Transient response of encapsulated enzymes in hollow-fiber reactor

A mathematical model for the transient response of encapsulated enzymes is developed showing the effects of the outer boundary layer, the encapsulating membrane, the partition coefficient, and diffusion with reaction within the encapsulating medium. The model incorporates both first-order kinetics and Michaelis-Menten kinetics for the reaction rate. Using typical hollow-fiber or microcapsule parameters, the model shows that (a) the partition coefficient affects the overall rate only when the rate-limiting step is diffusion through the membrane, (b) the transient overall effectiveness factor rises sharply with time and approaches an asymptotic value for most situations, and (c) the first-order approximation to Michaelis-Menten kinetics is not valid when the initial outside bulk concentration is higher than the Michaelis constant and the overall rate is reaction limited. The model is compared with experimental data using uricase in a hollow-fiber enzyme reactor configuration. Batch assay and CSTUER (continuous-stirred ultrafiltration enzyme reactor) studies were conducted on the free enzyme to provide some of the parameters used in the model. The CSTUER data fit the case of substrate inhibition kinetics with the apparent Michaelis constant approaching zero. The hollow-fiber reactor was conducted with uricase dissolved in both a buffer solution and a concentrated hemoglobin solution. Diffusivities of the solute were measured in both solutions as was the osmotic pressure of the hemoglobin solution. While experimental data for uricase in buffer solution could easily be matched by the model, that in the concentrated hemoglobin solution could not.     

Uptake and release protocol for assessing membrane binding and permeation by way of isothermal titration calorimetry

The activity of many biomolecules and drugs crucially depends on whether they bind to biological membranes and whether they translocate to the opposite lipid leaflet and trans aqueous compartment. A general strategy to measure membrane binding and permeation is the uptake and release assay, which compares two apparent equilibrium situations established either by the addition or by the extraction of the solute of interest. Only solutes that permeate the membrane sufficiently fast do not show any dependence on the history of sample preparation. This strategy can be pursued for virtually all membrane-binding solutes, using any method suitable for detecting binding. Here, we present in detail one example that is particularly well developed, namely the nonspecific membrane partitioning and flip-flop of small, nonionic solutes as characterized by isothermal titration calorimetry. A complete set of experiments, including all sample preparation procedures, can typically be accomplished within 2 days. Analogous protocols for studying charged solutes, virtually water-insoluble, hydrophobic compounds or specific ligands are also considered.     

Application of spectrofluorometry to the prediction of PHB concentrations in a fed-batch process

On-line estimation of biopolymer production during fermentation would be a useful adjunct to the development of strategies for process control and optimization. This study examined the applicability of spectrofluorometry, along with other on-line measurements, for the prediction of poly-ß-hydroxybutyric acid (PHB) concentrations in a high-cell density fed-batch fermentation of Ralstonia eutropha. Models previously used for modelling PHB evolution with time are not sufficiently accurate for situations where transient intermediate accumulations or PHB degradation occur. Thus, the mass balance in the model was modified to account for these situations. An estimation algorithm was developed that is based on a hybrid model consisting of a dynamic mass balance of PHB where the main reaction coefficient was regressed with respect to spectrofluorometric data. The regression between the kinetic parameter and the spectrofluorometric data was accomplished using partial least squares (PLS) regression to avoid high sensitivity to noise expected from highly correlated data, such as the spectrofluorometric readings. The model accounts for dynamics of intermediates and in this way allows the prediction of dynamic behaviour in PHB concentrations that cannot be predicted with other reported mathematical models.     

Discrete time models for two-species competition.

A discrete (difference) single age-class model for two-species competition is presented and its stability properties discussed. It resembles the Lotka-Volterra model in having linear zero growth isoclines, and thus, also in its general requirements for the coexistence of competing species. It differs in allowing the populations to show damped oscillations, stable cycles or even apparent “chaos” if competition is sufficiently severe. A similar two age-class model is discussed where there is both intra- and interspecific competition in one of the developmental stages, but only intraspecific competition in the other. Even this slight increase in complexity leads to markedly different properties. The zero growth curves become nonlinear and up to three equilibria between two competing species are possible.     

PCR in situ followed by microdissection allows whole chromosome painting probes to be made from single microdissected chromosomes

Whole-chromosome painting probes (WCPs) and chromosome-arm painting probes (CAPs) are an integral part of the cytogenetic analysis of chromosome abnormalities. While these are routinely made by chromosome microdissection, multiple copies of the dissected region have been necessary to achieve a library sufficiently complex to provide adequate painting. Performing multiple dissections of chromosomes or chromosome regions is time consuming and occasionally impossible, such as when working with species whose banded karyotype is not well defined. We have developed a method whereby chromosome paints can be reliably generated by dissecting single chromosomes. The technique consists of performing degenerate oligonucleotide-primed polymerase chain reaction (DOP-PCR) in situ on the chromosomes, prior to dissection. Enough amplification occurs to enable a single dissected chromosome to be used to create a painting probe sufficiently complex for use in fluorescence in situ hybridization (FISH). The amplification products remain localized on the chromosomes; this allows region-specific chromosome paints to be made. We detail this novel technique and show whole-chromosome, arm-specific, and contiguous region-specific probes for human and rat, each created from single dissected fragments of chromatin. Received: 14 January 1999 / Accepted: 28 January 1999     

Neotyphodium endophyte infection frequency in annual grass populations: relative importance of mutualism and transmission efficiency

Persistence and ubiquity of vertically transmitted Neotyphodium endophytes in grass populations is puzzling because infected plants do not consistently exhibit increased fitness. Using an annual grass population model, we show that the problems for matching endophyte infection and mutualism are likely to arise from difficulties in detecting small mutualistic effects, variability in endophyte transmission efficiency and an apparent prevalence of non-equilibrium in the dynamics of infection. Although endophytes would ultimately persist only if the infection confers some fitness increase to the host plants, such an increase can be very small, as long as the transmission efficiency is sufficiently high. In addition, imperfect transmission limits effectively the equilibrium infection level if the infected plants exhibit small or large reproductive advantage. Under frequent natural conditions, the equilibrium infection level is very sensitive to small changes in transmission efficiency and host reproductive advantage, while convergence to such an equilibrium is slow. As a consequence, seed immigration and environmental fluctuation are likely to keep local infection levels away from equilibrium. Transient dynamics analysis suggests that, when driven by environmental fluctuation, infection frequency increases would often be larger than decreases. By contrast, when due to immigration, overrepresentation of infected individuals tends to vanish faster than equivalent overrepresentation of non-infected individuals.     

The critical vaccination fraction for heterogeneous epidemic models

Given a population with m heterogeneous subgroups, a method is developed for determining minimal vaccine allocations to prevent an epidemic by setting the reproduction number to 1. The framework is sufficiently general to apply to several epidemic situations, such as SIR, SEIR and SIS models with vital dynamics. The reproduction number is the largest eigenvalue of the linearized system round the local point of equilibrium of the model. Using the Perron-Frobenius theorem, an exact method for generating solutions is given and the threshold surface of critical vaccine allocations is shown to be a compact, connected subset of a regular (m-1)-dimensional manifold. Populations with two subgroups are examined in full. The threshold curves are either hyperbolas or straight lines. Explicit conditions are given as to when threshold elimination is achievable by vaccinating just one or two groups in a multi-group population and expressions for the critical coverage are derived. Specific reference is made to an influenza A model. Separable or proportionate mixing is also treated. Conditions are conjectured for convexity of the threshold surface and the problem of minimizing the amount of vaccine used while remaining on the threshold surface is discussed.     

Compartmentalized energy transfer in cardiomyocytes: use of mathematical modeling for analysis of in vivo regulation of respiration.

The mathematical model of the compartmentalized energy transfer system in cardiac myocytes presented includes mitochondrial synthesis of ATP by ATP synthase, phosphocreatine production in the coupled mitochondrial creatine kinase reaction, the myofibrillar and cytoplasmic creatine kinase reactions, ATP utilization by actomyosin ATPase during the contraction cycle, and diffusional exchange of metabolites between different compartments. The model was used to calculate the changes in metabolite profiles during the cardiac cycle, metabolite and energy fluxes in different cellular compartments at high workload (corresponding to the rate of oxygen consumption of 46 mu atoms of O.(g wet mass)-1.min-1) under varying conditions of restricted ADP diffusion across mitochondrial outer membrane and creatine kinase isoenzyme "switchoff." In the complete system, restricted diffusion of ADP across the outer mitochondrial membrane stabilizes phosphocreatine production in cardiac mitochondria and increases the role of the phosphocreatine shuttle in energy transport and respiration regulation. Selective inhibition of myoplasmic or mitochondrial creatine kinase (modeling the experiments with transgenic animals) results in "takeover" of their function by another, active creatine kinase isoenzyme. This mathematical modeling also shows that assumption of the creatine kinase equilibrium in the cell may only be a very rough approximation to the reality at increased workload. The mathematical model developed can be used as a basis for further quantitative analyses of energy fluxes in the cell and their regulation, particularly by adding modules for adenylate kinase, the glycolytic system, and other reactions of energy metabolism of the cell.     

Drug residue formation from ronidazole, a 5-nitroimidazole. III. Studies on the mechanism of protein alkylation in vitro

Ronidazole (1-methyl-5-nitroimidazole-2-methanol carbamate) is reductively metabolized by liver microsomal and purified NADPH-cytochrome P-450 reductase preparations to reactive metabolites that covalently bind to tissue proteins. Kinetic experiments and studies employing immobilized cysteine or blocked cysteine thiols have shown that the principal targets of protein alkylation ara cysteine thiols. Furthermore, ronidazole specifically radiolabelled with 14C in the 4,5-ring, N-methyl or 2-methylene positions give rise to equivalent apparent covalent binding suggesting that the imidazole nucleus is retained in the bound residue. In contrast, the carbonyl-14C-labeled ronidazole gives approx. 6--15-fold less apparent covalent binding indicating that the carbamoyl group is lost during the reaction leading to the covalently bound metabolite. The conversion of ronidazole to reactive metabolite(s) is quantitative and reflects the amazing efficiency by which this compound is activated by microsomal enzymes. However, only about 5% of this metabolite can be accounted for as protein-bound products under the conditions employed in these studies. Consequently, approx. 95% of the reactive ronidazole metabolite(s) can react with other constituents in the reaction media such as other thiols or water. Based on these results, a mechanism is proposed for the metabolic activation of ronidazole.     

Controlling Malaria Using Livestock-Based Interventions: A One Health Approach

Where malaria is transmitted by zoophilic vectors, two types of malaria control strategies have been proposed based on animals: using livestock to divert vector biting from people (zooprophylaxis) or as baits to attract vectors to insecticide sources (insecticide-treated livestock). Opposing findings have been obtained on malaria zooprophylaxis, and despite the success of an insecticide-treated livestock trial in Pakistan, where malaria vectors are highly zoophilic, its effectiveness is yet to be formally tested in Africa where vectors are more anthropophilic. This study aims to clarify the different effects of livestock on malaria and to understand under what circumstances livestock-based interventions could play a role in malaria control programmes. This was explored by developing a mathematical model and combining it with data from Pakistan and Ethiopia. Consistent with previous work, a zooprophylactic effect of untreated livestock is predicted in two situations: if vector population density does not increase with livestock introduction, or if livestock numbers and availability to vectors are sufficiently high such that the increase in vector density is counteracted by the diversion of bites from humans to animals. Although, as expected, insecticide-treatment of livestock is predicted to be more beneficial in settings with highly zoophilic vectors, like South Asia, we find that the intervention could also considerably decrease malaria transmission in regions with more anthropophilic vectors, like Anopheles arabiensis in Africa, under specific circumstances: high treatment coverage of the livestock population, using a product with stronger or longer lasting insecticidal effect than in the Pakistan trial, and with small (ideally null) repellency effect, or if increasing the attractiveness of treated livestock to malaria vectors. The results suggest these are the most appropriate conditions for field testing insecticide-treated livestock in an Africa region with moderately zoophilic vectors, where this intervention could contribute to the integrated control of malaria and livestock diseases.     

DEVELOPMENTAL ANATOMY OF DIRECT SHOOT ORGANOGENESIS FROM LEAF PETIOLES OF VITIS VINIFERA (VITACEAE)

The anatomy of direct shoot organogenesis from leaf petioles of Vitis vinifera cv. French Colombard cultured in vitro was studied by light microscopy. Regenerating petiole stubs were fixed at 2- or 3-day intervals and sectioned longitudinally. By day 3 on regeneration medium, new cell divisions were observed. After 6 days, three distinct regions of meristematic activity were apparent within the expanding petiole stub: the wound-response, organogenic, and vascularization regions. In the organogenic region, rapid periclinal divisions of vacuolate outer cortical cells formed nodular bumps, many of which developed vascular strands and marginal meristems and formed adventitious leaves. Promeristems with small, densely staining cells and a distinct tunica layer also originated in the organogenic region, by cell division in the epidermal and subepidermal cell layers. With vascularization and the formation of leaf primordia, many promeristems became adventitious shoot meristems. Adventitious leaves and promeristems were initiated continuously from day 10 until day 33. Promeristems were often initiated near or upon adventitious leaves but could form either before or after the adventitious leaf developed. Adventitious leaves and shoot meristems developed vascular connections with the vascular bundles of the original expiant. The implication of this pattern of regeneration for Agrobacterium-mediated transformation of Vitis is discussed.     

Mathematical analysis of competition between sensory ganglion cells for neurotrophic factor in the skin

A model is presented of competition between sensory axons for trophic molecules (e.g. a neurotrophin such as NGF), produced in a region of skin small enough to permit their free diffusion throughout it; e.g., a touch dome, or a vibrissal follicle hair sinus. The variables specified are the number of high affinity trophic factor receptors per axon terminal and the concentration of trophic factor in the extracellular space. Previous models of this class predicted the loss of all the axons innervating the region except the one requiring least trophic factor for its maintenance, even with high rates of trophic factor production. In the present model, we have imposed upper limits to axonal growth, thereby introducing new equilibria, and we show by a global analysis using LaSalle's theorem, and also by local analysis, that several axons can then coexist if the rate of production of trophic molecules is sufficiently high.     

Phase behavior of a model bilayer membrane with coupled leaves

We discuss the thermodynamic behavior of a bilayer composed of two coupled leaves and derive the Gibbs Phase Rule for such a system. A simple phenomenological model of such a system is considered in which the state of the bilayer is specified by the relative number of ordering lipids in the outer leaf, and in the inner leaf. Two cases are treated. In the first, both inner and outer leaves could undergo phase separation when uncoupled from one another. The bilayer can exist in four different phases, and can exhibit three-phase coexistence. In the second case, an outer layer which can undergo phase separation by itself is coupled to an inner leaf which cannot. We find that when the coupling is weak, the bilayer can exist in only two phases, one in which the outer layer is rich in ordering lipids and the inner leaf is somewhat richer in them than when uncoupled, and another in which the outer layer is poor in ordering lipids and the inner leaf is poorer in them than when uncoupled. Increasing the coupling increases the effect on the inner leaf composition due to small changes in those of the outer leaf. For sufficiently large coupling, a phase transition occurs and the bilayer exhibits four phases as in the first case considered. Our results are in accord with several observations made recently.     

Electron microscopic and cytochemical studies of the mouse subcommissural organ

Summary In mice most of the ependymal cells of the subcommissural organ (SCO cells) are densely packed with dilated cisternae of the endoplasmic reticulum (ER) containing either finely granular or flocculent materials. The well developed supra-nuclear Golgi apparatus consists of stacks of flattened saccules and small vesicles; the two or three outer Golgi saccules are moderately dilated and exhibit numerous fenestrations; occasional profiles suggesting the budding of coated vesicles and formation of membrane-bound dense bodies from the ends of the innermost Golgi saccules are seen. A few coated vesicles and membrane-bound dense bodies of various sizes and shapes are also found in the Golgi region.The contents of the dilated ER cisternae are stained with periodic acid-silver methenamine techniques. In the Golgi complex the two or three inner saccules are stained as deeply as the dense bodies, and the outer saccules are only slightly stained. The stained contents of ER cisternae are more electron opaque than those of the outer but less opaque than those of the inner Golgi saccules and the dense bodies.Acid phosphatase activities are localized in the dense bodies, some of the coated vesicles in the Golgi region, and in the one or two inner Golgi saccules.On the basis of these results the following conclusions have been reached: (1) In mouse SCO cells the finely granular and the flocculent materials in the lumen of ER cisternae contain a complex carbohydrate(s) which is secreted into the ventricle to form Reissner's fiber; (2) the secretory substance is assumed to be synthesized by the ER and stored in its cisternae, and the Golgi apparatus might play only a minor role, if any, in the elaboration of the secretory material; (3) most of the dense bodies in the mouse SCO cells are lysosomal in nature instead of being so-called dark secretory granules.Sponsored by the National Science Council, Republic of China.     

Quantitative genetic models for the balance between migration and stabilizing selection

The evolution of a quantitative trait subject to stabilizing selection and immigration, with the immigrants deviating from the local optimum, is considered under a number of different models of the underlying genetic basis of the trait. By comparing exact predictions under the infinitesimal model obtained using numerical methods with predictions of a simplified approximate model based on ignoring linkage disequilibrium, the increase in the expressed genetic variance as a result of linkage disequilibrium generated by migration is shown to be relatively small and negligible, provided that the genetic variance relative to the squared deviation of immigrants from the local optimum is sufficiently large or selection and migration is sufficiently weak. Deviation from normality is shown to be less important by comparing predictions of the infinitesimal model with a model presupposing normality. For a more realistic symmetric model, involving a finite number of loci only, no linkage and equal effects and frequencies across loci, additional changes in the genetic variance arise as a result of changes in underlying allele frequencies. Again, provided that the genetic variance relative to the squared deviation of the immigrants from the local optimum is small, the difference between the predictions of infinitesimal and the symmetric model are small unless the number of loci is very small. However, if the genetic variance relative to the squared deviation of the immigrants from the local optimum is large, or if selection and migration are strong, both linkage disequilibrium and changes in the genetic variance as a result of changes in underlying allele frequencies become important.     

Kinetic schemes for post-synchronized single molecule dynamics

Recordings from single molecule experiments can be aggregated to determine average kinetic properties of the system under observation. The kinetics after a synchronized reaction step can be interpreted using all of the standard tools developed for ensemble perturbation experiments. The kinetics leading up to a synchronized event, determined by the lifetimes of the preceding states; however, are not as obvious if the reaction has reversible steps or branches. Here we describe a general procedure for dealing with these situations.     

A new device for the freeze-clamping of tissue samples

Measurement of metabolite concentrations in tissue samples involves the following procedures: Removal of the sample from the animal, temporary arrest of metabolism, extraction (including weighing, homogenization, final fixation, and neutralization) and assay. Rapid temporary fixation following the sampling of tissue is essential to prevent autolytic changes in metabolite concentrations (1,2). The freeze-clamping technique described by Wollenberger et al. (3) meets this requirement as long as the final thickness of the freeze-clamped sample is sufficiently small. For brain tissue the limit seems to be about 2 mm (4).In our laboratory we have made extensive use of the freeze-clamping tongs of Wollenberger et al., especially for small tissue samples freeze-clamped in situ. However, when in situ clamping can not be used when more than 2–3 g of tissue must be sampled, the freeze-clamping press described below has proven very useful.     

Inhibition kinetics of green crab (Scylla serrata) alkaline phosphatase by zinc ions: a new type of complexing inhibition

The Tsou method was used to study the kinetic course of inactivation of green crab alkaline phosphatase by zinc ions. The results show that the enzyme was inactivated by a complexing scheme which has not been previously identified. The enzyme first reversibly and quickly binds Zn(2+) and then undergoes a slow reversible course to inactivation and slow conformational change. The inactivation reaction is a single molecule reaction and the apparent inactivation rate constant is for a saturated reaction being independent of Zn(2+) concentration if the concentration is sufficiently high. The microscopic rate constants of inactivation and the association constant were determined from the measurements.     

Conformational mobility of proteins and activation energy of enzymatic charge transfer reactions: an analysis in dielectric formalism

In calculating the medium reorganization energy and the activation energy of charge transfer enzymatic reactions, an allowance is made for the enhanced conformational mobility of the protein external region. The two-layer model is proposed, the outer layer having a higher static dielectric constant. The calculations show that the higher mobility in the outer layer causes some quantitative rather than qualitative changes. The main result obtained earlier is confirmed: the reorganization energy for charge transfer reaction in protein globule is much lower than in water and for this reason the activation energy also decreases. The higher dielectric constant of the outer layer somewhat favours the introduction of charge into active site and hence favours the natural selection of proteins as enzymes. This effect cannot exclude the necessity of other factors stabilizing ionic forms inside the protein globule. Freezing of conformational mobility (say, at low temperatures) hinders the charge transfer process as a consequence of the difficulty in equalizing the initial and final energy levels.     

The effects of modifiers on enzyme catalysis: A non-classical nearest neighbor approach

We present a nearest neighbor lattice model of the effects of modifiers on two-state enzyme catalysis of the reaction s ? p-We do not in general make the assumptions of the classical approach to cooperative catalysis that yield (1) adsorption isotherms of the same form as those for the corresponding equilibrium system and (2) a rate of the catalyzed reaction proportional to the number of occupied catalytic sites. Closed form results are obtained for two approximations, the Bragg-Williams and the quasi-chemical. The latter requires (l),but is exact for several simple cases, including the concerted model, under this condition. Under (1) it is found that an interaction between modifier and catalytic sites, whether attractive or repulsive, increases the magnitudes of the slopes of the adsorption isotherms but that interactions between identical sites (catalytic or modifier) increase these magnitudes if attractive and decrease them if repulsive. Thus, the former interaction allows for phase transitions if sufficiently attractive or repulsive, but the latter only if sufficiently attractive. Herein also lies the explanation for why the concerted model displays only “positive cooperativity”. It is further seen that it is not possible to classify a modifier as an activator or inhibitor of the catalyzed reaction solely on the basis of the sign of the interaction energy between catalytic and modifier sites. For agiven energy, the rate of the reaction may increase or decrease in response to the modifier, or it may respond biphasically. Similarly, the rate may respond biphasically to the activities of s or p, lead- ing to instabilities. Thus, possibilities of multiple nonequilibrium stationary states or spatio-temporal patterns are raised-