## 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  
Figure 3: Experimental validation of the on-line software sensor for \(\mu\) and \(\Pi\) estimation in Chi.Bio batch cultivation. (**A**) Schematic representation of the Chi.Bio platform with the culture (_E. coli_ carrying the plasmid BBa_K2656105), and a diagram of the expression dynamics. (**B**) On-line estimation of \(\mu\) by the software sensor, validated against filtered off-line measurements. The vertical blue dashed line indicates the estimated convergence time of the sensor. (**C**) Reconstruction of the input signal for particle. The gray line shows the filtered particle measurements, and the colored line shows the reconstructed version generated as a byproduct of the sensor. (**D**) Estimation of \(\Pi\), compared with off-line validation data obtained from filtered data. The estimated convergence point is marked by the blue vertical line. (**E**) Analogous to (**C**), but for fluorescence expressed in MEFL per particle. The software sensor reconstructs the fluorescence signal and tracks its evolution throughout the cultivation. (**F**) Cross-experimental validation of the relationship between synthesis rate and specific growth rate. The green line represents the mean relationship derived from Cytation 3 measurements across multiple culture experiment. The blue-shaded region indicates the 95% confidence interval. The colored line represents an independent Chi.Bio experiment. All trajectories fall within the expected confidence bounds, confirming the robustness of the estimation framework under varying conditions. Only the variables in panels (**C**,**E**), particles and MEFL per particle, respectively, are plotted on a logarithmic scale. Data prior to the convergence time (approximately 1.5 h) in panels (**B**,**D**,**F**) correspond to the sensor transient of the software sensor and reflect the system dynamic response before reaching steady-state conditions. In panel (**F**), data points falling outside the blue-shaded confidence region are primarily associated with this transient period and illustrate early deviations prior to the sensor convergence. 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.