Finite element solution of the steady-state Smoluchowski equation for rate constant calculations

This article describes the development and implementation of algorithms to study diffusion in biomolecular systems using continuum mechanics equations. Specifically, finite element methods have been developed to solve the steady-state Smoluchowski equation to calculate ligand binding rate constants for large biomolecules. The resulting software has been validated and applied to mouse acetylcholinesterase. Rates for inhibitor binding to mAChE were calculated at various ionic strengths with several different reaction criteria. The calculated rates were compared with experimental data and show very good agreement when the correct reaction criterion is used. Additionally, these finite element methods require significantly less computational resources than existing particle-based Brownian dynamics methods.     

Stochastic models for chemical reactions: II. The unimolecular rate constant

Based on the author's stochastic treatment of the unimolecular reaction which contains a mathematical rationale for considering random fluctuations inherent in the reaction mechanism (Bartholomay, 1958,Bull. Math. Biophysics,20, 175-90), a new and simple formula is derived for calculating the rate constants of such reactions. This formula is then applied to data from the literature and the results compared with estimates obtained alternatively using current methods which attribute all irregularities about the usually expected smooth, decaying exponential curve to extraneous causes unrelated to reaction mechanism. Both estimates are seen to be almost identical despite the opposing assumptions about the origin of the random component of the kinetic data of such reactions.     

Independence of the radiobiological oxygen constant, K, and the respiration rate of mammalian cells.

The radiosensitivity, and the radiobiological oxygen-constant K for mouse Ehrlich ascites cells depend on the pre-irradiation growth conditions. Measurements of the oxygen-consumption rate of cells grown by different methods have been made to ascertain whether the differences in radiobiological properties could be associated with different rates of respiration. Inhibition of respiration by sodium amytal had no significant effect on either the radiosensitivity or the estimate of K.     

Instrumental assay of microbial lipase at constant pH

A rapid, accurate method with high sensitivity and reproducibility, and having the advantage of a short incubation period under constant pH, has been developed for routine measurement of microbial lipase. Assembled from readily available and economical instrumental components, the apparatus includes a pH meter, a thermoelectric heating and stirring device, a motor-driven burette, and an automatic recorder. The reaction mixture, consisting of 5 ml of a 10% olive oil-gum arabic emulsion, 2 ml of 3 m NaCl, 2 ml of sodium taurocholate (15 mg/ml) of 0.075 m CaCl(2), 5 ml of water, and 1 ml of enzyme solution, was adjusted to pH 8.0 and 37 C. The pH was maintained at a constant value by automatic addition of 0.01 n NaOH during the incubation period, which usually lasted 5 min. A lipase unit, derived from the use of this technique, may be defined as the number of microequivalents of acid liberated per minute under the specified conditions. The method was sensitive to 0.01 units. Various organisms tested produced 0.17 to 1.32 units per ml of the cell filtrate. An Arrhenius plot for staphylococcal lipase yielded 14,500 cal for function A (energy of activation).     

iNKT cells in microbial immunity: recognition of microbial glycolipids

Natural killer T cells expressing an invariant T cell antigen receptor (iNKT cells) are cells of the innate immune system. After recognizing glycolipid antigens presented by CD1d molecules on antigen presenting cells (APCs), iNKT cells rapidly produce large quantities of cytokines, thereby stimulating many types of cells. Recent studies have described several mechanisms of iNKT cell activation and the contribution of these cells to antimicrobial responses. iNKT cells can be activated by endogenous antigens and/or inflammatory cytokines from APCs. However, iNKT cells also recognize certain microbial glycolipids by their invariant T cell antigen receptor (TCR), and they contribute to pathogen clearance in certain microbial infections. These findings indicate that the iNKT TCR is useful for detecting certain microbial pathogens. Moreover, recent studies suggest that iNKT cell glycolipid antigens may be useful in antimicrobial therapy and vaccines.     

APUAMA: a software tool for reaction rate calculations

APUAMA is a free software designed to determine the reaction rate and thermodynamic properties of chemical species of a reagent system. With data from electronic structure calculations, the APUAMA determine the rate constant with tunneling correction, such as Wigner, Eckart and small curvature, and also, include the rovibrational level of diatomic molecules. The results are presented in the form of Arrhenius-Kooij form, for the reaction rate, and the thermodynamic properties are written down in the polynomial form. The word APUAMA means “fast” in Tupi-Guarani Brazilian language, then the code calculates the reaction rate on a simple and intuitive graphic interface, the form fast and practical. As program output, there are several ASCII files with tabulated information for rate constant, rovibrational levels, energy barriers and enthalpy of reaction, Arrhenius-Kooij coefficient, and also, the option to the User save all graphics in BMP format.     

Mammalian hormones in microbial cells.

Hormones and hormone-binding proteins resembling those of vertebrates are widespread in fungi, yeast and bacteria. Functional responses of microbial cells to mammalian hormones have also been found. The evolutionary roots of the vertebrate endocrine system may, therefore, be far more ancient than is generally believed.     

Improvement of biodesulfurization rate by assembling nanosorbents on the surfaces of microbial cells

To improve biodesulfurization rate is a key to industrialize biodesulfurization technology. The biodesulfurization rate is partially affected by transfer rate of substrates from organic phase to microbial cell. In this study, gamma-Al2O3 nanosorbents, which had the ability to selectively adsorb dibenzothiophene (DBT) from organic phase, were assembled on the surfaces of Pseudomonas delafieldii R-8 cell, a desulfurization strain. gamma-Al2O3 nanosorbents have the ability to adsorb DBT from oil phase, and the rate of adsorption was far higher than that of biodesulfurization. Thus, DBT can be quickly transferred to the biocatalyst surface where nanosorbents were located, which quickened DBT transfer from organic phase to biocatalyst surface and resulted in the increase of biodesulfurization rate. The desulfurization rate of the cells assembled with nanosorbents was approximately twofold higher than that of original cells. The cells assembled with nanosorbents were observed by a transmission electron microscope.     

Immobilization of microbial cells containing NAD-kinase.

Microbial cells having NAD-kinase activity, Brevibacterium ammoniagenes, were immobilized by the radiation-copolymerization method under low temperature with the activity recovery of more than 80%. Compared to the native microbial cells the immobilized cells were more stable against heat and pH change. The immobilized cells were subjected to the 5 hr reaction repeatedly 20 times without any activity loss.     

Immobilization of microbial cells by adsorption.

Immobilized cells cover a wide area of applications and are essential components of many biotechnological processes. In general it can be distinguished between two immobilization methods: (1) entrapment into polymers and (2) natural adsorption onto porous and inert support materials. The immobilization by adsorption is discussed by the following criteria: biomass loading, strength of adhesion, enzymatic stability/specific activity of the biocatalyst, effectivity/reaction engineering and operational stability.     

Developmental rate ofOpius concolor (HYM.: Braconidae) at various constant temperatures

Opius concolor Szépligeti is a parasite ofBactrocera oleae (Gmelin) and other Tephritid flies. Its development rate was studied with the Sharpe-DeMichele mathematical model, modified by Schoofieldet al. (1981), using the S.A.S. program elaborated by Wagneret al. (1984). This program chose a four parameter poikilotherm model with high temperatures inhibition. Duration of parasitoid development at seven constant temperatures ranged from 14.6±1.7 days at 28°C (males), to 77.2±5.5 days at 15°C (females). Male development was consistently found to be shorter than that of females. Low development threshold and degree-days needed to complete total development were determined with the “Regression Line” and “Thermal Summation” methods. Values (cumulated for both sexes) were found to be respectively 11.7°C and 11.8°C (low threshold), 255.9 and 251.9±16.8 days (thermal constant). Considerations on the possibility of establishingOpius concolor in northern and central Italian regions are discussed.     

Effects of microbial species,organic loading and substrate degradation rate on the power generation capability of microbial fuel cells

Four microbial fuel cells (MFCs) inoculated with different bacterial species were constructed. The species were Pseudomonas putida, Comamonas testosteroni, Corynebacterium gultamicum, and Arthrobacter polychromogenes. The MFCs were operated under identical continuous flow conditions. The factors affecting the capabilities of the MFCs for treating organic matter and generating power were evaluated and compared. The factors include microbial species type, organic loading, and substrate degradation rate. For all four MFCs, power output increased with the organic loading rate. Power density also increased with the substrate degradation rate. These findings implied that more organic matter was utilized for power generation at higher organic loading and substrate degradation rates. However, coulombic efficiency increased with decreased organic loading and substrate degradation rates. Apparently, all four MFCs had low efficiencies in generating power from organic matter. These low efficiencies are attributed to the long distance between the anode and the cathode, as well as to the small ratio of the proton exchange membrane surface area to the anode chamber surface area. These features may have caused most of the protons produced in the anode chamber to leave the chamber with the effluent, which led to the low power generation performance of the MFCs.     

Mapping regulatory networks in microbial cells.

Genome sequences are the blueprints of diverse life forms but they reveal little information about how cells make coherent responses to environmental changes. The combined use of gene fusions, gene chips, 2-D polyacrylamide gel electrophoresis, mass spectrometry and 'old-fashioned' microbial physiology will provide the means to reveal a cell's regulatory networks and how those networks are integrated.     

Nonlogarithmic death rate calculations for Byssochlamys fulva and other microorganisms.

Survivor curves for heat-resistant ascospores of Byssochlamys fulva exposed to lethal heat were nonlogarithmic. At lower heating temperatures, the log survivor curves were characterized by a shoulder plus an accelerating death rate; with increased temperatures, the rate approached logarithmic death. The formula (log No -- log N)a = kt + C was adapted to linearize these data. No and N are the initial and surviving numbers of organisms at the time t. The death rate is given by k, and C is a constant for a set of data. The a value is derived from the least-squares slope of a plot of log (log No -- log N) against log time and is used to linearize the thermal death rate curves. This formula permitted calculations of parameters analogous to those for logarithmic death (D and z). Use of formula is illustrated for selected nonlinear microbial death rate curves from the literature.     

Nonlogarithmic death rate calculations for Byssochlamys fulva and other microorganisms.

Survivor curves for heat-resistant ascospores of Byssochlamys fulva exposed to lethal heat were nonlogarithmic. At lower heating temperatures, the log survivor curves were characterized by a shoulder plus an accelerating death rate; with increased temperatures, the rate approached logarithmic death. The formula (log No -- log N)a = kt + C was adapted to linearize these data. No and N are the initial and surviving numbers of organisms at the time t. The death rate is given by k, and C is a constant for a set of data. The a value is derived from the least-squares slope of a plot of log (log No -- log N) against log time and is used to linearize the thermal death rate curves. This formula permitted calculations of parameters analogous to those for logarithmic death (D and z). Use of formula is illustrated for selected nonlinear microbial death rate curves from the literature.     

Proliferative capacity constant of metazoan cells in culture.

Proliferative capacity of metazoan cells in culture may be defined quantitatively by using GPAG-supplemented medium. For this purpose an expression called proliferative capacity constant (KPC) was introduced. KPC represents the logarithm of GPAG concentration over which the mitotic activity of cells is induced.     

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.     

Avoiding bias in calculations of relative growth rate

In classical growth analysis, relative growth rate (RGR) is calculated as RGR = (ln W2 - ln W1)/(t2 - t1), where W1 and W2 are plant dry weights at times t1 and t2. Since RGR is usually calculated using destructive harvests of several individuals, an obvious approach is to substitute W1 and W2 with sample means W1 and W2. Here we demonstrate that this approach yields a biased estimate of RGR whenever the variance of the natural logarithm-transformed plant weight changes through time. This bias increases with an increase in the variance in RGR, in the length of the interval between harvests, or in sample size. The bias can be avoided by using the formula RGR = (ln W2 - ln W1)/(t2 - t1),where ln W1 and ln W2 are the means of the natural logarithm-transformed plant weights.