Thermorheology of living cells—impact of temperature variations on cell mechanics

In its standard configuration (as described in Lincoln et al [26]), the μOS is a dual-beam laser trap as shown in figure 1. A square glass capillary (80 μm inner diameter, 40 μm wall thickness, ST8508, VitroCom, USA) is mounted perpendicular to two optical fibers (colored in yellow in figure 1) which are axially aligned facing each other at a distance of 200 μm. To avoid reflection and diffraction effects, the glass capillary and the optical fibers were submersed in index matching gel.

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Through the capillary, suspended cells can be transported to the trapping region where deformation is caused by optically induced surface stress σ(t) [24]. Cells, first trapped at low laser power, show creep behavior when exposed to a stepwise increased laser power P_stretch (video S1, available from stacks.iop.org/NJP/15/045026/mmedia). The relative deformation of the cell (t) is quantified using image analysis techniques (see section 2.2). Assuming linear viscoelastic behavior, the observed deformation directly translates into a creep compliance J(t) via

$$\begin{equation} J(t) = \frac{\epsilon(t)}{\sigma_0}. \end{equation}\noindent \tag{ 1 }$$

Herein, the optically induced stress σ₀(t) depends linearly on the applied laser power P_stretch [24, 25]. In our setup, cells were delivered out of a reservoir to the measurement region via a pressure-driven pump system connected to the capillary. The whole measurement procedure including the pump system, laser and temperature control was automatically executed by custom-made LabVIEW software (National Instruments, Austin, TX). As previously shown by several authors [27–29], optical stretching is unavoidably accompanied by a laser-induced temperature rise of cell medium and cells on a timescale of several milliseconds. Its impact on cell deformability, however, has not been investigated yet but will be clarified throughout this work.

To study temperature-dependent cell rheology on short and long timescales, we extended the standard setup by two slight modifications. Firstly, to control the temperature of the whole setup (including the cell container), we designed a custom-made aluminum sample holder, steadily flushed by temperate water from a thermostat (F10, Julabo, Germany). The thermostat was looped back by an external thermosensor positioned close to the measurement region, guaranteeing a stable setup temperature during experiments and stable temperature changes within approximately 20 min (shown in figure 6(D)). Secondly, to realize temperature jumps within a millisecond range we added two optical fibers positioned at a distance of 110 μm to the trapping region (colored in red in figure 1). When these fibers emit laser light of 1064 nm, the cell medium around the measurement region is quickly heated up, without direct exposition of trapped cells to laser light. As the expected temperature rise in the measurement region strongly depends on the distance of the laser fibers, we aimed at minimizing this distance by etching the heating laser fibers (standard HI-1060 single mode fibers) from 125 μm down to a diameter of 80 μm using hydrofluoric acid.

To calibrate the temperature rise in the measurement region for both stretch and heating laser emission, we used a temperature sensitive fluorescent dye, similar to the procedure described in [27]. In brief, as the temperature indicator we chose the fluorescent dye Rhodamine B (Sigma-Aldrich, St. Louis, Missouri), since it has high temperature sensitivity in the range of 0–120 °C [30]. To obtain temperature information for a large field of view, we used an Axioobserver.Z1 in combination with a 10 ×  objective (Carl Zeiss, Jena, Germany). The dye solution was prepared from Rhodamine B (0.1 mM) in carbonate buffer (20 mM), loaded into the μOS setup and calibrated by measuring the fluorescence intensity at different setup temperatures. For determining the laser-induced temperature rise inside the glass capillary, we took the average of six independent measurements performed at six different setup temperatures between 15 and 40 °C, to make sure that neither the setup temperature nor other nonlinearities of the Rhodamine B dye significantly affected our results. For the heating lasers, we measured an increase of temperature of ΔT_h = 7 °C W⁻¹ (per fiber) in the measurement region and for the stretch lasers an increase of ΔT_s = 26 °C W⁻¹ (per fiber) (figure 2). Note that all values of laser powers presented throughout the paper are reported per fiber of either stretch or heat laser pair.

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The extraction of quantitative values from single-cell experiments comprises the digital processing of image stacks, recorded at 30 frames per second by video phase contrast microscopy. An edge detection algorithm, as proposed by Lincoln et al [26], was implemented in MATLAB (The Mathworks, USA), detecting the outer edge of every measured cell with subpixel accuracy. Subsequently, we applied a shape-tracking algorithm on obtained contour data to minimize the influence of small rotations around the optical axis of the microscope. The rotation corrected data were then used to determine the deformation along the laser beam. In supplementary video S1 (available from stacks.iop.org/NJP/15/045026/mmedia), an image sequence recorded during a stretch experiment is shown, together with the applied laser pattern and the detected cell deformation. To demonstrate the working principle of the rotation correction, a cell showing a clear rotation is presented in video S1. Our shape-tracking algorithm is able to account for cells showing small rotations around the optical axis of the microscope (see the green bar in video S1). However, rotations around any other axis (e.g. the axis of the laser beam) principally hinder accurate detection of the optically induced deformation, thus those cells were excluded from further evaluation. The cell deformations were quantified in terms of relative deformation, calculated as (t) = (L_∥(t) − L_∥(0))/L_∥(0), where (t) is the relative deformation, L_∥(t) is the measured length of the cell along the laser axis at time t and L_∥(0) is the length of the cell before starting the stretch experiment.

Phenomenologically motivated and supported by basic polymer models (Rouse, Zimm, William, Landel, Ferry), the influence of temperature on the rheology of a broad class of polymers can be described by TTS, for creep experiments given by

$$\begin{equation} J(t,T_{\rm ref}) = \frac{J_i(t/a_{T_i},T_i)}{b_{T_i}}. \end{equation} \tag{ 2 }$$

Creep compliance curves J_i measured at an arbitrary temperature T_i can be shifted to overlap with a measurement J taken at a reference temperature T_ref by scaling time with a time shift factor a_Ti and the whole creep function by a modulus shift factor b_Ti [31]. For simple, thermally stable polymeric systems, b_Ti is expected to be not or only slightly temperature dependent, while the influence of temperature is mainly expressed by a rescaling of the time axis via a_Ti. In the literature therefore, materials following equation (2) are often called thermorheologically simple if all J_i(t) superimpose just by applying a temperature-dependent time shift factor a_Ti [32].

Considering viscous flow as a thermally activated process, the temperature dependence of a_Ti is of special interest to polymer physics as it provides information on the activation energy of molecular movement [32]. In the simplest case, a_Ti shows an Arrhenius dependency [31]

$$\begin{equation} \mathrm{log}{(a_{T_i})} = \frac{E_{\rm A}}{R}\left(\frac{1}{T_i}-\frac{1}{T_{\rm ref}}\right), \end{equation} \tag{ 3 }$$

where E_A is the (constant) activation energy and R is the universal gas constant. However, for glassy materials (which cells are frequently speculated to be [33–35]) in the vicinity of the glass transition temperature T_g, a_Ti is normally observed to not obey Arrhenius behavior as activation energy becomes a function of temperature [31, 32]. Then, the temperature dependence of a_Ti above T_g is often successfully described by the William–Landel–Ferry (WLF) equation

$$\begin{equation} \mathrm{log}{(a_{T_i})} = \frac{-C_1(T_i-T_{\rm ref})}{C_2+(T_i-T_{\rm ref})}, \end{equation}\noindent \tag{ 4 }$$

where C1 and C2 are empirical factors [2].

We implemented a custom-made algorithm to construct a master curve from mean creep compliance curves, measured at different temperatures. After selecting a reference curve, all the other curves were scaled according to equation (2), while scaling factors a_Ti and b_Ti were systematically varied to minimize the error of the overlap. To account for the stochastic nature of cell-rheological data, the procedure was repeated for various binning values, reference temperatures and random subsets of cells to construct the mean curves while the reported values for a_Ti, b_Ti and E_A (equation (3)) were found to be restored in most cases. Due to the lack of a clear curvature in the data when plotting a_Ti over T_eff (e.g. in figure 7(A)), fitting values for equation (4) (the WLF equation) were found to be sensitive to statistical variation. However, the ratio between the constants C2 and C1 was widely conserved and found to be close to a value of 10.

MCF-10A cells (CRL-10317), a non-tumorigenic epithelial cell line, were obtained from American Type Culture Collection (ATCC, Manassas, VA). MCF-10A were maintained in a 1:1 mixture of Dulbecco's modified Eagle's medium and Ham's F12 medium, supplemented with 5% horse serum, 20 ng ml⁻¹ epidermal growth factor, 10 μg ml⁻¹ insulin, 100 ng ml⁻¹ cholera toxin, 500 ng ml⁻¹ hydrocortisone and 100 U ml⁻¹ penicillin/streptomycin. Prior to measurements, cells cultured in 25 cm² flasks were detached by application of 1 ml 0.025% trypsin–EDTA solution, resuspended in 3 ml of culture medium and centrifuged at 100g for 4 min. Finally, single cells were resuspended in culture medium to a concentration of about 5 × 10⁵ cells ml⁻¹ and loaded into the μOS.

In the μOS (and in any other optical trap) a higher laser power produces higher optical forces, while—due to light absorption in aqueous medium—simultaneously raising the temperature in the trapping region. When assuming small deformations ((t)∝σ₀), then creep compliance J(t) is independent of the applied force (equation (1)). Consequently, instantaneous effects of temperature changes on optically induced cell deformability can be investigated experimentally by comparing creep compliance curves, obtained for different stretch laser powers.

In a standard μOS setup, creep experiments were sequentially performed on single cells with a random stretch laser power P_stretch for each experiment (figure 3(C)). This ensures that the final average curves for different laser powers (figure 3(A)) comprise cells that were measured at various time points of the whole experiment. Hence, possible long-term dependences of cell deformability, for example as reported in [33], should cancel out.

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In figure 3(A), average creep curves of 137 cells are displayed, binned by applied laser power P_stretch. Creep curves for different stresses (σ₀∝P_stretch) do not overlap as would be expected for a temperature-independent viscoelastic linear material, but rather show significant bigger compliance for higher laser powers. We state that the apparent drop of stiffness as seen in figure 3(A) is caused by laser-induced heating during the step stress experiment. This hypothesis is supported by the observation that creep compliance curves for different laser powers overlap surprisingly well by scaling exclusively with a_Ti (figure 3(B)).

In this experiment, each laser power P_stretch can be translated to an effective temperature T_eff via T_eff = T_setup + P_stretchΔT_s, including the setup temperature T_setup (constantly held at 15 °C throughout the whole measurement) and a laser-induced heating of ΔT_s = 26 °C W⁻¹ determined by calibration (see section 2.1). The time shift factors a_Ti used in figure 3(B) to scale the creep curves are plotted in figure 3(D) in an Arrhenius plot.

Hitherto no appropriate value for the activation energy E_A or the glass transition temperature T_g has been proposed for whole living cells. From our experimental data it cannot be decided whether the observed dependency displayed in figure 3(D) follows Arrhenius behavior (equation (3)) or rather represents a flat version of the WLF equation (equation (4)). When assuming Arrhenius behavior, the activation energy for the viscous flow of living suspended MCF-10A cells turns out to be E_A ≈ 74 kJ mol⁻¹. In contrast, the equivalent activation energy of pure water at T = 37 °C is much lower with E^water_A ≈ 17 kJ mol⁻¹ [36]. Thus, it is unlikely that we measure the temperature dependence of the free surrounding aqueous medium only. It would be interesting to compare E_A to values for the activation energy of reconstituted cell bio-polymers; however, to our knowledge there are no such values available in the literature up to now. Values of standard polymer melts like polystyrene are unintuitive as comparison since they are measured at temperatures of hundreds of celsius (e.g. polystyrene E_A = 59 kJ mol⁻¹ [37]). Due to the aforementioned coupling of heat and force in the optical stretcher, we had to make an assumption on how the creep compliance scales with the applied force, i.e. we assumed the simplest case of linear viscoelasticity. However, it is important to note that we do not state that cellular material is fully linear viscoelastic but rather that laser-induced heating can mostly explain the apparent increase of compliance for higher laser powers, shown in figure 3(A). In the next section, we modify our experimental setup rendering the need for assuming linear behavior superfluous.

The observed systematic shift of J(t) (figure 3(A)) can be explained as temperature induced but could also arise from a nonlinear response to applied stress, e.g. shear thinning. In order to exclude nonlinear viscoelastic effects, it is necessary to measure cells with the same stress σ₀(t) but at different temperatures T_eff.

To realize an experiment where the applied stress can be kept constant while temperature changes can be independently applied on a short timescale, we further exploit the effect of laser-induced heating. We designed a modified μOS setup, extended by two optical fibers (colored in red in figure 1), further denoted as heating fibers. By laser emission of the heating fibers, trapped cells can be heated on a millisecond timescale without being directly illuminated. The applied stress σ₀, exclusively determined by emission of the stretch fibers, however can be kept constant. Hence, heat generation and force application are partially decoupled in the modified μOS setup.

We measured cells with a fixed stretch laser power of P_stretch = 700 mW per fiber (figure 4(A)). One second before the stretch started, we activated the heating laser to randomly emit a power of P_heat between 0 and 1700 mW per fiber, causing a sudden change of temperature in the measurement region (figure 4(B)). Similar to the situation above, an effective temperature can be calculated for each single experiment via T_eff = T_setup + P_stretchΔT_s + P_heatΔT_h, including the temperature rise caused by emission of the heating fibers. A calibration measurement (figure 2) revealed a local temperature increase of ΔT_h ≈ 7 °C W⁻¹ (per fiber) in the measurement region (see methods and figure 2).

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Creep compliance curves of cells do not overlap when measured with the same stress σ₀(t) but different heating laser values P_heat. This confirms our hypothesis that cell deformability is strongly temperature dependent as effects of different forces can now be excluded. In figure 4(C), we demonstrate that measured curves again superimpose by only varying time shift factors a_Ti while b_Ti can be set to a constant value. Similar to the experiment with different stretch laser powers (figure 3), cells exhibit thermorheologically simple behavior. Fitting equation (3) (Arrhenius) leads to an activation energy of E_A ≈ 75 kJ mol⁻¹, a similar value as measured before in section 3.1.

With this experiment, we can reasonably argue that temperature instantaneously affects the deformability of single suspended cells. As nonlinear viscoelastic effects can now be excluded, laser-induced heating is identified as the dominant factor, responsible for the apparent drop of stiffness with increasing stretch laser power (figure 3(A)).

A necessary prerequisite for the applicability of TTS is the reversibility of temperature effects. As shown in the measurements above, creep rates were increased when temperature was raised. Consequently, a reduction of temperature should lead to a reduction of creep rates. At a setup temperature of T_setup = 23 °C, cells were measured with a constant stretch laser power P_stretch = 600 mW per fiber for 6 s (figure 5(A)). Within these 6 s, we activated the heat lasers for 2 s, emitting a random power P_heat between 0 and 1500 mW per fiber (figure 5(B)).

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Figure 5(C) shows creep compliance curves for 843 cells, binned by applied heat laser power P_heat. At t = 2 s, creep rates instantaneously increase upon activation of heat lasers. At t = 4 s, heat lasers are switched off and creep rates return back to baseline levels, comparable to cells where no temperature rise has been applied.

This experiment demonstrates that creep rates directly depend on temperature. However, as living cells are active systems and thermally fragile it is clear that reversibility and TTS can only be valid within certain limits. The applicability of TTS naturally cannot be expected a priori for timescales where regulatory processes actively alter the cytoskeleton as well as for temperatures where the structure of load-bearing proteins is irreversibly altered.

In previous sections, T_setup was kept constant while—using laser-induced heating—sudden effects of temperature changes were studied. To assess how cellular material changes with temperature over a longer period, we performed creep experiments at different setup temperatures T_setup, such that cells had several minutes and hours to adapt to the new ambient temperature before being optically trapped and deformed.

In the beginning, the setup temperature was set to 37 °C and ≈200 cells were measured within approximately 3 h. Subsequently, the setup was cooled down to 25 and 15 °C where measurements were repeated with approximately the same amount of cells and the same range of stretch laser power P_stretch, randomly chosen between 600 and 1300 mW per fiber (figure 6(C)/(D)). Each cooling step required about 20–25 min until the whole setup was thermally equilibrated (gray points in figure 6(D)). Cells measured during temperature transition were excluded from further evaluation.

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In figures 6(A) and (B), we demonstrate that the creep curves can be scaled according to equation (2) to overlap in a single master curve. Used time shift factors a_Ti and modulus shift factors b_Ti are plotted in figure 7 and listed in table A.3: in contrast to the previous experiments, the modulus shift factor b_Ti can no longer be kept constant. Creep curves obtained at T_setup = 15 °C still behave thermorheologically simple, as the corresponding values for b_Ti are equal for all stretch laser powers P_stretch (marked as circles in figures 6 and 7). However, curves obtained at T_setup = 25° have to be rescaled by a different value for b_Ti to superpose with the measurements at 15 °C. The same holds true for measurements carried out at T_setup = 37 °C. Despite the fact that several creep curves were obtained at the same effective temperature T_eff, a different value for b_Ti is required to make curves superpose when the setup temperature T_setup was changed in between. Apparently, the occurrence of thermorheological complexity is associated with the fact that cells had time to adapt to the changed setup temperature. For the same T_eff, cells appear stiffer when measured at higher T_setup.

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As shown in figure 7(B), thermorheologically complex behavior generally occurs for all creep curves measured at effective temperatures T_eff higher than a critical temperature T_crit ≈ 52 °C: a non-constant modulus shift factor b_Ti is necessary for sufficient superposition of curves, regardless of whether T_setup was changed in between or not. On long timescales, we proposed cellular adaptation to explain the occurrence of thermorheological complexity. On short timescales, thermal fragility of load bearing structures in the cell appears to be a more plausible explanation for the variation of b_Ti for T_eff > T_crit.

In tables A.1–A.3, the row with italic values were used as a reference curve for TTS and is the one closest to 37 °C.