Critical Behavior of Subcellular Density Organization During Neutrophil

Activation and Migration

SANDRA M. BAKER-GROBERG,1 KEVIN G. PHILLIPS,1 LAURA D. HEALY,2 ASAKO ITAKURA,2

JULIANA E. PORTER,3 PAUL K. NEWTON,3,4,5 XIAOLIN NAN,1 and OWEN J. T. MCCARTY1,2,6

1Department of Biomedical Engineering, School of Medicine, Oregon Health & Science University, Portland, OR 97239, USA;2Department of Cell, Developmental & Cancer Biology, Oregon Health & Science University, Portland, OR 97239, USA;

3Department of Aerospace and Mechanical Engineering, Viterbi School of Engineering, University of Southern California, LosAngeles, CA 90089, USA; 4Department of Mathematics, University of Southern California, Los Angeles, CA 90089, USA;

5Norris Comprehensive Cancer Center, Keck School of Medicine, University of Southern California, Los Angeles, CA 90089,USA; and 6Division of Hematology and Medical Oncology, School of Medicine, Oregon Health & Science University, Portland,

OR 97239, USA

(Received 22 April 2015; accepted 26 May 2015; published online 3 June 2015)

Associate Editor Michael R. King oversaw the review of this article.

Abstract—Physical theories of activematter continue to providea quantitative understanding of dynamic cellular phenomena,including cell locomotion. Although various investigations ofthe rheology of cells have identified important viscoelastic andtraction force parameters for use in these theoretical approaches,a key variable has remained elusive both in theoretical andexperimental approaches: the spatiotemporal behavior of thesubcellular density. The evolution of the subcellular density hasbeen qualitatively observed for decades as it provides the sourceof image contrast in label-free imaging modalities (e.g., differ-ential interference contrast, phase contrast) used to investigatecellular specimens. While these modalities directly visualize cellstructure, they do not provide quantitative access to thestructures being visualized. We present an established quantita-tive imaging approach, non-interferometric quantitative phasemicroscopy, to elucidate the subcellular density dynamics inneutrophils undergoing chemokinesis following uniform bacte-rial peptide stimulation. Through this approach, we identify apower law dependence of the neutrophil mean density on timewith a critical point, suggesting a critical density is required formotility on 2D substrates. Next we elucidate a continuum lawrelating mean cell density, area, and total mass that is conservedduring neutrophil polarization and migration. Together, ourapproach and quantitative findings will enable investigators todefine the physics coupling cytoskeletal dynamics with subcel-lular density dynamics during cell migration.

Keywords—Chemokinesis, Neutrophil, Active matter,

Rheology, Subcellular density, Quantitative phase microscopy,

Motility.

ABBREVIATIONS

NA Numerical apertureDIC Differential interference contrastNIQPM Non-interferometric quantitative phase

microscopyFWHM Full-width at half maximumBSA Bovine serum albuminPBS Phosphate buffered saline

INTRODUCTION

Neutrophils, the most plentiful white blood cellpopulation, are a central component of the innateimmune system. These highly mobile first-respondersto infection actively search out, recognize, and destroybacteria. Neutrophil locomotion is controlled byexternal cues of mechanical, electrical, and chemicalorigin.19,23,27 These stimuli activate molecular signalingnetworks that dynamically remodel the cellularcytoskeleton and its focal adhesions to the surroundingmicroenvironment to enable directed motility.20

The molecular basis of neutrophil locomotion fol-lowing bacterial exposure is well characterized: uponstimulation through activation of G-protein coupledreceptors, neutrophils extend membrane protrusions inthe direction of the attractant through Rac mediatedfilamentous actin assembly at the leading edge (LE) ofthe cell. At the trailing edge (TE), membrane con-traction is regulated through RhoA stimulation ofROCK and myosin light chain II (Fig. 1). Spanning

Address correspondence to Sandra M. Baker-Groberg, Depart-

ment of Biomedical Engineering, School of Medicine, Oregon Health

& Science University, Portland, OR 97239, USA. bakersa@ohsu.edu

Sandra M. Baker-Groberg and Kevin G. Phillips have equallycontributed as first authors.

Cellular and Molecular Bioengineering, Vol. 8, No. 4, December 2015 (� 2015) pp. 543–552

DOI: 10.1007/s12195-015-0400-0

1865-5025/15/1200-0543/0 � 2015 Biomedical Engineering Society

543

the entire cell body is a microtubule network (MN)that serves as both a sink and delivery system forcytoskeletal effectors of the LE and TE of the neu-trophil.15 The crosstalk among molecular componentsof the LE, TE, and MN are required for the coordi-nation of cellular shape change and motility.8,11

Pharmacologic perturbations of this circuitry haverevealed that the LE recruits the SCAR/WAVE com-plex, which both shapes the actin architecture andprovides a scaffold for inhibitors of RhoA/myosincomponents specific to the TE.26 In tandem, the TE ofthe cell opposes actin-based membrane protrusion.25

The MN delivers Rho family guanine nucleotideexchange factors to locally activate Rho/myosin com-ponents of the TE, while actin polymerized at the LEphysically excludes the MN.4,10 Together, thesemolecular events give rise to cell-wide coordination ofmembrane protrusions, retractions, and adhesions tobring about a polarized cell shape (Fig. 1) and directedcellular motion.7

The cell-level physics resulting from the collectivemolecular machinery governing cell motility continuesto be established.12–14 Studies of subcellular granuledynamics in response to physical perturbations haverevealed coexisting viscoelastic states within theneutrophil: the TE of the neutrophil was found to bemore solid-like with a structural-dampening rheology

compared to the less stiff, less viscous, and more fluid-like LE of the neutrophil.28 Further, neutrophil mem-brane tension has been shown to play a central role inthe constraint of actin-rich pseudopod formation tothe LE of motile neutrophils while extracellular matrixrigidity and concentration of available adhesive ligandsalters neutrophil morphology, spreading area, andmotility.6,22,23 In concert, traction force microscopyhas provided evidence that contraction forces arecentered at the TE of the neutrophil and these forcessqueeze intracellular material forward—causing a netflow of subcellular components towards the fluid-likeLE of the neutrophil.21

Despite knowledge that neutrophil motility requiresthe redistribution of cytoskeletal and intracellularcomponents, a quantitative understanding of the effectof these dynamics on the organization of the subcellularmass-density of neutrophils has remained elusive.Understanding the evolution of the subcellular densityis of primary importance in building a deterministicmodel of cellular motion. Label-free imaging modali-ties, such as differential interference contrast (DIC) andphase contrast, have been utilized for decades to quali-tatively investigate the subcellular density of biologicalspecimens.9,17 Although these label-free imaging tech-niques offer direct visualization of cell structure, theyprovide minimal quantitative information of the speci-mens. The direct measurement of the cell density withinany cell type of interest through label-free means willenable investigators to uncover new physical lawsdescribing the coupling of cytoskeletal dynamics withsubcellular density dynamics during cell migration.

Here, we present measurements of the spatialorganization of the subcellular neutrophil density usingnon-interferometric quantitative phase microscopy(NIQPM). We made use of label-free NIQPM infixed-cell assays over 6 time points to capture thespatiotemporal dynamics of subcellular density orga-nization in polarizing neutrophils undergoingchemokinesis following exposure to the bacterial pep-tide, formyl-Met-Leu-Phe (fMLP). We demonstratethat subcellular density decreases in a power-lawdependent fashion as neutrophils become activated,and that a critical density is reached when neutrophilspolarize and begin chemokinesis. Finally, we identify acontinuum law of mass conservation that links area,mean density, and total dry mass that holds for resting,activated, and motile neutrophils. These relationshipscan be utilized in multi-scale theoretical approaches tolink cell-wide density behaviors to the micro dynamicsof cytoskeletal and membrane motion underlyinglocomotion.

Our quantitative findings demonstrate a new meansto passively monitor the rheology of neutrophil loco-motion and can serve as a means to inform physical

FIGURE 1. Cytoskeletal dynamics underlying neutrophilmigration. DIC imagery (first row), phospho-myosin lightchain II (pMLC) staining (second row; shown in green), andactin staining (third row; shown in red) of neutrophils prior tofMLP stimulation (left) and 180 s after fMLP stimulation (right).

BAKER-GROBERG et al.544

theories of cell motion through the incorporation ofmass conservation and the critical behavior of celldensity required for the dynamical transition frombasal to activated and motile cell states. The mea-surement techniques in this study are readily accessibleto other researchers as the NIQPM approach and DICrely only on a standard optical microscope.16

MATERIALS AND METHODS

Neutrophil Isolation, Preparation for Imaging, andAntibody Labeling

Human venous blood was collected from healthyvolunteers into citrate–phosphate-dextrose (1:7 vol/vol).Written informed consent was obtained from studyparticipants, and the Oregon Health & ScienceUniversity Institutional Review Board approved theprotocol. Blood was layered over equal volume ofPolymorphprep (Fisher Scientific, Pittsburgh, PA) andcentrifuged at 500g for 45 min at 18 �C. The lower bandcontaining polymorphonuclear leukocytes was collectedand washed with Hank’s balanced salt solution (HBSS;Life Technologies, Grand Island, NY) by centrifugationat 400g for 10 min. To remove contaminating red bloodcells, the pellet was resuspended in sterile H2O for 30 s,followed by the immediate addition of 10 9 PIPESbuffer (250 mM PIPES, 1.1 mM NaCl, 50 mM KCl;pH 7.4). After centrifugation at 400 g for 10 min, thepellet was resuspended in HBSS containing 2 mMCaCl2, 2 mM MgCl2 and 1% w/v BSA.

Acid-washed 22 mm circular coverslips (# 1.5, 0.16–0.18 mm; Fisher Scientific) were coated withfibronectin (20 lg/mL; Sigma-Aldrich, St. Louis, MO)for 1 h and blocked with heat-inactivated BSA (1% w/v, Sigma-Aldrich) for 1 h. Purified human neutrophilswere incubated at 37 �C for 30 min on the coverslips.The buffer in the well was aspirated, and buffer con-taining 10 nM fMLP (Sigma-Aldrich) was added.Neutrophils were then fixed in 4% paraformaldehydeevery 20 s. Coverslips were mounted on microscopeslides with Fluoromount-G (SouthernBiotech, Birm-ingham, AL) for visualization.

For fluorescence studies, actin and phospho-myosinlight chain II (pMLC) staining was carried out aspreviously described.8 Briefly, following fixation, cellswere permeabilized with methanol. Cells were stainedwith anti-myosin light chain2 pSer19 (3675) (1:200dilution; Cell Signaling, Boston, MA), and anti-actin(1:100 dilution; Sigma-Aldrich) in blocking bufferovernight at 4 �C. Secondary antibodies conjugatedwith AlexaFluor 488 or TRITC (1:1000; Life Tech-nologies) in blocking buffer were added and incubatedfor 2 h in the dark.

Quantification of Subcellular Density:Non-interferometric Quantitative Phase Microscopy

(NIQPM)

We have previously characterized and made availablethe protocol and computer implementation ofNIQPM toquantify cell structure using a standard transilluminationmicroscope.16 Briefly, cellular density of neutrophils wasquantified using NIQPM on an upright optical micro-scope (Axio Imager; Carl Zeiss, Gottingen, Germany)equipped with a 9 63/1.4 numerical aperture (NA) oilimmersion objective and an air-coupled condenser lensprovidingKohler illumination at anNAof 0.1. Through-focus bright field imagery of the cells was acquired usingan illumination wavelength of 540 ± 20 nm. Bright fieldimages of the sample field were recorded with a charge-coupled device camera (AxioCam MRc5 12-bit camera;Carl Zeiss) under software control by Slidebook 5.5(Intelligent Imaging Innovations,Denver, CO). Through-focus images were acquired in 0.1 lm increments over a10 lm range along the optical axis. These images formedthe input to a transport of intensity equation (TIE) solverto extract phase of transmitted waves through the samplefrom intensity measurements.5

To fix the free parameters of the TIE solver andestablish the dynamic range of the method we performedmeasurements on polystyrene spheres whose sizes werevaried from below the diffraction limit of our system, upto 9.8 microns in diameter. We then ensured agreementbetween our measurements of phase with those deter-mined from the specified sphere diameters from themanufacturer (Figure S1H). We next established thenoise floor of NIQPM to verify that this approach issufficiently sensitive to quantify small features of cellularspecimens ranging in size from pseudopodia to the cellbody (Figure S1).We determined the noise floor throughmeasurements on a blank substrate with our embeddingmedia and glass coverslip overlaid. We found a full-width at half maximum (FWHM) phase fluctuations~0.02 radian enabling a density measurement of 0.01pg/lm2 as the smallest value on our density scale,(Figure S1A-C). This noise floor is sufficient to resolvetypical pseudopodia structures whose thickness rangesfrom 100 to 200 nm and possess a refractive index vari-ation of 0.01–0.02 about the background.

Knowledge of the phase of transmitted wavesthrough the sample enables the enumeration of theprojected mass density, defined as the sum of the three-dimensional density along the optical axis of themicroscope, through the following relationship,16,18

q x; yð Þ ¼ k/ðx; yÞ2pa

pg=lm2� �

: ð1Þ

Here qðx; yÞ denotes the projected mass density,/ðx; yÞ is the phase of the transmitted waves, k is the

Critical Behavior of Subcellular Density Organization 545

illumination wavelength, and a is the specific refractionincrement of the cell solids (~0.2 mL/g). The correctmass density map is verified by computing the digitalDIC image as previously described, (Figure S2).2,3,16

To examine cellular dry mass density parameters,histograms of the subcellular density maps were con-structed with bin sizes of 0.01 over the range of0–2 pg/lm2 for each cell.3 For each time point wedetermined: total dry mass, dry mass density mean,and standard deviation of the dry mass density.

High Numerical Aperture (NA) 2D & 3D DIC ImageSegmentation to Quantify Cell Area, Height,

and Approximate Cell Volume

3D Kohler illuminated DIC imaging was performedon an upright optical microscope (Axio Imager; CarlZeiss) equipped with a 9 63/1.4 NA oil immersionobjective with an air-coupled NA = 0.9 condenserlens as previously described.16 DIC images of thesample field were recorded with a charge-coupleddevice camera (AxioCam MRc5 12-bit camera; CarlZeiss) under software control by Slidebook 5.5.Through-focus images were acquired in 0.1 lm incre-ments over a 20 lm range along the optical axis.

DIC images were converted to binary imagesthrough the isolation of fluctuations in the DIC signalintensity as previously described.1,17 Briefly, DIC axial-intensity profiles were transformed according to thefollowing procedure: letting IDICðx; y; zÞ denote theDIC image cube intensity, for a particular choice of xand y we exaggerate DIC intensity fluctuations andthus enhance background rejection through

Iðx; y; zÞ ¼ d

dzð�IDICðzÞ � hIDICiÞ

� �2ð2Þ

in which �IDICðzÞ denotes the 5-point moving average ofIDICðx; y; zÞ over the axial (z) dimension. IDIC is thecube-wide mean of the DIC intensity. Lastly, to con-struct binary cross-sectional image cubes, we define r,the standard deviation of Iðx; y; zÞ, and l the mean ofI x; y; zð Þ. I x; y; zð Þ is then thresholded such that ifI x; y; zð Þ>ð2r� lÞ, Iðx; y; zÞ is set to 1 otherwise,I x; y; zð Þ is set to 0 resulting in binary images, as seen inFig. 4b.

In the final binary images, at each x position in theimage cube, cross-sectional images were summed alongthe y-direction to yield a Gaussian-like profile alongthe optical axis (Fig. 4c). The FWHM of the Gaussian-like profiles was used to establish the mean cell heightfor each time point explored in this study (Fig. 4d).Cell area was determined from outlining the cells in thecentral focal plane of the image cube (Fig. 4e). Acustom written MATLAB program was used to

outline cells at each time point and align their perime-ters along their major axis (Fig. 2b). To approximatecell volume we multiplied cell area and mean cell height(Fig. 4f). This approach was validated on (N = 50)resting neutrophils whose volumes were determined tobe 244 ± 24 fL in agreement with our previous resultsand those obtained by other investigators using micro-pipette aspiration.17,18,24

We remark that these optical approaches using ‘‘off-the-shelf’’ instruments are suitable for fixed samples.Slow z-stack acquisition time on commercial scopes,due to translation of the entire sample stage as opposedto just the objective lens, currently limits the investiga-tion of phenomena faster than roughly 1 frame/min.Further, diffraction effects restrict the utility of NIQPMand DIC to objects ranging in size from 0.2 up to 10 and20 lm in diameter, respectively. Hence, the specimenand its associated time dynamics of interest must meetcertain size and temporal constraints to enable the useof the methods used in this study.

Statistical Analysis

The Jarque–Bera test was used to evaluate nor-mality of all parameters. One-way analysis of variancewith Bonferonni post hoc correction was used to assessstatistical significance among parameters across mul-tiple normally distributed cell parameters. The Krus-kal–Wallis test was used to assess significance amongnon-normally distributed parameters. p values of 0.05or less were considered statistically significant. At eachtime point N = 40 cells were evaluated. All values arereported at mean ± standard deviation unless other-wise noted. Fits to the data are performed on averagequantities at each time point.

RESULTS

Characterization of Neutrophil Morphology FollowingBacterial Peptide Stimulation

Upon engagement of bacterial peptide receptors,neutrophils develop a distinct front or LE which is richin filamentous actin, called the lamellipodium, and aback or trailing edge, called the uropod, that is rich inacto-myosin complexes. The subcellular organizationof these elements into a polarized geometry enables thecell to convert cytoskeletal chemical reactions intocellular motion. To study the geometric properties ofneutrophils resulting from activation in response toexposure to the bacterial peptide fMLP, we utilized afixed cell assay in which purified neutrophils onfibronectin-coated cover glass were treated with auniform distribution of fMLP in solution before fixa-

BAKER-GROBERG et al.546

tion with paraformaldehyde. Neutrophils in parallelexperiments were fixed in 20-s intervals over a two-minperiod. We visualized neutrophils using DIC micro-scopy with high NA Kohler illumination.

The perimeter and area of each cell was determinedby tracing DIC images of the cells at each time point.

To investigate aspect ratio alterations in the cells, theextracted tracings were numerically fit to an ellipse todetermine the major and minor semi-axes lengths ofthe cell shape (Fig. 2a). Tracings were aligned tovisualize the ensemble behavior of the cells at eachinstant with a mean cell shape computed from the

FIGURE 2. Symmetry breaking of migrating neutrophils. (a) DIC imagery of neutrophils fixed with 4% paraformaldehyde at 0, 20,40, and 60 s after fMLP stimulation. (b) Alignment of neutrophil perimeter along semi-major axis at 0, 20, 40, and 60 s after fMLPstimulation. (c) Quantification of neutrophil aspect ratio, (d) perimeter [lm], (e) and cell area [lm2] at 20 s intervals after fMLPstimulation. *p value <0.05 compared to t< 60 s. (f) Scatter plot of area versus perimeter of measured neutrophils (blue) andprofiles of a circle (black) and ellipses with aspect ratios of 1.35 (cyan), 1.45 (red), and 2.15 (green). Error bars denote standarddeviation along each dimension.

Critical Behavior of Subcellular Density Organization 547

ensemble measurements (Fig. 2b). Symmetry wasquantified through the aspect ratio, defined as the ratioof the major and minor axis lengths. As seen in Fig. 2c,fMLP induced activation resulted in statistically sig-nificant increases in the aspect ratio within the first20 s; however, at subsequent times following fMLPstimulation, statistically significant alterations werenot observed, suggesting that symmetry breakingoccurs early in the evolution of cytoskeletal remodelingfollowing activation.

To elucidate the geometric organization of neu-trophils during activation and migration, we investi-gated the relationship of neutrophil area and perimeter.For reference we plot the area-perimeter relationshipsfor a circle and ellipses with aspect ratios of 1.35 and1.45. Upon plotting neutrophil area (ordinate) againstperimeter (abscissa), we found that neutrophil perimeteroutpaces increases in the area, due to non-uniformmembrane protrusions, and as a result, possesses anarea—perimeter relationship resembling an ellipse witha higher aspect ratio, ~2.15. This feature of neutrophilgeometry was conserved across the time points (Fig. 2f).

Critical Behavior of Subcellular Density OrganizationDuring Neutrophil Activation and Migration

It is known that DIC image contrast arises from thegradient of the phase of transmitted waves through thesample. As Eq. (1) relates, the phase is linearly pro-portional to the projected mass density, hence the DICimage contrast is linearly related to the derivative ofthe density along the shear direction of the Wollastonprisms utilized in the DIC optics.17 Further, the DICimagery in Fig. 2a demonstrates the evolution of theneutrophil geometry but does not provide quantitativeaccess to density information. To address this need,and to quantify potential changes in neutrophil sub-cellular density, we employed NIQPM in tandem withDIC imagery to characterize both cellular density andgeometric architecture following fMLP stimulation.

NIQPM is carried out through an image acquisitionstep and post processing procedure in which through-focus bright field imagery, under low NA Kohler illu-mination conditions, are inputted into a TIE solver toextract phase and then mapped through Eq. (1) to theprojected mass density.5 The correct density map isensured through a self-consistency procedure in which adigital DIC image is numerically determined from therecovered density map and compared to the true DICimage.3 This procedure was carried out on all cells at alltime points in this study; example comparisons of digitalDIC and DIC images are presented in Figure S2.

We observed a redistribution of intracellular com-ponents of the neutrophil following fMLP stimulation(Fig. 3). Image segmentation and histogram analysis

indicated that the sub-cellular density shifted from askewed distribution peaked at ~0.38 pg/lm2 to a moreeven distribution peaked about ~0.18 pg/lm2. More-over, computing the spatial mean of the projected massdensity over the extent of each cell, denoted q tð Þ, ateach time point revealed a power law dynamics(r2 = 0.99) given by Eq. (3):

q tð Þh i ¼ C tc�ttc

h i12þD; t<tc;

q tð Þh i ¼ D; t>tc:ð3Þ

wherein the basal level mean density, q t ¼ 0ð Þ ¼h iqodecreased from qo = C + D = 0.28 pg/lm2 toqc = D = 0.17 pg/lm2 over the course of t ¼ tc = 68 s(Fig. 2c). This decreased density persisted for t>tc in astatistically significant way (p<0.05) with respect to alltimes points t<tc. The maintenance of this persistentcritical density suggests a specific density thresholdrequired for neutrophil chemokinesis.

Continuum Law of Mass Conservation in Basal,Activated, and Motile Cell States

In the absence of staining for specific cellular com-ponents, label-free microscopy has largely been limitedto the 2D measurement of cell geometry and motility.Here we sought to elucidate potential relationshipsbetween subcellular density metrics, including totalmass and mean density quantified using NIQPM, and2D geometric features of neutrophils. We investigatedcorrelations among area, total mass, and mean densityat each time point.

We observed a linear correlation (r2 = 0.9) amongmass, M, and mean spatial density, q, whose slope wasgiven by the average of cell area, A. Interestingly, thisfinding was observed at each time point (Fig. 3d). Thisresult suggests a simple linear continuum law couplingthe cellular area, mean density, and total cell mass

M ¼ A tð Þ q tð Þh i; ð4Þ

independent of activation status.We further validated this simple law by investigating

fits to the data based on the variation of Eq. (4) givenby

AðtÞ ¼ M= q tð Þh i: ð5Þ

Using Eq. (5) we ascertained if we could fit scatterplots of area versus mean density for the mean neu-trophil mass. The results of this fit demonstrate theinverse density dependence of area (Fig. 3e) and theconservation of mass; the fit line denotes a mass of21.0 ± 3.8 pg (r2 = 0.9), over the time points of ourinvestigation.

BAKER-GROBERG et al.548

Characterization of Cell Height, Area, and Volumeof Stimulated Neutrophils

To determine if three-dimensional geometric alter-ations accompany the redistribution of neutrophilcytoskeletal and intracellular components duringpolarization, we utilized high NA through-focus DICimagery to visualize the volumetric extent of each cell.Figure 4a presents cross sectional DIC images ofneutrophils with the borders identified using fluctua-tion-based image segmentation of the DIC signal(Fig. 4b).17 Mean cell height was quantified from thenumerically determined cell boundaries (Fig. 4c).

Following fMLP-induced activation, cell heightdecreased in a power law dependent fashion, h ~ t�0.18,from an initial cell height of 3.6 ± 0.3 lm decreasing to2.1 ± 0.3 lm, at t = 120 s. In parallel, area increasedin a power law dependent fashion, A ~ t0.25, from68.7 ± 8.2 to 139.4 ± 18.9 lm2 (Fig. 2d). Cellular vol-ume, approximated by taking the product of mean cellheight and cell area, was found to be conserved fortimes t ‡ 20 s, while a statistically significant increase involume was observed when comparing t = 0 andt = 20 s treatment groups (Fig. 4f). We next ascer-tained to what degree density alterations were correlated

FIGURE 3. Neutrophil subcellular density dynamics. (a) Projected subcellular density map of neutrophils fixed with 4%paraformaldehyde at 0, 20, 40, and 60 s after fMLP stimulation. (b) Histograms of subcellular density of neutrophils fixed at 0, 20,40, and 60 s after fMLP stimulation. (c) Piece-wise continuous power law fit of subcellular density organization during neutrophilactivation and migration. Projected subcellular density versus (d) mass and (e) area of neutrophils fixed at 0 (blue), 20 (green), 100(cyan), and 180 (black) seconds after fMLP stimulation.

Critical Behavior of Subcellular Density Organization 549

FIGURE 4. Three-dimensional analyzes of neutrophil geometry. (a) Representative cross-sectional DIC images with a Kohlerillumination of NA = 0.9 of neutrophils fixed at 0, 20, 40, and 60 s after fMLP stimulation. (b) Binary image segmentation of crosssectional images in (a). (c) Transverse sum of binary images in (b) yielding a Gaussian-like distribution along the optical axis. Thefull width at half max (FWHM) is denoted by gray circles and lines in (a) and (b) correspond to the axial positions of the FWHM.(d) Scatter plot of mean projected density versus mean height of neutrophils fixed at 0 (blue), 40 (green), and 100 (cyan) secondsafter fMLP stimulation. Linear fit line denotes q tð Þh i ¼ 0:07ð Þ pg

fl

h ihh i½lm� þ 0:01½pg=lm2�. (e) Quantification of mean neutrophil height

at 20 s intervals after fMLP stimulation. *p value<0.05 compared to t = 0. **p value <0.05 compared to 20 £ t £ 60 s. (f) Approximateneutrophil volume at 20 s intervals after fMLP stimulation determined from the product of mean neutrophil height and area.*p value <0.05 in comparison to time points ‡20 s.

BAKER-GROBERG et al.550

with the three-dimensional geometry of the neutrophil.Scatter plots of mean projected dry mass density versuscell height revealed a linear relationship (Fig. 4d) thatenabled the quantification of the mean cell density.Letting C denote the spatial average of the threedimensional density with units pg/fL, and h denotingthe mean cell height in lm, we find that the qh i vs. h iswell described by the one parameter fit (r2 = 0.9)

qh i ¼ Ch i hh i þ 0:02: ð6Þ

Through this linear fit we observe that Ch i = 0.07pg/fL, independent of activation state. This value is inkeeping with our previous findings.17,18

DISCUSSION

Neutrophils serve as frontline defenders of the bodyand are a central component of the innate immuneresponse. Their dynamic recruitment to sites of infectionis a multistep process requiring rolling and adherence tothe endothelial wall of the vasculature, followed bytransmigration through the endothelial wall, andchemotaxis to the site of infection. Lastly neutrophilsphagocytose bacteria or release oxidative agents to killpathogens. Underlying these events is a host of differentchemical signaling events that are altered by thephysicochemical cues of the tissue microenvironment.The physics of neutrophil locomotion is still beingestablished with efforts currently centered on the inves-tigation of migration speed and neutrophil geometry.

Interestingly, the alteration of the neutrophil densityhas been observed for many years—owing to its con-tribution to image contrast in label-free imagingmodalities such as DIC microscopy. While DICapproaches have enabled the geometric characteriza-tion of neutrophil behaviors spanning states of acti-vation to migration, the corresponding evolution of thesubcellular density has remained quantitatively out ofreach. This time and space sensitive quantity is cur-rently omitted in theories of active matter that seek tolink cytoskeletal processes of actin (de)polymerizationto cell motion. A more complete physical theory ofneutrophil locomotion will link the molecular levelfunction of actin/myosin, and their effectors, todownstream cell density alterations at the micron scale.

Here we present the use of NIQPM, an accessibleoptical technique, to measure density alterations inmotile neutrophils. We quantify physical processesthat occur in parallel with the crosstalk amongmolecular components of the LE, TE, and MNrequired for the coordination of cellular shape changeand motility. We found that the mean subcellular

density decreases in a power-law dependent fashion asneutrophils become activated, and that a critical den-sity is reached when neutrophils polarize and undergolocomotion. Further, we identify a continuum law ofmass conservation that links area, mean density, andtotal dry mass that holds for resting, activated, andmotile neutrophils. Lastly, we connect three-dimen-sional alterations of cell geometry to subcellular den-sity dynamics by demonstrating the linear relationshipof mean cell density with cell height. Together thesefindings illustrate cell-wide laws governing neutrophildynamics that are currently missing in theories of cel-lular locomotion.

Our study elucidates fundamental constraints on thecollective material organization of the cell through therelationship of cell density, area, and volume. Thesefindings provide a quantitative guide for the ensembledynamics arising from many-body theories governingsmall-scale dynamics of the cytoskeleton, the cellmembrane, and the other components of the cell.These relationships can be utilized in multi-scale the-oretical approaches to link cell-wide density behaviorsto the micro dynamics of cytoskeletal motion under-lying locomotion.

ELECTRONIC SUPPLEMENTARY MATERIAL

The online version of this article (doi:10.1007/s12195-015-0400-0) contains supplementary material,which is available to authorized users.

ACKNOWLEDGMENTS

This work was supported by the National Institutesof Health under Grant Nos. U54CA143906 (K.G.P,O.J.T.M, P.N.) and R01HL101972 (O.J.T.M.), by theAmerican Heart Association (13EIA12630000 toO.J.T.M.), by a Medical Research Foundation EarlyClinical Investigator Award (K.G.P.), and by theOregon Clinical and Translational Research Institute(OCTRI; UL1 RR024140 to L.D.H). S.M.B is aWhitaker International Research Fellow and A.I. is aVertex Scholar. J.E.P is supported by the USC-VSOEUndergraduate Merit Research Program and a USC-Zumberge Foundation Award.

CONFLICT OF INTEREST

S.M.B., K.G.P, L.D.H., A.I., J.E.P., P.K.N., X.N.,and O.J.T.M. declare that they have no conflicts ofinterest.

Critical Behavior of Subcellular Density Organization 551

ETHICAL STANDARDS

All human subjects research was carried out inaccordance with institutional guidelines approved bythe Oregon Health & Science University InstitutionalReview Board. No animal studies were carried out bythe authors for this article.

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