Automated sampling assessment for molecular simulations using the effective sample size

To quantify the progress in the development of algorithms and forcefields used in molecular simulations, a general method for the assessment of the sampling quality is needed. Statistical mechanics principles suggest the populations of physical states characterize equilibrium sampling in a fundamental way. We therefore develop an approach for analyzing the variances in state populations, which quantifies the degree of sampling in terms of the effective sample size (ESS). The ESS estimates the number of statistically independent configurations contained in a simulated ensemble. The method is applicable to both traditional dynamics simulations as well as more modern (e.g., multi-canonical) approaches. Our procedure is tested in a variety of systems from toy models to atomistic protein simulations. We also introduce a simple automated procedure to obtain approximate physical states from dynamic trajectories: this allows sample-size estimation in systems for which physical states are not known in advance.     

Testing low‐degree polynomials over prime fields

We present an efficient randomized algorithm to test if a given function f : ?? → ??_p (where p is a prime) is a low‐degree polynomial. This gives a local test for Generalized Reed‐Muller codes over prime fields. For a given integer t and a given real ε > 0, the algorithm queries f at O( ) points to determine whether f can be described by a polynomial of degree at most t. If f is indeed a polynomial of degree at most t, our algorithm always accepts, and if f has a relative distance at least ε from every degree t polynomial, then our algorithm rejects f with probability at least . Our result is almost optimal since any such algorithm must query f on at least points. © 2009 Wiley Periodicals, Inc. Random Struct. Alg., 2009     

Measurement of the alpha-secondary kinetic isotope effect for the reaction catalyzed by mammalian protein farnesyltransferase

Protein farnesytransferase (FTase) catalyzes the transfer of a 15-carbon prenyl group from farnesyl diphosphate (FPP) to the cysteine residue of target proteins and is a member of the newest class of zinc metalloenzymes that catalyze sulfur alkylation. Common substrates of FTase include oncogenic Ras proteins, and therefore inhibitors are under development for the treatment of various cancers. An increased understanding of the salient features of the chemical transition state of FTase may aid in the design of potent inhibitors and enhance our understanding of the mechanism of this class of zinc enzymes. To investigate the transition state of FTase we have used transient kinetics to measure the alpha-secondary 3H kinetic isotope effect at the sensitive C1 position of FPP. The isotope effect for the FTase single turnover reaction using a peptide substrate that is farnesylated rapidly is near unity, indicating that a conformational change, rather than farnesylation, is the rate-limiting step. To look at the chemical step, the kinetic isotope effect was measured as 1.154 +/- 0.006 for a peptide that is farnesylated slowly, and these data suggest that FTase proceeds via a concerted mechanism with dissociative character.     

Simple estimation of absolute free energies for biomolecules

One reason that free energy difference calculations are notoriously difficult in molecular systems is due to insufficient conformational overlap, or similarity, between the two states or systems of interest. The degree of overlap is irrelevant, however, if the absolute free energy of each state can be computed. We present a method for calculating the absolute free energy that employs a simple construction of an exactly computable reference system which possesses high overlap with the state of interest. The approach requires only a physical ensemble of conformations generated via simulation and an auxiliary calculation of approximately equal central-processing-unit cost. Moreover, the calculations can converge to the correct free energy value even when the physical ensemble is incomplete or improperly distributed. As a "proof of principle," we use the approach to correctly predict free energies for test systems where the absolute values can be calculated exactly and also to predict the conformational equilibrium for leucine dipeptide in implicit solvent.     

Dynamics of probes in model glassy matrices

The dynamics of diatomic probe molecules in matrices composed of hard spheres are studied using molecular dynamics simulations. The matrix particles are connected to fixed attachment points by strings of length, l, which is varied from l-->infinity (fluid) to 0 ("glass"). The probe diffusion coefficient, D interpolates smoothly between these limits when l is changed. As l is decreased, D displays a transition from a power-law l dependence, which is well fit by the mode-coupling theory expression, to an Arrhenius l dependence. Single particle analysis shows that the hopping motion sets in for l much larger than a critical length, l(c), and Arrhenius behavior occurs when hopping becomes the dominant mode of transport. The system displays dynamic heterogeneity even though there is no growing dynamic correlation length of any kind.     

Quantitative characterization of degradation behaviors of antioxidants stabilized in lipid particles

This study describes a flexible approach that allows us to characterize the long-term stability of antioxidants by using a thermodynamically extended Arrhenius equation. We use retinol, Vitamin A, as a model antioxidant and its degradation behaviors are characterized for both stabilized and non-stabilized systems; in this study, by using a fluid bed technique, we immobilize the retinol in lipid particles, thus increasing its thermal stability in complex formulations, such as aqueous polymer gels and emulsions. Our approach demonstrates that the degradation behaviors of the retinol show a functional relationship with temperature and time, which makes it possible to use the Arrhenius approach. This result allows us to precisely characterize the stability of antioxidants in complex formulations for long time.     

Catalytic transfer hydrogenation of conjugated nitroalkenes using decaborane: synthesis of oximes

alpha,beta-Unsaturated nitroalkenes are readily reduced to the corresponding aldoximes and ketoximes in good yields, using a system of decaborane (B10H14) and DMSO in methanol in the presence of 10% Pd/C at room temperature under nitrogen.     

Synthesis of triphenylphosphonopropionbetainetriorganotin(IV) salts [(C6H5)3P(CH2)2CO2SnR3]+X−, by nucleophilic displacement of anions from triorganotins

Trimethyl- and triphenyl-tin(IV) hydroxide act on triphenyl(2-carboxyethyl)-phosphonium hydrochloride, which is made from 3-chloropropionic acid and triphenylphosphine, to release water in the presence of dimethylformamide (DMF) as a catalyst. The water is azeotropically distilled to drive the reaction forward and produce triphenylphosphonopropionbetainetrimethyl- and triphenyl-tin(IV) chlorides in high yield. The latter product also results from the displacement of chloride from triphenyltin(IV) chloride by the phosphobetaine, (C₆H₅)₃P(CH₂)₂CO₂, which is made by treating the phosphonium hydrochloride with bicarbonate, and the compounds [(C₆H₅)₃P(CH₂)₂CO₂Sn(C₆H₅)₃]⁺X^? where X = Cl, Br, I, N₃, NCS, NO₃, B(C₆H₅)₄ and Co(CO)₄ are made in the same way. The acetate salt results from metathesis from the chloride and lead(II) acetate. A double salt, [(C₆H₅)₃P(CH₂)₂CO₂SnR₃]⁺ [R₃SnX₂]^?, is formed for X = Cl, Br and N₃ by adding additional (C₆H₅)₃SnX to the already-formed simple salts. Double salts are also obtained from the $\text{1}\text{1}$ reactions between the phosphobetaine and triphenyltin(IV) isocyanate and methyldiphenyltin(IV) chloride. The phosphonium chloride double salt could be converted to the thiophosphonium derivative by heating with elemental sulfur in ethanol. The products of these novel nucleophilic displacement reactions are high melting solids. Tin-119m Mössbauer data are consistent with five-coordinated, triorganotin(IV) formulations with the exception of the diphenyl(8-hydroxyquinolinato)tin(IV) chloride salt in which the tin atom is six-coordinated, and the diphenyltin system cis-oriented. The parameters otherwise do not change with the nature of the X group, which is the tetracarbonylcobaltate derivative is tetrahedral by infrared, establishing the ionicity of the products. The chloride exhibits a molar conductivity indicative of a $\text{1}\text{1}$ electrolyte in DMF. A bridging acetate structure in the solid is consistent with the lowered ν(CO₂) frequencies. The Mössbauer spectra of the double salts give simple doublets of lowered isomer shift (IS) and raised quadrupole splitting (QS) which may arise from a cross-linking ion pairing of the polymer chains in the solid, and the NMR spectra of the two methyltin derivatives shows only a single resonance line and tin satellites which is rationalized by a dynamic exchange process. The products are formulated as associated in carboxylate polymers with dangling triphenylphosphonium cations.     

Multiple cover time

Motivated by applications in Markov estimation and distributed computing, we define the blanket time of an undirected graph G to be the expected time for a random walk to hit every vertex of G within a constant factor of the number of times predicted by the stationary distribution. Thus the blanket time is, essentially, the number of steps required of a random walk in order that the observed distribution reflect the stationary distribution. We provide substantial evidence for the following conjecture: that the blanket time of a graph never exceeds the cover time by more than a constant factor. In other words, at the cost of a multiplicative constant one can hit every vertex often instead of merely once. We prove the conjecture in the case where the cover time and maximum hitting time differ by a logarithmic factor. This case includes almost all graphs, as well as most “natural” graphs: the hypercube, k-dimensional lattices for k ≥ 2, balanced k-ary trees, and expanders. We further prove the conjecture for perhaps the most natural graphs not falling in the above case: paths and cycles. Finally, we prove the conjecture in the case of independent stochastic processes. © 1996 John Wiley & Sons, Inc. Random Struct. Alg., 9 , 403–411 (1996)