Affinity Distributions of a Molecularly Imprinted Polymer Calculated Numerically by the Expectation-Maximization Method

Abstract

Affinity distributions are calculated from adsorption isotherm data obtained for the enantiomers of Land D-phenylalanine anilide (PA) on native and thermally annealed polymers molecularly imprinted with L-PA. The calculation is obtained with an iterative algorithm called expectation-maximization that does not require prior fit of the data to an isotherm model before inversion and thus yields a distribution indicative of the data only. The results show bimodal distributions, suggestive of a two-site model describing relatively selective and nonselective adsorption modes of the L-enantiomer and a corresponding unimodal/ nonselective adsorption mode for the D-enantiomer. The nonselective adsorption region of the distributions exponentially decreases with increasing association constant, whereas the selective adsorption is Gaussian in appearance. The thermally annealed polymer exhibits altered affinity distributions that are somewhat less heterogeneous and more selective. Their selective sites have a lower saturation capacity than the native polymer. The capacity of the nonselective sites is inconclusive due to undersaturation of these lower energy sites, but it appears to be greater.

Effect of the temperature on the isotherm parameters of phenol in reversed-phase liquid chromatography

“…The EM method allows the calculation of the adsorption energy distribution, hence the characterization of the surface heterogeneity [22][23][24][25][26][27][28]. The apparent, global, or overall adsorption isotherm is related to the local isotherm and to the distribution of adsorption constants by the following equation:…”

“…The expectation maximization algorithm was used to calculate the affinity energy distribution from the raw adsorption data, without requiring any prior assumption on the isotherm model [23][24][25][26][27][28]. The AED derived from the EM method were used to validate the isotherm model selected from the fitting process.…”

Combination of Molecular Imprinting and Nanotechnology: Beginning of a New Horizon

“…With the same concept, Nematollahzadeh et al [7] developed a general technique, so-called polymerization packed bed, to obtain a hierarchically structured high capacity protein imprinted porous polymer beads by using silica porous particles for protein recognition and capture. Recently, some rules were very popularized for the MIP synthesis and that are collectively called as "Th e MIP: Rule of six" [8].…”

The development of a MIP-optosensor for the detection of monoamine naphthalenes in drinking water

“…They could be easily generated from equilibrium batch rebinding studies. For the heterogeneous population of binding sites, as frequently observed for molecularly imprinted polymers, the analysis can be made using the Langmuir-Freundlich (L-F) isotherm (Stanley et al, 2003;Bastide et al, 2005), which is a function that describes the relationship between the equilibrium adsorption capacity (Q) and the equilibrium template concentration in solution (F) for heterogeneous matrices according to Eq. (1):…”