Simulation of Protein-Imprinted Polymers. 2. Imprinting Efficiency - The

Nov 30, 2010 - Liora Levi and Simcha Srebnik. The Journal of Physical ... of molecularly imprinted polymers. Liora Levi , Vladimir Raim , Simcha Srebn...
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Simulation of Protein-Imprinted Polymers. 2. Imprinting Efficiency Liora Levi and Simcha Srebnik* Department of Chemical Engineering, Technion-Israel Institute of Technology, Haifa, 32000 Israel ReceiVed: September 14, 2010; ReVised Manuscript ReceiVed: NoVember 2, 2010

Molecular imprinting allows the creation of artificial recognition sites in synthetic materials through polymerization and cross-linking in the presence of template molecules. Removal of the templates leaves cavities that are complementary to the template molecules in size, shape, and functionality. Although this technique is effective when targeting small molecules, attempts to extend it to larger templates, such as proteins, have failed to show similar success. Here we present the second report on our model simulation study of protein imprinting, in which we apply on-lattice Monte Carlo simulations for an imprinting process using radical polymerization of hydrogels as a simple model for potein-imprinted polymers (PIPs). In this part we focus on two gel types: PIPs and templated polymers (TPs), which are polymerized in the presence of charged and neutral proteins, respectively. We calculate the imprinting factor (IF) for gels formed at various conditions and compare it for both gel types. Our results show a significantly higher IF for PIPs, and though the strongest influence on IF is found to be the monomer concentration (Φ), charge concentrations on the protein and in solution also affect IF. The percolation limit of protein-sized pores is found to be a significant turning point for the effect of concentration of functional sites within the gels on IF. 1. Introduction Molecular imprinting is an established technique for fabricating molecule-specific recognitive materials. The technique is simple, based on the lock-and-key analogy, and involves polymerization in the presence of a template molecule and functional monomers. Removal of the template (key) leaves a functional pore (lock) that is complementary to the template in size, shape, and functionality. A schematic of the process is shown Figure 1. Imprinting of small molecular templates, prominently drugs, has advanced significantly over the years,1 with applications including clinical analysis, medical diagnostics, environmental monitoring, and drug delivery.1-7 Molecular imprinting of biomacromolecules and proteins, if successfully achieved, could potentially offer a generic and cost-effective alternative to existing biological recognition techniques such as monoclonal antibodies that are used in isolation, extraction, biosensors, and other laboratory practices.8-12 However, efforts to generate imprints of protein targets have in general shown limited success of protein separation9,11,13 and show high affinity toward competitor proteins.11 The difficulties encountered with protein imprinting can be attributed to several factors, such as the use of water as solvent, the presence of multiple weak interactions on the surface of the protein, the relatively flexible conformation, and the large molecular size of the protein.8,10,11 The success of the imprinting process is frequently evaluated through the binding affinity (BA) of the imprinted gel which is measured by the absorption capacity, or through the mass of template that is absorbed per polymer unit, or by determining the retention time of the protein within the gel during chromatographic procedures. In addition, an imprinting factor (IF) is often used to evaluate the selectivity of the imprinted gel and is calculated as the ratio of the binding affinity of the template in the protein-imprinted polymer to that in a similarly * To whom correspondence [email protected].

should

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addressed.

E-mail:

synthesized nonimprinted polymer (NIP). While recent examples of small molecular imprinting experiments exhibit IFs of 8.5-26,14-17 most of protein-imprinting experimental procedures report on imprinting factors of 1.0-68,10,12-20 though with significant BAs. Various protocols have been developed to improve the performance of protein-imprinted polymers (PIPs), including surface imprinting or the epitope approach.11,12 However, the most extensive experimental work on PIPs has focused on 3-dimensional imprinting using polyacrylamide gels due to their biocompetability, neutrality, and inert nature that minimizes nonspecific interactions with proteins.8,11,12,16,21-25 Some of the important experimental studies of PAA protein-imprinted gels are referred to in our previous work.26 Two early examples23,24 report on acrylate-based lysosyme-imprinted polymer by free radical bulk polymerization using charged functional monomers. Ou et al.23 found selected imprinted polymers with modest imprinting factors of 1.83-3.38. However, rebinding of these polymers was not strictly template specific as the polymer also bound albumin. Furthermore, over 25% of the original template remained in the polymer, further contributing to the poor performance and efficiency of the PIP. Similarly, in competitive adsorption experiments of cytochrome c and lysozyme on lysozyme-imprinted polymer, Kimhi and Bianco-Peled24 showed a preference of absorption in favor of the template protein, though far less significant compared to cases of small molecular imprinting. In a more recent study,27 protein-imprinted polyacrylamide gel beads were prepared by inverse suspension polymerization using the bacterial Staphylococcus aureus protein A, displaying a rather high absorption capacity compared to nonimprinted beads, with IF of 5.6. However, competitor proteins were also absorbed by the imprinted beads with IF ranging from 1.7 to 2.4, indicating modest selectivity and separation capability. In an effort to further understand the poor performance of PIPs and offer means to improve upon existing protocols, we recently carried out lattice Monte Carlo (MC) simulations of

10.1021/jp108762t  2010 American Chemical Society Published on Web 11/30/2010

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Figure 1. Schematic illustration of molecular imprinting. Initially, a solution containing functional monomers, cross-linkers, and template is equilibrated (step 1) followed by polymerization (step 2). Removal of the template (step 3) leaves functional pores complementary to the template that can be used for molecule-specific adsorption (step 4).

the imprinting process using radical polymerization of hydrogels as a simple model for PIPs.26 Apart from our work, several computational approaches for moleculary-imprinted polymers of small molecular templates (MIPs) have been introduced during the past decade, though most of these computational studies of MIPs rely on ab initio calculations or fully atomistic models28-43 and many of these focus on screening for optimal combinations of functional monomers that will achieve minimal energy in the prepolymerization template-functional monomer complex.28,29,31-36,38,39 These studies mostly indicate a significant correlation between properties of the prepolymerization solution and final imprinting efficiency. This correlation has also been observed using NMR studies of preopolymerization solutions.44 Several authors have carried out more rigorous simulations of imprinted gels, focusing on imprinted pore properties.45,41,46 Wu et al.45 developed a two-dimensional stochastic lattice model of MIPs, focusing on the equilibrium processes in the prepolymerization solution and its relation to binding site heterogeneity. Their system consisted of functional monomers, crosslinkers, templates, and solute (empty sites) positioned within the lattice probabilistically according to their binding affinities. The functional monomers were modeled as directional and could only interact with the template if oriented properly. Despite its simplicity, this lattice model was able to replicate and give some insight into the origins of experimentally measured trends of MIPs, including the imprinting effect, binding site distributions, and selectivities. In particular, the authors considered the inherent binding-site heterogeneity of the MIP process and its relation to measurable quantities. The agreement with experimental findings further emphasizes the importance of the prepolymerization equilibrium stage for the overall imprinting process. Sarkisov and co-workers46 developed an off-lattice coarsegrained MC simulation of molecular imprinting of small functional analytes, where the templates were modeled as rigid chains of three tangent hard spheres with two unique functional sites. Equilibration of the prepolymerization solution was followed by quenching of the system and removal of the templates, and subsequent adsorption of the template and analogues was simulated through random insertions that were accepted according to the binding energy of the adsorption site. Notably, their simple model captured the molecular recognition phenomenon, i.e., the preferential recognition of the template molecule in the molecularly imprinted polymer, and hence was capable of assessing the effect of various conditions on the final properties of MIPs. Specifically, separation factor was shown to diminish with increased template loading, imprinting was found to improve with higher overall monomer concentration,

and the anticipated maximum in the selectivity was observed for cross-linker-to-functional monomer ratios in the prepolymerization mixture. Peppas and co-workers41 reported the first comprehensive atomistic simulation of the MIP polymerization process. They combined molecular dynamics (MD) with the kinetic gelation model (KGM) for simulating imprinting of glucose using a free radical polymerization mechanism. Their study revealed specific template-polymer interactions that were then validated by spectroscopic analysis and free energy evaluations of the imprinted network. In particular, they showed that the specific hydrogen bonds found in the prepolymerization complex in the system studied were maintained after polymerization as well, again providing further support for the importance of the prepolymerization complex. In our previous work26,47 we introduced a lattice KGM simulation model of a protein-imprinted polymer gel where for simplicity the protein was modeled as a rigid body with randomly located functional sites. We carried out a systematic investigation of the structure and porosity of the imprinted gel for various polymerization parameters and studied the structure and functionality of the imprinted pore by diffusion of the protein inside the pore immediately following polymerization. One of our prominent results showed that the binding energy of the protein within the imprinted pore is strongly influenced by the overall monomer concentration used in the prepolymerization solution, with minimal recognition of the protein below the percolation limit of protein-sized pores in the gel. PIP selectivity was evaluated by comparing the interaction energy of the protein in the imprinted gel with the energy of a random process (simulated as a statistical configuration of functional monomers and cross-linkers in solution prior to equilibration and gelation). This measure revealed that solution charge concentration has a considerable influence on the extent of recognition in the imprinted gel, achieving a maximum value at relatively low charge densities. The observation that solutions containing a high concentration of functional monomers result in increased nonspecific interactions has been also reported in previous experimental work on protein imprinting22 as well as simulations of model small molecular analytes.46 In this manuscript, we present further results of our coarsegrained simulations of PIP formation and characterization. We compare binding energies of the protein within imprinted and nonimprinted polymers for various compositions and model proteins. Additionally, imprinting factors of PIPs and the analogous templated polymers (TPs) are calculated and compared to isolate the effects of shape and functionality. (TPs are formed by imprinting nonfunctional molecules of the same size

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Figure 2. Two-dimensional illustration of the lattice simulation model for (a) initiation and polymerization of NIP and (b) initiation, equilibration, and polymerization of PIP. The spheres represent backbone monomers (white), functional monomers (blue), cross-linkers (black), neutral protein residues (yellow), and functional protein residues (red).

and shape as the protein in the analogous PIP.) Apart from providing a means to directly differentiate between the role of shape and functionality in our simulation, TPs are valuable as a means to control the porosity and inner shape of the resulting polymer48 using vesicles49 and solid particles such as silica,50 glass,51 and gold52 as templates. Theoretical evaluations of significant trends found by simulations are also used to apprehend the effect of the different parameters on the properties of the imprinted pore. 2. Simulation Model Our simulation presents a simple model of protein imprinting via acrylate-based bulk free radical polymerization.28,30,31 Details are elaborated in our previous work, which focused on gel and imprinted pore properties.33 Briefly, we carry out lattice simulations, where a fraction Φ of lattice sites is initially occupied by neutral and functional (charged) monomers, cross-linkers, in addition to a rigid cubic protein. Empty lattice sites correspond to solvent molecules. The protein has a fraction, fp, of randomly distributed charged residues that may interact with the functional monomers in solution. For simplicity, a sufficiently screened solution is considered such that only nearest-neighbor interactions are considered. We showed in our earlier study26 that crosslinkers not only are essential for the formation of a unified gel but also influence the structural characterization of the gel. The concentrations of functional monomers in the polymerizing solution and the final gel are defined according to φs ) Nc/L3 and fg ) Nc/N, respectively, where Nc is the number of charged functional monomers and N is the total number of monomers in the simulation box of dimension L. Note that N is the initial number of particles (monomers and cross-linkers) in the simulation. In all simulations we considered cases in which the gel fraction is close to unity, and so the difference

between N and the actual number of making up the gel is negligible. Simulations were performed on a lattice with L ) 20, which proved sufficiently large.47 The simulation model is depicted in Figure 2 in two dimensions for clarity. The simulation begins with random positioning of the template protein, cross-linkers, and monomers in the cubic lattice, followed by equilibration (formation of the prepolymerization complex) in which noncovalent complexation takes place between the protein and the functional monomers. Equilibration is achieved using 105 Monte Carlo (MC) iterations during which movements of a randomly selected particle (monomer, cross-linker, or protein) into neighboring vacant sites are attempted according to the Metropolis acceptance criterion53 (at concentrations of Φ > Φpc, the protein is essentially stagnant and its diffusion may be neglected). We consider only attractive interactions between charged protein residues and functional monomers since we obtained the same qualitative results in an earlier model47 that considered the presence of both positive and negative charges in solution and their interaction. Accordingly, the energy of nearest-neighbor contact between a functional monomer and a charged protein residue is assigned a value of -ε, while all other nearest-neighbor contacts do not contribute to the energy. Once equilibrium is reached, the kinetic gelation model (KGM) is used to simulate gelation,54-57 beginning with instantaneous initiation where radical “signatures” are randomly distributed among the monomers. Propagation of the polymerization reaction then follows and involves particle moves according to Metropolis acceptance rules and bond formation that takes place upon collision of free radicals with other monomers or cross-linkers. Gelation ends when a single cluster is formed, all free radicals have terminated, or the number of clusters does not change during the next 2 × 105 iterations, which indicates entrapment of all radicals. At this

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stage of our study, flexibility of the forming polymer chains is neglected, so that the system is quenched once gelation is completed and the template is removed. We calculate the effective pore size and average interaction energy of the proteins within the pores in the next stage of the simulation through diffusion of the protein within the pores of the gel. We compare pore structure and functionality within three types of polymers: protein-imprinted gels (PIPs), nonimprinted gels (NIPs), and templated polymer gels (TPs). Nonimprinted gels are formed through polymerization in the absence of the protein so that the functional monomers are randomly situated. Templated gels are formed using inert templates present in the polymerization solution in order to control polymer structure and to form cavities with strictly defined size and shape,48,58 but the functional monomers are still randomly situated. A similar concept was studied early on by Ward and Peppas;59 however, these authors simulated a relatively concentrated solution of small inert molecules, as opposed to dilute macromolecular-sized protein in our work. In addition, our study focuses on a considerably less concentrated system (with up to 50% site occupancy compared with 85% of ref 59). Interestingly, they found that the presence of the inert solute delayed the gelation point to higher conversions, by hindering monomer diffusion, but only for low concentrations of cross-linkers. Otherwise, gel properties were not influenced by the solute, in agreement with our previous studies.26,47

Figure 3. Binding energy of protein as a function of monomer concentration for fg ) 0.5 and fp ) 0.5. Symbols correspond to simulation data and solid curves to theoretical fit using eq 2. Dashed line shows the probability of belonging to a protein-percolating pore P(Φ), revealing the percolation threshold Φpc ) 0.2.26

3. Results and Discussion In our previous work26 we analyzed the effect of preparation conditions on gel properties and reported on the effect of solution and protein charge on the binding energy of the protein in the imprinted pore in our coarse-grained model of an acrylatebased hydrogel. Among our results we found that the presence of a protein template in solution during polymerization has no effect on the average gel structure characterized by chain composition and chain length. Interestingly, a recent examination of the morphological properties of highly cross-linked lysozymeimprinted and control gels revealed that lysozyme induces the formation of a striated porous structure with macroscopic order in PIP gels, though the presence of the template does not affect the composition or cross-linking of the network,60 in accord with our previous conclusion.26 In this paper we address the effect of imprinting conditions on the imprinting efficiency and on selectivity of recognition. We consider the properties of the imprinted gel in its quenched form immediately after gelation, which provides an indication on the optimal recognition potential.30,38,44 We address the aspects of multiple recognition sites, high surface area, and large size of the protein template. The effects of gel and protein flexibility will be addressed in a future communication. Template Binding Affinity. We evaluate the effect of polymer volume fraction (Φ ) N/L3) on protein binding energy and pore size through diffusion of the protein within pores formed in protein-imprinted, templated, and nonimprinted polymers, according to eq 1

Eb ) 〈

∑ εδ(|ri - rj| - σ)〉

(1)

ij

where Eb is the average interaction energy of the protein with the pore, σ is the lattice unit size, the summation is over all functional monomers and protein charged groups, and the Dirac

Figure 4. Binding energy as a function of monomer concentration for φs ) 0.0875 and fp ) 0.5. Symbols correspond to simulation data and solid curves to theoretical prediction of eq 2.

delta function ensures the sum accounts for nearest-neighbor interactions only. Not only Φ but also the relative concentration of functional monomers in the system has a substantial influence on the behavior of the system. Φ determines the overall size of the pores and, more specifically, the fraction of pores that are of the size of the protein or larger that percolate the lattice, P(Φ), shown as the dashed line in Figure 3. We have previously shown26 that for a template protein size of 125 lattice sites, Φ ) 0.2 is a transition below which percolation of imprinted pores occurs and the resulting pores are of infinite size. This transition defines the percolation threshold of protein-sized pores, Φpc, which is found to play a crucial role in PIP characterization, as discussed below. The effect of Φ on the energy of interaction between the protein and the pores of various gels is shown in Figure 3 for constant concentration of functional monomers, fg ) Nc/N, and in Figure 4 for constant number of functional monomers in the gel, φs ) Nc/L3. The energy in these figures is normalized by the magnitude of the maximal binding energy (Emax), equal to the number of functional residues on the protein surface multiplied by the bond energy (ε). Similar to ref 46 we observe that both imprinting and templating methods (PIP and TP) show a notable decrease in binding energy with increasing Φ when the relative concentration of functional monomers in the gel is

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fixed. Since at high Φ the imprinted pores are considerably smaller,26 the protein can interact with the polymer via a number of functional monomers simultaneously, thus increasing its binding capacity in comparison with gels prepared from low monomer concentrations. Furthermore, due to equilibrium prior to polymerization (step 1 in Figure 1), the distribution of functional monomers within the PIP gels is not random, as in TPs, such that the functionality of the imprinted pores more closely corresponds to that of the protein surface, resulting in significantly lower energy for the range of Φ at constant fg. Since templated pores are formed to fit the protein size and shape but not its functionality, it is reasonable to assume that templating has no effect on low-density polymers (Φ < Φpc), where percolation of pores of the size of the protein or larger occurs naturally. Hence, for these low values of Φ, we find that binding within TP and NIP is similar. NIP gels, however, exhibit low binding that is surprisingly hardly affected by Φ when fg is fixed (Figure 3) since the pores in this case are shaped randomly and hence do not exhibit the wrapping effect of high Φ gels seen with PIPs and TPs (for Φ > 0.4 there are essentially no pores that are large enough to accommodate the protein in NIPs). Figure 4 shows the effect of Φ on Eb in the various types of gels for fixed concentration of functional monomers, φs. In contrast to Figure 3, a nonmonotonic trend is observed for the imprinted and templated gels, with minimum binding (maximum energy) at the pore percolation limit (Φ ) Φpc). For NIP, Eb monotonically increases to an asymptotic value that is determined by the number of functional monomers in the solution. The maximum in binding energy observed for TP and PIP was previously explained by the competition of two opposing phenomena:26 On the one hand, the concentration of functional monomers in the gel decreases with increasing Φ for constant φs since the number of functional sites per unit pore surface area is effectively reduced, leading to a decrease in binding energy. On the other hand, increasing Φ leads to tighter pores and better wrapping of the protein, which increases binding. Combining these two terms and recalling that fg ) φs/Φ we obtained the following qualitative relation for imprinted gels26

(

)

Eb φs Φ φ ) - k1′fg + k2′ Φ fgΦ ∝ - k1 + k2 |Emax | Φ Φmax s Φmax (2)

(

)

where Φmax is the minimal volume fraction for which maximal wrapping of the protein is achieved and depends on the size of the protein. k1 and k2 are constants of proportionality that provide the relative strength of the two competing effects: reduced functional monomer concentration versus better wrapping. Equation 2 correctly predicts that Eb monotonously decreases with Φ for constant fg (as in Figure 3) and has a maximum at constant φs. Furthermore, the constants k1 and k2 provide information about the relative importance of the two competing effects. The best fits shown as solid curves in Figures 3 and 4 are obtained for the following values of these constants: k′1 ≈ 0.2 and k′2 ) 1.6, 0.7, and 0.1 for PIP, TP, and NIP, respectively; k1 ≈ 2.4 and k2 ) 2.2, 0.9, and 0.3 for PIP, TP, and NIP, respectively. The value of these constants reveals that structural fit of the template, or wrapping, is significantly different among the gels and follows the expected trend PIP > TP > NIP. The fact that k1 and k′1 have similar values for the different gels suggests that the amount of functional monomers in the gel affect the different procedures in a similar manner. However,

Figure 5. Pore size normalized by protein size as a function of Φ for constant fg (closed symbols) and φs (open symbols).

the wrapping effect also implicitly captures the effect of equilibration of the prepolymerization complex in PIPs, since these attractive interactions allow for the formation of a tighter pore surrounding the template. Imprinted Pore Size. Simulating diffusion of the protein within the pore allows us to estimate the average pore size that is accessible for the protein, which is plotted in Figure 5. In general, higher polymer density leads to a significant decrease in pore size, regardless of the concentration of functional monomers, suggesting that the primary influence on pore size is the polymer volume fraction and not the amount of functional monomers in the gel. While the differences in the various types of gels are small, the following trends are nonetheless observable: At low Φ, PIP pores are somewhat smaller than TP pores due to the attractive interactions in PIP that bring functional monomers closer to the protein during equilibration and gelation. However, below the pore percolation limit (Φ < Φpc) NIP pores are somewhat smaller than the imprinted pores of PIP gels, while above the percolation the trend is inversed. Since the presence of the large globular protein leads to the formation of relatively well-defined pores, the randomly shaped pores in the NIP gels at low monomer densities (Φ < Φpc) are likely to be smaller than the protein but at high polymer densities (Φ > Φpc) the protein-penetrable pores in the NIP gels are somewhat larger on average than the pores of the imprinted gels due to their random shape that does not match the regular shape of the protein. The presence of charged functional monomers also affects pore size, though only for PIPs and especially at low Φ (Figure 6) since at high Φ the size of the imprinted pore is limited by particle density while gels polymerized at low Φ are more flexible and hence more influenced by the monomer-protein interaction. In general, the size of the imprinted pore in PIP decreases with increasing fg due to increasing attraction between the protein and the functional monomers prior to and during polymerization. In the current model, the polymerization process is not affected by the amount of charge in the polymerizing solution since only protein-monomer interactions are considered, and for that reason fg has no influence on the size of templated and nonimprinted pores. The relationship between NIP and PIP pore size seen in Figure 5 is emphasized in Figure 6, in which it is clearly seen that below the pore percolation limit (Φ < Φpc, Figure 6a) PIP pores are larger than NIP pores while after percolation the trend is inversed (Figure 6b). Imprinting Efficiency. Imprinting performance is usually evaluated by the imprinting factor (IF), which is calculated as the ratio of the absorption capacity61,62 or binding strength41 of MIP to NIP. It has been previously shown that the calculated interaction energy of the template-monomer complex is cor-

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Figure 6. Pore size normalized by protein size as a function of fg for Φ ) (a) 0.1 and (b) 0.25.

Figure 7. Imprinting factor for PIP (circles) and TP (squares) gels as a function of monomer concentration Φ at constant fg (closed symbols, fg ) 0.5) and φs (open symbols, φs ) 0.0875) for fp ) 0.5.

related with the template-polymer binding strength and polymer recognition, as evaluated by chromatographic experiments.35,36 Therefore, we evaluate the imprinting factor as the ratio of the average binding energy of the protein within imprinted and nonimprinted pores

IF )

〈Ex〉 〈ENIP〉

(3)

where x refers to the imprinting method (PIP or TP), Ex and ENIP are template interaction energies within imprinted and nonimprinted polymers, respectively, and the average is calculated over the diffusion simulation of the protein within the respective pore as well as O(102) independent simulations. Note that TPs are prepared in the presence of an inert template of size and shape equivalent to that of the protein, but its IF is tested with the protein template. Although Eb shows very different dependencies on Φ at constant fg or constant φs (compare Figures 3 and 4), the IFs for both variables are similar, as seen in Figure 7. The linear increase in IF with Φ indicates that imprinting of dense gels is more efficient, as has been found experimentally,24 due to the formation of better defined cavities. In TP gels, however, the increase in IF is seen only for Φ > Φpc, providing another indication that large percolating pores are not affected by templating. Figure 7 emphasizes the two major factors that affect IF, i.e., the extent of wrapping of the protein by the gel which increases with Φ and the compatibility between the functionality of the pore and that of the protein as seen by the difference between the PIP and the TP curves. The effect of charge on IF is shown in Figure 8 for two extreme values of concentrations within PIP and TP gels. For PIPs, while high monomer concentrations lead to better imprint-

Figure 8. Imprinting factor of PIP (circles) and TP (squares) gels as a function of monomer concentration for fg ) 0.1 (open symbols) and 1.0 (closed symbols).

ing, low functional monomer concentrations diminish the effect. Interestingly, the curves for low and high concentrations of functional monomers intercept at the pore percolation limit (Φpc ) 0.2), which serves as a turning point in many features of the imprinted gel as well as in the correlation between IF and fg. Above the percolation limit (Φ > Φpc) highly charged gels exhibit lower imprinting efficiency since the high monomer concentration around the protein increases nonspecific binding. Below the percolation limit, although the pores are large, their functionality is low and hence their distribution closely matches that of the protein. In this case, when increasing the amount of functional monomers more charges can be “recruited” around the template protein during the imprinting process and specific binding in PIP is improved leading to an increase in IF. As expected, TPs are not affected by the presence of functional monomers since apart from excluded volume the template does not interact with the monomers so that the distribution of functional sites within TP gels is random and not affected by the imprinting process. Nonetheless, for sufficiently high Φ, TP gels show an ‘imprinting’ effect (IF > 1) due to the formation of protein-shaped pores which increase contact between the charged monomers in the gel and the protein surface. The dependence of IF on fg shows different trends for fixed values of Φ (Figure 9). At high monomer concentrations IF decreases with increasing fraction of functional monomers, at low concentrations IF increases with fg, and at intermediate concentrations IF is essentially independent of fg. That IF decreases with increasing concentrations of negatively charged functional monomers was previously reported by Kofinas and co-workers21 in a study focusing on the effect of charge on the recognition properties of protein-imprinted polymer gels (an optimum for positively charged monomers was found). The

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Levi and Srebnik IF is defined by the ratio of specific (PIP) to nonspecific (NIP) binding energy of the protein in the gel pores. Increasing the charge on the protein does not affect the structure and distribution of functional sites in NIP gels and therefore maintains on average a constant number of nonspecific links. On the other hand, the protein charge affects the number of binding sites formed within PIP gels during polymerization, and as a result IF increases. Concluding Remarks

Figure 9. Imprinting factor of PIP gels as a function of fg for Φ ) 0.1 (circles), 0.25 (squares), and 0.4 (triangles) for fp ) 0.5.

Figure 10. Imprinting factor of PIP gels as a function of monomer concentration for various values of protein surface charge, fp, for fg ) 0.5.

Figure 11. Imprinting factor of PIP gels as a function of fp for various monomer concentrations.

trend was explained by the improved swelling properties of highly charged gels that raise the amount of absorbed protein in NIPs as well as in MIPs. However, while we did not simulate swelling, we found that the binding strength of the protein in both imprinted and nonimprinted gels increases with the fraction of functional monomers due to an increase in nonspecific interactions,26 with an overall decrease in IF. A slight increase in IF with fg is observed at low Φ, where the imprinting effect on pore size is most significant (Figure 6), and the protein attracts the relatively small amount of functional monomers during equilibration in the most favorable way. The amount of charge on the protein surface, fp, also impacts the imprinting process (Figures 10 and 11). Highly charged proteins show better imprinting factors than weakly charged proteins. However, unlike the effect of functional monomer concentration in solution, the positive correlation of IF with fp for the various values of Φ suggests that this variable is independent of the percolation properties of the gel, though the effect of imprinting is lower for gels produced at low monomer volume fractions (lower slope of IF in Figure 11). Recall that

This work presents continuing work on the simulation of protein imprinting. In our previous work we studied the effect of different simulation parameters on gel structure and pore functionality in PIP and NIP gels. Here, we concentrate on the effect of various parameters on the performance of the gel, focusing on the contribution of site-specific interactions through modeling gelation in the presence of both charged and neutral protein templates. Given that most experimental studies use binding affinity and IF as a prominent measure for imprinting efficiency, we evaluate both of these variables for various simulation conditions. The fact that a significantly higher IF is seen in PIP over TP gels indicates that our model captures the main features of the imprinting process, where the pore functionality complements the positioning of functional groups on the template protein surface. Since binding energy is not sufficient to predict imprinting efficiency, IF is used in order to gain some knowledge on the protein imprinting process. Indeed, IF and Eb do not exhibit identical trends (i.e., Figure 4 versus Figure 7). In all cases, IF shows a significant monotonic increase with Φ which, in accordance to experimental reports,23 emphasizes the influence of polymer density on imprinting. High monomer density consistently shows up as the most influential factor for imprinting PIP performance, as was seen in previous experimental studies,23 which however must be weighed against the low diffusion rates and protein entrapment that occur in low-porosity imprinted gels.8,10,11 In contrast, TP gels show an increase in IF with Φ only above the percolation limit (Φ > Φpc), and their IF values are always significantly smaller than those of PIP gels. This result underlines the essence of imprinting as it shows the significance of combining shape and functionality in order to maximize recognition. The monomer concentration corresponding to the percolation limit of protein-sized pores in the gel presents an important turning point below which the effect of imprinting is not significant. Depending on the protein size this limit occurs at Φ ≈ 0.2, but higher concentrations may not be realistic for practical applications of PIPs (due to low protein mobility). While charge, both on the protein and ont the concentration in solution, may be somewhat optimized for a particular Φ, smart materials and/or methods may be required to achieve significant imprinting with proteins.63 In our next paper, we will show the effect of different parameters on the separation factor of PIPs, which measures the binding capacity of the imprinted gel toward its template compared with a competitor protein. We will show that increasing the protein charge impairs PIP selectivity toward the template protein since despite the higher IFs it does not improve the separation of the gel. Finally, we would like to comment on the importance of modeling gelation, as opposed to concentrating on the prepolymerization solution, especially for PIPs that are formed from low monomer concentrations. As Figure 2 suggests, gelation results in substantial rearrangement of the functional monomers within the imprinted pore. That is, the final functionality of the

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