Biased Brownian dynamics for rate constant calculation

An enhanced sampling method-biased Brownian dynamics-is developed for the calculation of diffusion-limited biomolecular association reaction rates with high energy or entropy barriers. Biased Brownian dynamics introduces a biasing force in addition to the electrostatic force between the reactants, and it associates a probability weight with each trajectory. A simulation loses weight when movement is along the biasing force and gains weight when movement is against the biasing force. The sampling of trajectories is then biased, but the sampling is unbiased when the trajectory outcomes are multiplied by their weights. With a suitable choice of the biasing force, more reacted trajectories are sampled. As a consequence, the variance of the estimate is reduced. In our test case, biased Brownian dynamics gives a sevenfold improvement in central processing unit (CPU) time with the choice of a simple centripetal biasing force.     

Robust biased Brownian dynamics for rate constant calculation

A reaction probability is required to calculate the rate constant of a diffusion-dominated reaction. Due to the complicated geometry and potentially high dimension of the reaction probability problem, it is usually solved by a Brownian dynamics simulation, also known as a random walk or path integral method, instead of solving the equivalent partial differential equation by a discretization method. Building on earlier work, this article completes the development of a robust importance sampling algorithm for Brownian dynamics-i.e., biased Brownian dynamics with weight control-to overcome the high energy and entropy barriers in biomolecular association reactions. The biased Brownian dynamics steers sampling by a bias force, and the weight control algorithm controls sampling by a target weight. This algorithm is optimal if the bias force and the target weight are constructed from the solution of the reaction probability problem. In reality, an approximate reaction probability has to be used to construct the bias force and the target weight. Thus, the performance of the algorithm depends on the quality of the approximation. Given here is a method to calculate a good approximation, which is based on the selection of a reaction coordinate and the variational formulation of the reaction probability problem. The numerically approximated reaction probability is shown by computer experiments to give a factor-of-two speedup over the use of a purely heuristic approximation. Also, the fully developed method is compared to unbiased Brownian dynamics. The tests for human superoxide dismutase, Escherichia coli superoxide dismutase, and antisweetener antibody NC6.8, show speedups of 17, 35, and 39, respectively. The test for reactions between two model proteins with orientations shows speedups of 2578 for one set of configurations and 3341 for another set of configurations.     

An improved apparatus for calibration of warburg manometers

• 1.1. By the use of a new piece of apparatus, a procedure is described that allows more accurate determination of gas volume in manometers than has been previously possible.
• 2.2. The standard error of the mean of ten readings of gas volume for a single manometer was found to be ±7 × 10⁻⁵ ml.
• 3.3. It is possible to obtain repeat readings rapidly and with very little spillage of mercury.
• 4.4. This method also allows easy removal of any air trapped by the rising mercury.

     

Theoretical calculation of the dielectric constant of a bilayer membrane.

The dielectric constant (epsilon) and refractive index (n) of a bilayer lipid membrane is determined from the known values of the polarizabilities of the carbon-carbon and carbon-hydrogen bonds. It is assumed that the hydrocarbon chains are hexagonally arranged in an all-trans conformation perpendicular to the plane of the membrane. The only variable in the calculation is the average separation between the chains and the theory relates epsilon to this separation. The calculation and results differ significantly from those presented in a 1968 publication by Ohki. It is shown that a thin membrane is not homogeneously polarized by the applied field. This effect is analysed and the dependence of epsilon on the membrane thickness is determined. The theoretical results are in good quantitative agreement with experimental measurements on bulk paraffins and on oriented multilayers of saturated fatty acids. The most important conclusion is that the dielectric constant for an applied field perpendicular to the membrane (which is the appropriate value for capacitance measurements) differs by only a few percent from the value for the macroscopic (bulk) liquid hydrocarbon. Thus the dielectric constant of a bilayer membrane can be approximated by the value for the appropriate bulk hydrocarbon.     

Accurate acid dissociation constant (pKa) calculation for the sulfachloropyridazine and similar molecules

In this work, the interaction of GaN nanotube (GaNNT) with common air pollutants of industrialized cities, such as NH₃, NO₂ and SO₂ in different configurations was studied. For this study, the single-walled (10,0) GaNNT was used. The analysis was done via the density functional theory implemented in the SIESTA simulation software. The analysis of the results shows that the air pollutants alter the properties of nanotubes when they interact with them. The stability analysis shows that the most stable configurations are those in which adsorption occurs through a chemical process. The systems remain semiconductors, but in the case of NO₂ and SO₂ molecules interacting with GaNNT, there was a significant reduction in the energy gap. Our results also indicate that GaNNT is a promising material to detect and remove NH₃ and NO₂ molecules from the environment; however, it may be not applicable to detect or remove SO₂, because the latter interacts strongly with the nanotube, which prevents the GaNNT from being reused.

     

The substrate constant for the ammonium ion of growing

The relation between ammonium concentration and growth rate was studied in steady state continuous cultures of Saccharomyces cerevisiae in nitrogenlimited glucose ammonium medium. This relation could be described by the Monod equation. A maximum specific growth rate of 0.41 h^-1 and a substrate constant for ammonium of 5–11 M were calculated. Ammonium was determined by a modification of the phenol hypochlorite method. A discussion of the results in view of literature data on the substrate constants for other nutrients is given.     

Continuum reaction field calculation of dielectric constant and vapor pressures for water and carbon disulfide.

Continuum reaction field theory is applied to calculations of dielectric constant, contribution of intermolecular interactions to the free energy of a liquid, and heat of vaporization. Introduction of repulsive interactions and the use of one adjustable parameter, the free volume, enables prediction of vapor pressures. The calculations are illustrated for a simple nonpolar liquid, carbon disulfide, and for liquid water. It is shown that when Onsager's equation is rearranged to a quadratic equation, and a recently found value of the polarizability is employed, its solutions for liquid water yield good agreement with experimental values throughout the whole temperature range. The decrease of the dielectric constant with temperature is essentially linear with the inverse of absolute temperature, but there is additional significant decrease due to the decrease of density with temperature. The relatively high value of the heat of vaporization of liquid water is expressed in terms of large dipolar interaction of a water molecule with the environment, which is due to polarization effects.