Standard Calibration and On-Line Estimation of Cell-Specific Growth and Protein Synthesis Rates in Chi.Bio Mini-Bioreactors

Abstract

Low-cost mini-bioreactor platforms are becoming increasingly important in synthetic biology and biotechnology for the characterization of genetic constructs and their initial scaling-up to large-scale cultures. Key process variables are the specific growth rate of cells and the synthesis rate of reporter proteins associated with transcriptional units of interest. These variables are of paramount importance for the characterization of gene synthetic circuits. In addition, their on-line estimation can be used for real-time monitoring of cells’ metabolic state and gene circuit dynamic performance, thus allowing for on-line decision taking. In this work, we first describe a procedure for the calibration of absorbance and fluorescence measurements, ensuring standardized and comparable units across different experimental setups and measurement devices. Then, we implement an observer-based software sensor that uses the calibrated on-line measurements to simultaneously estimate the specific growth and protein synthesis rates. We implemented the calibration procedure and software sensor in a Chi.Bio mini-bioreactor platform. The experimental results show very good performance and pave the way for the use of mini-bioreactor platforms in the real-time characterization of gene synthetic circuits under dynamically regulated time-varying complex scenarios.

1. Introduction

Bioreactors have played an increasingly important role in fields such as scientific research, industrial applications, biotechnology, and chemistry [1]. Typically, bioreactors are devices that provide a suitable environment for biochemical reactions where microbial biomass cultivation is essential [2,3]. Most conventional bioreactors operate in batch mode, where a fixed amount of nutrients and oxygen is provided and consumed gradually by the bacterial cultivation. In contrast, operating in continuous mode involves a steady inflow of a fresh medium and the simultaneous removal of culture fluid [4]. Continuous bioreactors have some advantages, such as increased productivity for biomass and growth associated products, or the possibility of analyzing cultures under sets of steady-state conditions [5,6]. In-between, fed batch operation offers the possibility of controlled cell growth, maximized cell density, and high yield [7,8,9]. A wide variety of bioreactors, such as industrial, experimental, and open-source platforms, are available on the market, each suited to different operational scales and research needs. While industrial bioreactors are typically designed for large-scale production processes, lab-scale systems are commonly used in laboratory environments to support research and development activities.

Indeed, the possibility of setting culture conditions such as maintaining a steady cell growth rate or constant cell density, allows for the characterization of gene synthetic devices under a controlled physiological state of host–cells [10,11]. Thus, constant cell density has allowed for the investigation of circuit performance under constant genetic load [12] and has been used to improve the predictability of gene synthetic devices [13]. On the other hand, the cell growth rate is directly linked to genetic noise [14] and affects the dynamics of gene expression. Indeed, the cell growth rate is representative of the cell metabolic state [15]. The growth rate reflects how cells allocate their metabolic resources and thus directly affects the behavior of synthetic circuits. Thus, control of the cell growth rate ensures that observed behaviors are not consequences of uncontrolled metabolic fluctuations and allows for the precise characterization and more accurate parameter fitting in mathematical models of gene regulation [16].

In this context, small-scale open-source bioreactors are increasingly being used for the characterization of gene synthesis devices under different culture environments, and for their design in the framework of Design–Build–Test–Learn (DBTL) iterative strategies [17,18,19,20]. Mini-bioreactors are small-volume, highly automated cultivation systems (typically 5–50 mL) that replicate the control features of large-scale fermenters. Their use of mini-bioreactors offers important advantages for the reliable characterization of genetic circuits over lab-scale and larger ones [21]. Mini-bioreactors enable parallel experiment to be used under precisely controlled conditions, which is ideal for characterizing libraries of genetic devices under uniform metabolic states. They can mimic chemostat or turbidostat conditions at a small scale, with reduced reagent cost and volume, and yet be informative towards scaling-up [22].

Most modern bioreactors have sensors that monitor key variables of bacterial cultures, such as temperature, pH, absorbance, and fluorescence. These variables offer valuable information on the physiological state of microbial cultures; additionally, they allow for the analysis of biomolecular interactions, quantification of nucleic acids and proteins, and monitoring of cellular processes [23]. Among these variables, absorbance and fluorescence are the most widely used, not only for monitoring cellular processes in bacterial cultures and quantifying biomolecular interactions [23] but also as core techniques in various laboratory analytical procedures [24]. Although bioreactors can quantify various characteristics of a bacterial culture, these measurements are often expressed in arbitrary units, making them not directly comparable to those obtained from other instruments or bioreactors. As a result, the characteristics of the culture are not interchangeable between them. To overcome this limitation, the use of standardized measurement units enables consistent, quantitative comparisons across different instruments and experimental setups. Standardized measurement units enhance comparability across experiments, laboratories, and measurement systems, improving reproducibility and reliability [25,26,27,28]. Moreover, the engineering of biological systems in a rational way, as pursued in synthetic biology, relies on the use of mathematical models for the design process. These models ideally require the use of parameters and process variables defined in precise standard biophysical units [25,29,30,31].

An approach for the standardization of measurement units is expressing absorbance in particle-based and fluorescence intensity in Molecules of Equivalent Fluorescein (MEFL), as shown in works [19,28]. This approach is valuable because it provides a clear physical and biological interpretation of optical measurements. In this way, absorbance measurements, typically recorded as optical density (OD), can be interpreted in terms of particle concentration, under the assumption that the particles have optical properties and scattering behavior comparable to an E. coli cell [26]. In addition, fluorescence measurements can be expressed in terms of Molecules of Equivalent Fluorescein (MEFL), a standardized unit that correlates raw fluorescence measurements with the number of Molecules of Equivalent Fluorescein. MEFL units offer a molecular-scale interpretation of fluorescence intensity, enabling the estimation of the average number of Green Fluorescent Protein (GFP) molecules per cell [28].

Although standard units are documented at a small scale, typically employed in microplates of 96-well plates with small volumes, 200 $\mathrm{\mu }$L per well, they have only occasionally been applied at larger scales, particularly in bioreactors. The successful implementation of standard units such as Particles and Molecules of Equivalent Fluorescein (MEFL) in the context of microplates demonstrates their potential utility and scalability. With the aim of enabling a physical and biophysical interpretation of optical measurements in experimental setups involving larger culture volumes, in this work we apply the standardized units’ approach to calibrate a Chi.Bio mini-bioreactor [20].

In addition, these standardized units can serve as input measurements for downstream applications, such as the estimation of the growth rate and protein synthesis rate. This type of information is particularly relevant in fields like microbiology, synthetic biology, and biotechnology, where precise control of cellular behavior enhances both experimental reproducibility and industrial process performance [32]. Since growth and protein synthesis rates cannot be directly measured, indirect estimation methods must be employed [33,34]. The growth rate can be estimated using on-line software sensors (i.e., mathematical observers) that track the accumulation of particles, which reflects the biomass concentration in the system [35,36]. This continuous estimation strategy offers greater temporal resolution and responsiveness compared to traditional off-line sampling, enabling on-line insights into growth dynamics and supporting data-driven decision making. Similarly, the protein synthesis rate can be estimated using software sensors based on MEFL per particle as a standardized unit of fluorescence per cell. This approach allows for the on-line monitoring of protein production during experiments, providing actionable information without interrupting the process. Such methods are particularly valuable in high-throughput screening bioprocessing workflows, where the continuous assessment of protein expression is essential for process optimization and control [32,37].

In this context, we implemented an on-line software sensor embedded in the main program of the Chi.Bio mini-bioreactor to estimate both the growth rate and protein synthesis rate in batch cultures. The on-line sensor integrates a second-order super-twisting observer, a robust mathematical tool designed for real-time estimation, which receives standardized measurements, particle concentration, and MEFL per particle as inputs to reconstruct unmeasured states on-line. This approach enables the continuous monitoring of culture dynamics without invasive sampling or interruptions, providing a robust framework for adaptive experimental protocols.

The remainder of this paper is organized as follows. Section 2 presents the materials and methods used for fluorescence and optical density calibration, the experimental setup implemented in the Chi.Bio mini-bioreactor, and the formulation of the on-line software sensor. Section 3 describes the results and discussion, highlighting the accuracy and robustness of the proposed approach. Finally, Section 4 summarizes the main conclusions of this study and outlines potential directions for future research.

2. Materials and Methods

2.1. Chi.Bio Mini-Bioreactor and Cytation 3 Plate Reader

Chi.Bio is an open-source mini-bioreactor (Labmaker, Berlin, Germany) used as an alternative in the experimental automation of biological research due to its versatility for automating a wide range of biological experiments [18,20]. It was selected due to its modular design, working volume, and capability to operate in batch, fed-batch and continuous mode, allowing bioprocess strategies to be carried out, such as chemostat and turbidostat operation. Furthermore, it has sensors that are used to measure different variables of biological interest, such as temperature, optical density (OD), fluorescence in up to four detection channels, temperature, and others. All measurements are handled without human contact to avoid contamination in the biological experiment inside a vial with a capacity of 30 mL and a working volume of 20 mL [20].

On the other hand, the Cytation 3 Plate Reader (Agilent BioTek, Winooski, VT, USA) is an instrument that integrates multiple detection modalities, including absorbance, OD, fluorescence, and luminescence. The Cytation 3 Plate Reader was chosen for its ability to perform multiplexed absorbance and fluorescence measurements with customizable excitation/emission filters, offering high sensitivity and flexibility for off-line validation in batch mode. The system was used to acquire measurements of OD and fluorescence using black 96-well microplates, used both as a reference standard for the calibration of the Chi.Bio and for cross-validation of the results obtained.

2.2. Experimental Setup

Plasmid

The plasmid used in this work was constructed in the framework of the IGEM competition 2018 as part of the work carried out by the grand prize-winning team Valencia UPV IGEM Team 2018 [38]. This plasmid has the constitutive promoter BBa_J23106, a RBS (BBa_B0030), and the transcriptional terminator BBa_B0015. All parts were taken from the Printeria Part Collection [38] in the Registry of Standard Biological Parts [39] and cloned using the Golden Gate assembly method [40,41]. Plasmid BBa_K2656105 [42] has the fluorescent protein GFPmut3, as shown in Figure 1.

Strain 10G (E. cloni^®, Lucigen) carrying one plasmid was incubated overnight at 37 °C and 250 rpm in LB medium with an appropriate antibiotic (Kanamycin, KanR) from the Glycerol stocks at −80 °C. Then, 3 mL of M9 minimal medium with KanR was inoculated with 300 $\mathrm{\mu }$L overnight culture and incubated 4 h at 37 °C and 230 rpm. Then, the culture was chilled on an ice-water bath, and the optical density at 600 nm, ${\mathrm{OD}}_{600}$, was measured. The culture was then diluted with M9 minimal medium with KanR in order to have an initial culture with ${\mathrm{OD}}_{600}=0.05$ in a final volume of 20 mL. Finally, the OD and fluorescent measurements were taken every 30 seconds with the Chi.Bio mini-bioreactor. Strain 10G was selected due to its high transformation efficiency, plasmid stability, and compatibility with a wide range of synthetic biology applications. On the other hand, the plasmid used encodes a constitutive GFP expression cassette, enabling continuous monitoring of cellular fluorescence as a proxy for protein production. This combination allowed for the validation of the calibration and the software sensor in a well-characterized condition.

2.3. Calibration Protocols

2.3.1. Optical Density Calibration

A manual calibration procedure was initially established to characterize the Chi.Bio sensor and obtain specific digital output values across its operational digital range, interval of digital output values. We used the preliminary methodology described in [43]. For this purpose, an E. coli culture was used with an initial ${\mathrm{OD}}_{600}$ of 3.5 measured using Cytation 3. Serial dilutions were manually prepared in standard 30 mL flat-bottom vials (Fisher Scientific, Waltham, MA, USA, part number 11593532). Measurements were concurrently obtained using both Chi.Bio (650 nm LED) and Cytation 3 (monochromator-based), with the latter being a calibrated instrument that served as the reference standard. Chi.Bio provided digital output values (x in Equation (1)), while Cytation 3 yielded reference OD measurements. These data were used to formulate a mathematical model (Equation (1)) that relates the two sets of readings. It should be noted that phosphate-buffered saline (PBS) was used as a blank to normalize the digital output values by dividing them by the digital output value of the blank sample (details are outlined in Section S1.1 in the Supplementary Materials). Finally, the OD values of the Chi.Bio, ${\mathrm{OD}}_{chi.Bio}$, where obtained by identifying the reference OD values obtained with Cytation 3 to the calibrated Chi.Bio ones using the nonlinear regression model:

$${\mathrm{OD}}_{Chi.Bio}={\displaystyle \frac{a{x}^n}{x^n+k^n}},$$

(1)

where x is the natural logarithm of the normalized digital output value of the sensor. In this model, a represents the saturation level of the sensor, k corresponds to the midpoint of its dynamic sensor range, and n determines how sharply the sensor response transitions from the linear to the saturated regime. All these parameters were estimated by fitting the model to the experimental data. This sigmoid model was used to compensate for the saturated response of the sensor at high optical densities. Additionally, the nonlinearity of the OD model helps capture the nonlinearity behavior given by the Beer–Lambert law at high concentrations [26].

The ${\mathrm{OD}}_{chi.Bio}$ values were further converted to particle counts using

$$\mathrm{Particles}={10}^{p_0+2}{\left(0.55·{\mathrm{OD}}_{chi.Bio}\right)}^{p_1},$$

(2)

with parameters $p_0$ and $p_1$ taken from prior characterization using silica beads [28]. Notice that this last step must be carried out for the spectrophotometer device used as base reference so as to obtain the corresponding parameters $p_0$ and $p_1$. In our case, these can be found in Table S1 (OD curve fitting parameters and the graph of the fitting curve) and in Figure S6 (fitting OD calibration curve (log-transformed) at 600 nm obtained from the Chi.Bio platform in the Supplementary Materials).

2.3.2. Fluorescence Calibration

A manual calibration protocol was similarly conducted for fluorescence measurements using fluorescein sodium salt (Sigma-Aldrich, CAS 518-47-8) as the reference fluorophore. Serial 1:2 dilutions were prepared from an initial stock solution of 21.17 $\mathrm{\mu }$M fluorescein. Fluorescence was recorded using both the Chi.Bio platform (excitation/emission: 457/35 nm and 550/42 nm) and a Cytation 3 Plate Reader (excitation/emission: 488 nm and 530 nm). To standardize fluorescence values across devices and fluorophores, a two-step normalization strategy was employed. First, spectral normalization was applied to convert raw fluorescence outputs into Normalized Fluorescence Radiance (NFR), a unit that accounts for the brightness of the fluorophore used. During the calibration with fluorescein, the Chi.Bio digital output was divided by the known molecular brightness of fluorescein (B_fluorescein$=597.5$) to compute NFR values.

However, when quantifying fluorescence signals from biological samples expressing GFP, the normalization must reflect the intrinsic brightness of GFP itself. Therefore, for GFP-expressing cells, the NFR was computed by dividing the Chi.Bio fluorescence signal by the molecular brightness of GFP (B_GFP), rather than fluorescein. This adjustment ensures that differences in fluorophore brightness are accounted for, enabling meaningful biological interpretation of fluorescence data. In the final calibration step, a nonlinear model was used to relate NFR values to Molecules of Equivalent Fluorescein (MEFL), thereby standardizing measurements in widely accepted units. The calibration model takes the following form:

$$\mathrm{MEFL}=a·e^{b·x}+c·e^{d·x^{0.955}},$$

(3)

where x is the NFR; $a,b,c,d$ are parameters estimated from calibration data (see Table S3 and Supplementary Figure S7). This dual-exponential function was chosen based on its superior fitting performance compared to linear and polynomial alternatives, which exhibited lower $R^2$ values and higher residuals [44].

3. Results

3.1. Automated Optical Density and Fluorescence Calibration Procedure in Chi.Bio

Even if the manual calibration protocols developed above need only be carried out once, or in cases of re-calibration either to compensate sensors’ aging drifts or to improve the calibration in some measurement range, they are time-consuming, as they require a large number of dilutions. To overcome this limitation, we implemented an automated protocol embedded in the Chi.Bio software. This protocol carries out the dilutions, takes the measurements for each dilution, manages the data acquisition and comparison with the reference values obtained with a plate reader for the same dilutions, and finally fits the model parameters. For the calibration of OD, only an ordinary culture is required if the reference spectrophotometer has not changed, so that the conversion to particles does not change either. Notice that silica beads are expensive. Therefore, the restriction of their use to one initial calibration in a reference spectrophotometer using small volumes is a desirable feature. For the calibration of fluorescence, the dilutions are carried out using fluorescein, so the results are independent of any particular culture.

Since sensor measurements were collected at several points while deriving the OD and MEFL mathematical models (Section 2.3), these measurements were later reused as markers for the automatic calibration implemented in the Chi.Bio platform. Subsequently, the Chi.Bio pumping system was used to automate the inflow of media and the outflow of the mixture as a dilution strategy. This automatization uses a series of point values (markers), within the operational digital range of the Chi.Bio spectrophotometer, to enable or disable the pumps in order to maintain a constant working volume. This dilution strategy was adopted to account for the limited accuracy of the pumps when handling small liquid volumes, as required in classical manual stepwise dilution protocols. As shown in Figure 2, the process begins with Chi.Bio containing a highly concentrated culture or fluorescein sample, followed by a continuous addition of fresh media to dilute the sample until a digital output value (marker), in the operational digital range, is reached. At that point, four consecutive digital values of the current sample are taken using the Chi.Bio spectrophotometer, and their average is calculated to improve measurement accuracy (Figure 2B). Subsequently, an extracted volume of the same current culture is taken from the Chi.Bio vial to measure its corresponding OD value or fluorescein concentration value in Cytation 3 (Figure 2C). Both the Chi.Bio averaged digital output and its corresponding OD or fluorescein concentration value measured by Cytation 3 are entered through the user interface (Figure S3: OD calibration interface; Figure S5: Fluorescence calibration interface in the Supplementary Materials) specifically developed for the OD or fluorescence calibration protocol (Figure 2D). This process is repeated n times, according to the number of dilution steps specified by the user. At the end of the calibration process, the algorithm uses the models of OD (Equation (1)) or MEFL (Equation (3)) to re-estimate its corresponding parameters with the data obtained by each dilution in the step n (Figure 2E). The resulting calibration curves demonstrated high accuracy and consistency, with $R^2$ values of 0.999 for OD and MEFL, an RMSE value of 0.035 for OD, and a normalized RMSE value of 0.035 for MEFL as shown in the following tables: Table S1: OD curve fitting parameters. Table S3: MEFL curve fitting parameters in the Supplementary Materials.

The comparison between OD and fluorescence values obtained from the automated Chi.Bio calibration and those measured with Cytation 3 confirmed strong agreement and robustness across multiple experimental measured data. This result is further supported by the acceptable absolute error calculated between measurements from both instruments, as detailed in the following: Table S2 Comparison measurements between reference OD values and Chi.Bio OD values. Table S4: Comparison between reference $log\left(\mathrm{MEFL}\right)$ values and $log\left(\mathrm{MEFL}\right)$ from Chi.Bio in the Supplementary Materials.

3.2. On-Line Software Sensor for Growth and Protein Synthesis Rates

We implemented an on-line software sensor based on second-order super-twisting sliding mode observers from De Battista et al. [35] to estimate the specific growth rate $\mu$ and the protein synthesis rate $\Pi$ expressed by the gene circuit. The only assumption required is for the culture to follow the dynamic mass balance in the bioreactor:

$$\begin{array}{cc}\hfill \dot{N}& =(\mu -D)N\hfill \\ \hfill \dot{p}& =\Pi -(\mu -D)p\hfill \end{array}$$

(4)

where N is the biomass expressed as number of particles (recall for one particle of E. coli is approximately equal to one cell), $p\left(\mathrm{MEFL}·{\mathrm{Particle}}^{-1}\right)$ is the amount of synthesized protein per cell, D is the dilution rate, $\mu \left({\min }^{-1}\right)$ is the specific growth rate of the bioreactor, and $\Pi \left(\mathrm{MEFL}·{\mathrm{Particle}}^{-1}·{\min }^{-1}\right)$ is the synthesis rate.

The software sensor consists of a joint observer structure including two hierarchically coupled estimation subsystems: the first estimates $\mu$ using the measured number of particles, while the second subsystem estimates $\Pi$ using fluorescence measurements (in MEFL $·$ Particle⁻¹) and $\mu$ provided by the first subsystems. Each estimation subsystem is implemented as a second-order super-twisting observer. This coupled configuration allows the system to reconstruct both unmeasured states ($\mu$, $\Pi$) on-line and ensures finite-time convergence of the sensor. The complete software sensor is formulated as a single dynamical system composed of four state variables: $(z_1,z_2)$, which estimates $\mu$, and $(z_3,z_4)$, which estimates $\Pi$. The sensor was defined in the following system of equations:

$$\begin{array}{c}\hfill \left\{\begin{array}{cc}{\dot{z}}_1=\hfill & \left(-{\displaystyle \frac{D}{N}}+{\rho }_1{z}_2+2{\rho }_1{\beta }_1{\left|{\sigma }_1\right|}^{{\displaystyle \frac{1}{2}}}\mathrm{sign}\left({\sigma }_1\right)\right)z_1\hfill \\ {\dot{z}}_2=\hfill & {\alpha }_1\mathrm{sign}\left({\sigma }_1\right)\hfill \\ {\dot{z}}_3=\hfill & \left({\rho }_2{z}_4+2{\rho }_2{\beta }_2{\left|{\sigma }_2\right|}^{{\displaystyle \frac{1}{2}}}\mathrm{sign}\left({\sigma }_2\right)\right)-(z_2-D)z_3\hfill \\ {\dot{z}}_4=\hfill & {\alpha }_2\mathrm{sign}\left({\sigma }_2\right)\hfill \\ {\sigma }_1=\hfill & {\rho }_1^{-1}ln\left({\displaystyle \frac{x}{z_1}}\right)\hfill \\ {\sigma }_2=\hfill & {\displaystyle \frac{v-w}{w+ϵ}}\hfill \\ \widehat{\mu }=\hfill & {\rho }_1{z}_2\hfill \\ \widehat{\Pi }=\hfill & {\rho }_2{z}_4\hfill \end{array}\right.\end{array}$$

(5)

where $z_1$ denotes the estimated number of particles, $z_2$ is the unscaled estimation of the growth rate $\mu$, $z_3$ represents the estimated MEFL per particle count, $z_4$ is the unscaled protein synthesis rate $\Pi$, $ϵ$ is a regularization term (avoid division by zero), ${\sigma }_1$ represents the sliding surfaces used to estimate $\mu$, ${\sigma }_2$ represents the sliding surfaces used to estimate $\Pi$, v is the dynamic scaling of $\rho$, w is the dynamic scaling of $z_3$, and $\widehat{\mu }$ and $\widehat{\Pi }$ correspond to the estimated growth rate and protein synthesis rate, respectively. Notice that Equations (4) and (5) retain the dilution rate term D for the sake of generality. However, in batch mode, $D=0$. Therefore, the equations will be simplified accordingly during the analysis in batch operation.

Given that MEFL per particle unit has a high order of magnitude, $\rho$ and $z_3$ were scaled by the dynamic scaling factor ${\xi }_t$ as shown in

$$\begin{array}{c}\hfill \left\{\begin{array}{cc}v=\hfill & {\displaystyle \frac{p}{{\xi }_t+ϵ}}\hfill \\ \\ w=\hfill & {\displaystyle \frac{z_3}{{\xi }_t+ϵ}}.\hfill \end{array}\right.\end{array}$$

(6)

The factor ${\xi }_t$ was computed using a mathematical model based on an Exponential Moving Average (EMA) recursive digital filter:

$${\xi }_t=(1-\lambda ){\xi }_{t-1}+\lambda \psi$$

(7)

with

$$\psi =max(\mid p\mid ,\mid z_3\mid )$$

(8)

where $\psi$ is the new input value (in MEFL $·$ Particle⁻¹), ${\xi }_{t-1}$ is the previous scaling factor value, and $\lambda \in [0,1]$ is a smoothing factor that controls the influence of the new input on the updated value. In our case, we set $\lambda =0.5$ because it attenuates the noise present in the estimation of $\Pi$. This scaling improvement in the dynamic of the software sensor helps reduce computational load, improves the numerical stability of the system solver [45], and allows compensation for signal imbalance by comparing them independently of their absolute scales [46]. Furthermore, the input signal $\psi$ was bounded within a dynamic threshold to maintain the system within a stable operating measurement range.

The observer parameters were tuned to the following values: ${\alpha }_1=286.107$, ${\beta }_1=48.503$, ${\rho }_1=0.325$, ${\alpha }_2=2\times {10}^5$, ${\beta }_2=15\times {10}^4$, and ${\rho }_2=0.01$. These values were obtained by optimizing the observer against off-line experimental data to minimize the estimation error for both $\mu$ and $\Pi$.

3.3. Experimental Validation in Batch Cultivation

The calibration procedure and the on-line software sensor were experimentally validated in several batch cultivations. Figure 3 exemplifies the results obtained with one batch culture. Additional results can be found in Section S3 (Figures S10 and S11) in the Supplementary Materials. The OD, particle count, total MEFL, and MEFL per particle were accurately quantified using the calibrated Chi.Bio platform. Additionally, the software sensor closely tracks the measurements of particles, MEFL per particle (Figure 3C,E), and estimates $\mu$ and $\Pi$ (Figure 3B,D). Comparative analysis with historical data collected using Cytation 3 (200 $\mathrm{\mu }$L sample volumes) demonstrated consistency in estimated growth and protein synthesis rates. Specifically, we validated the Chi.Bio results using three independent cultures, as shown in Figure S9 of the Supplementary Materials. The experimental relationships between $\Pi$ and $\mu$ obtained from Chi.Bio experiments aligned closely with previously collected reference data, confirming the reliability and scalability of the calibration methods implemented in the Chi.Bio platform (Figure 3F). Notice that the software sensor based on the super-twisting observer ensures finite-time convergence [36]. In our batch experiments, the worst-case scenario from this point of view was requiring around one hour and a half for convergence. This was enough to obtain good results, as demonstrated by the fact that the on-line estimations obtained in the Chi.Bio mini-bioreactor fully agree with the cell growth and expression synthesis rates obtained for the validation historical results. The latter were obtained with the plate reader and evaluated off-line using all the time-resolved experimental information and smoothed polynomial approximations of the time derivatives, so that the observed agreement could only be obtained if the convergence rate was fast enough.

4. Conclusions

This study has described a set of integrated enhancements added to the Chi.Bio mini-bioreactor platform. First, we have introduced a procedure for the calibration of optical density and fluorescence in terms of standardized particles and Molecules of Equivalent Fluorescein (MEFL), respectively. The standardized calibration procedure ensures consistent and comparable measurements of the cells’ population size and the synthesis of reporter proteins across different scales and devices in standard units derived from regular measurements of OD and fluorescence. The calibrated ChiBio showed that the resulting mathematical model curves used to obtain particles and MEFL measurements from OD and fluorescence intensity, respectively, were reliable enough to be applied for the interpretation of a bacterial culture dynamics in the bioreactor context.

The calibration response might be affected by the size and morphology of the cell, particularly in organisms significantly different in size from E. coli (approximately 950 nm) used during calibration. Notice, though, that only the step relation OD with particles in the reference spectrophotometer will be affected by having cells with a size and morphology significantly different from the ones of the cell used for calibration. On the other hand, the calibration of fluorescence to MEFL is independent of the characteristics of the genetic elements and optical density, as this calibration only relates the spectral properties of the reporter protein to those of fluorescein.

In addition, we have added an on-line software sensor for the cell growth rate and the expression synthesis rate, the two key variables required for the characterization of gene synthetic circuits. The implemented on-line software sensor effectively captured changes in both the specific growth and synthesis rates, demonstrating the possibility of obtaining meaningful insights into the physiological state of a culture using standard units, particles and MEFLs as sensor inputs.

Finally, our results underscore the importance of considering standard units, such as particles and MEFL measurements, as well as their effective integration into applications such as on-line software sensors, enabling the extraction of valuable information in real time from cultures in the context of a mini-bioreactor. Additionally, this approach enhances interpretability and reproducibility at the microscale, laying the groundwork for scalable implementation to larger bioreactor platforms to support data-driven decision making in batch-fed and continuous industrial processes.