CAN A CELL REALLY HEAT UP BY SEVERAL DEGREES?

Measuring temperature inside a single living cell has only been possible for about fifteen years, according to the paper. It has produced a puzzle. A growing body of work reports temperatures inside cells about 1 to 10 kelvin above their environment; one cited study is titled “Mitochondria are physiologically maintained at close to 50 °C”. But estimates based on how much heat a cell actually produces, and on ordinary heat conduction, predict differences below a thousandth of a degree.

Known measurement artefacts do not easily explain why several physically and chemically different nano-thermometers give similar results. Refinements of heat conduction at small scales remain far too small to close a gap of several orders of magnitude.

Look at the thermometer, not the source

Most attempts to resolve the puzzle focus on the heat source: a mitochondrion’s size, shape, structure and distance from the sensor, all hard to pin down. Taras Plakhotnik (University of Queensland) turns the problem around.

An ideal point source of heat would, in theory, reach an infinite temperature. But no real thermometer measures a point: it has a finite thermometric volume, and what it reports is an average over that volume. The sensor, he notes, is usually far better characterised than the biological source.

So he asks: placed anywhere inside a region that produces a known total amount of heat, how much can a sensor of a given volume warm up, at most, in a steady state?

A bound with three ingredients

Using only Fourier’s law of heat conduction and two classic inequalities of geometry and analysis, he derives a maximum-temperature theorem:

⟨T⟩ − T_ref ≤ 9 Q / (2 (36π)^(2/3) κ V^(1/3))

where Q is the total heat power produced, κ a lower bound on the thermal conductivity and V the sensor’s volume. Nothing else enters: not where the heat comes from, not how it is distributed, not how far away the sensor sits.

For a typical cultured mammalian cell, the paper takes a net heat output of 50 picowatts, a conductivity of 0.1 watt per metre per kelvin, at the low end of values reported for cells, and a sensor of 10⁻²² cubic metres, about a sphere 60 nanometres across. The maximum possible warming: about 2 millikelvin.

The bound is sharp: it is reached when a spherical heat source is wrapped in a shell-shaped sensor. Even in that most favourable arrangement, a 1-kelvin rise would require at least 25 nanowatts, five hundred times more than the cell’s measured output. If heat were instead spread evenly through a cell-sized volume, the limit would drop to about 2 microkelvin.

What about heat-producing and heat-absorbing reactions cancelling each other out? Calorimetry only measures the net output, while the theorem counts all the heat produced. A 1-kelvin reading with only 50 picowatts leaving the cell would then need at least 25 nanowatts released locally, and almost as much absorbed elsewhere in the same cell.

The result applies directly to the sensors in use: nanodiamonds, upconversion nanoparticles, fluorescent polymer particles and core–shell quantum dots.

A thermometer that lags behind

The theorem assumes that the sensor itself is internally at equilibrium. To show why that may fail, the author simulated two gas reservoirs, one hot and one cold, separated by an elastic membrane. The gases quickly reached a common temperature while the membrane relaxed much more slowly, and the gap widened as the membrane got stiffer. A small object can stay out of equilibrium even when its surroundings have settled, and a standard calibration against equilibrium temperatures would not reveal it.

Where the missing physics must hide

The paper does not claim the reported hot spots are artefacts. It states that if a kelvin-scale signal is truly thermal, at least one assumption of the theorem must fail. The candidates it lists: extra power injected by the probe itself, energy stored temporarily in long-lived states, a sensor that never fully equilibrates, or a non-thermal change in the sensor or its surroundings that mimics a temperature change. Telling them apart, the author concludes, will take experiments that follow how the thermometer itself relaxes.