Investigation of subpopulation heterogeneity and plasmid stability in recombinant escherichia coli via a simple segregated model

Investigation of the robustness of Cupriavidus necator engineered strains during fed-batch cultures

It is of major interest to ensure stable and performant microbial bioprocesses, therefore maintaining high strain robustness is one of the major future challenges in industrial microbiology. Strain robustness can be defined as the persistence of genotypic and/or phenotypic traits in a system. In this work, robustness of an engineered strain is defined as plasmid expression stability, cultivability, membrane integrity and macroscopic cell behavior and was assessed in response to implementations of sugar feeding strategies (pulses and continuous) and two plasmid stabilization systems (kanamycin resistance and Post-Segregational Killing hok/sok). Fed-batch bioreactor cultures, relevant mode to reach high cell densities and higher cell generation number, were implemented to investigate the robustness of C. necator engineered strains. Host cells bore a recombinant plasmid encoding for a plasmid expression level monitoring system, based on eGFP fluorescence quantified by flow cytometry. We first showed that well-controlled continuous feeding in comparison to a pulse-based feeding allowed a better carbon use for protein synthesis (avoiding organic acid excretion), a lower heterogeneity of the plasmid expression and a lower cell permeabilization. Moreover, the plasmid stabilization system Post-Segregational Killing hok/sok, an autonomous system independent on external addition of compounds, showed the best ability to maintain plasmid expression level stability insuring a greater population homogeneity in the culture. Therefore, in the case of engineered C. necator, the PSK system hok/sok appears to be a relevant and an efficient alternative to antibiotic resistance system for selection pressure, especially, in the case of bioprocess development for economic and environmental reasons.

Plasmid expression level heterogeneity monitoring via heterologous eGFP production at the single-cell level in Cupriavidus necator

A methodology for plasmid expression level monitoring of eGFP expression suitable for dynamic processes was assessed during fermentation. This technique was based on the expression of a fluorescent biosensor (eGFP) encoded on a recombinant plasmid coupled to single-cell analysis. Fluorescence intensity at single-cell level was measured by flow cytometry. We demonstrated that promoter evaluation based on single-cell analysis versus classic global analysis brings valuable insights. Single-cell analysis pointed out the fact that intrinsic fluorescence increased with the strength of the promoter up to a threshold. Beyond that, cell permeability increases to excrete the fluorescent protein in the medium. The metabolic load due to the increase in the eGFP production in the case of strong constitutive promoters leads to slower growth kinetics compared with plasmid-free cells. With the strain Cupriavidus necator Re2133, growth rate losses were measured from 3% with the weak constitutive promoter P_lac to 56% with the strong constitutive promoter P_j5. Through this work, it seems crucial to find a compromise between the fluorescence intensity in single cells and the metabolic load; in our conditions, the best compromise found was the weak promoter P_lac. The plasmid expression level monitoring method was tested in the presence of a heterogeneous population induced by plasmid-curing methods. For all the identified subpopulations, the plasmid expression level heterogeneity was significantly detected at the level of fluorescence intensity in single cells. After cell sorting, growth rate and cultivability were assessed for each subpopulation. In conclusion, this eGFP biosensor makes it possible to follow the variations in the level of plasmid expression under conditions of population heterogeneity.Key Points•Development of a plasmid expression level monitoring method at the single-cell level by flow cytometry.•Promoter evaluation by single-cell analysis: cell heterogeneity and strain robustness.•Reporter system optimization for efficient subpopulation detection in pure cultures.

Evolutionary model for the unequal segregation of high copy plasmids

Plasmids are extrachromosomal DNA elements of microorganisms encoding beneficial genetic information. They were thought to be equally distributed to daughter cells during cell division. Here we use mathematical modeling to investigate the evolutionary stability of plasmid segregation for high-copy plasmids—plasmids that are present in up to several hundred copies per cell—carrying antibiotic resistance genes. Evolutionary stable strategies (ESS) are determined by numerical analysis of a plasmid-load structured population model. The theory predicts that the evolutionary stable segregation strategy of a cell depends on the plasmid copy number: For low and medium plasmid load, both daughters receive in average an equal share of plasmids, while in case of high plasmid load, one daughter obtains distinctively and systematically more plasmids. These findings are in good agreement with recent experimental results. We discuss the interpretation and practical consequences.

In the last years, it becomes more and more clear that heterogeneity in isogenic bacterial populations is rather the rule than the exception. This observation is interesting as it reveals the complex social life of bacteria, and also because of tremendous practical implications in medicine, biotechnology, and ecology. The central questions in this field are the identification of the underlying proximate causes (molecular mechanisms) on the one hand and on the other hand the identification of ultimate causes (evolutionary forces) that shape the social life of bacteria. We focus on plasmid dynamics, in particular on plasmid segregation. Recent experiments showed that plasmid segregation depends on the plasmid load. We identify possible evolutionary factors that shaped this process. It turns out that the ambivalence in the effect of plasmids—advantageous if present in low copy numbers, a metabolic burden if present in high copy numbers—is able to explain the experimental observations. The experimental findings can be interpreted as a variant of the principle of division of labor, as it is well known from e.g. persister cells or sporulation. Our model extends the theory of unequal segregation of damage to the ambivalent role of plasmids. Similarly, it is known that certain gene regulatory proteins are acting in a dose-dependent manner. Due to differences in their cellular concentrations and in their affinities to various target promoters, differential gene expression patterns are achieved. Consequently, tight concentration control is observed [1]. Another example is the strict copy-dependent utilization of autolysins during cell division. These enzymes carefully open the bacterial cell wall to allow for its extension [2]. Overproduction of these enzymes leads to cell lysis [3]. These molecules are in principle also candidates for a segregation characteristic similar to that of high copy plasmids described here.

Eigensolutions and spectral analysis of a model for vertical gene transfer of plasmids

Plasmids are autonomously replicating genetic elements in bacteria. At cell division, plasmids are distributed among the two daughter cells. This gene transfer from one generation to the next is called vertical gene transfer. We study the dynamics of a bacterial population carrying plasmids and are in particular interested in the long-time distribution of plasmids. Starting with a model for a bacterial population structured by the discrete number of plasmids, we proceed to the continuum limit in order to derive a continuous model. The model incorporates plasmid reproduction, division and death of bacteria, and distribution of plasmids at cell division. It is a hyperbolic integro-differential equation and a so-called growth-fragmentation-death model. As we are interested in the long-time distribution of plasmids we study the associated eigenproblem and show existence of eigensolutions. The stability of this solution is studied by analyzing the spectrum of the integro-differential operator given by the eigenproblem. By relating the spectrum with the spectrum of an integral operator we find a simple real dominating eigenvalue with a non-negative corresponding eigenfunction. Moreover, we describe an iterative method for the numerical construction of the eigenfunction.

Serine integrase recombinational engineering (SIRE): A versatile toolbox for genome editing

Chromosomal integration of biosynthetic pathways for the biotechnological production of high-value chemicals is a necessity to develop industrial strains with a high long-term stability and a low production variability. However, the introduction of multiple transcription units into the microbial genome remains a difficult task. Despite recent advances, current methodologies are either laborious or efficiencies highly fluctuate depending on the length and the type of the construct. Here we present serine integrase recombinational engineering (SIRE), a novel methodology which combines the ease of recombinase-mediated cassette exchange (RMCE) with the selectivity of orthogonal att sites of the PhiC31 integrase. As a proof of concept, this toolbox is developed for Escherichia coli. Using SIRE we were able to introduce a 10.3 kb biosynthetic gene cluster on different locations throughout the genome with an efficiency of 100% for the integrating step and without the need for selection markers on the knock-in cassette. Next to integrating large fragments, the option for multitargeting, for deleting operons, as well as for performing in vivo assemblies further expand and proof the versatility of the SIRE toolbox for E. coli. Finally, the serine integrase PhiC31 was also applied in the yeast Saccharomyces cerevisiae as a marker recovery tool, indicating the potential and portability of this toolbox.

Synthetic auxotrophs for stable and tunable maintenance of plasmid copy number

Although plasmid-based expression systems have advantages in multi-copy expression of genes, heterogeneity of plasmid copy number (PCN) in individual cells is inevitable even with the addition of antibiotics. Here, we developed a synthetic auxotrophic system for stable and tunable maintenance of the PCN in Escherichia coli without addition of antibiotics. This auxotroph expresses infA, one of the essential genes encoding a translation initiation factor, on a plasmid instead of on the chromosome. With this system, the gene expression was stably maintained for 40 generations with minimized cell-to-cell variation under antibiotic-free conditions. Moreover, varying the expression level of infA enabled us to rationally tune the PCN by more than 5.6-fold. This antibiotic-free PCN control system significantly improved the production of itaconic acid and lycopene compared to the conventional system based on antibiotics (2-fold). Collectively, the developed strategy could be a platform for the production of value-added products in antibiotic-free cultivation.

Diverse genetic error modes constrain large-scale bio-based production

A transition toward sustainable bio-based chemical production is important for green growth. However, productivity and yield frequently decrease as large-scale microbial fermentation progresses, commonly ascribed to phenotypic variation. Yet, given the high metabolic burden and toxicities, evolutionary processes may also constrain bio-based production. We experimentally simulate large-scale fermentation with mevalonic acid-producing Escherichia coli. By tracking growth rate and production, we uncover how populations fully sacrifice production to gain fitness within 70 generations. Using ultra-deep (>1000×) time-lapse sequencing of the pathway populations, we identify multiple recurring intra-pathway genetic error modes. This genetic heterogeneity is only detected using deep-sequencing and new population-level bioinformatics, suggesting that the problem is underestimated. A quantitative model explains the population dynamics based on enrichment of spontaneous mutant cells. We validate our model by tuning production load and escape rate of the production host and apply multiple orthogonal strategies for postponing genetically driven production declines.

The declining performance of scale-up bioreactor cultures is commonly attributed to phenotypic and physical heterogeneities. Here, the authors reveal multiple recurring intra-pathway error modes that limit engineered E. coli mevalonic acid production over time- and industrial-scale fermentations.

Plasmid stability analysis based on a new theoretical model employing stochastic simulations

Here, we present a simple theoretical model to study plasmid stability, based on one input parameter which is the copy number of plasmids present in a host cell. The Monte Carlo approach was used to analyze random fluctuations affecting plasmid replication and segregation leading to gradual reduction in the plasmid population within the host cell. This model was employed to investigate maintenance of pEC156 derivatives, a high-copy number ColE1-type Escherichia coli plasmid that carries an EcoVIII restriction-modification system. Plasmid stability was examined in selected Escherichia coli strains (MG1655, wild-type; MG1655 pcnB, and hyper-recombinogenic JC8679 sbcA). We have compared the experimental data concerning plasmid maintenance with the simulations and found that the theoretical stability patterns exhibited an excellent agreement with those empirically tested. In our simulations, we have investigated the influence of replication fails (α parameter) and uneven partition as a consequence of multimer resolution fails (δ parameter), and the post-segregation killing factor (β parameter). All of these factors act at the same time and affect plasmid inheritance at different levels. In case of pEC156-derivatives we concluded that multimerization is a major determinant of plasmid stability. Our data indicate that even small changes in the fidelity of segregation can have serious effects on plasmid stability. Use of the proposed mathematical model can provide a valuable description of plasmid maintenance, as well as enable prediction of the probability of the plasmid loss.

Design and Assembly of DNA Sequence Libraries for Chromosomal Insertion in Bacteria Based on a Set of Modified MoClo Vectors

Efficient assembly of large DNA constructs is a key technology in synthetic biology. One of the most popular assembly systems is the MoClo standard in which restriction and ligation of multiple fragments occurs in a one-pot reaction. The system is based on a smart vector design and type IIs restriction enzymes, which cut outside their recognition site. While the initial MoClo vectors had been developed for the assembly of multiple transcription units of plants, some derivatives of the vectors have been developed over the last years. Here we present a new set of MoClo vectors for the assembly of fragment libraries and insertion of constructs into bacterial chromosomes. The vectors are accompanied by a computer program that generates a degenerate synthetic DNA sequence that excludes "forbidden" DNA motifs. We demonstrate the usability of the new approach by construction of a stable fluorescence repressor operator system (FROS).

Variability in subpopulation formation propagates into biocatalytic variability of engineered Pseudomonas putida strains

Pivotal challenges in industrial biotechnology are the identification and overcoming of cell-to-cell heterogeneity in microbial processes. While the development of subpopulations of isogenic cells in bioprocesses is well described (intra-population variability), a possible variability between genetically identical cultures growing under macroscopically identical conditions (clonal variability) is not. A high such clonal variability has been found for the recombinant expression of the styrene monooxygenase genes styAB from Pseudomonas taiwanensis VLB120 in solvent-tolerant Pseudomonas putida DOT-T1E using the alk-regulatory system from P. putida GPo1. In this study, the oxygenase subunit StyA fused to eGFP was used as readout tool to characterize the population structure in P. putida DOT-T1E regarding recombinant protein content. Flow cytometric analyses revealed that in individual cultures, at least two subpopulations with highly differing recombinant StyA-eGFP protein contents appeared (intra-population variability). Interestingly, subpopulation sizes varied from culture-to-culture correlating with the specific styrene epoxidation activity of cells derived from respective cultures (clonal variability). In addition, flow cytometric cell sorting coupled to plasmid copy number (PCN) determination revealed that detected clonal variations cannot be correlated to the PCN, but depend on the combination of the regulatory system and the host strain employed. This is, to the best of our knowledge, the first work reporting that intra-population variability (with differing protein contents in the presented case study) causes clonal variability of genetically identical cultures. Respective impacts on bioprocess reliability and performance and strategies to overcome respective reliability issues are discussed.

A reduced genome decreases the host carrying capacity for foreign DNA

Background

Host-plasmid interactions have been discussed largely in terms of the influences of plasmids, whereas the contributions of variations in host genomes to host interactions with foreign DNA remain unclear. A strain with a so-called “clean genome” (i.e., MDS42) of reduced genome size has recently been generated from the wild-type strain MG1655, a commonly used host strain. A quantitative evaluation of the influence of plasmid burdens in these two Escherichia coli strains can not only provide an understanding of how a reduced genome responds to foreign DNA but also offer insights into the proper application of these strains.

Results

The decreases in growth caused by the cost of carrying foreign DNA were similar for the wild-type and clean-genome strains. A negative correlation between the growth rate and the total amount of exogenous DNA was observed in both strains, but a better theoretical fit with a higher statistical significance was found for the strain with the clean genome. Compared to the wild-type strain, the clean-genome strain exhibited a reduced carrying capacity for exogenous DNA, which was largely attributed to its ability to restrict the replication of foreign DNA. A tendency to allocate energy and resources toward gene expression, but not DNA replication, was observed in the strain with the clean genome.

Conclusions

The possession of a clean genome constrained the plasmid copy number to a wild-type-equivalent load. The results indicate that the wild-type strain possesses a greater tolerance for foreign DNA, as in endosymbiosis, and that the use of strains with clean genomes will be favorable in the applications that require precise control and theoretical prediction.

Implementation of stable and complex biological systems through recombinase-assisted genome engineering

Evaluating the performance of engineered biological systems with high accuracy and precision is nearly impossible with the use of plasmids due to phenotypic noise generated by genetic instability and natural population dynamics. Minimizing this uncertainty therefore requires a paradigm shift towards engineering at the genomic level. Here, we introduce an advanced design principle for the stable installment and implementation of complex biological systems through recombinase-assisted genome engineering (RAGE). We apply this concept to the development of a robust strain of Escherichia coli capable of producing ethanol directly from brown macroalgae. RAGE significantly expedites the optimal implementation of a 34 kb heterologous pathway for alginate metabolism based on genetic background, integration locus, copy number and compatibility with two other pathway modules (alginate degradation and ethanol production). The resulting strain achieves a ~40% higher titre than its plasmid-based counterpart and enables substantial improvements in titre (~330%) and productivity (~1,200%) after 50 generations.

A Monte Carlo simulation of plasmid replication during the bacterial division cycle

Plasmids have cell cycle replication patterns that need to be considered in models of their replication dynamics. To compare current theories for control of plasmid replication with experimental data for timing of plasmid replication with the cell cycle, a Monte Carlo simulation of plasmid replication and partition was developed. High-copy plasmid replication was simulated by incorporating equations previously developed from the known molecular biology of ColE1-type plasmids into the cell-cycle simulation. Two types of molecular mechanisms for low-copy plasmid replication were tested: accumulation of an initiator protein in proportion to cell mass and binding of the plasmid origin to the cell membrane. The low-copy plasmids were partitioned actively, with a specific mechanism to mediate the transfer from mother to daughter cells, whereas the high-copy plasmids were partitioned passively with cell mass.The simulation results and experimental data demonstrate cell-cycle-specific replication for the low-copy F plasmid and cell-cycle-independent replication for the high-copy pBR322, ColBM, and R6K plasmids. The simulation results indicate that synchronous replication at multiple plasmid origins is critical for the cell-cycle-specific pattern observed in rapidly growing cells. Variability in the synchrony of initiation of multiple plasmid origins give rise to a cell-cycle-independent pattern and is offered as a plausible explanation for the controversy surrounding the replication pattern of the low-copy plasmids. A comparison of experimental data and simulation results for the low-copy F plasmid at several growth rates indicates that either initiation mechanism would be sufficient to explain the timing of replication with the cell cycle. The simulation results also demonstrate that, although cell-cycle-specific and cell-cycle independent replication patterns give rise to very different gene-expression patterns during short induction periods in age-selected populations, long-term expression of genes encoded on low-copy and high-copy plasmids in exponentially growing cells have nearly the same patterns. These results may be important for the future use of low-copy plasmids as expression vectors and validate the use of simpler models for high-copy plasmids that do not consider cell-cycle phenomena. (c) 1996 John Wiley & Sons, Inc.

Production of recombinant proteins in E. coli by the heat inducible expression system based on the phage lambda pL and/or pR promoters

The temperature inducible expression system, based on the pL and/or pR phage lambda promoters regulated by the thermolabile cI857 repressor has been widely use to produce recombinant proteins in prokaryotic cells. In this expression system, induction of heterologous protein is achieved by increasing the culture temperature, generally above 37 degrees C. Concomitant to the overexpression of heterologous protein, the increase in temperature also causes a variety of complex stress responses. Many studies have reported the use of such temperature inducible expression system, however only few discuss the simultaneous stress effects caused by recombinant protein production and the up-shift in temperature. Understanding the integral effect of such responses should be useful to develop improved strategies for high yield protein production and recovery. Here, we describe the current status of the heat inducible expression system based on the pL and/or pR lambda phage promoters, focusing on recent developments on expression vehicles, the stress responses at the molecular and physiological level that occur after heat induction, and bioprocessing factors that affect protein overexpression, including culture operation variables and induction strategies.

Estimating the instability parameters of plasmid-bearing cells. I. Chemostat culture

What determines the stability of plasmid-bearing cells in natural and laboratory conditions? In order to answer this question in a quantitative manner, we need tools allowing the estimation of parameters governing plasmid loss in different environments. In the present work, we have developed two methods for the estimation of the instability parameters of plasmid-bearing cells growing in chemostat. These instability parameters are: (i) selection coefficient (or cost of the plasmid)alpha and (ii) the probability of plasmid loss at cell division tau(0). We have found that generally selection coefficient alpha changes during elimination of plasmid-bearing cells due to changes in substrate concentration; hence, methods which assume constancy of alpha are intrinsically imprecise. Instead, one can estimate selection coefficient at the beginning and the end of cultivation when the substrate concentration is approximately constant. Applying developed techniques to two sets of experimental data, we have found that (i) the cost of the plasmid pBR322 depended on the dilution rate in chemostat and was higher at low dilutions; (ii) high levels of plasmid gene expression led to a high cost of the plasmid pPHL-7; (iii) the probability of plasmid loss was lower at high levels of plasmid gene expression and independent of the dilution rate. We have also discussed the application of our results to understanding the basic biology of bacterial plasmids.

Microbial metabolism as an evolutionary response: the cybernetic approach to modeling

The growth and metabolic capabilities of microorganisms depend on their interactions with the culture medium. Many media contain two or more key substrates, and an organism may have different preferences for the components. Microorganisms adjust their preferences according to the prevailing conditions so as to favor their own survival. Cybernetic modeling describes this evolutionary strategy by defining a goal that an organism tries to attain optimally at all times. The goal is often, but not always, maximization of growth, and it may require the cells to manipulate their metabolic processes in response to changing environmental conditions. The cybernetic approach overcomes some of the limitations of metabolic control analysis (MCA), but it does not substitute MCA. Here we review the development of the cybernetic modeling of microbial metabolism, how it may be combined with MCA, and what improvements are needed to make it a viable technique for industrial fermentation processes.

Stochastic kinetic analysis of the Escherichia coli stress circuit using sigma(32)-targeted antisense

A stochastic Petri net model was developed for simulating the sigma(32) stress circuit in E. coli. Transcription factor sigma(32) is the principal regulator of the response of E. coli to heat shock. Stochastic Petri net (SPN) models are well suited for kinetics characterization of fluxes in biochemical pathways. Notably, there exists a one-to-one mapping of model tokens and places to molecules of particular species. Our model was validated against experiments in which ethanol (inducer of heat shock response) and sigma(32)-targeted antisense (downward regulator) were used to perturb the sigma(32) regulatory pathway. The model was also extended to simulate the effects of recombinant protein production. Results show that the stress response depends heavily on the partitioning of sigma(32) within the cell; that is, sigma(32) becomes immediately available to mediate a stress response because it exists primarily in a sequestered, inactive form, complexed with chaperones DnaK, DnaJ, and GrpE. Recombinant proteins, however, also compete for chaperone proteins, particularly when folded improperly. Our simulations indicate that when the expression of recombinant protein has a low requirement for DnaK, DnaJ, and GrpE, the overall sigma(32) levels may drop, but the level of heat shock proteins will increase. Conversely, when the overexpressed recombinant protein has a strong requirement for the chaperones, a severe response is predicted. Interestingly, both cases were observed experimentally.

Effect of the growth conditions on the synthesis of a recombinant beta-1,4-endoglucanase in continuous and fed-batch culture

Continuous culture and fed-batch fermentations were used to test the behavior of the system Bacillus subtilis DN1885(pCH7) that synthesizes a recombinant beta-1,4-endoglucanase. Continuous culture experiments were focused on the study of the instability aspects of the system as well as determination of the biomass growth rate range at which the recombinant enzyme synthesis was improved. Fed-batch fermentations were carried out to study the possibility of enhancing recombinant enzyme synthesis through the control of medium addition. It was found that, in continuous culture fermentations, the culture is less unstable at low dilution rates (dilution rate < 0.1 h(-)(1)). Also, low dilution rates give a higher specific recombinant enzyme concentration (10 times more than that obtained at high dilution rates). In fed-batch fermentation, the final recombinant enzyme concentration can be manipulated through the medium addition strategy. To increase the recombinant enzyme concentration, the carbon source has to be fed slowly, otherwise enzyme synthesis is impaired due to catabolite repression. Therefore, an increase in the biomass concentration does not necessarily imply an increase in the recombinant enzyme concentration. Higher recombinant enzyme concentrations were found in fed-batch fermentations compared to those obtained in continuous culture.

Optimizing initial plasmid copy number distribution for improved protein activity in a recombinant fermentation

Recombinant bacterial cells in a fermentation broth rarely contain the same number of plasmids, even though this simplification is often used. Recent work has however indicated limitations of the simplified approach. Based on these studies, the distribution of plasmid copy numbers per cell has been represented macroscopically here in a Gaussian form for the fraction of biomass as a function of the copy number. Applying this distribution and an experimentally validated kinetic model to glyceraldehyde-3-phosphate dehydrogenase (GAPDH) synthesis by Escherichia coli containing the plasmid pBR Eco gap, it is seen that GAPDH production in a batch fermentation is maximized by a particular initial (non-zero) copy number variance and an optimal duration. To implement this distribution in a bioreactor, it is suggested that the profile may be discretized, inocula corresponding to the mean copy number of each fraction prepared, and then combined to obtain the seed culture.

Characterization of stress and protein turnover from protein overexpression in fed-batch E. coli cultures

A structured kinetic model that accounts for proteolytic degradation due to recombinant protein overexpression is introduced and its performance evaluated by comparison with previously reported fed-batch experimental data. This mathematical model contains an additional pool for a generic key precursor (in our case phenylalanine), an improved IPTG transport term, a phenylalanine transport term, and a variable protein turnover expression that accounts for proteolytic activity. The model predictions concerning proteolytic activity, glucose level, and cell growth are in very good agreement with an amino acid depletion hypothesis. Cultures exposed to greater stress showed higher and/or longer proteolysis, whereas less overall proteolytic activity was observed when the effect of induction was somewhat ameliorated.

Optimization for a recombinant E. coli fed-batch fermentation

The operating strategy that produces the maximum foreign protein expression for a fed-batch process is desired. This is achieved by using a feasible quadratic programming (FSQP) algorithm with a structured model that describes cell growth and product formation for recombinant E. coli. Optimization calculations for a fed-batch culture have not been performed with a model of this complexity up to this point. A constraint on the maximum cell concentration was included. For a fixed value of batch time, the results show that the optimal time profile of feed flow rate can increase the yield of foreign protein by 12-29% over a constant feed rate policy. Also, it was found that the computation time for the FSQP algorithm can be reduced significantly by considering suboptimal profiles of the feed rate, with a minor effect on calculated protein yield.