The Mystery of the 10⁵ Temperature Gap Inside Cells: The Limits and Challenges of Nanothermometry

Abstract

Researchers at Osaka University in Japan and the University of Queensland in Australia have published a review analysing the enormous gap between theory and measured values that confronts luminescence nanothermometry, the technique used to measure temperature inside cells. The authors argue that the concept of temperature itself remains valid in statistical-thermodynamic terms even at the 10 nm scale, but report that the so-called "10⁵ gap issue", in which measured values (~1 K) run 100,000 times larger than calculated ones (~10 μK), remains unresolved. Attempts have been made to narrow the gap by assigning a lower thermal conductivity to intracellular membranes and by taking Kapitza resistance into account, but the authors call for more refined measurement methods alongside a theoretical rethink before the phenomenon can be fully explained. [Quantum Biology Society] Pinning down quantitatively when, where and how much heat is generated at the cellular level is a central problem in understanding how organisms maintain body temperature and run their metabolism. As luminescence nanothermometry has advanced, using fluorescent proteins, quantum dots and nanodiamonds among other probes, striking results have been reported: stable temperature differences of more than 1 K between organelles even in unstimulated cells, and mitochondrial temperatures that may possibly rise as high as 323 K (about 50 °C) under full activation of respiration in human embryonic kidney 293 cells and primary skin fibroblasts. A review by Madoka Suzuki of Osaka University and Taras Plakhotnik of the University of Queensland, published in Biophysical Reviews in 2020, takes on the fundamental dilemma sitting behind those spectacular observations. ■ Is the Concept of Temperature Valid at the Nanoscale? Before weighing the reliability of nanothermometers, the authors first examine whether temperature, a macroscopic state function, can even be defined in the microscopic world of the nanometre scale. Statistical mechanics says that the smaller the system, the more severe its temperature fluctuations become. Molecular dynamics simulations put the temperature fluctuation of a single amino acid residue at around 70 K, and the textbook formula gives the same figure for a spherical volume of water with a radius of 0.25 nm. But the characteristic correlation time of these fluctuations is extremely short: roughly 15 ps for a spherical region of radius 1.5 nm in water, and about 12 ns for a nanodiamond of radius 50 nm. At the 10 nm scale the fluctuations run on the order of 1 K, with a characteristic time on the order of 0.1 ns. Since real measurement times are far longer than this, random temperature fluctuations average out. The authors put a number on it: the thermodynamically limited noise floor for a 50 nm thermometer is a few μK s^1/2, more than three orders of magnitude below the best experimental figure achieved so far. The upshot is that in aqueous conditions and with luminescent temperature probes, the concept of temperature holds even at the 10 nm scale, and thermal fluctuation is not what limits present-day nanothermometry. ■ The Heart of the Contradiction: The 10⁵ Gap Issue The hardest problem in this field is the gap between calculation and measurement that refuses to close. The calculation: when cells are assumed to have the thermal conductivity of water and the heat equation is applied, the rise in whole-cell temperature from a local heat source comes out very small. Suzuki's own group calculated that whole-cell temperature in HeLa cells could rise by only 10 μK (0.00001 K) if the sarco/endoplasmic reticulum Ca²⁺-ATPase (Serca) were solely responsible for the temperature changes measured on Ca²⁺ shock. The measurement: Yang and colleagues measured a local temperature rise of about 1 K in the NIH3T3 cell line using quantum-dot nanothermometry. Yet accounting for that rise theoretically would require a heat source of about 1 μW or more, a figure that appears to be three orders of magnitude larger than what has been determined in stimulated brown adipocytes, cells known for generating heat. The name for this 100,000-fold (10⁵) discrepancy comes from a 2015 paper by Suzuki's group, the review's first author, and it has been the subject of fierce debate ever since, running through a published exchange between Baffou's group, which set out the critique, and researchers working with fluorescent thermometers. ■ Cross-Checking With Non-Luminescent Probes, and Rethinking Thermal Conductivity Could the fluorescent thermometers be responding to intracellular variables other than temperature, such as viscosity, pH or ionic strength, and producing an artefact? Cross-checks with non-luminescent probes: the authors point to significant temperature rises observed with probes working on entirely different principles. Bimetal microcantilevers registered about 0.2 K in stimulated brown adipocytes. Micro-thermocouple arrays inside a thermally stabilised system detected frequent fluctuations of about 60 mK and, in one detection area, a continuous elevation of up to 285 mK, while other areas stayed stable. A microscale thermocouple probe detected rapid rises of about 7.5 K near mitochondria in neurons of the sea slug Aplysia californica when the cells were stimulated with a proton uncoupler. Given this variety of probes and methods, the authors conclude that it may be unnecessary to decide that the temperature increase is unmeasurable in individual cells. Thermal conductivity and Kapitza resistance: one attempt to narrow the gap has been to question the thermal conductivity used in the calculations. Bastos and colleagues measured the thermal conductivity of a single lipid bilayer experimentally at about 0.2 W m⁻¹ K⁻¹ at 300 K, only a third that of water. Bringing in Kapitza resistance, the thermal resistance at the boundary between two different materials, the authors' modelling brings the average effective thermal conductivity inside a cell down to around 0.1 W m⁻¹ K⁻¹, roughly six times smaller than water. ■ Significance and Open Questions Resetting thermal conductivity to a lower value to reflect the complexity of the cell's interior does close some of the distance between calculation and measurement, but nowhere near enough to fill a 100,000-fold gap. The authors put it plainly: the gap still remains although it has narrowed, and they suggest this may give some ground for optimism about eventually closing it. The review settles that the concept of temperature stays physically valid down to the 10 nm scale, while summing up coolly the divide between theory and experiment that the field now faces. Temperature is more than an index of heat. It shifts chemical equilibria, affects flows driven by electrochemical gradients, and has been shown to drive directional motion of particles and to induce the accumulation of nucleotides and lipids, which makes it a core variable in the metabolism of living things. The authors conclude that resolving the 10⁵ dilemma will require approaching the gap from both sides at once: refining the theoretical estimates as the complexity of cellular processes becomes better understood, and developing new measurement methods that are more accurate and less susceptible to artefacts. #IntracellularTemperature #Nanothermometry #LuminescenceNanothermometry #FiveOrdersGap #ThermalConductivity #KapitzaResistance #ThermalFluctuations #StatisticalMechanics #Nanodiamond #ODMR #Thermogenesis #Mitochondria #Review #QuantumBiology #BiophysicalReviews Source (Biophysical Reviews, open access): https://doi.org/10.1007/s12551-020-00683-8 Commentary from the sceptical side (How hot are single cells?, free): https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7398142/ Perspective defending the measurements (2021, free): https://pmc.ncbi.nlm.nih.gov/articles/PMC8660847/