Dielectrophoresis: From molecular to micrometer scale analytes

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Review

Dielectrophoresis: From molecular to micrometer scale analytes Daihyun Kim, Mukul Sonker, and Alexandra Ros Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.8b05454 • Publication Date (Web): 27 Nov 2018 Downloaded from http://pubs.acs.org on December 1, 2018

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Analytical Chemistry

Dielectrophoresis: From molecular to micrometer scale analytes 1,2Daihyun 1

Kim, 1,2Mukul Sonker, 1,2Alexandra Ros*

School of Molecular Sciences, Arizona State University, Tempe, Arizona, United States

2Center

for Applied Structural Discovery, The Biodesign Institute, Arizona State University,

Tempe, Arizona, United States

*Corresponding Author:

Prof. Alexandra Ros School of Molecular Sciences and Center for Applied Structural Discovery, The Biodesign Institute Box 871604 Arizona State University Tempe, Arizona 85287-1604 Alexandra. [email protected]

ACS Paragon Plus Environment

Analytical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1. Introduction The complexity of biological analytes demands powerful analysis techniques in order to reveal cellular processes and pathways on the molecular level.1 Thus, ever refining analytical tools or combinations of various analysis techniques are required to reveal such complexities. Dielectrophoresis (DEP) refers to an analytical technique in which a polarizable particle experiences an attractive or repulsive force when placed in a non-uniform electric field. Realized in microenvironments, DEP phenomena have allowed innovative analytical applications due to the strong dependency on the size of the analyte in conjunction with its dielectric properties and are especially suitable for manipulating µm-sized, cellular bioanalytes. However, the demonstration of DEP for smaller sub-cellular entities or non-biological, sub-µm sized particles has been more difficult, as the required DEP forces impose design challenges.2 In addition, the structural complexity of sub-cellular bioanalytes, and the huge variety of microbes such as bacteria and viruses as well as innovative nanoparticles imposes the need of refined theoretical models as well as suitable DEP platforms for these analytes. Here, we specifically focus on recent DEP studies and applications for analyte dimensions below the size of a typical mammalian cells and include DEP studies related to microbes, sub-cellular entities such as organelles and exosomes but also to biomolecules such as nucleic acids and proteins. We also include non-biological analytes that fall under this size range and review related DEP applications in the past 10 years. In recent years, DEP-based devices have played a vital role as platforms to demonstrate manipulation, preconcentration, trapping, sorting, separation, patterning, characterization and purification not only in bioanalysis but also in nanotechnological applications.3-5 This underlines the importance of DEP for analytical applications, which was fostered through the advancement of miniaturization and micro- as well as nanofabrication techniques.6 The generation of controlled and tailored electric field gradients for DEP applications has first been realized through microfabricated electrodes, and more recently through the integration of tailored hurdles and constrictions in microfluidic devices filled with a variety of liquid media.5,7 Thus, numerous DEPbased devices have been outlined for rapid and efficient analysis of diagnostic and clinical analytes 2,8

often realized in lab-on-a-chip systems. Moreover, the manipulation and analysis of sub-cellular

analytes, such as organelles and exosomes and even biomolecules such as DNA, RNA and proteins has been reported.7,9-11


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Advantages of DEP over other analysis techniques comprise the fact that it is intrinsically labelfree (although labelling strategies are often required for more sensitive read out), specific, fast, and potentially a low-cost diagnostic technique. It therefore opens a large number of analytical opportunities to access and characterize various bioanalytical and biomedical applications.5 Moreover, the complexity and heterogeneity of biological species offers a huge parameter space for DEP-based analytical applications, but their underlying complex dielectric properties also make it difficult to predict and describe DEP phenomena with theoretical models. Depending on the nature of the analytes, key factors such the conductivities and permittivities of each component composing the complex bioanalyte structure determines the DEP responses, which may arise from charged protein complexes, ion gradients across a cell wall or membrane, ionic composition of the cytoplasm or lipidic components and are also strongly influenced by the size and shape of the analyte. The theoretical descriptions therefore focus mainly on global particle descriptions following classical approaches for polarized interfaces,12,13 although newly emerging models are surfacing to describe biomolecule DEP.14,15 Understanding the key factors affecting DEP response for complex bioanalytes in recent applications not only allowed detailed insight into their dynamics but also lead to development of improved and targeted applications in the field of biotechnology including therapeutics, point-of-care diagnostics, and sub-cellular biology.13,16 Here, we review and discuss DEP for analytes in a size range as small as biomolecules such as proteins or nucleic acids over organelles various microbes up to blood cells. We first present the theory of DEP and models describing the frequency-dependent dielectric properties of these analytes and then briefly present various technical realization platforms for DEP. Next, we review DEP applications for inorganic and biological particles in the past decade with an emphasis on connecting to the DEP model most appropriate for these analytes. We conclude with a summary of advantages and major challenges in the field of DEP and discuss future directions realizing DEP-based platforms as a powerful tool for various biological analytes.

2. DEP Theory The term dielectrophoresis (DEP) has been coined by Pohl17 in 1970 and refers to the motion of a suspensoid caused by a spatial non-uniformity of the electric field, 𝐸 and is governed by the



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differences in dielectric properties between the particle and the surrounding medium.18 In this section, we provide an overview of the basic DEP theory starting out from a spherical particle over more complex double-shell and multiple shell spheroids to particles with various non-spherical shapes. The underlying force expression and dielectric properties of the respective model will be presented which are the basis for the experimental observations but have also been used in modeling and analysis of various analytes ranging from colloidal particles to complex biological entities. The fundamentals of DEP theory were reviewed in the past in several review articles providing a detailed explanation of dielectrophoretic theory.12,19,20 Here, we will focus on the underlying theoretical models relevant to the applications summarized in this review article. 2.1 Spherical DEP model 2.1.1 Homogeneous spherical model A common approach for describing the DEP force acting on a particle is based on the model of a homogeneous sphere with dielectric properties as shown in Figure 1 (a). The time averaged DEP force (𝐹𝐷𝐸𝑃) acting on a homogeneous spherical particle suspended in a medium can be expressed as follows :21

〈𝐹𝐷𝐸𝑃〉 = 2𝜋𝑟3𝜀𝑚Re[𝑓𝑐𝑚(𝜔)]∇|𝐸𝑟𝑚𝑠|2

(1)

where, 𝜀𝑚 is the permittivity of the medium surrounding the particle, 𝑟 is the radius of the particle, and 𝐸𝑟𝑚𝑠 is the root mean square electric field. The term Re[𝑓𝑐𝑚(𝜔)] refers to the real part of the Clausius-Mossotti (CM) factor given by :22 Re[𝑓𝑐𝑚(𝜔)] =

(

ℰ𝑝∗ ― ℰ𝑚∗ ℰ𝑝∗ + 2ℰ𝑚∗

)

(2)

where ℰ𝑝∗ and ℰ𝑚∗ denote the frequency dependent complex permittivity of the particle (p) and medium (m), respectively. The complex permittivity of the polarizable particle and the medium 𝜎𝑝

𝜎𝑚

are given by ℰ𝑝∗ = ℰ𝑝 ―𝑗 𝜔 and ℰ𝑚∗ = ℰ𝑚 ―𝑗 𝜔 , where 𝜎𝑝 and 𝜎𝑚 denote the particle and medium conductivity respectively, and 𝑗 =

―1. The CM factor defines the DEP characteristics of

particles, i.e. the DEP force causes particles to migrate towards or away from the high electric field regions. If the particles are transported to high electric field regions, then the response is termed


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positive DEP (pDEP) and Re[𝑓𝑐𝑚(𝜔)] > 0. If particles are repelled from the high electric field regions, the response is negative DEP (nDEP) and Re[𝑓𝑐𝑚(𝜔)] < 0.

Figure 1. Schematic illustration of selected spherical models (left), plots for the Re[𝑓𝑐𝑚(𝜔)] with varying frequency for each respective model (middle) and example of spherical particle models (right). (a) Homogeneous particle model with radius, 𝑟, conductivity (𝜎𝑚∗ ,𝜎𝑝∗ ) and permittivity (ℰ𝑚∗ , ℰ𝑝∗ ) for particle and medium (left) with the computed Re[𝑓𝑐𝑚(𝜔)] of a polystyrene bead (middle) and the respective spherical particle model of a polystyrene bead (right). (b) Single shell model where a spherical particle is comprised of a core with radius, r1 and permittivity ℰ𝑝∗ , and a membrane with radius, r2, with permittivity, ℰ𝑠∗ (left). The Re[𝑓𝑐𝑚(𝜔)] of a 5 µm single-shelled liposome is represented according to parameters



established by Chan et al.23 (middle) and the spherical particle model of a single-shelled liposome with liposome core and phospholipid bilayer as membrane is also represented (right). (c) Double-shell model ∗ ∗ with a core, membrane and wall comprising two shells around the core. ℰ𝑝∗ , ℰ𝑠1 and ℰ𝑠2 are the permittivity ∗ ∗ ∗ of the particle inner core, membrane and wall respectively. 𝜎𝑝 , 𝜎𝑠1 and 𝜎𝑠2 are the conductivity of the particle inner core, membrane and wall respectively. The radii of r1, r2 and r3 represent the core, membrane and wall radius respectively (left). Re[𝑓𝑐𝑚(𝜔)] of a 7 µm double-shelled yeast cell (Saccharomyces cerevisiae) was computed with parameters established by Huang et al. 24. A double-shell particle model for spherical bacteria with cytoplasm in the core, cell membrane and cell wall are also depicted (right). (d) Sequence showing the transition of the multi-shell model exhibiting N shells of radius, r(N+1) to an equivalent ∗ homogeneous sphere model with the effective permittivity, ℰ𝑒𝑓𝑓 , according to the “smearing out” approach.

At high-frequencies (𝜔→∞), the dielectric displacement current dominates, thus 𝐹𝐷𝐸𝑃 is typically governed by the particle and medium permittivity.12 In contrast, at lower frequencies ( 𝜔→ 0), including DC conditions, the CM factor is dictated by the conductivity of the particle and the medium since the current is dominated by the conduction of free charges.12 Figure 1 (a) illustrates the frequency spectrum of DEP response calculated using a homogeneous particle model in case of 𝜎𝑝> 𝜎𝑚 and ℰ𝑝> 𝜎𝑠, ℰ𝑝 >> ℰ𝑠), the single-shell model can be approximated for frequencies between 50 kHz and 1 MHz as :25



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𝑟2

∗ ~ ℰ𝑠∗ 𝑟2 ― 𝑟 ℰ𝑒𝑓𝑓

1

(6)

Thus, the permittivity of the single-shelled bioparticle is simplified to contributions from the membrane permittivity, the outer core radius of the particle and the membrane thickness (𝑟2 ― 𝑟1 ).26 Many prokaryotic and eukaryotic microorganisms are composed of multiple membranes or enveloped structures that may define their complex effective permittivity. Multiple interfaces arise from these layers along with the conductivity of the internal media and individual shell thickness governing the interfacial polarization in electric fields, therefore dictating the dielectric properties of such organisms in frequencies ranging from several kHz up to MHz.26,27 These characteristics determining the CM factor and causing unique DEP responses is further discussed in the next section.

2.1.3 Multi-shell model Most biological analytes are more complex than accounted for by the single-shell model due to the heterogeneity in their structure and subcellular entities. For example, Gram-negative bacteria consist of an outer membrane, periplasmic spaces, peptidoglycans, and an inner cell membrane.28 Each structure has different electric and dielectric properties. In this case, the single-shell model cannot be employed to describe the DEP characteristics of biological particles. Therefore, a multishell model should be utilized to compensate for the complex subcellular structures. The first model we discuss to describe this biological complexity is the double-shell approach. As shown in Figure 1 (c), the double-shell model represents a biological particle comprised of a core as well as inner and outer shells, with radii 𝑟1, 𝑟2, and 𝑟3 respectively. This could for example represent a bacterium with a membrane and wall, such as S. cerevisiae. The double-shell model first ∗ accounts for an effective complex permittivity, ℰ𝑠1 , that takes into account the permittivity of the

core (or cytoplasm), ℰ𝑝∗ , and inner shell (or cell membrane), which is expressed as:21 𝑟2 3 𝑟1

∗ ℰ𝑝∗ ― ℰ𝑠1 ∗ ∗ ℰ𝑝 + 2ℰ𝑠1

( ) +2 ∗ ∗ ℰ1𝑒𝑓𝑓 = ℰ𝑠1 ()― 𝑟2 3 𝑟1

∗ ℰ𝑝∗ ― ℰ𝑠1 ∗ ∗ ℰ𝑝 + 2ℰ𝑠1


(7)

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∗ Then, the second effective complex permittivity, ℰ2𝑒𝑓𝑓 , that takes into account the contributions ∗ from the next shell, e.g. the cell wall with permittivity ℰ𝑠2 , is expressed as :21 𝑟3 3 𝑟2

( ) +2 ∗ ∗ ℰ2𝑒𝑓𝑓 = ℰ𝑠2 ()― 𝑟3 𝑟2

∗ ∗ ℰ1𝑒𝑓𝑓 ― ℰ𝑠2

∗ ∗ ℰ1𝑒𝑓𝑓 + 2ℰ𝑠2

(8)

∗ ∗ ℰ1𝑒𝑓𝑓 ― ℰ𝑠2

3

∗ ∗ ℰ1𝑒𝑓𝑓 + 2ℰ𝑠2

And finally, the Clausius-Mossotti (CM) factor is given by:21 Re[𝑓𝑐𝑚(𝜔)] =

(

∗ ℰ2𝑒𝑓𝑓 ― ℰ𝑚∗ ∗ ℰ2𝑒𝑓𝑓 + 2ℰ𝑚∗

)

(9)

∗ where ℰ2𝑒𝑓𝑓 and ℰ𝑚∗ are the effective complex permittivities of the double-shell particle and

medium, respectively. Based on this description, we can further extend this model to describe a general multi-shell model starting from a spherical multi-shell particle with N shells surrounding a core in the center, where 𝑟1 is assigned to the radius of the core and 𝑟𝑁 + 1 to the radius of the outermost shell, (i.e. 𝜎𝑖

the radius of entire particle). Each layer has its own complex permittivity of ℰ𝑖∗ = ℰ𝑖 ―𝑗 𝜔 with 𝑖 from 1 to N+1. According to the dielectric theory of the multi-shell model proposed by Irimajiri et al.29, effective complex permittivity of multi-shell analytes can be determined by calculating each layer as homogeneous particle encapsulated by another surrounding layer using a previously described smeared-out approach24 as shown in Figure 1 (d). The complex heterogeneous multishell particle can then be replaced conceptually with an equivalent homogeneous particle having a similar effective permittivity, ℰ𝑝∗𝑒𝑓𝑓.12 Thus, the overall DEP force and effective complex permittivity accounting for a core and all shells with finite thickness and given number of shells, N, is then given by :4

〈𝐹𝐷𝐸𝑃〉 = 2𝜋(𝑟𝑁)3𝜀𝑚Re[𝑓𝑐𝑚(𝜔)]∇|𝐸𝑟𝑚𝑠|2 𝑟𝑁 + 1 3 𝑟𝑁

( ) ( )―

ℰ𝑝∗𝑒𝑓𝑓 = ℰ𝑁∗ + 1

∗ ∗ ℰ𝑁 ― 1 𝑒𝑓𝑓 ― ℰ𝑁 + 1 ∗ ∗ ℰ𝑁 ― 1 𝑒𝑓𝑓 ― 2ℰ𝑁 + 1

(9)

+2

𝑟𝑁 + 1 3 𝑟𝑁

∗ ∗ ℰ𝑁 ― 1 𝑒𝑓𝑓 ― ℰ𝑁 + 1 ∗ ∗ ℰ𝑁 ― 1 𝑒𝑓𝑓 ― 2ℰ𝑁 +1

For a multi-shell particle, Re[𝐾(𝑤)] can then be written as :4,30


(10)


Re[𝑓𝑐𝑚(𝜔)] =

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(ℰ𝑝∗𝑒𝑓𝑓 ― 𝜀𝑚∗ )(𝜀𝑝∗𝑒𝑓𝑓 + 2𝜀𝑚∗ ) +

(

𝜀𝑝∗𝑒𝑓𝑓

+

2 2𝜀𝑚∗

)

+

(

∗ )(𝜎 ∗ ∗ (𝜎𝑝∗ ― 𝜎𝑚 𝑝𝑒𝑓𝑓 + 2 𝜎𝑚) 𝑒𝑓𝑓 𝜔2 ∗) (𝜎𝑝∗ ― 2𝜎𝑚 𝑒𝑓𝑓 𝜔

)

2

(11)

where, 𝜀𝑝∗𝑒𝑓𝑓 and 𝜎𝑝∗𝑒𝑓𝑓 denote the complex effective permittivity and conductivity of the simplified model which is reduced from the heterogeneous multi-shell particle, respectively. This standard approach for determining the complex permittivity of many concentric shells has been implemented to calculate the CM factor of various multi-shelled biological analytes.26,30,31 2.2 Non-spherical model Most microorganisms or cells in nature occur in non-spherical shapes such as ellipsoids which may be elongated or flattened, or even cylindrical shape. For example, microbes such as a bacteria have a wide variety of shapes defined through their cell wall and cell membrane consisting of polysaccharides, S-layer glycoproteins, or bilipid layers and their electrophysiological cytoplasm characteristics arising from various compositions of aqueous phase.32,33 Due to such heterogeneity in size, shape, and composition, an analytical expression for the DEP force acting on various shaped particles has been derived. Details about non-spherical DEP models are found in many reviews accounting for force shapes such as ellipsoids, rod and spiral shapes.31,34. In this section, we discuss the fundamental factors to characterize the most representative shapes of biological species and colloidal nano- and microparticles. 2.2.1 Ellipsoidal shape Ellipsoidal particles do not display equal polarization along the directions of the applied electric field unlike spherical particles. i.e the polarizabilities are different for different directions. Thus, the orientation of the particle in response to the applied electric field can be varied with the applied frequency. At low frequency, an ellipsoidal particle subjected to DEP in an inhomogeneous electric field may align with its longest axis parallel to the electric field, where the maximum polarization is induced along this axis. In contrary as the frequency increases, the particle may rotate and align perpendicular to the applied field along its long axis due to the dispersion of the dipole.34,35 The different orientations of non-spherical particles in relation to the applied electric field, can be accounted for by a direction-dependent polarization factor, the so-called depolarization factor A𝛼.


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Figure 2. Schematic illustration of the ellipsoidal model. (a) Homogeneous oblate model with semi-axes a>b=c (b) homogeneous prolate model with semi-axes a=b 𝑐 ) as shown in Figure 2 (a), A𝑥 is given by :36,37

[

1

A𝑥 = 2 1 ―

]

1 ― 𝑒2 𝑒

(𝑒 ― arctan 𝑒) , 𝑤𝑖𝑡ℎ 𝑒 =

3

𝑎 2

() 𝑐

―1

(14)

and for the prolate case (𝑎 < 𝑐) in Figure 2(b),

[

1

A𝑥 = 2 1 ―

1 ― 𝑒2 3

2𝑒

1+𝑒

]

(ln 1 ― 𝑒 ― 2𝑒) , 𝑒 = 1 ―

𝑎 2

() 𝑐

(15)

where, 𝑒 is the eccentricity of the oblate or prolate spheroid. If c >> a, as in the case of the prolate ellipsoid, the eccentricity becomes unity (𝑒 = 1), and the spheroid is reduced to the shape of a long needle and the depolarizing factor approaches zero. This case reflects a high aspect ratio particle such as a rod or fibers which will be discussed below in section 2.2.2. An ellipsoidal single-shell model to reflect the membrane structure of biological analytes as shown in Figure 2 (c) can be proposed in a similar way to spherical particles with shells. The corresponding CM factor modified to account for the membrane thickness, d, and the effective ∗ complex permittivity, ℰ𝑒𝑓𝑓 of the non-spherical single-shell model is well described in several

excellent reviews on ellipsoidal shaped DEP related to manipulation of bioparticles, aiding in experimental design, modeling and analysis of such particles.34,38-40 In addition to the single-shell ellipsoidal model, a multi-shell model can further be proposed for complex microorganisms such as Escherichia coli (E. coli) which is composed of a cytoplasm (core) surrounded by a plasma


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membrane (inner shell) and a thicker cell wall (outer shell). A similar theoretical model that reflects the complicated morphological structure of E. coli was reported by Bai et al.41

2.2.2 Rod shape Most models of rod shaped particles including elongated filaments or polymeric fibrils are described in the extension of an oblate ellipsoid model as shown in Figure 2d. For example, the rod-shaped tobacco mosaic virus was characterized with an elongated prolate ellipsoidal model by Morgan et al.35 The DEP force for the elongated oblate ellipsoid particle parallel to the applied electric field direction is given by:35,42

〈𝐹𝐷𝐸𝑃〉 =

𝜋𝑙𝑟2 3

𝜀𝑚Re[𝐾(𝑤)]∇|𝐸𝑟𝑚𝑠|

2

(16)

where r and 𝑙 are the radius and length, respectively, as shown in Figure 2 (d). The CM factor in this case can also be described with Eq. (13), in which A𝛼 is depolarization factor as defined above. For the rod shaped particle, A𝑥, A𝑦 and A𝑧 are given by :43,44 A𝑥 =

1 ― 𝑒2 2

2𝑒

[𝑙𝑛 ( ) ― 2𝑒] and A 1+𝑒

1―𝑒

𝑦,𝑧

=

(

1 ― A𝑥 2

(17)

)

𝑠2

which includes the term for the eccentricity with 𝑒2 = 1 ― 𝑙2 . Using this model, rod-shaped biological particles, inorganic cylindrical colloidal particles such as Au or ZnO rods as well as carbon nanotubes (CNTs) can be modeled using Eq. (16). In addition, in the case of a hollow tube such as a single-walled carbon nanotube (SWNT), the geometry factor, 2𝜋𝑙𝑟2 3

, will be replaced by 𝜋𝑙𝛿(2𝑟 ― 𝛿) with the wall thickness 𝛿. For 𝑙 ≫ 𝑠, the depolarization

factor from Eq. (25) is approximated as:21,44 A𝑥 =

𝑟2 𝑙2[ln

(2𝑙𝑟) ― 1]

(19)

The various models overviewed in this section are summarized in Table 1 in respect to the various DEP analytes reviewed in the section 4 of this review.



2.2.3 Macromolecules Macromolecules such as proteins and nucleic acids (DNA and RNA) are important since they carry out most cellular functions that are required for the structural integrity, signaling pathways, and regulation. DEP manipulation of these macromolecules has drawn considerable interests in the past decades due to its potential for bioanalytical applications. Manipulation, fractionation, preconcentration, and separation of various biomolecules that are different from each other not only in chemical composition but also in structure, size and shape has been demonstrated based on their DEP properties. By using DEP-based manipulation techniques, proteins and DNA can also be effectively manipulated for the concentration, trapping, detection and purification of analytes.45 Hence, investigating the theoretical background of the DEP properties of biomolecules is significant for future applications. It is commonly accepted that the ion cloud surrounding biomolecules contributes significantly to the dielectric response and that dielectric dispersions play a role in the DEP response of biomolecules13. Most biomolecules, including DNA and proteins are charged in aqueous environment and electric double layers are formed around them by attracting counter ions in solution. In case of DNA, a free-draining coil configuration is apparent for sufficiently long DNA molecules, where the negatively charged backbone is surrounded by positive counter ions. Placed in an electric field, a charge redistribution of these counter ions is induced resulting in an effective dipole. The dipole moment is proportional to the applied electric field and the proportionality constant can be described as the polarizability of the DNA molecule11. There are some cases where theoretical models and predictions match experimental observations, such as for example in the model presented by Zhao et al.15 which was compared to the experimentally observed DEP response of kbp sized DNA46 or for very short, rod-like DNA molecules.47 The experimental DEP observations are, however, complex and depend on DNA length and topology, medium and buffer conditions as well as tested frequencies, for which a general model is still lacking. For a detailed discussion, see recent reviews by Viefhues et al. and Holzel et al. 11,13,48 From the pioneer work on protein DEP by Washizu et al.49, various experimental realizations of DEP-based manipulation of proteins have been reported (see section 4). However, the dielectric response and mechanism of protein DEP phenomena still remains elusive. Proteins are more


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heterogeneous and complex in their structure than DNA, and their dynamic behavior in various solutions, on various time scales and interactions with other proteins and biomolecules, make model descriptions particularly difficult. The variations in the DEP behavior of these macromolecules suggest that detailed model studies for the underlying polarization mechanism that governs the dielectric characteristics are required.9 According to classical theory, DEP of proteins would be expected at extremely high electric field strengths due to their nm-scale dimension and may only occur if other forces such as Brownian or even small convective forces are suppressed. While predicted difficult to be observed experimentally, DEP with a variety of proteins could be reported.9 Therefore, other mechanisms, resulting either from the counter ions surrounding proteins or intrinsic polarization effects should also account for protein DEP responses. Seyedi and Mathyushov14 have recently reported that the interactions of proteins with surrounding water might significantly contribute to the DEP response reasonably well accounting for observed dielectric constants for a specific protein (cytochrome c). While this model still needs to be adapted for a wider variety of proteins, it demonstrates that DEP forces arising from the classical theory and CM factor calculations likely underestimate DEP forces acting on proteins.

3. Technical realization platforms for DEP To realize the DEP manipulation of various biological particles as well as organic and inorganic particles, many technical platforms have been realized in the past. There are two major ways to achieve high electric fields and gradients thereof. The first comprises the fabrication of microelectrodes – in many cases integrated in a microfluidic platform - and enables the particles to experience large DEP forces near the microelectrodes.50 This approach is termed electrodebased DEP (eDEP). Various shapes of electrodes and structures have been demonstrated for eDEP manipulation applications. The second major approach realizes high electric fields with nonconducting constrictions surrounded by aqueous solutions where electrical potentials are applied via electrodes immersed in reservoirs with fluidic connection to the device containing the constrictions. This method is termed insulator-based DEP (iDEP).51



The choice for the ideal design and fabrication process thus heavily relies on the requirement for the DEP application. In addition to these two major categories, contactless DEP (cDEP) which eliminates many challenges from the conventional DEP methods has also been developed.52 In this approach, a nonuniform electric field is induced in the sample channel using electrodes in other microchannels that are separated from the analyte channel by thin non-conducting materials. This platform provides high sensitivity towards specific cell types by avoiding any contaminating effects due the electrodes.53 Numerous innovations for DEP device designs, electrode patterns, and shape variations have been reported for various eDEP,45,54-56, iDEP,7,51,54,55,57 and cDEP54,58 applications. Here, we briefly review the different categories of technical realization methods for DEP including eDEP, iDEP and cDEP. 3.1 eDEP In conventional eDEP, the microelectrodes to generate non-uniform electric fields are positioned inside of the fluidic channel where they are in direct contact with the medium and the analytes. Various electrode configurations of 2D planar electrodes have been realized including parallel, interdigitated, curved, and quadruple geometries but also 3D electrode design including side-wall, microwell, extruded, top-bottom, castellated and oblique patterns. These are accomplished through fabrication processes that include photolithography, thin-film deposition, lift-off and etching techniques using metals such a copper, gold or indium tin oxide.5,8,56 Although a high magnitude of DEP forces can arise from only a few volts applied, eDEP has drawbacks such as fouling effects and electrolysis resulting in the degradation of the biological particles. Furthermore, the fabrication process of the electrodes includes complex deposition steps or etching steps to realize the various electrode configurations.55 3.2 iDEP In iDEP, the non-uniform electric field is induced by an insulating material forming structures such as constrictions, hurdles or obstacles in combination with the external electrodes immersed in the microchannel reservoirs.31,57 Using photo- and soft-lithography, various polymer-based insulator configurations have been fabricated and in many instances allow for facilitated prototyping and low-cost fabrication methods, which is advantageous over eDEP. Polydimethylsiloxane (PDMS), having a high compatibility with various biological analytes,


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transparency and flexibility, is one of the most common polymers utilized in iDEP microfluidic systems. The oxidization process for the bonding of PDMS on substrates such as glass, silica or other polymers without an adhesive to make a microfluidic chip is also advantageous. In addition to polymers, patterned glass substrates represent another approach for iDEP. Conventionally, a wet etching process is utilized to pattern the glass for fabrication of devices with various posts or constrictions to induce non-uniform electric fields.55 Although iDEP devices are often realized with simple fabrication processes, robust DEP systems without electrochemical reactions of analytes in the high electric field regions are created. However, larger potentials need to be applied to induce an equivalent magnitude of electric fields as compared to eDEP platforms.59 3.3 cDEP Recently, a technique that is called cDEP has been demonstrated for providing the inhomogeneous electric field without any contact between electrodes and the sample fluid.58 This technique uses a thin insulating layer (e.g. PDMS) located between electrode-creating side channels and the main fluidic channel to avoid the direct contact between electrodes and sample fluid.60 The main reason of this special structure is to eliminate the problems of contamination, gas bubble formation and to reduce fouling effects and Joule heating. Fabrication methods for cDEP devices are similar to iDEP using photolithography and soft lithography. Since the insulating layer isolates the fluidic channel and the electrode channel, the capacitive property of the membrane barrier material and the thickness of this barrier affect the performance of cDEP. To generate inhomogeneous electric fields across the insulating barriers, a highly conductive solution,58 conductive composites such as CNTs or carbon-black mixed into polymers61 or liquid metals such as mercury62 and gallium61 have been embedded into the electrode channel. Other approaches for DEP realizations have been reviewed recently in the literature. 12,32,45,51,54-57,63

4. DEP Manipulation of biological and non-biological analytes Manipulation of both biological and non-biological analytes under a non-uniform electric field using DEP microdevices has gained immense interest over the past few decades due to its nondestructive nature enabling researchers to study in-detail how physical and chemical properties of an analyte affect its DEP characteristics. With continued exploration, several researchers have



confirmed various factors such as size, surface characteristics, and presence of multiple layers, compartments, and shells etc. that determine the DEP behavior of an analyte. This increased understanding of DEP behavior of different analytes has led to implementation of DEP microfluidics for various applications like trapping, deflection, enrichment, deposition, and separation using innovative designs and device geometries.7,10 In addition, a wide range of polarizable analytes from both biological and non-biological origin ranging from inorganic beads to live microbial cells have been computationally and experimentally studied for their dielectrophoretic properties in a microfluidic setup using different theoretical models as mentioned in section 2. In this section, we discuss various DEP devices and applications reported in the past decade for non-biological and biological analytes ranging from biomolecules to blood cells.

4.1 Non-biological Analytes 4.1.1 Microparticles Microparticles like polystyrene beads, colloidal beads, and other sub-µm to µm scale inorganic particles have been actively used as model analytes for initial optimization of various DEP microdevices prior to analyzing biological samples. This popularity as model analyte for DEP applications stems from their well-defined dielectric properties and description with a spherical DEP model (see above) allowing the characterization of novel geometries and devices for DEP applications but also facilitating fundamental studies such as the effect of shape on DEP response. Microparticles DEP characterization can also lead to the discovery of novel phenomena and applications such as the realization of self-assembling structures or for affinity-based target capture and separation applications using microfluidic devices.45,55 Here, we will discuss the use of microparticles as model analytes and summarize DEP facilitated applications of microparticles in different technical realization platforms. Numerous innovative microelectrode and device designs have surfaced in the past decade to induce electric field inhomogeneity in eDEP microdevices using microparticles as model analytes. Choi et al.64 reported a trapezoidal-shaped electrode array-based DEP device for separation of fluorescent polystyrene microspheres. Particles with a diameter difference of >50% were separated due to their varying DEP characteristics while flowing through alternate nDEP regions formed in


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the electrode array. Gadish et al.65 used interdigitated electrodes to report high-throughput preconcentration and mixing of polystyrene beads and bacterial spores. Kralj et al.66 also used interdigitated slanted Pt electrodes to generate asymmetric electric field regions for size-based sorting of monodispersed microparticle suspensions. Yunus et al.67 reported a microfluidic device containing two sets of interdigitated electrodes at the top and bottom of a separation microchannel as shown in Figure 3a. These arrays of electrodes were used to deflect a colloidal solution of subµm latex spheres based on nDEP for continuous flow separation. Lewpiriyawong et al.68 developed a silver-PDMS conductive composite used as sidewall electrodes in a PDMS microchannel. On application of AC potentials, microparticles exhibit nDEP behavior of various intensity based on their size leading to separation by deflection.

Figure 3: DEP manipulation of non-biological analytes. (a) Continuous size-based dielectrophoretic separation of colloidal microparticles using two sets of interdigitated microelectrodes in a microfluidic device (Adapted and reprinted with permission from Yunus, N. A. M.; Nili, H.; Green, N. G. Electrophoresis 2013, 34, 969-978 (ref. 67), Copyright (2013) John Wiley and Sons); (b) Enrichment and isolation of 2 µm particles (green) from 500 nm particles (red) using an iDEP device (Reprinted with permission from LaLonde, A.; Romero-Creel, M. F.; Saucedo-Espinosa, M. A.; Lapizco-Encinas, B. H. Biomicrofluidics 2015, 9, 064113 (ref 69), Copyright (2015) AIP Publishing); (c) Selective trapping of single-walled CNTs between insulating posts in an iDEP device (Adapted and reprinted with permission from Rabbani, M. T.; Schmidt, C. F.; Ros, A. Anal. Chem. 2017, 89, 13235-13244 (ref 44), Copyright (2017) American Chemical Society); (d) Formation of Au-ZnO hetero-nanostructures by dielectrophoretic alignment of ZnO nanowires and Au-nanoparticle deposition in an eDEP microfluidic setup (Reprinted with permission from Ding, H.;



Shao, J.; Ding, Y.; Liu, W.; Tian, H.; Li, X. ACS Appl. Mater. Interfaces 2015, 7, 12713-12718 (ref 70), Copyright (2015) American Chemical Society).

iDEP devices for the manipulation of microparticles have also gained immense interest recently due to their ease in fabrication compared to the complicated metal deposition processes to fabricate microelectrodes. As discussed in Section 3, non-uniformity in the electric field in such devices is introduced by insulating geometries like constrictions or posts. In the early 2000s, Fintschenko and coworkers reported circular insulating post arrays in a DEP microdevice for preconcentration and separation of polystyrene beads and bacterial cells.71 Later, Lapizco-Encinas and coworkers further developed iDEP microfluidic devices with various insulating geometries like channel constrictions72, cylindrical69,73, diamond74, and asymmetric novel post shapes75 with different sizes for selective trapping, preconcentration, releasing and separation of polystyrene beads, bacterial cells, and yeast cells. An example of such iDEP device design for separation of microparticles is shown in Figure 3b. Kang et al.76 reported a microchannel with an insulating constriction for nDEP based focusing and separation of polystyrene microparticles dependent on size. Later, the same group added embedded Cu electrodes to this design to report a hybrid device for improved separation of microbeads and yeast cells with less Joule heating.77 Abdallah et al.78-80 also used constriction based iDEP devices for continuous size-based sorting of protein crystals. Beech et al.81 used iDEP to improve separation characteristics of a deterministic lateral displacement (DLD) device. Fluorescent polystyrene beads were used at low electric fields and frequencies (~100 Hz) to improve the separation by decreasing the analyte size for DLD-based separations by up to 50%. Kale et al.82 reported a triangular post-based ratchet device for dielectrophoretic trapping and patterning of sub-µm colloidal particles and then further studied the electrothermal enrichment of microparticles around insulating posts using a similar iDEP device design.83 Recently, Ros and coworkers84,85 used polystyrene microbeads to develop and optimize deterministic absolute negative mobility and ratchet devices for size-based bioparticle separation. The devices exploited the ratchet effect induced by an asymmetric post array for size-based separation of particles and organelles under periodic electrophoretic and dielectrophoretic forces. Crowther et al.86 studied various insulator post shapes for iDEP-based trapping and streaming


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separations. Computational simulations were used to study different insulating post shapes. A novel multi-length scale post-shape was reported for efficient trapping and deflection-based separation applications using polystyrene and silica beads. Despite the popularity of various iDEP device designs, alternative approaches to induce inhomogeneity in the electric field other than insulating posts have also been developed for DEPbased microfluidic analysis. Barbulovic-Nad et al.87 used oil droplets instead of insulating posts to induce size-based dielectrophoretic separation of polystyrene microparticles at low electric field strength (105-fold either by trapping (pDEP) or by repulsion (nDEP) around the nanoconstrictions as shown in Figure 4b. Chaurey et al. 152 reported a dissipation of trapped molecules due to Joule heating in high conductivity buffers. Later, Sanghavi et al.153 used graphene-modified electrodes in a nanochannel for preconcentration and electrochemical detection of neuro-peptides down to pM concentrations. Recently, the same group reported selective enrichment of prostatespecific antigen (PSA) in a mixture containing rat IgG using a nanoslit device. DC-offset AC electric fields were used to exploit electrophoretic and dielectrophoretic characteristics of these proteins to selectively enrich PSA and voltammetric detection was also shown using graphenemodified surfaces.154 Zhang et al.155 recently reported an iDEP device with a sub-µm scale constricted channel for preconcentration of BSA. The constriction was fabricated in a PDMS device using Au-coated DNA chains as molds eliminating the need of complicated fabrication techniques like e-beam lithography and BSA was preconcentrated around the constriction by nDEP using low-frequency AC electric fields with a DC-offset. Mohamad et al.156 used DEP manipulation of BSA to report a label-free detection method by monitoring impedance change in an electrode-based device. Very recently, Velmanickam et al.157 used biotinylated polystyrene beads for immobilization of avidin.


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These beads were then used for DEP-based preconcentration and quantification of avidin molecules down to low pM concentrations in buffered solutions and serum samples. Such DEP platforms not only offer potential in understanding electrokinetic and dielectrophoretic properties of biomolecules but can also be used to explore novel treatment strategies and diagnostic applications in the future. With the advent of X-ray free electron lasers (XFELs), structural elucidation studies using protein crystals have gained immense interest. Microfluidics has also been exploited recently to assist in crystal delivery and sample purification in XFEL related applications. Abdallah et al.7880

developed constriction-based iDEP devices for size-based fractionation of membrane protein

crystals for structural elucidation studies. A PDMS device with microscale constriction was used to induce non-uniformity in the electric field and crystals of photosystem I were continuously sorted based on size and DEP characteristics. Such devices can reduce sample consumption and provide purified crystal samples for XFEL based crystallization studies.

4.2.3 Subcellular organelles and liposomes Eukaryotic cells possess specialized subcellular structures called organelles like the mitochondrion, the nucleus or the endoplasmic reticulum etc., which are responsible for specific cellular functions to maintain cell viability. Organelle subpopulation fractionation can be used for diagnostic purposes as diseased or infected organelles may differ from healthy organelles in shape or size. This difference in physical properties can be exploited for DEP-based purification/separation applications. Additionally, studying the DEP properties of an organelle can lead to better understanding of the physical construct, permeability, and functionality of these organelles. In this section, we discuss the dielectrophoretic manipulation of organelles and liposomes. Recently, Rohani et al.158 studied DEP characteristics of cells based on the mitochondrial dynamics within the cell. Authors observed a ~10-fold higher pDEP response in cells with a more connected mitochondrial network compared to the cells where the mitochondrial network was fragmented. Moschallski et al.144 previously reported a device for continuous dielectrophoretic sorting of human mitochondria in complex biological samples. The device was hydrodynamically



operated and consisted of two sets of electrodes for deflecting mitochondria, as shown in Figure 4c. Using this device, human mitochondria were purified and collected separately from a mixture of cell homogenate. Luo et al.159 studied the DEP characteristics of rat and mouse mitochondria using a microchannel with insulating posts under various AC and DC conditions in a low conductivity medium. The authors observed nDEP behavior exhibited by mitochondria under given experimental conditions and then used a constriction based iDEP device for continuous sizebased dielectrophoretic sorting of mitochondrial subpopulations. Later, Luo et. al.84 also reported a non-linear post-array iDEP device for dANM based separation of submicron polystyrene beads and mouse liver mitochondria. The authors employed an AC electric field with a DC offset to combine electrokinetic and DEP forces that resulted in size-based separation as large particles exhibited dANM and small particles exhibited normal migration response. Kim et al.85 also used a combination of AC electric field with DC offset in a non-linear post-array device and reported the deterministic DEP-based high-resolution ratchet separation of submicron polystyrene beads, mouse mitochondria, and liposomes. Liposomes are vesicular structures containing a lipid bilayer that can be used for transporting therapeutic agents or other material into cells or tissues. Thus, DEP manipulation of liposomes could also lead to the development of targeted drug delivery systems in the future. Froude et al.160 initially studied the DEP characteristics of lipid uni-lamellar vesicles (liposomes) using different surface functionalization strategies employing a quadruple electrode array device. The authors monitored the crossover frequency for liposome particles with modified surface conductivities and concluded that the entire particle construct plays a major role compared to surface conductivity alone in governing the DEP behavior of a shell-like particle such as a liposome. Peterlin et al.161 studied electro-deformation in phospholipid vesicles using AC electric field and correlated the experimentally observed prolate-to-oblate transition frequency ranges with previous literature.162 Hadady et al.163 used liposomes to study the single-shell DEP model at high frequencies in various conductivity media. They observed an upper crossover frequency in the range of 9-60 MHz and reported a linear dependency of upper crossover frequency on the interior conductivity of liposomes, in agreement with the single-shell DEP theoretical model. Very recently, Shi et al.164 reported a glass nano-pipette tip for entrapment of nanoparticles. Authors exploited electrokinetic


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forces including DEP, electrophoresis, and electroosmosis using low DC voltage for selective trapping and separation applications using nanoparticles, liposomes, and exosomes.

4.2.4 Blood Cells DEP-based cellular analysis can have a major impact in the field of pharmaceuticals and diagnostics. Infected or diagnostically valuable cells may have altered DEP characteristics compared to healthy cells and can be used for selective detection, separation, and collection using microdevices leading to novel diagnostic and therapeutic applications. Numerous DEP platforms have been characterized specifically for single or multi-cell analysis including microbial cells, blood cells, cancer cells etc.2,165 Advancements in DEP based cancer cell analysis for diagnostic applications have also been reviewed recently8 and will not be further addressed here. Microbial cell analysis in DEP devices will be discussed in the next section. In this section, the DEP applications involving only blood cells are discussed. Gagnon et al.166 previously studied DEP characteristics of bovine red blood cells (RBCs) using the single-shell oblate spheroid model in a quadruple electrode device. Authors used glutaraldehyde for cell fixation to reduce the dielectric constant of the cell membrane and reported separation of cells based on age due to variation in DEP characteristics. Han et al.145 reported continuous separation of blood cells from diluted blood samples using an interdigitated electrode array device as shown in Figure 4d. The electrode array was placed at an angle to fluid flow and acted as micro-separator for separation of RBCs and white blood cells (WBCs) with ~90% efficiency in high conductivity buffer. Chang et al.88 also previously reported separation of RBCs and WBCs with 99% purity. Srivastava et al.167 used differences in DEP characteristics of RBCs to separate O+ blood-type RBCs from other blood-type cells using a Pt electrode microdevice. Su et al.168 described a dielectrophoretic spring method to study the electrical properties of cells in a continuous flow device. The dielectrophoretic spring method takes into account the balance between DEP force and hydrodynamic drag exerted on a cell to determine the electrical properties and was used to isolate activated and inactivated neutrophils based on their electrical properties. Du et al.169 reported an interdigitated electrode array device for characterizing mechanical properties of cells by studying DEP forces as a function of deformation. Using this device, RBCs



infected by malarial parasites were distinguished from healthy and uninfected RBCs as a labelfree diagnostic tool. Fritzsch et al.170 recently reported a microfluidic device for trapping of cells independent of cell size and morphology. The device consisted of multiple electrodes that were used for deflection, transportation, and nDEP-based trapping of numerous cell types including RBCs. Very recently, Frusawa et al.171 reported frequency-modulated wave DEP for pDEP- and nDEP-based manipulation of RBCs and vesicles in the range near the crossover frequencies. Gimsa et al.172 used single-shell ellipsoidal and three-shell spherical theoretical models for studying the DEP, electrorotation, and electro-orientation characteristics of chicken RBCs. The authors concluded that the single-shell ellipsoidal model qualitatively reflects the experimentally observed electrokinetic properties of chicken RBCs.

4.2.5 Microbes Infectious diseases caused by pathogenic microorganisms are a global threat to human health and cost millions of dollars in health care expenditures every year. Thus, microorganisms like bacteria, virus, algae, yeasts etc. have also been studied recently for dielectrophoretic manipulation or separation from biological solutions for diagnostics or therapeutic applications32 and such DEP applications are further discussed in the next sections. 4.2.5.1 Bacteria Bacteria are prokaryotic microorganisms and their cells do not contain any specialized organelles unlike eukaryotic cells. In nature, bacterial cells are found in different shapes (spherical, rod, ellipsoidal etc.), and sizes (0.5 to 5 µm) making them an ideal model analyte for studying various theoretical DEP models based on shape and number of shells. Recently, several microdevices have been reported for studying dielectrophoretic manipulation of bacterial cells based on both spherical and non-spherical shape DEP models. Aldaeus et al.173 initially studied bacterial trapping using E. coli by superimposing pDEP and nDEP regions under low and high conductivity buffers using a solid prolate ellipsoid based numerical model. Cho et al.174 compared two designs (posttype or pore-type) for insulator-based dielectrophoretic trapping of E. coli. The authors reported


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higher DEP tapping forces in pore-type designs while the cross-sectional area for trapping was found to be higher and more suitable for high-throughput applications in post-type designs. Braff et al.175 used constriction based iDEP devices for trapping E. coli and B. cereus at low electric fields (

Dielectrophoresis: From molecular to micrometer scale analytes

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