Dieter Walz

Electronic Wiring of a Multi-Redox Site Membrane Protein in a Biomimetic Surface Architecture

Bioelectronic coupling of multi-redox-site membrane proteins was accomplished with cytochrome c oxidase (CcO) as an example. A biomimetic membrane system was used for the oriented immobilization of the CcO oxidase on a metal electrode. When the protein is immobilized with the CcO binding side directed toward the electrode and reconstituted in situ into a lipid bilayer, it is addressable by direct electron transfer to the redox centers. Electron transfer to the enzyme via the spacer, referred to as electronic wiring, shows an exceptionally high rate constant. This allows a kinetic analysis of all four consecutive electron transfer steps within the enzyme to be carried out. Electron transfer followed by rapid scan cyclic voltammetry in combination with surface-enhanced resonance Raman spectroscopy provides mechanistic and structural information about the heme centers. Probing the enzyme under turnover conditions showed mechanistic insights into proton translocation coupled to electron transfer. This bioelectronic approach opens a new field of activity to investigate complex processes in a wide variety of membrane proteins.

Biothermokinetics of processes and energy conversion

E. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 7 3 Systems, phases and compartments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 Thermodynamic potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 The dissipation function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 Flows and forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 1. Chemical reactions and redox neactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 2. Transport processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 3. Flows and forces in the dissipation function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 Steady states and equilibrium state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 1. The equilibrium state, and equilibrium conslants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 2. Steady ~,tates, and the chemical capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

An electrostatic mechanism closely reproducing observed behavior in the bacterial flagellar motor.

A mechanism coupling the transmembrane flow of protons to the rotation of the bacterial flagellum is studied. The coupling is accomplished by means of an array of tilted rows of positive and negative charges around the circumference of the rotor, which interacts with a linear array of proton binding sites in channels. We present a rigorous treatment of the electrostatic interactions using minimal assumptions. Interactions with the transition states are included, as well as proton-proton interactions in and between channels. In assigning values to the parameters of the model, experimentally determined structural characteristics of the motor have been used. According to the model, switching and pausing occur as a consequence of modest conformational changes in the rotor. In contrast to similar approaches developed earlier, this model closely reproduces a large number of experimental findings from different laboratories, including the nonlinear behavior of the torque-frequency relation in Escherichia coli, the stoichiometry of the system in Streptococcus, and the pH-dependence of swimming speed in Bacillus subtilis.

Energy Coupling and Thermokinetic Balancing in Enzyme Kinetics Microscopic Reversibility and Detailed Balance Revisited

A survey of the development of the concepts of microscopic reversibility and detailed balancing is given. Considerable confusion surrounds these concepts. To obviate this, an unambiguous relation is presented that holds under all conditions and for which we propose the term “thermokinetic balancing”. The utility of this relation, which in contrast to detailed balancing is independent of reactant and product concentrations, is demonstrated in a detailed discussion of the kinetics and thermodynamics of the calcium-transporting ATPase according to the principles worked out by Hill. This includes a critical analysis of the different concepts advocated by Jencks and Tanford. The advantage of thermokinetic balancing over detailed balancing is illustrated by examples, high-lighting the relationship of these procedures to standard free energies and basic free energies.

Bacterial flagellar motor and H+/ATP synthase: two proton-driven rotary molecular devices with different functions

Both the bacterial flagellar motor and the H(+)/ATP synthase are membrane-bound macromolecular complexes in which the movement of protons through channels across the membrane is coupled to the rotation of a part of the complex around an axis perpendicular to the membrane. Despite this similarity, the two devices are designed for quite different functions. The flagellar motor is responsible for a practically smooth rotation of the flagellar filament in order to propel the cell. Smooth rotation is not essential for the H(+)/ATP synthase, which accumulates torque by twisting a rod-shaped structure. Possible mechanisms for generating torque in the two devices are presented, based on the models which have been proposed. The performances of the various mechanisms are discussed.

Conformational transitions and molecular hysteresis of cytochrome c oxidase: Varying the redox state by electronic wiring

Even though the structures of cytochrome c oxidase (CcO) from different sources have been determined by X-ray crystallography in both the reduced and oxidized redox states, information about redox-induced structure-function relationships is still very limited. In the current work, redox-dependent structural changes are determined for CcO reconstituted in a protein-tethered bilayer lipid membrane by surface-enhanced infrared absorption spectroscopy in the ATR mode. Significantly, the redox changes in the enzyme are attained by direct wiring of CcO to a gold electrode, ensuring that sequential intra-protein electron transfer occurs by a directed pathway that is natural to the system. The characteristics of CcO were observed to be dramatically altered after the reconstituted enzyme was allowed to turn over in the presence of O2. The data suggest that the enzyme is initially in an “inactive” state, but that direct electron transfer in the presence of O2 converts the enzyme to an “activated” form which returns to the inactive conformation when the enzyme remains idle under anaerobic conditions. Potentiometric titrations are performed and reduced-minus-fully oxidized and oxidized-minus-fully reduced absorbance spectra are recorded at decreasing and increasing potentials, respectively, applied to the electrode in a regular succession. The two sets of difference spectra show mirror symmetry, however, they markedly differ from those measured in the presence of redox mediators. Plots of band area of individual bands obtained by Fourier self deconvolution vs. applied potential show a sigmoid dependence as expected for a redox process. However, the sigmoid curves do not coincide but are displaced depending on the direction of the potential change. In other words, these curves show hysteresis, which is an indication of cooperativity and non-equilibrium states for electron transfer and/or conformational changes of the protein. This is discussed in terms of known concepts of molecular hysteresis.

The thermostatics and thermodynamics of cotransport revisited: a restatement of the Zeroth Law

Abstract The assertions by Naftalin ((1984) Biochim. Biophys. Acta 778, 155–175) that “(a) the static-head equilibrium state cannot exist; (b) the stoichiometry of cotransport … does not affect the static-head distribution of cotransported ligands; … (d) the only equilibrium state where there is zero net flow of both driving and driven transported ligand is at true equilibrium when the ligands are uniformly distributed across the membrane” are incorrect and hence misleading. These assertions are based on a faulty application of the lattice-gas models of Hill and Kedem ((1966) J. Theor. Biol. 10, 399–441), as well as a misunderstanding of the Zeroth Law of Thermodynamics. Furthermore the claim that “cotransport is not entirely an affinity-driven, but is partially an entropy-driven process” is unwarranted. A consistent treatment of the thermodynamics of cotransport is given which completely covers all the arguments put forward by Naftalin against the existence of static head.

Chemical oscillations arise solely from kinetic nonlinearity and hence can occur near equilibrium

A minimal kinetic scheme for a system displaying sustained chemical oscillations is presented. The system is isothermal, and all steps in the scheme are kinetically reversible. The oscillations are analyzed and the crucial points elucidated. Both positive and negative feedback, if properly introduced, support oscillations, provided the state responsible for feedback is optimally buffered. It is shown that the requisite nonlinearity is introduced at the kinetic level because of feedback regulation and not, as is usually assumed, by large affinities that introduce nonlinearity at the thermodynamic level. Hence, sustained oscillations may occur near equilibrium.

The radial velocity of spherical particles in tubular pinch effect experiments

Abstract This paper on the so-called Tubular Pinch Effect (TPE) is specifically concerned with the radial velocity ur of spherical particles in TPE experiments. To begin with, the experiments carried out by Segre and Silberberg are evaluated in a new way in order to gain more information about ur than has hitherto been available. The results of this re-evaluation are then used as a basis for a critical assessment of the data yielded by experiments carried out by authors other than Segre and Silberberg. Finally our present knowledge concerning the function ur is summed up and the regularities of this function are pointed out. In an appendix to the paper, proof is given of a mathematical theorem on which our reevaluation of the Segre-Silberberg experiments is based.

Methods of mathematical modelling

Nonequilibrium thermodynamics and kinetics as presented in chapter 1 are adequate and sufficient for the analysis of systems or processes in the steady state. On the other hand, they only provide necessary tools for the analysis of a system on its way to a steady state, but not the actual means of performing the analysis. To carry out such an analysis one must invoke mathematical modelling. Moreover, even in the steady state modelling proves to be a valuable means of exploring the behavior of complex systems. Thus mathematical modelling is an important subject in bioelectrochemistry and hence is dealt with in this chapter. Furthermore, this chapter includes a number of carefully-chosen worked examples. These examples are not only illustrative and designed to cover most features of modelling, but they are also biologically realistic, and in an important sense extend the treatment given in chapter 1. In addition, they present novel aspects of bioelectrochemistry which are difficult to display without the aid of simulation.