Martin A. Hjortso

Model predictive control of continuous yeast bioreactors using cell population balance models

Abstract Continuous cultures of budding yeast are known to exhibit autonomous oscillations that adversely affect bioreactor stability and productivity. We demonstrate that this phenomenon can be modeled by coupling the population balance equation (PBE) for the cell mass distribution to the mass balance of the rate limiting substrate. An efficient and robust numerical solution procedure using orthogonal collocation on finite elements is developed to approximate the PBE model by a coupled set of nonlinear ordinary differential equations (ODEs). A controller design model is obtained by linearizing and temporally discretizing the ODEs derived from spatial discretization of the PBE model. The resulting linear state-space model is used to develop model predictive control (MPC) strategies that regulate the discretized cell number distribution by manipulating the dilution rate and the feed substrate concentration. Two choices of the controlled output vector are considered: (i) the entire discretized distribution; and (ii) a subset of the discretized distribution. The ability of the MPC controllers to stabilize steady-state and periodic solutions is evaluated via simulation. We show that superior closed-loop performance is obtained when a subset of the distribution is employed as controlled outputs.

A conceptual model of autonomous oscillations in microbial cultures

Autonomous oscillations in continuous microbial cultures can be modelled by periodic solution of the age distribution balance. When substrate or product concentrations in the medium affects passage through control points in the cell cycle, a positive feedback loop can form between the age distribution and the medium concentrations, and this may stabilize the oscilations and prevent a gradual loss of synchrony. An illustrative example is solved analytically and numerical simulations are used to determine the range of operating conditions over which oscillations may exist. Finally, autonomous oscillations in continuous cultures of Saccharomyces cerevisiae are discussed in the light of this model.

Statistical analysis of elicitation strategies for thiarubrine A production in hairy root cultures of Ambrosia artemisiifolia

Elicitation strategies were studied for yield enhancement of thiarubrine A, a secondary metabolite and a potential pharmaceutical, produced by hairy root cultures of Ambrosia artemisiifolia. Abiotic elicitation was performed using vanadyl sulfate solution and biotic elicitation using autoclaved cell wall filtrates of the fungi Protomyces gravidus, a pathogen of A. artemisiifolia and Botrytis cinereae. The factors considered were age of the culture, concentration of the elicitor used and the time period of exposure or contact. Statistical methods were used to determine the strength of the interaction between the various factors and their response on the yield of the secondary metabolite. The maximum increase in the yield relative to the control, 8-fold corresponding to 569 microg g(-1) of biomass, was observed when 16-day-old cultures were elicited with 50 mg l(-1) of vanadyl sulfate for a time period of 72 h. The maximum yield of 647 microg g(-1) was achieved when the cultures were exposed to 5 microM autoclaved cell wall filtrates of P. gravidus for a time period of 48 h. The yield increase was 3-fold in the case of elicitation with autoclaved cell wall filtrates of B. cinereae. The methodology used in this report can be extended to determine the optimum conditions of other elicitors.

Population balance models of autonomous microbial oscillations

Autonomous oscillations in continuous microbial cultures is well documented for the case of bakers yeast, Saccharomyces cerevisiae, for which it has been observed under a range of operating conditions. We have found that autonomous microbial oscillations can be modeled by unstructured population balance models in which a key cell cycle parameter is a function of the environmental conditions, e.g., the concentration of a substrate or product. Although these models are remarkably simple, they can display a wide range of dynamic behaviors. These behaviors include, for binary fission organisms, solutions containing a single synchronous population and, for budding yeasts, two synchronized subpopulations with a period of oscillation similar to that of the cell cycle length, a pattern that has been observed experimentally in S. cerevisiae. Numerical simulations of the model equations also show that complex periodic solutions with periods very different from the cell cycle length are possible. The ability of the population balance approach to accurately describe the available data of yeast culture dynamics will be discussed.

Coupling pore-scale networks to continuum-scale models of porous media

Network modeling is a useful tool for investigating pore-scale behavior and in some cases for determining macroscopic information such as permeability, relative permeability, and capillary pressure. Physically representative network models are particularly useful because quantitative and predictive results can be obtained. In the past, network models have been used as stand-alone tools for predicting flow behavior at the pore scale. In these cases, simple boundary conditions such as a pressure gradient in one direction are generally imposed on the network. However, with the increasing emphasis on multiscale modeling techniques, the real potential of network models is as a bridge from the pore to the continuum scale. In this context, continuum-scale and pore-scale models are used jointly; pore-scale behavior is upscaled and substituted into a continuum-scale simulator. Methods for integrating these techniques are being developed, and one important question is how to match boundary conditions for the two scales. In this work, physically representative network models created from computer-generated sphere packings are coupled to adjacent continuum-scale models. By coupling the two regions, realistic boundary conditions are enforced, which reflect the heterogeneity of the packed bed as well as the resistance of the adjacent medium. Results of the direct coupling show that both pore-scale phenomena and macroscopic behavior (such as flowrate) are significantly different than when these same parameters are obtained by implementing simple (decoupled) boundary conditions.

Cell population models for bifurcation analysis and nonlinear control of continuous yeast bioreactors

Saccharomyces cerevisiae (bakers yeast) can exhibit sustained oscillations over a wide range of operating conditions when produced in a continuous bioreactor. In this paper the bifurcations leading to these periodic solutions are investigated using an unstructured, segregated model in which the population balance equation (PBE) for the cell mass distribution is coupled to the mass balance of the rate limiting substrate. The PBE model is shown to produce periodic solutions over a range of dilution rates due to the presence of two supercritical Hopf bifurcations. The problem of oscillation attenuation using nonlinear feedback control with four candidate input/output variable pairings is investigated. The controller designs are based on a low dimensional moment representation of the PBE model. The performance of the nonlinear controllers are compared and discussed.

Biosynthetic studies of lactucin derivatives in hairy root cultures of Lactuca floridana

Abstract Biosynthetic studies of the guaianolide-type sesquiterpene lactones 11βH,13-dihydrolactucin-8-O-acetate and 8-desoxylactucin were performed in Agrobacterium rhizogenes—transformed hairy root cultures of blue-flowered lettuce, Lactuca floridana. The 13C NMR spectra of the two guaianolides labelled by incorporation of [1-13C], [2-13C], [1,2-13C2]acetate and [2-13C]mevalolactone showed patterns of enrichment consistent with a previously proposed biogenetic pathway for guaianolide-type sesquiterpene lactones via the acetate-mevalonate-germacradiene route.

Cell Population Modeling and Parameter Estimation for Continuous Cultures of Saccharomyces cerevisiae

Saccharomyces cerevisiae is known to exhibit sustained oscillations in chemostats operated under aerobic and glucose‐limited growth conditions. The oscillations are reflected both in intracellular and extracellular measurements. Our recent work has shown that unstructured cell population balance models are capable of generating sustained oscillations over an experimentally meaningful range of dilution rates. A disadvantage of such unstructured models is that they lack variables that can be compared directly to easily measured extracellular variables. Thus far, most of our work in model development has been aimed at achieving qualitative agreement with experimental data. In this paper, a segregated model with a simple structured description of the extracellular environment is developed and evaluated. The model accounts for the three most important metabolic pathways involved in cell growth with glucose substrate. As compared to completely unstructured models, the major advantage of the proposed model is that predictions of extracellular variables can be compared directly to experimental data. Consequently, the model structure is well suited for the application of estimation techniques aimed at determining unknown model parameters from available extracellular measurements. A steady‐state parameter selection method developed in our group is extended to oscillatory dynamics to determine the parameters that can be estimated most reliably. The chosen parameters are estimated by solving a nonlinear programming problem formulated to minimize the difference between predictions and measurements of the extracellular variables. The efficiency of the parameter estimation scheme is demonstrated using simulated and experimental data.

Dynamics analysis of an age distribution model of oscillating yeast cultures

The ability of an age-population balance model to capture experimentally observed oscillatory dynamics of continuous cultures of budding yeast was investigated through numerical simulations. Experiments with continuous yeast cultures have shown that several oscillatory modes can occur at the same operating condition, and that the mode attained depends on the start-up conditions. Numerical simulations of the model did reveal the existence of several stable periodic solutions. However, each occurred over a di3erent range of dilution rates. Experiments also have shown that the steady state in continuous yeast cultures is stable, even under conditions that allow oscillatory dynamics. The stability of the steady state of the age population balance model under conditions that allow oscillatory dynamics was not resolved. The Jacobian matrix at the steady state is highly ill conditioned, with some eigenvalues very close to the imaginary axis. Using di3erent integration routines to solve the model gave di3erent results with regard to the stability of the steady state, one solver 6nding the steady state to be stable, another 6nding the steady state to be unstable. ? 2002 Elsevier Science Ltd. All rights reserved.

Sesquiterpenes and thiarubrines from Ambrosia trifida and its transformed roots

Abstract The roots of giant ragweed ( Ambrosia trifida ) afforded β-farnesene, β-bisabolene and squalene. In addition, thiarubrine B and its related thiop