Final Project:
Applications of Dielectric Spectroscopy in Biology

Proposal

Introduction

A material is classified as “dielectric” if it has the ability to store energy when an external electric field is applied. If a DC voltage source is placed across a parallel plate capacitor, more charge is stored when a dielectric material is between the plates than if no material (a vacuum) is between the plates. The dielectric material increases the storage capacity of the capacitor by neutralizing charges at the electrodes, which ordinarily would contribute to the external field. The capacitance with the dielectric material is related to dielectric constant.

Fig. 1: Definition of dielectric constant.

If a DC voltage source V is placed across a parallel plate capacitor (Figure 1), more charge is stored when a dielectric material is between the plates than if no material (a vacuum) is between the plates. In the image, C and C0 are capacitance with and without dielectric, k' real dielectric constant or permittivity, and A and t are the area of the capacitor plates and the distance between them (Figure 1). The dielectric material increases the storage capacity of the capacitor by neutralizing charges at the electrodes, which ordinarily would contribute to the external field. The capacitance of the dielectric material is related to the dielectric constant as indicated in the above equations.

A material may have several dielectric mechanisms or polarization effects that contribute to its overall permittivity (see Fig. 2). A dielectric material has an arrangement of electric charge carriers that can be displaced by an electric field. The charges become polarized to compensate for the electric field such that the positive and negative charges move in opposite directions.

At the microscopic level, several dielectric mechanisms can contribute to dielectric behavior. Dipole orientation and ionic conduction interact strongly at microwave frequencies. Water molecules, for example, are permanent dipoles, which rotate to follow an alternating electric field. These mechanisms are quite lossy – which explains why food heats in a microwave oven.

Fig. 2: Dielectric spectroscopy is coupled with inter- and intra-atomic movements.

Atomic and electronic mechanisms are relatively weak, and usually constant over the microwave region. Water (and other polar liquids), has a strong dipolar effect at low frequencies – but its dielectric constant rolls off dramatically around 22 GHz. Teflon, on the other hand, has no dipolar mechanisms and its permittivity is remarkably constant well into the millimeter-wave region.

Relaxation time τ is a measure of the mobility of the molecules (dipoles) that exist in a material. It is the time required for a displaced system aligned in an electric field to return to 1/e of its random equilibrium value (or the time required for dipoles to become oriented in an electric field). Liquid and solid materials have molecules that are in a condensed state with limited freedom to move when an electric field is applied.

Constant collisions cause internal friction so that the molecules turn slowly and exponentially approach the final state of orientation polarization with relaxation time constant τ. When the field is switched off, the sequence is reversed and random distribution is restored with the same time constant. Relaxation frequency is the inverse of the relaxation time. At frequencies below relaxation the alternating electric field is slow enough that the dipoles are able to keep pace with the field variations.

The main principles of time domain dielectric spectroscopy, its application to conductive systems and possible methods of electrode polarization corrections in time domain are introduced. A comprehensive theoretical and experimental study of static and dynamic dielectric properties of different biological systems including globular, and membrane proteins, hydrate water, human erythrocytes, and normal and malignant blood cells of different types is presented in the paper.

Fig. 3: Dielectric spectroscopy can reveal a moiety of biological phenomena.

Time domain dielectric spectroscopy can reveal static and dynamic dielectric properties of different biological systems including globular, and membrane proteins, hydrate water, human erythrocytes, and normal and malignant blood cells of different types. Searching for applications, I found this interesting paper where they perform several dielectric spectroscopy measurements on a variety of biological samples, which I can correlate with my results for cross-validation.

Application: Bacterial Growth

Fig. 4: Cheap, continuous bacterial growth measurements.

Application: DNA Nanostructures

Structural DNA/RNA nanotechnology focuses on synthesizing and characterizing nucleic acid complexes and materials where the assembly has a static, equilibrium endpoint. Because the nucleic acid double helix has a robust, defined three-dimensional geometry, it is possible to predict and design the structures of complicated nucleic acid complexes, including two- and three-dimensional structures (see William Shih, Ping Yin). Novel CAD tools have been developed for the design of DNA structures caDNAno, NUPACK, DMDesign-CBA and the advancements in DNA oligos synthesis Gen9 allow for rapid prototyping and iterative optimization of the designed structures.

Fig. 5: DNA Nanostructures are wideley designed and used today.

Yet, a limiting factor in the workflow of building structures with biological components in the nanometer scale, is being sure that the structure has been formed - folded, when talking about DNA/RNA - the desired way. Two of the most used methods are gel electrophoresis and atomic force microscopy (AFM). The first, while cheap does not always represent a valid confirmation of the desired structure as it gives us only a ballpark figure about the size and charge of the formed DNA complexes. AFM on the other side produces very accurate images of the constructed structures, but is extremely expensive for almost every lab but academic institutions and major companies.

A challenging goal for my final project is to develop a system for the characterization of DNA nanostructures via dielectric spectroscopy. Dielectric spectroscopy (also known as electrochemical impedance spectroscopy), measures the dielectric properties of a medium as a function of frequency. It is based on the interaction of an external field with the electric dipole moment of the sample. I assume that different DNA nanostructures exhibit distinct electric dipole moments, mainly due to the negative charge of the nucleic acid chain backbone. I will employ a differential dielectric spectroscopy setup, that will compare a given nL sample of an assembled DNA nanostructure against a set of reference samples. The responses will be given as input to a naive Bayesian inference algorithm that will have as an output a confidence value for the correct assembly of the nanostructure.

To sum up, my final project comprises of the following:

  1. Implementation of an electronic system that performs differential dielectric measurements. [ Skills from Week 15 ]

  2. Design and fabrication of a device for the measurement of bacteria cultures and corresponding experiments for bacterial growth. [ Skills from Week 12 ]

  3. Design and fabrication of a microfluidic chip for the measurement of DNA Nanostructures and corresponding experiments for a set of DNA tiles. [ Skills from Week 2 ]

  4. An application interface for readouts and data analysis including a naive Bayesian decision system.

Design

Electronics

Based on the high noise levels of the board I fabricated for week 15, I decided to redesign the board including a series of source voltage regulating capacitors and inductors as well as a more robust ground connection.

Fig. 6: Circuit schematic designed in EAGLE software.
Fig. 7: Circuit board designed in EAGLE software.

Device for Bacteria

Fig. 8: Dual cuvette setup for differential measurement.
Fig. 9: Lid will be attached after the placement of the electrodes.

Device for DNA Nanostructures

Fig. 10: Design of the PDMS on glass microfluidic chip for the small volume measurements.

Implementation

Electronics Fabrication

Fig. 11: The version 3.0 of the board fabricated with a Modela MDX-20.

Cuvette holder Fabdrication

The cuvette holder was printed with an Eden260VS. Unfortunately my electrodes haven't arrived yet, so I had to use thin copper sheets which didn't allow the top of the holder to fully close.

Fig. 12: 3D Printed cuvette holder with electrodes.

Data collection

Having the new, improved board ready, I finally connected everything to do initial experiments before moving on with bacterial cultures. To make sure everything works as intended, I performed a series of single-ended measurements with water to be able to trace the charge and discharge curves. As you can see in Fig. 15, the measurements look fine and I can recover smoothly the curves. The interval between the ADC measurements is 1us, thus setting the relaxation time of water in the order of 25us.

Fig. 13: Experimental setup with electronics hooked up to the holder.

To visualize the results, I implemented a web interface using NodeJS with modules serialport, Express and socketIO. There is a very nice tutorial here on how to receive serial data from a MCU to your webpage through a websocket. THe graphs were created using FlotJS.

Fig. 14: Initial measurements with new device look promising! I can trace charge and discharge of the capacitance in a single-ended measurement.