(576g) A Novel Computational Framework For The Optimal Design Of A Protein Biosensor That Recognizes A Known Set Of Ligands

A biosensor is any ensemble of biological sensing elements which, upon interacting with an analyte or chemical species in an environment, is capable of marking that interaction by reacting measurably. The sensing elements can be biomolecules such as proteins, nucleic acids, or polysaccharides, viruses or bacteriophages, prokaryotes or eukaryotes, cellular organelles, cells, or organisms [1-2]. In this work, we propose a novel approach for designing a biosensor with protein receptors, whose ranges of stimuli can vary drastically. The problem can be stated as: given a blood sample in which a known set of drug ligands is present, and a set of protein receptors, we would like to design a biosensor with the minimal subset of receptors (i.e., optimal receptors) that is required for the optimal recognition of all ligands.

In order to address the biosensor design problem, we first devise a nonlinear programming (NLP) model to estimate the dissociation constants and efficacy values between each receptor-ligand pair. The model solves the parameter estimation problem based on the least squares minimization of the differences in the activation levels of any two receptors. The estimated values are then input into a novel mixed-integer nonlinear programming (MINLP) model [3] which both maximizes the sum of differences in the activation of any pair of receptors and minimizes the number of receptors needed to recognize all ligands. Constraints in the model include those relating the activation of each receptor to its dissociation constant and ligand concentrations, as well as others that guarantee concentration of each ligand is greater than the minimum of the dissociation constants for that ligand and all receptors selected to constitute the biosensor. The latter is to ensure that each ligand present in the blood sample will be recognized by the biosensor. In addition, we also impose upper and lower bounds on the ligand concentrations. Instead of generating only the optimal solution, we run the model multiple times with an increasing number of integer cuts [3] to produce a rank-ordered list of the optimal designs for the biosensor.

The model is applied to a case study in which we have to choose from a set of 11 receptors to recognize eight ligands in a sample. It is found that the top ten designs require only two or three receptors to optimally recognize all ligands.

[1]- J. M. Cooper and A. E. G. Cass, eds., Biosensors: A Practical Approach. Oxford University Press (2004).

[2]- A. T. Wright and E. V. Anslyn and J. T. McDevitt. "A Differential Array of Metalated Synthetic Receptors for the Analysis of Tripeptide Mixtures." J. Am. Chem. Soc. 127 (2005): 17405-17411.

[3]- C.A. Floudas. Nonlinear and Mixed-Integer Optimization: Fundamentals and Applications. Oxford University Press (1995).