Reduced models of the dynamics of light impurity stripping

“Closed” and “open” reduced models of two or three most abundant light impurity ions in an optically thin hydrogen plasma are considered. The models are shown to satisfactorily describe the average ion charge and radiative losses within a wide range of parameters typical of laboratory and astrophysical plasmas, including the case when the relaxation time of the impurity distribution over ionization states is comparable to or longer than the characteristic times of the most important dynamic processes. The potentialities of the models are demonstrated using the carbon impurity as an example. The models proposed make it possible to analytically study the dynamics of a radiating plasma, obtain qualitatively new results, and significantly reduce the computation time when solving complicated self-consistent dynamical problems.     

Investigation of the 'n-1' impurity in phosphorothioate oligodeoxynucleotides synthesized by the solid-phase beta-cyanoethyl phosphoramidite method using stepwise sulfurization.

Electrospray ionization mass spectrometry (ESI-MS) of reversed-phase HPLC-purified phosphorothioate oligodeoxynucleotides (S-ODNs), and the single-('n - 1') and double-nucleotide deletion ('n - 2') impurities subsequently isolated from them by preparative polyacrylamide gel electrophoresis (PAGE), has provided direct analytical data for the identification of both S-ODN products and their major oligomeric impurities. The 'n - 1' impurity seen by PAGE consists of a mixture of all possible single deletion sequences relative to the parent S-ODN (n-mer) and results from repetitive, though minor, imperfections in the synthesis cycle, such as incomplete detritylation, or incomplete coupling followed by incomplete capping or incomplete sulfurization. Therefore each possible 'n - 1', 'n - 2', and other short-mer sequence is present only in very low abundance. The conversion of the gel-isolated 'n - 1' impurity from phosphorothioate to phosphodiester followed by base composition-dependent anion-exchange chromatography allowed for independent confirmation of its heterogeneity and quantitation of its various components. ESI-MS of both S-ODN products and their gel-isolated impurities allowed for this first molecular identification of 'n - 1', 'n - 2' and other oligomeric impurities in S-ODNs obtained from state-of-the-art solid-phase synthesis and reversed-phase HPLC purification methods.     

Kinetics of impurity charge-state distributions in tokamak plasmas

An analysis of impurity behavior in tokamak plasmas with the use of the observation results on impurity emission shows that it is necessary to distinguish between the ion dynamics (for example, ion transport) and ion kinetics, i.e., the processes related to the motion of ions on the charge states and/or excited states due to atomic processes in plasma. This paper presents a systematic analysis of the kinetics of impurity chargestate distributions and the related effects, as well as their typical scales and conditions for their observation. The quantitative analysis is performed in terms of the lowest moments of charge-state distributions such as the average charge m and dispersion D. Analytic approaches to solving charge-state kinetic equations are considered. An approach based on the symmetry properties of the kinetic matrix is proposed for the first time. The simplest types of impurity charge-state kinetics and the most important limiting cases are considered. A detailed analysis of the nonstationary behavior of the function of the moments D(m) of the charge-state distribution is presented. A quantitative analysis of the available experimental and model charge-state distributions of C, O, Ne, and Ar impurities in the JET, DIII-D, TORE SUPRA, ALCATOR-C, TEXTOR, PLT, TFR, and DAMAVAND tokamaks is performed in terms of the moments D(m). It is shown that the moments D(m)of the model charge-state distributions of the above impurities in the plasma core are essentially insensitive to the empirical diffusion coefficient. The equivalent curves D(m) obtained for the plasma periphery can be attributed to the convective fluxes of ionizing and/or recombining impurity ions.     

Impurity radiation from a tokamak plasma

In tokamak operating modes, energy balance is often governed by impurity radiation. This is the case near the divertor plates, during impurity pellet injection, during controlled discharge disruptions, etc. The calculation of impurity radiation is a fairly involved task (it is sometimes the most difficult part of the general problem) because the radiation power is determined by the distribution of ions over the excited states and by the rate constants of elementary processes of radiation and absorption. The objective of this paper is to summarize in one place all the approximate formulas that would help investigators to describe radiation from the most often encountered impurities in a fairly simple way in their calculations accounting for plasma radiation, without reference to special literature. Simple approximating formulas describing ionization, recombination, and charge-exchange processes, as well as radiative losses from ions with a given charge, are presented for five impurity species: beryllium, carbon, oxygen, neon, and argon. Estimating formulas that allow one to take into account plasma opacity for resonant photons in line impurity radiation are also presented.     

Analysis of gene network robustness based on saturated fixed point attractors

The analysis of gene network robustness to noise and mutation is important for fundamental and practical reasons. Robustness refers to the stability of the equilibrium expression state of a gene network to variations of the initial expression state and network topology. Numerical simulation of these variations is commonly used for the assessment of robustness. Since there exists a great number of possible gene network topologies and initial states, even millions of simulations may be still too small to give reliable results. When the initial and equilibrium expression states are restricted to being saturated (i.e., their elements can only take values 1 or −1 corresponding to maximum activation and maximum repression of genes), an analytical gene network robustness assessment is possible. We present this analytical treatment based on determination of the saturated fixed point attractors for sigmoidal function models. The analysis can determine (a) for a given network, which and how many saturated equilibrium states exist and which and how many saturated initial states converge to each of these saturated equilibrium states and (b) for a given saturated equilibrium state or a given pair of saturated equilibrium and initial states, which and how many gene networks, referred to as viable, share this saturated equilibrium state or the pair of saturated equilibrium and initial states. We also show that the viable networks sharing a given saturated equilibrium state must follow certain patterns. These capabilities of the analytical treatment make it possible to properly define and accurately determine robustness to noise and mutation for gene networks. Previous network research conclusions drawn from performing millions of simulations follow directly from the results of our analytical treatment. Furthermore, the analytical results provide criteria for the identification of model validity and suggest modified models of gene network dynamics. The yeast cell-cycle network is used as an illustration of the practical application of this analytical treatment.     

Mathematical properties of pump-leak models of cell volume control and electrolyte balance

Homeostatic control of cell volume and intracellular electrolyte content is a fundamental problem in physiology and is central to the functioning of epithelial systems. These physiological processes are modeled using pump-leak models, a system of differential algebraic equations that describes the balance of ions and water flowing across the cell membrane. Despite their widespread use, very little is known about their mathematical properties. Here, we establish analytical results on the existence and stability of steady states for a general class of pump-leak models. We treat two cases. When the ion channel currents have a linear current-voltage relationship, we show that there is at most one steady state, and that the steady state is globally asymptotically stable. If there are no steady states, the cell volume tends to infinity with time. When minimal assumptions are placed on the properties of ion channel currents, we show that there is an asymptotically stable steady state so long as the pump current is not too large. The key analytical tool is a free energy relation satisfied by a general class of pump-leak models, which can be used as a Lyapunov function to study stability.     

Erratum to: Mathematical properties of pump-leak models of cell volume control and electrolyte balance

Homeostatic control of cell volume and intracellular electrolyte content is a fundamental problem in physiology and is central to the functioning of epithelial systems. These physiological processes are modeled using pump-leak models, a system of differential algebraic equations that describes the balance of ions and water flowing across the cell membrane. Despite their widespread use, very little is known about their mathematical properties. Here, we establish analytical results on the existence and stability of steady states for a general class of pump-leak models. We treat two cases. When the ion channel currents have a linear current-voltage relationship, we show that there is at most one steady state, and that the steady state is globally asymptotically stable. If there are no steady states, the cell volume tends to infinity with time. When minimal assumptions are placed on the properties of ion channel currents, we show that there is an asymptotically stable steady state so long as the pump current is not too large. The key analytical tool is a free energy relation satisfied by a general class of pump-leak models, which can be used as a Lyapunov function to study stability.     

Membrane transport models with fast and slow reactions: General analytical solution for a single relaxation

Summary Membrane transport models are usually expressed on the basis of chemical kinetics. The states of a transporter are related by rate constants, and the time-dependent changes of these states are given by linear differential equations of first order. To calculate the time-dependent transport equation, it is necessary to solve a system of differential equations which does not have a general analytical solution if there are more than five states. Since transport measurements in a complex system rarely provide all the time constants because some of them are too rapid, it is more appropriate to obtain approximate analytical solutions, assuming that there are fast and slow reaction steps. The states of the fast steps are related by equilibrium constants, thus permitting the elimination of their differential equations and leaving only those for the slow steps. With a system having only two slow steps, a single differential equation is obtained and the state equations have a single relaxation. Initial conditions for the slow reactions are determined after the perturbation which redistribute the states related by fast reactions. Current and zero-trans uptake equations are calculated. Curve fitting programs can be used to implement the general procedure and obtain the model parameters.     

Optimization of ultrafiltration/diafiltration processes for partially bound impurities

Ultrafiltration and diafiltration processes are used extensively for removal of a variety of small impurities from biological products. There has, however, been no experimental or theoretical analysis of the effects of impurity- product binding on the rate of impurity removal during these processes. Model calculations were performed to account for the effects of equilibrium binding between a small impurity and a large (retained) product on impurity clearance. Experiments were performed using D-tryptophan and bovine serum albumin as a model system. The results clearly demonstrate that binding interactions can dramatically reduce the rate of small impurity removal, leading to large increases in the required number of diavolumes. The optimal product concentration for performing the diafiltration shifts to lower product concentrations in the presence of strong binding interactions. Approximate analytical expressions for the impurity removal were developed which can provide a guide for the design and optimization of industrial ultrafiltration/diafiltration processes.     

Impact of mass spectrometry on combinatorial chemistry

In the past few years, the emergence of combinatorial chemistry has drawn increasing attention and a great deal of analytical research has been centered around this new methodology. These new methods capable of producing vast numbers of samples, which are in many cases highly complex, demand fast and reliable analytical techniques able to provide high quality information concerning sample compositions. Mass spectrometry (MS) is the method of choice to face these analytical challenges. In particular, the introduction of electrospray ionization (ESI and matrix assisted laser desorption/ionization (MALDI)) have been the driving forces for many of the recent innovations, not only within the fields of the biosciences, but also in combinatorial chemistry. These ionization techniques are extremely versatile for the characterization of both single compound collections and compound mixture collections. The high-throughput capabilities, as well as many possible couplings with separation techniques (HPLC, CE) have been thus facilitated. However, mass spectrometry is not only limited to use as an instrument for synthesis control, but also plays an increasing role in the identification of active compounds from complex libraries. Recently, new initiatives for library analysis and screening have arisen from the application of the latest developments in mass spectrometry, Fourier transform ion cyclotron resonance (FTICR).     

Limiting models for calcification in fibrous tissues adjacent to orthopedic implants: Variational indicator functions and influences of implant stiffness

Calcification and eventual integration of orthopedic implants into bone is important to many load-bearing devices, and the influence of load and implant stiffness on this process are assessed in this mathematical modelling study. Three research questions are posed in this study. First, can limiting material models provide useful information on the overall behavior of the tissue adjacent to a loaded orthopedic implant? Second, can the limiting models lead to optimization criteria? Third, can an optimization approach be used to differentiate between the four prospective remodeling rate equations which are proposed? The answers are yes, yes, and no, respectively. A two degree of freedom lumped parameter model for axial loading of an intramedullary implant is considered. Two limiting composite material models are used, and the strain energy density in the calcified and non-calcified phases are assessed as stimuli for calcification. The rate equations posed here assume that the calcified material volume fraction decreases at high strain-energy densities, and increases at small strain-energy densities. In all four cases (both models, both phases) the steady states for these rate equations find equilibrium points of indicator functions which are a weighted sum of total strain energy and the mass of calcified tissue in the layer considered. The weights on strain-energy density and mass differ in each case. This shows that for appropriate choices of parameters, all four models can yield the same results, and it also shows that an optimization approach does not uniquely determine the appropriate rate equation in these cases. The rate equations showed complicated dynamic behavior and a phase-plane analysis was used which led to upper bounds on load, which depended on implant stiffness and distal support. The predictions of the four cases studied are compared.     

化学药物杂质研究进展

药物杂质的分析和控制是用药安全有效的基础。从杂质谱分析、杂质检测、杂质限度的制定等方面综述了近年来国内外化学药 物杂质研究进展,旨在为化学药物杂质的研究提供有效思路和方法。     

Effect of inactive impurities on the burning of ICF targets

The efficiency of thermonuclear burning of the spherical deuterium-tritium (DT) plasma of inertial confinement fusion (ICF) targets in the presence of low-Z impurities (such as lithium, carbon, or beryllium) with arbitrary concentrations is investigated. The effect of impurities produced due to the mixing of the thermonuclear fuel with the material of the structural elements of the target during its compression on the process of target burning is studied, and the possibility of using solid noncryogenic thermonuclear fuels in ICF targets is analyzed. Analytical dependences of the ignition energy and target thermonuclear gain on the impurity concentration are obtained. The models are constructed for homogeneous and inhomogeneous plasmas for the case in which the burning is initiated in the central heated region of the target and then propagates into the surrounding relatively cold fuel. Two possible configurations of an inhomogeneous plasma, namely, an isobaric configuration formed in the case of spark ignition of the target and an isochoric configuration formed in the case of fast ignition, are considered. The results of numerical simulations of the burning of the DT plasma of ICF targets in a wide range of impurity concentrations are presented. The simulations were performed using the TEPA one-dimensional code, in which the thermonuclear burning kinetics is calculated by the Monte Carlo method. It is shown that the strongest negative effect related to the presence of impurities is an increase in the energy of target ignition. It is substantiated that the most promising solid noncryogenic fuel is DT hydride of beryllium (BeDT). The requirements to the plasma parameters at which BeDT can be used as a fuel in noncryogenic ICF targets are determined. Variants of using noncryogenic targets with a solid thermonuclear fuel are proposed.     

Formation of a charge-exchange target for fast ions in the plasma of large-scale toroidal devices under NBI conditions

High-energy (E>0.2 MeV) charge-exchange diagnostics allow the determination of the distribution function of fast atoms produced via the neutralization of hydrogen isotope ions by target hydrogen-like impurity ions. To derive the distribution function from the experimental data requires knowledge of the composition and spatial distribution of the target ions in a tokamak plasma. A charge-exchange target forms as a result of the interaction between the main impurity nuclei and the heating neutral beams. In different devices, the heating beams are arranged in different ways with respect to the diagnostics; hence, in order to accurately estimate the contribution of the secondary ions to the detected signal, it is necessary to calculate their trajectories for every particular case. A model is proposed that takes into account elementary processes resulting in the ionization equilibrium of the ions of different impurities with allowance for ion motion in a specific tokamak configuration. As an example, the model is applied to the plasma of the JT-60U tokamak. Mechanisms for the formation of charge-exchange atomic flows in various energy ranges are considered. The relative contributions of different heating injectors to the charge-exchange flow are estimated. Based on the calculated results, a method is proposed for local measurements of the ion distribution function with the help of a stationary analyzer.     

Conformational transition of poly(alpha-L-glutamic acid). A polyelectrolytic approach

The charge-induced conformational transition of poly(alpha-L-glutamic acid) (PLGA) is considered in this paper from the point of view of proton dissociation. Equations for the excess electrostatic Gibbs energy of dissociation (i.e., delta pKa) are derived as a function of the degree of ionization, alpha. These analytical equations are used to describe some experimental dissociation curves at different polymer and salt concentrations. The dependence of the calculated delta pKa with respect to the ionic strength for the two conformational states, alpha-helical and extended coil, respectively, is rather satisfactorily explained. Even more interesting are the predictions which are derived from this approach for the transition point, alpha tr which is found to be ionic-strength dependent, in full agreement with the experimental results.     

ECR heating power modulation as a means to ease the overcoming of the radiation barrier in fusion devices

A method is proposed to ease the overcoming of the impurity radiation barrier during current drive in tokamaks, as well as in alternative fusion and plasmochemical systems with ECR plasma heating. The method is based on the fact that the dependence of the ionization rate on the electron temperature is strongly nonlinear and the dependence of the recombination rate on the latter is weaker. The result is that, during temperature oscillations, the effective temperature for ionization-recombination processes is higher than that in a steady state, so the ionization equilibrium is shifted and strongly emitting ions are stripped more rapidly. Thereby, ECR plasma heating in the initial discharge stage can be made more efficient by modulating the heating power at a low frequency. The evolution of the electron temperature in a homogeneous hydrogen plasma with a carbon impurity and in small ISX-scale tokamaks is simulated numerically, as well as the evolution of the electron and ion temperatures and of the current during discharge startup in the ITER device. Numerical simulations of the effect of modulation of the ECR heating power on the rate of heating of nitrogen, oxygen, and argon plasmas were also carried out. The assumption of coronal equilibrium is not used. It is shown that the low-frequency modulation of the heating power can substantially ease the overcoming of the radiation barrier.     

Evaluation of four methods for computing parameter sensitivities in dynamic system models

Computation of state sensitivities with respect to parameters can be a difficult and costly numerical problem when the number of states and parameters is large, or when sensitivities must be computed repeatedly, as with many optimization algorithms. Four methods are evaluated in terms of solution accuracy, and computer-time and storage requirements: direct numerical integration of the complete sensitivity-system differential equations, a reduced-order method based on the controllable states of the sensitivity system, a numerical-quadratures technique applied directly to the analytic solution of the original system, and an approach based on the solution of the transition matrix. Three linear system models, with four different types of inputs, were used as test cases, the largest having 6 states and 12 parameters. The reduced-order method was the most time-efficient in a majority of cases, but it was prone to numerical instability problems in certain situations which may be encountered in applications. It also had the largest storage requirements. For the highest-order system, only direct numerical integration and the transition-matrix method produced sufficiently accurate results for most applications, because of matrix-inversion problems with the other methods. For impulse inputs, the transition-matrix and the numerical-quadratures methods overall were the most computationally efficient, but the transition-matrix approach required much more memory storage.     

Product and contaminant measurement in bioprocess development by SELDI‐MS

Bioprocesses for therapeutic protein production typically require significant resources to be invested in their development. Underlying these efforts are analytical methods, which must be fit for the purpose of monitoring product and contaminants in the process. It is highly desirable, especially in early‐phase development when material and established analytical methods are limiting, to be able to determine what happens to the product and impurities at each process step with small sample volumes in a rapid and readily performed manner. This study evaluates the utility of surface‐enhanced laser desorption ionization mass spectroscopy (SELDI‐MS), known for its rapid analysis and minimal sample volumes, as an analytical process development tool. In‐process samples from an E. coli process for apolipoprotein A‐IM (ApoA‐IM) manufacture were used along with traditional analytical methods such as HPLC to check the SELDI‐MS results. ApoA‐IM is a naturally occurring variant of ApoA‐I that appears to confer protection against cardiovascular disease to those that carry the mutated gene. The results show that, unlike many other analytical methods, SELDI‐MS can handle early process samples that contain complex mixtures of biological molecules with limited sample pretreatment and thereby provide meaningful process‐relevant information. At present, this technique seems most suited to early‐phase development particularly when methods for traditional analytical approaches are still being established. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2010     

Reactive Impurities in Excipients: Profiling,Identification and Mitigation of Drug–Excipient Incompatibility

Reactive impurities in pharmaceutical excipients could cause drug product instability, leading to decreased product performance, loss in potency, and/or formation of potentially toxic degradants. The levels of reactive impurities in excipients may vary between lots and vendors. Screening of excipients for these impurities and a thorough understanding of their potential interaction with drug candidates during early formulation development ensure robust drug product development. In this review paper, excipient impurities are categorized into six major classes, including reducing sugars, aldehydes, peroxides, metals, nitrate/nitrite, and organic acids. The sources of generation, the analytical method for detection, the stability of impurities upon storage and processing, and the potential reactions with drug candidates of these impurities are reviewed. Specific examples of drug–excipient impurity interaction from internal research and literature are provided. Mitigation strategies and corrective measures are also discussed.