Using sliding mode observers to estimate BtuB concentration from measured vitamin B₁₂ concentration

A simple model for the B₁₂-riboswitch regulatory network in Escherichia coli is first described and the same analysis is applied when changing the strain to Salmonella enterica. Model validation is undertaken by linking the dynamics of the riboswitch model to bacterial growth and comparing the results obtained with in vivo experimental measurements. Measurements of bacterial growth are relatively straightforward to obtain experimentally, but experimental measurements relating to the operation of the riboswitch are more difficult. Using the validated model, sliding mode observer design methods are used to estimate BtuB given measurements of the concentration of vitamin B₁₂. The sliding mode approach is selected because of its inherent robustness properties as well as for the ease of implementation. Validation of the estimates of BtuB produced by the observer is undertaken by comparing the BtuB and vitamin B₁₂ concentrations estimated from the observer with green fluorescent protein production and the concentration of vitamin B₁₂ obtained experimentally. These experimental results also provide further validation of the underpinning mathematical model. The results establish that using a sliding mode observer as a soft sensor is a useful approach to explore the operation of a vitamin B₁₂ riboswitch given measurements of the concentration of vitamin B₁₂.