Bennett's acceptance ratio and histogram analysis methods enhanced by umbrella sampling along a reaction coordinate in configurational space

Free energy perturbation, a method for computing the free energy difference between two states, is often combined with non-Boltzmann biased sampling techniques in order to accelerate the convergence of free energy calculations. Here we present a new extension of the Bennett acceptance ratio (BAR) method by combining it with umbrella sampling (US) along a reaction coordinate in configurational space. In this approach, which we call Bennett acceptance ratio with umbrella sampling (BAR-US), the conditional histogram of energy difference (a mapping of the 3N-dimensional configurational space via a reaction coordinate onto 1D energy difference space) is weighted for marginalization with the associated population density along a reaction coordinate computed by US. This procedure produces marginal histograms of energy difference, from forward and backward simulations, with higher overlap in energy difference space, rendering free energy difference estimations using BAR statistically more reliable. In addition to BAR-US, two histogram analysis methods, termed Bennett overlapping histograms with US (BOH-US) and Bennett-Hummer (linear) least square with US (BHLS-US), are employed as consistency and convergence checks for free energy difference estimation by BAR-US. The proposed methods (BAR-US, BOH-US, and BHLS-US) are applied to a 1-dimensional asymmetric model potential, as has been used previously to test free energy calculations from non-equilibrium processes. We then consider the more stringent test of a 1-dimensional strongly (but linearly) shifted harmonic oscillator, which exhibits no overlap between two states when sampled using unbiased Brownian dynamics. We find that the efficiency of the proposed methods is enhanced over the original Bennett's methods (BAR, BOH, and BHLS) through fast uniform sampling of energy difference space via US in configurational space. We apply the proposed methods to the calculation of the electrostatic contribution to the absolute solvation free energy (excess chemical potential) of water. We then address the controversial issue of ion selectivity in the K(+) ion channel, KcsA. We have calculated the relative binding affinity of K(+) over Na(+) within a binding site of the KcsA channel for which different, though adjacent, K(+) and Na(+) configurations exist, ideally suited to these US-enhanced methods. Our studies demonstrate that the significant improvements in free energy calculations obtained using the proposed methods can have serious consequences for elucidating biological mechanisms and for the interpretation of experimental data.     

"Click"-capture, ring-opening metathesis polymerization (ROMP), release: facile triazolation utilizing ROMP-derived oligomeric phosphates

Soluble, high-load ring-opening metathesis polymerization (ROMP)-derived oligomeric triazole phosphates (OTP) are reported for application as efficient triazolating reagents of nucleophilic species. Utilizing a "Click"-capture, ROMP, release protocol, the efficient and purification-free, direct triazolation of N-, O-, and S-nucleophilic species was successfully achieved. A variety of OTP derivatives were rapidly synthesized as free-flowing solids on a multigram scale from commercially available materials.     

Monomer-on-monomer (MoM) Mitsunobu reaction: facile purification utilizing surface-initiated sequestration

A monomer-on-monomer (MoM) Mitsunobu reaction utilizing norbornenyl-tagged (Nb-tagged) reagents is reported, whereby purification was rapidly achieved by employing ring-opening metathesis polymerization, which was initiated by any of three methods utilizing Grubbs catalyst: (i) free catalyst in solution, (ii) surface-initiated catalyst-armed silica, or (iii) surface-initiated catalyst-armed Co/C magnetic nanoparticles.     

Diads and their Application to Topoi

It is well known that the category of coalgebras for a finite-limit preserving comonad on a topos is again a topos, and the category of algebras for a finite-limit preserving monad is a topos if the monad is idempotent, but not in general. A generalisation of this result (Paré et al., Bull Aus Math Soc 39(3):421–431, 1989) is that the full subcategory of fixed points for any idempotent finite-limit preserving endofunctor is again a topos (and indeed a subquotient in the category of topoi and geometric morphisms). Here, we present a common generalisation of all the above results, based on a notion which we call a diad, which is a common generalisation of a monad and a comonad. Many of the constructions that can be applied to monads and comonads can be extended to all diads. In particular, the category of algebras or coalgebras can be generalised to a category of dialgebras for a diad. The generalisation we present here is that the category of dialgebras for a finite-limit preserving left diad (for example, the diad corresponding to a comonad, or any idempotent endofunctor) on a topos is again a topos.     

An experimental and theoretical study of the self-assembly of gold nanoparticles at the surface of functionalized multiwalled carbon nanotubes

This paper reports the findings of a detailed study of the self-assembly of gold nanoparticles at the surface of carbon nanotubes (CNTs). The study included the development of a predictive model for the interactions (charge transfer, van der Waals, osmotic, elastic, nonelastic, and covalent) between tetraoctylammonium bromide-stabilized (TOAB) gold nanoparticles and alkyl- and alkylthiol-modified multiwalled carbon nanotubes (MWCNTs). It also included the measurement of the coverage of gold nanoparticles at the surface of the above MWCNTs as a function of increasing alkyl chain length. One key finding is that it is possible to predict with a high degree of accuracy using the above model the measured coverage of gold nanoparticles adsorbed, either noncovalently or covalently, at the surface of a MWCNT. Another key finding is that, as predicted, under well-defined conditions the measured coverage of nanoparticles is very sensitive to the nature of the modified CNT surface and the contiguous environment, providing valuable insights that will underpin the rational design of functional nanoscale devices assembled from nanoparticle and CNT building blocks.