Monitoring state deviations in bioreactors

Abstract

The invention relates to a system (100) for monitoring deviations of a state of a cell culture in a bioreactor (104, 106) from a reference state of a cell culture in a reference bioreactor (102). The bioreactor comprises the same medium (M1) as the reference bioreactor. The system comprises: •—a storage medium (114) comprising: •a PACO-reference profile (116) indicative of a deviation of a CO2 off gas rate (ACO.sub.R-M-.sub.ti) measured in the reference bioreactor from a predicted CO2 off gas rate (ACO.sub.R-EXP-ti) of the reference bioreactor; •a data object comprising a medium-specific relation (136) between the pH value of the medium (M1) and a respective fraction of CO2 gas in a gas volume when said medium is in pH-CO2 equilibrium state with said gas volume and lacks the cell culture; •—an interface (128) for receiving (212) a current CO2 off gas rate (ACO.sub.Bi-M-ti, ACO.sub.B2-M-.sub.t i) and a current pH value (pH.sub.Bi-ti) of the medium of the bioreactor (104, 106); •—a comparison unit (130) configured for computing (214, 216): •a PACO value (PACO.sub.B1-tir PACO.sub.Bi-ti) the PACO-value being indicative of a deviation of a CO2 off gas rate (ACO.sub.Bi-M-ti, ACO.sub.B2-M-.sub.ti) measured in the bioreactor from a predicted CO2 off gas rate (ACO.sub.B1-EXP-ti, ACO.sub.B2-E xp-.sub.t i). a difference between the computed PACO value (PACO.sub.Bi-ti, PACO.sub.B2-ti) and a respective reference PACO value (PACO.sub.R-ti) in the PACO-reference profile (116).

Claims

1. A system for monitoring deviations of a state of a cell culture in a bioreactor from a reference state of a cell culture in a reference bioreactor, the bioreactor comprising a same type of medium as the reference bioreactor, the system comprising: the bioreactor comprising a medium; a CO2 off gas analyzer configured to measure a current CO2 off gas rate of the bioreactor; a pH measurement device configured to measure a current pH value of the medium of the bioreactor; a non-transitory computer-readable storage medium comprising: a PACO-reference profile comprising a representation of the variation in a reference PACO value associated with the reference bioreactor versus time, the PACO-reference profile indicating the difference of a CO2 off gas rate measured in the reference bioreactor from a predicted CO2 off gas rate of the reference bioreactor, said predicted CO2 off gas rate in the reference bioreactor being the predicted off gas rate of said medium in the reference bioreactor in pH-CO2 equilibrium state under absence of the cell culture and under the condition that the pH value of the medium in equilibrium state is identical to the pH value of the reference bioreactor measured when measuring the CO2 off gas rate in the reference bioreactor, the PACO reference profile depending on the amount of CO2 off gas produced by the cells of the cell culture in the reference bioreactor while cultivating the cell culture; a data object comprising a medium-specific relation, the medium-specific relation being specific for the medium and indicating a relation between the pH value of the medium and a respective fraction of CO2 gas in a gas volume when said medium is in pH-CO2 equilibrium state with said gas volume and lacks the cell culture; an interface for repeatedly receiving, at a current time, the current CO2 off gas rate of the bioreactor and the current pH value of the medium of the bioreactor measured during the cultivation of the cell culture in the bioreactor; a comparison unit configured to compute, for each of the received current CO2 off gas rates: a predicted CO2 off gas rate of said medium in said bioreactor in pH-CO2 equilibrium state under absence of the cell culture and under the condition that the pH value of the medium in equilibrium state is identical to the received current pH value of the bioreactor measured when measuring the received current CO2 off gas rate in the bioreactor, the predicted CO2 off gas rate being calculated based on the received current pH value, the medium-specific relation, and a total gas inflow rate of the bioreactor at the time of measuring the received current CO2 off gas rate in the bioreactor, a computed PACO value comprising a difference of the received current CO2 off gas rate measured in the bioreactor from the predicted CO2 off gas rate at the time of measuring the received current CO2 off gas rate in the bioreactor, the PACO value depending on the amount of CO2 off gas produced by the cells of the cell culture in the bioreactor while cultivating the cell culture, a difference between the computed PACO value and a respective reference PACO value in the PACO-reference profile, and outputting the computed difference, the computed difference being indicative of a deviation of the state of the cell culture in the bioreactor from the reference state.

2. The system of claim 1, the medium-specific relation being an equation FCO2.sub.M1(pH)=REL-M1(pH) obtained by mathematically fitting multiple empirically determined pairs of a pH-value of the medium and a respectively measured fraction of CO2 gas in a gas volume, wherein: FCO2.sub.M1(pH) is the predicted fraction of CO2 gas in a gas volume above a sample of the medium when said medium has a given pH-value and is in pH-CO2 equilibrium state with said gas volume and lacks the cell culture; the pH value is an input parameter value and represents the pH value of the medium in ph-CO2 equilibrium state under the absence of the cell culture; wherein REL-M1 is a set of one or more parameters connected by operators, the parameters having been obtained by: adjusting samples of the medium lacking the cell culture, to multiple different pH values, thereby letting the samples reach pH-CO2 equilibrium with the gas volume, determining the fraction of CO2 gas in a respective gas volume being in ph-CO2 equilibrium with the medium in the samples, plotting the determined CO2 gas fractions against the respective equilibrium pH values of the samples, fitting a curve in the plotted values and deriving the parameters of the medium-specific relation from the fitted curve.

3. The system of claim 1, wherein the received current CO2 off gas rate, the received current pH value, the total gas inflow rate of the bioreactor at a particular time and the medium-specific relation are the only input parameters for calculating the computed PACO value for the monitored bioreactor.

4. The system of claim 1, the system being configured to compute the predicted CO2 off gas rate by: inputting the received current pH value into the medium-specific-relation to compute a predicted CO2 concentration in the gas volume of the bioreactor in equilibrium state with the medium at the time of measuring the current CO2 off gas rate and the current pH value; and multiplying the predicted CO2 concentration with the total gas inflow rate of the bioreactor to obtain the predicted CO2 off gas rate of the bioreactor, the predicted CO2 off gas rate being the predicted off gas rate of said medium in pH-CO2 equilibrium state under absence of the cell culture and under the condition that the pH value of the medium in equilibrium state is identical to the received current pH value input into the medium-specific relation.

5. The system of claim 4, the computation of the predicted CO2 off gas rate of the bioreactor at the current time being performed according to: ${\mathrm{ACO}}_{\mathrm{EXP}-\mathrm{ti}}\left[\mathrm{mol}\text{/}\min \right]=\left(\frac{\mathrm{FCO}{2}_{B1-\mathrm{EXP}-\mathrm{ti}}\left[\%\right]}{100}\right)\times {\mathrm{TGI}}_{B1}\left[\frac{\mathrm{mol}}{\min }\right],$ wherein the ACO.sub.EXP-ti is the predicted CO2 off gas rate, wherein the TGI.sub.B1 is the total amount of gas influx of the bioreactor at the current time, and wherein FCO2.sub.EXP is the predicted CO2 concentration in the gas volume of the bioreactor in equilibrium state with the medium at the time of measuring the current CO2 off gas rate and the current pH value.

6. The system of claim 1, the outputting of the computed difference comprising: in case the computed difference between the computed PACO value and the respective reference PACO value in the PACO-reference profile exceeds a threshold value, automatically outputting an alarm signal.

7. The system of claim 1, the medium being a carbonate-buffered medium.

8. The system of claim 1, the reference bioreactor differing from the bioreactor in respect to one or more of the following features: a) the gas volume in the bioreactor, b) the medium volume in the bioreactor, c) the Reynolds number of the bioreactor, d) the Newton number of the bioreactor, e) the dimensions of the bioreactor f) geometrical features of the bioreactor and/or bioreactor baffles, g) the stirrer configuration h) the stirring rate, i) the volumetric mass transfer coefficient for oxygen of the bioreactor, j) total gas influx rate and/or O2 influx rate and/or N2 influx rate and/or CO2 influx rate, k) power input, l) pressure in the bioreactor, m) gas bubble hold time in the medium, n) gas bubble size and distribution in the medium, o) surface speed, p) a parameter calculated as a derivative from one or more of the parameters a)-o).

9. The system of claim 1, the computation of the predicted CO2 off gas rate at the current time comprising computing, for each of the received current CO2 off gas rates and pH values of the bioreactor: an expected CO2 off gas fraction of a current outgas volume of the bioreactor according to: FCO2.sub.B1-EXP-ti [%]=REL-M1 (pH.sub.B1-ti), wherein FCO2.sub.B1-EXP-ti [%] is a predicted CO2 off gas fraction of the total off gas volume of the bioreactor in % at the current time, the prediction being calculated by using the received current pH value as input for REL-M1 (pH.sub.B1-ti), wherein REL-M1 is the medium-specific relation of the medium, wherein pH.sub.B1-ti is the received current pH value in the medium of the bioreactor at the current time, and the predicted CO2 off gas rate value according to: ${\mathrm{ACO}}_{B1-\mathrm{EXP}-\mathrm{ti}}\left[\mathrm{mol}\text{/}\min \right]=\left(\frac{\mathrm{FCO}{2}_{B1-\mathrm{EXP}-\mathrm{ti}}\left[\%\right]}{100}\right)\times {\mathrm{TGI}}_{B1}\left[\frac{\mathrm{mol}}{\min }\right],$ wherein the ACO.sub.B1-EXP-ti [mol/min] value is the predicted CO2 off gas rate of the bioreactor when the medium of the bioreactor has the currently measured pH value and is in pH-CO2 equilibrium with the gas phase above said medium in $\left[\frac{\mathrm{mol}}{\min }\right],$ wherein the TGI.sub.B1 is the total amount of gas influx of the bioreactor at the current time.

10. The system of claim 1, the medium in the reference bioreactor having a first volume and a first total mass, the medium in the bioreactor having a second volume and a second total mass, the first volume and the second volume differing from each other, the computation of the difference between each one of the computed PACO values and its respective reference PACO value in the PACO-reference profile comprising: dividing, by the processor, the computed PACO value by the second volume; and dividing, by the processor, the respective reference PACO value in the PACO-reference profile by the first volume; or dividing, by the processor, the computed PACO value by the second mass; and dividing, by the processor, the respective reference PACO value in the PACO-reference profile by the first mass.

11. The system of claim 1, the PACO reference profile covering multiple phases of operating the reference bioreactor, the phases comprising: a feed-free phase during which the cell culture is cultivated in the reference bioreactor without feeding; a feeding phase during which the cell culture is cultivated in the reference bioreactor in the presence of a given feeding rate, the cell culture not excreting a metabolite affecting the pH value of the medium; a feeding phase during which the cell culture is cultivated in the reference bioreactor in the presence of a given feeding rate, the cell culture excreting a metabolite affecting the pH value of the medium.

12. The system of claim 1, the system comprising a control unit configured to automatically modify one or more control parameters of the bioreactor such that the difference between the computed PACO values and the respective reference PACO values in the PACO-reference profile is minimized.

13. The system of claim 12, wherein in case the computed PACO values are higher than the respective reference PACO values in the PACO reference profile, the control unit is configured to automatically modify one or more control parameters of the bioreactor by performing one or more of the following operations: reduce total air influx rate and/or reduce O2 gas influx rate and/or reduce the CO2 gas influx rate and/or reduce the base influx rate to the bioreactor and/or modify the pressure or the temperature of the bioreactor; wherein in case the computed PACO values are lower than the respective reference PACO values in the PACO reference profile, the control unit is configured to automatically modify one or more control parameters of the bioreactor by performing one or more of the following operations: increase the total air influx rate and/or increase the O2 gas influx rate and/or increase the CO2 gas influx rate and/or increase the base influx rate to the bioreactor and/or modify the pressure or the temperature of the bioreactor.

14. The system of claim 1, the reference bioreactor differing from the bioreactor in respect to the gas volume in the bioreactor.

15. A method for monitoring deviations of a state of a cell culture in a bioreactor from a reference state of a cell culture in a reference bioreactor, the bioreactor comprising a same type of medium as the reference bioreactor, the method comprising: repeatedly measuring, by a CO2 off gas analyzer, a current CO2 off gas rate of the bioreactor, the bioreactor comprising a medium; repeatedly measuring, by a pH measurement device, a current pH value of the medium of the bioreactor; receiving, by a comparison unit of a bioreactor state monitoring system, a PACO-reference profile, the PACO-reference profile comprising a representation of the variation in a reference PACO value associated with the reference bioreactor versus time, the PACO-reference profile indicating the difference of a CO2 off gas rate measured in the reference bioreactor from a predicted CO2 off gas rate of the reference bioreactor, said predicted CO2 off gas rate being the predicted off gas rate of said medium in the reference bioreactor in pH-CO2 equilibrium state under absence of the cell culture and under the condition that the pH value of the medium in equilibrium state is identical to the pH value of the reference bioreactor measured when measuring the CO2 off gas rate in the reference bioreactor, the PACO reference profile depending on the amount of CO2 off gas produced by the cells of the cell culture in the reference bioreactor while cultivating the cell culture; receiving, by the comparison unit, a data object comprising a medium-specific relation, the medium-specific relation being specific for the medium and indicating a relation between the pH value of the medium and a respective fraction of CO2 gas in a gas volume when said medium is in pH-CO2 equilibrium state with said gas volume and lacks the cell culture; repeatedly receiving, at a current time, a current CO2 off gas rate of the bioreactor and a current pH value of the medium of the bioreactor measured during the cultivation of the cell culture in the bioreactor; computing, by the comparison unit, for each of the received current CO2 off gas rates: a predicted CO2 off gas rate of said medium in the bioreactor in pH-CO2 equilibrium state under absence of the cell culture and under the condition that the pH value of the medium in equilibrium state is identical to the received current pH value of the bioreactor measured when measuring the received current CO2 off gas rate in the bioreactor, the predicted CO2 off gas rate being calculated based on the received current pH value, the medium-specific relation, and a total gas inflow rate of the bioreactor at the time of measuring the received current CO2 off gas rate in the bioreactor, a computed PACO value comprising a difference of the received current CO2 off gas rate measured in the bioreactor from the predicted CO2 off gas rate at the time of measuring the received current CO2 off gas rate in the bioreactor, the PACO value depending on the amount of CO2 off gas produced by the cells of the cell culture in the bioreactor while cultivating the cell culture, and a difference between the computed PACO value and a respective reference PACO value in the PACO-reference profile; and outputting, by the comparison unit, the computed difference, the computed difference being indicative of a deviation of the state of the cell culture in the bioreactor from the reference state.

16. The method of claim 15, the PACO reference profile comprising a plurality of reference PACO values, the method further comprising calculating the reference PACO values by: receiving a data object comprising the medium-specific relation; repeatedly receiving, at a current time, a current CO2 off gas rate of the reference bioreactor in $\left[\frac{\mathrm{mol}}{\min }\right]$ and a current pH value of the medium of the reference bioreactor measured at said current time while cultivating the cell culture in the reference bioreactor; computing, for each of the received pairs of a current CO2 off gas rate and a current pH value, one of the reference PACO values, the computation of the reference PACO value using as input: the received current CO2 off gas rate of the reference bioreactor; the received current pH value of the reference bioreactor; the total gas inflow rate of the reference bioreactor at the time of receiving the current CO2 off gas rate; and the medium-specific relation.

17. The method of claim 16, further comprising creating, the PACO-reference profile of the reference bioreactor by: plotting the reference PACO values in a CO2 off gas rate versus time plot; and fitting a curve in the plotted reference PACO values, said curve constituting the reference PACO profile.

18. The method of claim 16, the computation of each of the reference PACO values at respective current times comprising computing, for each of the received current CO2 off gas rates and pH values of the reference bioreactor: an expected CO2 off gas fraction of a current outgas volume of the reference bioreactor according to: FCO2.sub.R-EXP-ti [%]=REL-M1 (pH.sub.R-ti), wherein FCO2.sub.R-EXP-ti [%] is a predicted CO2 off gas fraction of the total off gas volume of the reference bioreactor in % at the current time, the prediction being calculated, by using the received current pH value as input for REL-M1 (pH.sub.R-ti), wherein REL-M1 is the medium-specific relation of the medium, wherein pH.sub.R-ti is the current pH value in the medium of the reference bioreactor received at the time, an expected CO2 off gas rate value according to: ${\mathrm{ACO}}_{R-\mathrm{EXP}-\mathrm{ti}}\left[\mathrm{mol}\text{/}\min \right]=\left(\frac{\mathrm{FCO}{2}_{R-\mathrm{EXP}-\mathrm{ti}}\left[\%\right]}{100}\right)\times {\mathrm{TGI}}_R\left[\frac{\mathrm{mol}}{\min }\right],$ wherein the ACO.sub.R-EXP-ti [mol/min] value is the expected CO2 off gas rate of the reference bioreactor in $\left[\frac{\mathrm{mol}}{\min }\right],$ wherein the TGI.sub.R is the total amount of gas influx of the reference bioreactor at the current time, and the reference PACO value according to: PACO.sub.R-ti=ACO.sub.R-EXP-ti [mol/min]−ACO.sub.R-M-ti [mol/min], wherein PACO.sub.R-ti [mol/min] is the reference PACO value at a given time, wherein ACO.sub.R-M-ti [mol/min] is the CO2 off gas rate in $\left[\frac{\mathrm{mol}}{\min }\right]$ measured at the given time in the reference bioreactor.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) In the following embodiments of the invention are explained in greater detail, by way of example only, making reference to the drawings in which:

(2) FIG. 1 shows a block diagram of a system for monitoring and/or controlling one or more bioreactors;

(3) FIG. 2 shows flowcharts of methods for monitoring and/or controlling a bioreactor;

(4) FIG. 3 shows components of a bioreactor;

(5) FIG. 4 shows various phases of cultivating and growing a cell culture;

(6) FIG. 5 shows diagrams illustrating the dependence of the CO2 concentration in the off gas of a bioreactor from other parameters;

(7) FIG. 6 shows a plot used for obtaining a medium-specific pH-CO2 concentration relation;

(8) FIG. 7a shows the pH values of four different bioreactors while growing a cell culture in four different bioreactors;

(9) FIG. 7b shows the CO2 fraction in the off gas predicted for each of the four bioreactors using the pH values and the medium-specific relation as input;

(10) FIG. 7c shows the CO2 off gas fraction actually measured in each of the four bioreactors;

(11) FIG. 7d shows a PACO profile resulting from the difference of the predicted and actually measured CO2 off gas fractions;

(12) FIG. 8a is a diagram showing PACO profiles of two bioreactors and a reference bioreactor, whereby the PACO profile of one bioreactor differs from the PACO profile of the reference bioreactor already before inoculation;

(13) FIG. 8b is a diagram showing the PACO profile differences of the two bioreactors of FIG. 8a to said reference bioreactor.

DETAILED DESCRIPTION

(14) FIG. 1 shows a block diagram of a system 100 for monitoring and/or controlling one or more bioreactors according to an embodiment of the invention. In the following, said embodiment will be described by making reference to a corresponding method for monitoring and/or controlling a bioreactor as indicated in the flow charts of FIGS. 2a and 2b.

(15) FIG. 1 shows a system 100 allowing for real-time and accurate comparison of said culture states of different bioreactors even in case the size, shape, temperature or other engineering or environment parameters of the two compared bioreactors differ from each other. The comparison is based on a so called “PACO” parameter calculated for a particular bioreactor as a derivative of a current pH value and a current CO2 off gas rate of said bioreactor and of a relation 136, 138 being specific for the cell culture medium used in said bioreactor.

(16) The system 100 comprises a processor 110, a main memory 112 and a non-transitory storage medium 114. The storage medium comprises computer readable instructions which, when executed by the processor 110 cause the processor to perform a method for automatically monitoring and/or controlling one or more bioreactors 104, 106 as described for embodiments of the invention.

(17) The storage medium 114 comprises at least one reference PACO profile being specific for a particular medium M1 and a particular project for cultivating a particular cell culture in said medium M1 over a predefined time interval and with a predefined goal. For example, the project could be to grow CHO cells (Chinese hamster ovary cells) over 14 days in the cell culture medium M1 under optimal or nearly optimal cell growth conditions until a cell density of about 100×10.sup.5 cells/milliliter is reached. In addition, the storage medium 114 comprises a data structure 136, e.g. a file or a database record, being indicative of a pH-CO2-concentration relation that is particular for said cell culture medium M1.

(18) In addition, the storage medium may comprise medium-specific relations 138 of other cell culture media and/or may comprise reference PACO profiles 118 of other cell culture projects with different cell types and/or with a different medium M2. The reference PACO profiles and the medium-specific relations may be received via a data communication interface 120, e.g. a network interface, an USB-port, a CDROM drive or the like. According to some embodiments, the reference PACO profile may be received dynamically for enabling a real-time comparison of the cell culture states of two monitored bioreactors.

(19) The system 100 may further comprise an interface 126 for dynamically receiving current measurement values from one or more monitored and/or controlled bioreactors 104, 106. The measurement values are in particular a current pH value and a current CO2 off gas rate. A PACO comparison unit 130 uses the received measurement values and the medium-specific relation 136 of the medium M1 in the monitored bioreactor 104, 106 for repeatedly calculating current PACO values and comparing said current PACO values to a PACO reference profile 116 of a cell culture project in a reference bioreactor 102 that shall be repeated in the monitored bioreactor 104. Any difference in the current PACO values from respective reference PACO values can be displayed to a user via a display device 134, e.g. a computer monitor or a monitor of a smartphone.

(20) Optionally, the system 100 further comprises a control unit 132 that controls one or more parameters of the bioreactors 104, 106 such that the difference of the currently obtained PACO values from a respective reference PACO value is minimized. The control unit can be, for example, a software and/or hardware module being operatively coupled to the comparison unit 130 for receiving the results of the PACO value comparison. The control unit is capable of controlling the configuration and operation of one or more engineering processes and parameters. For example, the control unit 132 may be operable to increase or decrease the influx of liquids having an impact on the pH value, e.g. may increase or decrease the influx of a citric acid or of a 1M NaOH solution.

(21) The medium M1 can be, for example, Kaighn's Modification of Ham's F-12 Medium comprising, for example, putrescine, thymidine, hypoxanthine, zinc, and higher levels of all amino acids and sodium pyruvate. These additions allow the medium to be supplemented with very low levels of serum or defined components, for some cell types. Ham's F-12K (Kaighn's) Medium contains no proteins or growth factors, and is therefore often supplemented with growth factors and Fetal Bovine Serum (FBS) that may be optimized for a particular cell line. Ham's F-12K (Kaighn's) Medium uses a sodium bicarbonate buffer system (2.5 g/L).

(22) The medium M2 may be an LB medium, and there may exist reference profiles for a plurality of other media M3, M4, e.g. for cultivating bacteria or plants for a variety of purposes and corresponding “projects”.

(23) The system is operatively coupled to one or more bioreactors 104 106 which are to be monitored and/or controlled. The dimensions and other engineering parameters (stirring rate and configuration, bubble size, dimension, etc.) of the monitored or controlled bioreactors may differ from each other and/or may differ from the respective parameters of the reference bioreactor. The operative coupling may comprise the sending of monitoring data (current pH and CO2 off gas rates) to the comparison unit 130 and optionally also the sending of control data from the control unit 132 to the respective bioreactor 104, 106. The reference bioreactor may but does not have to be coupled to the system 100. It is sufficient that the PACO reference profile gathered from the reference bioreactor is accessible by the comparison unit 130.

(24) In the following paragraphs, an overview is given how the system 100 and a corresponding method according to embodiments of an invention allows to control the operation of a bioreactor 104, 106 comprising a medium M1 in a way that the cell culture in said bioreactor is cultivated under almost identical physiological conditions as a reference cell culture cultivated in a reference bioreactor in the same medium even in case the dimension and other engineering parameters of said two bioreactors differ.

(25) In a first step 202, a medium specific relation 136 between a pH value of a cell-free medium and a corresponding CO2 partial pressure in an air volume above said medium when the medium is in ph-CO2 equilibrium state at predefined conditions (e.g. 20° C. and normal atmospheric pressure) is empirically determined. This step is described in greater detail in FIGS. 5D) and 6. As the goal is to grow CHO cells for 14 days in Kaighn's Modification of Ham's F-12 Medium, a relation is determined specifically for said medium.

(26) In step 204, a reference PACO profile is obtained from the reference bioreactor 102. At first, the reference bioreactor is filled with the cell-free medium M1 and is initiated by starting continuously adding gas, e.g. by transporting environmental air and/or its individual components (N2, O2 and/or CO2) to the bioreactor and optionally also by starting continuously adding liquids (the cell-free medium, optionally additional liquids such as feed, bases, etc.). In addition, the stirrers may be started. The reference bioreactor may be operated at a temperature and pressure that differs from the temperature and pressure used for obtaining the medium-specific relation. After some time (typically minutes or hours), the medium in the reference bioreactor and the air volume in the reference bioreactor above the medium will have reached pH-CO2 equilibrium state and one or more PACO values are calculated for the reference bioreactor from the medium-specific relation 136 and current pH- and CO2 values of the reference bioreactor.

(27) According to embodiments, during the generation of the reference PACO profile, the reference bioreactor is fed with one or more liquids such as a feeding solution or a base in addition to a cell-free medium. In this case, additional reference profiles are generated in some embodiments. Said additional profiles respectively indicate the amount of feeding solution or base added to the reference bioreactor at a given moment in time of the profile. When initiating and operating the monitored and/or controlled bioreactor, the same amount of feeding solution or base per volume unit of the medium and per unit time is added to said bioreactor as specified in the respective profiles. Thus, it is ensured that even in case the composition of the medium in the bioreactor changes, the medium in the bioreactor is “the same” or “approximately the same” as in the reference bioreactor at a given moment in time ti. As the feeding solution and/or the base typically does not significantly modify the composition of the medium, the medium-specific relation can be used for computing the current PACO values even in case the medium specific relation was empirically determined for a medium lacking said feeding solution. If, however, the composition of the medium in the reference bioreactor should dramatically change while cultivating the cells in the reference medium, e.g. because of a switch from a first medium to another, second medium of a completely different composition, in fact two consecutive PACO reference plots and two different media-specific relations need to be determined and transferred to a control unit of the monitored and/or controlled bioreactor.

(28) Preferentially, the monitored and/or controlled bioreactor 104, 106 at least at the time point of initialization is operated under the same temperature and pressure as the reference bioreactor. However, it is possible that while operating the bioreactor 104, 106, the temperature and/or pressure is modified in order to minimize PACO difference.

(29) Then in step 206, the PACO reference profile and the medium-specific relation 136 are used for monitoring and/or controlling the cell culture state in a different bioreactor 104, 106, e.g. by transferring the obtained reference PACO profile and the relation 136 via the Internet or via a portable storage medium to the system 100 and storing the profile and the relation in the storage medium 114. As can be inferred from FIG. 1, the one or more monitored bioreactors 104, 106 may differ from the reference bioreactor 102 in respect to many parameters, e.g. the size and shape of the bioreactor, stirring parameters, total gas influx rate, the temperature, the pressure, the surface speed, bubble size and distribution, and other parameters.

(30) The use 206 of the PACO reference profile in embodiments of the invention may comprise the steps 208-220 depicted in FIG. 2b.

(31) The system 100 is capable of monitoring a state of a cell culture in a bioreactor 104, 106 and comparing the cell culture state of said bioreactor with the cell culture state in the reference bioreactor at a corresponding time after inoculation. The reference bioreactor and each of the monitored bioreactors 104, 106 comprise the same medium M1 and are inoculated with the same type of cell culture. The reference PACO profile may be gathered from the reference bioreactor before the monitored bioreactor(s) are initialized and inoculated with a cell culture, but it is also possible that the reference bioreactor and the one or more monitored bioreactors are operated in parallel or with a delay of e.g. one or more days. In this case, the reference PACO profile is received dynamically while cultivating the cell culture in the monitored bioreactor.

(32) In a first step 208, the comparison unit 130 of the bioreactor state monitoring system 100 receives the PACO-reference profile 116, e.g. by reading a file comprising the profile from the storage medium 114 or receiving said profile via the interface 120 from a system-external data source, e.g. the Internet. The PACO-reference profile is a representation of the variation in a PACO-reference value PACO.sub.R-ti versus time ti, i indicating one of a series of times, e.g. t0, t1, t2, . . . , tmax. The time t0 is preferentially a time point lying a predefined time interval before the time point of inoculating the reference bioreactor with the cell culture. For example, t0 may represent 1 h before inoculation of the reference bioreactor, t1 may represent 45 minutes before inoculation, t2 may represent 30 minutes before inoculation, t3 may represent 15 minutes before inoculation, t4 may represent the time of inoculation, t6 may represent 15 minutes after inoculation and so on until tmax is reached at the end of duration of the cell culture project.

(33) Moreover, the PACO-reference profile is indicative of a deviation of a CO2 off gas rate measured in the reference bioreactor from a predicted CO2 off gas rate for said reference bioreactor. The measured CO2 off gas rate can be obtained by measuring the CO2 concentration of the reference bioreactor and the total gas influx rate TGI.sub.R-ti of the reference bioreactor at a given time. The predicted CO2 off gas rate is the derived by inputting the currently measured pH value pH.sub.R-M-ti of the medium in the reference bioreactor into the medium-specific relation, thereby assuming said medium would be cell-free and is in pH-CO2 equilibrium state under the predefined temperature and pressure (e.g. 20° C. and normal atmospheric pressure) used when generating the medium-specific relation. Thus, the PACO reference profile is indicative of a deviation of the expected from the measured CO2 off gas rate and depends on the amount of CO2 off gas produced by the cells of the cell culture in the reference bioreactor while cultivating the cell culture and depends on other factors having an impact on the pH-CO2 equilibrium such as temperature, pH, pressure, and the like.

(34) In step 210, the comparison unit 130 receives a data object comprising a medium-specific relation 136 of the medium M1 in the bioreactor 104, 106 to be monitored. The medium-specific relation indicates a relation between multiple different pH values of the medium M1 lacking the cell culture and respective CO2 fraction in a gas volume in pH-CO2 equilibrium state with said medium at the predefined pressure and temperature.

(35) In step 212, the comparison unit 130 repeatedly receives, at a current time ti, a current CO2 off gas rate ACO.sub.B1-M-ti of the monitored bioreactor 104 and a current pH value pH.sub.B1-ti of the medium M1 of the bioreactor 104 via the interface 128. The measured CO2 off gas rates and pH values are received at least during the cultivation of the cell culture in the bioreactor 104, and may optionally be received already before inoculation to compare the state of the bioreactors in a cell free state.

(36) For each of the received pairs of CO2 off gas rates and pH values in the bioreactor 104, the comparison unit 130 in step 214 computes a PACO value PACO.sub.B1-ti. The PACO-value is indicative of a deviation of a CO2 off gas rate measured in the bioreactor 104 from a predicted CO2 off gas rate. Said predicted CO2 off gas rate is derived from the CO2 fraction predicted for the gas volume above a sample of said medium M1 in pH-CO2 equilibrium state with said volume under absence of the cell culture, under the predefined temperature and pressure and under the condition that the pH value of the medium in equilibrium state is identical to the pH value of the monitored bioreactor 104 at the time ti. The computed PACO value is indicative of the deviation of the predicted CO2 off gas rate produced by the cells of the cell culture in the bioreactor at a particular time ti while cultivating the cell culture from the CO2 off gas rate actually measured at that time. The computation of the PACO value uses as input: the received current CO2 off gas rate of the monitored bioreactor 104 at time ti; the received current pH value rate of the monitored bioreactor 104 at time ti; the total gas inflow rate TGI.sub.B1 of the bioreactor 104 at the time ti; and the medium-specific relation 136 of the medium M1;

(37) In step 216, the comparison unit 130 computes a difference between the computed PACO value PACO.sub.B1-ti of the monitored bioreactor 104 and a respective reference PACO value PACO.sub.R-ti in the PACO-reference profile 116. For example, the PACO.sub.B1-t100 of the monitored bioreactor 104 is compared with a respective PACO.sub.R-t100 in the PACO-reference profile 116, whereby t100 corresponds to the begin of the 24.sup.th hour after inoculation.

(38) In step 220, the comparison unit 130 outputs the computed difference, e.g. on the display 134. The computed difference is indicative of a deviation of the state of the cell culture in the bioreactor 104 from the reference state of the cell culture in the reference bioreactor 102 according to profile 116.

(39) According to embodiments, the comparison unit 130 or a control unit coupled to the comparison unit may in addition monitor the state of one or more additional bioreactors 106 as described above.

(40) FIG. 3 shows an embodiment of a bioreactor 102, 104, 106. The bioreactor is coupled to a first pipe for transferring liquids such as acids, bases, fresh medium, and the like into the bioreactor and to an outflow. The bioreactor is in addition coupled to one or more second pipes for transferring gases, e.g. environmental air and/or N2 gas and/or O2 gas and/or CO2 gas into the bioreactor and is coupled to a third pipe for the off gas. The second pipe may comprise a sensor 144 for determining a current total gas influx rate. The third pipe may comprise a sensor 122, e.g. a CO2 off gas analyzer, to selectively measure the amount of CO2 gas transferred through the third pipe per time unit. According to other embodiments, there may be not pipes for the influx and outflux of liquids and nutrients may be fed to the bioreactor by means of step-wise bolus addition of a feed solution.

(41) FIG. 4 shows various phases of cultivating and growing a cell culture in a reference bioreactor 102 according to a particular cell culture project (e.g. growing CHO cells over 18 days) and a PACO reference profile 402 having been derived from said project. During the project, different feeds (feed 1, feed 2, feed 3) and/or basic liquids were added and the impact of the PACO value in the reference PACO profile is shown. In order to reproduce the project in another bioreactor 104, 106, the same feeds and/or basic substances have to be added to the culture medium at respective time intervals, and any deviations of the PACO values in the monitored bioreactor 104 from respective reference PACO values in the profile 402 are determined and optionally minimized by modifying engineering parameters and configurations of the monitored and controlled bioreactor 104, 106.

(42) The PACO profile 402 depicted in FIG. 4 clearly shows different process phases that can be observed when growing the set culture in the reference bioreactor 102 during that project. Thus, the profile shows that a single parameter, the PACO parameter computed from easily and dynamically derivable measurement values can identify different process phases correlating with different states of the cell culture cells. Nevertheless, the PACO value does not quantify single effects of individual parameters (basic feed, base addition, lactate production, etc.) having an impact on the pH-CO2 equilibrium of the medium M1 in the reference bioreactor 102.

(43) As can be seen in FIG. 4, the growing of said culture cells after inoculation leads to an increased difference in the measured version of a predicted CO2 off gas rate (“ACO” (CO2 off gas rate), measured e.g. in [mol CO2/min]). While growing the cells, the pH of the medium typically decreases and the CO2 off gas rate may increase in dependence on the decrease of the pH value and other parameters. The profile 402 covers four different phases: in a first phase following inoculation, no feed is added and the PACO value rises. The rise may be caused by the cell metabolism. In a second phase, a first feed is added to the medium and the PACO value decreases. Then, in a third phase, a second, basic feed is added that increases the PACO value. Later in said “third feed” phase, however, the cell metabolism results in a reduction of the PACO value and the cell culture may enter a fourth phase. In the fourth phase, the second, basic feed is still added to the medium M1. In addition, the cell culture cells start to produce lactate and/or other substances which decrease the pH value of the medium. As a result, the PACO value of the reference bioreactor rises in the fourth phase.

(44) The “lower DB” indicates the lowest allowed pH value of the medium. In case the pH value of the medium falls below the “lower DB” threshold, a controller unit may automatically decrease CO2 influx rate in order to increase the pH value. The “upper DB” indicates the highest allowed pH value of the medium. In case the pH value of the medium exceeds the “upper DB” threshold, a controller unit may automatically increase CO2 influx rate in order to increase the pH value. In-between said thresholds, the control of the CO2 influx rate may be controlled solely based on the PACO value.

(45) FIG. 4 shows that when growing a cell culture, the actual CO2 concentration will significantly differ from the CO2 concentration expected for the cell-free medium because base addition, feed addition, lactate generation, different CO2 accumulation and removal rates in the medium and so on will affect the pH-CO2 equilibrium of the medium and the CO2 concentration in a gas volume above said medium in a bioreactor.

(46) FIG. 5 shows diagrams A, B, C and D illustrating the dependence of the CO2 concentration in the off gas (and thus, implicitly, the off gas rates) of four different bioreactors from the pH value and the independence of said CO2 concentration of engineering- and size parameters of the respective bioreactors.

(47) The four different bioreactors have the following engineering properties:

(48) TABLE-US-00001 Bioreactor I Bioreactor II Bioreactor III Bioreactor IV Total volume (volume 0.94 L  1.2 L  1.5 L  1.8 L of medium + gasphase) Aeration rate 26.3 mL/L/min 20.8 mL/L/min 16.6 mL/L/min 13.8 mL/L/min Number of stirrers 1 1 2 2

(49) Each of said bioreactors I-IV was filled with a particular cell culture medium M1 which did not comprise any cells. The original pH value of said medium was 6.85 (see diagram B). Then, the pH value was increased in each of the bioreactors by decreasing the CO2 concentration in the gas volume above said medium in the respective bioreactor. At the beginning of the test and for each of a set of predefined pH values, the medium in each bioreactor was allowed to reach pH-CO2 equilibrium with the gas volume above the medium at a predefined temperature and pressure, e.g. 20° C. and normal atmospheric pressure. After that equilibrium was reached, the CO2 concentration in Vol. % of the total off gas (“fraction CO2 gas”−“FCO2 [%]”, “CO2 concentration”) was determined for each of said four bioreactors (see diagram A showing, in combination with diagram B, the impact of the pH-value on the measured CO2 concentration in the off gas). Diagram C) shows the impact of the 15 pH-value on the measured CO2 concentration of each of the four bioreactors in the form of a bar chart. The maximum deviation of the FCO2 [%] obtained for each of the four bioreactors was less than 0.4% of the total off gas rate of the bioreactor.

(50) The diagram D) is a plot comprising the CO2 [%] values measured at each of the four bioreactors I-IV at each of the set pH values (6.85, 6.95, 7.05, 7.15, 7.25, 7.35) at a time when the medium M1 of said bioreactor reached pH-CO2 equilibrium state.

(51) It should be noted that the pH-CO2 equilibrium in a bioreactor may be challenged by the rate of CO2 gas entering and/or leaving the bioreactor, so the pH-CO2 equilibrium may in fact be a dynamic equilibrium. Nevertheless, it is possible to control a bioreactor in a manner that the dynamic pH-CO2 equilibrium is established at a particular pH value, e.g. by decreasing or increasing the CO2 concentration in the gas volume above the medium in the bioreactor by modifying the total CO2 influx rate in the bioreactor.

(52) The pH value may be modified by adding acidic or basic substances or liquids. However, as said substances may modify the composition of the medium, preferentially the dynamic pH-CO2 equilibrium state is established in a bioreactor at a particular pH value solely by controlling the CO2 influx rate in a manner that a desired pH value is reached. Using the CO2 influx rate for establishing the pH-CO2 equilibrium rather than a basic or an acidic substance has the advantage that the composition of the medium is not altered (except for the concentration of the solved CO2 and its dissociation products) and thus the medium specific relation can be empirically derived from the same medium at different pH values.

(53) Then, a curve 502 is fitted to the plot in order to empirically determine parameters for a relation 316 being specific for the medium M1 contained in the four bioreactors. This approach allows to empirically determine, for a particular cell culture medium, a medium-specific relation used as input for predicting the CO2 volume fraction expected in a gas phase above said medium when said medium has a particular pH value pressure and temperature (e.g. 20° C. and normal atmospheric pressure), lacks any cells and is in pH-CO2 equilibrium. The obtained relation is independent of bioreactor scale, aeration rate and other engineering parameters in processes that use CO2 gas as acidic component for pH control. The medium-specific relation is determined only once for a particular medium M1. The determination may be performed in a single bioreactor, e.g. in the reference bioreactor before the reference bioreactor is inoculated. In order to increase accuracy, it is also possible to perform the determination in multiple bioreactors or other containers allowing the measurement of a pH value and a CO2 gas fraction (CO2 concentration) and then use the information obtained in the multiple bioreactors or containers for obtaining a more accurate, fitted curve 502. In the example depicted in FIG. 5, four different bioreactors were used for empirically determining a fitted curve 502 and a corresponding, medium-specific relation between equilibrium pH value and equilibrium CO2 concentration.

(54) FIG. 6 shows the diagram in FIG. 5D) in greater detail. The medium-specific relation 136 of medium M1 is an equation FCO2.sub.M1(pH)=REL−M1(pH) obtained by mathematically fitting multiple empirically determined pairs of a pH-value and a respective CO2 concentration in the gas phase above said medium, the CO2 concentration in the gas phase being in pH-CO2 equilibrium with said medium according to the above mentioned Henderson-Hasselbalch equation.

(55) The “FCO2M1(pH)[%]” parameter is the predicted CO2 concentration at the predefined temperature and the predefined pressure in a gas volume in pH-CO2 equilibrium state with said medium having a given pH-value, the prediction being specific for the medium M1 for which the relation was empirically obtained.

(56) The “pH” parameter indicates the pH value used as input of said equation, the input pH value being considered as the pH value of the medium in ph-CO2 equilibrium state of the medium based on which the prediction of the CO2 concentration is performed.

(57) “REL−M1” is a set of one or more parameters a1, a2, b1, b2, b3 connected by operators. The parameters have been obtained by adjusting samples of the medium M1 lacking the cell culture to multiple different pH values as described above, thereby letting the samples reach pH-CO2 equilibrium at the predefined pressure and temperature, by determining the equilibrium CO2 concentrations in respective gas volumes being in contact with the medium in the samples, by plotting the measured equilibrium CO2 concentrations against the respective equilibrium pH values of the samples (see FIGS. 5D and 6), fitting a curve 502 in the plotted values and deriving the parameters a1, a2 or b1, b2, b3 from the fitted curve.

(58) According to some embodiments, the equation FCO2.sub.M1(pH)=REL−M1(pH) is a linear equation according to FCO2.sub.M1(pH)[%]=a1×pH+a2. In this case, the parameters a1 and a2 are the parameters derived from the fitted curve. In the depicted example, a linear fit would yield the following equation:
FCO2.sub.M1(pH)=−19,177×pH+143,61. In this example, a1=−19,177 and a2=143,61.

(59) According to other embodiments, the equation FCO2.sub.M1(pH)=REL−M1(pH) is a polynomial equation according to FCO2.sub.M(pH)[%]=b1×pH.sup.2+b2×pH+b3. In this case, the parameters b1, b2 and b3 are the parameters derived from the fitted curve. In the depicted example, a polynomial fit would yield the following equation:
FCO2.sub.M1(pH)=19.969×pH.sup.2−302.25×pH+1146.2.
In this example, b1=19.969 and b2=−302.25 and b3=1146.2. Using a polynomial fit has the advantage that it is more accurate than a linear fit, although a linear fit is already sufficiently accurate for a PACO based cell culture comparison and monitoring.

(60) FIGS. 7a-d illustrate how a PACO value of a bioreactor 104, 106 can be calculated from a medium-specific relation 136 and some easily and dynamically obtainable measurement values.

(61) FIG. 7a shows the variation of a pH value measured in four different bioreactors I-IV while growing a cell culture in a particular medium M1 over multiple days. Preferentially, each pH value is measured using a pH-measuring device, e.g. a potentiometric pH-meter, immersed in the medium M1 of the bioreactor at pH-CO2 equilibrium of said medium.

(62) FIG. 7b shows the CO2 concentration in [%] of the total off gas of a bioreactor predicted for each of the four bioreactors using the measured, actual pH values of FIG. 7a and the medium-specific relation as input. For example, the medium-specific relation for medium M1 follows a polynomial equation according to FCO2.sub.M1(pH)[%]=b1×pH.sup.2+b2×pH+b3. The parameters b1, b2 and b3 are the parameters derived from the fitted curve depicted in FIGS. 5D and 6.

(63) For example, 4 days after t0 (the start of the project), the pH value measured in all bioreactors is about 6.95. Accordingly, the expected CO2 concentration at the fourth day is calculated by using the pH-value 6.95 as input:
FCO2.sub.M1(pH)[%]1=b1×6−95.sup.2+b2×6.95+b3.

(64) B1, b2 and b3 are the empirically determined parameters of the medium M1. The unit [%] means: the fraction of the CO2 outgas volume of the total off gas volume (corresponding to the total gas influx TGI

(65) $\left[\frac{\mathrm{mL}}{\min }\right])$
of the bioreactor at a particular time.

(66) FIG. 7c shows the actual (“measured”) CO2 off gas fraction measured in each of the four bioreactors. As can be inferred from a comparison of the predicted CO2 off gas fractions [%] and the actual (measured) CO2 off gas fractions of each bioreactor, significant differences exist which may stem from the impact of the metabolism of the cells in the cell culture and other factors having an impact on the pH-CO2 equilibrium of a medium.

(67) For example, a CO2 analyzer device 122, also referred to as “carbon dioxide sensor” as depicted in FIG. 3 may be used for repeatedly measuring the concentration of CO2 in the off gas per time unit. Common examples for CO2 sensors are infrared gas sensors (NDIR) and chemical gas sensors. NDIR sensors are spectroscopic sensors to detect CO2 in a gaseous environment by its characteristic absorption. Alternatively, the CO2 sensor may be a microelectromechanical sensor.

(68) FIG. 7d shows a PACO profile of one of the bioreactors generated as the difference of the predicted CO2 off gas concentrations of FIG. 7b and the measured CO2 off gas concentrations of FIG. 7c of said one bioreactor.

(69) To calculate the PACO values of the profile 402, the predicted and measured CO2 off gas concentrations (“CO2” or “FCO2” [%]) are transformed, according to embodiments of the invention, into CO2 off gas rates [mol/min].

(70) For example, the calculation can be performed for each of the measured pH values of FIG. 7a) according to:

(71) Expected CO2 Off Gas Rate:

(72) ${\mathrm{ACO}}_{M1-\mathrm{EXPECTED}}\left(\mathrm{pH}\right)\left[\frac{\mathrm{mol}}{\min }\right]=\frac{\mathrm{FCO}{2}_{M1-\mathrm{EXP}}\left(\mathrm{pH}\right)\left[\%\right]}{100}]=\times \frac{\mathrm{TGI}\left[\frac{\mathrm{mL}}{\min }\right]}{1000\times 22.414\left[\frac{L}{\mathrm{mol}}\right]}.$

(73) Measured (“Actual”) CO2 Off Gas Rate:

(74) 0${\mathrm{ACO}}_{M1-M}\left(\mathrm{pH}\right)\left[\frac{\mathrm{mol}}{\min }\right]=\frac{\mathrm{FCO}{2}_{M1-M}\left(\mathrm{pH}\right)\left[\%\right]}{100}]=\times \frac{\mathrm{TGI}\left[\frac{\mathrm{mL}}{\min }\right]}{1000\times 22.414.Math.\frac{L}{\mathrm{mol}}.Math.}.$

(75) Thereby, TGI

(76) $\left[\frac{\mathrm{mL}}{\min }\right]$
is the total off gas volume of the bioreactor for which the current PACO value is calculated, whereby the total amount of gas influx TGI

(77) $\left[\frac{\mathrm{mL}}{\min }\right]$
in the bioreactor may be used as the total off gas volume. In case the total off gas volume of the bioreactor is not constant, the TGI

(78) $\left[\frac{\mathrm{mL}}{\min }\right]$
needs to be determined at each time when the pH value used as input for calculating the CO2 off gas rate is measured. For example, in case the bioreactor has a first gas influx pipe for CO2, a second gas influx pipe for O2, a third gas influx pipe for N2 and a fourth gas influx pipe for environmental air, the gas flow in each of the four pipes being individually modifiable, the TGI

(79) $\left[\frac{\mathrm{mL}}{\min }\right]$
can be calculated as

(80) $\mathrm{CO}2\left[\frac{\mathrm{mL}}{\min }\right]+O2\left[\frac{\mathrm{mL}}{\min }\right]+N2\left[\frac{\mathrm{mL}}{\min }\right]+\mathrm{air}\left[\frac{\mathrm{mL}}{\min }\right].$
The value 2.414

(81) $\left[\frac{L}{\mathrm{mol}}\right]$
is the volume of a Mol of an ideal gas.

(82) Then, the PACO value

(83) $\left[\frac{\mathrm{mol}}{\min }\right]$
is calculated for each of the measured pH values (corresponding to a time ti) as the difference between the absolute CO2 off gas rate expected at said pH value in a cell-free medium M1 and the actually measured CO2 off gas rate

(84) $\left[\frac{\mathrm{mol}}{\min }\right]$
of the bioreactor.

(85) ${\mathrm{PACO}}_{M1-\mathrm{ti}}\left[\frac{\mathrm{mol}}{\min }\right]={\mathrm{ACO}}_{M1-\mathrm{EXP}}\left(\mathrm{ti}\right)\left[\frac{\mathrm{mol}}{\min }\right]-{\mathrm{ACO}}_{M1-M}\left(\mathrm{ti}\right)\left[\frac{\mathrm{mol}}{\min }\right].$

(86) The computation of the PACO value according to the above formulas may have the advantage that the formulas may be validly applied for comparing states of two or more bioreactors having different scales, types or equipment. The PACO value is computed from input data that does not involve an offline measurement. Offset measurements, e.g. for determining the pH value or biomass content of a sample according to previous approaches for determining the state of a bioreactor, might add offsets to the measurement values. Said offsets often depend on the equipment used in the respective plant and production site and thus might be an obstacle in reliably comparing the states of bioreactors located in different production sites. The above formulas thus may provide for an error-robust, global comparison of bioreactor states.

(87) However, the above formula can be adjusted in a lot of ways: the formula may be modified to include correction factors for the gas volume: the above formula assumes an ideal gas having a mol volume of 22.414 liters at 273.15 K and 1.01325*105 Pa pressure. In reality temperature, pressure and therefore volumes might differ. Therefore correction factors or measured data can be used to adjust formula and accuracy of the output. the formula may be modified to include correction factors for the measured CO2 off gas concentrations to compensate for pressure effects: thereby, the impact of environmental pressure changes on the CO2 off gas concentration may be compensated for; the formula may be modified to include correction factors for the humidity of the off gas to compensate for effects of the humidity in the off gas CO2 concentration measurements; the formula may be modified to include correction factors for the temperature to compensate for effects of the temperature on the pH measurement device used; pH values measured by two or more online pH meters may be received simultaneously and used for computing an average measured pH value for increasing the accuracy of the pH measurement; the formula may be modified to account for or compensate the effect of probe calibration, the compensation may be implemented e.g. in the form of a compensation curve that, if superimposed on a measured voltage of a pH meter, shifts the measured voltage per unit of modified pH (e.g. mV/pH); the curve may have a slope and amplitude suited for compensating current offsets of a pH measurement obtained from neutral pH probes. As an example, a temperature compensation facility of the pH meter could lead to different pH readings if switched on and off. Alternatively, the pH meter may support different algorithms for computing the pH from a measured voltage difference. All said effects may be compensated by introducing one or more compensation factors in the formula.

(88) Preferentially, the calculation of a reference PACO value is performed in the same way as the calculation of the PACO value, whereby the current pH values and CO2 off gas rates are measured in the reference bioreactor.

(89) According to embodiments, the controller unit controls the monitored bioreactor 104 such that the difference between a PACO value currently calculated for the controlled bioreactor 104 (from a pH value and a CO2 concentration [%] measured at a time ti after inoculation) and a corresponding reference PACO value in a reference profile 402 is minimized.

(90) Normalized PACO Values

(91) According to some embodiments, a normalized PACO value is calculated that takes into account the volume of the medium M1 in the bioreactor for which the PACO value is calculated.

(92) This may allow leveling out different bioreactor volumes and thus may allow to scale a bioreactor process up or down and/or to compare cell cultures of bioreactors having different dimensions.

(93) At first, normalized CO2 off gas rates “NACO.sub.M1” are calculated according to:

(94) 0${\mathrm{NACO}}_{M1-\mathrm{EXP}}\left(\mathrm{pH}\right)\left[\frac{\frac{\mathrm{mol}}{\min }}{L}\right]=\frac{\frac{{\mathrm{ACO}}_{M1-\mathrm{EXP}}\left(\mathrm{pH}\right)\left[\%\right]}{100}]=\times \frac{\mathrm{TGI}\left[\frac{\mathrm{mL}}{\min }\right]}{1000\times 22.414\left[\frac{L}{\mathrm{mol}}\right]}}{\mathrm{volume}\mathrm{of}\mathrm{medium}M1\mathrm{in}\mathrm{bioreactor}\left[L\right]}.{\mathrm{NACO}}_{M1-M}\left(\mathrm{pH}\right)\left[\frac{\frac{\mathrm{mol}}{\min }}{L}\right]=\frac{\frac{{\mathrm{ACO}}_{M1-M}\left(\mathrm{pH}\right)\left[\%\right]}{100}]=\times \frac{\mathrm{TGI}\left[\frac{\mathrm{mL}}{\min }\right]}{1000\times 22.414\left[\frac{L}{\mathrm{mol}}\right]}}{\mathrm{volume}\mathrm{of}\mathrm{medium}M1\mathrm{in}\mathrm{bioreactor}\left[L\right]}.$

(95) In case the PACO is calculated for the reference bioreactor 102, the volume of the medium M1 in the bioreactor is the “volume of the medium in the reference bioreactor”. In case the PACO is calculated for the monitored and/or controlled bioreactor 104, the volume of the medium M1 in the monitored and/or controlled bioreactor is the “volume of the medium in the bioreactor”. Said volume does not comprise the gas phase above the medium.

(96) Then, a volume-normalized PACO value is calculated for a particular time ti when the pH value used for predicting the CO2 off gas value was measured:

(97) ${\mathrm{NPACO}}_{M1-\mathrm{ti}}\left[\frac{\frac{\mathrm{mol}}{\min }}{L}\right]={\mathrm{NACO}}_{M1-\mathrm{EXP}}\left(\mathrm{ti}\right)\left[\frac{\frac{\mathrm{mol}}{\min }}{L}\right]-{\mathrm{NACO}}_{M1-M}\left(\mathrm{ti}\right)\left[\frac{\frac{\mathrm{mol}}{\min }}{L}\right].$

(98) According to embodiments, the normalized CO2 off gas rates and the PACO values can also be calculated by using the total mass of the medium M1 in the bioreactor instead of the volume of the medium in the bioreactor. Thereby, 1 L of the medium typically corresponds to a mass of 1 kg.

(99) FIG. 7d shows a PACO profile resulting from the difference of the predicted and actually measured CO2 off gas rate.

(100) FIG. 8a is a diagram showing a reference PACO profile 402 of a reference bioreactor 102, a PACO profile 802 of a first monitored and/or controlled bioreactor 104 and a further PACO profile 804 of a second monitored/and controlled bioreactor 106. The diagram indicates that already at time t0 (in the example depicted in FIG. 8 time t0 is the time of inoculation of a bioreactor with the cell culture), the PACO value of the bioreactor 104 (“B1”) significantly differs from the PACO value at t0 of the reference bioreactor. According to embodiments, this can be used as an indication that the pH-meters of the bioreactors whose profiles are compared have been calibrated differently. Assuming that the pH measuring device of the reference bioreactor was calibrated correctly, the PACO deviation at t0 (i.e., at or before the medium comprises any cell culture cells which could modulate the PACO), can be used as an indication that the pH measuring device of the monitored bioreactor 106 (“B2”), 104 (“B1”) was erroneously calibrated and should be correctly calibrated before starting to grow the cell culture.

(101) In the depicted example, the PACO value of profile 804 of the monitored bioreactor 106 (“B2”) at time t0 is identical to the reference PACO value of the reference PACO profile 402 at time t0. The PACO value of profile 802 of the monitored bioreactor 104 (“B4”) at time t0 significantly differs the reference PACO value of the reference PACO profile 402 at time t0.

(102) Alternatively, instead of the PACO values, the CO2 concentration of the off gas of the two bioreactors can be compared to determine if the pH measuring devices of the two compared bioreactors were calibrated identically. The two bioreactors are initiated and filled with the same cell-free medium at the same pressure and temperature and a current pH value and a current CO2 concentration of the medium in the two bioreactors are measured and compared when the two bioreactors have reached pH-CO2 equilibrium. If the CO2 concentration in the off gas of the two bioreactors are identical while the pH value are not, or if the pH values of the two bioreactors are identical and the CO2 concentration in the off gas are not, the comparison unit determines that the two bioreactors were calibrated differently.

(103) Wrongly calibrated pH meters may result in inaccurate results when comparing the cell culture states of two cell cultures based on PACO values. This is because the PACO value is a derivative of the pH value. As a consequence, also any action taken by the controller to minimize the PACO difference may fail to minimize the PACO differences (this effect is not shown in FIGS. 8a and 8b, because during the growing of the cell culture in bioreactor B2, the pH-CO2 equilibrium was modified by adding a base and increasing the total gas influx rate; thus, the PACO profile of B2 significantly differs from the reference PACO profile although the pH meters of the reference bioreactor and of bioreactor B2 were calibrated in the same way).

(104) FIG. 8b is a diagram showing the PACO profile differences of the PACO profiles 802, 804 of two bioreactors 104, 106 to the reference PACO profile 402 of the reference bioreactor 102. Curve 810 represents PACO profile differences of the bioreactor 104 and the reference bioreactor and curve 808 represents PACO profile differences of the bioreactor 106 and the reference bioreactor. The PACO profile differences of the bioreactor 106 to the PACO reference profile 402 are significantly larger than the PACO differences of the bioreactor 104, because while growing the cell culture in B2, the pH-CO2 equilibrium was modified.

LIST OF REFERENCE NUMERALS

(105) 100 system for monitoring and/or controlling cell culture states in a bioreactor 102 reference bioreactor 104 monitored and/or controlled bioreactor B1 106 monitored and/or controlled bioreactor B2 108 pH-measuring device 110 processor 112 memory 114 storage medium 116 reference PACO profile 118 reference PACO profile 120 interface for receiving one or more reference PACO profiles and medium-specific relations 122 CO2 off gas analyzer 124 CO2 off gas analyzer 126 CO2 off gas analyzer 128 interface for receiving parameters measured in one or more bioreactors 130 PACO comparison unit 132 control unit 134 display 136 medium-specific relation for medium M1 138 medium-specific relation for medium M2 140 sensor for total gas influx 142 pH-measuring device 144 sensor for total gas influx 146 pH-measuring device 202-220 steps 402 PACO reference profile 502 medium-specific relation plotted for four bioreactors 802 PACO profile of a monitored bioreactor 804 PACO profile of a monitored bioreactor 808 profile difference to reference PACO profile 810 profile difference to reference PACO profile M1 cell culture medium TGI.sub.B1 total gas influx into bioreactor B1 TGI.sub.B2 total gas influx into bioreactor B2 TGI.sub.R total gas influx into the reference bioreactor TGO.sub.B1 total off gas of bioreactor B1 TGO.sub.B2 total off gas of bioreactor B2 TGO.sub.R total off gas of reference bioreactor TLI.sub.B1 total liquid influx into bioreactor B1 TLI.sub.B2 total liquid influx into bioreactor B2 TLI.sub.R total liquid influx into the reference bioreactor TLO.sub.B1 total (liquid) outflow of bioreactor B1 TLO.sub.B2 total (liquid) outflow of bioreactor B2 TLO.sub.R total (liquid) outflow of reference bioreactor