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Citation: Egun, E.; Wilson, T.; Rashad,
Z.A.; Valentine, R.; Adams, T.N.G.
Transient Slope: A Metric for
Assessing Heterogeneity from the
Dielectrophoresis Spectrum.
Biophysica 2024,4, 695–710. https://
doi.org/10.3390/biophysica4040045
Academic Editor: Attila Borics
Received: 18 November 2024
Revised: 8 December 2024
Accepted: 13 December 2024
Published: 14 December 2024
Copyright: © 2024 by the authors.
Licensee MDPI, Basel, Switzerland.
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4.0/).
Article
Transient Slope: A Metric for Assessing Heterogeneity from the
Dielectrophoresis Spectrum
Emmanuel Egun
1,2
, Tia Wilson
2,3
, Zuri A. Rashad
1,2
, Rominna Valentine
1,2
and Tayloria N. G. Adams
1,2,3,4,5,
*
1Department of Chemical and Biomolecular Engineering, University of California Irvine, Irvine, CA 92697,
USA; eegun@uci.edu (E.E.); zrashad@uci.edu (Z.A.R.)
2
Sue and Bill Gross Stem Cell Research Center, University of California, Irvine, CA 92697, USA; tiaw1@uci.edu
3Department of Materials Science Engineering, University of California, Irvine, CA 92697, USA
4Department of Biomedical Engineering, University of California, Irvine, CA 92697, USA
5Department of Anatomy and Neurobiology, University of California, Irvine, CA 92697, USA
*Correspondence: tayloria@uci.edu
Abstract: Cellular heterogeneity, an inherent feature of biological systems, plays a critical role in
processes such as development, immune response, and disease progression. Human mesenchymal
stem cells (hMSCs) exemplify this heterogeneity due to their multi-lineage differentiation potential.
However, their inherent variability complicates clinical use, and there is no universally accepted
method for detecting and quantifying cell population heterogeneity. Dielectrophoresis (DEP) has
emerged as a powerful electrokinetic technique for characterizing and manipulating cells based
on their dielectric properties, offering label-free analysis capabilities. Quantitative information
from the DEP spectrum, such as transient slope, measure cells’ transition between negative and
positive DEP behaviors. In this study, we employed DEP to estimate transient slope of various cell
populations, including relatively homogeneous HEK-293 cells, heterogeneous hMSCs, and cancer
cells (PC3 and DU145). Our analysis encompassed hMSCs derived from bone marrow, adipose, and
umbilical cord tissue, to capture tissue-specific heterogeneity. Transient slope was assessed using two
methods, involving linear trendline fitting to different low-frequency regions of the DEP spectrum.
We found that transient slope serves as a reliable indicator of cell population heterogeneity, with
more heterogeneous populations exhibiting lower transient slopes and higher standard deviations.
Validation using cell morphology, size, and stemness further supported the utility of transient
slope as a heterogeneity metric. This label-free approach holds promise for advancing cell sorting,
biomanufacturing, and personalized medicine.
Keywords: heterogeneity; dielectrophoresis; dielectrophoresis spectrum; transient slope; label-free
cell analysis; mesenchymal stem cells; cancer cells
1. Introduction
Cellular heterogeneity is an intrinsic property of biological systems that manifests at
multiple levels, ranging from individual cells to entire tissues [
1
]. This variability arises
from genetic, epigenetic, and environmental factors, leading to diverse cell functions within
a population [
2
]. Heterogeneity plays a crucial role in various biological processes, such as
human development, immune response, and disease progression [
3
]. The ability to measure
and characterize cellular heterogeneity is essential in understanding complex biological
phenomena such as cell differentiation, optimizing cell sorting and biomanufacturing
processes, and improving treatment outcomes in personalized medicine. However, despite
its significance, quantifying cell population heterogeneity remains challenging due to the
lack of universally accepted markers.
Human mesenchymal stem cells (hMSCs) are a prime example of a heterogeneous
cell population. HMSCs are multipotent cells that can differentiate into various lineages,
including osteoblasts, adipocytes, and chondrocytes [
4
]. They are widely studied for
Biophysica 2024,4, 695–710. https://doi.org/10.3390/biophysica4040045 https://www.mdpi.com/journal/biophysica
Biophysica 2024,4696
their potential in regenerative medicine and tissue engineering. For example, hMSCs are
frequently used to repair bone defects, particularly in cases of non-union bone fractures
or large bone defects where traditional healing is insufficient [
5
]. Additionally, hMSCs
play a role in modulating immune responses by secreting anti-inflammatory cytokines
and inhibiting T-cell proliferation, making them promising for treating immune-related
disorders [
6
]. However, the inherent heterogeneity within hMSC populations complicates
their clinical applications. Variations in cell size, morphology, differentiation potential,
and surface marker expression contribute to differences in their therapeutic efficacy [
7
].
Therefore, understanding and characterizing cell population heterogeneity is essential
in optimizing hMSC-based therapies, as it can impact their ability to repair tissues and
modulate immune responses.
Dielectrophoresis (DEP) has emerged as a promising technique for analyzing and
addressing challenges associated with heterogeneity by characterizing and manipulating
cell populations based on their dielectric properties. By leveraging the differences in
dielectric properties of cell subpopulations, DEP can manipulate and sort cells based on
variations in their cell membrane and cytoplasm without the need for labels [
8
]. In the
context of hMSCs, DEP analysis offers potential for selecting specific subpopulations of cells
and refining cell population heterogeneity. For instance, Song et al. enriched osteoblasts
from a mixture of differentiated and undifferentiated hMSCs, demonstrating that DEP can
yield reasonably pure, homogeneous subpopulations [
9
]. Similarly, Yoshioka et al. achieved
good purity when enriching immortalized hMSCs from a mixture of hMSCs and HL-60
cells [10].
Fundamentally, DEP involves the polarization of cells using nonuniform electric fields,
causing cell movement that is dependent on their inherent dielectric properties. The key
principle is that cells experience a force based on the gradient of the nonuniform electric
field, with the direction of the force depending on the relative polarizability of the cell and
the surrounding medium [11]. The DEP force, FDEP , is described by [11],
FDEP =2πr3εmRe[K(ω)]∇ | E|2, (1)
where
r
is the radius of the cell,
εm
is the permittivity of the surrounding medium, Re[K(
ω
)]
is the real part of the Clausius–Mossotti factor, which depends on frequency,
ω
, and
∇ | E|2
is the gradient of the squared magnitude of the electric field. The Clausius–Mossotti factor
is given by [11]
K(ω)=ε∗
cell −ε∗
m/ε∗
cell +2ε∗
m(2)
where
ε∗
cell
is the complex permittivity of the cell and
ε∗
m
is the complex permittivity of
the medium. These equations show that the DEP force depends on cell size, dielectric
properties of the suspending medium and cell, and spatial variations of the nonuniform
electric field.
The movement of cells with DEP is categorized as positive or negative DEP, where
cells move toward areas where the nonuniform electric field gradient is strongest (positive
DEP) or weakest (negative DEP). By measuring the DEP response at varying frequencies,
a DEP spectrum can be generated for a cell population, providing valuable insights into
cellular composition and heterogeneity through positive and negative DEP behaviors.
Quantitative information can be obtained from the DEP spectrum, such as membrane
capacitance [
12
,
13
], cytoplasm conductivity [
12
,
13
], as well as the transient behavior of cells.
One approach to examining the transient behavior is by analyzing the slope of the low-
frequency region of the DEP spectrum. The transient slope, assessed using principles from
signal processing, has previously been used to characterize neural stem and progenitor cells,
astrocytes, neurons, hMSCs, red blood cells, and polystyrene beads [
13
–
15
]. By analyzing
the DEP spectrum, transient slope emerges as a reliable, label-free metric for detecting
cellular heterogeneity, representing the transition of cells from negative to positive DEP
behavior [13].
Biophysica 2024,4697
In this study, we used DEP and estimated the transient slope of homogeneous and
heterogeneous cell populations. Specifically, we examined the transient slope of HEK-
293 cells as a relatively homogeneous cell population [
13
] and hMSCs as a well-known
heterogeneous cell population [
16
]. Next, we evaluated the transient slope of differentiated
and undifferentiated hMSCs, as differentiation is known to produce more homogeneous
cell populations. We then compared multiple cell populations with varying heterogeneity,
including HEK-293 cells, cancer cells (PC3 and DU145), and hMSCs. Lastly, our focus
on hMSCs was further expanded to include different tissue sources, bone-marrow (BM),
adipose tissue (AT), and umbilical cord (UC) tissue-derived cells, as they are commonly
used in transplantation studies. Transient slope was estimated using two methods: a
linear trendline fitted to the low-frequency portion of the DEP spectrum, defined by
10 kHz–20 MHz
(~13 data points) and 2 kHz–250 kHz (~17 data points). The number of data
points illustrates the level of detail captured from the DEP spectrum for fitting the trendline
and assessing transient slope. Transient slope and the standard deviation of transient slope
were used as indicators of heterogeneity, based on the premise that more heterogeneous
cell populations will have lower transient slope values and higher standard deviations.
In contrast, more homogeneous cell populations will have higher transient slope values
and lower standard deviations. To validate transient slope as a metric of heterogeneity,
we assessed cell morphology, cell size, and cell stemness. We found that both methods
for estimating transient slope yielded similar transient slopes, with the choice of method
depending on intended application. Additionally, transient slope consistently tracked with
the heterogeneity of all cell types investigated with hMSCs being most heterogeneous and
HEK-293 cells being most homogeneous. This transient slope analysis provides a label-free
metric of heterogeneity for critically important cell populations.
2. Materials and Methods
2.1. Cell Culture
All cells used in this study were obtained from the American Type Culture Collection
(ATCC, Manassas, VA, USA). HEK-293 cells were cultured in Eagle’s Minimum Essential
Medium (Life Technologies, Carlsbad, CA, USA) supplemented with 10% fetal bovine
serum (Corning, Corning, NY, USA). AT-hMSCs and UC-hMSCs were cultured in MSC
basal media supplemented with 2% fetal bovine serum (ATCC), 5 ng/mL FGF-1 (ATCC),
5 ng/mL FGF-2, 5 ng/mL EGF (ATCC), and 0.1
×
antibiotic-antimycotic. BM-hMSCs
were cultured in MSC basal media supplemented with 7% fetal bovine serum (ATCC),
15 ng/mL FGF-1, 125 pg/mL FGF-2, 2.4 mM L-alanyl-L-glutamine (ATCC), and 0.1
×
antibiotic-antimycotic. PC3 and DU145 cells were cultured in Roswell Park Memorial
Institute (RPMI)-1640 media (Thermo Fisher, Waltham, MA, USA) supplemented with 10%
(v/v) heat-inactivated fetal bovine serum (Corning), and 1% (v/v) penicillin-streptomycin
(Fisher Scientific, Hanover Park, IL, USA). The cells were cultured at 37
◦
C in a humidified
5% CO
2
incubator using tissue culture-treated T-75 flasks, seeded at 5000 cells/cm
2
, and
passaged upon reaching ~80% confluency.
When passaging, the proliferation media was aspirated, the cell monolayer was
rinsed using 1
×
DPBS (Life Technologies), and detached from the flask using 0.05%
trypsin-ethylenediaminetetraacetic acid (Life Technologies) for 5 min at 37
◦
C. Once the
cells were detached, the trypsin was neutralized with an equal volume of proliferation
media. Then, the cells were pipetted into a 15 mL falcon tube, centrifuged at 275
×
g
for 5 min, resuspended in new growth media, and counted using a hemacytometer for
accurate seeding.
2.2. HMSC Differentiation
Tissue culture-treated 6-well plates were coated with 0.2% gelatin to prepare AT-hMSC
for differentiation. The coating was prepared by dissolving lyophilized porcine skin gelatin
(Sigma Aldrich, St. Louis, MO, USA) in Milli-Q water and autoclaving. Then, 900
µ
L of
the gelatin solution was added to each well in the 6-well plate and allowed to coat at room
Biophysica 2024,4698
temperature for 30 min. The excess gelatin solution was aspirated, and the coated plates
were placed in the biosafety cabinet to dry for at least 2 h.
AT-hMSCs were seeded at 10,000 cells/cm
2
in the gelatin-coated 6-well plate with
growth media and allowed to proliferate for 2 days. For osteoblast differentiation, the
growth media was aspirated, and the cells were rinsed once with 1
×
DPBS and the os-
teogenic medium was added, which consisted of
α
MEM (Life Technologies) supplemented
with 10% fetal bovine serum, 50
µ
g/mL l-ascorbic acid 2-phosphate (FUJIFILM Wako,
Osaka, Japan), 100 nM dexamethasone (MP Biomedicals, Santa Ana, CA, USA), 10 mM
β
-glycerophosphate (Alfa Aesar, Ward Hill, MA, USA), and 0.1
×
antibiotic-antimycotic.
For adipocyte differentiation, the growth media was replaced with StemPro adipogenesis
media (Life Technologies). The differentiation media was changed every 4 days for 21 days.
2.3. Transient Slope Characterization and Analysis
For the transient slope characterization, trypsinized cells were resuspended in a DEP
buffer solution made of 8.5% (w/v) sucrose and 0.3% (w/v) glucose. The conductivity of the
DEP buffer solution was adjusted to 100
µ
S/cm or 300
µ
S/cm with RPMI-1640. The cells
were washed three times before final resuspension in the DEP buffer at
1×106cells/mL.
Cell viability was visually assessed using trypan blue. The prepared cells were then
analyzed by the 3DEP analyzer (LabTech, Heathfield, UK), which features a microfluidic
chip with 20 microwells containing 3-dimensional electrodes along with outer walls of the
microwell. Two frequency ranges were investigated: 2 kHz–250 kHz and
10 kHz–20 MHz
,
at 10 V
pp
. The resulting DEP spectrum reflected changes in light intensity as a function of
frequency [
17
]. For quality control, each DEP spectrum underwent several checks. Initially,
data obtained from each microwell of the 3DEP chip was visually screened for bubbles or
insufficient power (visualized as smaller changes in light intensity). Data from affected
microwells were excluded from the spectrum, and if four or more data points were excluded,
the entire DEP spectrum was discarded. Next, each DEP spectrum obtained from a DEP
run was compared to the 3DEP analyzer’s built-in single-shell model to assess its shape.
DEP runs with an R
2
value of 0.9 or higher when the model was fit to the experimental data
were retained for further analysis. After this initial quality control screening, all of the DEP
runs for a biological repeat (at least 10) were pooled together for a quartile test to identify
outliers. No more than 4 outliers were removed per DEP run. If more than 4 outliers were
identified, then the entire DEP run was no longer considered for the transient slope analysis.
The transient slope of the DEP spectrum was determined by fitting a linear trendline to
20–80% of the rise time of the DEP spectrum with 80,000 cells tested per DEP run. Statistical
analysis of transient slope was completed using one-way ANOVA with Tukey’s post hoc
test for multiple comparisons.
2.4. Cell Morphology and Size Analysis
At 80% confluency, each cell type was imaged at 10
×
magnification for cell morphology
and size analysis. Morphology was assessed by examining the cells for characteristic shapes
such as cobblestone, elongated, and spindle-like. Cell size was analyzed by quantifying cell
area and diameter. For cells area measurements, images of cultured cells were processed in
ImageJ version 1.80, where the scale bar on each image was measured and set for analysis.
Utilizing the area measurement tool, at least 150 cells per cell type were selected and
measured by outlining their perimeters. For cell diameter measurements, cells suspended
in DEP buffer solution were imaged on a hemacytometer. The images were also processed
in ImageJ, with the appropriate scale bar calibration. At least 100 cells per cell type were
selected and measured by drawing a line across the width of each cell. Statistical analysis
of cell areas and diameters was completed using one-way ANOVA with Tukey’s post hoc
test for multiple comparisons.
Biophysica 2024,4699
2.5. Cell Stemness Analysis with Immunostaining
Cells were seeded at a density of 1
×
10
4
; cells per well in 48-well plate (Nunc
Lab-Tek, Thermo Fisher Scientific) and cultured for 24–48 h until they reached 60–70%
confluence. Then, cells were washed with phosphate-buffered saline (PBS) and fixed with
4% paraformaldehyde for 15 min at room temperature. After fixation, cells were washed
three times with PBS and permeabilized using 0.1% Triton X-100 in PBS for 10 min at
room temperature. To block nonspecific binding, cells were incubated in blocking buffer
containing 5% bovine serum albumin in PBS for 30 min at room temperature.
Primary antibodies used to detect cell stemness included anti-SOX2 (rabbit polyclonal,
1:100, Abcam, Cambridge, United Kingdom) and anti-NANOG (mouse monoclonal, 1:200,
Abcam). The AT-hMSCs, BM-hMSCs, UC-hMSCs, PC3 cells, and DU145 cells were individ-
ually incubated with each primary antibody diluted in blocking buffer overnight at 4
◦
C.
Following incubation, the cells were washed three times with PBS, and incubated with
Hoechst (Thermo Fisher) for 10 min at room temperature in the dark. Cells were washed
three more times with PBS following Hoechst staining.
Immunofluorescence images were acquired using a Zeiss Axio Observer fluorescence
microscope (Zeiss, Oberkochen, Germany) equipped with appropriate filters, capturing
three fields per cell per antibody. These images were processed in ImageJ by conversion to
an 8-bit scale, enhancing the green fluorescence signal using LookUp Tables (LUTs), and
increasing brightness by 40–60% with corresponding contrast adjustments. Quantitative
intensity analysis was performed to complement the visual assessment. Statistical analysis
of cell areas and diameters was completed using one-way ANOVA with Tukey’s post hoc
test for multiple comparisons.
3. Results
3.1. Optimization of Transient Slope Obtained from DEP Spectra
This research required the execution of experiments that utilized the 3DEP ana-
lyzer [
17
]. Figure 1a depicts the DEP behavior of cells within the microwells (cells attracted
towards walls display positive DEP, and cells repelled away from walls display negative
DEP). Figure 1b provides a visual of a hypothetical DEP spectrum. Transient slope can
be estimated from the spectrum by fitting a linear trendline to a wider (Figure 1c) and
narrower (Figure 1d) frequency range, as demonstrated for a heterogeneous cell population
(indicated by a schematic with red dashed box and red circles in hypothetical spectrum)
and homogeneous cell population (represented by schematic with a blue dashed box and
blue circles in hypothetical spectrum). We illustrate differences in the transient slope for ho-
mogeneous and heterogeneous cell populations with higher and lower values, respectively
(Figure 1e).
Two methods were employed for transient slope data collection. In method 1, a wide
frequency range (10 kHz–20 MHz) was tested, consistent with standard DEP experiments,
and in method 2 a narrow frequency range (2 kHz–250 kHz) was tested. Figure 2illustrates
the efficiency of methods 1 and 2. Method 1 fitted an average of 13 data points to the
transient slope trendline of the DEP spectrum (Figure 2a), and method 2 fitted an average
of 17 data points to the transient slope trendline of the DEP spectrum (Figure 2b). The
transient slopes from the two methods are plotted and compared in Figure 2c. The average
transient slope was similar for both methods and the average R
2
value of the trendlines
were similar (Figure 2d). This assessment was completed on a relatively homogenous cell
population (Figure 2a–d) and a relatively heterogeneous cell population (Figure 2e–h). In
this comparison, it can be seen that the average transient slope is higher in the homogeneous
cell population independent of the method used and the R
2
values of the trendlines are
high for both cell populations.
Biophysica 2024,4700
biophysica2024,4700
Figure1.Schematicoverviewoftransientslopeanalysis.(a)Cellpolarizationindielectrophoresis
(DEP)characterizationofcells.Thecellswilleitheraracttoareasofhighelectricfieldstrength
(positiveDEP)orberepelledtoareasoflowelectricfieldstrength(negativeDEP).(b)DEPspectrum
generatedfromcellanalysis.Twotransientslopemethods(c)samplingfewerdatapointsand(d)
samplingmoredatapoints.Thebluecirclesandschematicoutlinedwithbluedashedboxrepresent
hypotheticalhomogeneouscellpopulation.Theredcirclesandtheschematicoutlinedwithred
dashedboxrepresenthypotheticalheterogeneouscellpopulation.(e)Dotplotoftransientslopeof
hypotheticalhomogeneousandheterogeneouscellpopulations.Homogeneouscellpopulationsex-
pectedtohavehighertransientslopeandheterogeneouscellpopulationsexpectedtohavelower
transientslope.Note:thisfigureisaconceptualschematicanddoesnotrepresentactualexperi-
mentaldata.GraphicsinthisfigurewerecreatedwithBiorender.com.
Twomethodswereemployedfortransientslopedatacollection.Inmethod1,awide
frequencyrange(10kHz–20MHz)wastested,consistentwithstandardDEPexperiments,
andinmethod2anarrowfrequencyrange(2kHz–250kHz)wastested.Figure2illus-
tratestheefficiencyofmethods1and2.Method1fiedanaverageof13datapointsto
thetransientslopetrendlineoftheDEPspectrum(Figure2a),andmethod2fiedanav-
erageof17datapointstothetransientslopetrendlineoftheDEPspectrum(Figure2b).
ThetransientslopesfromthetwomethodsareploedandcomparedinFigure2c.The
averagetransientslopewassimilarforbothmethodsandtheaverageR
2
valueofthe
trendlinesweresimilar(Figure2d).Thisassessmentwascompletedonarelativelyho-
mogenouscellpopulation(Figure2a–d)andarelativelyheterogeneouscellpopulation
(Figure2e–h).Inthiscomparison,itcanbeseenthattheaveragetransientslopeishigher
inthehomogeneouscellpopulationindependentofthemethodusedandtheR
2
valuesof
thetrendlinesarehighforbothcellpopulations.
Figure 1. Schematic overview of transient slope analysis. (a) Cell polarization in dielectrophoresis
(DEP) characterization of cells. The cells will either attract to areas of high electric field strength
(positive DEP) or be repelled to areas of low electric field strength (negative DEP). (b) DEP spectrum
generated from cell analysis. Two transient slope methods (c) sampling fewer data points and
(d) sampling more data points. The blue circles and schematic outlined with blue dashed box
represent hypothetical homogeneous cell population. The red circles and the schematic outlined with
red dashed box represent hypothetical heterogeneous cell population. (e) Dot plot of transient slope
of hypothetical homogeneous and heterogeneous cell populations. Homogeneous cell populations
expected to have higher transient slope and heterogeneous cell populations expected to have lower
transient slope. Note: this figure is a conceptual schematic and does not represent actual experimental
data. Graphics in this figure were created with Biorender.com.
3.2. Transient Slope Assessments of Heterogenous and Homogenous Cell Populations
The transient slope was assessed for several cell populations that are classified as
heterogeneous and homogeneous. As an initial assessment of the utility of transient
as an indicator of cell heterogeneity, we examined undifferentiated and differentiated
hMSCs. The hMSCs were differentiated toward osteoblasts and adipocytes (Figure 3).
In this analysis, the average transient slope was highest for the differentiated hMSCs
(osteoblast and adipocyte) and statistically different from that of the undifferentiated
hMSCs (
**** p< 0.0001
), Figure 3a. A violin plot was utilized to emphasize the average
and spread of transient slope for each cell population analyzed, illustrating a distinct
distribution between differentiated and undifferentiated hMSCs, with the undifferentiated
cells having the higher standard deviation (Figure 3b).
Biophysica 2024,4701
biophysica2024,4701
Figure2.Comparisonoftwotransientslopemethods.(a,e)Method1transientslopetrendlinefied
toDEPspectrumdefinedbywidefrequencyrange,10kHz–20MHz.(b,f)Method2transientslope
trendlinefiedtoDEPspectrumdefinedbynarrowfrequencyrange,2kHz–255kHz.(c,g)Transient
slopesand(d,h)trendlineR2valuesformethod1andmethod2.(a–d)Depictsthecollecteddata
fromahomogenouscellsample.(e–h)Depictsthedatacollectedfromaheterogeneouscellsample.
TheaverageR2valueformethod1andmethod2forthehomogeneouscellsampleis0.941and0.903,
respectively.TheaverageR2valueformethod1andmethod2fortheheterogeneouscellsampleis
0.904and0.906,respectively.Errorbarsin(c,g)arestandarddeviation.Forstatisticalsignificance:
**p<0.01and****p<0.0001.
3.2.TransientSlopeAssessmentsofHeterogenousandHomogenousCellPopulations
Thetransientslopewasassessedforseveralcellpopulationsthatareclassifiedas
heterogeneousandhomogeneous.Asaninitialassessmentoftheutilityoftransientasan
indicatorofcellheterogeneity,weexaminedundifferentiatedanddifferentiatedhMSCs.
ThehMSCsweredifferentiatedtowardosteoblastsandadipocytes(Figure3).Inthisanal-
ysis,theaveragetransientslopewashighestforthedifferentiatedhMSCs(osteoblastand
adipocyte)andstatisticallydifferentfromthatoftheundifferentiatedhMSCs(****p<
0.0001),Figure3a.Aviolinplotwasutilizedtoemphasizetheaverageandspreadoftran-
sientslopeforeachcellpopulationanalyzed,illustratingadistinctdistributionbetween
differentiatedandundifferentiatedhMSCs,withtheundifferentiatedcellshavingthe
higherstandarddeviation(Figure3b).
Figure 2. Comparison of two transient slope methods. (a,e) Method 1 transient slope trendline fitted
to DEP spectrum defined by wide frequency range, 10 kHz–20 MHz. (b,f) Method 2 transient slope
trendline fitted to DEP spectrum defined by narrow frequency range, 2 kHz–255 kHz. (c,g) Transient
slopes and (d,h) trendline R
2
values for method 1 and method 2. (a–d) Depicts the collected data
from a homogenous cell sample. (e–h) Depicts the data collected from a heterogeneous cell sample.
The average R
2
value for method 1 and method 2 for the homogeneous cell sample is 0.941 and 0.903,
respectively. The average R
2
value for method 1 and method 2 for the heterogeneous cell sample is
0.904 and 0.906, respectively. Error bars in (c,g) are standard deviation. For statistical significance:
** p< 0.01 and **** p< 0.0001.
biophysica2024,4702
Figure3.Transientslopeofdifferentiatedhumanmesenchymalstemcells(hMSCs).(a)Violinplot
representationoftransientslope.(b)Standarddeviationoftransientslopes.Forstatisticalsignifi-
cance:****p<0.0001.
Asasecondassessmentoftheutilityoftransientslopeasameasureofheterogeneity,
weexaminedHEK-293,PC3,DU145,andAT-hMSCs.InFigure4a,theaveragetransient
slopeishighestfortheHEK-293cellsandlowestforthehMSCs.Aone-wayANOVAre-
vealedthateachcellpopulationcomparedtotheHEK-293cellswasdifferentwithstatis-
ticalsignificance(****p<0.0001).Theviolinplotshowsdistinctdistributionswiththe
HEK-293cellshavingawidertopandtaperedboom,thePC3cellshavingataperedtop
andwiderboom,andtheDU145cellsandAT-hMSCshavingamoreevendistribution
acrosstherangeoftransientslopes.Thestandarddeviation(orspread)oftransientslopes
waslargestforthehMSCsandsmallestforHEK-293cells(Figure4b).SupplementaryFig-
ureS1illustrateshowvariabilityintransientslopeforheterogeneouspopulations,such
ashMSCs,maybeaributedtodifferencesinsurfacecomplexity.
Figure4.TransientslopesofHEK-293,PC3,DU145,andhMSCs.(a)Violinplotrepresentationof
transientslope.(b)Standarddeviationoftransientslopes.Forstatisticalsignificance:****p<0.0001.
AcellareaandcelldiameterassessmentwascompletedontheHEK-293,PC3,
DU145,andhMSCsinImageJasapointofcomparisonfortransientslope.Figure5shows
Figure 3. Transient slope of differentiated human mesenchymal stem cells (hMSCs). (a) Violin plot
representation of transient slope. (b) Standard deviation of transient slopes. For statistical significance:
**** p< 0.0001.
As a second assessment of the utility of transient slope as a measure of heterogeneity,
we examined HEK-293, PC3, DU145, and AT-hMSCs. In Figure 4a, the average transient
slope is highest for the HEK-293 cells and lowest for the hMSCs. A one-way ANOVA
revealed that each cell population compared to the HEK-293 cells was different with
Biophysica 2024,4702
statistical significance (**** p< 0.0001). The violin plot shows distinct distributions with the
HEK-293 cells having a wider top and tapered bottom, the PC3 cells having a tapered top
and wider bottom, and the DU145 cells and AT-hMSCs having a more even distribution
across the range of transient slopes. The standard deviation (or spread) of transient slopes
was largest for the hMSCs and smallest for HEK-293 cells (Figure 4b). Supplementary
Figure S1 illustrates how variability in transient slope for heterogeneous populations, such
as hMSCs, may be attributed to differences in surface complexity.
biophysica2024,4702
Figure3.Transientslopeofdifferentiatedhumanmesenchymalstemcells(hMSCs).(a)Violinplot
representationoftransientslope.(b)Standarddeviationoftransientslopes.Forstatisticalsignifi-
cance:****p<0.0001.
Asasecondassessmentoftheutilityoftransientslopeasameasureofheterogeneity,
weexaminedHEK-293,PC3,DU145,andAT-hMSCs.InFigure4a,theaveragetransient
slopeishighestfortheHEK-293cellsandlowestforthehMSCs.Aone-wayANOVAre-
vealedthateachcellpopulationcomparedtotheHEK-293cellswasdifferentwithstatis-
ticalsignificance(****p<0.0001).Theviolinplotshowsdistinctdistributionswiththe
HEK-293cellshavingawidertopandtaperedboom,thePC3cellshavingataperedtop
andwiderboom,andtheDU145cellsandAT-hMSCshavingamoreevendistribution
acrosstherangeoftransientslopes.Thestandarddeviation(orspread)oftransientslopes
waslargestforthehMSCsandsmallestforHEK-293cells(Figure4b).SupplementaryFig-
ureS1illustrateshowvariabilityintransientslopeforheterogeneouspopulations,such
ashMSCs,maybeaributedtodifferencesinsurfacecomplexity.
Figure4.TransientslopesofHEK-293,PC3,DU145,andhMSCs.(a)Violinplotrepresentationof
transientslope.(b)Standarddeviationoftransientslopes.Forstatisticalsignificance:****p<0.0001.
AcellareaandcelldiameterassessmentwascompletedontheHEK-293,PC3,
DU145,andhMSCsinImageJasapointofcomparisonfortransientslope.Figure5shows
Figure 4. Transient slopes of HEK-293, PC3, DU145, and hMSCs. (a) Violin plot representation of
transient slope. (b) Standard deviation of transient slopes. For statistical significance: **** p< 0.0001.
A cell area and cell diameter assessment was completed on the HEK-293, PC3, DU145,
and hMSCs in ImageJ as a point of comparison for transient slope. Figure 5shows cell
culture images of all cells analyzed. The area of example cells is traced in yellow with
an inset for better view. Visually, the HEK-293 cells and the DU145 cells looked similar
in size (Figure 5a,b), with a cobblestone morphology. While the PC3 cells look similar in
size to the HEK-293 cells and the DU145 cells, their morphology consisted of cobblestone
and elongated cells (Figure 5c). The hMSCs had mostly elongated cells (Figure 5d). The
cell area was tabulated and is represented as a violin plot in Figure 5e. The average cell
area for the HEK-293 cells, DU145 cells, and PC3 cells was similar, while the average
cell area for the hMSCs was higher. The average cell area of HEK-293 cells, DU145 cells,
and PC3 cells was statistically significant in comparison to the hMSCs (**** p< 0.0001).
Interestingly, the average of these cells, HEK-293, DU145, and PC3, was not statistically
significant in comparison to each other. The violin plot illustrates a distinct distribution in
cell area for the hMSCs, with this cell population having the highest standard deviation
(Figure 5f). Supplementary Figure S2 presents the cell diameters of cells prepared for DEP
analysis, which followed a similar trend to cell areas, though the differences between cell
types were less pronounced. The hMSCs had the highest average diameter and largest
standard deviation, while the HEK-293 cells had the lowest average diameter and the
smallest standard deviation.
Biophysica 2024,4703
biophysica2024,4703
cellcultureimagesofallcellsanalyzed.Theareaofexamplecellsistracedinyellowwith
aninsetforbeerview.Visually,theHEK-293cellsandtheDU145cellslookedsimilarin
size(Figure5a,b),withacobblestonemorphology.WhilethePC3cellslooksimilarinsize
totheHEK-293cellsandtheDU145cells,theirmorphologyconsistedofcobblestoneand
elongatedcells(Figure5c).ThehMSCshadmostlyelongatedcells(Figure5d).Thecell
areawastabulatedandisrepresentedasaviolinplotinFigure5e.Theaveragecellarea
fortheHEK-293cells,DU145cells,andPC3cellswassimilar,whiletheaveragecellarea
forthehMSCswashigher.TheaveragecellareaofHEK-293cells,DU145cells,andPC3
cellswasstatisticallysignificantincomparisontothehMSCs(****p<0.0001).Interest-
ingly,theaverageofthesecells,HEK-293,DU145,andPC3,wasnotstatisticallysignificant
incomparisontoeachother.Theviolinplotillustratesadistinctdistributionincellarea
forthehMSCs,withthiscellpopulationhavingthehigheststandarddeviation(Figure
5f).SupplementaryFigureS2presentsthecelldiametersofcellspreparedforDEPanaly-
sis,whichfollowedasimilartrendtocellareas,thoughthedifferencesbetweencelltypes
werelesspronounced.ThehMSCshadthehighestaveragediameterandlargeststandard
deviation,whiletheHEK-293cellshadthelowestaveragediameterandthesmallest
standarddeviation.
Figure5.Cellareaassessmentof(a)HEK-293,(b)DU145,(c)PC3,and(d)hMSCs.(e)Violinplotof
thecellarea.(f)Standarddeviationofthecellarea.Thescalebaris400µm.Forstatisticalsignifi-
cance:**p<0.01and****p<0.0001.
3.3.EffectofDEPBufferConductivityonTransientSlope
Tofurtherassesstheefficacyoftransientslope,weadjustedakeyDEPexperimental
condition,bufferconductivity,andexpandedthetypesofhMSCsanalyzed.Figure6il-
lustratesthetransientslopeofcancercells(PC3andDU145)andthreedifferentsources
ofhMSCs(AT,BM,andUC)measuredat300µS/cm.Thetransientslopewashighestfor
thecancercells,withtheBM-hMSCshavingthelowesttransientslope(Figure6a).Com-
paredtoFigure3,thedistributionandspreadoftransientslopeforthePC3andDU145
cellsissmaller.ThePC3andDU145cellswerestatisticallydifferentfromtheBM-
hMSCs(****p<0.0001)andUC-hMSCs(**p<0.01and*p<0.05,respectively)whilethe
AT-hMSCsandBM-hMSCswerestatisticallydifferent(****p<0.0001)alongwithBM-
hMSCsandUC-hMSCs(***p<0.001).Thereweredistinctdistributions,withthePC3and
DU145cellshavingwidertopsandtaperedbooms,andAT-,BM-,andUC-hMSCshav-
ingmoreevendistributionacrosstherangeoftransientslopes.PC3andDU145cellshad
smallerstandarddeviationsthanthehMSCs(Figure6b).
Figure 5. Cell area assessment of (a) HEK-293, (b) DU145, (c) PC3, and (d) hMSCs. (e) Violin plot of
the cell area. (f) Standard deviation of the cell area. The scale bar is 400
µ
m. For statistical significance:
** p< 0.01 and **** p< 0.0001.
3.3. Effect of DEP Buffer Conductivity on Transient Slope
To further assess the efficacy of transient slope, we adjusted a key DEP experimental
condition, buffer conductivity, and expanded the types of hMSCs analyzed. Figure 6
illustrates the transient slope of cancer cells (PC3 and DU145) and three different sources
of hMSCs (AT, BM, and UC) measured at 300
µ
S/cm. The transient slope was highest
for the cancer cells, with the BM-hMSCs having the lowest transient slope (Figure 6a).
Compared to Figure 3, the distribution and spread of transient slope for the PC3 and DU145
cells is smaller. The PC3 and DU145 cells were statistically different from the BM-hMSCs
(
**** p< 0.0001
) and UC-hMSCs (** p< 0.01 and * p< 0.05, respectively) while the AT-hMSCs
and BM-hMSCs were statistically different (**** p< 0.0001) along with BM-hMSCs and
UC-hMSCs (*** p< 0.001). There were distinct distributions, with the PC3 and DU145 cells
having wider tops and tapered bottoms, and AT-, BM-, and UC-hMSCs having more even
distribution across the range of transient slopes. PC3 and DU145 cells had smaller standard
deviations than the hMSCs (Figure 6b).
3.4. Histogram Representation of Transient Slope
To identify the modality of transient slopes, histogram plots were generated. Figure 7
illustrates the histograms of all cell types we assessed. Each plot gives a Gaussian distribu-
tion, which shows how the transient slope data clusters around the mean value. Within the
histograms, the Gaussian distribution formulates a bell curve over the area of the graph
where the transient slope is most concentrated. The bins shown in each histogram plot
indicate the frequency at which data points fell into those specific ranges. Figure 7a–c rep-
resents the transient slope of the HEK-293 (purple), PC3 (orange), and DU145 (green) cells.
Figure 7d–f represents AT-hMSCs (blue), BM-hMSCs (dark blue), and UC-hMSCs (light
blue). The bins represent the transient slope values (x-axis) while the DEP runs (y-axis)
represent the number of technical replicates (~10 for each biological replicate) that yielded
the binned transient slope value (synonymous to a frequency). The bins represent transient
slope values for each experimental run with the various cell types. Figure 7a’s largest bin
was formulated from 7 data points with a range of 1.35 (
±
0.03). Each histogram plot is
Biophysica 2024,4704
defined by a unimodal Gaussian distribution of different widths reflective of the standard
deviations. The three sources of hMSCs had larger widths in the Gaussian distribution than
the HEK-293 cells, PC3 cells, and the DU145 cells.
biophysica2024,4704
Figure6.TransientslopeofPC3,DU145,andAT-hMSCs,BM-hMSCs,andUC-hMSCstestedina
300µS/cmDEPbuffersolution.(a)Violinplotrepresentationoftransientslope.(b)Standarddevi-
ationoftransientslopes.Forstatisticalsignificance:*p<0.05,**p<0.01,***p<0.001,and****p<
0.0001.
3.4.HistogramRepresentationofTransientSlope
Toidentifythemodalityoftransientslopes,histogramplotsweregenerated.Figure
7illustratesthehistogramsofallcelltypesweassessed.EachplotgivesaGaussiandistri-
bution,whichshowshowthetransientslopedataclustersaroundthemeanvalue.Within
thehistograms,theGaussiandistributionformulatesabellcurveovertheareaofthe
graphwherethetransientslopeismostconcentrated.Thebinsshownineachhistogram
plotindicatethefrequencyatwhichdatapointsfellintothosespecificranges.Figure7a–
crepresentsthetransientslopeoftheHEK-293(purple),PC3(orange),andDU145(green)
cells.Figure7d–frepresentsAT-hMSCs(blue),BM-hMSCs(darkblue),andUC-hMSCs
(lightblue).Thebinsrepresentthetransientslopevalues(x-axis)whiletheDEPruns(y-
axis)representthenumberoftechnicalreplicates(~10foreachbiologicalreplicate)that
yieldedthebinnedtransientslopevalue(synonymoustoafrequency).Thebinsrepresent
transientslopevaluesforeachexperimentalrunwiththevariouscelltypes.Figure7a’s
largestbinwasformulatedfrom7datapointswitharangeof1.35(±0.03).Eachhistogram
plotisdefinedbyaunimodalGaussiandistributionofdifferentwidthsreflectiveofthe
standarddeviations.ThethreesourcesofhMSCshadlargerwidthsintheGaussiandis-
tributionthantheHEK-293cells,PC3cells,andtheDU145cells.
Figure 6. Transient slope of PC3, DU145, and AT-hMSCs, BM-hMSCs, and UC-hMSCs tested in
a 300
µ
S/cm DEP buffer solution. (a) Violin plot representation of transient slope. (b) Standard
deviation of transient slopes. For statistical significance: * p< 0.05, ** p< 0.01, *** p< 0.001, and
**** p< 0.0001.
biophysica2024,4705
Figure7.Histogramanalysisofthetransientslopeof(a)HEK-293cells,(b)PC3cells,(c),DU145
cells,(d)AT-hMSCs,(e)BM-hMSCs,and(f)UC-hMSCs.AGaussiandistributionisploedwiththe
binsoftransientslopevalues.
3.5.StemnessMarkerEvaluation
Lastly,weassessedthecancercells(PC3andDU145)alongwiththehMSCs(AT,BM,
andUC)forstemnessasabiologicalindicatorofheterogeneity.Figure8displaysthepro-
teinexpressionofSOX2andNANOG,twostemnessmarkersforhMSCsandcancercells,
alongwiththeirquantification.BothcancercelllinesstainedpositiveforSOX2and
NANOG,buttheirintensitieswerelowercomparedtothehMSCs.AmongthehMSCs,
UC-hMSCsexhibitedthehighestSOX2intensity,whileAT-hMSCsexhibitedthehighest
NANOGintensity.TheaverageintensityofSOX2forPC3andDU145cellswasstatisti-
callysignificantwithcomparisontotheUC-hMSCs(*p<0.05),whiletheaverageintensity
ofNANOGforDU145cellsandUC-hMSCswasstatisticallysignificantcomparedtothe
AT-hMSCs(*p<0.05).
Figure8.StemnessassessmentofPC3cells,DU145cells,AT-hMSCs,BM-hMSCs,andUC-hMSCs.
ImmunofluorescentstainingofSOX2(toprow)andNANOG(boomrow)withquantification.Im-
ageswereprocessedforimprovedresolution,brightness,andcontrast.Thescalebaris800µm.For
statisticalsignificance:*p<0.05.
4.Discussion
Assessingtheheterogeneityofcellpopulationsisessentialtounderstandtheirbasic
functions.Forinstance,hMSCsareinvolvedinvariousbiologicalprocesses,includinghu-
mandevelopment,immuneresponseanddiseaseprogression[3].Additionally,havinga
Figure 7. Histogram analysis of the transient slope of (a) HEK-293 cells, (b) PC3 cells, (c), DU145 cells,
(d) AT-hMSCs, (e) BM-hMSCs, and (f) UC-hMSCs. A Gaussian distribution is plotted with the bins of
transient slope values.
Biophysica 2024,4705
3.5. Stemness Marker Evaluation
Lastly, we assessed the cancer cells (PC3 and DU145) along with the hMSCs (AT, BM,
and UC) for stemness as a biological indicator of heterogeneity. Figure 8displays the
protein expression of SOX2 and NANOG, two stemness markers for hMSCs and cancer
cells, along with their quantification. Both cancer cell lines stained positive for SOX2 and
NANOG, but their intensities were lower compared to the hMSCs. Among the hMSCs,
UC-hMSCs exhibited the highest SOX2 intensity, while AT-hMSCs exhibited the highest
NANOG intensity. The average intensity of SOX2 for PC3 and DU145 cells was statistically
significant with comparison to the UC-hMSCs (* p< 0.05), while the average intensity
of NANOG for DU145 cells and UC-hMSCs was statistically significant compared to the
AT-hMSCs (* p< 0.05).
biophysica2024,4705
Figure7.Histogramanalysisofthetransientslopeof(a)HEK-293cells,(b)PC3cells,(c),DU145
cells,(d)AT-hMSCs,(e)BM-hMSCs,and(f)UC-hMSCs.AGaussiandistributionisploedwiththe
binsoftransientslopevalues.
3.5.StemnessMarkerEvaluation
Lastly,weassessedthecancercells(PC3andDU145)alongwiththehMSCs(AT,BM,
andUC)forstemnessasabiologicalindicatorofheterogeneity.Figure8displaysthepro-
teinexpressionofSOX2andNANOG,twostemnessmarkersforhMSCsandcancercells,
alongwiththeirquantification.BothcancercelllinesstainedpositiveforSOX2and
NANOG,buttheirintensitieswerelowercomparedtothehMSCs.AmongthehMSCs,
UC-hMSCsexhibitedthehighestSOX2intensity,whileAT-hMSCsexhibitedthehighest
NANOGintensity.TheaverageintensityofSOX2forPC3andDU145cellswasstatisti-
callysignificantwithcomparisontotheUC-hMSCs(*p<0.05),whiletheaverageintensity
ofNANOGforDU145cellsandUC-hMSCswasstatisticallysignificantcomparedtothe
AT-hMSCs(*p<0.05).
Figure8.StemnessassessmentofPC3cells,DU145cells,AT-hMSCs,BM-hMSCs,andUC-hMSCs.
ImmunofluorescentstainingofSOX2(toprow)andNANOG(boomrow)withquantification.Im-
ageswereprocessedforimprovedresolution,brightness,andcontrast.Thescalebaris800µm.For
statisticalsignificance:*p<0.05.
4.Discussion
Assessingtheheterogeneityofcellpopulationsisessentialtounderstandtheirbasic
functions.Forinstance,hMSCsareinvolvedinvariousbiologicalprocesses,includinghu-
mandevelopment,immuneresponseanddiseaseprogression[3].Additionally,havinga
Figure 8. Stemness assessment of PC3 cells, DU145 cells, AT-hMSCs, BM-hMSCs, and UC-hMSCs.
Immunofluorescent staining of SOX2 (top row) and NANOG (bottom row) with quantification.
Images were processed for improved resolution, brightness, and contrast. The scale bar is 800
µ
m.
For statistical significance: * p< 0.05.
4. Discussion
Assessing the heterogeneity of cell populations is essential to understand their basic
functions. For instance, hMSCs are involved in various biological processes, including
human development, immune response and disease progression [
3
]. Additionally, hav-
ing a label-free marker of heterogeneity such as transient slope can be instrumental in
developing electrokinetic based cell sorting strategies for cell biomanufacturing. Thus, we
developed a methodology for estimating transient slope for a variety of cell populations.
Since hMSCs are a well-known heterogeneous cell population [
7
], we compared them
to differentiated hMSCs, suspected homogeneous cell populations HEK-293 cells, and
cancer cells (PC3 and DU145 cells). HEK-293 cells were selected as a relatively homoge-
neous comparison population due to their well characterized DEP spectra [
13
], which
remained consistent over several passages, reflecting their stability in cell culture [
18
]. PC3
and DU145 cells were chosen as comparison populations due to the presence of cancer
stem-like cells [
19
], offering a contrasting population for assessing heterogeneity. DEP
was chosen to measure transient slope because it provides a label-free workflow, enabling
rapid cell analysis. Specifically, the 3DEP system allows for a full DEP spectrum to be
generated for a cell population in just one hour. Additionally, in DEP, transient slope
represents a measure of cells transitioning from negative DEP to positive DEP, providing
insights into cell population heterogeneity.
We estimated transient slopes using methods 1 and 2 on relatively homogeneous HEK-
293 cells and heterogeneous hMSCs. The homogeneous HEK-293 cells and heterogeneous
hMSCs displayed typical DEP spectrum (Figure 2). Figure 2a,e illustrates that method
1 fitted ~13 data points to the transient slope trendline of the DEP spectra. Figure 2b,f
illustrates that method 2 fitted ~17 data points to the transient slope trendline of the DEP
Biophysica 2024,4706
spectrum. Both methods overall yielded similar transient slopes, despite method 2 fitting
to more data points (Figure 2c,g). For the heterogeneous hMSCs specifically, the transient
slope obtained from method 2 was slightly higher than that from method 1, though the
difference was not statistically significant. To maintain quality control of the transient
slopes, we accepted only runs with an R
2
value of 0.9 or higher (Figure 2d,h). This analysis
confirmed that both methods are valuable tools, and selection should be based on the
intended application. Method 1 is ideal for obtaining a general DEP profile and transient
slope of a cell population, as it provides data across the typical frequency range used in
DEP analyses. In contrast, method 2, which samples a smaller frequency range, is more
suitable for closely examining cell heterogeneity, particularly in suspected heterogeneous
cell population. Lastly, the values of transient slope reflect underlying cell population
characteristics with suspected homogeneous cell populations exhibiting higher slopes, as
similar cell types within these populations transition more rapidly from negative DEP to
positive DEP. Suspected heterogeneous cell populations show lower slopes, as the presence
of subpopulations causes a slower transition from negative DEP to positive DEP.
To validate the utility of transient slope as an indicator of cell population heterogeneity,
we analyzed (a) undifferentiated hMSCs alongside hMSCs differentiated toward osteoblasts
and adipocytes, and (b) compared hMSCs to more homogeneous cell populations (HEK-
293, PC3, and DU145 cells). When hMSCs undergo osteogenesis and adipogenesis, they
differentiate into more specialized and a homogeneous cell populations. This is reflected in
our transient slope results (Figure 3), where the average transient slopes of hMSCs differen-
tiated into osteoblasts and adipocytes were higher compared to those of undifferentiated
hMSCs, indicating the differentiated cells are more homogeneous than the undifferentiated
hMSCs. In the second comparison, the average transient slopes of HEK-293, PC3, and
DU145 cells were higher than those of hMSCs, confirming that hMSCs are more hetero-
geneous than these cell populations (Figure 4). The transient slope values of both cancer
cell populations were similar, falling between those of HEK-293 and hMSCs, indicating the
cancer cells had greater heterogeneity than the HEK-293 cells but less heterogeneity than
the hMSCs.
These findings align with the known cell biology: HEK-293 cells are relatively homo-
geneous [
20
], hMSCs display high heterogeneity [
7
,
21
], and studies report the presence of
cancer stem-like cells in PC3 and DU145 populations at levels of 0.2% [
22
] and 7–10% [
23
],
respectively. Additionally, the violin plots and standard deviations support these findings.
The spread of the transient slope data was greatest for the hMSCs and least for the differenti-
ated hMSCs. This variability in transient slope for hMSCs may be influenced by differences
in surface complexity, such as membrane proteins and glycosylation patterns (Supplemen-
tary Figure S1). To further substantiate our findings, we analyzed the cell size of HEK-293,
PC3, DU145, and hMSCs (Figures 5and S2). Visually, HEK-293 cells appeared uniform
in size and shape, exhibiting an epithelial-like, polygonal morphology, while AT-hMSCs
displayed more variation, with a spindle-like, elongated shape. Among these populations,
hMSCs had the largest cell size with the greatest spread in cell area and diameter. The
HEK-293 cells were the smallest; however, similar standard deviations were observed
among HEK-293, PC3, and DU145 cells. Literature reports that cell size corresponds to the
differentiation potential of hMSCs [24], which is indicative of heterogeneity.
A standard DEP buffer, 100
±
5
µ
S/cm, was used to collect transient slope values
shown in Figures 2–4. To determine if there were a dependency of transient slope on
conductivity, we increased the DEP buffer conductivity to 300
±
5
µ
S/cm (Figure 6). This
is also relevant in developing electrokinetic cell sorting strategies, as buffer conductivity is
a useful parameter to tune cell behavior [
25
,
26
]. We assessed cancer cells (PC3 and DU145
cells) and three sources of hMSCs (AT-, BM-, and UC-derived) and found that the increased
buffer conductivity produced identical transient slope patterns to those obtained from our
analyses with the 100
±
5
µ
S/cm DEP buffer. Cancer cells were still less heterogenous
than hMSCs, suggesting no dependency of transient slope on buffer conductivity within
the range of 100 to 300
µ
S/cm. The histogram representation of transient slope for all cell
Biophysica 2024,4707
types examined (Figure 7) shows the number of DEP runs (i.e., technical replicates) that
yielded each specific transient slope value. Cancer cells’ Gaussian distribution peaked at
transient slope value 1.0, where the DU145 cells had more variability than PC3 cells, as
most values above 1.0 had a single DEP run. In contrast, the Gaussian distributions were
flatter, and the peak varied for the hMSCs, further substantiating the use of transient slope
as an indicator of cell population heterogeneity. Lastly, the phenotype assessment of cancer
cells and hMSCs showed that the hMSCs (AT, BM, and UC) exhibited greater heterogeneity
than the cancer cells based on stemness marker expression (Figure 8).
Overall, these results (Figures 2–8) support that transient slope reflects underlying cell
population characteristics, with heterogeneous cell populations exhibiting lower slopes
and homogeneous cell populations showing higher slopes.
Current methods for assessing cell population heterogeneity include flow cytometry,
immunostaining, and various omics approaches (e.g., RNA sequencing, transcriptomics,
proteomics). While these methods offer valuable insights into cellular characteristics, they
often require predefined marker sets, extensive instrumentation, and significant sample
preparation. For instance, flow cytometry and immunostaining are commonly used to
assess protein expression in hMSCs but are limited by their dependency on a predetermined
set of markers, which can vary across studies and may overlap with markers in other cell
types [
27
,
28
]. In contrast, RNA sequencing does not require a predetermined set of markers,
but it generates vast amounts of data that are resource-intensive to analyze and may still
lack specificity in identifying functional heterogeneity within cell populations. Additionally,
current methods tend to be time-consuming and costly, requiring substantial resources.
Using transient slope as a heterogeneity metric offers a label-free, quantitative approach that
simplifies sample comparisons and reduces variability associated with marker selection.
Measuring transient slope with DEP also addresses limitations such as instrumentation
size, lengthy processing times, and high costs, providing a versatile tool for assessing
heterogeneity across various cell systems.
Some DEP studies have alluded to the importance of transient slope as a metric for
distinguishing cell types or stem cell heterogeneity, but none have taken a systematic
approach to demonstrate its utility. For example, Adams et al. [
14
] presented the idea of cell
trapping curves derived from the DEP spectra, proposing that the slopes of these curves
indicated cell population heterogeneity. This was applied to undifferentiated mouse neural
stem and progenitor cells (mNSPCs) along with mNSPCs differentiated into astrocytes and
neurons. While this methodology involved an additional processing step of converting
the DEP spectra to a cell trapping curved based on the positive DEP behavior of cells, the
estimated slopes corresponded with cell population heterogeneity. Similarly, we previously
estimated transient slope from the DEP spectra of BM-hMSCs and AT-hMSCs, comparing
them against a homogeneous control [
13
]. Our results demonstrated that transient slope
effectively distinguished sources of hMSCs and reflected differences in heterogeneity. Col-
lectively, these studies underscore the potential of transient slope from the DEP spectra as
a label-free parameter of heterogeneity. Our study builds on this foundation by system-
atically establishing transient slope as an important heterogeneity metric by expanding
on the parameter space explored. We extended the range of cell populations examined,
varied buffer conductivity, and visualized transient slope distributions with histograms,
comparing our findings with cell area and stemness assessments.
While our study has provided valuable insights into the validity of transient slope from
the DEP spectrum for detecting cell population heterogeneity, it is important to note the
limitations as opportunities for future research and enhancement. We validated transient
slope on two clinically relevant cell systems, hMSCs stem cells and cancer cells, along with
a relatively homogeneous cell population, HEK-293 cells. Although the average transient
slope among these populations differed with statistical significance, incorporating a broader
range of cell types, including a truly homogeneous control, would strengthen its validation.
Such a control could be achieved using polystyrene beads, provided that buffer conductivity
Biophysica 2024,4708
can be tuned to allow the beads to display both negative and positive DEP behavior
(typically, polystyrene beads exhibit negative DEP behavior at low conductivities [15]).
Single-cell measurements would further strengthen the use of transient slope as a
metric of cell population heterogeneity. Quadrupole DEP devices will enable the characteri-
zation of transient slope of individual cells, while pseudo single-cell DEP measurements
using the 3DEP system with low-density cell samples will provide an additional approach
for single-cell assessment. Additionally, exploring nonlinear curve fitting techniques may
yield more nuanced insights into transient slope and cell population heterogeneity.
Expanding the assays used to biologically confirm heterogeneity alongside transient
slope measurements could enhance our findings. Enhancing cell morphology and area
assessments through immunostaining with
β
-tubulin would offer structural insights. Sim-
ilarly, broadening our stemness marker panel and integrating gene expression analyses
would provide a more nuanced, quantitative assessment of cell heterogeneity.
Despite these limitations, our findings are significant. Studying cell population het-
erogeneity with transient slope offers a low cost, label-free metric that is not limited to the
3DEP system. Detecting heterogeneity is important for applications in cell characterization,
cell differentiation, drug screening, cell biomanufacturing, and the study of human and
disease development.
5. Conclusions
Transient slope values derived from the DEP spectrum are a promising label-free
metric for assessing cell population heterogeneity. This study introduces important ad-
vancements, including the development of two methodologies for implementing transient
slope, its application in characterizing the heterogeneity of stem cells and cancer cells,
and a demonstration of its sensitivity in detecting heterogeneity. Integrating transient
slope with existing methods for assessing cell population heterogeneity may facilitate the
development of label-free cell sorting strategies, which are critical for downstream cell
bioprocessing steps. Future investigations will focus on analyzing the transient slope of the
high-frequency portion of the DEP spectra to further develop cell heterogeneity characteri-
zation. This will include DEP analysis, comprehensive cellular profiling to assess a broader
range of stemness markers, and detailed morphological assessments. Ultimately, a label-
free metric of cell population heterogeneity is essential to advancing our understanding of
diverse cell systems.
Supplementary Materials: The following supporting information can be downloaded at: https://www.
mdpi.com/article/10.3390/biophysica4040045/s1, Figure S1. Schematic representation of hypothetical
subpopulations of cells with varying surface complexity [
29
–
31
]. Figure S2. (a) Diameter comparison
of HEK-293 cells, PC3 cells, DU145 cells, and hMSCs. (b) Standard deviation of transient slopes.
Author Contributions: Conceptualization, E.E. and T.N.G.A.; methodology, E.E., T.W., Z.A.R., R.V.
and T.N.G.A.; formal analysis, E.E.; investigation, E.E. and T.W.; resources, T.N.G.A.; data curation,
E.E. and T.W.; writing—original draft preparation, E.E., T.W., Z.A.R. and T.N.G.A.; writing—review
and editing, E.E., T.W., Z.A.R. and T.N.G.A.; supervision, T.N.G.A.; funding acquisition, T.N.G.A. All
authors have read and agreed to the published version of the manuscript.
Funding: This research was funded by National Science Foundation, grant number 2048221.
Data Availability Statement: Data are contained within the article.
Conflicts of Interest: The authors declare no conflicts of interest.
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