Baldwin Robertson

Nonlinear effect of an oscillating electric field on membrane proteins

The nonlinear response of a two‐state chemical transition to an oscillating electric field is examined. A reaction for which this analysis is particularly relevant is a conformational transition of a membrane protein exposed to an ac electric field. Even a modest externally applied field leads to a very large local field within the membrane. This gives rise to nonlinear behavior. The applied ac field causes harmonics in the polarization and can cause a dc shift in the state occupancy, both of which can be observed and used to determine kinetic parameters. Fourier coefficients are calculated for the enzyme state probability in the ac field, exactly for infinite frequency, and in powers of the field for finite frequency. Kramers–Kronig relations are proved and response functions are given for the leading terms of the harmonics. The results are extended to the spherical symmetry relevant to suspensions of spherical cells, vesicles, or colloidal particles. If the protein catalyzes a reaction, free energy is t...

Frequency dependence of catalyzed reactions in a weak oscillating field

The frequency dependence of the average rates of reactions catalyzed by one or more catalysts in a weak oscillating field is derived. The average rates are sums of Lorentzian curves whose characteristic frequencies are the inverse relaxation times of the normal modes of the kinetic system and whose amplitudes are quadratic in the field. The signs of the Lorentz amplitudes can be either positive or negative, so the rates versus frequency can have a variety of shapes, including frequency windows. One can get relaxation times and amplitudes by measuring steady‐state rates as a function of the frequency of the field. The theory is applied to determine the Lorentz amplitudes and characteristic frequencies of ion transport rates catalyzed by Na+–K+–ATPase in erythrocytes.

Bacteriorhodopsin immobilized in sol-gel glass

Abstract The 96N mutant of bacteriorhodopsin (BR) has been successfully entrapped in a sol-gel glass. The protein retains it light-sensitive properties when immobilized at pH 9.0. Spectroscopic studies on the immobilized BR shows properties similar to the those observed when in suspension.

Energy transduction between a concentration gradient and an alternating electric field

A four‐state transport protein that has electric charges that move concomitantly with conformational changes can transduce energy in either direction between an alternating membrane potential and a concentration gradient. An alternating electric potential of very large amplitude is considered, and the rapid‐equilibrium approximation is used for the conformational changes. This permits deriving simple expressions for the transport flux, the power supplied by the alternating potential, and the power applied to the concentration gradient.

Quantum Statistical Mechanical Derivation of Generalized Hydrodynamic Equations

Differential conservation equations are derived for the mass‐, momentum‐, and energy‐density operators for a 1‐component simple fluid of Bose or Fermi particles with arbitrary pairwise interactions. These equations are used in a statistical mechanical derivation of exact equations of motion for the expectations of these operators. The equations of motion are coupled to equations relating these expectations to the local temperature, chemical potential, and fluid velocity. The coupled equations are closed in the sense that the expectations and their thermodynamic conjugates listed above are the only unknowns, although some of the dependence in the equations on the conjugates is expressed only implicitly. The equations of motion are memory‐retaining nonlocal generalizations of the classical hydrodynamic equations and apply to a normal fluid arbitrarily far from equilibrium. The formalism is not carried as far as has the corresponding classical formalism because the local equilibrium expectation of the moment...

Quadratic response of a chemical reaction to external oscillations

We develop a second‐order response theory to investigate the effects of external periodic perturbations on a chemical reaction at a stable steady state in an open reactor. We apply the theory to the quadratic Schlogl model, a single‐variable nonlinear reaction. In the presence of oscillating reactant or product concentrations or oscillating rate coefficients, the average intermediate concentration, the fluxes, and the dissipation are each a Lorentzian function of frequency with midpoint at the inverse relaxation time of the system. Thus even very short relaxation times can be determined by measuring average rates as a function of frequency of the perturbation. The amplitude of the Lorentzian depends on the chemical mechanism of the reaction and is proportional to the square of the amplitude of the applied perturbation. We also show that energy from the perturbation can be used to drive the reaction in a direction opposite of that predicted by the Gibb’s free energy difference of reactants and products, ev...

Equations of Motion in Nonequilibrium Statistical Mechanics. III. Open Systems

A simple hypothesis on the effect of the interaction between a system and its surroundings is used to generalize nonequilibrium statistical mechanics to apply to open systems. Thermal driving of a system by its surroundings is defined in statistical mechanics by analogy with the first law of thermodynamics, which describes exchange of heat between the system and an external source. The assumption that an isolated system is thermally driven is used to derive a Liouville equation with an additional term that is linear in the external source strength. The generalized Liouville equation is used to derive closed equations of motion that are the same as for an isolated system except for an additional term, which is just the source strength. This formalism is attractive because the source strength, which is assumed known, appears in the equations linearly just as in classical thermodynamics or hydrodynamics. A microscopic expression for the source strength is obtained by comparing the thermal driving formalism with an exact dynamical analysis of the system interacting with its surroundings.

Phototransformation and proton pumping activity of the 14-fluoro bacteriorhodopsin derivatives

The photoinduced behavior and proton pumping characteristics of some bacteriorhodopsin (BR) analogs with fluorinated chromophores (all-trans 14-fluorinated [14-F] retinal and 13-cis 14-F retinal) derived from wild type (WT) and D96N mutant BR were investigated. These analogs were characterized using spectrophotometry and a highly sensitive electrochemical technique. Similar to the white membrane JW2N, the apomembranes WT ET 1000 and D96N form photoactive pigments with the 14-F chromophores. The resulting analogs have a major absorption band at 588 nm. Red-shifted pigment (lambdamax</=680 nm) has been previously observed as a minor component of the major 587-nm pigment in 14-F BR made with white membrane JW2N. A similar red-shifted pigment is formed under yellow light (lambda>500 nm) only in the 14-F analogs derived from WT ET 1000. The measurements of the photoinduced transformation in 14-F WT analogs show that the photocycle of the major pigment occurs simultaneously with the process in the red region and is partially masked by the formation of the red-shifted species. The 14-F D96N samples have a significantly slower and more complicated photoinduced behavior. Electrochemical measurements show that the photoinduced transformation of the red species is not accompanied by proton transport.

Physics of DNA Threading Through a Nanometer Pore and Applications to Simultaneous Multianalyte Sensing

Polymer transport is central to many biological processes, including protein translocation, bacterial gene transduction and some modes of viral infection. To better understand the mechanisms of macromolecular transport, we are studying the ability of polymers to partition into and thread through single protein ion channels. It was recently shown in our laboratory that individual molecules of single-stranded DNA and RNA can be detected and characterized as they are driven electrophoretically through a single channel formed by Staphylococcus aureus α-hemolysin. We demonstrate that polynucleotides partition more readily into one entrance of this channel than the other and that the rate at which the polymer enters the pore increases exponentially with the magnitude of the applied electrostatic potential. A simple model provides an estimate for both the height of the energy barrier that limits polynucleotide entry into the channel and the number of charges on polyanionic ssDNA that initiate voltage-driven transport through the pore. We show that polynucleotides can be used to probe the geometric properties of an ion channel, and that the interaction between the polynucleotides and a nanopore can be used to estimate the concentration of analytes in solution. A statistical analysis of the current blockades provides information about the structures of both the polymer and the nanopore.

Frequency response of alternating currents through the Staphylococcus aureus α‐hemolysin ion channel†

Alternating currents were measured through transmembrane ion channels formed by Staphylococcus aureus alpha-hemolysin proteins in planar bilayer membranes as part of an investigation to determine the channels frequency response and the appropriateness of an equivalent circuit commonly used to model electrical interactions at the surface of cells. The experimental approach includes a novel method for separating the alternating current through one or more channels, which is conductive in nature, from the capacitively coupled current through the membrane. Separation of the conductive and capacitive alternating currents made it possible to measure the frequency response of the alpha-hemolysin channels. The results of the study are consistent with an equivalent circuit of a membrane capacitor in parallel with one or more channel resistors over the frequency range 30-120 Hz. The possible usefulness of frequency response data for ion channels in cell membranes during investigations of biological effects of time-varying magnetic fields is briefly discussed.