Residual symmetry reductions and interaction solutions of the (2+1)-dimensional Burgers equation

In nonlinear physics,it is very difficult to study interactions among different types of nonlinear waves.In this paper,the nonlocal symmetry related to the truncated Painleve′expansion of the(2+1)-dimensional Burgers equation is localized after introducing multiple new variables to extend the original equation into a new system.Then the corresponding group invariant solutions are found,from which interaction solutions among different types of nonlinear waves can be found.Furthermore,the Burgers equation is also studied by using the generalized tanh expansion method and a new Ba¨cklund transformation(BT)is obtained.From this BT,novel interactive solutions among different nonlinear excitations are found.     

Drug-dendrimer supramolecular complexation studied from molecular dynamics simulations and NMR spectroscopy

Fully atomistic molecular dynamics (MD) simulations and NMR spectroscopy were employed to get insights about the molecular details of drug-dendrimer supramolecular association phenomena, using piroxicam (PRX) and the third generation poly(amido amine) (PAMAM-G3) dendrimer as model systems. Theoretical results concerning the complex stoichiometry suggest that PRX forms drug-dendrimer complexes of the type 24:1 at pH 7.0. This result was validated with the experimental quantities obtained from aqueous solubility profiles, which led to an empiric stoichiometry of 23:1 for the PRX:PAMAM-G3 system. The predicted binding mode between PRX and PAMAM-G3 accounts for the preferred encapsulation of the drug inside dendrimer cavities, which is mainly driven by van der Waals and hydrogen bonding interactions, and to a lesser extent, for the external association of the guest through electrostatic contacts with the positively charged amino groups of PAMAM periphery. The binding mode obtained from MD simulations was confirmed with 2D-NOESY experiments, which evidence the preferred internal complexation of PRX with PAMAM-G3. The predominance of internal encapsulation over external contacts in the PRX:PAMAM-G3 system differs from the general behaviour expected for acidic anionic guests, for which external electrostatic interactions with the positively charged PAMAM surface have been postulated as the most relevant factor for drug association.     

Simultaneous In Situ Quantification of Two Cellular Lipid Pools Using Orthogonal Fluorescent Sensors

Lipids regulate a wide range of biological activities. Since their local concentrations are tightly controlled in a spatiotemporally specific manner, the simultaneous quantification of multiple lipids is essential for elucidation of the complex mechanisms of biological regulation. Here, we report a new method for the simultaneous in situ quantification of two lipid pools in mammalian cells using orthogonal fluorescent sensors. The sensors were prepared by incorporating two environmentally sensitive fluorophores with minimal spectral overlap separately into engineered lipid‐binding proteins. Dual ratiometric analysis of imaging data allowed accurate, spatiotemporally resolved quantification of two different lipids on the same leaflet of the plasma membrane or a single lipid on two opposite leaflets of the plasma membrane of live mammalian cells. This new imaging technology should serve as a powerful tool for systems‐level investigation of lipid‐mediated cell signaling and regulation.     

Electro-Mechanochemical Atom Transfer Radical Cyclizations using Piezoelectric BaTiO3

The formation and regeneration of active Cu^I species is a fundamental mechanistic step in copper-catalyzed atom transfer radical cyclizations (ATRC). Typically, the presence of the catalytically active Cu^I species in the reaction mixture is secured by using high Cu^I catalyst loadings or the addition of complementary reducing agents. In this study it is demonstrated how the piezoelectric properties of barium titanate (BaTiO₃) can be harnessed by mechanical ball milling to induce electrical polarization in the strained piezomaterial. This strategy enables the conversion of mechanical energy into electrical energy, leading to the reduction of a Cu^II precatalyst into the active Cu^I species in copper-catalyzed mechanochemical solvent-free ATRC reactions.     

Direct Derivation of Free Energies of Membrane Deformation and Other Solvent Density Variations From Enhanced Sampling Molecular Dynamics

We report a methodology to calculate the free energy of a shape transformation in a lipid membrane directly from a molecular dynamics simulation. The bilayer need not be homogeneous or symmetric and can be atomically detailed or coarse grained. The method is based on a collective variable that quantifies the similarity between the membrane and a set of predefined density distributions. Enhanced sampling of this “Multi-Map” variable re-shapes the bilayer and permits the derivation of the corresponding potential of mean force. Calculated energies thus reflect the dynamic interplay of atoms and molecules, rather than postulated effects. Evaluation of deformations of different shape, amplitude, and range demonstrates that the macroscopic bending modulus assumed by the Helfrich–Canham model is increasingly unsuitable below the 100-Å scale. In this range of major biological significance, direct free-energy calculations reveal a much greater plasticity. We also quantify the stiffening effect of cholesterol on bilayers of different composition and compare with experiments. Lastly, we illustrate how this approach facilitates analysis of other solvent reorganization processes, such as hydrophobic hydration. Published 2019. This article is a U.S. Government work and is in the public domain in the USA.     

On the strength of hydrogen bonding within water clusters on the coordination limit

Hydrogen bonds (HB) are arguably the most important noncovalent interactions in chemistry. We study herein how differences in connectivity alter the strength of HBs within water clusters of different sizes. We used for this purpose the interacting quantum atoms energy partition, which allows for the quantification of HB formation energies within a molecular cluster. We could expand our previously reported hierarchy of HB strength in these systems (Phys. Chem. Chem. Phys., 2016, 18 , 19557) to include tetracoordinated monomers. Surprisingly, the HBs between tetracoordinated water molecules are not the strongest HBs despite the widespread occurrence of these motifs (e.g., in ice I_h). The strongest HBs within H₂O clusters involve tricoordinated monomers. Nonetheless, HB tetracoordination is preferred in large water clusters because (a) it reduces HB anticooperativity associated with double HB donors and acceptors and (b) it results in a larger number of favorable interactions in the system. Finally, we also discuss (a) the importance of exchange-correlation to discriminate among the different examined types of HBs within H₂O clusters, (b) the use of the above-mentioned scale to quickly assess the relative stability of different isomers of a given water cluster, and (c) how the findings of this research can be exploited to indagate about the formation of polymorphs in crystallography. Overall, we expect that this investigation will provide valuable insights into the subtle interplay of tri- and tetracoordination in HB donors and acceptors as well as the ensuing interaction energies within H₂O clusters.