Effect of diffusion limitations on multianalyte determination from biased biosensor response

Abstract

The optimization-based quantitative determination of multianalyte concentrations from biased biosensor responses is investigated under internal and external diffusion-limited conditions. A computational model of a biocatalytic amperometric biosensor utilizing a mono-enzyme-catalyzed (nonspecific) competitive conversion of two substrates was used to generate pseudo-experimental responses to mixtures of compounds. The influence of possible perturbations of the biosensor signal, due to a white noise- and temperature-induced trend, on the precision of the concentration determination has been investigated for different configurations of the biosensor operation. The optimization method was found to be suitable and accurate enough for the quantitative determination of the concentrations of the compounds from a given biosensor transient response. The computational experiments showed a complex dependence of the precision of the concentration estimation on the relative thickness of the outer diffusion layer, as well as on whether the biosensor operates under diffusion- or kinetics-limited conditions. When the biosensor response is affected by the induced exponential trend, the duration of the biosensor action can be optimized for increasing the accuracy of the quantitative analysis.

Figure 1.

Principal structure of the biosensor.

Figure 2.

The dynamics of the biosensor current affected by the exponential trends (Left) and in conjugation with the white Gaussian noise (Right, σ = 0.05) simulated at the following values of the model parameters: V₁ = 0.5 μM/s, V₂ = 5 μM/s, S_1,0 = 0.32 mM, S_2,0 = 1.28 mM. The other parameters are as defined in Equation (16).

Figure 3.

The set of the dimensionless concentrations, c₁ and c₂, of the substrates, S₁ and S₂, used in the investigation, as well as the noise-free biosensor responses to these concentrations simulated at and V₁ = 0.5 μM/s, V₂ = 5 μM/s and β = 0.4.

Figure 4.

Contour lines of the objective function given by Equation (17) for the noise-free biosensor responses simulated at V₁ = 0.5 μM/s, V₂ = 5 μM/s assuming zero (β = ∞) and a relatively thick (β = 0.4) thickness of the external diffusion layer, (c₁, c₂) = (8, 8).

Figure 5.

The impairment, Δε_i, of the relative error, ε_i, of the evaluation of the concentration, c_i, of the substrate, S_i, versus the duration, t_m, of the biosensor operation at four values of the Biot number, β, when the biosensor response is affected by white Gaussian noise with σ = 0.05, i = 1,2. The other parameters are as in Figure 2.

Figure 6.

The relative error, ε₁, of the evaluation of the concentration, c₁, versus the duration, t_m, of the biosensor operation at different values of the Biot number, β, when the response is affected by white Gaussian noise with σ = 0.05 and the exponential trend of a different rate. The other parameters are as in Figure 2.

Figure 7.

The relative error, ε₁, of the evaluation of the concentration, c₁, of the substrate, S₁, versus the Biot number, β, and the duration, t_m, of the biosensor operation when the response is affected by white Gaussian noise with σ = 0.05 and the exponential trend of a different rate. The other parameters are as in Figure 2.

Figure 8.

The relative errors, ε₁ and ε₂, of the evaluation of the concentrations, c₁ and c₂, of both substrates, S₁ and S₂, versus the duration, t_m, of the biosensor operation at different values of the maximal enzymatic rates, V₁ and V₂, and the Biot number β = 1, when the response is affected by white Gaussian noise with σ = 0.05 and the exponential trend of a different rate. The other parameters are as in Figure 2.