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Stiffness fluctuations in T cells

Finn Bastian Molzahn, Julien Husson

► To cite this version:

Finn Bastian Molzahn, Julien Husson. Stiffness fluctuations in T cells. European Physical Journal E: Soft matter and biological physics, 2025, 48 (10-12), pp.75. 10.1140/epje/s10189-025-00540-0 .
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# Stiffness fluctuations in T cells

F. B. Molzahn¹ and J. Husson¹,ᵃ

¹ Laboratoire d'Hydrodynamique (LadHyX), CNRS, Ecole polytechnique, Institut Polytechnique de Paris, Palaiseau, France

ᵃ e-mail: julien.husson@polytechnique.edu (corresponding author)

## Abstract

The actomyosin cortex is a highly dynamic cellular structure that regulates cell shape, migration, and division, while also contributing to specialized functions such as microvillar search. Previous studies have documented fluctuations in microvillar shape and cortical thickness over time. Building on these observations, we investigated whether these morphological changes are accompanied by corresponding fluctuations in cellular stiffness. We used profile microindentation and micropipette aspiration to examine the mechanical properties of human CD4+ T cells. Our results revealed that a substantial proportion of T cells exhibit spontaneous stiffness fluctuations, with approximately one-third displaying clear, periodic peaks with an average period of 30-35 seconds. Disrupting the actin cytoskeleton with Latrunculin A eliminated these fluctuations, confirming their actin-dependent nature. Low-pressure micropipette aspiration experiments showed periodic movements of cell bodies within the micropipette that correlated with stiffness peaks. These findings demonstrate that the mechanical properties of resting T cells are far from static. Instead, T cells exist in a highly dynamic state characterized by significant stiffness oscillations that may be integral to the microvillar search process. This work raises questions about whether similar mechanical dynamics occur in other cell types and how these periodic stiffness changes might influence T cell immune functions. Our study underscores the importance of temporal resolution when investigating cellular mechanics, as static measurements may miss these fundamental dynamic properties.

## 1 Introduction

The cellular membrane and the actomyosin cortex play a fundamental role in various biological processes, providing the cell with the ability to change shape, contributing to its migration and division [1-3]. The membrane and actomyosin cortex also provide cells with a range of sensory organelles at their surface, such as filopodia or microvilli [4]. These surface structures fluctuate in shape not only because of the thermal agitation of the liquid medium surrounding the cell [5], but also and mainly because of the active reorganization of the actin cortex [3,6]. These fluctuations in shape have been described decades ago using atomic force microscopy and as a superposition of well correlation periodic motions and random fluctuations [7]. While the latter are expected because of thermal fluctuations, the periodic motions were shown to be cytoskeleton dependent [6].

These active changes in shape are associated with functions; for instance, at the surface of immune cells, microvilli constantly scan the opposing antigen-presenting cell surface in search of antigens [8-14]. As these dynamic microvilli explore the cell environment, the cortex also changes in thickness over time, as shown using atomic force microscopy [15] and recently magnetic beads to pinch the cortex of dendritic and *Dictyostelium discoideum* cells [16]. As a result, even in the so-called resting cells, the cortex is a dynamic system showing shape and thickness fluctuations. As the structure of the actomyosin cortex is associated with cell mechanical properties [17, 18], this raises the possibility that the shape fluctuations in a resting cell correlate with fluctuations in cell stiffness.
Spontaneous fluctuations in contractility that translated into measurable changes in effective stiffness and/or tension have been reported in embryos [19, 20], with a quantified typical oscillatory timescale of 30-40 s in *Caenorhabditis elegans* [20]. Periodic contractions have also been observed in cellular aggregates, with a typical timescale of 200 s [21]. At the single-cell level, pulsations and waves have been described in the cortex of single cells [6, 22, 23, 24] but without direct measurement of changes in stiffness. However, atomic force microscopy studies have reported stiffness changes in adherent cells over a large span of timescales: 10-30 min in endothelial cells [25], from a few tens to a few hundreds of seconds in smooth muscle cells [26], and 200 s in epithelial cells [27]. Schlosser et al. used dual optical traps on detached fibroblasts and measured faster stiffness fluctuations in the range of 0.1-10s [28]. To the best of our knowledge, stiffness fluctuations have not been reported in single leukocytes. In this study, we aimed to describe stiffness fluctuations in resting T cells by performing time-resolved profile microindentation [29] and micropipette aspiration.

# 2 Materials and Methods

## 2.1 Cells and reagents

### 2.1.1 T cells

C. Hivroz' group kindly provided purified primary human CD4+ T cells. Details on the purification can be found in the work of Zucchetti et al. [30]. T cells were stored in liquid nitrogen until 1-5 days before performing the experiments. They were thawed rapidly and kept in RPMI 1640 culture medium supplemented with GlutaMax, 10% heat-inactivated fetal bovine serum, and 1% penicillin-streptomycin (all from ThermoFisher Scientific, Waltham, MA), at 37 °C, 5% CO₂ and at concentrations of 10⁶ cells per ml. The experiments were performed in the same culture medium at room temperature and without a CO₂ supply. During the transition from the cell flask to the Petri dish on the microscope stage, the cells were maintained in 2-ml tubes within a custom-made incubator, which provided control over the air temperature (37 °C) but not over the CO₂ levels. The experiments typically lasted 2 hours, during which no trend in the obtained contact stiffness could be observed (see Supplementary Material S1, Online Resource 1).

### 2.1.2 Actin-disruptive cell treatment

To disrupt the actin cytoskeleton in T cells, we used Latrunculin A (LatA, Sigma ref. 428026-50UG) at a final concentration of 0.2 µM during incubation and experiments. Four of the 32 cells were incubated at 1 µM LatA; we observed no difference in the fluctuating behavior between the treatments and pooled them. The cells were left incubating for 20 min in a custom-made incubator that provided a constant air temperature of 37 °C (but lacks a CO₂ control) before starting the experiments. Experiments were performed in medium at the same LatA concentration and typically lasted 2 hours. As stated previously, we observed no trend in the contact stiffness over this time.

## 2.2 Micropipette and microindenter preparation and calibration

The stiff micropipettes used to hold the cells were prepared as described previously [29, 31, 32]. Glass capillaries (borosilicate, from Harvard Apparatus, Holliston, MA, USA) were pulled with a P-97 micropipette puller (Sutter Instruments, Novato, CA, USA), then cut with an MF-200 microforge (World Precision Instruments Ltd, United Kingdom) to obtain an inner diameter of approximately 3.5 µm, and finally bent to a 45° angle using an MF-900 microforge (Narishige, Tokyo, Japan). See the videos and details about the process in [29]. The 45° angle allows the placement of the pipette in the Petri dish, as schematically shown in Figure 1A.
We formed microindenters by first pulling micropipettes with settings on the P-97 puller, leading to much thinner micropipettes than those used for holding cells. We then cut these micropipettes and either melted their extremities to form a glass bead (of typical 8 µm diameter) or created a needle (using a lower temperature of the microforge filament) with a micronic or submicronic tip, which was then bent at 90° into a final hook shape. We refer to these microindenters as spherical, hook, and submicronic hook microindenters, respectively. A 45° angle was added for all of them, as already described for the stiff cell-holding micropipettes. The radii/thickness of both spherical and hook-shaped tips were measured optically with an accuracy of typically 3 pixels (about 0.2 µm). An overview of the indenter sizes can be found in Supplementary Table 1 (see Supplementary Material S2, Online Resource 1). An example of each microindenter type is shown in Figure 1B.

As previously described [29, 31], we calibrated the bending stiffness of the flexible micropipettes by pressing them against standard microindenters of known stiffness. The stiffness of the standard microindenters was calibrated using a commercial force probe (model 406A; Aurora Scientific, Aurora, ON, Canada). The spherical microindenters had a bending stiffness of 0.194 to 0.275 nN/µm; the hook microindenters had a typical bending stiffness of 0.09 to 0.125 nN/µm (see Supplementary Material S2, Online Resource 1).

## 2.3 Profile microindentation

### 2.3.1 Principle and setup

We have previously described in detail the profile microindentation technique [29], which allows sideways observation of cells under the microscope during indentation. An inverted microscope (TiE, Nikon Instruments, Tokyo, Japan) was placed on an air suspension table (Newport, Irvine, CA, USA) equipped with a Flash 4.0 CMOS camera (Hamamatsu Photonics, Hamamatsu City, Japan), and a 100x oil immersion 1.3 numerical aperture objective (Nikon Instrument).

A stiff micropipette was attached to a piezoelectric single-axis translation stage (P-611.1S Piezo Nanopositioner and E-709.SRG Digital Piezo Controller, Physik Instrumente, Karlsruhe, Germany), which was itself placed on a custom-made adapter piece attached to a motorized micropipulator (MP-285; Sutter Instruments) for 3D placement of the cell before any microindentation. A microindenter was attached to a non-motorized micropositioner (Thorlabs, Newton, NJ). The micropipette and microindenter tips were then immersed into a glass-bottom Petri dish (Fluorodish, World Precision Instruments) filled with 3 mL of culture medium (RPMI, see above). A schematic of the experimental setup is shown in Figure 1A.

The stiff micropipette is connected to a water-filled reservoir (made of a 50-mL syringe body) whose height is adjusted to control the hydrostatic pressure inside the micropipette [29]. A typical aspiration of a 2-mm H₂O difference (i.e., about 20 Pa) was set to hold the cells gently. The experiments were performed at room temperature to avoid thermal drift.

The experiment was automated by a Matlab (Mathworks, Natick, MA) code that controls the piezo stage position and the Micromanager software [33] that controls the microscope camera. The position of the microindenter tip is detected by analyzing a line crossing the shaft of the microindenter on the live-microscopy image acquired by the camera. The intensity profile along this line was analyzed at an acquisition frequency of about 400 Hz and cross-correlated with a reference intensity profile recorded at the beginning of the experiment. The position of the microindenter was measured with a subpixel accuracy of approximately 20-30 nm (one pixel represents 65 nm using the 100x objective) [34]. Images of the region of interest showing the micropipette, the cell, and the microindenter's tip were acquired at a frequency of 1 frame per second. One representative movie for each indenter geometry and the different treatment conditions (normal and Latrunculin A) can be found in the Supplementary Movies 1-5 (Online Resource 2).

The experiment consisted of holding a cell with a stiff micropipette. The cell is then pushed against the (spherical or hook-shaped) tip of the microindenter. By detecting the position of the microindenter tip on the live camera image, the deflection of the microindenter can be measured, from
which the force applied to the cell can be deduced. To apply the desired force, the position of the piezo stage is adjusted via a live feedback loop. From the difference between the piezo position and the microindenter's tip, the indentation of the cell was calculated [29].

<figure><img src="image_3.png" /><figcaption>Figure 1. (A) Schematic of the profile microindentation setup (not to scale). The micropipette and microindenter tips are aligned such that translating the pipette with a piezo stage along the x-axis results in the bending of the microindenter. The region of interest for image acquisition (orange) was adjusted with the software to be large enough to visualize the full cell and the indenter's deflection when applying a force to the cells. This applied force resulted in an indentation of the cell. (B) Microscopy images of T cells indented with different types of microindenters: a spherical microindenter (1st row), a hook (2nd row), a submicronic hook (3rd row), a hook on a non-treated T cell (4th row, left), and a hook on a Latrunculin A-treated T cell (4th row, right). The scale bar represents 5 µm. Movies of the shown cells taken at 1 Hz during the indentation experiments can be found in the Supplementary Movies 1-5 (Online Resource 2).</figcaption></figure>

### 2.3.2 Profile microindentation protocol to measure cell stiffness

The measurement process unfolds in three phases: Phases I, II, and III, as detailed below.

During Phase I, the micropipette holding the cell is translated at a constant velocity of 0.5 µm/s and pressed against the tip of the microindenters until a force threshold $F_{max}$ is reached, which ends Phase I and starts Phase II. In this study, we did not exploit the data obtained during Phase I.

During Phase II, a live feedback loop is used to apply a sinusoidally modulated force $F(t) = \langle F \rangle + \Delta F \cos(\omega t)$ to the cell, where $\langle F \rangle$ is the average of $F(t)$ over one period of 1 s and is chosen equal to the force threshold $F_{max}$, $\Delta F$ is the amplitude of the force oscillations, $\omega = 2\pi f$ is the angular frequency of the oscillations, and $f = 1$ Hz is their frequency. The SNR of the force signal is typically 8.9 ± 2.1 (see Supplementary Material S3, Online Resource 1 for more details). The amplitude $\Delta F$ was chosen to be sufficiently large for the resulting modulation in indentation, $\Delta\delta$, to be large relative
to the indentation noise, which is 22 ± 3 nm. The SNR for the indentation is 2.4 ± 0.5 for spherical indenters, 2.5 ± 0.7 for hooks, and 3.4 ± 0.8 for submicronic hooks (see Supplementary Material S3, Online Resource 1 for more details). Under the oscillatory force, the cell indentation $\delta(t)$ is sinusoidal and at the same frequency $f = 1$ Hz: $\delta(t) = \delta_m + \Delta\delta\cos(\omega t - \varphi)$, where $\delta_m$ is the average of $\delta(t)$ over a period (1 s), $\Delta\delta$ the amplitude of the oscillations, and $\varphi$ is a phase lag due to the cell's viscous properties [35]. The force applied and indentation obtained for the three indenters shown in Figure 1B were obtained by applying:

- $\langle F \rangle = 50$ pN and $\Delta F = 25$ pN for the hook, leading to $\delta_m$ of 1.3 ± 0.4 µm and $\Delta\delta$ of 60 ± 20 nm.

- $\langle F \rangle = 50$ pN and $\Delta F = 25$ pN for the submicronic hooks, leading to $\delta_m$ of about 1.6 ± 0.6 µm and $\Delta\delta$ of 80 ± 20 nm.

- $\langle F \rangle = 150$ pN and $\Delta F = 50$ pN for the spherical indenters, leading to $\delta_m$ of 1.5 ± 0.4 µm and $\Delta\delta$ of 50 ± 10 nm.

Typical curves of force and indentation over time for a hook indenter are shown in Figure 2A and 2C for a fluctuating cell, and Figure 2B and 2D for a more passive cell.

As previously done [34, 35], we consider a complex number formalism where the complex force is $F^*(t) = \langle F \rangle + \Delta F e^{i\omega t}$ and the corresponding complex indentation is $\delta^*(t) = \delta_m + \Delta\delta e^{i(\omega t - \varphi)}$. We define the complex contact stiffness of the cell $K^*$ by writing $F^*(t) - \langle F \rangle = K^*(\delta^* - \delta_m)$. The term “contact stiffness” is borrowed from continuum mechanics and is defined as the equivalent spring constant of the cell when indented by the microindenter. The complex contact stiffness $K^* = K' + iK''$ has a real part $K' = \frac{\Delta F}{\Delta\delta}\cos\varphi$ and an imaginary part $K'' = \frac{\Delta F}{\Delta\delta}\sin\varphi$. $K^*$ is fully determined experimentally independently of any model, but it depends on the geometry of the indenter. If one were to extract from $K^*$ some geometry-independent properties intrinsic to the cell, a rheological model of the cell would be required. We have already shown that it can be difficult to decouple the surface properties of the cell (cell tension) from its inner viscoelastic properties. Thus, we decided here to consider a model-independent observable, the contact stiffness, keeping in mind that it depends on the size and geometry of the indenter (averages of the contact stiffness depending on indenter type are shown in Supplementary Material S4, Online Resource 1). This measured contact stiffness also depends on both the cell tension and the inner viscoelasticity of the cell, but extracting the latter is model-dependent [34]. The norm of the stiffness, $|K^*| = \frac{\Delta F}{\Delta\delta}$, depends only on the amplitudes $\Delta F$ and $\Delta\delta$, not on the phase lag $\varphi$. Given that accurately evaluating the latter is difficult in our setup, we chose to consider the norm of the complex stiffness. In this study, we call for simplicity $|K^*|$ the cell stiffness, and ask if we can detect fluctuations of $|K^*|$ over time.

Phase II lasts 200 seconds and is followed by phase III, during which the piezoelectric stage is withdrawn at a constant velocity of 0.5 µm/s. In this study, we did not exploit the data obtained during this phase.

### 2.3.3 Effect of the location of the indenters on the measured stiffness

As we intersect the shaft of the microindenter at a location that is not exactly its tip, we underestimate its bending, thus the applied force. This underestimation depends on the microindenter placement along the y-axis of the region of interest (ROI) (see Figure 1A). To verify that the induced error was negligible, we tested four different indenter y-locations using a second spherical indenter as a surrogate cell (see Supplementary Material S5, Online Resource 1). For both the spherical indenter and the hook, we found no statistical difference in the average measured stiffness $|K^*|$ between the different y-locations (see Supplementary Material S6, Online Resource 1).

## 2.4 Micropipette aspiration

The micropipettes were prepared in the same manner as the stiff micropipettes (see Sec. 2.2). Cells were aspirated with approximately 20 Pa and observed using bright field microscopy, using the same
100x oil objective as for microindentation. Time-lapse acquisition was performed at one frame per second for 200 s. Images were analyzed using the ImageJ software [36, 37].

## 2.5 Signal processing

### 2.5.1 Smoothing of the raw cell contact stiffness $|K^*|(t)$

The force and indentation signals were sampled at about 400Hz. We discretized the time, considering instants $t_i$ spaced by 1 s. At each time $t_i$, we fitted these signals over a time interval centered around $t_i$: $[t_i - 1$ s, $t_i + 1$ s]. Over this time interval, we fit the force and indentation signals as a sinusoidal signal with an added linear trend for the indentation to consider that the indentation mean $\delta_m$ varies over time. The best fit was determined using a squared error minimization algorithm in Python 3, leading to the amplitudes $\Delta F(t_i)$ and $\Delta\delta(t_i)$, from which we deduced the value of $|K^*|$ at time $t_i$, $|K^*|(t_i) = \frac{\Delta F(t_i)}{\Delta\delta(t_i)}$. This raw $|K^*|$ stiffness signal is noisy; thus, we filter it with a 10-s window moving median filter (see Figures 2E-F). This allows us to smooth out the high-frequency noise while preserving the global stiffness fluctuations and ensures that occasional “freezes” that sporadically occur in the automated setup do not influence the final results (see Supplementary Material S7, Online Resource 1). We call this the smoothed stiffness value $|K^*|_{sm}(t)$. For simplicity, we used the notation $|K^*|$ instead of $|K^*|_{sm}(t)$ in the results.

### 2.5.2 Quantifying fluctuations in the cell stiffness

To quantify the cell stiffness variations over time, we measured the amplitude of $|K^*|_{sm}(t)$ over each time interval $[t_i - \Delta T_{amp}/2, t_i + \Delta T_{amp}/2]$ of the window size $\Delta T_{amp}$. This amplitude signal at time $t_i$, which is the difference between the maximum and the minimum of $|K^*|_{sm}$ over this time interval, is called $\text{amp}(|K^*|)(t_i)$ for each $t_i$. For a given cell, the strength of the fluctuations was taken as the median of $\text{amp}(|K^*|)$ over the whole time trace (200 s). We chose $\Delta T_{amp}$ to be close to the experimentally found oscillation duration (see section 3.1), with $\Delta T_{amp} = 30$ s. In Supplementary Table 2, we show that the qualitative results obtained do not strongly depend on the window size $\Delta T_{amp}$ (see Supplementary Material S8, Online Resource 1).

## 2.6 Statistics

Experiments were performed on at least 4 and typically 10 cells per donor, for at least 3 different donors. An overview of the total number of cells measured and donors used per sample type and indenter geometry is given in Supplementary Table 3 (see Supplementary Material S9, Online Resource 1). For the statistical comparisons, two different approaches were used. All pairwise comparisons (e.g., normal vs actin-disrupted cells for a respective indenter) were done using a Mann-Whitney U test. If multiple comparisons were conducted simultaneously, a Kruskal-Wallis test was used to determine whether at least a dataset differed from the others. If the obtained p-value was below 0.05, a Dunn's post hoc test was performed, applying the correction by Benjamini & Hochberg for controlling the false discovery rate [38]. Labels used for indicating p-values are: \* for $p<0.05$, \*\* for $p<0.01$, and \*\*\* for $p<0.001$.

# 3 Results

## 3.1 T cells undergo stiffness fluctuations with a typical timescale of 30 s
By following the stiffness of resting T cells over 200 seconds, we observed that their stiffness fluctuates over time, with fluctuations ranging from about 7.5% to 110% of their average contact stiffness. In Figure 2A and 2B, we show the sinusoidal force applied over 200 s to a single resting T cell each. The resulting cell indentation is shown in Figure 2C and 2D. Large variations in the average indentation $\delta_m$ while keeping the average force $\langle F \rangle$ constant, visible in Figure 2C, are the first indication that the cell stiffness fluctuates. We note that the cell shown on the left of Figure 2 shows stronger variations in the indentation than on the right.

These fluctuations are further quantified by measuring the contact stiffness $|K^*|$ shown in Figure 2E and 2F (gray line), and quantifying the fluctuations observed in this signal after smoothing it ($|K^*|_{sm}$), also shown in Figure 2E and 2F (black line). The fluctuation amplitude signal $\text{amp}(|K^*|)$, also shown in Figure 2E and 2F (green line), ranges from about 40% to about 140% for the cell shown in the left half, while not surpassing 25% for the right cell. In the left example, fluctuations are obvious, with a clear timescale of about 40 s (5 peaks over 200 s).

Counting the oscillations by hand (three classifications by three appraisers, see Supplementary Material S10, Online Resource 1 for detailed procedure), we found an average oscillation duration of 35 ± 8 s for all three indenter types (find detailed results in Supplementary Table 4, Supplementary Material S10, Online Resource 1). We classify a cell as fluctuating if counting a minimum of 4 peaks in the 200 s of acquisition. We observed fluctuations in 64 ± 15% of cells using the hook, in 61 ± 12% using the spherical indenter and in 51 ± 11% using the submicronic hook. The LatA-treated cells reached fluctuating percentages of 15 ± 11% for the Hook and 11 ± 11% for the submicronic hook. For the spherical indenter, none were classified as fluctuating. The same goes for the control experiments using two indenters.

Manual classification implied operator dependence. Classifying only strong and repeated oscillations (three classifications by two operators) slightly decreased the typical duration of the observed fluctuations to 32 ± 7 s and decreased the percentage in all negative controls (LatA-treated cells and two-indenter setup) to 0%. The hook maintained the highest percentage, at 34 ± 8%, followed by the spherical indenter at 22 ± 9%, and the submicronic hook at 13 ± 6%. This stricter classification will be used as a comparison when working on the kymographs later.
<figure><img src="image_4.png" /><figcaption>Figure 2. Examples of force (A,B), indentation (C,D), and contact stiffness $|K^*|$ (E, F) measured by profile microindentation over time on T cells using hook-shaped indenters. The unfiltered contact stiffness is shown in gray, the smoothed contact stiffness in black (E,F). The normalized stiffness fluctuation amplitudes are also shown in (E,F) in green. The left and right columns are data obtained on a cell showing strong or no oscillations, respectively.</figcaption></figure>
## 3.2 Passive targets do not fluctuate on a comparable timescale

In control experiments, we replaced the cells by a spherical microindenter (see Supplementary Figure 4A for a schematic and Supplementary Material S5, Online Resource 1), i.e., a passive system that should lead to no stiffness fluctuations. Although the noise in our measurement system led to non-zero fluctuations, the latter were significantly smaller than those observed when indenting cells with a spherical indenter (Figure 3). We ran experiments similar to the ones using a hook and a submicronic hook. In those experiments, the tip of the hook slid on the spherical indenter used as a surrogate cell leading to large noise and artefactual variations in $|K^*|$ on the 1-s timescale, making a reliable comparison with experiments on cells impossible (Figure 3 and Supplementary Figure 4B, Supplementary Material S5, Online Resource 1).

<figure><img src="image_5.png" /></figure>

Figure 3. Tukey's boxplot comparing the mean stiffness fluctuation normalized by the mean stiffness of the spherical indenter (sphere), the hook, and the submicronic hook in normal and actin-disrupted conditions (LatA). Each dot represents the mean stiffness fluctuation over 200 s of a cell. The control experiments indenting a flexible glass indenter (glass bead) are added on the right. Each point represents a 200 s measurement performed on a different cell. Outliers above 0.55 normalized mean stiffness fluctuations (5 outliers for the hook, 1 for the submicronic hook, 1 for the hook on glass bead) were cut off for better visibility. Labels for p-values are: * for $p<0.05$, ** for $p<0.01$, *** for $p<0.001$ (see section 2.6 for details).
## 3.3 Similar fluctuation dynamics for the spherical and hook microindenters

We compared the dynamics of cell stiffness fluctuations using three different shapes of microindenters: spherical microindenters, hook microindenters, and submicronic hook microindenters. We measured the same stiffness fluctuation amplitudes with the hook and the spherical microindenter, but observed lower fluctuation amplitudes with the submicronic hook when compared to the hook ($p = 0.011$, Dunn's post hoc test). However, this difference did not persist in the comparison with the spherical indenter ($p = 0.244$, Dunn's post hoc test), and fluctuation levels remained distinct from the drug-treated control (see section 3.4). Combined with the indentation depth not changing significantly and difficulties in setting the submicronic hook in focus due to its size (see Supplementary Table 1, Supplementary Material S2, Online Resource 1), we hypothesize that the non-perfect alignment with the equator of the cell allows the hook to slide, which may compensate the fluctuations of the cell while not affecting our average measure of $|K^*|$.

## 3.4 Cell stiffness fluctuations are actin-dependent

We asked if these stiffness fluctuations depend on the cell actin cortex, so we destabilized it using the actin-disruptive drug Latrunculin A. Fluctuations were strongly reduced in the presence of Latrunculin A, regardless of the indenter type (Figure 3A). This confirms that the observed stiffness fluctuations depend on the actin cytoskeleton integrity.

## 3.5 Micropipette aspiration observations are consistent with fluctuations in the cell tension

Work by Yu et al. modelled the cortex and concluded that fluctuations in cell stiffness are mainly due to fluctuations in cell tension [39], so we used micropipette aspiration to assess if the tension of resting T cells would fluctuate. We aspirated T cells with a small aspiration pressure (about 20 Pa) and observed in some cells that the part of the cell aspirated inside the micropipette oscillated back and forth. We interpreted these movements inside the micropipette as an oscillation in the cell tension. However, we did not quantify the latter because established models to quantify cell tension by micropipette aspiration require that the cell reaches an equilibrium state or require to assume a model for rheology of the cell cortex [40]. Thus, we focused only on the cell shape changes (and did not quantify the cell tension) and quantified them using kymographs. In the absence of any microindenter, we observed that 39% of the cells (13 out of 33 cells from 3 donors) displayed oscillations in the lengths of their aspirated part. The average period of these oscillations was 28.3 ± 2.3 s (mean ± SD). To confirm the presence of these shape oscillations during the microindentation experiments, we analyzed the 1-Hz time-lapse acquired during the microindentation experiments and visually assessed the instant at which the cells periodically moved inside the holding micropipette. We only considered a subset of cells that we classified as strongly fluctuating (five cells for the spherical indenter, nine for the hook, and four for the submicronic hook) and found an oscillation period of 36 ± 7 s for the spherical indenter, 32 ± 5 s for the hook, and 37 ± 6 s for the submicronic hook. We compared the oscillation period obtained using (i) a kymograph in the absence of an indenter and (ii) visual inspection in presence of a microindenter, with the timescale found in the oscillations of the contact stiffness. When considering the different microindenter geometries separately in our comparison, we found no statistical difference between the timescales observed (see Figure 4C, $p = 0.26$ Kruskal-Wallis test). Merging the geometries decreases this to $p = 0.07$ (Kruskal-Wallis test), but the timescales remain statistically indifferent.
To go beyond comparing the oscillation timescale observed in stiffness and cell movement inside the micropipette, we asked if individual peaks in stiffness were correlated with individual movements of the cell body (see Figure 4D and 4E). Thus, we computed the correlation between the time points at which a maximum in contact stiffness was reached and those at which the cell tongue (i.e., the part of the cell entering the aspirating micropipette) was at its longest. We obtained a Pearson R coefficients of *r* = 0.995 ± 0.005 (*p* = 0.0005, N=9) for the hook, *r* = 0.998 ± 0.002 (*p* = 0.0006, N=5) for the spherical indenter, and *r* = 0.997 ± 0.002 (*p* = 0.0178, N=4). Furthermore, when plotting y, the timepoints of movement into the micropipette, vs. x, the timepoints of oscillations in contact stiffness and fitting the linear relationship *y* = *ax* + *b*, we obtain a slope *a* and an intersect *b*. The slope *a* was close to 1 (0.99 ± 0.05 for the spherical indenter, 1.07 ± 0.14 for the hook, and 1.06 ± 0.10 for the submicronic hook), confirming the consistency of the timescales determined in cell movement and cell stiffness. The intersect informs about a phase shift between the cell movement and the peak in cell stiffness. This intersect was -1.0 ± 5.2 s for the spherical indenter, -11.9 ± 25.5 s for the hook, and -2.5 ± 10.4 s for the submicronic hook. For the spherical indenter and submicronic hook, this small value relative to the typical period indicated that movement of the cell tongue occurred almost simultaneously with a maximum in contact stiffness. This is counterintuitive as a higher stiffness, which can be assumed to be linked to a higher cell tension, should result in the cell tongue shortening, and not lengthening. This observation could be consistent with the cell being stiffer on the side being indented but softer on the other side being aspirated by the micropipette. In the Discussion section, we propose different possible explanations for this observation.
<figure><img src="image_6.png" /><figcaption>Figure 4. (A) Microscopy image of a T cell aspirated in a micropipette (see Supplementary Movie 6, Online Resource 2). A kymograph was plotted at the location of the yellow dashed line. The scale bar represents 5 µm. (B) Kymograph based on (A). Vertical red dashed lines highlight the location of oscillations in the length of the aspirated part of the cell. The yellow dashed line from A is reported on the y axis, with the same spatial scale. The x-axis corresponds to time (horizontal scale bar: 50 s). (C) Average period of the oscillations in the aspirated part of the cell in the absence (pipette only) and presence of the respective indenter (visual, sphere; visual, hook; visual, subm. hook) compared to the oscillations observed in contact stiffness (stiffness, sphere; stiffness, hook; stiffness, subm. hook). The horizontal bars represent the median and the vertical represent the IQR. (D) Microscopy image of a T cell aspirated into a micropipette (see Supplementary Movie 7, Online Resource 2). A first kymograph was plotted at the location of the blue dashed line to track the position of the holding micropipette, $x_{\text{pipette}}$, a second one was plotted at the location of the red dashed line to track the position of the cell tongue, $x_{\text{tongue}}$. The scale bar in (A) applies to (D). (E) Kymographs based on (D). At the bottom, the length of the cell tongue, $L_{\text{tongue}}$, obtained by difference between $x_{\text{pipette}}$ and $x_{\text{tongue}}$, is shown in gray. The contact stiffness is shown in black. The vertical gray dashed lines highlight the locations of maxima in tongue length. The yellow dashed line from (D) is reported on the y axis, with the same spatial scale.</figcaption></figure>
# 4 Discussion

We have demonstrated that the stiffness of resting T cells fluctuates in most cells (around 60 %), with median fluctuations ranging from approximately 10% to 100%. However, only close to a third of the cells exhibit strong and repeated stiffness oscillations. We found a typical fluctuation timescale of 30-35 seconds. The fluctuations were observable with three different indenter sizes, ranging from submicronic to several microns in diameter. Upon destabilizing the actin cytoskeleton, the fluctuations vanished. Furthermore, we demonstrated that the movements of the cell body aspirated inside a micropipette correlate with the stiffness fluctuations. The timescale observed in cell movement and cell stiffness fluctuations aligned well with the typical time found when holding a cell with a micropipette in the absence of a microindenter.

We have shown in a previous study that indenting cells with sharp tips favors probing the mechanical properties of the cell cortex, whereas using larger indenters, such as beads of several micrometers in diameter, probes the cell interior. Thus, we thought that hooks would allow exhibiting larger cortex-related stiffness fluctuations than beads, but this was not the case. Our interpretation relies on the fact that T cells have very low tension and that the threshold in the indenter's tip diameter between probing the cortex and the cell interior is set by an elastocapillary length (given by the ratio of cell cortex tension to cell effective Young's modulus) that is small, 2.7 µm, for T cells [34]. This makes it challenging to distinguish between the surface and interior effects using the micronic tips of the hook microindenters. Thus, we employed submicron tips to try to isolate cell cortex effects more effectively. However, these thinner tips did show lower stiffness fluctuations when compared directly with the thicker hooks. Lowering the applied forces from 50 ± 25 pN to, for example, 20 ± 10 pN to minimize the contact area of the indenter with the cell [34] could potentially enable us to better differentiate between surface and interior effects; however, it is not possible to reliably perform experiments at such low forces with the currently reached noise levels on the microindentation setup.

Our measured stiffness oscillation period of approximately 30 s is close to the typical duration of 20 s reported by Laplaud et al. for fluctuations in cell cortex thickness [16]. We performed experiments at room temperature, and by analogy with previous work by us on the activation of T cells [35], we expect that experiments at 37°C would lead to qualitatively similar but faster oscillations, thus on a timescale closer to the one observed by Laplaud et al. These authors concluded that the thickness fluctuations are local rather than resulting from a global cell contraction. This does not fully align with our findings of a correlation between the stiffness fluctuations probed at one extremity of a cell and the movement of the cell tongue inside the micropipette holding its opposite side. Although, at first sight, this correlation might be more consistent with a global increase in cell tension, similar to the one occurring at the onset of mitosis [41, 42], we observed rather counterintuitively that a peak in stiffness correlated with a longer cell tongue. This suggests that the part held by the micropipette became softer when the side compressed by the microindenter was stiffer. This could be a sign that tension changes are neither fully local, nor fully global, but rather localized to regions of the cell. This might be explained by the presence of travelling waves in the actin cortex similar to those described by Driscoll et al. in CHO cells [24]. Alternatively, this counterintuitive observation might be a viscoelastic effect, i.e., a consequence of the delay between a cortex contraction and the time for this increased tension to translate into a shortening of the tongue given the viscoelastic properties of the cell surface [43], which might also involve the recently characterized delay needed to propagate tension from one location of the cell to another [44].

Although more work will be required to better characterize these stiffness fluctuations temporally and spatially, we note that the microvillar search described by Cai et al. showed that T cells cover the whole opposing cell surface within a timescale comparable to the fluctuation timescale that
we measured [8]. Cai et al. also measured dwell times that fall in the same order of magnitude. Thus, we speculate that stiffness fluctuations are linked to cytoskeletal reorganization associated with the microvillar search.

Our observations offer new insights into characterizing the resting state of human T cells. We found a general actin dependence, although we are not yet able to describe the reorganizational process causing the fluctuations. Our results provide parallels in timescale to other work performed on the cell cortex and microvillar dynamics. Our results raise the question of how the measured fluctuations are linked to the dynamics of immune synapse formation that we quantified previously, as well as the applicability of our findings to other cell types.

**5 Conclusion**

Cell stiffness measurements are often used to distinguish healthy from diseased cellular states, with studies typically reporting average values. However, we demonstrate that cellular mechanical properties are dynamic rather than constant, exhibiting temporal fluctuations that provide an additional dimension for characterizing the cell state beyond simple averages. This discovery highlights the importance of measurement approaches that can capture temporal dynamics, as single-timepoint techniques may miss important information about the mechanical state of a cell.

**6 Acknowledgements**

The authors thank C. Hivroz and S. Dogniaux for providing T cells. This work has received financial support from the AXA Research Fund and from the National Research Agency grant "Criticality" (ANR-23-CE30-0006).

**7 Author Contribution Statement**

J.H. designed experiments, F.B.M. performed experiments. F.B.M. and J.H. analyzed the data. F.B.M and J.H. wrote the manuscript. For the purpose of open access, the authors have applied a Creative Commons Attribution (CC BY) license to any Author Accepted Manuscript version arising from this submission.

**8 Data Availability Statement**

The data that support the findings of this study are available from the authors upon reasonable request.

**9 References**

[1] T. M. Svitkina, Trends in Cell Biology (2020) https://doi.org/10.1016/j.tcb.2020.03.005

[2] P. Chugh and E. K. Paluch, Journal of Cell Science (2018)
https://doi.org/10.1242/jcs.186254

[3] G. Salbreux, G. Charras, and E. Paluch, Trends in Cell Biology (2012)
https://doi.org/10.1016/j.tcb.2012.07.001

[4] A. Jawahar, J. Vermeil, J. Heuvingh, O. Du Roure, and M. Piel, Current Opinion in Cell Biology (2024)
https://doi.org/10.1016/j.ceb.2024.102381

[5] D. Schmidt, C. Monzel, T. Bihr, R. Merkel, U. Seifert, K. Sengupta, and A.-S. Smith, Physical Review X (2014)
https://doi.org/10.1103/PhysRevX.4.021023
[6] A. E. Pelling, F. S. Veraitch, C. P. Chu, B. M. Nicholls, A. L. Hemsley, C. Mason, and M. A. Horton, Journal of Molecular Recognition (2007)
https://doi.org/10.1002/jmr.832

[7] A. Yu. Krol, M. G. Grinfeldt, S. V. Levin, and A. D. Smilgavichus, European Biophysics Journal (1990)
https://doi.org/10.1007/BF00185092

[8] E. Cai, K. Marchuk, P. Beemiller, C. Beppler, M. G. Rubashkin, V. M. Weaver, A. Gérard, T.-L. Liu, B.-C. Chen, E. Betzig, F. Bartumeus, and M. F. Krummel, Science (2017)
https://doi.org/10.1126/science.aal3118

[9] A. Pierres, A.-M. Benoliel, D. Touchard, and P. Bongrand, Biophysical Journal (2008)
https://doi.org/10.1529/biophysj.107.125278

[10] A. Pierres, V. Monnet-Corti, A.-M. Benoliel, and P. Bongrand, Trends in Cell Biology (2009)
https://doi.org/10.1016/j.tcb.2009.05.009

[11] K. Sengupta, P. Dillard, and L. Limozin, Biophysical Journal (2024)
https://doi.org/10.1016/j.bpj.2024.02.023

[12] C. Hivroz and M. Saitakis, Frontiers in Immunology (2016)
https://doi.org/10.3389/fimmu.2016.00046

[13] R. Orbach and X. Su, Frontiers in Immunology (2020)
https://doi.org/10.3389/fimmu.2020.02187

[14] M. L. Dustin and J. A. Cooper, Nature Immunology (2000)
https://doi.org/10.1038/76877

[15] F. Eghiaian, A. Rigato, and S. Scheuring, Biophysical Journal (2015)
https://doi.org/10.1016/j.bpj.2015.01.016

[16] V. Laplaud, N. Levernier, J. Pineau, M. S. Roman, L. Barbier, P. J. Sáez, A.-M. Lennon-Duménil, P. Vargas, K. Kruse, O. Du Roure, M. Piel, and J. Heuvingh, Science Advances (2021)
https://doi.org/10.1126/sciadv.abe3640

[17] P. Chugh, A. G. Clark, M. B. Smith, D. a. D. Cassani, K. Dierkes, A. Ragab, P. P. Roux, G. Charras, G. Salbreux, and E. K. Paluch, Nature Cell Biology (2017)
https://doi.org/10.1038/ncb3525

[18] R. Bulteau, L. Barbier, G. Lamour, Y. Lemseffer, M. Verlhac, N. Tessandier, E. Labrune, M. Lenz, M. Terret, and C. Campillo, Small (2025)
https://doi.org/10.1002/smll.202500221

[19] J. B. Michaux, F. B. Robin, W. M. McFadden, and E. M. Munro, The Journal of Cell Biology (2018)
https://doi.org/10.1083/jcb.201806161

[20] M. Nishikawa, S. R. Naganathan, F. Jülicher, and S. W. Grill, eLife (2017)
https://doi.org/10.7554/elife.19595

[21] K. Guevorkian, D. Gonzalez-Rodriguez, C. Carlier, S. Dufour, and F. Brochard-Wyart, Proceedings of the National Academy of Sciences (2011)
https://doi.org/10.1073/pnas.1105741108

[22] Y. Yang and M. Wu, Philos Trans R Soc Lond B Biol Sci. 2018 May 26;373(1747):20170116. doi: 10.1098/rstb.2017.0116.

[23] W. M. Bement, M. Leda, A. M. Moe, A. M. Kita, M. E. Larson, A. E. Golding, C. Pfeuti, K.-C. Su, A. L. Miller, A. B. Goryachev, and G. Von Dassow, Nature Cell Biology (2015)
https://doi.org/10.1038/ncb3251

[24] Driscoll MK, Losert W, Jacobson K, Kapustina M. Spatiotemporal relationships between the cell shape and the actomyosin cortex of periodically protruding cells. Cytoskeleton (Hoboken). 2015 Jun;72(6):268-81.
doi: 10.1002/cm.21229
[25] Végh AG, Fazakas C, Nagy K, Wilhelm I, Krizbai IA, Nagyoszi P, Szegletes Z, Váró G. Spatial and temporal dependence of the cerebral endothelial cells elasticity. J Mol Recongnit. 2011 May-Jun;24(3):422-8.
doi: 10.1002/jmr.1107

[26] Sehgel NL, Zhu Y, Sun Z, Trzeciakowski JP, Hong Z, Hunter WC, Vatner DE, Meininger GA, Vatner SF. Increased vascular smooth muscle cell stiffness: a novel mechanism for aortic stiffness in hypertension. Am J Physiol Heart Circ Physiol. 2013 Nov 1;305(9):H1281-7.
doi: 10.1152/ajpheart.00232.2013

[27] Schillers H, Wälte M, Urbanova K, Oberleithner H. Real-time monitoring of cell elasticity reveals oscillating myosin activity. Biophys J. 2010 Dec 1;99(11):3639-46.
doi: 10.1016/j.bpj.2010.09.048. Erratum in: Biophys J. 2011 Sep 21;101(6):1556.

[28] Schlosser F, Rehfeldt F, Schmidt CF. Force fluctuations in three-dimensional suspended fibroblasts. Philos Trans R Soc Lond B Biol Sci. 2015 Feb 5;370(1661):20140028.
doi: 10.1098/rstb.2014.0028

[29] J. Husson, Methods in Molecular Biology (2023)
https://doi.org/10.1007/978-1-0716-2851-5_1

[30] A. E. Zucchetti, N. Paillon, O. Markova, S. Dogniaux, C. Hivroz, and J. Husson, Biology of the Cell (2021)
https://doi.org/10.1111/boc.202000133

[31] A. Sawicka, A. Babataheri, S. Dogniaux, A. I. Barakat, D. Gonzalez-Rodriguez, C. Hivroz, and J. Husson, Molecular Biology of the Cell (2017)
https://doi.org/10.1091/mbc.E17-06-0385

[32] L. Guillou, A. Babataheri, P. -h. Puech, A. I. Barakat, and J. Husson, Scientific Reports (2016)
https://doi.org/10.1038/srep21529

[33] A. D. Edelstein, M. A. Tsuchida, N. Amodaj, H. Pinkard, R. D. Vale, and N. Stuurman, Journal of Biological Methods (2014)
doi: https://doi.org/10.14440/jbm.2014.36

[34] O. Markova, C. Clanet, and J. Husson, Biophysical Journal (2023)
https://doi.org/10.1016/j.bpj.2023.12.008

[35] A. Zak, S. V. Merino-Cortés, A. Sadoun, F. Mustapha, A. Babataheri, S. Dogniaux, S. Dupré-Crochet, E. Hudik, H.-T. He, A. I. Barakat, Y. R. Carrasco, Y. Hamon, P.-H. Puech, C. Hivroz, O. Nüsse, and J. Husson, Biophysical Journal (2021)
https://doi.org/10.1016/j.bpj.2021.02.042

[36] J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J.-Y. Tinevez, D. J. White, V. Hartenstein, K. Eliceiri, P. Tomancak, and A. Cardona, Nature Methods (2012)
https://doi.org/10.1038/nmeth.2019

[37] C. A. Schneider, W. S. Rasband, and K. W. Eliceiri, Nature Methods (2012)
https://doi.org/10.1038/nmeth.2089

[38] Y. Benjamini and Y. Hochberg, Journal of the Royal Statistical Society Series B (Statistical Methodology) (1995)
https://doi.org/10.1111/j.2517-6161.1995.tb02031.x

[39] Q. Yu, J. Li, M. P. Murrell, and T. Kim, Biophysical Journal (2018)
https://doi.org/10.1016/j.bpj.2018.10.008

[40] J. Lam, M. Herant, M. Dembo, and V. Heinrich, Biophysical Journal (2008)
https://doi.org/10.1529/biophysj.108.139154

[41] M. Kelkar, P. Bohec, and G. Charras, Current Opinion in Cell Biology (2020)
https://doi.org/10.1016/j.ceb.2020.05.008
[42] M. P. Stewart, J. Helenius, Y. Toyoda, S. P. Ramanathan, D. J. Muller, and A. A. Hyman, *Nature* (2011)
https://doi.org/10.1038/nature09642

[43] M. Herant, V. Heinrich, and M. Dembo, *Journal of Cell Science* (2005)
https://doi.org/10.1242/jcs.02275

[44] H. De Belly, S. Yan, H. B. Da Rocha, S. Ichbiah, J. P. Town, P. J. Zager, D. C. Estrada, K. Meyer, H. Turlier, C. Bustamante, and O. D. Weiner, *Cell* (2023)
https://doi.org/10.1016/j.cell.2023.05.014