A critique of methods for temperature imaging in single cells

Guillaume Baffou* & Hervé Rigneault are at the Institut Fresnel, CNRS, Aix-Marseille
Université, Centrale Marseille, Marseille, France. Didier Marguet is at the Centre
d'Immunologie de Marseille-Luminy, Aix-Marseille Université, Inserm, CNRS,
Marseille, France. Ludovic Jullien is at the Ecole Normale Supérieure, Paris Sciences et
Lettres Research University, Sorbonne Universités, Université Pierre et Marie Curie,
Université Paris 06, CNRS, Paris, France

*guillaume.baffou@fresnel.fr

**We argue that standard thermodynamic considerations and scaling laws show that a single cell cannot substantially raise its temperature by endogenous thermogenesis. This statement seriously questions the interpretations of recent work reporting temperature heterogeneities measured in single living cells.**

Life on planet Earth has managed to adapt to a wide range of temperatures: most living organisms blossom around 15°C but psychrophiles and thermophiles can thrive at temperatures as extreme as -15°C and 122°C. Cellular compositions are tightly thermoregulated, in particular in microorganisms¹ and in plants², which may be exposed to large temperature variations. Much research has been recently devoted to uncover the mechanisms of temperature-controlled processes in biology.

Several microscopy techniques for mapping temperature at the single cell level have been developed (Table 1)³⁻¹⁹. Some of these thermal microscopy techniques have been evaluated by means of external (exogenous) heating (labeled "Ex." in Table 1), using for instance a focused infrared laser beam or illuminated gold nanoparticles (Fig. 1a)⁴,⁷⁻⁹,¹³⁻¹⁶,¹⁹. Other techniques have recorded temperature variations in living cells in the absence of any exogenous heating source, in an attempt to scrutinize endogenous thermogenesis at the single cell level (labeled "Endo." in Table 1)³,⁵,⁶,¹⁰⁻¹²,¹⁷,¹⁸. In the latter case, temperature heterogeneities of up to a few Kelvins have been reported (Fig. 1b). Here we develop thermodynamic arguments to show that such substantial
temperature variations cannot physically result from thermogenesis, which casts
doubt on the interpretation of the results reported in these works.

For a dense medium (solid or liquid) of thermal conductivity $\kappa$ and volumetric heat capacity $c$ the evolution of the temperature distribution $T(\mathbf{r},t)$ is governed by the heat diffusion equation:

$$c \partial_t T(\mathbf{r},t) - \kappa \nabla^2 T(\mathbf{r},t) = p(\mathbf{r},t) \quad (1)$$

where $p(\mathbf{r},t)$ is the heat source density (power per unit volume). This equation is valid, even for small systems, as long as the system is not too dilute and the thermal diffusion characterized by a ballistic regime, instead of a conductive regime. It is typical in physics to use dimensional analysis of differential equations to retrieve the proper orders of magnitude of involved physical quantities. We apply this approach to a system consisting of a single cell in culture, for which the heat generation term $p$ originates from the conversion of chemical energy²⁰ (thermogenesis). Microcalorimetry measurements have shown that the typical heat power delivered by a cell can reach $P \sim 100$ pW (ref. 21), without notable deviation after normalization to cell size²². In order to estimate the expected temperature increase, we will first consider a simple steady state problem where the heat is uniformly delivered within the cell volume. In this simplistic case, we can derive a simple estimation of the expected temperature increase of the system from a dimensional analysis of Eq 1 in the steady state:

$$\Delta T = \frac{P}{\kappa L} \qquad (2)$$

where $L$ is the typical size of the heat source (for a spherical source of diameter $L$, the exact solution is $\Delta T=P/2\pi\kappa L$). Hence, for a cell $L=10$ µm in size delivering a power $P=100$ pW in a watery environment ($\kappa \sim 1$ W/m/K), the expected temperature increase should be on the order of $\Delta T \sim 10^{-5}$ K. This estimated
temperature increase is much smaller than the temperature increase of around 1
K reported in the literature and which is presumed to stem from thermogenesis.

We note that typical glucose consumption is reported as 0.2 pmol/h/cell (refs. 23, 24). If we consider glucose consumption by metabolism as the main source of heat, this value yields 150 pW per cell using a α-D-glucose oxidation enthalpy ΔH=-2.8x10³ kJ/mol (ref. 25). This is consistent with the above mentioned heat production of 100 pW per cell²¹. It is relevant to consider only glucose consumption since it is the dominant source of thermogenesis in cells; taking into account other biosynthetic pathways would not change the estimations by orders of magnitude. According to equation 2, to produce a temperature increase of 1 K, a cell would have to generate a heat power of around 10 µW, which would require an unrealistic 10⁵ larger glucose consumption than what is commonly observed. Some authors have reported calculation of the typical expected temperature increase within a cell¹² and found ΔT~2 K. This study used an equation involving the heat capacity of a living cell but discarded the influence of the thermal conductivity of the surrounding medium. Such a calculation would be relevant only for a cell in vacuum that burns its whole content of glucose at once. Such a scheme does not match reality.

Next, we consider a non-uniform heat source distribution, coming for instance
from mitochondria scattered within the cytoplasm. This would be more realistic
than uniform heat delivery throughout the cells, and could lead to higher local
temperature variations. Let us consider the most favorable case to produce a high
temperature increase, which would be a situation where the whole heat power P
would come from a single location within the cell, say a small spherical region of
diameter L. Using equation 2, a temperature increase of 1 K would require the
heat source diameter to be less than 1 nm, which is unrealistic and also
undetectable. We can also estimate what would be the temperature increase if
the whole power P were delivered by a single mitochondrion. Since the typical
size of a mitochondrion is L=500 nm, using Eq 2 yields a temperature increase on the order of 10⁻⁴ K. Hence, non-uniformities cannot contribute to notably increase the temperature, even very locally.

Let us further consider a transient state. As measured in calorimetric experiments, 100 pW is the average heat power of a cell. But the heat may not be delivered continuously. Bursts of heat delivery could occur and yield substantial, albeit transient, temperature increases²⁶. A temperature increase of 1 K over a volume of 1 µm³ (i.e. the volume of a mitochondrion or the diffraction limited volume of the microscope) during ΔT=1 s (we choose this interval to match the most favorable time scale reported experimentally) would require an energy of around E= *P*Δ*t*≈Δ*T*κLΔ*t*~10⁻⁶ J. Producing such an energy would necessitate the oxidation of 0.4 pmol of glucose in 1 s, which typically exceeds by one or two orders of magnitude the total glucose amount contained within a whole cell²⁷. We note that some published work reports even more unrealistic situations, where the temperature increase within a cell lasts for more that 100 s following a calcium stress¹⁸, or where temperature increases seem to never return to zero¹². This appears to be an indication that the signal is due to a permanent modification of cell integrity, rather than a transient temperature increase. From our analysis, we do not expect that attempts to optimize the response time of a temperature probe to reveal fast brief variations will reveal anything more.

Let us finally consider the influence of a possible surface thermal resistivity of biological membranes. Heat release to the surroundings is dictated by the liquid thermal conductivity, but also by a membrane thermal resistivity that may hamper the heat release and lead to a higher cell temperature. Let us note *g* (W/m²/K) as the surface thermal conductivity of the plasma membrane or endomembranes. The effect of a finite value of *g* is to produce a temperature discontinuity *δT* across the membrane such that²⁸
$$ \delta T = \frac{\kappa}{g} |\nabla T| \qquad (3) $$

where $\nabla T$ is the temperature gradient on the outer part of the membrane. This equation leads to an estimation of the temperature discontinuity $\delta T$ (ref. 28):

$$ \delta T = \frac{P}{gL^2} \qquad (4) $$

The exact solution for a sphere of diameter $L$ is $\delta T=P/\pi gL^2$. The smaller the surface thermal conductivity $g$, the higher the temperature discontinuity. Interestingly, the smaller the system, the stronger the effect. However, typical values of $g$ for lipid bilayers are on the order of $10^8$ (ref. 29) and typical values for molecular interfaces do not go below $10^6$ $^{28}$. Hence, temperature discontinuities across biological membranes due to a finite membrane thermal conductivity cannot theoretically exceed $10^{-5}$ K. Such an effect could thus not allow a higher temperature value within an organelle, for example as has been proposed within the nucleus$^{12}$.

Consequently, neither spatial nor temporal temperature variations, nor a finite thermal conductivity of membranes, could realistically lead to a temperature increase of a few degrees within a cell in standard conditions. We note a study where heat production arising from a single cell matches theoretical predictions$^{26}$, which provides further evidence that probing heat generation in single cells requires drastic cautions. The approach used was not based on fluorescence measurements, but on the use of a mechanical microresonator with a sensitivity of 1 mW. The authors of the study did not try to map the heat production within the cell, but only collected the overall heat power. Moreover, the system was insulated in a vacuum chamber to reduce heat loss (an artificial manner to decrease the effective thermal conductivity of the surroundings $\kappa$ in equation 2 down to $10^{-5}$ W/m/K). In this setup, a heat delivery of 5.2 pJ led to a temperature
increase of 1 mK, the temperature sensitivity of the resonator. Finally, the samples studied were brown fat cells, which are responsible for temperature regulation in mammals, with an average heat power that can reach approximately 1 nW and bursts of heat delivery of 560 pJ (ref.26).

There is no contradiction between our arguments here and the fact that endothermic organisms such as mammals and birds are able to increase their body temperature by a few degrees. This originates from a collective effect: An organism containing *N* cells of individual typical size *L* and individually delivering a heat power *P* has a typical size *N*¹/³*L* and delivers a heat power *PN*. Hence the order of magnitude of its temperature rise scales as³⁰:

$$ \Delta T = \frac{P}{\kappa L} N^{2/3} \qquad (5) $$

Using typical numbers of cells in endotherms, about 10¹³-10¹⁴ (ref.31), the factor *N*²/³ in equation 2 can yield a temperature change of the right order of magnitude (a few Kelvins).

The preceding derivations cast doubt on the validity of endogenous thermogenesis studies reporting temperature rises of a few Kelvins at the single cell level. The natural concern is now to decipher what could be the origin of the signal in these measurements. As further experiments would be required to definitively ascertain the origin of these artifacts, here we only make some speculative suggestions.

Some reported techniques may simply suffer from too large a standard deviation. For instance, some authors measure an average temperature increase of 1.84 K among 31 cells following a Ca²⁺ shock, while the standard deviation is 2.9 K¹⁰, with 23% of the cells showing an apparent temperature decrease after the shock. Such large standard deviations suggest that factors other than temperature affect
the signal. Without identifying these factors, it is unwise to attribute the signal
variation solely to temperature variation. Fluorescence properties such as the
fluorescence spectrum or fluorescence lifetime are indeed known to be dependent
on many parameters. In particular, fluorescence lifetime is dependent on the
microenvironment of the fluorophores, such as the microviscosity, pH or ion
concentrations. Whereas most authors do assess these effects to some extent in
test tubes, any such observations must be tempered by the fact that the interior
of a living cell is more complex. For instance, the optical properties of genetically
encoded fluorescent thermosensors¹⁷ are dependent of the folding/unfolding of an
α-helical coiled-coil protein, which will be governed by many more constraints in
the cytosolic compartment of a cell. To conclude, thermal imaging techniques that
have been reported in the literature may indeed be temperature sensitive, but
they certainly do not report only on temperature changes when used in a system
as complex as the interior of a living cell.

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**Figure 1** Temperature mapping in living cells. (a) Exogenous heating of stained human embryonic fibroblast WS1 cells, stained with calcein AM. The bar graph shows the temperature of a single nanodiamond (circle) with local heat applied at two different locations (crosses). Error bars represent standard deviation (reproduced with permission from ref. 14). (b) Endogenous heat generation in COS-7 cells stained with fluorescent polymeric thermometer and MitoTracker Deep Red FM. Confocal fluorescence images (upper panel and left lower panel) and fluorescence lifetime image (right lower panel) from which the temperature is measured. Arrowheads point to local heat production. In the right lower panel, N indicates the nucleus. Scale bars represent 10 µm (reproduced with permission from ref. 12).

<table><caption>**Table 1** Papers reporting temperature imaging techniques for single cells.</caption><thead><tr><td>Year</td><td>Last author</td><td>Approach</td><td>Cells</td><td>Thermometry method</td><td>Ref</td></tr></thead><tbody><tr><td>1998</td><td>Yoshioka</td><td>Endo.</td><td>CHO cells</td><td>EuTTA fluo. Spectrum</td><td>3</td></tr><tr><td>2004</td><td>Ishiwata</td><td>Ex.</td><td>None</td><td>Micropipette &amp; EuTTA fluo. spectrum</td><td>4</td></tr><tr><td>2007</td><td>Ishiwata</td><td>Endo.</td><td>HeLa cells</td><td>Micropipette &amp; EuTTA fluo. spectrum</td><td>5</td></tr><tr><td>2009</td><td>Uchiyama</td><td>Endo.</td><td>COS-7 cells</td><td>Fluo. Intensity</td><td>6</td></tr><tr><td>2010</td><td>García Solé</td><td>Ex.</td><td>HeLa cells</td><td>Quantum dot fluo.</td><td>7</td></tr><tr><td>2010</td><td>Capobianco</td><td>Ex.</td><td>HeLa cells</td><td>Er<sup>3+</sup> doped NP spectrum</td><td>8</td></tr><tr><td>2011</td><td>Hernandez</td><td>Ex.</td><td>E. coli</td><td>Fluorescence</td><td>9</td></tr><tr><td>2011</td><td>Lin</td><td>Endo.</td><td>NIH/3T3 fibroblast</td><td>Quantum dot spectrum</td><td>10</td></tr><tr><td>2011</td><td>Gu</td><td>Endo.</td><td>U-251 glioblastoma</td><td>Thermocouple</td><td>11</td></tr><tr><td>2012</td><td>Uchiyama</td><td>Endo.</td><td>COS-7 cells</td><td>FLIM</td><td>12</td></tr></tbody></table>
<table><tr><td>2012</td><td>Quidant</td><td>Ex.</td><td>HeLa cells &amp; U-87 glioblastoma</td><td>GFP fluo. Anisotropy</td><td>13</td></tr><tr><td>2013</td><td>Lukin</td><td>Ex.</td><td>WS1 fibroblast</td><td>NV centres/diamond NP</td><td>14</td></tr><tr><td>2013</td><td>Nienhaus</td><td>Ex.</td><td>HeLa cells</td><td>FLIM</td><td>15</td></tr><tr><td>2013</td><td>Uchiyama</td><td>Ex.</td><td>S. cerevisiae &amp; MOLT-4 cells</td><td>FLIM</td><td>16</td></tr><tr><td>2013</td><td>Mori</td><td>Endo.</td><td>HeLa cells</td><td>GFP fluo. Spectrum</td><td>17</td></tr><tr><td>2014</td><td>Suzuki</td><td>Endo.</td><td>HeLa cells</td><td>EuTTA fluo. Spectrum</td><td>18</td></tr><tr><td>2014</td><td>Teng</td><td>Ex.</td><td>HepG2 carcinoma cells</td><td>Doped silica NP fluo intensity</td><td>19</td></tr></table>

EuTTA: Europium (III) thenoyltrifluoro-acetonate. NP: Nanoparticle. GFP: Green Fluorescent Protein.

FLIM: Fluorescence life time imaging. NV: Nitrogen vacancy. Endo.: Endogenous thermogenesis. Ex.: External (exogenous) heating.

## COMPETING FINANCIAL INTERESTS

The authors declare no competing financial interests.

## ACKNOWLEDGMENTS

We acknowledge support from the Centre National de la Recherche Scientifique (CNRS), Aix-Marseille University A*Midex (ANR-2011-IDEX-0001-02) and ANR grants Tkinet (ANR-2011-BSV5-019-05), France Bio Imaging (ANR-2010-INSB-04-01) and France Life Imaging (ANR-2011-INSB-0006).