two-parameter Young integral of -variation rather than a Lebesgue–Stieltjes integral. In the special case that is independent of , we give a new condition for Meyer's formula and is defined pathwise as a Young integral. For this we prove the local time is of -variation in for each , for each almost surely (-variation in the sense of Lyons and Young, i.e. ).     

-framework for continuous dependence and error estimates for quasilinear anisotropic degenerate parabolic equations

We develop a general -framework for deriving continuous dependence and error estimates for quasilinear anisotropic degenerate parabolic equations with the aid of the Chen-Perthame kinetic approach. We apply our -framework to establish an explicit estimate for continuous dependence on the nonlinearities and an optimal error estimate for the vanishing anisotropic viscosity method, without imposition of bounded variation of the approximate solutions. Finally, as an example of a direct application of this framework to numerical methods, we focus on a linear convection-diffusion model equation and derive an error estimate for an upwind-central finite difference scheme.

     

Strong convergence theorems for uniformly continuous pseudocontractive maps

Let K be a nonempty closed convex subset of a real Banach space E and let be a uniformly continuous pseudocontraction. Fix any u∈K. Let {xn} be defined by the iterative process: x₀∈K, xn+1:=μn(αnTxn+(1−αn)xn)+(1−μn)u. Let δ(?) denote the modulus of continuity of T with pseudo-inverse ?. If and {xn} are bounded then, under some mild conditions on the sequences n{αn} and n{μn}, the strong convergence of {xn} to a fixed point of T is proved. In the special case where T is Lipschitz, it is shown that the boundedness assumptions on and {xn} can be dispensed with.     

连续并既约元及其在刻画Fuzzy关系方程解集中的应用

本文首先引入连续并既约元(是并既约元但不是完全并既约元的元)的概念,并讨论了它的性质,然后应用连续并既约元的性质去刻画完备Brouwer格上无限Fuzzy关系方程A☉X=b的解集(其中A=(aj)j∈J和b已知,b为连续并既约元,X= (xj)j∈JT未知,“☉”表示“sup-inf”,J为无限集):给出了方程存在可达解与不可达解的充要条件及可达解与不可达解的一些性质,进一步刻画了方程的解集．     

Criterions for detecting the existence of the exponential dichotomies in the asymptotic behavior of the solutions of variational equations

We prove that the admissibility of any pair of vector-valued Schäffer function spaces (satisfying a very general technical condition) implies the existence of a “no past” exponential dichotomy for an exponentially bounded, strongly continuous cocycle (over a semiflow). Roughly speaking the class of Schäffer function spaces consists in all function spaces which are invariant under the right-shift and therefore our approach addresses most of the possible pairs of admissible spaces. Complete characterizations for the exponential dichotomy of cocycles are also obtained. Moreover, we involve a concept of a “no past” exponential dichotomy for cocycles weaker than the classical concept defined by Sacker and Sell (1994) in [23]. Our definition of exponential dichotomy follows partially the definition given by Chow and Leiva (1996) in [4] in the sense that we allow the unstable subspace to have infinite dimension. The main difference is that we do not assume a priori that the cocycle is invertible on the unstable space (actually we do not even assume that the unstable space is invariant under the cocycle). Thus we generalize some known results due to O. Perron (1930) [14], J. Daleckij and M. Krein (1974) [7], J.L. Massera and J.J. Schäffer (1966) [11], N. van Minh, F. Räbiger and R. Schnaubelt (1998) [26].     

Spectral theory of discontinuous functions of self-adjoint operators and scattering theory

In the smooth scattering theory framework, we consider a pair of self-adjoint operators H₀, H and discuss the spectral projections of these operators corresponding to the interval (−∞,λ). The purpose of the paper is to study the spectral properties of the difference D(λ) of these spectral projections. We completely describe the absolutely continuous spectrum of the operator D(λ) in terms of the eigenvalues of the scattering matrix S(λ) for the operators H₀ and H. We also prove that the singular continuous spectrum of the operator D(λ) is empty and that its eigenvalues may accumulate only at “thresholds” in the absolutely continuous spectrum.     

Weakly convex sets and modulus of nonconvexity

We consider a definition of a weakly convex set which is a generalization of the notion of a weakly convex set in the sense of Vial and a proximally smooth set in the sense of Clarke, from the case of the Hilbert space to a class of Banach spaces with the modulus of convexity of the second order. Using the new definition of the weakly convex set with the given modulus of nonconvexity we prove a new retraction theorem and we obtain new results about continuity of the intersection of two continuous set-valued mappings (one of which has nonconvex images) and new affirmative solutions of the splitting problem for selections. We also investigate relationship between the new definition and the definition of a proximally smooth set and a smooth set.