A modified discrete random pore model allowing for different initial surface reactivity

We investigate here a modification of the discrete random pore model [Bhatia SK, Vartak BJ, Carbon 1996;34:1383], by including an additional rate constant which takes into account the different reactivity of the initial pore surface having attached functional groups and hydrogens, relative to the subsequently exposed surface. It is observed that the relative initial reactivity has a significant effect on the conversion and structural evolution, underscoring the importance of initial surface chemistry. The model is tested against experimental data on chemically controlled char oxidation and steam gasification at various temperatures. It is seen that the variations of the reaction rate and surface area with conversion are better represented by the present approach than earlier random pore models. The results clearly indicate the improvement of model predictions in the low conversion region, where the effect of the initially attached functional groups and hydrogens is more significant, particularly for char oxidation. It is also seen that, for the data examined, the initial surface chemistry is less important for steam gasification as compared to the oxidation reaction. Further development of the approach must also incorporate the dynamics of surface complexation, which is not considered here.

Rectification of the olfactory cyclic nucleotide-gated channel by intracellular polyamines

Polyamine-induced inward rectification of cyclic nucleotide-gated channels was studied in inside-out patches from rat olfactory neurons. The polyamines, spermine, spermidine and putrescine, induced an 'instantaneous' voltage-dependent inhibition with K-d values at 0 mV of 39, 121 mu M and 2.7 mM, respectively. Hill coefficients for inhibition were significantly < 1, suggesting an allosteric inhibitory mechanism. The Woodhull model for voltage-dependent block predicted that all 3 polyamines bound to a site 1/3 of the electrical distance through the membrane from the internal side. Instantaneous inhibition was relieved at positive potentials, implying significant polyamine permeation. Spermine also induced exponential current relaxations to a 'steady-state' impermeant level. This inhibition was also mediated by a binding site 1/3 of the electrical distance through the pore, but with a K-d of 2.6 mM. Spermine inhibition was explained by postulating two spermine binding sites at a similar depth. Occupation of the first site occurs rapidly and with high affinity, but once a spermine molecule has bound, it inhibits spermine occupation of the second binding site via electrostatic repulsion. This repulsion is overcome at higher membrane potentials, but results in a lower apparent binding affinity for the second spermine molecule. The on-rate constant for the second spermine binding saturated at a low rate (similar to 200 sec(-1) at +120 mV), providing further evidence for an allosteric mechanism. Polyamine-induced inward rectification was significant at physiological concentrations.

Mechanisms of substitution reactions on cyclometallated platinum(IV) complexes: "Quasi-labile" systems

The substitution reactions of SMe2 by phosphines (PMePh2, PEtPh2, PPh3, P(4-MeC6H4)(3), P(3-MeC6H4)(3), PCy3) on Pt-IV complexes having a cyclometalated imine ligand, two methyl groups in a cis-geometrical arrangement, a halogen, and a dimethyl sulfide as ligands, [Pt(CN)(CH3)(2)(X)(SMe2)], have been studied as a function of temperature, solvent, and electronic and steric characteristics of the phosphines and the X and CN ligands. In all cases, a limiting dissociative mechanism has been found, where the dissociation of the SMe2 ligand corresponds to the rate-determining step. The pentacoordinated species formed behaves as a true pentacoordinated Pt-IV compound in a steady-state concentration, given the solvent independence of the rate constant. The X-ray crystal structures of two of the dimethyl sulfide complexes and a derivative of the pentacoordinate intermediate have been determined. Differences in the individual rate constants for the entrance of the phosphine ligand can only be estimated as reactivity ratios. In all cases an effect of the phosphine size is detected, indicating that an associative step takes place from the pentacoordinated intermediate. The nature of the (CN) imine and X ligands produces differences in the dimethyl sulfide dissociation reactions rates, which can be quantified by the corresponding DeltaS double dagger values (72, 64, 48, 31, and 78 J K-1 mol(-1) for CN/X being C6H4CHNCH2C6H5/Br, C6H4CHNCH2-(2,4,6-(CH3)(3))C6H2/Br, C6H4CHNCH2C6H5/Cl, C6Cl4CHNCH2C6H5/Cl, and C6W4CH2NCHC6H5/ Pr, respectively). As a whole, the donor character of the coordinated C-aromatic and X atoms have the greatest influence on the dissociativeness of the rate-determining step.

Determination of activation energy distributions for chemisorption of oxygen on carbon: an improved approach

The present paper proposes an approach to obtaining the activation energy distribution for chemisorption of oxygen onto carbon surfaces, while simultaneously allowing for the activation energy dependence of the pre-exponential factor of the rate constant. Prior studies in this area have considered this factor to be uniform, thereby biasing estimated distributions. The results show that the derived activation energy distribution is not sensitive to the chemisorption mechanism because of the step function like property of the coverage. The activation energy distribution is essentially uniform for some carbons, and has two or possibly more discrete stages, suggestive of at least two types of sites, each with its own uniform distribution. The pre-exponential factors of the reactions are determined directly from the experimental data, and are found not to be constant as assumed in earlier work, but correlated with the activation energy. The latter results empirically follow an exponential function, supporting some earlier statistical and experimental work. The activation energy distribution obtained in the present paper permits improved correlation of chemisorption data in comparison to earlier studies. (C) 2000 Elsevier Science Ltd. All rights reserved.

Mathematical models in percutaneous absorption

A number of mathematical models have been used to describe percutaneous absorption kinetics. In general, most of these models have used either diffusion-based or compartmental equations. The object of any mathematical model is to a) be able to represent the processes associated with absorption accurately, b) be able to describe/summarize experimental data with parametric equations or moments, and c) predict kinetics under varying conditions. However, in describing the processes involved, some developed models often suffer from being of too complex a form to be practically useful. In this chapter, we attempt to approach the issue of mathematical modeling in percutaneous absorption from four perspectives. These are to a) describe simple practical models, b) provide an overview of the more complex models, c) summarize some of the more important/useful models used to date, and d) examine sonic practical applications of the models. The range of processes involved in percutaneous absorption and considered in developing the mathematical models in this chapter is shown in Fig. 1. We initially address in vitro skin diffusion models and consider a) constant donor concentration and receptor conditions, b) the corresponding flux, donor, skin, and receptor amount-time profiles for solutions, and c) amount- and flux-time profiles when the donor phase is removed. More complex issues, such as finite-volume donor phase, finite-volume receptor phase, the presence of an efflux. rate constant at the membrane-receptor interphase, and two-layer diffusion, are then considered. We then look at specific models and issues concerned with a) release from topical products, b) use of compartmental models as alternatives to diffusion models, c) concentration-dependent absorption, d) modeling of skin metabolism, e) role of solute-skin-vehicle interactions, f) effects of vehicle loss, a) shunt transport, and h) in vivo diffusion, compartmental, physiological, and deconvolution models. We conclude by examining topics such as a) deep tissue penetration, b) pharmacodynamics, c) iontophoresis, d) sonophoresis, and e) pitfalls in modeling.

On the validity of the dispersion model of hepatic drug elimination when intravascular transit time densities are long-tailed

The dispersion model with mixed boundary conditions uses a single parameter, the dispersion number, to describe the hepatic elimination of xenobiotics and endogenous substances. An implicit a priori assumption of the model is that the transit time density of intravascular indicators is approximated by an inverse Gaussian distribution. This approximation is limited in that the model poorly describes the tail part of the hepatic outflow curves of vascular indicators. A sum of two inverse Gaussian functions is proposed as ail alternative, more flexible empirical model for transit time densities of vascular references. This model suggests that a more accurate description of the tail portion of vascular reference curves yields an elimination rate constant (or intrinsic clearance) which is 40% less than predicted by the dispersion model with mixed boundary conditions. The results emphasize the need to accurately describe outflow curves in using them as a basis for determining pharmacokinetic parameters using hepatic elimination models. (C) 1997 Society for Mathematical Biology.

Effect of saponin treatment on the sarcoplasmic reticulum of rat, cane toad and crustacean (yabby) skeletal muscle

1. Mechanically skinned fibres from skeletal muscles of the rat, toad and yabby were used to investigate the effect of saponin treatment on sarcoplasmic reticulum (SR) Ca2+ loading properties. The SR was loaded submaximally under control conditions before and after treatment with saponin and SR Ca2+ was released with caffeine. 2. Treatment with 10 mu g ml(-1) saponin greatly reduced the SR Ca2+ loading ability of skinned fibres from the extensor digitorum longus muscle of the rat with a rate constant of 0.24 min(-1). Saponin concentrations up to 150 mu g ml(-1) and increased exposure time up to 30 min did not further reduce the SR Ca2+ loading ability of the SR, which indicates that the inhibitory action of 10-150 mu g ml(-1) saponin is not dose dependent. The effect of saponin was also not dependent on the state of polarization of the transverse-tubular system. 3. Treatment with saponin at concentrations up to 100 mu g ml(-1) for 30 min did not affect the Ca2+ loading ability of SR in skinned skeletal muscle fibres from the twitch portion of the toad iliofibularis muscle but SR Ca2+ loading ability decreased markedly with a time constant of 0.22 min(-1) in the presence of 150 mu g ml(-1) saponin. 4. The saponin dependent increase in permeability could be reversed in both rat and toad fibres by short treatment with 6 mu M Ruthenium Red, a potent SR Ca2+ channel blocker, suggesting that saponin does affect the SR Ca2+ channel properties in mammalian and anuran skeletal muscle. 5. Treatment of skinned fibres of long sarcomere length (> 6 mu m) from the claw muscle of the yabby (a freshwater decapod crustacean) with 10 mu g ml(-1) saponin for 30 min abolished the ability of the SR to load Ca2+, indicating that saponin affects differently the SR from skeletal muscles of mammals, anurans and crustaceans. 6. is concluded that at relatively low concentrations, saponin causes inhibition of the skeletal SR Ca2+ loading ability in a species dependent manner, probably by increasing the Ca2+ loss through SR Ca2+ release channels.

Free-radical bulk polymerization of styrene: ESR and near-infrared spectroscopic study of the entire conversion range

The free radical polymerization of styrene in bulk was monitored by ESR and FT near-infrared spectroscopy at 70°C for a series of concentrations of the initiator, dimethyl 2,2′-azobis(isobutyrate). In order to obtain detailed kinetic information over the intire conversion range, and the gel effect range in particular, conversion and free radical concentration data points were accumulated with exceptionally short time intervals. The polystyrene radical concentration ([St•]) went through a sharp maximum at the gel effect, a feature that has hitherto escaped observation due to the rapid concentration changes in the gel effect range relative to the data point time intervals of previous studies. Temperature measurements throughout the polymerization were employed to calculate that a temperature increase was not the cause of the [St•] maximum, which thus appeares to be a genuine feature of the gel effect of this system under isothermal conditions. The propagation rate constant (kp) as a function of monomer conversion exhibited a marked dependence on initiator concentration at high monomer conversion; the sharp decrease in kp with increasing conversion was shifted to higher conversions with increasing initiator concentration.

Time-dependent master equation simulation of complex elementary reactions in combustion: Application to the reaction of (CH2)-C-1 with C2H2 from 300-2000 K

Computational simulations of the title reaction are presented, covering a temperature range from 300 to 2000 K. At lower temperatures we find that initial formation of the cyclopropene complex by addition of methylene to acetylene is irreversible, as is the stabilisation process via collisional energy transfer. Product branching between propargyl and the stable isomers is predicted at 300 K as a function of pressure for the first time. At intermediate temperatures (1200 K), complex temporal evolution involving multiple steady states begins to emerge. At high temperatures (2000 K) the timescale for subsequent unimolecular decay of thermalized intermediates begins to impinge on the timescale for reaction of methylene, such that the rate of formation of propargyl product does not admit a simple analysis in terms of a single time-independent rate constant until the methylene supply becomes depleted. Likewise, at the elevated temperatures the thermalized intermediates cannot be regarded as irreversible product channels. Our solution algorithm involves spectral propagation of a symmetrised version of the discretized master equation matrix, and is implemented in a high precision environment which makes hitherto unachievable low-temperature modelling a reality.

The modelling of froth zone recovery in batch and continuously operated laboratory flotation cells

This paper proposes an integrated methodology for modelling froth zone performance in batch and continuously operated laboratory flotation cells. The methodology is based on a semi-empirical approach which relates the overall flotation rate constant to the froth depth (FD) in the flotation cell; from this relationship, a froth zone recovery (R,) can be extracted. Froth zone recovery, in turn, may be related to the froth retention time (FRT), defined as the ratio of froth volume to the volumetric flow rate of concentrate from the cell. An expansion of this relationship to account for particles recovered both by true flotation and entrainment provides a simple model that may be used to predict the froth performance in continuous tests from the results of laboratory batch experiments. Crown Copyright (C) 2002 Published by Elsevier Science B.V. All rights reserved.

Cationic drug pharmacokinetics in diseased livers determined by fibrosis index, hepatic protein content, microsomal activity, and nature of drug

The disposition kinetics of six cationic drugs in perfused diseased and normal rat livers were determined by multiple indicator dilution and related to the drug physicochemical properties and liver histopathology. A carbon tetrachloride (CCl4)induced acute hepatocellular injury model had a higher fibrosis index (FI), determined by computer-assisted image analysis, than did an alcohol-induced chronic hepatocellular injury model. The alcohol-treated group had the highest hepatic alpha(1)- acid glycoprotein, microsomal protein (MP), and cytochrome P450 (P450) concentrations. Various pharmacokinetic parameters could be related to the octanol-water partition coefficient (log P-app) of the drug as a surrogate for plasma membrane partition coefficient and affinity for MP or P450, the dependence being lower in the CCl4-treated group and higher in the alcohol-treated group relative to controls. Stepwise regression analysis showed that hepatic extraction ratio, permeability-surface area product, tissue-binding constant, intrinsic clearance, partition ratio of influx (k(in)) and efflux rate constant (k(out)), and k(in)/k(out) were related to physicochemical properties of drug (log P-app or pK(a)) and liver histopathology (FI, MP, or P450). In addition, hepatocyte organelle ion trapping of cationic drugs was evident in all groups. It is concluded that fibrosis-inducing hepatic disease effects on cationic drug disposition in the liver may be predicted from drug properties and liver histopathology.

Rates of electronic energy transfer in conformationally flexible bichromophoric macrocyclic complexes: a combined experimental and molecular modeling study

Electronic energy transfer (EET) rate constants between a naphthalene donor and anthracene acceptor in [ZnL4a](ClO4)(2) and [ZnL4b](ClO4)(2) were determined by time-resolved fluorescence where L-4a and L-4b are the trans and cis isomers of 6-((anthracen-9-yl-methyl)amino)-6,13-dimethyl-13-((naphthalen-1-yl-methyl)amino)-1,4,8,11-tetraazacyclotetradecane, respectively. These isomers differ in the relative disposition of the appended chromophores with respect to the macrocyclic plane. The trans isomer has an energy transfer rate constant (k(EET)) of 8.7 x 10(8) s(-1), whereas that of the cis isomer is significantly faster (2.3 x 10(9) s(-1)). Molecular modeling was used to determine the likely distribution of conformations in CH3CN solution for these complexes in an attempt to identify any distance or orientation dependency that may account for the differing rate constants observed. The calculated conformational distributions together with analysis by H-1 NMR for the [ZnL4a](2+) trans complex in the common trans-III N-based isomer gave a calculated Forster rate constant close to that observed experimentally. For the [ZnL4b](2+) cis complex, the experimentally determined rate constant may be attributed to a combination of trans-Ill and trans-I N-based isomeric forms of the complex in solution.

Heterogeneous kinetics of the reduction of chromium (VI) by elemental iron

Zero valent iron (ZVI) has been extensively used as a reactive medium for the reduction of Cr(VI) to Cr(III) in reactive permeable barriers. The kinetic rate depends strongly on the superficial oxidation of the iron particles used and the preliminary washing of ZVI increases the rate. The reaction has been primarily modelled using a pseudo-first-order kinetics which is inappropriate for a heterogeneous reaction. We assumed a shrinking particle type model where the kinetic rate is proportional to the available iron surface area, to the initial volume of solution and to the chromium concentration raised to a power ˛ which is the order of the chemical reaction occurring at surface. We assumed α= 2/3 based on the likeness to the shrinking particle models with spherical symmetry. Kinetics studies were performed in order to evaluate the suitability of this approach. The influence of the following parameters was experimentally studied: initial available surface area, chromium concentration, temperature and pH. The assumed order for the reaction was confirmed. In addition, the rate constant was calculated from data obtained in different operating conditions. Digital pictures of iron balls were periodically taken and the image treatment allowed for establishing the time evolution of their size distribution.

Synchronization in Von Bertalanffy’s models

Many data have been useful to describe the growth of marine mammals, invertebrates and reptiles, seabirds, sea turtles and fishes, using the logistic, the Gom-pertz and von Bertalanffy's growth models. A generalized family of von Bertalanffy's maps, which is proportional to the right hand side of von Bertalanffy's growth equation, is studied and its dynamical approach is proposed. The system complexity is measured using Lyapunov exponents, which depend on two biological parameters: von Bertalanffy's growth rate constant and the asymptotic weight. Applications of synchronization in real world is of current interest. The behavior of birds ocks, schools of fish and other animals is an important phenomenon characterized by synchronized motion of individuals. In this work, we consider networks having in each node a von Bertalanffy's model and we study the synchronization interval of these networks, as a function of those two biological parameters. Numerical simulation are also presented to support our approaches.

Modelling of the kinetics of municipal solid waste composting in full-scale mechanical-biological treatment plants

A thesis submitted in fulfilment of the requirements for the Degree of Doctor of Philosophy in Sanitary Engineering in the Faculty of Sciences and Technology of the New University of Lisbon