Numerical Modeling and Investigation of Amperometric Biosensors with Perforated Membranes

Operational stability study of lactate biosensors: modeling, parameter identification, and stability analysis

Introduction

This paper investigates the operational stability of lactate biosensors, crucial devices in various biomedical and biotechnological applications. We detail the construction of an amperometric transducer tailored for lactate measurement and outline the experimental setup used for empirical validation.

Methods

The modeling framework incorporates Brown and Michaelis-Menten kinetics, integrating both distributed and discrete delays to capture the intricate dynamics of lactate sensing. To ascertain model parameters, we propose a nonlinear optimization method, leveraging initial approximations from the Brown model's delay values for the subsequent model with discrete delays.

Results

Stability analysis forms a cornerstone of our investigation, centering on linearization around equilibrium states and scrutinizing the real parts of quasi-polynomials. Notably, our findings reveal that the discrete delay model manifests marginal stability, occupying a delicate balance between asymptotic stability and instability. We introduce criteria for verifying marginal stability based on characteristic quasi-polynomial roots, offering practical insights into system behavior.

Discussion

Qalitative examination of the model elucidates the influence of delay on dynamic behavior. We observe a transition from stable focus to limit cycle and period-doubling phenomena with increasing delay values, as evidenced by phase plots and bifurcation diagrams employing Poincaré sections. Additionally, we identify limitations in model applicability, notably the loss of solution positivity with growing delays, underscoring the necessity for cautious interpretation when employing delayed exponential function formulations. This comprehensive study provides valuable insights into the design and operational characteristics of lactate biosensors, offering a robust framework for understanding and optimizing their performance in diverse settings.

Design of a methotrexate-controlled chemical dimerization system and its use in bio-electronic devices

Natural evolution produced polypeptides that selectively recognize chemical entities and their polymers, ranging from ions to proteins and nucleic acids. Such selective interactions serve as entry points to biological signaling and metabolic pathways. The ability to engineer artificial versions of such entry points is a key goal of synthetic biology, bioengineering and bioelectronics. We set out to map the optimal strategy for developing artificial small molecule:protein complexes that function as chemically induced dimerization (CID) systems. Using several starting points, we evolved CID systems controlled by a therapeutic drug methotrexate. Biophysical and structural analysis of methotrexate-controlled CID system reveals the critical role played by drug-induced conformational change in ligand-controlled protein complex assembly. We demonstrate utility of the developed CID by constructing electrochemical biosensors of methotrexate that enable quantification of methotrexate in human serum. Furthermore, using the methotrexate and functionally related biosensor of rapamycin we developed a multiplexed bioelectronic system that can perform repeated measurements of multiple analytes. The presented results open the door for construction of genetically encoded signaling systems for use in bioelectronics and diagnostics, as well as metabolic and signaling network engineering.