Educational Project for the Teaching of Control of Electric Traction Drives

Electric vehicles constitute a multidisciplinary subject that involves disciplines such as automotive, mechanical, electrical and control engineering. Due to this multidisciplinary technical nature, practical teaching methodologies are of special relevance. Paradoxically, in the past, the training of engineers specializing in this area has lacked the practical component represented by field tests, due to the difficulty of accessing real systems. This paper presents an educational project specifically designed for the teaching and training of engineering students with different backgrounds and experience. The teaching methodology focuses on the topology of electric traction drives and their control. It includes two stages, a simulation computer model and a scaled laboratory workbench that comprises a traction electrical drive coupled to a vehicle emulator. With this equipment, the effectiveness of different traction control strategies can be analyzed from the point of view of energy efficiency, robustness, easiness of implementation and acoustic noise.

Co-simulation Methodologies for Hybrid and Electric Vehicle Dynamics

In recent decades, full electric and hybrid electric vehicles have emerged as an alternative to conventional cars due to a range of factors, including environmental and economic aspects. These vehicles are the result of considerable efforts to seek ways of reducing the use of fossil fuel for vehicle propulsion. Sophisticated technologies such as hybrid and electric powertrains require careful study and optimization. Mathematical models play a key role at this point. Currently, many advanced mathematical analysis tools, as well as computer applications have been built for vehicle simulation purposes. Given the great interest of hybrid and electric powertrains, along with the increasing importance of reliable computer-based models, the author decided to integrate both aspects in the research purpose of this work. Furthermore, this is one of the first final degree projects held at the ETSII (Higher Technical School of Industrial Engineers) that covers the study of hybrid and electric propulsion systems. The present project is based on MBS3D 2.0, a specialized software for the dynamic simulation of multibody systems developed at the UPM Institute of Automobile Research (INSIA). Automobiles are a clear example of complex multibody systems, which are present in nearly every field of engineering. The work presented here benefits from the availability of MBS3D software. This program has proven to be a very efficient tool, with a highly developed underlying mathematical formulation. On this basis, the focus of this project is the extension of MBS3D features in order to be able to perform dynamic simulations of hybrid and electric vehicle models. This requires the joint simulation of the mechanical model of the vehicle, together with the model of the hybrid or electric powertrain. These sub-models belong to completely different physical domains. In fact the powertrain consists of energy storage systems, electrical machines and power electronics, connected to purely mechanical components (wheels, suspension, transmission, clutch…). The challenge today is to create a global vehicle model that is valid for computer simulation. Therefore, the main goal of this project is to apply co-simulation methodologies to a comprehensive model of an electric vehicle, where sub-models from different areas of engineering are coupled. The created electric vehicle (EV) model consists of a separately excited DC electric motor, a Li-ion battery pack, a DC/DC chopper converter and a multibody vehicle model. Co-simulation techniques allow car designers to simulate complex vehicle architectures and behaviors, which are usually difficult to implement in a real environment due to safety and/or economic reasons. In addition, multi-domain computational models help to detect the effects of different driving patterns and parameters and improve the models in a fast and effective way. Automotive designers can greatly benefit from a multidisciplinary approach of new hybrid and electric vehicles. In this case, the global electric vehicle model includes an electrical subsystem and a mechanical subsystem. The electrical subsystem consists of three basic components: electric motor, battery pack and power converter. A modular representation is used for building the dynamic model of the vehicle drivetrain. This means that every component of the drivetrain (submodule) is modeled separately and has its own general dynamic model, with clearly defined inputs and outputs. Then, all the particular submodules are assembled according to the drivetrain configuration and, in this way, the power flow across the components is completely determined. Dynamic models of electrical components are often based on equivalent circuits, where Kirchhoff’s voltage and current laws are applied to draw the algebraic and differential equations. Here, Randles circuit is used for dynamic modeling of the battery and the electric motor is modeled through the analysis of the equivalent circuit of a separately excited DC motor, where the power converter is included. The mechanical subsystem is defined by MBS3D equations. These equations consider the position, velocity and acceleration of all the bodies comprising the vehicle multibody system. MBS3D 2.0 is entirely written in MATLAB and the structure of the program has been thoroughly studied and understood by the author. MBS3D software is adapted according to the requirements of the applied co-simulation method. Some of the core functions are modified, such as integrator and graphics, and several auxiliary functions are added in order to compute the mathematical model of the electrical components. By coupling and co-simulating both subsystems, it is possible to evaluate the dynamic interaction among all the components of the drivetrain. ‘Tight-coupling’ method is used to cosimulate the sub-models. This approach integrates all subsystems simultaneously and the results of the integration are exchanged by function-call. This means that the integration is done jointly for the mechanical and the electrical subsystem, under a single integrator and then, the speed of integration is determined by the slower subsystem. Simulations are then used to show the performance of the developed EV model. However, this project focuses more on the validation of the computational and mathematical tool for electric and hybrid vehicle simulation. For this purpose, a detailed study and comparison of different integrators within the MATLAB environment is done. Consequently, the main efforts are directed towards the implementation of co-simulation techniques in MBS3D software. In this regard, it is not intended to create an extremely precise EV model in terms of real vehicle performance, although an acceptable level of accuracy is achieved. The gap between the EV model and the real system is filled, in a way, by introducing the gas and brake pedals input, which reflects the actual driver behavior. This input is included directly in the differential equations of the model, and determines the amount of current provided to the electric motor. For a separately excited DC motor, the rotor current is proportional to the traction torque delivered to the car wheels. Therefore, as it occurs in the case of real vehicle models, the propulsion torque in the mathematical model is controlled through acceleration and brake pedal commands. The designed transmission system also includes a reduction gear that adapts the torque coming for the motor drive and transfers it. The main contribution of this project is, therefore, the implementation of a new calculation path for the wheel torques, based on performance characteristics and outputs of the electric powertrain model. Originally, the wheel traction and braking torques were input to MBS3D through a vector directly computed by the user in a MATLAB script. Now, they are calculated as a function of the motor current which, in turn, depends on the current provided by the battery pack across the DC/DC chopper converter. The motor and battery currents and voltages are the solutions of the electrical ODE (Ordinary Differential Equation) system coupled to the multibody system. Simultaneously, the outputs of MBS3D model are the position, velocity and acceleration of the vehicle at all times. The motor shaft speed is computed from the output vehicle speed considering the wheel radius, the gear reduction ratio and the transmission efficiency. This motor shaft speed, somehow available from MBS3D model, is then introduced in the differential equations corresponding to the electrical subsystem. In this way, MBS3D and the electrical powertrain model are interconnected and both subsystems exchange values resulting as expected with tight-coupling approach.When programming mathematical models of complex systems, code optimization is a key step in the process. A way to improve the overall performance of the integration, making use of C/C++ as an alternative programming language, is described and implemented. Although this entails a higher computational burden, it leads to important advantages regarding cosimulation speed and stability. In order to do this, it is necessary to integrate MATLAB with another integrated development environment (IDE), where C/C++ code can be generated and executed. In this project, C/C++ files are programmed in Microsoft Visual Studio and the interface between both IDEs is created by building C/C++ MEX file functions. These programs contain functions or subroutines that can be dynamically linked and executed from MATLAB. This process achieves reductions in simulation time up to two orders of magnitude. The tests performed with different integrators, also reveal the stiff character of the differential equations corresponding to the electrical subsystem, and allow the improvement of the cosimulation process. When varying the parameters of the integration and/or the initial conditions of the problem, the solutions of the system of equations show better dynamic response and stability, depending on the integrator used. Several integrators, with variable and non-variable step-size, and for stiff and non-stiff problems are applied to the coupled ODE system. Then, the results are analyzed, compared and discussed. From all the above, the project can be divided into four main parts: 1. Creation of the equation-based electric vehicle model; 2. Programming, simulation and adjustment of the electric vehicle model; 3. Application of co-simulation methodologies to MBS3D and the electric powertrain subsystem; and 4. Code optimization and study of different integrators. Additionally, in order to deeply understand the context of the project, the first chapters include an introduction to basic vehicle dynamics, current classification of hybrid and electric vehicles and an explanation of the involved technologies such as brake energy regeneration, electric and non-electric propulsion systems for EVs and HEVs (hybrid electric vehicles) and their control strategies. Later, the problem of dynamic modeling of hybrid and electric vehicles is discussed. The integrated development environment and the simulation tool are also briefly described. The core chapters include an explanation of the major co-simulation methodologies and how they have been programmed and applied to the electric powertrain model together with the multibody system dynamic model. Finally, the last chapters summarize the main results and conclusions of the project and propose further research topics. In conclusion, co-simulation methodologies are applicable within the integrated development environments MATLAB and Visual Studio, and the simulation tool MBS3D 2.0, where equation-based models of multidisciplinary subsystems, consisting of mechanical and electrical components, are coupled and integrated in a very efficient way.

Passenger Exposure to Magnetic Fields due to the Batteries of an Electric Vehicle

In electric vehicles, passengers sit very close to an electric system of significant power. The high currents achieved in these vehicles mean that the passengers could be exposed to significant magnetic fields. One of the electric devices present in the power train are the batteries. In this paper, a methodology to evaluate the magnetic field created by these batteries is presented. First, the magnetic field generated by a single battery is analyzed using finite elements simulations. Results are compared to laboratory measurements, taken from a real battery, in order to validate the model. After this, the magnetic field created by a complete battery pack is estimated and results are discussed.

Analysis and Design Considerations of an Electric Vehicle Powertrain regarding Energy Efficiency and Magnetic Field Exposure

En esta tesis se analiza el sistema de tracción de un vehículo eléctrico de batería desde el punto de vista de la eficiencia energética y de la exposición a campos magnéticos por parte de los pasajeros (radiación electromagnética). Este estudio incluye tanto el sistema de almacenamiento de energía como la máquina eléctrica, junto con la electrónica de potencia y los sistemas de control asociados a ambos. Los análisis y los resultados presentados en este texto están basados en modelos matemáticos, simulaciones por ordenador y ensayos experimentales a escala de laboratorio. La investigación llevada a cabo durante esta tesis tuvo siempre un marcado enfoque industrial, a pesar de estar desarrollada en un entorno de considerable carácter universitario. Las líneas de investigación acometidas tuvieron como destinatario final al diseñador y al fabricante del vehículo, a pesar de lo cual algunos de los resultados obtenidos son preliminares y/o excesivamente académicos para resultar de interés industrial. En el ámbito de la eficiencia energética, esta tesis estudia sistemas híbridos de almacenamiento de energía basados en una combinación de baterías de litio y supercondensadores. Este tipo de sistemas son analizados desde el punto de vista de la eficiencia mediante modelos matemáticos y simulaciones, cuantificando el impacto de ésta en otros parámetros tales como el envejecimiento de las baterías. Respecto a la máquina eléctrica, el estudio se ha centrado en máquinas síncronas de imanes permanentes. El análisis de la eficiencia considera tanto el diseño de la máquina como la estrategia de control, dejando parcialmente de lado el inversor y la técnica de modulación (que son incluidos en el estudio como fuentes adicionales de pérdidas, pero no como potenciales fuentes de optimización de la eficiencia). En este sentido, tanto la topología del inversor (trifásico, basado en IGBTs) como la técnica de modulación (control de corriente en banda de histéresis) se establecen desde el principio. El segundo aspecto estudiado en esta tesis es la exposición a campos magnéticos por parte de los pasajeros. Este tema se enfoca desde un punto de vista predictivo, y no desde un punto de vista de diagnóstico, puesto que se ha desarrollado una metodología para estimar el campo magnético generado por los dispositivos de potencia de un vehículo eléctrico. Esta metodología ha sido validada mediante ensayos de laboratorio. Otros aspectos importantes de esta contribución, además de la metodología en sí misma, son las consecuencias que se derivan de ella (por ejemplo, recomendaciones de diseño) y la comprensión del problema proporcionada por esta. Las principales contribuciones de esta tesis se listan a continuación: una recopilación de modelos de pérdidas correspondientes a la mayoría de dispositivos de potencia presentes en un vehículo eléctrico de batería, una metodología para analizar el funcionamiento de un sistema híbrido de almacenamiento de energía para aplicaciones de tracción, una explicación de cómo ponderar energéticamente los puntos de operación par-velocidad de un vehículo eléctrico (de utilidad para evaluar el rendimiento de una máquina eléctrica, por ejemplo), una propuesta de incluir un convertidor DC-DC en el sistema de tracción para minimizar las pérdidas globales del accionamiento (a pesar de las nuevas pérdidas introducidas por el propio DC-DC), una breve comparación entre dos tipos distintos de algoritmos de minimización de pérdidas para máquinas síncronas de imanes permanentes, una metodología predictiva para estimar la exposición a campos magnéticos por parte de los pasajeros de un vehículo eléctrico (debida a los equipos de potencia), y finalmente algunas conclusiones y recomendaciones de diseño respecto a dicha exposición a campos magnéticos. ABSTRACT This dissertation analyzes the powertrain of a battery electric vehicle, focusing on energy efficiency and passenger exposure to electromagnetic fields (electromagnetic radiation). This study comprises the energy storage system as well as the electric machine, along with their associated power electronics and control systems. The analysis and conclusions presented in this dissertation are based on mathematical models, computer simulations and laboratory scale tests. The research performed during this thesis was intended to be of industrial nature, despite being developed in a university. In this sense, the work described in this document was carried out thinking of both the designer and the manufacturer of the vehicle. However, some of the results obtained lack industrial readiness, and therefore they remain utterly academic. Regarding energy efficiency, hybrid energy storage systems consisting in lithium batteries, supercapacitors and up to two DC-DC power converters are considered. These kind of systems are analyzed by means of mathematical models and simulations from the energy efficiency point of view, quantifying its impact on other relevant aspects such as battery aging. Concerning the electric machine, permanent magnet synchronous machines are studied in this work. The energy efficiency analysis comprises the machine design and the control strategy, while the inverter and its modulation technique are taken into account but only as sources of further power losses, and not as potential sources for further efficiency optimization. In this sense, both the inverter topology (3-phase IGBT-based inverter) and the switching technique (hysteresis current control) are fixed from the beginning. The second aspect studied in this work is passenger exposure to magnetic fields. This topic is approached from the prediction point of view, rather than from the diagnosis point of view. In other words, a methodology to estimate the magnetic field generated by the power devices of an electric vehicle is proposed and analyzed in this dissertation. This methodology has been validated by laboratory tests. The most important aspects of this contribution, apart from the methodology itself, are the consequences (for instance, design guidelines) and the understanding of the magnetic radiation issue provided by it. The main contributions of this dissertation are listed next: a compilation of loss models for most of the power devices found in a battery electric vehicle powertrain, a simulation-based methodology to analyze hybrid energy storage performance in traction applications, an explanation of how to assign energy-based weights to different operating points in traction drives (useful when assessing electrical machine performance, for instance), a proposal to include one DC-DC converter in electric powertrains to minimize overall power losses in the system (despite the new losses added by the DC-DC), a brief comparison between two kinds of loss-minimization algorithms for permanent magnet synchronous machines in terms of adaptability and energy efficiency, a predictive methodology to estimate passenger magnetic field exposure due to power devices in an electric vehicle, and finally some useful conclusions and design guidelines concerning magnetic field exposure.

Electric Field–directed Cell Motility Involves Up-regulated Expression and Asymmetric Redistribution of the Epidermal Growth Factor Receptors and Is Enhanced by Fibronectin and Laminin

Wounding corneal epithelium establishes a laterally oriented, DC electric field (EF). Corneal epithelial cells (CECs) cultured in similar physiological EFs migrate cathodally, but this requires serum growth factors. Migration depends also on the substrate. On fibronectin (FN) or laminin (LAM) substrates in EF, cells migrated faster and more directly cathodally. This also was serum dependent. Epidermal growth factor (EGF) restored cathodal-directed migration in serum-free medium. Therefore, the hypothesis that EGF is a serum constituent underlying both field-directed migration and enhanced migration on ECM molecules was tested. We used immunofluorescence, flow cytometry, and confocal microscopy and report that 1) EF exposure up-regulated the EGF receptor (EGFR); so also did growing cells on substrates of FN or LAM; and 2) EGFRs and actin accumulated in the cathodal-directed half of CECs, within 10 min in EF. The cathodal asymmetry of EGFR and actin staining was correlated, being most marked at the cell–substrate interface and showing similar patterns of asymmetry at various levels through a cell. At the cell–substrate interface, EGFRs and actin frequently colocalized as interdigitated, punctate spots resembling tank tracks. Cathodal accumulation of EGFR and actin did not occur in the absence of serum but were restored by adding ligand to serum-free medium. Inhibition of MAPK, one second messenger engaged by EGF, significantly reduced EF-directed cell migration. Transforming growth factor β and fibroblast growth factor also restored cathodal-directed cell migration in serum-free medium. However, longer EF exposure was needed to show clear asymmetric distribution of the receptors for transforming growth factor β and fibroblast growth factor. We propose that up-regulated expression and redistribution of EGFRs underlie cathodal-directed migration of CECs and directed migration induced by EF on FN and LAM.

An electric lobe suppressor for a yeast choline transport mutation belongs to a new family of transporter-like proteins

Choline is an important metabolite in all cells due to the major contribution of phosphatidylcholine to the production of membranes, but it takes on an added role in cholinergic neurons where it participates in the synthesis of the neurotransmitter acetylcholine. We have cloned a suppressor for a yeast choline transport mutation from a Torpedo electric lobe yeast expression library by functional complementation. The full-length clone encodes a protein with 10 putative transmembrane domains, two of which contain transporter-like motifs, and whose expression increased high-affinity choline uptake in mutant yeast. The gene was called CTL1 for its choline transporter-like properties. The homologous rat gene, rCTL1, was isolated and found to be highly expressed as a 3.5-kb transcript in the spinal cord and brain and as a 5-kb transcript in the colon. In situ hybridization showed strong expression of rCTL1 in motor neurons and oligodendrocytes and to a lesser extent in various neuronal populations throughout the rat brain. High levels of rCTL1 were also identified in the mucosal cell layer of the colon. Although the sequence of the CTL1 gene shows clear homology with a single gene in Caenorhabditis elegans, several homologous genes are found in mammals (CTL2–4). These results establish a new family of genes for transporter-like proteins in eukaryotes and suggest that one of its members, CTL1, is involved in supplying choline to certain cell types, including a specific subset of cholinergic neurons.

Manipulating the genetic identity and biochemical surface properties of individual cells with electric-field-induced fusion

A method for cell–cell and cell–liposome fusion at the single-cell level is described. Individual cells or liposomes were first selected and manipulated either by optical trapping or by adhesion to a micromanipulator-controlled ultramicroelectrode. Spatially selective fusion of the cell–cell or cell–liposome pair was achieved by the application of a highly focused electric field through a pair of 5-μm o.d. carbon-fiber ultramicroelectrodes. The ability to fuse together single cells opens new possibilities in the manipulation of the genetic and cellular makeup of individual cells in a controlled manner. In the study of cellular networks, for example, the alteration of the biochemical identity of a selected cell can have a profound effect on the behavior of the entire network. Fusion of a single liposome with a target cell allows the introduction of the liposomal content into the cell interior as well as the addition of lipids and membrane proteins onto the cell surface. This cell–liposome fusion represents an approach to the manipulation of the cytoplasmic contents and surface properties of single cells. As an example, we have introduced a membrane protein (γ-glutamyltransferase) reconstituted in liposomes into the cell plasma membrane.

Electric field-induced reorganization of two-component supported bilayer membranes

Application of electric fields tangent to the plane of a confined patch of fluid bilayer membrane can create lateral concentration gradients of the lipids. A thermodynamic model of this steady-state behavior is developed for binary systems and tested with experiments in supported lipid bilayers. The model uses Flory’s approximation for the entropy of mixing and allows for effects arising when the components have different molecular areas. In the special case of equal area molecules the concentration gradient reduces to a Fermi–Dirac distribution. The theory is extended to include effects from charged molecules in the membrane. Calculations show that surface charge on the supporting substrate substantially screens electrostatic interactions within the membrane. It also is shown that concentration profiles can be affected by other intermolecular interactions such as clustering. Qualitative agreement with this prediction is provided by comparing phosphatidylserine- and cardiolipin-containing membranes.

Electrostatic surface plasmon resonance: Direct electric field-induced hybridization and denaturation in monolayer nucleic acid films and label-free discrimination of base mismatches

We demonstrate that in situ optical surface plasmon resonance spectroscopy can be used to monitor hybridization kinetics for unlabeled DNA in tethered monolayer nucleic acid films on gold in the presence of an applied electrostatic field. The dc field can enhance or retard hybridization and can also denature surface-immobilized DNA duplexes. Discrimination between matched and mismatched hybrids is achieved by simple adjustment of the electrode potential. Although the electric field at the interface is extremely large, the tethered single-stranded DNA thiol probes remain bound and can be reused for subsequent hybridization reactions without loss of efficiency. Only capacitive charging currents are drawn; redox reactions are avoided by maintaining the gold electrode potential within the ideally polarizable region. Because of potential-induced changes in the shape of the surface plasmon resonance curve, we account for the full curve rather than simply the shift in the resonance minimum.

Electric Signaling and Pin2 Gene Expression on Different Abiotic Stimuli Depend on a Distinct Threshold Level of Endogenous Abscisic Acid in Several Abscisic Acid-Deficient Tomato Mutants1

Experiments were performed on three abscisic acid (ABA)-deficient tomato (Lycopersicon esculentum Mill.) mutants, notabilis, flacca, and sitiens, to investigate the role of ABA and jasmonic acid (JA) in the generation of electrical signals and Pin2 (proteinase inhibitor II) gene expression. We selected these mutants because they contain different levels of endogenous ABA. ABA levels in the mutant sitiens were reduced to 8% of the wild type, in notabilis they were reduced to 47%, and in flacca they were reduced to 21%. In wild-type and notabilis tomato plants the induction of Pin2 gene expression could be elicited by heat treatment, current application, or mechanical wounding. In flacca and sitiens only heat stimulation induced Pin2 gene expression. JA levels in flacca and sitiens plants also accumulated strongly upon heat stimulation but not upon mechanical wounding or current application. Characteristic electrical signals evolved in the wild type and in the notabilis and flacca mutants consisting of a fast action potential and a slow variation potential. However, in sitiens only heat evoked electrical signals; mechanical wounding and current application did not change the membrane potential. In addition, exogenous application of ABA to wild-type tomato plants induced transient changes in membrane potentials, indicating the involvement of ABA in the generation of electrical signals. Our data strongly suggest the presence of a minimum threshold value of ABA within the plant that is essential for the early events in electrical signaling and mediation of Pin2 gene expression upon wounding. In contrast, heat-induced Pin2 gene expression and membrane potential changes were not dependent on the ABA level but, rather, on the accumulation of JA.

Molecular dynamics of a grid-mounted molecular dipolar rotor in a rotating electric field

Classical molecular dynamics is applied to the rotation of a dipolar molecular rotor mounted on a square grid and driven by rotating electric field E(ν) at T ≃ 150 K. The rotor is a complex of Re with two substituted o-phenanthrolines, one positively and one negatively charged, attached to an axial position of Rh\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}{\mathrm{_{2}^{4+}}}\end{equation*}\end{document} in a [2]staffanedicarboxylate grid through 2-(3-cyanobicyclo[1.1.1]pent-1-yl)malonic dialdehyde. Four regimes are characterized by a, the average lag per turn: (i) synchronous (a < 1/e) at E(ν) = |E(ν)| > Ec(ν) [Ec(ν) is the critical field strength], (ii) asynchronous (1/e < a < 1) at Ec(ν) > E(ν) > Ebo(ν) > kT/μ, [Ebo(ν) is the break-off field strength], (iii) random driven (a ≃ 1) at Ebo(ν) > E(ν) > kT/μ, and (iv) random thermal (a ≃ 1) at kT/μ > E(ν). A fifth regime, (v) strongly hindered, W > kT, Eμ, (W is the rotational barrier), has not been examined. We find Ebo(ν)/kVcm−1 ≃ (kT/μ)/kVcm−1 + 0.13(ν/GHz)1.9 and Ec(ν)/kVcm−1 ≃ (2.3kT/μ)/kVcm−1 + 0.87(ν/GHz)1.6. For ν > 40 GHz, the rotor behaves as a macroscopic body with a friction constant proportional to frequency, η/eVps ≃ 1.14 ν/THz, and for ν < 20 GHz, it exhibits a uniquely molecular behavior.

Electric-field-induced Schiff-base deprotonation in D85N mutant bacteriorhodopsin.

The application of an external electric field to dry films of Asp-85-->Asn mutant bacteriorhodopsin causes deprotonation of the Schiff base, resulting in a shift of the optical absorption maximum from 600 nm to 400 nm. This is in marked contrast to the case of wild-type bacteriorhodopsin films, in which electric fields produce a red-shifted product whose optical properties are similar to those of the acid-blue form of the protein. This difference is due to the much weaker binding of the Schiff-base proton in the mutant protein, as indicated by its low pK of approximately 9, as compared with the value pK approximately 13 in the wild type. Other bacteriorhodopsins with lowered Schiff-base pK values should also exhibit a field-induced shift in the protonation equilibrium of the Schiff base. We propose mechanisms to account for these observations.

Rectification and signal averaging of weak electric fields by biological cells.

Oscillating electric fields can be rectified by proteins in cell membranes to give rise to a dc transport of a substance across the membrane or a net conversion of a substrate to a product. This provides a basis for signal averaging and may be important for understanding the effects of weak extremely low frequency (ELF) electric fields on cellular systems. We consider the limits imposed by thermal and "excess" biological noise on the magnitude and exposure duration of such electric field-induced membrane activity. Under certain circumstances, the excess noise leads to an increase in the signal-to-noise ratio in a manner similar to processes labeled "stochastic resonance." Numerical results indicate that it is difficult to reconcile biological effects with low field strengths.

Effects of the environment on the electric conductivity of double-stranded DNA molecules

We present a theoretical analysis of the effects of the environment on charge transport in double-stranded synthetic poly(G)-poly(C) DNA molecules attached to two ideal leads. Coupling of the DNA to the environment results in two effects: (i) localization of carrier functions due to static disorder and (ii) phonon-induced scattering of the carriers between the localized states, resulting in hopping conductivity. A nonlinear Pauli master equation for populations of localized states is used to describe the hopping transport and calculate the electric current as a function of the applied bias. We demonstrate that, although the electronic gap in the density of states shrinks as the disorder increases, the voltage gap in the I-V characteristics becomes wider. A simple physical explanation of this effect is provided.