Biosensors Characterization: Formal methods from the Perspective of Proteome Fractions

Many studies characterize transcription factors and other regulatory elements to control the expression of heterologous genes in recombinant systems. However, most lack a formal approach to analyse the parameters and context-specific variations of these regulatory components. This study addresses this gap by establishing formal and convenient methods for characterising regulatory circuits. We model the bacterial cell as a collection of a small number of proteome fractions. Then, we derive the proteome fraction over time and obtain a general theorem describing its change as a function of its expression fraction, which represents 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, 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. The expression fractions estimated from the slopes of these intervals and those obtained from maximum protein amount points can both be independently fitted to a Hill function. In the case of an IPTG biosensor, in five cellular contexts, expression fractions determined by the maximum method and the slope method produced similar dose-response parameters. Additionally, by analysing two more biosensors, for mercury and cumate detection, we demonstrate that the slope method can be effectively applied to various systems, generating reliable Hill function parameters.