What Does Temperature Really Mean in Living Cells? Beyond Equilibrium Abstractions in Molecular Biology

What Does Temperature Really Mean in Living Cells? Beyond Equilibrium Abstractions in Molecular Biology Ian Todd Sydney Medical School University of Sydney Sydney, NSW, Australia [email protected] December 2025 Abstract Temperature is a deceptively simple concept that becomes surprisingly slippery in biological contexts. While a thermometer might read 37°C, what does that actually mean for a molecule in the cytoplasm? For a motor protein burning ATP? For chromatin undergoing phase separation? The standard answer—“temperature is average kinetic energy”—quietly assumes thermal equilibrium, random exploration of states, and uniform conditions. But living cells violate all of these assumptions: they’re driven systems far from equilibrium, with spatially heterogeneous viscosity, active energy injection, and non-random dynamics confined to metastable attractors. This creates a fundamental problem: many of our computational and thermodynamic tools (from kBTas an energy scale to Landauer’s principle for information erasure) implicitly rely on equilibrium assumptions that simply don’t hold in biology. Here we show that temperature in biological systems must be understood as operational and context-dependent: different processes, timescales, and cellular compartments can have different effective temperatures (Teff), measured through fluctuation-dissipation relations rather than assumed from the environment. This framework resolves apparent paradoxes (how can sub-thermal signals be functional?), explains why cells aren’t “water baths,” and provides practical guidance for interpreting molecular measurements in non-equilibrium contexts. For biotechnology applications—from drug design to synthetic biology—recognizing these distinctions is not academic pedantry but essential for understanding what actually controls molecular behavior in living systems. 1 The Problem: When Your Thermometer Lies You measure the temperature of a cell culture: 37°C. Your incubator is stable. The medium is well-mixed. Everything should be at thermal equilibrium. But then: •Motor proteins consume ATP and generate forces that look thermally equivalent to thousands of degrees Kelvin [8] •Phase-separated condensates show diffusion coefficients implying local “temperatures” 10-20% higher than the surrounding cytoplasm [3] •Molecular signals at energies < kBTln 2 (below Landauer’s limit for bit erasure) somehow coordinate cellular responses [5] 1 •Chromatin shows non-ergodic dynamics—it doesn’t explore all possible configurations even given infinite time [2] •The viscosity of cytoplasm varies by 100-fold across subcellular regions and changes with cell cycle phase [4] The Core Frustration Standard molecular modeling treats temperature as a single number that sets the energy scale for thermal fluctuations. This is correct only if the system is at equilibrium: energy distributed according to Boltzmann statistics, all states explored randomly, and no net energy flows. Living cells violate every single one of these assumptions. So what does “temperature” actually mean in a cell? And more importantly, how do we do molecular modeling when our fundamental thermodynamic assumptions are wrong? 2 What Temperature Means (and Doesn’t Mean) 2.1 The Equilibrium Definition In classical thermodynamics, temperature has a precise meaning: Temperature is the parameter Tsuch that: P(Ei)∝e−Ei/kBT(1) In other words: the probability of finding a system in state iwith energy Eifollows a Boltzmann distribution characterized by temperature T. From this, several useful facts follow: •Equipartition: Each degree of freedom carries average energy (1/2)kBT, so a free molecule has kinetic energy (3/2)kBTfrom its three translational modes. •Energy scale: Thermal fluctuations have characteristic energy ∼kBT(at 300K, kBT≈ 4.1×10−21 J≈2.5 kJ/mol). •Landauer’s principle: Erasing one bit of information requires dissipating at least kBTln 2 ≈ 0.7kBT. This framework is incredibly powerful when it applies. The problem: it doesn’t apply to most of biology. 2.2 Why Cells Aren’t at Equilibrium The fundamental issue: Temperature is defined as an equilibrium concept. When a system isn’t at equilibrium, “temperature” becomes ambiguous or undefined. This isn’t a minor technical detail—it’s a conceptual crisis. If we can’t define temperature, how do we use kBTas an energy scale? How do we apply thermodynamic bounds like Landauer’s principle? How do we interpret molecular dynamics simulations that assume a temperature? 2 Table 1: Equilibrium vs biological reality Equilibrium assumption Reality in cells Single temperature TSpatially heterogeneous, modedependent Teff(ω) Boltzmann distribution P(E)∝ e−E/kBT Active processes inject energy, creating non-thermal distributions Random exploration of states Confined to metastable attractors, non-ergodic dynamics No net energy flows Constant ATP consumption, ion pumps, metabolic gradients Thermal noise is white (frequencyindependent) Colored noise with spectral structure from active processes Viscosity uniform and constant 100-fold spatial variation, cell-cycle dependent 3 The Solution: Operational Temperature 3.1 Effective Temperature from Fluctuation-Dissipation The way forward is to define temperature operationally: measure it from what the system actually does, rather than assuming it from the environment. The key tool is the fluctuation-dissipation relation (FDR). In equilibrium, the noise spectrum Sη(ω)and the dissipative response Re[Γ(ω)] are related by: Sη(ω) = 2kBTRe[Γ(ω)] (2) where: •Sη(ω)is the power spectral density of fluctuations at frequency ω •Re[Γ(ω)] is the real (dissipative) part of the response kernel •Tis the equilibrium temperature Key insight: We can invert this relation to define an effective temperature even out of equilibrium: Teff(ω) = Sη(ω) 2kBRe[Γ(ω)] (3) This Teff(ω)is: •Operational: Measured from noise and response, not assumed •Frequency-dependent: Different processes can have different effective temperatures •Observable: Accessible via spectroscopy, single-molecule tracking, or perturbation-response experiments 3 Practical Interpretation Teff(ω)tells you: “For fluctuations at frequency ω, the system behaves as if it were at temperature Teff(ω).” This can be higher or lower than the actual environmental temperature, depending on active driving, viscosity, and noise structure. Important caveat:Teff(ω)is only meaningful when the FDR ratio is approximately constant over a frequency band. If the ratio varies strongly with ω, report the full frequency-dependent violation rather than collapsing to a single number. How to Measure Teff(ω)in Cells Step 1: Choose an observable q(t)(bead displacement, membrane undulation, chromatin locus position) Step 2: Measure spontaneous fluctuations →power spectral density Sq(ω) Step 3: Apply weak, band-limited probe (optical trap, electric field, microstimulation), measure linear response χ(ω); the dissipative part is Re Γ(ω) = ωIm χ(ω) Step 4: Compute Teff(ω) = Sq(ω)/(2kBRe Γ(ω)) Report band-averaged Teff only where this ratio is flat; otherwise report the full frequencydependent FDR-violation ratio. 3.2 What This Means for Different Cellular Processes Table 2: Effective temperatures in biological contexts Process Teff relative to 310K Physical interpretation Fast molecular collisions (ns-ps) ≈310K True thermal equilibration with water bath Diffusion of small molecules (s-ms) 300 −320K Slightly elevated by crowding/activity Motor protein stepping (ms) 500 −2000K ATP hydrolysis creates “hot” effective fluctuations [8] Chromatin dynamics (seconds-minutes) 280 −300K High viscosity increases damping, lowers Teff Phase-separated condensates 320 −340K Elevated due to confinement [3] Membrane protein conformational changes Variable Depends on lipid environment, crowding Key takeaway: There is no single “temperature of the cell.” Fast processes see the water bath (310K). Slow, viscous processes see effectively lower temperatures. Active, driven processes see much higher effective temperatures. 4 4 Practical Implications 4.1 What About kBTas an Energy Scale? If temperature is mode-dependent, what happens to the ubiquitous kBTthat appears in: •Binding affinities (Kd∼e−∆G/kBT) •Reaction rates (Arrhenius: k∼e−Ea/kBT) •Landauer’s principle (Eerase ≥kBTln 2) •Thermal fluctuation scales Answer: Use the appropriate Teff for the process in question. Practical Rule •Fast equilibration (< microseconds): Use bath temperature (310K for mammalian cells) •Slow, viscous processes: Effective temperature may be lower due to damping •Active, driven processes: Effective temperature may be much higher due to energy injection •When in doubt: Measure Teff from fluctuation-dissipation When to Use Bath T Bath T(310K): Fast DOFs (ps–ns timescales), dilute small-molecule diffusion, clear timescale separation Teff(ω):Colored noise or active driving, but FDR ratio approximately constant over a frequency band No single T:Strong nonlinearity, aging systems with evolving spectra, or FDR-violation ratio strongly frequency-dependent—report full spectra instead of collapsing to a number 4.2 How Viscosity and Cell Phases Matter The viscosity ηappears in the dissipation kernel Γ(ω). For simple Stokes drag on a spherical particle: Re[Γ(ω)] ≈6πηr (4) where ris particle radius. This means: Teff =Sη 2kB·6πηr (5) High viscosity →Lower Teff (if noise spectrum Sηis unchanged) Important: This assumes the noise power doesn’t change. Active processes can simultaneously increase both viscosity and noise power—in which case Teff may actually increase despite higher damping. This is why phase-separated condensates can show elevated Teff despite their high viscosity [3]. This is why: 5 •Crowded cytoplasm (η∼10 −100×water): Diffusion slows, effective temperature for diffusion-limited reactions is lower •Phase-separated condensates: If noise is also elevated (from confinement), Teff can be higher despite high viscosity •Membrane vs cytoplasm: Different viscosity regimes →different Teff for the same thermal bath Cell cycle phases: •Interphase: Chromatin decondensed, ηmoderate •Mitosis: Chromatin condensed, cytoplasm reorganized, effective temperatures shift •Phase transitions (e.g., gel-sol in cytoskeleton): Sudden changes in ηand Teff 4.3 Can Cells Be Modeled as Water Baths? Short answer: Sometimes yes, mostly no. When water bath approximation works: •Fast processes (ps-ns) where molecules thermalize with solvent •Small molecules in dilute solution •Local equilibrium holds (fast relaxation relative to process timescale) When it fails: •Active processes (motors, pumps) injecting energy •Crowded/viscous regions where relaxation is slow •Processes operating at sub-Landauer energies (below kBTln 2) •Non-ergodic dynamics (e.g., chromatin, protein aggregation) •Phase-separated compartments with different local properties The Right Model Instead of “cell = water bath at 310K,” think: “cell = heterogeneous active medium with mode-dependent, spatially varying Teff(ω, x)plus non-equilibrium driving.” For practical modeling: •Identify the relevant process and its timescale •Measure or estimate local viscosity and activity •Use appropriate Teff for that context •Don’t assume ergodicity or Boltzmann distributions 6 5 The Sub-Landauer Domain and Timing Inaccessibility 5.1 When Molecular Signals Operate Below kBTln 2 Landauer’s principle states that erasing one bit of information requires dissipating at least: Eerase ≥kBTln 2 ≈0.7kBT≈2.9×10−21 J at 310K (6) But many biological signals operate below this threshold: •Ephaptic coupling between neurons: ∼10−23 J (300×below Landauer) [1] •Weak synaptic noise: Individual events below detection threshold, yet causally effective •Chromatin loop formation: Sub-threshold contacts accumulate to functional structures •Stochastic gene expression: Transcription factor binding at sub-Landauer energies How is this possible? Doesn’t Landauer’s principle forbid sub-thermal information processing? 5.2 Amplitude vs Timing: The Key Distinction The resolution comes from recognizing two different kinds of information: 1. Amplitude information: “Did something happen? What was its magnitude?” 2. Timing information: “When did it happen? In what order?” Stochastic resonance and population integration allow detection of sub-Landauer amplitude signals: •Many weak signals add coherently: signal scales as N, noise as √N •SNR improves with population size: SNR ∼√N •Can detect presence of periodic signals well below individual threshold But timing reconstruction requires Landauer-scale energy: To irreversibly record the temporal order of Mevents requires: Etiming ≥kBTln(M!) ≈kBT·Mln M(7) This is equivalent to kBTln 2 ·log2(M!) bits—the information-theoretic cost of specifying one ordering out of M!possible orderings. Example: 10 molecular events •Detecting that 10 events occurred: Can be done sub-Landauer via integration •Determining which specific order they occurred: Requires ln(10!) ≈21.8bits →21.8× kBTln 2 ≈6×10−20 J 7 If signal energies are ∼10−23 J, measurement energy exceeds signal energy by 6000×. Biological Implication Cells can detect that sub-threshold coordination occurred (amplitude), but cannot resolve when individual events happened (timing). This creates path degeneracy: exponentially many microscopic trajectories correspond to the same macroscopic outcome. This isn’t a measurement limitation—it’s a fundamental thermodynamic constraint. The timing information is genuinely inaccessible without destroying the coherence that makes it functional. 6 What This Means for Biotech 6.1 Drug Design and Binding Affinities Standard drug design uses: Kd=e∆G/kBT(8) But if the binding site has local Teff =Tbath: •Crowded active sites: Lower Teff →tighter binding than expected •Membrane proteins: Different Teff in lipid environment •Allosteric sites: Conformational dynamics may have elevated Teff Practical tip: When affinity measurements in vitro don’t match cellular context, consider whether local Teff differs from assay conditions. 6.2 Synthetic Biology and Minimal Cells Creating synthetic minimal cells requires understanding: •What’s the minimum ATP consumption to maintain non-equilibrium organization? •How do phase separation and viscosity affect gene circuits? •Can we exploit sub-Landauer signaling for ultra-low-power biocomputing? Key insight: You can’t just “run the same chemistry slower.” Many cellular functions depend on active, non-equilibrium processes that maintain specific Teff values in specific compartments. 6.3 Diagnostics and Biomarkers Measuring local Teff could be a novel diagnostic: •Cancer cells: Altered metabolism →different Teff distributions? •Protein aggregation diseases: Changes in viscosity/phase separation detectable via Teff? •Drug mechanism: Does the drug change local Teff as part of its action? Technologies: fluorescence correlation spectroscopy, single-molecule tracking, optical tweezers—all can measure fluctuation-dissipation and extract Teff. 8 6.4 Understanding Molecular Mechanisms When you see published molecular dynamics simulations at “310K,” ask: •Is that the right effective temperature for this process? •Are we modeling equilibrium sampling when the real system is driven? •Should different regions have different temperatures? •Are we missing non-equilibrium effects by assuming thermal noise? Better approach: •Use non-equilibrium MD with active processes explicitly modeled •Measure Teff from experimental fluctuation spectra •Don’t assume ergodicity—check if the system actually explores its phase space •Consider sub-Landauer signaling: amplitude detection without timing resolution •Model biological systems as high-dimensional coherence fields rather than low-dimensional discrete states [7] 7 Conclusion: Beyond Gentle Molecular Modeling The frustration with equilibrium abstractions in biology is justified. Temperature is not a single number in living cells. kBTis not a universal energy scale. Cells are not water baths. But this doesn’t mean we abandon thermodynamics—it means we use the right thermodynamics: 1. Operational temperature: Define Teff(ω)from fluctuation-dissipation, measured not assumed 2. Non-equilibrium framework: Recognize cells as driven systems with energy injection and spatial heterogeneity 3. Mode-dependent analysis: Different processes see different effective temperatures 4. Sub-Landauer domain: Amplitude vs timing distinction; path degeneracy from inaccessibility 5. Context matters: Viscosity, phase separation, active processes all modulate effective thermodynamics For molecular biologists and biotech: This isn’t abstract theory. It’s the reality of how molecules actually behave in cells. Ignoring non-equilibrium effects doesn’t make them go away—it just makes our models wrong in ways we don’t understand. For theorists and modelers: The tools exist (fluctuation-dissipation, stochastic thermodynamics, path integral methods for non-equilibrium systems). We don’t need to pretend cells are water baths anymore. The temperature of a cell is not 37°C. It’s a spatially and temporally varying effective temperature field Teff(ω, x, t)that reflects the non-equilibrium nature of life itself. Embrace it. 9