On the dangers of adjusting the parameters values of mechanism-based mathematical models.

Mechanism-based mathematical models describe systems in terms of identifiable physical processes, and the parameters are assumed to have fundamental physical significance. Ideally, the parameter values are measured independent of the system being modeled, but these values are often adjusted to give the best fit of model predictions to experimental data. A systematic investigation of the effects of such parameter adjustment was conducted by developing a model system comprising a known reaction mechanism and known rate constants. Simulations of experiments were run, and then attempts were made to model the system under a variety of problematic, but realistic, conditions. (1) When one rate constant was seriously in error, adjustment of a different rate constant gave the greatest improvement in the model fit. (2) When a contaminant was present in the experiment, the effects could be hidden by the adjustment of the rate constants. (3) When an incorrect reaction mechanism was assumed, the error could be hidden by parameter adjustment if the concentrations of only one of the reacting species were considered or if an unweighted fit was used for the optimization. (4) Parameter values adjusted for one set of experimental conditions gave a poorer fit than did the unadjusted parameter values when attempting to model a new set of experimental condition (addition of an inhibitor). These results show the potential dangers of adjusting parameter values and the importance of measuring as many variables as possible in a complex system.

Mathematical model of serine protease inhibition in the tissue factor pathway to thrombin.

A mathematical model has been developed to simulate the generation of thrombin by the tissue factor pathway. The model gives reasonable predictions of published experimental results without the adjustment of any parameter values. The model also accounts explicitly for the effects of serine protease inhibitors on thrombin generation. Simulations to define the optimum affinity profile of an inhibitor in this system indicate that for an inhibitor simultaneously potent against VIIa, IXa, and Xa, inhibition of thrombin generation decreases dramatically as the affinity for thrombin increases. Additional simulations show that the reason for this behavior is the sequestration of the inhibitor by small amounts of thrombin generated early in the reaction. This model is also useful for predicting the potency of compounds that inhibit thrombosis in rats. We believe that this is the first mathematical model of blood coagulation that considers the effects of exogenous inhibitors. Such a model, or extensions thereof, should be useful for evaluating targets for therapeutic intervention in the processes of blood coagulation.

Synthesis of non-translating or translating specialized ribosomes causes feedback regulation of ribosomal RNA synthesis in Escherichia coli.

Specialized ribosomes carry a mutant anti-Shine-Dalgarno region that disrupts the complementary base pairing that stabilizes the translation initiation complex with E. coli mRNAs. It has been reported that production of specialized ribosomes does not cause the inhibition of chromosomal rRNA synthesis that follows production of wild-type ribosomes. We proposed that enabling translation on specialized ribosomes by providing mRNA with a complementary mutation in the Shine-Dalgarno region would restore feedback regulation and inhibit chromosomal rRNA synthesis. With both our system and the system studied previously, we saw feedback regulation regardless of whether the specialized ribosomes were translating. As reported previously, transcription from plasmid-borne promoters decreased as chromosomal rRNA synthesis was repressed, suggesting that the lambda PL and tac promoters may be sensitive to the effector(s) of feedback regulation.

Mathematical model of temperature-sensitive plasmid replication.

The copy number of a series of plasmids constructed at Odense University is regulated by the lambda PR/PRM promoters and the temperature-sensitive cI857 repressor. At low temperatures, these plasmids exhibit the low copy number of the parent plasmid R1 (5-6 per cell). At high temperatures, the plasmids exhibit runaway replication, reaching copy numbers of greater than 1,000 per cell. A detailed mathematical model of the temperature-sensitive replication of these plasmids has been developed incorporating three features: replication of the parent plasmid, regulation of the lambda PR/PRM promoters by the cI repressor, and thermal denaturation of the cI857 repressor. Models of the first two of these features have been described by others. We revised and extended those models, described the thermal denaturation of the cI857 repressor, and integrated these features to give a comprehensive model of temperature-sensitive plasmid replication. Model predictions were compared to experimental measurements of both steady-state copy numbers as a function of temperature and the change in copy number following temperature shifts up and down. The model accurately describes the qualitative behavior of the system and gives reasonable quantitative results. This is particularly significant since all the parameter values used in this model were determined independently: that is, there was no adjustment of parameter values to match our experimental data. The regulatory system that gives rise to the temperature-sensitive replication of these plasmids is widely used in biotechnology applications, so the elements of the model related to this regulation should be applicable to a wide variety of systems.

High-level expression and purification of secreted forms of herpes simplex virus type 1 glycoprotein gD synthesized by baculovirus-infected insect cells.

Two forms of herpes simplex virus glycoprotein gD were recombined into Autographa californica nuclear polyhedrosis virus (baculovirus) and expressed in infected Spodoptera frugiperda (Sf9) cells. Each protein was truncated at residue 306 of mature gD. One form, gD-1(306t), contains the coding sequence of Patton strain herpes simplex virus type 1 gD; the other, gD-1(QAAt), contains three mutations which eliminate all signals for addition of N-linked oligosaccharides. Prior to recombination, each gene was cloned into the baculovirus transfer vector pVT-Bac, which permits insertion of the gene minus its natural signal peptide in frame with the signal peptide of honeybee melittin. As in the case with many other baculovirus transfer vectors, pVT-Bac also contains the promoter for the baculovirus polyhedrin gene and flanking sequences to permit recombination into the polyhedrin site of baculovirus. Each gD gene was engineered to contain codons for five additional histidine residues following histidine at residue 306, to facilitate purification of the secreted protein on nickel-containing resins. Both forms of gD-1 were abundantly expressed and secreted from infected Sf9 cells, reaching a maximum at 96 h postinfection for gD-1(306t) and 72 h postinfection for gD-1(QAAt). Secretion of the latter protein was less efficient than gD-1(306t), possibly because of the absence of N-linked oligosaccharides from gD-1(QAAt). Purification of the two proteins by a combination of immunoaffinity chromatography, nickel-agarose chromatography, and gel filtration yielded products that were > 99% pure, with excellent recovery. We are able to obtain 20 mg of purified gD-1(306t) and 1 to 5 mg of purified gD-1(QAAt) per liter of infected insect cells grown in suspension. Both proteins reacted with monoclonal antibodies to discontinuous epitopes, indicating that they retain native structure. Use of this system for gD expression makes crystallization trials feasible.

Specialized ribosomes in Escherichia coli.

Specialized ribosomes, developed by de Boer and co-workers at Genentech, carry a mutation in the anti-Shine-Dalgarno region of 16 S ribosomal RNA, the site of messenger RNA binding. A complementary mutation in the ribosome binding site (the Shine-Dalgarno region) of a particular messenger RNA results in specific and efficient translation of that messenger RNA on the specialized ribosomes. With this system, a fraction of the cell's ribosomes can be dedicated to the translation of a single messenger RNA; the remaining wild-type ribosomes carry out the normal cellular translation processes. Specialized ribosomes have been used for the overproduction of proteins, analysis of the feedback regulation of ribosomal RNA synthesis, and mutational analysis of 16 S ribosomal RNA. Experimental results related to each of these topics are summarized and discussed, and other potential applications are described. In particular, we propose a novel technique for mutational analysis of 23 S ribosomal RNA, the primary RNA constituent of the large ribosomal subunit, using the specialized ribosome approach.

Construction and characterization of a specialized ribosome system for the overproduction of proteins in Escherichia coli.

A recombinant Escherichia coli system was constructed to overexpress proteins using the specialized ribosomes developed by Herman de Boer and co-workers at Genentech. Specialized ribosomes carry a mutation in the anti-Shine-Dalgarno region of 16 S ribosomal RNA, which is the site of messenger RNA binding. A complementary mutation in the ribosome binding site (the Shine-Dalgarno region) of a particular mRNA results in specific and efficient translation of this mRNA on the specialized ribosomes. Production of beta-galactosidase with this system was characterized with respect to transcription, translation, plasmid replication, and cell growth rate. Translation of specialized mRNA on specialized ribosomes gave 5 times more enzyme activity than did translation of wild-type mRNA on wild-type ribosomes under similar conditions. The system described here offers a number of advantages when compared to a similar system described recently: (1) two separate specialized systems were constructed; (ii) the genes for specialized mRNA and specialized rRNA are on separate plasmids, allowing for different combinations of mRNA and rRNA; and (iii) appropriate controls were constructed for each plasmid.