Photopolymerized, multilaminated matrix devices with optimized nonuniform initial concentration profiles to control drug release.

This paper describes a novel approach to obtain desired release profiles from diffusion-controlled matrix devices by employing nonuniform initial concentration profiles theoretically and experimentally. Theoretically, a model was developed to examine the effect of nonuniform initial concentration profiles on matrix release behavior, and an optimization technique was investigated to determine suitable nonuniform initial concentration profiles which provide desired release patterns. Experimentally, release rates of an organic dye from photopolymerized matrix devices were measured to test the application of these mathematical techniques and the efficacy of photolaminated matrices in approximating the optimized release behavior. All system parameters were measured by independent experiments, and the experimental release data agree very well with the computed results.

Mathematical modeling and optimization of cellulase protein production using Trichoderma reesei RL-P37.

The enzyme cellulase, a multienzyme complex made up of several proteins, catalyzes the conversion of cellulose to glucose in an enzymatic hydrolysis-based biomass-to-ethanol process. Production of cellulase enzyme proteins in large quantities using the fungus Trichoderma reesei requires understanding the dynamics of growth and enzyme production. The method of neural network parameter function modeling, which combines the approximation capabilities of neural networks with fundamental process knowledge, is utilized to develop a mathematical model of this dynamic system. In addition, kinetic models are also developed. Laboratory data from bench-scale fermentations involving growth and protein production by T. reesei on lactose and xylose are used to estimate the parameters in these models. The relative performances of the various models and the results of optimizing these models on two different performance measures are presented. An approximately 33% lower root-mean-squared error (RMSE) in protein predictions and about 40% lower total RMSE is obtained with the neural network-based model as opposed to kinetic models. Using the neural network-based model, the RMSE in predicting optimal conditions for two performance indices, is about 67% and 40% lower, respectively, when compared with the kinetic models. Thus, both model predictions and optimization results from the neural network-based model are found to be closer to the experimental data than the kinetic models developed in this work. It is shown that the neural network parameter function modeling method can be useful as a "macromodeling" technique to rapidly develop dynamic models of a process.

Three-dimensional modeling, estimation, and fault diagnosis of spacecraft air contaminants.

A description is given of the design and implementation of a method to track the presence of air contaminants aboard a spacecraft using an accurate physical model and of a procedure that would raise alarms when certain tolerance levels are exceeded. Because our objective is to monitor the contaminants in real time, we make use of a state estimation procedure that filters measurements from a sensor system and arrives at an optimal estimate of the state of the system. The model essentially consists of a convection-diffusion equation in three dimensions, solved implicitly using the principle of operator splitting, and uses a flowfield obtained by the solution of the Navier-Stokes equations for the cabin geometry, assuming steady-state conditions. A novel implicit Kalman filter has been used for fault detection, a procedure that is an efficient way to track the state of the system and that uses the sparse nature of the state transition matrices.

Application of ultrasonic backscattering for level measurement and process monitoring of expanded-bed adsorption columns.

Expanded-bed adsorption is a newly commercialized technique for the purification of proteins from cellular debris in downstream processing. An expanded bed presents the possibility of protein recovery in a single step, eliminating the often costly clarification processing steps such as ultrafiltration, centrifugation, and precipitation. A major obstacle to the successful commercialization of this technology is the inability to accurately monitor and control the bed height in these systems. Fluctuations in the feedstock viscosity are common during normal operation and tend to make the operation and control of expanded beds for biological applications complex and difficult. We develop a level measurement technique based upon ultrasonics. It is shown that this technique has great promise for bed-height measurement in expanded-bed adsorption systems. Furthermore, the bed-height measurement can be used in feedback control strategies for bed-height regulation. The proposed ultrasonic sensor is also capable of monitoring for plugging and bubbling in the column.

Air-quality monitoring and detection of air contamination in an enclosed environment.

We report on the development of an air-quality monitoring and early detection system for an enclosed environment with specific emphasis on manned spacecraft. The proposed monitoring approach is based on a distributed parameter model of contaminant dispersion and real-time contaminant concentration measurements. Kalman filtering is identified as a suitable method for generating on-line estimation of the spatial contamination profile, and an implicit Kalman filtering algorithm is shown to be preferable for rear-time implementation. The identification of the contaminant concentration profile allows for a straightforward solution of the early detection of an air contamination event and provides information that enables potential automatic diagnosis of an unknown contamination source.

Implicit Kalman filtering.

For an implicitly defined discrete system, a new algorithm for Kalman filtering is developed and an efficient numerical implementation scheme is proposed. Unlike the traditional explicit approach, the implicit filter can be readily applied to ill-conditioned systems and allows for generalization to descriptor systems. The implementation of the implicit filter depends on the solution of the congruence matrix equation (A1)(Px)(AT1) = Py. We develop a general iterative method for the solution of this equation, and prove necessary and sufficient conditions for convergence. It is shown that when the system matrices of an implicit system are sparse, the implicit Kalman filter requires significantly less computer time and storage to implement as compared to the traditional explicit Kalman filter. Simulation results are presented to illustrate and substantiate the theoretical developments.

Modeling and optimization of a batch process for in vitro RNA production.

RNA molecules are commonly produced in vitro by transcription, utilizing a DNA template, an RNA polymerase enzyme, and nucleoside triphosphate substrates (NTPs). In addition to the full-length RNA molecule coded for by the DNA template, significant amounts of shorter RNA molecules are produced. A simplified model of this complex transcription process is presented, with the shorter RNA molecules lumped into a single pool. The rate equations do not depend on the stoichiometry of the RNA molecule of interest, which facilitates application of the model to other RNA molecules. Optimal initial conditions for batch in vitro RNA transcription to produce a dodecamer RNA containing three different nucleotides have been predicted using the model. The predicted optimal values for equimolar NTPs are 10 to 15 mM initial concentration for each NTP and 50 to 60 mM for magnesium acetate, yielding a maximum final dodecamer concentration of 0.8 +/- 0.1 mM at the 90% confidence interval. Experimental data agree well with the model results. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 56: 210-220, 1997.

Inhalation risk in low-gravity spacecraft.

Inhalation risks on long-duration manned spaced flight include gasses chronically released by outgassing of materials, gasses released during spills, thermodegradation events (including fires) with their attendant particulates, and fire extinguishment. As an example, an event in which electronic insulation consisting of polytetrafluoroethylene undergoes thermodegradation on the Space Station Freedom was modeled experimentally and theoretically from the initial chemistry and convective transport through pulmonary deposition in humans. The low-gravity environment was found to impact various stages of event simulation. Critical unknowns were identified, and these include the extent of production of ultrafine particles and polymeric products at the source in low gravity, the transport of ultrafine particles in the spacecraft air quality control system, and the biological response of the lung, including alveolar macrophages, to this inhalation risk in low gravity.

Mathematical modeling of induced foreign protein production by recombinant bacteria.

A new generalized mathematical model for recombinant bacteria which includes inducer effects on cell growth and foreign protein production is developed. The model equation set was applied to a host-vector system, Escherichi coli D1210 and plasmid pSD8. Batch experiments were designed and performed in shake flasks to verify the model. A parameter estimation method was developed and proven to be efficient. Although simple, the model can effectively describe the dynamics of the production of foreign protein in recombinant bacteria and can be used for optimization and control studies to maximize foreign protein production.

Optimal chemostat cascades for periplasmic protein production.

This theoretical work predicts the optimal system design for the steady-state production of secreted protein in a chemostat cascade, using bakers' yeast (Saccharomyces cerevisiae) as the host organism. The protein of interest, mutant invertase, is secreted to the periplasmic space instead of the culture medium on account of its large size. This work uses the secretion model developed and tested by Park and Ramirez (1988). It is shown that the highest productivity is achieved when the chemostat cascade contains two stages, although the improvement over the single-stage productivity is small. When no recycle is used, the advantage of two stages results from the tradeoff between maximizing the cell concentration and maximizing the rate of protein production per cell. When recycle is used, the cell concentration and protein productivity are increased, and the advantage of two stages results from the tradeoff between maximizing the specific protein production rate and maximizing the specific protein secretion rate. Cascades with three stages were also investigated, but these were found to have no improvement over the corresponding two-stage cascades.

Effect of transcription promoters on the optimal production of secreted protein in fed-batch reactors.

Production of heterologous proteins by yeast secretion imposes additional factors that need to be considered, which do not appear with production by direct expression. These include additional intracellular polypeptide processing dynamics through the secretory organelles and the protein concentration in the culture medium, which is the usual final destination of the product. Optimal control theory is applied to optimize fed-batch production of secreted protein. We maximize an objective function that includes both total production rate and product concentration. A mutant invertase is chosen as the model heterologous secretory protein. Optimal control control strategies have been obtained for the use of two different promoters for the gene transcription, a dere-pressible SUC2 promoter and a strong glycolytic GPD promoter. With the use of the strong GPD promoter, achieving maximum production occurs on the singular arc of maximum specific growth rate. As the object switches to maximum product concentration, operation occurs for longer periods of time at a slow glucose singular arc condition. The optimal control for maximizing protein production with the weak SUC2 promoter requires transitions between high and low glucose concentrations associated with multiple distinct singular arc conditions. For maximum product concentration, the high concentration branches of the singular arc supporting maximum growth rate and maximum secretion rate disappear. Operation stays essentially on the low glucose concentration branch of the singular arc, which maximizes the protein production rate and minimizes the dilution of the broth product concentration.

Dynamics of foreign protein secretion from Saccharomyces cerevisiae.

A mathematical model describing the dynamics of foreign protein secretion from yeast cells is developed. The secretion events, which are a series of complicated enzymatic reactions and carrier-involved transport, are lumped to a practically applicable model structure, based on the major interactions between the heterologous polypeptides and the host cell's secretory machinery through the pathway. The developed model structure predicts that the secretion rate constant is represented as a saturated form with respect to the host cell's specific growth rate. The validity of the proposed model structure is tested by generating dynamic response data to a step input of cycloheximide. The model system used in the experiment is SEY2102-s21, which has an integrated copy of a yeast secretion-mutant invertase that simulates well typical gene cassettes designed to secrete mature foreign proteins utilizing the yeast cell's secretion signals. Protein quantification is done by gel electrophoresis followed by immuno-blot on nitrocellulose filters and subsequent scanning with a reflectance densitometer. Experimental data confirm the proposed model structure.

Optimal temperature control for batch beer fermentation.

Optimal control theory was applied to the process of batch beer fermentation. The performance functional considered was a weighted sum of maximum ethanol production and minimum time. Calculations were based on the model of Engasser et al. modified to include temperature effects. Model parameters were determined from isothermal batch fermentations. The fermentor cooling duty was the single available control. Temperature state variable constraints as well as control variable constraints were considered. The optimal control law is shown to be bang-bang control with the existence of a singular arc corresponding to isothermal operation at the maximum temperature constraint. An iterative algorithm is presented for computing appropriate switching times using a penalty-function-augmented performance functional.