High Amplification Rates from the Association of Two Enzymes Confined within a Nanometric Layer Immobilized on an Electrode: Modeling and Illustrating Example Benoı ˆt Limoges,* Damien Marchal, Francois Mavre ´ , and Jean-Michel Save ´ ant* Laboratoire d’Electrochimie Mole ´ culaire, UMR CNRS 7591, UniVersite ´ de Paris 7 - Denis Diderot, 2 place Jussieu, 75251 Paris Cedex 05, France Received February 2, 2006; E-mail: limoges@paris7.jussieu.fr; saveant@paris7.jussieu.fr Connecting an electrode with a soluble or an immobilized redox enzyme allows the transduction of specific chemical events taking place at its prosthetic group into easy-to-use electric signals. A route is thus opened to the gathering of mechanistic and kinetic informa- tion on the functioning of this class of enzymes on one hand and to biosensors applications on the other (substrate sensing or bio- affinity assays). 1 In all cases, establishing a model resulting in pre- cise relationships linking the enzymatic kinetics and the electro- chemical responses is an essential step for gaining meaningful ki- netic data, which may additionally be used for rational sensor design and analytical performance optimization. So far such theoretical models have been derived for monoenzymatic systems, either in- volving direct electron transfer to the electrode 2 or mediated transfer by a redox cosubstrate with a soluble or an immobilized enzyme. 3-5 For the reasons mentioned below, multienzymatic systems are gaining increasing attention, thus calling for an extension of theoret- ical treatments to schemes involving the coupling of two or more enzymes. Among multienzymatic systems, the coupling of several enzymes through substrate or cosubstrate regeneration allows the indirect investigation of redox-inactive enzymes and seems quite promising for amplifying the electrochemical responses in substrate detection 6 or bioaffinity assay 7 applications. However, in most previous examples, the coupled enzymes were entrapped in a thick membrane to the detriment of the biocomponents as well as the integrity and accessibility of the enzymes, resulting thus in rather modest amplification rates. We have found on theoretical and experimental bases that confin- ing two enzymes within one or within a small number of mono- layers (Scheme 1) allows high amplification rates (higher than 1000), avoids membrane transport limitations, and lends itself to precise kinetic analyses that provide guidelines for optimization of the analytical sensitivity. The first enzyme converts the substrate S into an electroactive product P, which is oxidized 8 at the electrode surface to give Q. Q serves as cosubstrate to the second enzyme in the conversion of the substrate R into the product O. We consider the case where detection is chronoamperometric with the electrode potential poised at a value positive enough for P to be immediately and entirely converted into Q. The first enzyme is assumed to follow a simple Michaelis-Menten kinetics (involving two forms, E 1 and E 1 S) while the second, auxiliary, enzyme operates according to a ping-pong mechanism (involving the three forms E 2 ,E 2 R, and E 3 ). In the ab- sence of the amplifying enzyme, the current is obtained from eq 1. 9 In the coupled enzyme system, the flux balances of P and Q write: respectively. 10 It follows that the amplification factor, A is expressed by: 9,10 When looking for the detection of either very small concentrations of the substrate S or for very small amounts of the affinity-deposited enzyme 1, the second term in the denominator vanishes, and the amplification factor becomes independent of either [S] x)0 or Γ 1 0 , as follows: The main factors for a good amplification are thus an auxiliary enzyme running fast toward Q and a large amount of this deposited onto the electrode. 11 As an illustrative example, we have selected the -galactosidase- diaphorase-coupled system. -Galactosidase (-Gal) was chosen as the primary enzyme label 12 because it is able to hydrolyze the p-aminophenyl--D-galactopyranoside (PAPG) substrate into an electroactive product, p-aminophenol (PAP). The PAP thus gener- ated is next oxidized at the electrode into p-quinoneimine (PQI) according to a -(2e - + 2H + ) reaction. In the presence of the auxiliary enzyme, diaphorase (DI) from Bacillus stearothermophi- lus, PQI is reduced back to PAP, and the oxidized form of DI is finally regenerated in its reduced native state by its natural substrate, NADH. Selection of this bi-enzymatic system was guided by the following observations: (i) DI is very reactive toward PAP (bimolecular rate constant, k 3 larger than 10 8 M -1 s -1 ); 4 (ii) both enzymes have their optimal activity at approximately the same pH (∼7.5-8.5); (iii) the PAPG substrate is commercially available, essentially free from residual traces of PAP; (iv) both enzymes can be easily biotinylated. The step-by-step procedure for assembling Scheme 1 i 1 nFS ) k 1,2 [S] x)0 K 1,M + [S] x)0 Γ 1 0 (1) i nFS ) k 1,2 Γ E 1 S + k 3 [Q] x)0 Γ E 3 ) k 3 [Q] x)0 Γ E 3 - D Q( d[Q] dx 29 x)0 (2) A ) i i 1 ) 1 + k 3 Γ 2 0 δ D Q 1 + k 1,2 Γ 1 0 [S] x)0 K 1,M + [S] x)0 k 3 k 2,2 δ D Q ) 1 + k 3 Γ 2 0 δ D Q 1 + i 1 nFS k 3 k 2,2 δ D Q (3) A f k 3 Γ 2 0 δ D Q (4) Published on Web 04/11/2006 6014 9 J. AM. CHEM. SOC. 2006, 128, 6014-6015 10.1021/ja060801n CCC: $33.50 © 2006 American Chemical Society