An analytical tool for elucidating ion-channel molecular mechanisms from macroscopic current traces

Building models to describe the dynamics of macroscopic currents through ion channels has been the object of numerous studies in the literature with the aim of understanding ion-channel function. Following a perturbation, typically a step in voltage or ligand concentration, the response is formed by a combination of different processes such as activation or inactivation that pull the measured quantity (macroscopic current) in the same or opposite directions with different strengths and different time constants. Although this dynamic response can be readily recorded in time, the relationship between the underlying processes cannot be easily teased apart without structural analysis or single-channel recordings. An example is the classic problem of determining from sodium-channel macroscopic traces whether the activation and inactivation processes occur in parallel or inactivation is dependent on previous activation. We present a mathematical tool to analyze electrophysiological traces and derive molecular kinetic schemes that reflect the interplay between the different processes involved. This tool is based on system-identification algorithms and consists of three modules as summarized in Figure 1. The identifier takes the input and output signals in the time domain and applies autoregressive ARX methods to obtain a transfer function in the Laplace domain yielding a set of poles, zeros and gain that provide a unique signature of the channel response. The classifier capitalizes on this signature to reveal the block diagram associated with the interplay of the processes, that are here described as first order systems in classic engineering terms (a relaxation with one time constant and a gain for each process). Finally, the molecular kinetic converter uses the transfer function together with the block diagram and maps them into a molecular kinetic scheme, a description with states associated with a system of differential equations

Elucidation of molecular kinetic schemes from macroscopic traces using system identification

Overall cellular responses to biologically-relevant stimuli are mediated by networks of simpler lower-level processes. Although information about some of these processes can now be obtained by visualizing and recording events at the molecular level, this is still possible only in especially favorable cases. Therefore the development of methods to extract the dynamics and relationships between the different lower-level (microscopic) processes from the overall (macroscopic) response remains a crucial challenge in the understanding of many aspects of physiology. Here we have devised a hybrid computational-analytical method to accomplish this task, the SYStems-based MOLecular kinetic scheme Extractor (SYSMOLE). SYSMOLE utilizes system-identification input-output analysis to obtain a transfer function between the stimulus and the overall cellular response in the Laplace-transformed domain. It then derives a Markov-chain state molecular kinetic scheme uniquely associated with the transfer function by means of a classification procedure and an analytical step that imposes general biological constraints. We first tested SYSMOLE with synthetic data and evaluated its performance in terms of its rate of convergence to the correct molecular kinetic scheme and its robustness to noise. We then examined its performance on real experimental traces by analyzing macroscopic calcium-current traces elicited by membrane depolarization. SYSMOLE derived the correct, previously known molecular kinetic scheme describing the activation and inactivation of the underlying calcium channels and correctly identified the accepted mechanism of action of nifedipine, a calcium-channel blocker clinically used in patients with cardiovascular disease. Finally, we applied SYSMOLE to study the pharmacology of a new class of glutamate antipsychotic drugs and their crosstalk mechanism through a heteromeric complex of G protein-coupled receptors. Our results indicate that our methodology can be successfully applied to accurately derive molecular kinetic schemes from experimental macroscopic traces, and we anticipate that it may be useful in the study of a wide variety of biological systems

Optimal design of an axially displaced ellipse antenna

Reflectors antennas in Ku band are primarily used for satellite communications. They are mainly employed for establishing the communications for data transmission. In this paper, a displaced axis dual reflector antenna, usually referred as Axially Displaced Ellipse (ADE) antenna, is presented, demonstrating its advantages compared to the classical dual reflector antennas. Results show that the design antenna meets the expectations for SATCOM communications

Multi-level spherical wave expansion for fast near-field to far-field transformation

Traditional near-field to far-field transformation algorithms based on modal expansion are unable to deal with arbitrary measurement surfaces. To approach these problems, a matrix inversion method can be used to retrieve the spherical wave expansion (SWE) of the antenna under test (AUT) fields. Modeling the antenna with a set of multiple SWEs centered at arbitrary points over its surface offers a flexible approach for the solution of field transformation problems over arbitrary surfaces. The coefficients of each SWE are obtained using an iterative inversion approach where the matrix-vector products can be replaced by multilevel operators based on recursive aggregations and interpolations of the partial SWE fields, reducing the computational complexity from ?(?) to ? ? ? . The proposed algorithm is tested using synthetic data and measurements showing good scalability and reduced transformation error

Iterative method for near field to far field transformation over arbitrary measurement surfaces

Classical near field to far field transformation algorithms are unable to deal with irregularly distributed measurement samples. As frequency increases, this may be a serious limitation in certain scenarios. In this paper a near field to far field transformation algorithm that works with samples over arbitrary measurement surfaces is investigated. The approach is based on the modeling of the measured fields using a spherical wave expansion. The spherical modes are obtained solving a linear system of equations using an iterative method. The algorithm is validated using analytical antenna models, showing controllable transformation errors. To reduce the computation time of the iterative solver, a matrix preconditioner implemented by means of a fast operator is presented

Near-field to far-field transformation on arbitrary surfaces via multi-level spherical wave expansion

This paper presents a general technique for the farfield transformation of near-fields measured over arbitrary surfaces and multimode probe correction in an efficient and accurate way. The use of not only one but several spherical wave expansions to model the antenna under test fields allows to incorporate full probe correction for arbitrary orientations with low computation cost. Combining this approach with a hierarchical subdomain decomposition strategy, the transformation problem is solved with a low computational complexity. In this method, the fields produced by neighbor subdomains are gradually aggregated and interpolated following a multilevel scheme, leading to a good scalability with frequency compared with other matrix-based transformation methods. Numerical and experimental results are provided to show the efficiency and capabilities of the proposed algorithm

Multi-level spherical wave expansion for fast near-field to far-field transformation

Traditional near-field to far-field transformation algorithms based on modal expansion are unable to deal with arbitrary measurement surfaces. To approach these problems, a matrix inversion method can be used to retrieve the spherical wave expansion (SWE) of the antenna under test (AUT) fields. Modeling the antenna with a set of multiple SWEs centered at arbitrary points over its surface offers a flexible approach for the solution of field transformation problems over arbitrary surfaces. The coefficients of each SWE are obtained using an iterative inversion approach where the matrix-vector products can be replaced by multilevel operators based on recursive aggregations and interpolations of the partial SWE fields, reducing the computational complexity from ?(?) to ? ? ? . The proposed algorithm is tested using synthetic data and measurements showing good scalability and reduced transformation error

Iterative method for near field to far field transformation over arbitrary measurement surfaces

Classical near field to far field transformation algorithms are unable to deal with irregularly distributed measurement samples. As frequency increases, this may be a serious limitation in certain scenarios. In this paper a near field to far field transformation algorithm that works with samples over arbitrary measurement surfaces is investigated. The approach is based on the modeling of the measured fields using a spherical wave expansion. The spherical modes are obtained solving a linear system of equations using an iterative method. The algorithm is validated using analytical antenna models, showing controllable transformation errors. To reduce the computation time of the iterative solver, a matrix preconditioner implemented by means of a fast operator is presented

Circularly polarized c-band lens-Horn antenna for radar remote sensing calibration

In this paper the design and optimization process of a radar remote sensing calibration antenna is presented. The solution consists in a septum polarizer and a high gain Potter horn with exceptionally low axial ratio (0.2 dB) and low SLL at 5.3 GHz. To obtain a compact design, a dielectric lens has been designed to correct the horn phase error and reduce the final length. As the lens degrades the return loss, impedance matching transformers are designed and simulated in order to fulfill the system specifications. Finally measurements of the septum polarizer are shown and discussed

Design and optimization of a C-Band lens horn for scatterometer calibration

In this paper the design and optimization process of a scatterometer calibration antenna is presented. The solution consists in a septum polarizer and a high gain Potter horn with exceptionally low axial ratio (0.2 dB) and low SLL at 5.3 GHz. To obtain a compact design, the horn length has been reduced and a dielectric lens has been designed to correct the horn phase error. Several types of lenses are presented and analyzed, and their effects on the radiation pattern and aperture fields are discussed. The discontinuity in electric permeability produced by the lens degrades the horn adaptation. To solve this issue, impedance matching transformers are designed and simulated in order to fulfill the mentioned specifications