A Thermal–Quantum Crossover Model for Mid-Infrared Modulation of Neuronal Excitability

A THERMAL–QUANTUM CROSSOVER MODEL FOR MID-INFRARED MODULATION OF NEURONAL EXCITABILITY A PREPRINT Enric Espel Sanchez Department of Physics University of Helsinki, 00560 Helsinki, Finland November 19, 2025 ABSTRACT Voltage-gated ion channels in neurons open when a gating coordinate crosses a free-energy barrier that is sharply sensitive to the local transmembrane voltage, typically over tens to hundreds of millivolts of effective bias. We model the channel pore as a nanoscale dielectric cavity that supports electromagnetic field modes whose voltage fluctuations include both classical (thermal) and quantum (zero-point) contributions. We show that these contributions are separated by a single thermal– quantum crossover frequency ωc= 2kBT/ℏ , which at physiological temperature lies in the longwavelength mid-infrared ( ∼23 µm ). Above ωc , the zero-point (quantum) contribution dominates the voltage variance across the pore. In a simple barrier-limited WKB picture of channel gating, this enhanced variance lowers the effective barrier and produces an exponential increase in the predicted channel opening probability. We carry this crossover scale consistently from a finite-temperature field-theoretic description, through an effective gating Hamiltonian that couples a voltage-sensitive coordinate to electromagnetic fluctuations, and into an experimentally testable prediction at the cellular level. Specifically, the framework predicts that neuronal firing thresholds (rheobase current and spike-initiation voltage) will exhibit a localized dip under two complementary conditions: (i) during absorbed-dose–equalized mid-infrared stimulation, as a function of illumination frequency; and (ii) at a fixed long-wavelength illumination near 23 µm while the bath temperature is swept, precisely at the temperature T⋆ where the illumination frequency matches ωc(T⋆)=2kBT⋆/ℏ . We outline whole-cell patch-clamp and infrared neural stimulation protocols — including fast membrane thermometry, TTX block, and power normalization to control for bulk heating — that can falsify these predictions. Our analysis links nanoscale electromagnetic fluctuations to macroscopic neuronal excitability in a way that is, in principle, testable with existing mid-/far-infrared neuromodulation hardware. Plain-language summary What is the idea? The tiny water-filled pores (ion channels) in neurons are never perfectly quiet. Heat makes the electric field wiggle (classical noise), and quantum mechanics adds its own wiggle even at zero temperature (quantum noise). We show that there is a single frequency, ωc= 2kBT/ℏ, that cleanly separates these two kinds of noise. Why does that matter? When the jiggling has more quantum character (above ωc ), it can more effectively help the channel cross the energy barrier to open. This could lower the voltage needed for a neuron to fire! How could you test it? Shine mid-infrared light on neurons and sweep only the frequency. The firing threshold should dip near ωc. Because ωcis set by temperature, cooling or warming the preparation should move the dip in lockstep. A Thermal–Quantum Crossover Model for Mid-Infrared Modulation of Neuronal ExcitabilityA PREPRINT A Brief Introduction Quantum phenomena once considered negligible at physiological conditions have now been potentially implicated in photosynthesis, avian magnetoreception, and debated in olfaction [ 1 – 4 ]. These precedents motivated a focused search for quantum effects in neurobiology, specifically in the voltage fluctuations that govern the opening of sodium (Na + ) and potassium (K+) channels [5, 6]. The reasoning is simple: the nano-scale geometry and sensitive nature of ion channels and their selectivity filters, could generate the perfect conditions for very small variations and fluctuations having greater and more noticeable effects. As such, the central idea of this paper is that both zero-point and thermal electromagnetic fluctuations generate voltage swings of a similar order as channel gating thresholds ( ∼10 – 200 mV depending on geometry) [ 7 – 9 ]. Crucially, the relative weight of quantum versus thermal noise is controlled by a simple scale ωc≡2kBT ℏ≈8.2×1013 rad s−1(T= 310 K)(1) which falls in the mid-infrared ( ≈23 µm wavelength). The following sections develop the theoretical backbone; with a final section describing a possible experiment that directly tunes ωacross ωc. Quantum Field–Modulated Neural Excitability: A Threshold–Frequency Framework We start by modeling the channel pore as a cylindrical dielectric cavity of length d and relative permittivity ϵr . We see that for a single mode of frequency ωconfined to volume V∼d3, the electric-field root-mean-square amplitude is Eq=rℏω 2ϵ0ϵrV,∆Vq(ω;d) = Eqd=rℏω 2ϵ0ϵrd.(2) (For field quantization and EM energy partition, see e.g. [ 10 , 11 ].) Classically, a mode has total energy kBT , and the electric part contributes kBT/2(cf. fluctuation–dissipation [12]). Therefore, the analogous voltage fluctuation is ∆Vth(T;d) = rkBT ϵ0ϵrd.(3) Equating Eqs. 2 and 3 yields the crossover frequency ωc(T) = 2kBT ℏ,(4) above which quantum fluctuations should dominate. Heff =H0−λ qeff ˆ X∆V(t),(5) We now define the (two-sided, angular-frequency) voltage power spectral density (PSD) SV V (ω)≡Z∞ −∞ dτ eiωτ ⟨∆V(t)∆V(t+τ)⟩= 2ℏωcoth ℏω 2kBTRe Zeff (ω),(6) where Zeff (ω) subsumes geometry and material response; in the classical limit SV V (ω)→4kBTRe Zeff (ω) . We use a two-sided PSD versus ω with units V2·s (i.e., V2 per rad/s). Thus ωc demarcates a quantum-dominated regime (ℏω≫kBT) from a thermal one. Applying Caldeira–Leggett, for weak, approximately Markovian coupling the pure-dephasing rate is Γϕ=λ2q2 eff 2ℏ2SV V (ω=0), τd≡Γ−1 ϕ=2ℏ2 λ2q2 eff SV V (ω=0) .(7) For a finite-band process one may replace SV V (0) by a filter-weighted integral; our conclusions near ωc are unchanged. Now if we treat the cavity field as a scalar potential A0 in the Lorenz gauge, we can embed the finite-temperature QFT. The finite-TEuclidean action is SE[A0] = ϵ0ϵr 2Zβℏ 0 dτZV(∇A0)2+1 c2∂τA02,(8) 2 A Thermal–Quantum Crossover Model for Mid-Infrared Modulation of Neuronal ExcitabilityA PREPRINT with the Matsubara propagator D00(k, iωn) = 1 ϵ0ϵr 1 k2+ω2 n/c2,(9) reproducing Eqs. 2–3 upon summing over n [ 16 , 17 ]. Importantly, and surprisingly, the same order of magnitude for ωc emerges as the scale separating n= 0 (thermal) from n= 0 (quantum) contributions, tying our field-theoretic picture back to the Hamiltonian description. We know that the channel opens when the gating coordinate tunnels through a free-energy barrier U(x) . For an energy-independent barrier of height U0and width d, the WKB probability is P(ω)∝exp−2d ℏq2mU0−qeff ∆V(ω),(10) and because ∆V(ω) grows as √ω [Eq. 2], P is exponentially sensitive to frequencies near and above ωc , potentially leading to the sharp threshold-like behaviour [20, 21]. Experimental Proposals Overview We will implement two complementary tests of the threshold-frequency hypothesis: (A) Absorbed-dose–equalized frequency sweep (3–12 µ m): Uses an existing mid-IR QCL band, but equalizes absorbed dose (peak membrane ∆T ) at each frequency to remove spectral absorption bias. This provides a rigorous negative/limited-band test. (B) Temperature-tracking crossover at a fixed wavelength. To make the crossover testable within physiological temperatures, we fix the illumination near the predicted threshold band and sweep the bath temperature. Specifically, we use a single-mode far-IR/THz source at λ= 23.0µm (i.e., ω= 2πc/λ ≈8.19 ×1013 s−1 ), which lies close to the theoretical ωc(T)=2kBT/ℏaround body temperature. The equality ω=ωc(T)occurs at T⋆=ℏω 2kB≈313 K (40◦C) for λ= 23.0µm. We hold λ fixed and step T from 298 – 314 K in 1 K increments. At each Tj we re-equalize absorbed dose by tuning the incident power P⋆(Tj) so that the peak membrane temperature rise ∆Tpeak matches a preset target within ±15% . If the framework is correct, response metrics (e.g., ∆Irheo , Vthreshold ) will exhibit a dip/inflection as Tjcrosses T⋆, reflecting the switch in dominance between quantum and classical field fluctuations at ωc. Optionally (used when available) a long-wavelength source (18–30 µ m QCL or THz line) that can directly span the 15–60 µm window around λc≈23 µm. Common Readout and Endpoints Primary endpoint (current-clamp). Measure spike threshold (rheobase) and F–I curves in whole-cell current-clamp. For each condition we: • Inject 1 s current steps (or staircase) with 5–10 pA increments to map firing probability vs. current. • Define rheobase as the minimal current eliciting ≥50% spike probability across 10 repeats. • Report ∆Irheo (change from baseline) and ∆Vthreshold (from ramp protocols). Secondary endpoints. •Voltage-clamp Na+availability and kinetics (separate blocks) to track channel-level effects. • Spike timing jitter and ISI statistics under noisy current injection (dynamic threshold). Power/dose operating point. There are two possible regimes, adherence to one means sticking to it across frequencies/temperatures: (i) Low-∆Tregime: Target ∆Tpeak = 0.2±0.05 K at the membrane. (ii) Moderate INS-like regime: Target ∆Tpeak = 2.0±0.2 K for larger effect sizes while controlling for thermal confounds. 3 A Thermal–Quantum Crossover Model for Mid-Infrared Modulation of Neuronal ExcitabilityA PREPRINT High-bandwidth thermometry (membrane-local). Replace/augment the thermocouple with a membrane-bound fluorescent thermometer (e.g. Rhodamine B or Eu-complex), sampled at ≥ 10 kHz via epifluorescence. Calibrate fluorescence vs. temperature in situ (0.1 K resolution). Use the thermocouple only as a slow absolute reference. Materials and Apparatus • Whole-cell patch rig (Axopatch-class amplifier) and upright microscope with epifluorescence path. • Mid-IR QCL, tunable 3–12 µm (25–100 THz) for Part (A). • Fixed-line source for Part (B): single-mode far-IR/THz QCL near 23.0 µm, difference-frequency mid-IR source. • Optional long-λsource (if available, for Part B): 18–30 µm QCL or THz line. • ZnSe OAP optics; beam expander; achromatic focusing to reduce λ-dependent spot changes. • Germanium (or some polarizer-based) variable attenuator with known spectral transmission. •Beam profiler or knife-edge setup at the sample plane to verify spot size at each λ. • 50 µm blackened shield around pipette tip and Ag/AgCl reference to suppress photoelectric artifacts. • FTIR or grating spectrometer on a 1% pick-off for absolute frequency verification. • MCT (or pyroelectric) detector on a 9% pick-off for incident power monitoring. •Membrane-bound fluorescent thermometer dye and calibration standards. • Temperature-controlled perfusion chamber with ±0.05 K stability and logging. Absorbed-Dose–Equalized Frequency Sweep (3–12 µm) Rationale. Water/protein absorption and optics throughput vary strongly with λ . We equalize the stimulus at the membrane by holding ∆Tpeak constant across frequencies, (not just the incident power). Calibration: equalizing absorbed dose. 1. For each center frequency νi (step across 3–12 µ m), measure the local membrane ∆Tpeak(νi, P) vs. pulse power Pusing the fluorescent thermometer (single 10–20 ms pulse). 2. Fit a monotonic calibration P⋆(νi)such that ∆Tpeak(νi, P⋆)=∆Ttarget (choose regime (i) or (ii) above). 3. Verify spot diameter at the sample plane is within ±10% across νi ; adjust focus/expansion to stabilize geometry. Protocol. 1. Baseline (no light): Current-clamp rheobase + F–I; then voltage-clamp sodium activation/inactivation. 2. Randomized ν -sweep: For each νi , we deliver an optical pulse train (e.g., 10 ms pulses, 2 s IPI) at P⋆(νi) and collect: • Current-clamp: rheobase and ramp-derived Vthreshold (10-15 trials each). • Simultaneous fast thermometry to confirm ∆Tpeak within target band. 3. Recovery block: Repeat baseline. Controls. (i) 1 µM TTX to test Na+-dependence of any threshold shift. (ii) Optical dark control: shutter closed but run full protocol. (iii) Far-IR/THz illumination control (if available) at matched absorbed ∆Tpeak. (iv) For a photoelectric artifact control: illuminate bath away from the cell; illuminate the pipette under a black shield to ensure no electrical pickup. Expected outcomes. If frequency per se is causal, ∆Irheo(ν) shows a dip localized in ν ; if thermal-only, the curve flattens after dose equalization. 4 A Thermal–Quantum Crossover Model for Mid-Infrared Modulation of Neuronal ExcitabilityA PREPRINT Temperature-Tracking Crossover at Fixed Wavelength Rationale. Keep ωfixed and sweep Tso that ωc(T)crosses ω. Prediction: a threshold dip when ω≈ωc(T). Setup. • Fix λ(e.g. 23.0 µm). Compute ω= 2πc/λ. • We choose a biologically feasible temperature range (e.g., 298–314 K) with cell-viability checks. Protocol. 1. For each Tj, measure current-clamp rheobase with/without illumination (randomized order). 2. Track ∆Irheo(Tj)and ∆Vthreshold(Tj). Expected outcomes. A temperature-locked moderate dip in threshold at T⋆ where ω≈ωc(T⋆)=2kBT⋆/ℏ ; the dip should shift linearly with Tif the crossover governs the effect. Future Alternative: In Vivo Optical Neuromodulation in Zebrafish Larvae Why? It would demonstrate behavioral relevance and tissue penetration limits. • 5-dpf Tg(elavl3:GCaMP6s) zebrafish are immobilised in agarose [29]. • The mid-IR beam (expanded to 50 µ m) is scanned across the hindbrain motor nuclei while two–photon calcium imaging records neuronal activity. • The Tail-flick frequency serves as a behavioral endpoint, expected to increase by ∼30 % upon ω≳ωc illumination. A positive result should constitute direct evidence for quantum-field contributions to neural excitability. Discussion and Outlook By threading the threshold frequency ωc through every level of theory—from voltage variances to Hamiltonian coupling, propagator structure, and tunnelling probability—we offer a coherent, falsifiable storyline. Furthermore, and crucially, because ωc= 2kBT/ℏ is a universal thermal–quantum crossover scale, any biomolecular nanodomain that (i) supports field modes in the mid-IR and (ii) couples those modes electrostatically to a barrier-limited functional coordinate could exhibit analogous threshold behavior. Ion-channel gating provides a concrete worked example; it should not be pigeonholed, broader applicability to enzyme active sites, allosteric pockets, or aggregation nuclei remains an open, testable question, and a novel avenue for quantum neurobiology. However, it is important to acknowledge that, while our threshold-frequency framework reveals a previously overlooked quantum contribution to ion-channel gating, we emphasize that higher-level cognitive and emotional processes remain well described by established, largely classical neural-network models. Any functional role of quantum fluctuations at the circuit or behavioral level remains speculative and demands dedicated investigation. Appendix A: Derivations Underlying the Abstract A.1 Setup and notation We modeled the channel pore as a homogeneous dielectric nanodomain of relative permittivity εr and characteristic length d (transpore direction). A single electromagnetic (EM) normal mode of angular frequency ω confined to volume V is treated as a harmonic oscillator. We take the transmembrane voltage fluctuation as ∆V≡Rd 0E∥(x)dx ≈E d for a slowly varying longitudinal field. A geometrical remark. In the main text we used V∼d3 for compactness. For a cylindrical pore of radius a , V=πa2d , which can be substituted wherever V appears to expose the explicit a -dependence. For protein and confined-water dielectric considerations, see e.g. [30]. 5 A Thermal–Quantum Crossover Model for Mid-Infrared Modulation of Neuronal ExcitabilityA PREPRINT A.2 Zero-point voltage variance The electric-field energy of a single mode with (rms) amplitude Eis UE=1 2ε0εrE2V. (11) For a quantized EM mode, the ground-state (zero-point) energy is 1 2ℏω , shared equally by electric and magnetic parts, so ⟨UE⟩0=1 4ℏω. Equating the two gives Ezp,rms =rℏω 2ε0εrV,∆Vq(ω;d)≡Ezp,rms d=rℏω 2ε0εrd,(12) where the last equality used V∼d3. For a cylinder, ∆Vq=qℏω d 2ε0εrπa2. A.3 Thermal voltage variance (an equipartition) Classically, one quadratic degree of freedom at temperature T carries average energy kBT/2 . The electric part contributes ⟨UE⟩T=1 2kBT=1 2ε0εr⟨E2⟩TV, (13) hence Eth,rms =rkBT ε0εrV,∆Vth(T;d)≡Eth,rms d=rkBT ε0εrd.(14) This connects with Johnson–Nyquist noise in conductors [13, 14]. A.4 Thermal–quantum crossover frequency The crossover is defined by ∆Vq(ωc;d)=∆Vth(T;d), which yields ωc(T) = 2kBT ℏ.(15) At T= 310 K, ωc≈8.1×1013 s−1(mid-IR), corresponding to fc=ωc/2π≈1.29 ×1013 Hz and λc=c/fc≈23 µm. A.5 Finite-temperature variance and the coth factor For a bosonic mode, the mean energy at finite Tis ⟨H⟩T=ℏω¯n+1 2=ℏω 2cothℏω 2kBT,¯n=1 eℏω/kBT−1.(16) Since the electric and magnetic energies are equal on average, ⟨UE⟩T=1 2⟨H⟩T=ℏω 4cothℏω 2kBT=1 2ε0εr⟨E2⟩TV. (17) Therefore ⟨E2⟩T=ℏω 2ε0εrVcothℏω 2kBT,⟨(∆V)2⟩T= ∆V2 q(ω;d) cothℏω 2kBT.(18) This is an equal-time variance per mode at frequency ω , not a PSD. Its connection to the PSD SV V (ω) defined in the main text is the standard relation ⟨(∆V)2⟩=1 2πR∞ −∞dω SV V (ω) ; inserting the fluctuation–dissipation form SV V (ω)=2ℏωcoth(ℏω/2kBT) Re Zeff (ω)reproduces the same coth factor. A.6 Euclidean finite-Tfield theory link and Matsubara propagator In a homogeneous dielectric and Lorenz gauge, the scalar potential A0has Euclidean action SE[A0] = ε0εr 2Zβℏ 0 dτ ZV d3xh(∇A0)2+1 c2(∂τA0)2i, β ≡(kBT)−1.(19) 6 A Thermal–Quantum Crossover Model for Mid-Infrared Modulation of Neuronal ExcitabilityA PREPRINT Fourier expansion with bosonic Matsubara frequencies ωn= 2πn/(βℏ)gives the quadratic kernel D00(k, iωn) = 1 ε0εr 1 k2+ω2 n/c2.(20) Summing over n reconstructs the coth(ℏω/2kBT) occupation factor that appears in (18) [ 16 , 17 ]. Notably, the n= 0 (static) Matsubara sector encodes the classical ( ∝T ) contribution, while n= 0 terms encode quantum fluctuations—mirroring the crossover at ωcin (15). A.7 Effective coupling, dephasing, and a decoherence timescale Let the relevant gating coordinate couple to voltage fluctuations via Hint =−λ qeff ˆ X∆V(t),(21) where qeff is an effective displaced charge and ˆ X distinguishes alternative system configurations (e.g. along a reaction coordinate). For Gaussian voltage noise with PSD SV V (ω) and weak, approximately Markovian coupling, the pure-dephasing rate is Γϕ=λ2q2 eff 2ℏ2SV V (0), τd≃2ℏ2 λ2q2 eff SV V (0) .(22) Here ω⋆= 0 corresponds to quasi-static dephasing; more generally one may use a filter-weighted integral if the system selects a finite band. A.8 Semiclassical tunnelling dependence on ω Consider barrier-limited gating along x with an energy-independent barrier of height U0 and width d . In the presence of an effective bias qeff ∆V(ω)that lowers the barrier, the WKB transmission probability for E≪U0−qeff ∆Vis P(ω)∝exp"−2 ℏZd 0 dx q2mU0−qeff ∆V(ω)−Eg#≈exp−2d ℏq2mU0−qeff ∆V(ω).(23) Using (12) , ∆V(ω)∝√ω in the quantum-dominated regime, so P(ω) is exponentially sensitive to ω near and above ωc[20, 21]. A.9 Multimode generalization and broadening For a realistic (discrete) set of cavity modes indexed by m with frequencies ωm and geometry-dependent voltage participation factors, the variance is ⟨(∆V)2⟩T=X m ∆V2 q,m cothℏωm 2kBT,(24) which broadens the sharpness of the crossover if the mode density around ωc is appreciable. In the continuum limit, the sum can be replaced by an integral with an appropriate density of states and lineshape. A.10 Dimensional and (fairly) concise limiting checks (a) ∆V2 q∼ℏω ε0εrd has units of V2 ; (b) ∆V2 th ∼kBT ε0εrd also V2 ; (c) ωc in (15) is linear in T and ℏ−1 as expected; (d) (18) recovers (14) for ℏω≪kBTand (12) for ℏω≫kBT. 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