Monte Carlo simulation of super-selective supramolecular polymers on cell membranes

Super-selectivity is a key challenge to design multivalent nano-entities that can bind ideally in a binary response “on-off”to selective receptor-concentration targeting. In this study, it is simulated a 2D canonical ensemble Monte Carlo to sample semiflexible polymer chains conformations with determined percentage of functionalized monomers, which are capable to be bound to a receptor. In addition, it is quantized the adsorption of polymers to cell membranes and analyzed their behaviour depending on potentially selective sources. In closing, it is simulated a novel self-assembled nanofiber to analyze its therapeutic potential for drug delivery. I. MULTIVALENCY EFFECTS One novel challenge in nano-medicine is the ability to design supramolecular entities that can bind selectively to pathogenic cells. Selectivity provides the capability of these entities to distinguish between substrates with different densities of binding sites, deducing from it a binary response to which the adsorption can be carried out or not depending on optimal conditions. In this “onoff”case, it is designated a super-selective regime which applications are broadly found in [1]. Recent experiments indicate that such selective behaviour can be obtained using multivalency [3]. Thus, it is necessary a theoretical analysis to describe the origin of the receptor-concentration threshold in the guesthost binding of multiligand nano-particles and the mechanism by which multivalency can lead to a super-selective regime. The analytical model presented by Francisco J. Martinez-Veracoechea and Daan Frenkel compare the targeting selectivity of monovalent and multivalent guest nano-particles [1]. Results obtained not only show that monovalent guests yield the Langmuir isotherm, ergo, adsorption θ depends linearly on the density of hosts nR in log− log form, but also that selectivity α is never larger than one (deduced by definition in Eq. 1). α ≡ d log θ d log nR (1) In contrast, the parameter α for multivalent binding results to be extremely sensitive to changes in nR, showing super-selective regimes over a broad range of concentrations. In Fig. 1 is displayed a comparison between two monovalent guests and a multivalent guest, which behaviours are simulated with same parameters but changing the considered origin of super-selectivity: the guesthost binding energy. Simulations, then, denote a significant difference in binding energies such that multivalent bonds are necessary to be weaker than monovalent bonds. ∗Electronic address: adria.terradellas@gmail.com Moreover, it is also suggested that this enhanced adsorption is owing to the overall contribution of weak bonds, which are capable to bind stronger than a strong bond. In fact, and this is explained in detail at section II, making a ligand-receptor bond stronger means making also the energy state of the system more negative (less probable). Thus, it is well-known that the increased value of α is not as a result of strong ligand-receptors interactions but sensitive to receptor-concentration [1]. FIG. 1: Results of the analytical model from Francisco J. Martinez-Veracoechea and Daan Frenkel [1]. A direct comparison of two monovalent guests is distinguished although both responses are sigmoidal at different regimes. The multivalent guest presents a steep non-linear function typical from super-selective regimes. A recent work developed by Tine Curk, Jure Dobnikar and Daan Frenkel presents a deep study on this emergent property of multivalency, which reveals that its origin is not only due to the sensitive binding energy but also remarks the entropic degeneracy pre-factor [6]. The degeneracy Ω, defined in Eq. 2, measures the number of ways in which i bonds can be formed in the flexible binding case between k ligands and nR receptors. Thanks to the flexible capability of ligands, Ω becomes a very steep and non-linear function of k and nR, a response super-selectivity does in a same way (Fig. 1). Super-selective supramolecular polymers on cell membranes Adrià Terradellas Igual