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Previously, we have developed a genetically structured mathematical model to describe the inhibition of Escherichia coli lac operon gene expression by antigene oligos. Our model predicted that antigene oligos targeted to the operator region of the lac operon would have a significant inhibitory effect on beta-galactosidase production. In this investigation, the E. coli lac operon gene expression in the presence of antigene oligos was studied experimentally. A 21-mer oligo, which was designed to form a triplex with the operator, was found to be able to specifically inhibit beta-galactosidase production in a dose-dependent manner. In contrast to the 21-mer triplex-forming oligonucleotide (TFO), several control oligos showed no inhibitory effect. The ineffectiveness of the various control oligos, along with the fact that the 21-mer oligo has no homology sequence with lacZYA, and no mRNA is transcribed from the operator, suggests that the 21-mer oligo inhibits target gene expression by an antigene mechanism. To simulate the kinetics of lac operon gene expression in the presence of antigene oligos, a genetically structured kinetic model, which includes transport of oligo into the cell, growth of bacteria cells, and lac operon gene expression, was developed. Predictions of the kinetic model fit the experimental data quite well after adjustment of the value of the oligonucleotide transport rate constant (9.0 x 10(-)(3) min(-)(1)) and oligo binding affinity constant (1.05 x 10(6) M(-)(1)). Our values for these two adjusted parameters are in the range of reported literature values.

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Gene transcription is regulated by transcription factors that can bind to specific regions on DNA. Antigene oligonucleotides (oligos) can bind to specific regions on DNA and form a triplex with the double-stranded DNA. The triplex can competitively inhibit the binding of transcription factors and, as a result, transcription can be inhibited. A genetically structured model has been developed to quantitatively describe the inhibition of the Escherichia coli lac operon gene expression by triplex-forming oligos. The model predicts that the effect of triplex-forming oligos on the lac operon gene expression depends on their target sites. Oligonucleotides targeted to the operator are much more effective than those targeted to other regulatory sites on the lac operon. In some cases, the effect of oligo binding is similar to that of a mutation in the lac operon. The model provides insight as to the specific binding site to be targeted to achieve the most effective inhibition of gene expression. The model is also capable of predicting the oligo concentration needed to inhibit gene expression, which is in general agreement with results reported by other investigators.

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A radioactive tracer technique was used to evaluate the in vivo mass transfer properties of a tissue engineered bioartificial organ. To obtain these measurements, bioartificial organs were first implanted in ten rats and allowed to vascularize for 4 weeks. After vascularization, radioactive inulin was placed within the cell chamber of the device. Following the addition of tracer, blood samples were taken over a 4-h time period and inulin levels were determined. The results of these experiments were interpreted using a compartmental model that describes the transport of inulin from the cell chamber, across the immunoisolation membrane, and into the neovascularized region contained within the adjacent scaffold material. Nonlinear regression analysis of the plasma inulin levels using a four-compartment pharmacokinetic model provided estimates of the membrane permeability, the product of the capillary wall surface area and capillary permeability, and the glomerular filtration rate (GFR). The permeability of the membrane was found to be 3.50 x 10(-5) +/- 1.15 x 10(-5) cm/sec (95% confidence interval, n = 10), which compares favorably to previous in vitro permeability data for this membrane. The capillary wall permeability was found to be 0. 0087 6 0.0029 cm(3)/sec/100 g of tissue. This compares well to a reported value for inulin of 0.01 cm(3)/sec/100 g of tissue. The GFR was found to be 0.44 +/- 0.07 ml/h/g BW, which compares well with a reported value of 0.40 ml/hr/g BW. The inulin tracer technique reported here is a useful tool for assessing the in vivo transport characteristics of a bioartificial organ as well as the vascularization within tissue engineered structures.

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Oxygen transport is crucial for the proper functioning of a bioartificial organ. In many cases, the immunoisolation membrane used to protect the transplanted cells from the host's immune system can be a significant barrier to oxygen transport. A method is described for measuring the in vitro and in vivo oxygen transport characteristics of a planar immunoisolation membrane. The in vitro oxygen permeability of the membrane was found to equal 9.22 x 10(-4) cm/sec and was essentially the same as the in vivo value of 9.51 x 10(-4) cm/sec. The fact that the in vitro and in vivo membrane permeabilities are identical indicates that any fibrotic tissue adjacent to the immunoisolation membrane did not present a significant resistance to the transport of oxygen. The measured oxygen permeability was also found consistent with the solute permeabilities obtained in a previous study for larger molecules. Based on the oxygen permeability results, theoretical calculations for this particular membrane indicate that about 1,100 islets of Langerhans/cm2 of membrane area can be sustained at high tissue densities and only 660 islets/cm2 can be supported at low tissue densities.

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An optimal pH control technique has been developed for multistep enzymatic synthesis reactions where the optimal pH differs by several units for each step. This technique separates an acidic environment from a basic environment by the hydrolysis of urea within a thin layer of immobilized urease. With this technique, a two-step enzymatic reaction can take place simultaneously, in proximity to each other, and at their respective optimal pH. Because a reaction system involving an acid generation represents a more challenging test of this pH control technique, a number of factors that affect the generation of such a pH gradient are considered in this study. The mathematical model proposed is based on several simplifying assumptions and represents a first attempt to provide an analysis of this complex problem. The results show that, by choosing appropriate parameters, the pH control technique still can generate the desired pH gradient even if there is an acid-generating reaction in the system.

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Photodynamic therapy (PDT) is a relatively new protocol for cancer treatment which has recently been approved for limited clinical use. Traditionally, the success of treatment with PDT has been compared on the basis of total light delivery. Using the mathematical model of Henning et al. (Radiat. Res. 142, 221-226, 1995), we have determined that when oxygen is not depleted from the tissue, the concentration of singlet oxygen that is generated is directly proportional to the product of the light fluence rate (phi) and the concentration of the photosensitizer (Cs). Therefore, phiCs is an appropriate parameter for comparing the potential success of PDT protocols under these conditions. For a treatment of time t, the observed photodynamic effect resulting from singlet oxygen exposure should be directly related to phiCst. For high phiCs, the model predicts that oxygen depletion occurs within the tumor tissue. As a result, the photodynamic effect is no longer proportional to phiCst. We have expanded the model of Henning et al. to include the changes in oxygen concentration which occur within the capillary as blood flows through the tissue. Our new predictions with the mathematical model for optimal PDT treatment conditions are significantly different from those predicted by the previous models. Predictions of the model are given using parameters relevant for treatment of solid tumors with Photofrin.

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Helicobacter pylori has been established as the major causative agent of human active gastritis and is an essential factor in peptic ulcer disease and gastric cancer. The mechanism that has been proposed for H. pylori to control its inhospitable microenvironment happens to coincide with the pH control technique developed by us. This technique was developed to separate an acidic environment from a basic environment for a sequential enzymatic reaction by the hydrolysis of urea within a thin layer of immobilized urease. In this paper, a mathematical model is presented to consider how H. pylori survives the gastric acidity. The computed results explain well the experimental data available involving H. pylori.

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An immunoisolation membrane formed by incorporating a high water content polyvinyl alcohol (PVA) hydrogel into a microporous polyether sulfone (PES) filter has been investigated in this study. The PVA hydrogel is formed in situ within the filter pores via glutaraldehyde (GA) crosslinking under acidic conditions. The tortuous nature of the microporous filter pores securely anchors the embedded hydrogel to provide excellent structural integrity. The high void fraction of the PES filter support (>80%) and high water content of the PVA hydrogel (>85% water by weight) allow excellent solute transport rates, while an appropriate level of glutaraldehyde crosslinking supplies the required molecular size selectivity. In vitro permeability measurements made with solutes covering a wide range of molecular sizes demonstrate high transport rates for small nutrient molecules with rapidly diminishing permeabilities above a molecular weight of approximately 1,000 Dalton. Implantation experiments show that the membrane properties are not deleteriously affected by prolonged in vivo exposure or common sterilization techniques. Thus, this hybrid hydrogel/filter membrane system offers a promising approach to the immunoisolation of implanted cells.

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The synthesis of a variety of important biochemicals involves multistep enzyme-catalyzed reactions. In many cases, the optimal operating pH is much different for the individual enzymatic steps of such synthesis reactions. Yet, it may be beneficial if such reaction steps are combined or paired, allowing them to occur simultaneously, in proximity to one another, and at their respective optimal pH. This can be achieved by separating the micro-environments of the two steps of a reaction pathway using a thin urease layer that catalyzes an ammonia-forming reaction. In this article, the pH control system in a commercial immobilized glucose (xylose) isomerase pellet, which has an optimal pH of 7.5, is demonstrated. This system allows the glucose isomerase to have near its optimal pH activity when immersed in a bulk solution of pH 4.6. A theoretical analysis is also given for the effective fraction of the immobilized glucose isomerase, which remains active when the bulk pH is at 4.6 in the presence of 20 mM urea versus when the bulk pH is at its optimal pH of 7.5. Both theoretical and experimental results show that this pH control system works well in this case. (c) 1996 John Wiley & Sons, Inc.

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A transient one-dimensional mathematical model is presented to help visualize the qualitative and quantitative effects on inter-capillary tissue undergoing photodynamic therapy (PDT). The model is solved by a Crank-Nicholson finite difference formulation to provide time-dependent concentrations of the Type II mechanism's photo-oxidation species in the tissue surrounding a capillary. The time-dependent solution allows educated decisions to be made as to the optimum timing of light fractionation (on/off) cycles. Qualitative and quantitative optimization of the PDT process is considered along with a case study of data in the literature, the main goal being to provide optimized light therapy regimens for eventual clinical use.

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An in vivo tracer technique that uses radiolabeled insulin as the tracer molecule has been developed to assess the rate of chemical transport between the cell transplantation chamber of an implantable bioartificial device and the host's circulatory system. The device considered here employs site-directed neovascularization of a porous matrix to induce capillary growth adjacent to an immunoisolated cell implantation chamber. This device design is being investigated as a vehicle for therapeutic cell transplantation, with the advantages that it allows the cells to perform their therapeutic function without the danger of immune rejection and it avoids damaging contact of blood flow with artificial surfaces. A pharmacokinetic model of the mass transport between the implantation chamber, the vascularized matrix, and the body has been devised to allow proper analysis and understanding of the experimental tracer results. Experiments performed in this study have been principally directed at evaluation of the tracer model parameters, but results also provide a quantitative measure of the progression of capillary growth into a porous matrix. Measured plasma tracer levels demonstrate that chemical transport rates within the implanted device increase with the progression of matrix vascular ingrowth. Agreement between the fitted model curves and the corresponding measured concentrations at different levels of capillary ingrowth demonstrate that the model provides a realistic representation of the actual capillary-mediated transport phenomena occurring within the device.

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Several examples of two-step sequential reactions exist where, because of the poor equilibrium conversion by the first reaction, it is desirable to conduct the two reactions simultaneously. In such a scheme, the product of the first reaction is continuously removed by the second reaction, thus not allowing the first reaction to approach chemical equilibrium. Therefore, the first reaction is allowed to proceed in the desired direction at an appreciable rate. However, in many biochemical applications where enzyme catalysts are involved, the enzyme's activities are strong functions of pH. Where the pH optima of the first and second reaction differ by three to four units, the above reaction scheme would be difficult to implement. In these cases, the two reactions can be separated by a thin permeable membrane across which the desired pH gradient is maintained. In this article, it was shown, both by theory and experiment, that a thin, flat membrane of immobilized urease can accomplish this goal when one face of the membrane is exposed to the acidic bulk solution (pH(b) = 4.5) containing a small quantity of urea (0.01 M). In this particular case, the ammonia that was produced in the membrane consumed the incoming hydrogen ions and thus maintained the desired pH gradient. Experimental results indicate that with sufficient urease loading, the face of the membrane opposite to the bulk solution could be maintained at a pH that would allow many enzymes to realize their maximum activities ( approximately 7.5). It was also found that this pH gradient could be maintained even in the presence of a buffer, which greatly enhances the transport of protons into the membrane.

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Transplantation of the islets of Langerhans has received considerable attention as a means of treating insulin-dependent diabetes mellitus. However, the number of islets needed and the level of plasma glucose control that results from this treatment method still needs to be defined. A pharmacokinetic model of glucose and insulin dynamics which includes the islet insulin response to plasma glucose is used to compare the effectiveness of subcutaneous insulin injections and transplanted islets of Langerhans for the treatment of a hypothetical patient with insulin dependent diabetes mellitus. For a patient receiving 60 U of insulin per day the results show that 500,000 human islets would be needed to obtain glucose control comparable to that obtained with insulin injections and at least 1.5 million human islets are needed to obtain normoglycemia.

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A novel spiral wound membrane sandwich (SWMS) design for an implantable bioartificial pancreas is presented and is numerically evaluated using a comprehensive model of the glucose-insulin kinetics within the device. The spiral blood flow pattern in this design induces a convective flow of blood ultrafiltrate directly through the islet chamber. Use of ultrafiltration in addition to diffusion allows rapid transmission of blood glucose changes to the islet chamber and efficient transport of insulin from the islet chamber back to the blood stream. Simulation results suggest that the implantable bioartificial pancreas design presented in this paper may offer a means of improving the control of blood glucose levels in type I diabetics.

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The economics of a process for the production of ethanol employing a hollow fiber extractive fermentor have been investigated. A computer simulation of the process incorporating a mathematical model of the fermentor was used to calculate the mass and energy balances. The results of the process simulation were read into a computer spreadsheet programmed with the economic calculations from which a final ethanol product cost was obtained. The process was found to be as competitive as conventional fermentation processes even at the currently high cost--$4/sq ft--of hollow fibers. It was determined that the 1986 price of 46.2 cents/L of ethanol produced by the process would be reduced by 1.8 cents/L for every $1/sq foot drop in the price of hollow fibers. A comparison of this process with conventional fermentation processes indicates that its potential savings lie in its ability to use a concentrated sugar feed, and the fermentor's increased productivity and ability to produce a concentrated ethanol stream which is removed by the extracting solvent.

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A mathematical model is presented for a microporous hollow-fiber membrane extractive fermentor (HFEF). The model is based on the continuous flow of the aqueous nutrient phase and cells through the shell space of the fermentor where the fermentation reaction occurs. The product diffuses from the shell space through the hollow-fiber membrane where it is continuously removed by solvent flowing concurrently through the fiber lumen. Results for ethanol production show that the HFEF has a volumetric productivity significantly higher than that possible using conventional methods. The model predicts the existence of an optimum volume fraction of hollow fibers in the fermentor that maximizes the total volumetric productivity. This optimum is the result of a classic trade-off between the volume fraction of the fermentor required for fermentation and that required for efficient removal of the ethanol product to minimize product inhibition.

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A mathematical model has been developed for the process of extractive fermentation. The model rigorously treats the material balance, reaction kinetics, and liquid-liquid equilibrium relationships. Convergence is promoted through use of the Quasi-Newton Method. Extractive fermentation is particularly attractive for those bioreactions where the cell growth and product formation is inhibited by the product or other secondary cellular products. The model is illustrated for the production of ethanol. The results show an increase in specific productivity and the ability to process a more concentrated feed. However, volumetric productivity is reduced in the presence of a low capacity solvent.