ArticleNovember 2, 2025

Interfacial Energy Balance Governs Initial Cell Spreading Dynamics
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Jifeng Ren
Jifeng Ren
School of Biomedical Engineering, Capital Medical University, Beijing 100069, China
Beijing Key Laboratory of Fundamental Research on Biomechanics in Clinical Application, Capital Medical University, Beijing 100069, China
Department of Biomedical Engineering, College of Biomedicine, City University of Hong Kong, Hong Kong 999077, China
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Shuhuan Hu*
Shuhuan Hu
Department of Biomedical Engineering, College of Biomedicine, City University of Hong Kong, Hong Kong 999077, China
BGI-Shenzhen, Shenzhen,Guangdong 518083, China
*Email: [email protected]
More by Shuhuan Hu
https://orcid.org/0000-0002-4163-1242
Yi Liu
Yi Liu
Department of Biomedical Engineering, College of Biomedicine, City University of Hong Kong, Hong Kong 999077, China
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Siping Huang
Siping Huang
Department of Biomedical Engineering, College of Biomedicine, City University of Hong Kong, Hong Kong 999077, China
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https://orcid.org/0000-0001-8721-5255
Jingqian Zhang
Jingqian Zhang
Department of Biomedical Engineering, College of Biomedicine, City University of Hong Kong, Hong Kong 999077, China
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https://orcid.org/0009-0008-6016-2390
Qi Gao
Qi Gao
Department of Biomedical Engineering, College of Biomedicine, City University of Hong Kong, Hong Kong 999077, China
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King Wai Chiu Lai
King Wai Chiu Lai
Department of Biomedical Engineering, College of Biomedicine, City University of Hong Kong, Hong Kong 999077, China
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https://orcid.org/0000-0001-5002-2273
Raymond H. W. Lam*
Raymond H. W. Lam
Department of Biomedical Engineering, College of Biomedicine, City University of Hong Kong, Hong Kong 999077, China
City University of Hong Kong Shenzhen Research Institute, Shenzhen Guangdong 518172, China
*Email: [email protected]. Phone: +852-3442-8577. Fax: +852-3442-0172.
More by Raymond H. W. Lam
https://orcid.org/0000-0002-5188-3830

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Langmuir

Cite this: Langmuir 2025, 41, 44, 29494–29501

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https://doi.org/10.1021/acs.langmuir.5c03250

Published November 2, 2025

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Abstract

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Cell spreading is a fundamental process in physiological and pathological contexts, including tissue formation, wound healing, and cancer cell extravasation. Previous studies have examined biophysical mechanisms governing early spreading (around 1–10 min) while biomolecular processes also begin to emerge, yet initial spreading in an even earlier stage (<1 min) remains largely unexplored. Here, we present a deterministic model based on interfacial energy balance─integrating strain energy, surface adhesion energy, and viscous dissipation─to quantitatively describe initial spreading dynamics. Using interference reflection microscopy (IRM), we characterize spreading behaviors of three breast cell lines (MCF-10A, MCF-7, and MDA-MB-231) on extracellular matrix-coated substrates. Model predictions, incorporating biomechanical and biochemical parameters measured through IRM and atomic force microscopy (AFM), show strong agreements with experimental observations. This work provides a universal framework for understanding initial spreading and offers insights into strategies to regulate initial cell spreading, with potential applications in cancer treatment and tissue engineering.

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Introduction

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Cell spreading plays a critical role in physiological and pathological processes, including tissue formation, wound healing, inflammation, and cancer cell extravasation. (1−4) In the earliest stage, initial spreading determines the yield of integrin binding, focal adhesion formation, actin filament extension, and subsequent cell spreading and migration.

Models describing cell spreading have been developed over the past few decades. Cuvelier et al. categorized the process into early spreading (1–10 min) and late spreading (>10 min), proposing power-law relationships that incorporate viscous dissipation of the cell cortex and cell–ECM adhesion (governed by effects such as integrin-ligand binding) to predict early spreading behaviors. (5) Frisch and Thoumine modeled late spreading as a viscous droplet wetting process to estimate the cell–substrate contact radius. (6) However, these models presume at the beginning of cell spreading a noticeable cell–substrate attachment area, which is not guaranteed. Biological responses over the attachment area also initiate during early spreading but not initial spreading. For example, the mechanosensitive protein paxillin begins to aggregate near integrins along the perimeter of the cell–substrate contact area starting approximately 3–5 min of cell spreading. (7,8) This suggests the dynamics of initial spreading without the involvement of biological responses can be different for those of early spreading. Hence, the initial spreading phase (<2 min) is required to further investigated to better understand the roles of the key biophysical properties governing initial spreading and formation of the attachment area.

Recent studies have explored the influence of biophysical cues on cell spreading. For example, coatings of various extracellular matrix proteins (ECMs) have been applied to modulate cell–substrate adhesion strength via integrin clustering, thereby affecting cell spreading behaviors. (8) Substrate stiffness has also been shown to affect late spreading, involving both the spreading rate and area. (9,10) Additionally, cell viscoelasticity plays a significant role in cell spreading, as cells deform under external stresses. (11,12) Prior to attachment and spreading on substrates, a cell can be modeled as a spherical soft-shell structure, (13) with its membrane contributing primarily to elasticity and its cytoplasmic liquid to viscosity. While previous studies have analyzed individual biophysical factors in early and late spreading, a comprehensive analytical framework for initial spreading, along with systematic parametric studies, remains lacking.

In this paper, we present a first-principles model based on interfacial energy balance to describe the dynamics of the initial cell–substrate contact area. The model integrates strain energy, surface adhesion energy, and viscous dissipation. The model can reveal the roles of a more comprehensive set of biophysical properties, including whole-cell elasticity and cell–substrate adhesion strength, which are sometimes overlooked. (5) To validate our approach, we conduct parametric studies by applying an interference reflection microscope (IRM) (14) to characterize initial spreading dynamics under various conditions. We examine three breast cell lines (MCF-10A, MCF-7, and MDA-MB-231), modulating cell–substrate binding strength through different ECM protein coatings and substrate stiffness through different substrate materials. Average cell properties (body size, viscosity, and elastic modulus) are measured by our previously developed microfluidic deformability cytometer, (15,16) while viscoelastic properties of individual cells are measured using atomic force microscopy (AFM) for further analysis. In essence, this work provides insights into how surface conditions can modulate cell growth and morphology on different surfaces for potential applications, such as cancer treatment and tissue engineering.

Results and Discussion

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Model

Here, we hypothesize that initial cell spreading dynamics is a deterministic process governed by the biomechanical energy-balanced interactions between cells and ECMs, (6,17) as shown in Figure 1a. Briefly, cell deformation during initial spreading can be expressed by the radial displacement of this first contact point (δ). The cortical strain energy (ΔU_s) corresponds to the cell deformation should vary with δ; and the viscous dissipation (W_v) cell deformation should be a function of δ̇ and the underlying shear strain rates (γ̇) generated in the cytoplasm. Cell–substrate adhesion energy change (ΔU_b) is a function of the cell–substrate contact area (A_c), which increases with δ. We have derived dynamic A_c as a function of time (t) and other key factors based on the energy balance between ΔU_b, ΔU_s, and W_v:

Δ U_{b} = Δ U_{s} + W_{v}

(1)

Figure 1. Visualization of initial cell spreading. (a) Key parameters involved in the initial cell spreading process. (b) Configuration of IRM using a laser scanning confocal microscope. (c) Glass and PDMS substrates coated with fluorescent fibronectin. (d) IRM images of an initial spreading MCF-10A cell on fibronectin-coated glass (upper) and their cross-sectional views (lower, processed with intensity inversion and thresholding for better visualization), captured as 10s, 60s, and 300s. All other cases are available in Figure S1. (e) Transient spreading area (A_c) of MCF-10A cells spreading on fibronectin-coated glass substrates. Gray lines represent single-cell dynamics; and the black line represents the average A_c (t). Error bars are standard errors of the mean. All cases with N numbers are available in Figure S2. Scale bar: 10 μm.

ΔU_b and ΔU_s can be calculated by integrating the corresponding effective cell–substrate adhesion force (F_b) and compressive force to the substrate (F_s), respectively, over the maximum radial displacement (δ) of the cell. The rate of viscus dissipation (

{\dot{W}}_{v}

) is calculated based on effects of strain rate over the cytoplasmic region.

ΔU_b is approximated as

Δ U_{b} \approx ζ_{b} {\cdot A}_{c}

(2)

where ζ_b is the cell–substrate adhesion energy per unit contact area and the instantaneous cell spreading area is denoted as A_c. ζ_b summarizes cell-ECM adhesion events, including integrin-ligand binding. For instance, integrins α5β1 and αvβ3 bind to fibronectin, and integrins α1β1 and α2β1 bind to collagen (type I), (18) and therefore ζ_b for collagen and fibronectin can have different values for the same cell type. During the initial spreading on flat surfaces, the cell shape can be considered to have a circular A_c, whereas the remaining cell surface maintains as spherical (radius: R). A_c is a function of R and the radial displacement of the first contact point (δ), for small deformation (δ ≪ R):

A_{c} = 2 π δ R

(3)

The cell body stiffness is approximated to have consistent whole-cell mechanical properties over the cytoplasmic region. For small deformation, the pressure distribution P_c over the contact area can be approximated as a parabolic function of the radial position r, with r = 0 at the center of the circular contact area. (19) Previous studies suggest that the stiffness of the cell nucleus is at least 1 order of magnitude larger than that of the cytoplasmic region, (20,21) and hence we assume the cell nucleus (radius: R_n) does not deform during the initial spreading. P_c can then be approximated as a soft-shell deforming process:

P_{c} = \frac{E \times A_{c}}{2 π R (R - R_{n})} (1 - \frac{π r^{2}}{A_{c}})

(4)

where E* (=E/(1–ν²)) is the effective elastic modulus of a cell, with E as the whole-cell elastic modulus and ν ≈0.4 as Poisson’s ratio. (22,23)

Recalling eq 3, the compressive force to the cell (F_c) can be derived by

F_{c} = \int_{0}^{R_{c}} \frac{E \times δ}{R - R_{n}} (1 - \frac{π r^{2}}{A_{c}}) \cdot 2 π r d r = \frac{E \times A_{c} δ}{2 (R - R_{n})}

(5)

On the other side of the cell–substrate interface, the substrate should deform together with the cell. The results displacement of the first contact point on the substrate side (δ_s) for the case δ_s ≪ δ can be approximated as δ_s ≈ δ•E*/E_s*, where E_s* is the effective elastic modulus of the substrate material. The compressive force to the substrate (F_s) can then be approximated as

F_{s} = \frac{π R}{R - R_{n}} \cdot \frac{{E_{s}^{*}}^{2}}{E^{*}} \cdot {δ_{s}}^{2}

(6)

The change in total strain energy during the initial spreading (ΔU_s) can then be derived by summing the integral of F_c over δ and the integral of F_s over δ_s:

{Δ U}_{s} = \int_{0}^{δ} \frac{π E \times R}{R - R_{n}} δ^{2} d δ + \int_{0}^{δ_{s}} \frac{π R}{R - R_{n}} \cdot \frac{{E_{s}^{*}}^{2}}{E^{*}} \cdot {δ_{s}}^{2} d δ_{s}

(7)

{Δ U}_{s} = \frac{1}{24 π^{2}} (E^{*} + \frac{{E^{*}}^{2}}{E_{s}^{*}}) \frac{{A_{c}}^{3}}{(R - R_{n}) R^{2}}

(8)

During cell deformation, flow presents between the cell nucleus and the cytoplasmic region. Based on the scaling argument, the viscous dissipation per volume during the cell deformation should be in the scale of

μ {\dot{γ}}^{2}

, where μ is whole-cell viscosity and γ̇ is the average strain rate of cytoplasmic flow. (5) Hence, we estimate the rate of viscous dissipation

{\dot{W}}_{v}

during the initial spreading is an integrative effect over the cytoplasmic region as

{\dot{W}}_{v} = λ (\frac{4 π R^{3}}{3} - \frac{4 π {R_{n}}^{3}}{3}) \cdot μ {\dot{γ}}^{2}

(9)

where λ is a correction factor, which is estimated by fitting the key expression with the least-squared error together with other parameters obtained by experiments as described in the next section. γ̇ should scale with variations in the angular velocity (V_θ) of cytoplasmic flow per radial thickness of the cell cytoplasmic region, i.e.,

\dot{γ} \sim V_{θ} / (R - R_{n})

. By considering the conservation of mass/volume, one can obtain the following scaling relationship by comparing the radial velocity (in the scale of δ̇) over the deforming cell membrane and V_θ during cell deformation in the initial spreading process:

A_{c} \cdot \dot{δ} \sim 2 \sqrt{π A_{c}} (R - R_{n}) \cdot V_{θ}

(10)

Recalling eq 3, one can obtain

\dot{γ} \sim \frac{\sqrt{A_{c}} \cdot \dot{A_{c}}}{4 π^{3 / 2} R {(R - R_{n})}^{2}}

(11)

Substituting eq 11 into eq 9,

{\dot{W}}_{v}

can be expressed as

{\dot{W}}_{v} = \frac{λ μ R (R^{3} - {R_{n}}^{3})}{12 π^{2} R {(R - R_{n})}^{4}} \cdot A_{c} {A_{c}}^{2}

(12)

By differentiating eq 1 with respect to time t and substituting with eqs 2, 8, and 12

Φ A_{c} \dot{A_{c}} + {A_{c}}^{2} = Ψ

(13)

where

Φ = \frac{2 λ μ (R^{3} - {R_{n}}^{3})}{3 π E^{*} (1 + E^{*} / E_{s}^{*}) {(R - R_{n})}^{3}}

and

Ψ = \frac{8 π^{2} ζ_{b} R^{2} (R - R_{n})}{E^{*} (1 + E^{*} / E_{s}^{*})}

Solving eq 14, one can obtain

A_{c} = \sqrt{α (1 - e^{- β t})}

(14)

where α = Ψ is defined as the “length scale” of spreading and β = 2/Φ is defined as the “time constant” of spreading.

Experimental Validation

To examine dynamics of initial cell spreading with experiments, we performed IRM imaging using a laser scanning confocal microscope (Figure 1b), visualizing the cell spreading for different breast cell types (MCF-10A, MCF-7, and MDA-MB-231) on collagen (type I)-coated glass, collagen-coated polydimethylsiloxane (PDMS), fibronectin-coated glass, and fibronectin-coated hexane-softened PDMS, as described in Methods. To examine ECM protein coating, we coated fibronectin conjugated with fluorescent molecules (50 μg/mL, Alexa Fluor 488 protein label kit, Thermo Fisher Scientific, Waltham, MA) on glass and PDMS substrates (2 h of immersion). No significant difference in fluorescence intensity was observed between the two substrate materials (Figure 1c), suggesting that the major difference of the substrate properties is the stiffness rather than the molecular conditions.

Next, we seeded cells on the substrate placed inside a confocal dish, followed by recording stacks of IRM images near the cell–substrate contacts at every 10s for 3 h after cell seeding to capture the cell spreading process occurring at any time within such period. We extracted the images showing the cells before attachment to measure cell radius (R) and then the first 5 min of cell spreading of different cells (Figures 1d and S1).

Results (Figures 1e and S2) confirm that the cell spreading area (A_c) is roughly a stabilizing function of time (t), agreeing with previous works. (17) Curve fitting of exponentially stabilizing functions over two spreading intervals (1 and 5 min) reveals that the 5 min fits do not match early stage dynamics (within 1 min). This indicates that initial cell spreading is primarily governed by a distinct mechanism, compared to early spreading occurring over 5 min–10 min.

To validate the biophysical model describing early cell spreading, one can determine α and β by obtaining the least-squared error of the measured A_c with the correction factor λ = 22.39 (eq 9) over the first 60s. The measured R and other premeasured bulk parameters (nuclear radius (R_n), effective elastic modulus (E*), cell–substrate adhesion energy per unit contact area (ζ_b), and whole-cell viscosity (μ)) are substituted in eq 14 to predict the length scale (α) and time constant (β) of spreading for each cell. The measurement procedures of these bulk parameters are described in Table I. The correlations between measured and predicted α and β (R² ≈0.71 and R² ≈0.80, respectively, for proportional fitting) demonstrate the representativeness of the reported biophysical model (Figure 2a).

Table I. Measured Key Parameters for MCF-10A, MCF-7, and MDA-MB-231 (MDA) Cells

	MCF-10A	MCF-7	MDA
E (kPa)	1.30 ± SE0.06	0.74 ± SE0.04	0.66 ± SE0.04
η (kPa•s)	2.62 ± SE0.16	2.55 ± SE0.17	3.89 ± SE0.25
ζ_b, Col (μJ/m²)	1256 ± SE69	2218 ± SE462	1892 ± SE259
ζ_b, FN (μJ/m²)	529 ± SE101	1185 ± SE65	1974 ± SE153
R_n (μm)	3.52 ± SE0.08	4.01 ± SE0.07	4.12 ± SE0.16

Figure 2. Prediction and measurement of the cell spreading area (A_c). (a) Scatter plots of predicted and measured α (left) and β (right) for MCF-10A, MCF-7, and MDA-MB-231 cells spreading on different substrate materials coated with collagen type 1 (Col) or fibronectin (FN). N = 112 in total; and N for different cases are mentioned in Figure S2. (b) Power-law fittings of measured cell–substrate contact radius (R_c = √(A_c/π)) against scaled time βt for. The black dash line indicates the expected power–law relation (∼t^1/4) predicted by the model.

The transient contact radius, defined as R_c = √(A_c/π), follows a power-law relationship with t. For example, previous studies have reported that R_c ∼t^1/2 in early spreading (60s < t < 600s). (5) As analyzed in this work, initial spreading (0s < t < 60s) should correspond to roughly 0 < βt < 3, as 0.01 s^–1 < β < 0.05 s^–1 based on the experiment results. Recalling eq 14 that A_c (2) = π²R_c (4) = α(1 −e^-βt), one can expect that R_c ∼t^1/4 as 1 – e^–βt ≈ βt for βt < 1. Experimental results (Figures 2b and S3) confirm this scaling behavior, supporting the predictive capabilities of the model.

Parametric Study of Initial Spreading Rate

We further investigate the roles of key factors in influencing initial spreading. Theoretically, ∂A_c/∂t|_t=0 → ∞ and therefore this expression fails to reflect the key interfacial properties according to eq 14. As a remedy, we consider the “spreading rate” as the rate of change of A_c (2) at t = 0:

{\frac{\partial {A_{c}}^{2}}{\partial t} |}_{t = 0} = α β = K_{R} \frac{R^{2} {(R - R_{n})}^{4}}{(R^{3} - {R_{n}}^{3})}

(15)

where K_R = 24π³ζ_b/(λμ). For consistency throughout this paper, we present the spreading rate as the values obtained from IRM measurements, whereas α and β are computed from the measured R, and cellular and interfacial properties. We plot the measured spreading rate against αβ (Figure 3a) with a reasonable correlation coefficient (R² ≈0.68). The measured spreading rate scaled with a factor of K_R^–1 R_n^–3 should be a function of the body-nuclear radius ratio (r = R/R_n), i.e., r²(r – 1)⁴/(r³ – 1). Results show that the values of r for individual cells lie around the prediction (Figure 3b), confirming the role of cell size (presented with R) in initial spreading. Further comparisons of spreading rates across different conditions (Figure 3c) indicate that cells spread faster on collagen-coated surfaces, which exhibit higher ζ_b, than on fibronectin-coated surfaces. Additionally, spreading rates on glass are comparable to those on (hexane-softened) PDMS with the same ECM protein coating, suggesting that the ECM protein is a dominant factor over substrate stiffness. This can be explained by the fact that E* is canceled out in K_R (eq 15). Notably, it has been reported that the spreading characteristics can be influenced by substrate stiffness in the later spreading stages (>1 min), owing to the occurrence of active intracellular processes such as focal complexes clustering and actin polymerization. (10) Results (Figure 3d) also show that cells with larger ratios of μ/ζ_b tend to exhibit faster spreading rates. Collectively, these trends align with the expression of αβ, supporting the reported biophysical model as a universal prediction approach for initial spreading across different cell–substrate interfacial conditions. Thus, the key cell and interfacial properties (e.g., μ) can be reflected by the initial spreading dynamics.

Figure 3. Roles of key parameters. (a) Scatter plot of αβ against measured initial spreading rate. The dash line indicates proportional linear fitting of all points (legends are shared with the same one in Figure 2a). (b) Scatter plot of measured initial spreading rate against R/R_n. The solid line indicates the prediction based on the model with average cell properties (legends are shared with the same one in Figure 2a). (c) Average initial spreading rates of cells spreading on different substrate conditions. Asterisks represent p < 0.05. (d) Correlations between initial spreading rate and the derived μ/ζ_b for all cases. The dash line indicates the linear regression of the average values. Error bars are standard errors of the mean. N = 112 in total; and N for different cases are mentioned in Figure S2.

Individual Cell Viscoelasticity

To further examine the roles of body viscoelasticity, we integrated IRM and AFM to quantify cell properties during initial spreading, as shown in Figure 4a. Because of a technical challenge that both measurements cannot be conducted simultaneously, we first employed IRM to quantify cell spreading, followed by measuring body viscoelasticity using AFM. Considering also that both IRM and AFM needed to be applied on the same cell, we reduced the magnification to enable more cells to be captured in each IRM image. Substrates containing the cells were then transferred to an AFM machine for force relaxation analysis (see Methods) to obtain cell biomechanical properties (R, E^*, and μ). ζ_b and R_n are assumed to be constant.

Figure 4. Characterization of single-cell viscoelasticity. (a) IRM (left) and AFM (right) measurements of MDA-MB-231 cells during the initial spreading process. Scale bar: 20 μm. (b) Scatter plots of single-cell E^*/μ against R for individual cells. (c) Scatter plots of αβ against single-cell E^*. Blue dash lines indicate fitting results of “fast spreading” cells, and red dash lines indicate fitting results of “slow spreading” cells. (d) Correlation of μ and E* for different individual cells. Each dash line indicates the linear fitting of individual cells with the same cell type.

Afterward, we examined micrographs for IRM and AFM to identify the matching individual cells. We classify two groups of cells for each cell type based on the value of β. The cells with time constants of initial spreading, i.e., measured 1/β, above the average level (0.0348 s^–1 for MCF-10A, 0.03 s^–1 for MCF-7, and 0.0355 s^–1 for MDA-MB-231) are considered as the “fast-spreading” cells; otherwise, they are the “slow-spreading” ones. Results (Figure 4b) agree with the reported model (eq 14) in which the fast-spreading cells possess larger values of R and E*/μ. The fast-spreading cells also exhibit larger αβ values on average (Figure 4c). Furthermore, it can be observed that αβ is negatively correlated with E*, despite that the expression of αβ (eq 15) is inversely proportional to μ but not a function of E*. This can be explained by the fact that the measured E* and μ tend to correlate with each other (Figure 4d), consistent with our previous works. (16) Collectively, these findings confirmed the involvement of different key cells and interfacial properties in initial spreading.

Methods

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Substrate Preparation and Cell Seeding

Confocal culture dishes with coverslips as their bases were used as the glass substrates. For PDMS substrates, a prepolymer mixture containing monomer and curing agent (weight ratio 10:1) was poured onto a coverslip, followed by spin-coating at 800 rpm for 30s and baking at 80 °C overnight. The PDMS-coated coverslip was then glued onto a culture dish with a precut hole at its base. The “soft-PDMS” substrates were prepared by mixing PDMS monomer and curing agent at a 50:1 weight ratio, achieving an equivalent stiffness in the scale of ∼10 kPa based on our AFM measurements, also agreeing with the reported values. (24) This mixture was poured into confocal culture dishes and baked at 80 °C overnight.

Afterward, the fabricated substrates were immersed with 50 μg/mL of fibronectin (FN; Invitrogen) or collagen type I (from rat tail; Sigma-Aldrich) for 2 h, then briefly rinsed with PBS. Cells were seeded onto the substrates at a density of 6 × 10³ cells/cm² for IRM imaging.

Interference Reflection Microscopy

IRM offers high sensitivity and resolution for visualizing the close contact between cells and the substrate. IRM was implemented using a laser scanning confocal microscope (TCS-SP8, Leica Microsystems, Wetzlar, Germany), as shown in Figure 1b. A 555 nm laser source generated a high-coherence light beam, which was directed by a reflection/transmission lens. Imaging was performed using a 63× oil immersion objective, enabling high-resolution time-lapse acquisition. Two photomultiplier tubes (PMTs) were utilized: one captured interference reflection light to track cell spreading dynamics, while the other recorded transmitted light to measure the cell diameter. Incident light is reflected at both the substrate-medium and medium–cell interfaces, generating an interference beam detected by the PMT. Due to interference effects, closely contacted regions appear dark, while noncontact regions appear bright. This contrast allows precise visualization of the cell–substrate adhesion, enabling direct observation of cell spreading dynamics with high fidelity.

IRM Image Processing

IRM images were analyzed by using a customized MATLAB (MathWorks, Natick, MA) script. The Canny algorithm (25) was applied to detect the spreading edge of cells in each time frame captured by IRM. Individual cells were then segmented by dissecting the image into multiple subimages, each containing a single cell. Following intensity thresholding, the spreading area was quantified.

Cell Properties Quantification

An elasticity microcytometer, as previously reported, (15) was utilized to quantify key cellular and interfacial properties of three breast cell lines (MCF-10A, MCF-7, and MDA-MB-231). These properties include cell radius (R), whole-cell elasticity (E), whole-cell viscosity (μ), and cell–substrate adhesion energy per contact area (ζ_b), as summarized in Table I.

Cell suspensions were injected into confining microchannels in the device using a controlled driving pressure (P), as shown in Figure S4a. Cells were captured along the microchannels at positions (L) dependent on E and R over time (t). R of a captured cell was measured with its deformed shape, while E was determined from R and L using Hertz and Tatara’s theories. (26) By tracking dynamic cell deformation (R and L) along the confining channel, we quantified μ based on a standard linear solid (SLS) model. (16) Our measured μ were comparable to previously reported values. (16)

To determine ζ_b, additional experiments were conducted. (15) The elastic microcytometer was coated with 50 μg/mL fibronectin or collagen (type I) as the substrate preparation procedure. Cells were injected into the device under a low-pressure level, such that the cells were captured along the confining microchannels. After a 30 min incubation period, facilitating cell adhesion to the channel walls, contact area (A_c) was measured. P was then gradually increased to dislodge the cells (Figure S4b). The minimal P required to remove a captured cell (with a projected cross-section area along the confining channel at L) reflected the cell–substrate binding force (F_b). ΔU_b was then obtained by ΔU_b = F_b/F_ligand × U_ligand, where F_ligand (=45 pN) (27) represents the binding force per ligand and U_ligand (=50 × 10^–18 J) corresponds to the binding energy per ligand. (6) ζ_b was subsequently determined as ζ_b = ΔU_b/A_c, aligning with previously reported values (∼10³ μJ/m²). (27)

Additionally, the cell nuclear radius (R_n) was measured from fluorescence micrographs of Hoechst 33342-stained cells (Sigma-Aldrich).

Measurement of In Situ Single-Cell Viscoelasticity

Measurements on single-cell viscoelasticity were conducted using AFM. An AFM system (BioScope Catalyst; Bruker Nano, Santa Barbara, CA) with a conical tip (tilt angle: 20°; tip radius: 60 nm; spring constant 0.06 N/m) was applied to conduct stress-relaxation nanoindentation on an attached cell. (28) The tip approached the cell at a velocity of 6 μm/s until a trigger force of 2 nN, followed by keeping the tip at a static position and recording the force relaxation for 2s.

Cell Culture

Human breast epithelial cells (MCF-10A) and breast cancer cells (MCF-7 and MDA-MB-231) were obtained from ATCC (Manassas, VA). MCF-10A cells were cultured in Mammary Epithelial Growth Medium (MEGM; CC-3150, Lonza, Walkersville, MD) supplemented with 0.4% (v/v) bovine pituitary extract (BD, Franklin Lakes, NJ), 0.1% (v/v) human epithelial growth factor (hEGF; Cell Signaling Technology, Beverly, MA), 0.1% (v/v) hydrocortisone (Sigma-Aldrich, St. Louis, MO), 0.1% (v/v) insulin (Sigma-Aldrich), and 0.1% (v/v) of a reagent containing 30 mg/mL gentamicin and 15 μg/mL amphotericin (GA-1000, Lonza). MCF-7 cells were cultured in high-glucose Dulbecco’s modified Eagle’s medium (DMEM; Invitrogen, Carlsbad, CA) supplemented with 10% fetal bovine serum (Atlanta Biologicals, Atlanta, GA), 0.5 μg/mL fungizone (Invitrogen), 5 μg/mL gentamicin (Invitrogen), 100 units/mL penicillin, and 100 μg/mL streptomycin. MDA-MB-231 cells were maintained in DMEM-F12 (Invitrogen) with 10% fetal bovine serum and 100 units/ml of penicillin.

All cells were cultured at 37 °C with 5% CO₂ in a humidified incubator. For experimental preparation, cells were detached using 0.25% trypsin–EDTA in phosphate-buffered saline (PBS; Sigma-Aldrich), followed by centrifugation and replacement with fresh culture medium. The cell suspension was then diluted to a target density of 4 × 10⁴ cells/mL by adding additional medium, ensuring optimal conditions for biochemical adhesion measurements.

Statistics

p-values were calculated using the two-tailed unpaired Student’s t-test. Significant differences are indicated by p < 0.05.

Conclusion

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In summary, we present a theoretical model grounded in viscoelastic cell deformation to quantitatively describe the initial spreading dynamics. This model is derived based on the energy balance of strain energy, surface adhesion energy, and viscous dissipation. The model accurately predicts the initial spreading dynamics across various cell types and substrate conditions. A parametric study incorporating IRM and AFM measurements further elucidates the roles of key cell properties (e.g., viscosity, elastic modulus, and body size) and interfacial factors (e.g., binding strength and substrate stiffness). Possible improvements of the measurement include (1) the higher imaging rate for capturing any more rapid dynamic effects during initial cell spreading and (2) hardware integration of AFM and confocal microscopy, such that any dynamics in viscoelastic properties of the cell body can also be captured.

Collectively, these findings establish a universal scheme for understanding the initial spreading of individual cells as a process governed by the interfacial energy balance. Noted, successful initial cell spreading can offer sufficient contact area downstream biological events, such as aggregation of focal adhesion molecules and subsequent actin filament formation, determining cell morphology and survival on the surface. The initial spreading characteristics can be guided by modulating the key factors, offering broad potential bioapplications such as suppression of cancer cell spreading and improved prediction of early tissue formation.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.langmuir.5c03250.

Representative IRM images for selected cell types spreading on different substrate conditions; fitting of cell spreading area; power-law relationship of the spreading radius; and cell properties measurement using an elasticity microcytometer (PDF)

la5c03250_si_001.pdf (1.62 MB)

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Author Information

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Corresponding Authors
- Shuhuan Hu - Department of Biomedical Engineering, College of Biomedicine, City University of Hong Kong, Hong Kong 999077, China; BGI-Shenzhen, Shenzhen,Guangdong 518083, China; https://orcid.org/0000-0002-4163-1242; Email: [email protected]
- Raymond H. W. Lam - Department of Biomedical Engineering, College of Biomedicine, City University of Hong Kong, Hong Kong 999077, China; City University of Hong Kong Shenzhen Research Institute, Shenzhen Guangdong 518172, China; https://orcid.org/0000-0002-5188-3830; Email: [email protected]
Authors
- Jifeng Ren - School of Biomedical Engineering, Capital Medical University, Beijing 100069, China; Beijing Key Laboratory of Fundamental Research on Biomechanics in Clinical Application, Capital Medical University, Beijing 100069, China; Department of Biomedical Engineering, College of Biomedicine, City University of Hong Kong, Hong Kong 999077, China
- Yi Liu - Department of Biomedical Engineering, College of Biomedicine, City University of Hong Kong, Hong Kong 999077, China
- Siping Huang - Department of Biomedical Engineering, College of Biomedicine, City University of Hong Kong, Hong Kong 999077, China; https://orcid.org/0000-0001-8721-5255
- Jingqian Zhang - Department of Biomedical Engineering, College of Biomedicine, City University of Hong Kong, Hong Kong 999077, China; https://orcid.org/0009-0008-6016-2390
- Qi Gao - Department of Biomedical Engineering, College of Biomedicine, City University of Hong Kong, Hong Kong 999077, China
- King Wai Chiu Lai - Department of Biomedical Engineering, College of Biomedicine, City University of Hong Kong, Hong Kong 999077, China; https://orcid.org/0000-0001-5002-2273
Author Contributions
J.R. and S.H. contributed equally to this work.
Notes
The authors declare no competing financial interest.

Acknowledgments

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We thank financial supports from the Hong Kong Research Grant Council (GRF 11217323 and 11206324) and the National Natural Science Foundation of China (NSFC 12402380).

References

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This article references 28 other publications.

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Abstract
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Figure 1
Figure 1. Visualization of initial cell spreading. (a) Key parameters involved in the initial cell spreading process. (b) Configuration of IRM using a laser scanning confocal microscope. (c) Glass and PDMS substrates coated with fluorescent fibronectin. (d) IRM images of an initial spreading MCF-10A cell on fibronectin-coated glass (upper) and their cross-sectional views (lower, processed with intensity inversion and thresholding for better visualization), captured as 10s, 60s, and 300s. All other cases are available in Figure S1. (e) Transient spreading area (A_c) of MCF-10A cells spreading on fibronectin-coated glass substrates. Gray lines represent single-cell dynamics; and the black line represents the average A_c (t). Error bars are standard errors of the mean. All cases with N numbers are available in Figure S2. Scale bar: 10 μm.
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Figure 2
Figure 2. Prediction and measurement of the cell spreading area (A_c). (a) Scatter plots of predicted and measured α (left) and β (right) for MCF-10A, MCF-7, and MDA-MB-231 cells spreading on different substrate materials coated with collagen type 1 (Col) or fibronectin (FN). N = 112 in total; and N for different cases are mentioned in Figure S2. (b) Power-law fittings of measured cell–substrate contact radius (R_c = √(A_c/π)) against scaled time βt for. The black dash line indicates the expected power–law relation (∼t^1/4) predicted by the model.
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Figure 3
Figure 3. Roles of key parameters. (a) Scatter plot of αβ against measured initial spreading rate. The dash line indicates proportional linear fitting of all points (legends are shared with the same one in Figure 2a). (b) Scatter plot of measured initial spreading rate against R/R_n. The solid line indicates the prediction based on the model with average cell properties (legends are shared with the same one in Figure 2a). (c) Average initial spreading rates of cells spreading on different substrate conditions. Asterisks represent p < 0.05. (d) Correlations between initial spreading rate and the derived μ/ζ_b for all cases. The dash line indicates the linear regression of the average values. Error bars are standard errors of the mean. N = 112 in total; and N for different cases are mentioned in Figure S2.
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Figure 4
Figure 4. Characterization of single-cell viscoelasticity. (a) IRM (left) and AFM (right) measurements of MDA-MB-231 cells during the initial spreading process. Scale bar: 20 μm. (b) Scatter plots of single-cell E^*/μ against R for individual cells. (c) Scatter plots of αβ against single-cell E^*. Blue dash lines indicate fitting results of “fast spreading” cells, and red dash lines indicate fitting results of “slow spreading” cells. (d) Correlation of μ and E* for different individual cells. Each dash line indicates the linear fitting of individual cells with the same cell type.
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References
This article references 28 other publications.
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9. 9
  Chaudhuri, O.; Gu, L.; Darnell, M.; Klumpers, D.; Bencherif, S. A.; Weaver, J. C.; Huebsch, N.; Mooney, D. J. Substrate Stress Relaxation Regulates Cell Spreading. Nat. Commun. 2015, 6 (1), 6365, DOI: 10.1038/ncomms7365
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10. 10
  Nisenholz, N.; Rajendran, K.; Dang, Q.; Chen, H.; Kemkemer, R.; Krishnan, R.; Zemel, A. Active Mechanics and Dynamics of Cell Spreading on Elastic Substrates. Soft Matter 2014, 10 (37), 7234– 7246, DOI: 10.1039/C4SM00780H
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11. 11
  Li, J.; Han, D.; Zhao, Y.-P. Kinetic Behaviour of the Cells Touching Substrate: The Interfacial Stiffness Guides Cell Spreading. Sci. Rep. 2014, 4 (1), 3910, DOI: 10.1038/srep03910
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12. 12
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13. 13
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14. 14
  Liu, Y.; Ren, J.; Zhang, R.; Hu, S.; Pang, S. W.; Lam, R. H. Spreading and Migration of Nasopharyngeal Normal and Cancer Cells on Microgratings. ACS Appl. Bio Mater. 2021, 4 (4), 3224– 3231, DOI: 10.1021/acsabm.0c01610
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15. 15
  Hu, S.; Liu, G.; Chen, W.; Li, X.; Lu, W.; Lam, R. H.; Fu, J. Multiparametric Biomechanical and Biochemical Phenotypic Profiling of Single Cancer Cells Using an Elasticity Microcytometer. small 2016, 12 (17), 2300– 2311, DOI: 10.1002/smll.201503620
  There is no corresponding record for this reference.
16. 16
  Hu, S.; Lam, R. H. W. Characterization of Viscoelastic Properties of Normal and Cancerous Human Breast Cells Using a Confining Microchannel. Microfluid. Nanofluidics 2017, 21 (4), 68, DOI: 10.1007/s10404-017-1903-x
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17. 17
  Chamaraux, F.; Fache, S.; Bruckert, F.; Fourcade, B. Kinetics of Cell Spreading. Phys. Rev. Lett. 2005, 94 (15), 158102, DOI: 10.1103/PhysRevLett.94.158102
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18. 18
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19. 19
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20. 20
  Guilak, F.; Tedrow, J. R.; Burgkart, R. Viscoelastic Properties of the Cell Nucleus. Biochem. Biophys. Res. Commun. 2000, 269 (3), 781– 786, DOI: 10.1006/bbrc.2000.2360
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21. 21
  Ren, J.; Li, Y.; Hu, S.; Liu, Y.; Tsao, S. W.; Lau, D.; Luo, G.; Tsang, C. M.; Lam, R. H. W. Nondestructive Quantification of Single-Cell Nuclear and Cytoplasmic Mechanical Properties Based on Large Whole-Cell Deformation. Lab Chip 2020, 20 (22), 4175– 4185, DOI: 10.1039/D0LC00725K
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22. 22
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23. 23
  Lam, R. H. W.; Weng, S.; Lu, W.; Fu, J. Live-Cell Subcellular Measurement of Cell Stiffness Using a Microengineered Stretchable Micropost Array Membrane. Integr. Biol. 2012, 4 (10), 1289– 1298, DOI: 10.1039/c2ib20134h
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24. 24
  Varner, H.; Cohen, T. Explaining the Spread in Measurement of PDMS Elastic Properties: Influence of Test Method and Curing Protocol. Soft Matter 2024, 20 (46), 9174– 9183, DOI: 10.1039/D4SM00573B
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25. 25
  Cao, Y.; Wu, D.; Duan, Y. A New Image Edge Detection Algorithm Based on Improved Canny. J. Comput. Methods Sci. Eng. 2020, 20 (2), 629– 642, DOI: 10.3233/JCM-193963
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26. 26
  Zhang, Z. L.; Kristiansen, H.; Liu, J. A Method for Determining Elastic Properties of Micron-Sized Polymer Particles by Using Flat Punch Test. Comput. Mater. Sci. 2007, 39 (2), 305– 314, DOI: 10.1016/j.commatsci.2006.06.009
  There is no corresponding record for this reference.
27. 27
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  There is no corresponding record for this reference.
28. 28
  Chim, Y. H.; Mason, L. M.; Rath, N.; Olson, M. F.; Tassieri, M.; Yin, H. A One-Step Procedure to Probe the Viscoelastic Properties of Cells by Atomic Force Microscopy. Sci. Rep. 2018, 8 (1), 14462, DOI: 10.1038/s41598-018-32704-8
  There is no corresponding record for this reference.
Supporting Information
Supporting Information
The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.langmuir.5c03250.
- Representative IRM images for selected cell types spreading on different substrate conditions; fitting of cell spreading area; power-law relationship of the spreading radius; and cell properties measurement using an elasticity microcytometer (PDF)
- la5c03250_si_001.pdf (1.62 MB)
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Interfacial Energy Balance Governs Initial Cell Spreading DynamicsClick to copy article linkArticle link copied!

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Abstract

Note

Introduction

Results and Discussion

Model

Figure 1

Experimental Validation

Figure 2

Parametric Study of Initial Spreading Rate

Figure 3

Individual Cell Viscoelasticity

Figure 4

Methods

Substrate Preparation and Cell Seeding

Interference Reflection Microscopy

IRM Image Processing

Cell Properties Quantification

Measurement of In Situ Single-Cell Viscoelasticity

Cell Culture

Statistics

Conclusion

Supporting Information

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Author Information

Acknowledgments

References

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Interfacial Energy Balance Governs Initial Cell Spreading Dynamics
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