Biosensor characterization: formal methods from the perspective of proteome fractions.

Many studies characterize transcription factors and other regulatory elements to control gene expression in recombinant systems. However, most lack a formal approach to analyse the inherent and context-specific variations of these regulatory components. This study addresses this gap by establishing a formal framework from which convenient methods are inferred to characterize regulatory circuits. We modelled the bacterial cell as a collection of proteome fractions. Deriving the time-dependent proteome fraction, we obtained a general theorem that describes its change as a function of its expression fraction, a specific portion of the total biosynthesis flux of the cell. Formal deduction reveals that when the proteome fraction reaches a maximum, it becomes equivalent to its expression fraction. This equation enables the reliable measurement of the expression fraction through direct protein quantification. In addition, the experimental data demonstrate a linear correlation between protein production rate and specific growth rate over a significant time period. This suggests a constant expression fraction within this window. For an Isopropyl β- d-1-thiogalactopyranoside (IPTG) biosensor, in five cellular contexts, expression fractions determined by the maximum method and the slope method produced strikingly similar dose-response parameters when independently fit to a Hill function. Furthermore, by analysing two more biosensors, for mercury and cumate detection, we demonstrate that the slope method can be applied effectively to various systems. Therefore, the concepts presented here provide convenient methods for obtaining dose-response parameters, clearly defining the time interval of their validity and offering a framework for interpreting typical biosensor outputs in terms of bacterial physiology. Graphical Abstract Nutrients, transformed by the action of the Nutrient Fixators (purple arrow), are used at a rate of ρ for Protein biosynthesis. The total rate ρ is multiplied by expression fractions f_R, f_C, f_H, and f_Q to obtain the biosynthesis rate (black arrows) of each proteome fraction Φ_R, Φ_C, Φ_H, Φ_Q, respectively. In a graph of Growth rate versus Proteome Fraction Production Rate, a linear function (green lines) can be observed, and its slope is equal to the expression fraction at each condition.