MATLAB implementation of the model and sensitivity analysis
The implementation of the model was done in MATLAB (additional file 1: MATLAB implementation of the kinetic model), and in its framework it is based on the work by Bibila et al. [22, 32]. The model is formulated as set of ordinary differential equations, which are then solved over time using an ODE solver. For our secretion model we used an implicit linear multistep solver (MATLAB ode15s), because it is more appropriate for chemical or biochemical problems than an explicit Runge-Kutta pair solver .
To evaluate the behavior of the model concerning the input parameters, namely degradation, secretion and intracellular protein formation, always two of these parameters were varied against each other. The values were then plotted against the extracellular Fab3H6 concentrations in a three dimensional representation. The three dimensional plots were created using the MATLAB functions meshgrid and surf (additional file 2: Sensitivity analysis of the kinetic parameters).
The P. pastoris strain X-33 used in this study expressed the antibody fragment Fab3H6, previously described by Baumann et al.  and Dragosits et al. . Both antibody chains are under the control of the constitutive GAP-promoter and are secreted via the Saccharomyes cerevisiae α-mating factor secretion signal. Fab3H6 is the anti-idiotypic antibody of the HIV neutralizing antibody 2F5. It has a molecular weight of 47.38 kDa and has 16 sulfur containing amino acids, 11 cysteines and 5 methionines [35, 36].
A preculture was incubated at 28°C for 24 h and 180 rpm on YPG (per liter: 10 g yeast extract, 20 g peptone, 10 g glycerol). The culture was harvested by centrifugation, resuspended in 50 ml sterile batch medium and used to inoculate 1.0 L batch medium in the bioreactor (Minifors, Infors, Switzerland) to a starting optical density (OD600) of 1.0.
After a batch phase of approximately 24 hours the continuous culture was started at a dilution rate of D = 0.1 h-1 with a corresponding feed medium and harvest flow rate of 100 g h-1. Cultivation conditions were controlled constantly, the temperature at 25°C, pH at 5.0 with 25% ammonium hydroxide and pO2 at 20% by controlling the stirrer speed between 600 and 1200 rpm. Air flow was kept constant at 1.5 vvm (volume gas per volume medium and minute).
The batch medium contained per liter: 40 g glycerol, 2.0 g citric acid, 12.6 g (NH)2HPO4, 0.5 g MgSO4 • 7 H2O, 0.9 g KCl, 0.022 g CaCl2 • 2 H2O, 2 ml biotin stock solution (0.2 g L-1) and 4.6 ml PTM1 trace salt stock solution. The pH was set to 5.0 with 25% HCl. The PTM1 trace salt stock solution contained per liter: 65.0 g FeSO4 • 7 H2O, 20.0 g ZnCl2, 6.0 g CuSO4 • 5 H2O, 3.36 g MnSO4 • 1 H2O, 0.82 g CoCl2 • 6 H2O, 0.2 g Na2MoO4 • 2 H2O, 0.08 g NaI, 0.02 g H3BO3 and 5 ml H2SO4 (95 - 98%).
In the chemostat medium sodium sulfate was used as the only sulfur source. Per liter this medium contained 1.0 g citric acid monohydrate, 55 g glucose • 1 H2O, 9.83 g (NH4)2HPO4, 0.41 g MgCl2 • 6 H2O, 0.29 g Na2SO4, 1.7 g KCl, 0.01 g CaCl2 • 2 H2O, 2.0 ml biotin stock solution (0.2 g L-1) and 1.6 g PTM2 trace salt stock solution. The trace salt stock solution PTM2 contained (per liter): 63.3 g FeCl2 • 6 H2O, 20.0 g ZnCl2, 5.77 g CuCl2 2H2O, 3.94 g MnCl2 • 4 H2O, 0.82 g CoCl2 • 6 H2O, 0.2 g Na2MoO4 • 2 H2O, 0.08 g NaI, 0.02 g H3BO3 and 5 ml HCl (32%).
For the continuous labeling enriched 34S sodium sulfate (isotopic distribution: < 0.1% 32S, 1.1% 33S, 98.8% 34S and < 0.05% 36S) from Isoflex USA was used in the chemostat medium.
Cells were grown for at least 5 resident times in chemostat to ensure steady state conditions. Continuous 34S labeling was started by changing the feed to the 34S enriched medium. In addition, at the same time, a labeled sodium sulfate pulse, 5 mL sterile solution containing in total 600 mg of 34S-labeled sodium sulfate, was administered into the bioreactor. The change in the 32S to 34S ratio of the intra- and extracellular Fab3H6 was followed for 8 hours.
Samples were taken to determine the yeast cell dry mass, the extra- and intracellular Fab3H6 concentration and for immunoprecipitation of extra- and intracellular Fab3H6. During the 34S labeling samples were taken up to 6 times per hour. In this cases sample volume has to be kept small and therefore no biomass analysis was performed thereof.
The dead volume of the harvest port is 5 mL and therefore the first 5 mL culture broth were withdrawn. 10 mL culture broth were used for yeast dry mass (YDM) determination. For intracellular Fab3H6 measurements four cell pellets of 2 mL culture (0.05 g YDM each in capped screw tube, Biozym) were collected (1 min centrifugation at 4°C and 13.000 rpm, followed by quick freezing in liquid nitrogen). The supernatant was used for all extracellular measurements.
To enable the necessary sampling volume of at least 13 mL, the continuous harvest was replaced by discontinuous sampling. The sample volumes taken out from the bioreactor were exactly the volumes that should have been harvested by the pump. This caused a slight variation of the preset dilution rate of 0.1 h-1. However, the calculated dilution rates are in the range of minimum 0.0998 h-1 and maximum 0.1013 h-1 (calculation not shown) and it can be assumed that these changes have no significant influence.
Mechanical cell lysis of P. pastoris
The cell pellets, containing 0.05 g YDM in capped screwing tubes, were washed with 0.5 mL PBS (per liter: 8.0 g NaCl, 0.2 g KCl, 1.8 g Na2HPO4 • 2 H2O, 0.24 g KH2PO4) and further resuspended in 0.5 mL lysis buffer. 0.5 mL of glass beads (acid washed, 0.4-0.6 mm, Satorius) were added. Cells were mechanically disrupted by using the FastPrep system (MP Biomedicals; settings: 3 times 20 s shaking at 6.5 m s-1). At the bottom of the tubes small holes were pierced with a hot needle and the tubes were put onto a 2 mL eppendorf tube. Cell lysates were collected by moderate centrifugation (1 min with 1.000 g). Cells debris and glass beads were washed with 0.5 mL lysis buffer followed by the same moderate centrifugation step. Lysates were cleared by centrifugation (15 min at 13.000 g) and the supernatants were taken for further analysis (Fab immunoprecipitation or quantification). During the whole procedure samples were kept at maximum 4°C.
Lysis buffer: 1% (w/v) triton X-100, 50 mM Tris·HCl pH = 7.4, 300 mM NaCl, 5 mM EDTA and 0.02% (w/v) sodium azide. Immediately before use inhibitors were added: 1 tablet of protease inhibitor (Sigma, S8820) per 20 mL buffer, proteasome inhibitor MG-132 to a final concentration of 5 μM and lysosomal inhibitor chloroquine to a final concentration of 50 μM.
The procedure was adapted from the Current Protocols in Molecular Biology, chapter 10.16 "Immunoprecipitation" . 80 μL of the anti-human IgG agarose suspension (Sigma-Aldrich) were added to 1 mL cleared cell lysate or 1 mL of culture supernatant and incubated for 2 hours at 4°C in a tube rotator. The agarose slurry was transferred onto PVDF membranes (Ultrafree®-MC Centrifugal Filter Units, 0.45 μm, Millipore) and washed four times with 0.5 mL ice-cold washing buffer and twice with 0.5 mL ice-cold PBS (centrifuged each time 5 sec at 3.000 g). To disaggregate the proteins from the matrix, the agarose suspension was incubated two times for 10 minutes with 120 μL elution buffer at room temperature. The eluates were collected by centrifugation (5 sec at 3.000 g). The buffer was changed to PBS and the solution was concentrated by the factor 10 by using the 10 kDa Amicon® Ultra-0.5 centrifugal filter devices (Millipore). The immunopurified Fab3H6 solutions were used for sulfur isotope determination (see below).
Wash buffer: 0.1% (w/v) triton X-100, 50 mM Tris·HCl pH = 7.4, 300 mM NaCl, 5 mM EDTA and 0.02% (w/v) sodium azide. Immediately before use 0.1% sodium deoxycholate was added.
Elution buffer: 6 M guanidine hydrochloride, 100 mM Tris·HCl pH = 8.5, 5 mM EDTA and 0.02% (w/v) sodium azide.
Sulfur isotope ratio determination
An inert titanium HPLC gradient system (Rheos 2000, Flux Instruments AG, Basel, Switzerland) with a metal-free autosampler (HTC PAL Autosampler, Thermo Fisher Scientific Inc., Waltham, USA) was used in combination with a high resolution inductively coupled plasma sector field mass spectrometer, ICP-SFMS (Element 2, Thermo Scientific Inc., Bremen, Germany). Sample introduction system consisted of a nebulizer (PFA-ST, Elemental Scientific Inc., Omaha, Nebrasca, USA) and a cooled (5°C) cyclonic silica glass spray chamber (PC3, ISA Elemental Scientific). Measured isotopes were 34S and 32S. Mass resolution was set to 4000. 32S was used as lock mass during measurement for instrumental mass drift correction. Dwell time per isotope was 0.1 sec. For separation by size exclusion chromatography a KW402.51E column (Shodex, Showa Denko K. K., Kawasaki, Japan) was used. Column dimensions were 1 × 150 mm. Separation was carried out under native conditions, with a 50 mM ammonium acetate, pH 6 eluent. The SEC flow was 50 μL min-1; injection volume was set to 2 μL. The integration of all chromatographic data from SEC-ICP-SFMS analysis was carried out using Chromeleon software (Version 6.7, Dionex, Sunnyvale, California, USA). Fab monomer and heterodimer dimer coeluted from the SEC column under the selected conditions. The 34S/32S ratio in the Fab samples was determined with a long term repeatability of 5% (12 hours, N = 5).
Sulfur isotope determination of the inorganic compounds in the supernatant
The supernatant of the culture broth has been separated from all molecules with a size larger than 3 kDa by ultrafiltration (3 kDa Amicon®, Millipore). The sulfur in the remaining solution, mainly from inorganic sulfate, was analyzed by ICP-SFMS for its sulfur ratio (see above).
Biomass determination by dry cell mass
Two times 5 mL culture broth were centrifuged. The pellets were resuspended in 10 mL RO-H2O (reverse osmosis water) and recentrifuged. The washed pellets were again resuspended in RO-H2O, transferred to weighed beakers and dried at 105°C until constant weight.
SDS-PAGE and silver staining
10 μL of the IP concentrate were run on a non-reducing sodium dodecyl sulfate (SDS) 4 to 12% polyacrylamide gel (Invitrogen) with MOPS buffer (morpholinepropanesulfonic acid) at 200 V for one hour and silver stained according to the protocol in the Current Protocols in Molecular Biology, chapter 10.6 .
Quantification was done by sandwich ELISA as described in a previous study .