Valid and efficient formula for free energy difference from nonequilibrium work

Atomic force microscopes and optical tweezers afford direct probe into the inner working of single biomolecules by mechanically unfolding them.^1-15^ Critical to the success of this type of probe is to correctly extract the free energy differences between the various conformations of a protein/nucleic acid along its forced unfolding pathways. Current studies rely on the Jarzynski equality^16^ (JE) or its undergirding Crooks fluctuation theorem^17^ (CFT), even though questions remain on its validity^17-19^ and on its accuracy.^13,20-21^ The validity of JE relies on the assumption of microscopic reversibility.^17,18^ The dynamics of biomolecules, however, is Langevin stochastic in nature. The frictional force in the Langevin equation breaks the time reversal symmetry and renders the dynamics microscopically irreversible even though detailed balance holds true. The inaccuracy of JE has largely been attributed to the fact that one cannot sample a large enough number of unfolding paths in a given study, experimental or computational.^13,15^ Here I show that both of these questions can be answered with a new equation relating the nonequilibrium work to the equilibrium free energy difference. The validity of this new equation requires detailed balance but not microscopic reversibility. Taking into the new equation equal number of unfolding and refolding paths, the accuracy is enhanced ten folds in comparison to a JE study based on a similar but larger number of unfolding paths

Glycerol Modulates Water Permeation through Escherichia coli Aquaglyceroporin GlpF

Among aquaglyceroporins that transport both water and glycerol across the cell membrane, Escherichia coli glycerol uptake facilitator (GlpF) is the most thoroughly studied. However, one question remains: Does glycerol modulate water permeation? This study answers this fundamental question by determining the chemical-potential profile of glycerol along the permeation path through GlpF's conducting pore. There is a deep well near the Asn-Pro-Ala (NPA) motifs (dissociation constant 14 microM) and a barrier near the selectivity filter (10.1 kcal/mol above the well bottom). This profile owes its existence to GlpF's perfect steric arrangement: The glycerol-protein van der Waals interactions are attractive near the NPA but repulsive elsewhere in the conducting pore. In light of the single-file nature of waters and glycerols lining up in GlpF's amphipathic pore, it leads to the following conclusion: Glycerol modulates water permeation in the microM range. At mM concentrations, GlpF is glycerol-saturated and a glycerol dwelling in the well occludes the conducting pore. Therefore, water permeation is fully correlated to glycerol dissociation that has an Arrhenius activation barrier of 6.5 kcal/mol. Validation of this theory is based on the existent in vitro data, some of which have not been given the proper attention they deserved: The Arrhenius activation barriers were found to be 7 kcal/mol for water permeation and 9.6 kcal/mol for glycerol permeation; The presence of up to 100 mM glycerol did not affect the kinetics of water transport with very low permeability, in apparent contradiction with the existent theories that predicted high permeability (0 M glycerol)

Hopf Bifurcation and Chaos in a Single Inertial Neuron Model with Time Delay

A delayed differential equation modelling a single neuron with inertial term is considered in this paper. Hopf bifurcation is studied by using the normal form theory of retarded functional differential equations. When adopting a nonmonotonic activation function, chaotic behavior is observed. Phase plots, waveform plots, and power spectra are presented to confirm the chaoticity.Comment: 12 pages, 7 figure

Black hole entropy arising from massless scalar field with Lorentz violation induced by the coupling to Einstein tensor

We have investigated quantum entropy of a static black hole arising from the massless scalar field with Lorentz violation induced by the coupling to Einstein tensor. Our results show that the coupled massless scalar field contributes to the classical Bekenstein-Hawking term in the black hole entropy. The corrected classical Bekenstein-Hawking entropy is not one quarter of the event horizon area of the original background black hole, but of a corresponding effective metric related to the coupling. It means that the classical Bekenstein-Hawking entropy depends not only on the black hole parameter, but also on the coupling which reduces Lorentz violation.Comment: 5 pages, no figure. Accepted by PLB for publicatio

On the valence bond solid in the presence of Dzyaloshinskii-Moriya interaction

We examine the stability of the valence bond solid (VBS) phase against the Dzyaloshinskii-Moriya (DM) interaction in the bipartite lattice. Despite the VBS is vulnerable against the antiferromagnetic interaction, for example in the Q-J model proposed by Sandvik, where the quantum phase transition occurs at $J^*/Q = 0.04$, we found that on the contrary the VBS is very stable against the DM interaction. The quantum phase transition does not occur until D/Q goes to infinity, where D is the strength of the DM interaction. The VBS in the ALKT model and the Haldane gap system also exhibit the same property.Comment: 5 pages and 5 figure

Calculation and Analysis of Two Level Traps Model in Polymeric Materials

Space charge formation in polymeric materials can cause some serious concern for design engineers as the electric field may severely be distorted, leading to part of the material being overstressed, resulting in material degradation and possibly premature failure at the worst. It is therefore important to understand charge generation, trapping, and detrapping processes in the material. Trap depths and concentration of materials are important as they are potentially related to microstructure of the material. Changes in these parameters may reflect aging taken place in the material. In the present paper, characteristics of charge trapping and detrapping in low density polyethylene (LDPE) under dc electric field have been investigated using the pulsed electroacoustic (PEA) technique. A simple trapping and detrapping model based on two trapping levels has been used to qualitatively explain the observation. Numerical simulation based on the above model has been carried out to extract parameters related to the material. It has been found that trap depths and concentration of both shallow and deep traps show significant differences for the sample with different periods of electric field application. Besides, the trap energy levels of these shallow and deep traps are compared with the values in literature to evaluate the model. The results indicate that trap depths and concentration of both shallow and deep traps may be used as aging markers as changes in the material will certainly affect trapping characteristics (trap depth and concentration)