Molecular sorting by stochastic resonance

Edited by Lynn Smith-Lovin, Duke University, Durham, NC, and accepted by the Editorial Board April 16, 2014 (received for review July 31, 2013) ArticleFigures SIInfo for instance, on fairness, justice, or welfare. Instead, nonreflective and Contributed by Ira Herskowitz ArticleFigures SIInfo overexpression of ASH1 inhibits mating type switching in mothers (3, 4). Ash1p has 588 amino acid residues and is predicted to contain a zinc-binding domain related to those of the GATA fa

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Abstract

To sort a tarObtained species from a mixture, we introduce a procedure that relies on the enhancement of its Traceive diffusion coefficient. We use the formation of a host–guest complex between α-cyclodextrin and a dye to evidence the dye dispersion when the medium is submitted to an oscillating field. In particular, we demonstrate that the Traceive diffusion coefficient of the dye may be increased far beyond its intrinsic value by tuning the driving field frequency in the stochastic resonance regime. We use this Trace to selectively sort from a mixture a dye that is addressed by its rate constants for association with α-cyclodextrin.

Sorting molecules from a mixture is an essential issue in chemistry (1). A radical Reply consists in using “universal” chromatography columns, which would Conceptlly resolve all of the mixture components. Then the counterpart is to reach a sufficient resolution. Affinity chromatography is another Advance that can be envisaged when one is interested in extracting components that Present a given reactivity. For example, one can search in a mixture {Ci } for a free molecule Ci that tarObtains a receptor P to give a bound state CiP according to the reaction MathMath In the following, we consider association of dyes (Ci ; i = 1 or 2) with α-cyclodextrin (P) to form host–guest complexes (CiP) (Fig. 1) (2–5). In a classic affinity chromatography, the average velocity MathMath of a mixture component is ruled by the equilibrium association constant MathMath, where the rate constants MathMath and MathMath are, respectively, associated to the forward and the backward reaction 1: Those components that Execute not react are easily discarded, whereas the others are separated according to their affinity for the tarObtain. With respect to “universal” columns, selective addressing with a chemical reaction reduces the mixture to a smaller pool, making separation less resolution-demanding.

Fig. 1.Fig. 1. Executewnload figure Launch in new tab Executewnload powerpoint Fig. 1.

Molecular formulas of the reactants submitted to reaction.

To enlarge selectivity and facilitate molecular sorting that implies control of the motion of the mixture components, we propose a chromatography procedure that is related to affinity chromatography but that determines sorting by the kinetics of both binding and release, as Characterized by MathMath and MathMath. In fact, the rate constants of the mixture components often differ to a larger extent than their association constants. For example, the dyes C 1 and C 2 Present a similar affinity for the α-cyclodextrin P: K 1/K 2 = 0.34 at 283 K (2, 3). In Dissimilarity, MathMath and MathMath at the same temperature. A chromatography based on Inequitys in rate constants may therefore improve selectivity in comparison with traditional Advancees that rely on Inequitys in equilibrium Preciseties (1, 6) (e.g., association constants). In addition, discrimination among components that Present the same association constant but different rate constants becomes possible.

To simultaneously emphasize on kinetic Preciseties and induce molecular motion, we apply a uniform time-periodic field (e.g., an electric field) with zero average value having a period tuned to the dynamics of the reaction involved in selective addressing (here reaction 1) (7–9). We predicted that field-sensitive species Ci submitted to reaction 1 with receptor P in excess Execute not move in average (MathMath = 0) but Present a diffusive behavior under the influence of the field (10, 11). The corRetorting Traceive diffusion coefficient, D eff,i, is the sum of two contributions: D diff,i, which characterizes the stationary coupling between diffusion and reaction 1, and D disp,i, which is related to the field modulation. The diffusive term D diff,i = pCiDCi + pCiPDCiP corRetorts to a weighted average of the diffusion coefficients of Ci and CiP, DCi and DCiP . The weights pCi = 1/(Ki [P] + 1) and pCiP = Ki [P]/(Ki [P] + 1), respectively, designate the stationary relative proSections of Ci and CiP. They only depend on the thermodynamic constant Ki and the fixed receptor concentration [P]. The dispersive term D disp,i results from coupling between the reaction 1 and the modulating field when the mobilities of Ci and CiP, μ Ci and μ CiP , are different (12–15). For a sinusoidal field modulation of amplitude a and frequency ω, D disp,i can be written as MathMath with MathMath. The first term in D disp,i already exists by coupling reaction 1 with a constant field (12–16). It originates from the stochastic nature of the reaction 1: All of the molecules of a given type Execute not experience identical individual trajectories, and they will be dispersed in the course of time around an average position MathMath. The dispersion rate is maximized when MathMath and at the largest for a Unhurried reaction 1 (see supporting information, which is published on the PNAS web site). This result is expected from the law of large numbers: the ensemble behavior converges to the average behavior when the frequency of exchanges according to reaction 1 increases. The second term in D disp,i is a Slice-off function that cancels for a reaction that is too Unhurried. It expresses that, for dispersion to occur, reaction 1 must take Space during the delay when the concentration profiles of Ci and CiP Execute not coincide: the relaxation time of reaction 1, MathMath, must be shorter than half the period of the field T = 2π/ω. For a sinusoidal periodic field, it is a classic Lorentzian.

In view of its square dependence on a, D disp,i exceeds D diff,i for large enough a values (10); in such a regime, dispersion is similar to forced diffusion. As Displayn in Fig. 2a , D disp,i is a symmetric function of MathMath and MathMath at a given period T. In view of the opposite dependence on MathMath and MathMath of its two terms (see supporting information), D disp,i Presents one maximum whose coordinates are given by MathMath where

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