A mathematical approach to molecular organization and proteolytic disintegration of bacterial inclusion bodies.

The in vivo proteolytic digestion of bacterial inclusion bodies (IBs) and the kinetic analysis of the resulting protein fragments is an interesting approach to investigate the molecular organization of these unconventional protein aggregates. In this work, we describe a set of mathematical instruments useful for such analysis and interpretation of observed data. These methods combine numerical estimation of digestion rate and approximation of its high-order derivatives, modelling of fragmentation events from a mixture of Poisson processes associated with differentiated protein species, differential equations techniques in order to estimate the mixture parameters, an iterative predictor-corrector algorithm for describing the flow diagram along the cascade process, as well as least squares procedures with minimum variance estimates. The models are formulated and compared with data, and successively refined to better match experimental observations. By applying such procedures as well as newer improved algorithms of formerly developed equations, it has been possible to model, for two kinds of bacterially produced aggregation prone recombinant proteins, their cascade digestion process that has revealed intriguing features of the IB-forming polypeptides.

In situ proteolytic digestion of inclusion body polypeptides occurs as a cascade process.

Misfolded proteins undergo a preferent degradation ruled by the housekeeping bacterial proteolytic system, but upon precipitation as inclusion bodies their stability dramatically increases. The susceptibility of aggregated polypeptides to proteolytic attack remains essentially unexplored in bacteria and also in eukaryotic cells. We have studied here the in vitro proteolysis of beta-galactosidase fusion proteins by trypsin treatment of purified inclusion bodies. A cascade digestion process similar to that occurring in vivo has been observed in the insoluble fraction of the digestion reaction. This suggests that major protease target sites are not either lost or newly generated by protein precipitation and that the digestion occurs in situ probably on solvent-exposed surfaces of inclusion bodies. In addition, the sequence of the proteolytic attack is influenced by protein determinants other than amino acid sequence, the early digestion steps having a dramatic influence on the further cleavage susceptibility of the intermediate degradation fragments. These observations indicate unexpected conformational changes of inclusion body proteins during their site-limited digestion, that could promote protein release from aggregates, thus partially accounting for the plasticity of in vivo protein precipitation and solubilization in bacteria.

Cell lysis in Escherichia coli cultures stimulates growth and biosynthesis of recombinant proteins in surviving cells.

Cell growth and production of recombinant proteins in stationary phase cultures of Escherichia coli recover concomitantly with spontaneous lysis of a fraction of the ageing cell population. Further exploration of this event has indicated that sonic cell disruption stimulates both cell growth and synthesis of plasmid-encoded recombinant proteins, even in exponentially growing cultures. These observations indicate an efficient cell utilisation of released intracellular material and also that this capability is not restricted to extreme nutrient-starving conditions. In addition, the efficient re-conversion of waste cell material can be viewed as a potential strategy for an extreme exploitation of carbon sources and cell metabolites in production processes of both recombinant and non-recombinant microbial products.

Fine architecture of bacterial inclusion bodies.

The molecular organisation of protein aggregates, formed under physiological conditions, has been explored by in vitro trypsin treatment and electron microscopy analysis of bacterially produced inclusion bodies (IBs). The kinetic modelling of protein digestion has revealed variable proteolysis rates during protease exposure that are not compatible with a surface-restricted erosion of body particles but with a hyper-surfaced disintegration by selective enzymatic attack. In addition, differently resistant species of the IB proteins coexist within the particles, with half-lives that differ among them up to 50-fold. During in vivo protein incorporation throughout IB growth, a progressive increase of proteolytic resistance in all these species is observed, indicative of folding transitions and dynamic reorganisations of the body structure. Both the heterogeneity of the folding state and the time-dependent folding transitions undergone by the aggregated polypeptides indicate that IBs are not mere deposits of collapsed, inert molecules but plastic reservoirs of misfolded proteins that would allow, at least up to a certain extent, their in vivo recovery and transference to the soluble cell fraction.

Numerical techniques and mathematical modelling for CI857-controlled gene expression and cell growth in recombinant E. coli.

Recombinant gene expression, monitored by beta-galactosidase activity, is studied in a pL, pR-CI857 plasmid expression system in temperature-induced E. coli batch cultures. The experimental procedure has been mathematically modelled, and the corresponding parameters are estimated from specific statistical and numerical methods, basically by using a global least-squares procedure under some constraints induced by the model. The numerical techniques proposed in this work act by accumulation of data coming from several runs of the modelled experiment, so that more accuracy is obtained in the parameter estimation. In particular, for the production process, an extra-model parameter depending on an indicator vector is introduced for each run of the experiment in order to globalize the data. The analysis of the data obtained leads to an integrated model for both cell growth and gene expression, which describes an asymmetric dynamics between culture growth and recombinant protein yield, and can serve to predict the maximal value of accumulated gene expression and the time required for it to be achieved at any age of the preinducing cell growth.

Optimized release of recombinant proteins by ultrasonication of E. coli cells.

The release kinetics of beta-galactosidase protein have been determined during small-scale ultrasonication of E. coli cells. Among several studied parameters, ionic strength and cell concentration have the least influence on the rate of protein recovery, whereas sample volume and acoustic power dramatically affect the final yield of soluble protein in the cell-free fraction. The analysis of these critical parameters has prompted us to propose a simple model for E. coli disintegration that only involves acoustic power and sample volume, and which allows prediction of optimal sonication times to recover significant amounts of both natural and recombinant proteins in a given set of relevant conditions.

Limited in vivo proteolysis of aggregated proteins.

Degradation pathways of insoluble proteins have been analyzed in Escherichia coli by using a N-terminal beta-galactosidase fusion protein (VP1LAC) that aggregates immediately after its synthesis. In recombinant E. coli cells, lower molecular mass products, antigenically related to the entire fusion, accumulate together with the entire fusion. In absence of protein synthesis, the insoluble intact protein declines, suggesting that degradation of the recombinant protein also affects aggregated protein. Time course analysis of both soluble and insoluble cell fractions has revealed a limited proteolysis of the insoluble protein that removes the heterologous domain and permits the resulting beta-galactosidase fragments to refold and solubilize. Further extensive degradation occurs exclusively on soluble protein. The restricted proteolysis of misfolded, insoluble protein is the initiating event of a subsequent degradative pathway in which rate-limiting steps permit the accumulation of stable degradative intermediates.

Fine regulation of cI857-controlled gene expression in continuous culture of recombinant Escherichia coli by temperature.

The expression at different temperatures of the lacZ gene, which is controlled by the lambda pL and pR tandem promoters and the cI857 temperature-sensitive repressor, was studied in Escherichia coli continuous cultures. At temperatures between 30 and 42 degrees C, beta-galactosidase activity behaved according to an exponential equation. By inducing a culture at a temperature within this range, predefined, nearly constant submaximal levels of gene expression and recombinant product yield can be obtained.