Impedance spectroscopy and biosensing.

This chapter introduces the basic terms of impedance and the technique of impedance measurements. Furthermore, an overview of the application of this transduction method for analytical purposes will be given. Examples for combination with enzymes, antibodies, DNA but also for the analysis of living cells will be described. Special attention is devoted to the different electrode design and amplification schemes developed for sensitivity enhancement. Finally, the last two sections will show examples from the label-free determination of DNA and the sensorial detection of autoantibodies involved in celiac disease.

Inter-subunit rotation and elastic power transmission in F0F1-ATPase.

ATP synthase (F-ATPase) produces ATP at the expense of ion-motive force or vice versa. It is composed from two motor/generators, the ATPase (F1) and the ion translocator (F0), which both are rotary steppers. They are mechanically coupled by 360 degrees rotary motion of subunits against each other. The rotor, subunits gamma(epsilon)C10-14, moves against the stator, (alphabeta)3delta(ab2). The enzyme copes with symmetry mismatch (C3 versus C10-14) between its two motors, and it operates robustly in chimeric constructs or with drastically modified subunits. We scrutinized whether an elastic power transmission accounts for these properties. We used the curvature of fluorescent actin filaments, attached to the rotating c ring, as a spring balance (flexural rigidity of 8.10(-26) N x m2) to gauge the angular profile of the output torque at F0 during ATP hydrolysis by F1. The large average output torque (56 pN nm) proved the absence of any slip. Angular variations of the torque were small, so that the output free energy of the loaded enzyme decayed almost linearly over the angular reaction coordinate. Considering the three-fold stepping and high activation barrier (>40 kJ/mol) of the driving motor (F1) itself, the rather constant output torque seen by F0 implied a soft elastic power transmission between F1 and F0. It is considered as essential, not only for the robust operation of this ubiquitous enzyme under symmetry mismatch, but also for a high turnover rate under load of the two counteracting and stepping motors/generators.

F-ATPase: forced full rotation of the rotor despite covalent cross-link with the stator.

In ATP synthase (F(O)F(1)-ATPase) ion flow through the membrane-intrinsic portion, F(O), drives the central "rotor", subunits c(10)epsilongamma, relative to the "stator" ab(2)delta(alphabeta)(3). This converts ADP and P(i) into ATP. Vice versa, ATP hydrolysis drives the rotation backwards. Covalent cross-links between rotor and stator subunits have been shown to inhibit these activities. Aiming at the rotary compliance of subunit gamma we introduced disulfide bridges between gamma (rotor) and alpha or beta (stator). We engineered cysteine residues into positions located roughly at the "top," "center," and "bottom" parts of the coiled-coil portion of gamma and suitable residues on alpha or beta. This part of gamma is located at the center of the (alphabeta)(3) domain with its C-terminal part at the top of F(1) and the bottom part close to the F(O) complex. Disulfide bridge formation under oxidizing conditions was quantitative as shown by SDS-polyacrylamide gel electrophoresis and immunoblotting. As expected both the ATPase activities and the yield of rotating subunits gamma dropped to zero when the cross-link was formed at the center (gammaL262C <--> alphaA334C) and bottom (gammaCys(87) <--> betaD380C) positions. But much to our surprise disulfide bridging impaired neither ATP hydrolysis activity nor the full rotation of gamma and the enzyme-generated torque of oxidized F(1), which had been engineered at the top position (gammaA285C <--> alphaP280C). Apparently the high torque of this rotary engine uncoiled the alpha-helix and forced amino acids at the C-terminal portion of gamma into full rotation around their dihedral (Ramachandran) angles. This conclusion was supported by molecular dynamics simulations: If gammaCys(285)-Val(286) are attached covalently to (alphabeta)(3) and gammaAla(1)-Ser(281) is forced to rotate, gammaGly(282)-Ala(284) can serve as cardan shaft.

Viscoelastic dynamics of actin filaments coupled to rotary F-ATPase: angular torque profile of the enzyme.

ATP synthase (F(O)F(1)) operates as two rotary motor/generators coupled by a common shaft. Both portions, F(1) and F(O), are rotary steppers. Their symmetries are mismatched (C(3) versus C(10-14)). We used the curvature of fluorescent actin filaments, attached to the rotating c-ring, as a spring balance (flexural rigidity of 8. 10(-26) Nm(2)) to gauge the angular profile of the output torque at F(O) during ATP hydrolysis by F(1) (see theoretical companion article (. Biophys. J. 81:1234-1244.)). The large average output torque (50 +/- 6 pN. nm) proved the absence of any slip. Variations of the torque were small, and the output free energy of the loaded enzyme decayed almost linearly over the angular reaction coordinate. Considering the threefold stepping and high activation barrier of the driving motor proper, the rather constant output torque implied a soft elastic power transmission between F(1) and F(O). It is considered as essential, not only for the robust operation of this ubiquitous enzyme under symmetry mismatch, but also for a high turnover rate of the two counteracting and stepping motor/generators.

F-ATPase: specific observation of the rotating c subunit oligomer of EF(o)EF(1).

The rotary motion in response to ATP hydrolysis of the ring of c subunits of the membrane portion, F(o), of ATP synthase, F(o)F(1), is still under contention. It was studied with EF(o)EF(1) (Escherichia coli) using microvideography with a fluorescent actin filament. To overcome the limited specificity of actin attachment through a Cys-maleimide couple which might have hampered the interpretation of previous work, we engineered a 'strep-tag' sequence into the C-terminal end of subunit c. It served (a) to purify the holoenzyme and (b) to monospecifically attach a fluorescent actin filament to subunit c. EF(o)EF(1) was immobilized on a Ni-NTA-coated glass slide by the engineered His-tag at the N-terminus of subunit beta. In the presence of MgATP we observed up to five counterclockwise rotating actin filaments per picture frame of 2000 microm(2) size, in some cases yielding a proportion of 5% rotating over total filaments. The rotation was unequivocally attributable to the ring of subunit c. The new, doubly engineered construct serves as a firmer basis for ongoing studies on torque and angular elastic distortions between F(1) and F(o).

On the stator of rotary ATP synthase: the binding strength of subunit delta to (alpha beta)3 as determined by fluorescence correlation spectroscopy.

ATP synthase is conceived as a rotary enzyme. Proton flow drives the rotor (namely, subunits c12 epsilon gamma) relative to the stator (namely, subunits ab2 delta(alpha beta)3) and extrudes spontaneously formed ATP from three symmetrically arranged binding sites on (alpha beta)3 into the solution. We asked whether the binding of subunit delta to (alpha beta)3 is of sufficient strength to hold against the elastic strain, which is generated during the operation of this enzyme. According to current estimates, the elastically stored energy is about 50 kJ/mol. Subunit delta was specifically labeled without impairing its function. Its association with solubilized (alpha beta)3 gamma in detergent-free buffer was studied by fluorescence correlation spectroscopy (FCS). A very strong tendency of delta to dimerize in detergent-free buffer was apparent (K(d)

Kinetic modeling of rotary CF0F1-ATP synthase: storage of elastic energy during energy transduction

F0F1-ATP synthase uses proton-motive force to produce ATP from ADP and Pi. With regard to its rotary mechanics, this energy transducing molecular machine assumes a unique position among all enzymes. In the work presented here we put forward a detailed functional model which is based on experimental results obtained with ATP synthase from spinach chloroplasts. We focus on the role of the elastic element, realized by the stalk-like subunit gamma, whose function is energy transduction between F0 and F1 taking into account the H+/ATP coupling ratio of four. Fitting parameters are the rate constants and the torsional rigidity of gamma, which have been adjusted according to the experimental results where the influence of transmembrane DeltapH on the rates of ATP synthesis/hydrolysis is put to the test. We show that the input and output of torsional energy are regulated by purely statistical principles, giving rise to the amount of transiently stored energy to be sliding, depending on DeltapH. During conditions of maximal turnover gamma turns out to be wound up towards 102 degrees which corresponds to a torque of 5.3. 10-20 N.m.

Kinetic modelling of the proton translocating CF0CF1-ATP synthase from spinach.

The rate of both ATP synthase and hydrolysis catalysed by the thiol-modulated and activated ATP synthase from spinach is measured as a function of all substrates including the protons inside the thylakoid lumen. The most important findings are: (1) sigmoid kinetics with respect to H+in, (2) hyperbolic kinetics with respect to ADP, ATP and phosphate, with Km for phosphate and ADP decreasing upon increasing H+in, (3) binding of ADP and phosphate in random order and competitive to ATP. Simulation of the complete set of experimental data is obtained by a kinetic model featuring Boyer's binding-chain mechanism.