Thermophoresis induced by photothermal shock alters reversal potential and capacitance in neurons

Abstract

Laser-induced thermal shock is widely encountered in neuroscience and biology, yet its effects on cellular thermodynamics remain poorly understood. Using whole-cell patch-clamp recordings paired with two-photon laser stimulation, we reveal that photothermal shock causes a pronounced depolarizing shift in the potassium channel reversal potential in cortical neurons—a deviation from classical Nernstian predictions. We propose that thermophoresis-driven ion fluxes within intra- and extracellular spaces disrupt conventional thermodynamic equilibria, necessitating a revision of the traditional Nernst formulation for reversal potential. To validate this hypothesis, we integrate thermophoretic dynamics into a Poisson-Nernst-Planck model coupled with transient thermal diffusion. Our analysis demonstrates that although thermal gradients dissipate within sub-millisecond timescales, cellular relaxation persists much longer, imparting a residual thermal memory that governs ion redistribution—an effect overlooked by standard Hodgkin-Huxley and Goldman-Hodgkin-Katz models. This extended model accurately predicts the observed depolarizing shift in potassium reversal potential following photothermal shock. Furthermore, we show that the increase in membrane capacitance—often attributed solely to thermally induced membrane deformation—can also arise from thermophoresis-mediated ionic rearrangements. Together, these findings introduce a unified biophysical model for ionic transport under thermal gradients and establish a new theoretical foundation for the principled development of next-generation photothermal neurotechnologies.

INTRODUCTION

Over the past two decades, optical techniques have been extensively employed in neuroscience research and in treatment of neurological disorders. These techniques have been used either to activate nanoparticles,¹ neurotransmitters,² and other chemical and genetic agents^3,4 or as standalone methods for neural stimulation^5–7 and therapeutic interventions.^8–11 Among these, infrared laser pulses have emerged as a powerful tool for direct neural stimulation and therapy without prior chemical or genetic modifications.⁶ Notably, infrared laser pulses can induce neural signaling, including the triggering of action potentials in neurons,¹² and can even cause tissue damage.¹³

Despite extensive research on the underlying mechanisms of infrared (IR) neural stimulation, uncertainty remains about how these pulses affect neurons. It is generally understood that laser pulses induce temperature changes across the cell membrane, thereby altering the intrinsic electrical properties of neurons, both passive and active. More specifically, IR stimulation can excite neurons through three distinct mechanisms: presynaptic currents, arising from temperature-dependent vesicular release; postsynaptic currents, due to the temperature sensitivity of ion channel gating (activation/inactivation)^12,14; and capacitive currents, resulting from temperature-dependent electrical charge displacement.¹⁵ Notably, the latter effect has been shown to depend on the rate of thermal change (dT/dt), i.e., thermal shock, rather than the absolute temperature increase itself.¹⁵

Shapiro et al.¹⁶ demonstrated that an IR laser pulse can induce a depolarizing current and excite neurons via a transient increase in the electrical capacitance of the cell membrane, driven by a rapid temperature rise. Their study examined oocytes, HEK cells, and artificial lipid bilayers, ruling out any influence of voltage-gated ion channels on this mechanism, as neither channel expression nor blockade altered the observed depolarizing current. Notably, capacitive currents were significantly higher in H₂O than in D₂O, which the authors attributed to H₂O’s higher infrared absorption coefficient. However, they did not consider the potential contributions from other thermodynamic properties, such as the higher viscosity (~25%) and lower thermal diffusivity (~25%) of D₂O relative to H₂O, both of which could significantly reduce ionic thermodiffusion within the extracellular solution. They developed a model based on Gouy-Chapman-Stern theory^17,18 to describe the capacitive currents induced by infrared laser pulses. However, their model failed to predict the experimental results.¹⁹

To address these limitations, Plaksin et al.²⁰ proposed a modification to the model by incorporating the effect of temperature-induced changes in the phospholipid bilayer’s dimensions. In their model, they considered the cell membrane as the ideal plate capacitor with capacitance $\mathrm{C}={\mathrm{\epsilon }}_{\mathrm{m}}\mathrm{A}/\mathrm{\delta }$. They attributed the change in the capacitance to the change in the membrane dimension resulting from thermal stress. Although this model fitted the experimental results, it had several key assumptions that require further scrutiny.

1. Stationary ions & equilibrium assumption: Both models assumed that ions in the extracellular and intracellular domains remain stationary, effectively imposing an equilibrium condition.

2. Neglecting thermally induced ionic diffusion: Neither model accounted for the effect of temperature gradients on ionic diffusion in the extracellular and intracellular solutions.

3. Transient effects excluded: By relying on the Boltzmann distribution, both models were inherently limited to steady-state conditions, failing to capture transient thermal and electrical responses.

Together, these assumptions overlook the dynamic interplay between Brownian diffusion, thermodiffusion, and electromigration, which is central to understanding how ions redistribute under photothermal perturbation. As a result, the existing framework remains purely static and does not capture the dynamic behavior of the ions upon thermal perturbation. This highlights the need for a more comprehensive model that integrates temperature-driven ionic transport and transient effects better to capture the underlying physics of IR-induced capacitive currents. It has been experimentally demonstrated that temperature changes influence the diffusion of micelles,²¹ lysozyme proteins,²² and DNA²³ in aqueous solutions via thermophoresis. In the presence of a thermal gradient, ions and charged particles redistribute, altering electrochemical equilibrium.^24–26 This phenomenon is analogous to the thermoelectric (Seebeck) effect, where a thermal gradient generates an electric potential or current.²⁷ In biological systems, such an alteration in the electrochemical equilibrium can result in an imbalance of fluxes on both sides of the membrane and thereby a shift in the reversal potential. However, a mechanistic model explaining how thermal perturbations influence both the reversal potential and membrane capacitance in neurons remains lacking in the current literature.

A comprehensive model describing ionic dynamics in a neuron under photothermal shock must therefore account for the combined effects of Brownian diffusion, thermodiffusion, and electromigration in a nonequilibrium system. In this study, we first perform whole-cell recording to see how laser-induced thermal shock can affect the reversal potential as an indicator of a change in electrochemical equilibrium. We then model transport phenomena in a cell by incorporating thermophoretic effects into the Nernst-Planck formulation and coupling it to the Poisson equation and a transient thermal-diffusion framework. Using scaling analysis, we examine ionic diffusion dynamics induced by thermal shock and compare them to physiological processes such as ion channel activation during action potentials (micro- to sub-millisecond).²⁸ We then numerically solve the governing equations to examine how thermal shock affects ion redistribution, ion channel flux, and, consequently, the cell membrane’s reversal potential and capacitance. Additionally, we develop an approximate analytical solution to characterize the fundamental physics, providing key insights into the impact of thermal gradients on ionic transport in biological systems.

MATERIALS AND METHODS

Experiments

We used whole-cell patch-clamp recordings in layer 5 (L5) cortical neurons from mouse brain slices to investigate the effects of laser-induced thermal transients on potassium ion channel behavior. The experimental procedures are summarized below.

Acute slice preparation

All experimental procedures were conducted in accordance with the guidelines set forth by the NIH and Purdue Institutional Animal Care and Use Committee (IACUC). All physiological solutions were fully oxygenated (95% O₂ and 5% CO₂), pH adjusted to 7.3 to 7.4, and osmolarity maintained between 300 and 310 mOsm. Adult C57BL/6 (Jackson Laboratory) mice (8–12 weeks of age) were deeply anesthetized with 3%–4% isoflurane followed by trans-cardiac perfusion with ice-cold NMDG cutting solution²⁹ consisting of (in mM) 92 NMDG, 30 NaHCO₃, 1.2 NaH₂PO₄, 20 HEPES, 2.5 KCl, 25 glucose, 5 sodium ascorbate, 3 sodium pyruvate, 2 thiourea, 0.5 CaCl₂, 10 MgCl₂, and 5 N-acetyl-L-cysteine, before decapitation. Coronal slices (300–350 μm thickness) were prepared using a vibratome (Leica VT1200S) in 0°C–4°C NMDG cutting solution. Brain slices were then allowed to recover in 34°C NMDG cutting solution with gradual perfusion of 0.25–0.5 mL ${\mathrm{Na}}^{+}$-rich NMDG solution (2M NaCl in NMDG cutting solution) over 6 to 10 min depending on the mouse age³⁰ and transferred to room temperature HEPES artificial cerebrospinal fluid (ACSF) holding solution consisting of (in mM) 92 NaCl, 2.5 KCl, 1.25 NaH₂PO₄, 30 NaHCO₃, 20 HEPES, 25 glucose, 5 sodium ascorbate, 3 sodium pyruvate, 2 thiourea, 2 CaCl₂, 2 MgCl₂, and 5 N-acetyl-L-cysteine for at least 1 h before recording.

Electrophysiological recording

Slices were transferred to a chamber, continuously superfused with oxygenated ACSF, and visualized with an upright two-photon microscope (Bruker Nano, Madison, WI) composed of an Olympus BX51WI body (Olympus, Tokyo, Japan) fitted with IR Dodt gradient contrast (DGC) optics, an IR sensitive camera (IR-2000, Dage-MTI, Michigan City, IN), and a 40× water immersion objective (0.8 NA, Nikon USA). Recordings were performed in 35°C recording ACSF consisting of (in mM) 125 NaCl, 3 KCl, 25 NaHCO₃, 1.25 NaH₂PO₄, 25 glucose, 3 sodium pyruvate, 1 sodium ascorbate, 1.3 CaCl₂, and 1 MgCl₂. 4 to 8 MΩ borosilicate patch pipette (Sutter Instruments, CA, USA) was pulled using a P1000 pipette puller (Sutter Instruments, Novato, CA), filled with internal solution containing (in mM) 130 potassium gluconate, 7 KCl, 10 HEPES, 5 NaCl, 35 sucrose, 2 MgSO₄, 2 sodium pyruvate, 4 Mg-ATP, 0.4 Tris GTP, and 7 phosphocreatine disodium (pH 7.3, osmolarity 290 mOsm). L5 neurons were patch-clamped and had resting membrane potentials between −60 mV and −70 mV at rest without any current injection. Currents of ~−50 pA to −100pA were injected in cases where the resting membrane potential (RMP) was more negative (−75 mV) or needed to be maintained. Whole-cell recordings were made using a Multiclamp 700B (Molecular Devices, San Jose, CA), Bessel-filtered at 4 kHz, and digitized at 4 to 20 kHz using a Digidata 1550B interface (Molecular Devices, San Jose, CA) and winwcp software.

Two-photon optical stimulation

Optical modulation was performed using a two-photon microscope (Bruker Nano) equipped with a femtosecond-pulsed laser (Insight X3, Spectra Physics) and two independent optical paths for imaging and photostimulation. Laser intensity was precisely regulated by electro-optical modulators (model 350–50; Conoptics). After patching neurons and labeling them with a fluorescent dye, the photostimulation beam was positioned within 5 μm of the soma, guided by an overlay of fluorescent and DGC infrared images under 810-nm illumination. Photostimulation was delivered via the fixed 1040-nm laser path using galvanometric mirrors to scan a 1-μm-diameter point pattern. To minimize unintended exposure, a hard shutter was used in conjunction with the electro-optical modulator. RMP and cell/dendrite morphology were continuously monitored during stimulation. Neurons exhibiting photodamage—such as dendritic blebbing or elevated RMP—were excluded from further analysis.

Local temperature measurement using a glass electrode

Temperature changes induced by near-infrared (NIR) stimulation on brain tissue were assessed by monitoring the resistance of a glass micropipette. Resistance measurements were obtained using 10-mV voltage pulses delivered through a MultiClamp 700B amplifier (Molecular Devices). To calibrate the temperature of the glass pipette based on the pipette resistance, in a separate experiment, the pipette was placed in a heated ACSF bath alongside a k-type temperature sensor (Omega, 80-mm wires, product number 5SC-TT-K-40–72). The ACSF was initially heated to approximately 50°C and then allowed to cool gradually, enabling the construction of a resistance-temperature calibration curve. This relationship was modeled using an Arrhenius/Steinhart-Hart-type relationship. While the resistance of a glass micropipette provides a reliable estimate of steady-state or slowly varying temperature changes, the thermal mass of the glass and the surrounding ACSF impose a finite response time. As a result, pipette-based thermometry reports a temporally filtered version of the local temperature profile and cannot fully resolve sub-millisecond transients. In this study, pipette measurements were therefore used to validate the magnitude and spatial falloff of laser-induced heating, whereas the fast temperature dynamics were obtained from the thermal diffusion model.

Mathematical modeling

Governing equations

The transport of ions between intracellular and extracellular domains and in the presence of electric fields, concentration gradients, and temperature gradients is governed by the Poisson-Nernst-Planck (PNP) equations. Incorporating the Soret effect, which describes the thermophoretic drift of ions in temperature gradients, is critical for understanding systems such as biological membranes and electrochemical cells undergoing thermal shocks. A two-dimensional model is considered to describe the thermo-electrodiffusion in the intracellular and extracellular domains, which are separated by a 5-nm-thick cell membrane, as illustrated in Figure 1A. The model accounts for four primary ionic species—${\mathrm{Na}}^{+}$, ${\mathrm{K}}^{+}$, ${\mathrm{Cl}}^{-}$, and ${\mathrm{Ca}}^{2+}$—which are present at higher concentrations than other ions in neuronal cells. Additionally, ${\mathrm{K}}^{+}$ and ${\mathrm{Na}}^{+}$ channels are embedded within the membrane domain, as shown in Figure 1B.

Figure 1.

Schematic representation of the neural membrane and ion channel configuration under thermal stimulation. (A) Conceptual illustration of a neural cell exposed to a localized thermal stimulus. The zoomed-in region shows the redistribution of ions across the intra- and extracellular spaces near the membrane, with ${\mathrm{Na}}^{+}$ and ${\mathrm{K}}^{+}$ ions accumulating near their respective channels due to thermophoretic effects. (B) Schematic of the simulation geometry, showing ${\mathrm{Na}}^{+}$ and ${\mathrm{K}}^{+}$ channels embedded in the membrane. Note: illustrations are not to scale. Simulation parameters are detailed in Table 1.

To accurately describe ion transport in the presence of a temperature gradient, the Nernst-Planck equation is modified to incorporate the effect of thermophoresis^24,25:

$$\begin{gathered} \frac{\partial C_i}{\partial t}=-\nabla .J_i,J_i=-D_i\nabla c_i-D_i{c}_i\frac{e{z}_i}{k_{B}T}\nabla \varphi \\ -2D_i{c}_i{\alpha }_T\frac{\nabla T}{T}\text{for}i=\left\{{Na}^{+},K^{+},{Cl}^{-},{Ca}^{2+}\right\} \end{gathered}$$ (1)

The first, second, and third terms on the right-hand side represent concentration variation due to ionic diffusion, electric migration, and thermophoresis, respectively. Here, $\varphi$ denotes the electric potential, $C_i$ represents the concentration of ionic species, and $T$ is the temperature. The parameters $D$ and ${\alpha }_T$ correspond to the ionic diffusion coefficient and Soret coefficient, respectively. Additionally, $e$ is the elementary charge, $k_B$ is the Boltzmann constant, and $z_i$ represents the valence of ion species. The modified Nernst-Planck equation is coupled with Poisson’s equation and the thermal diffusion equation to determine the electric potential and temperature distribution across the domains:

$${ϵ}_r{ϵ}_0{\nabla }^2\varphi =-{\rho }_i=-F\mathrm{\Sigma }{z}_i{c}_i$$ (2)

$$\rho C_p\frac{\partial \mathrm{T}}{\partial t}=k{\nabla }^{2}T$$ (3)

Here, ${\rho }_i$ is the charge density, ${ϵ}_0$ is the vacuum permittivity, ${ϵ}_r$ is the relative permittivity of the cytoplasm, $F$ is the Faraday’s constant, and $\rho ,C_p$, and $k$ are the density, heat capacity, and thermal conductivity of the cytoplasm, respectively. This coupled system provides a comprehensive framework for modeling the thermo-electrodiffusion dynamics within the neuronal environment.

The set of coupled equations (Equations 1, 2, and 3) are solved subject to the biophysical boundary conditions Equation 4. In order to find numerical solution for the problem, the extracellular and intracellular domains are truncated to a finite computational region, and on each edge, the boundary conditions are applied. A block representing the computational domain is specified in Figure 1B and Table 1, and the boundary conditions for electric potential, concentration, and temperature are applied at the far-field intracellular and extracellular boundaries as follows:

$$\left\{\begin{array}{c}\varphi ={\varphi }_i,c_k={\bar{c}}_{k,i},T=T_{\mathit{ref}}\mathit{at}{\mathrm{\Gamma }}_i\\ \varphi ={\varphi }_e,c_k={\bar{c}}_{k,e},\nabla T=-\frac{g\left(t\right)}{k}\mathit{at}{\mathrm{\Gamma }}_e\end{array}\right.$$ (4)

Table 1.

Default geometry parameter values used in the PNP simulations (see Figure 1B)

Thermal Model		PNP Model
Parameter	Value	Parameter	Value
$L_i$	10 μm	$L_i$	100 nm
$L_e$	5 μm	$L_m$	5 nm
$H$	30 μm	$L_e$	100 nm
–	–	$d_c$	0.5 nm
–	–	$H$	500 nm

Here, $g\left(t\right)$ is the transient heat flux, modeled using a Gaussian function in time. The top and bottom boundaries are subject to zero-flux conditions, while the far-field intracellular boundary (${\mathrm{\Gamma }}_i$) is held at a constant temperature $T_{\mathit{ref}}$. The location of this boundary was determined from a convergence analysis of the thermal model (see Figure S1 in the supplemental information), as discussed in Section numerical solution. This boundary therefore acts as a numerical far-field condition ensuring thermal stability of the solution rather than representing the physical temperature at that location.

To obtain realistic temperature gradients near the membrane while maintaining computational efficiency for the ion transport simulations, we adopted a two-step modeling approach. First, a thermal diffusion model with a microscale geometry was solved to capture the two-dimensional heat dissipation resulting from laser heating (see Table 1). In this model, the laser stimulus was represented as a heat flux boundary condition applied over a 1-μm segment in the middle of the extracellular boundary corresponding to the approximate laser focal region. The magnitude of the applied heat flux was calibrated such that the resulting temperature rise at the membrane interface matched the experimentally measured values. The resulting temperature field and temperature gradient at the membrane surface were then extracted and used as inputs for the PNP simulations performed on a smaller membrane patch domain (see Table 1) where ion dynamics were resolved with nanometer-scale spatial resolution.

The value of Soret coefficient for different ions depends on the molality and temperature of the solution. Although there are no direct measurements of the Soret coefficient in the intra- and extracellular fluids, the experimental and simulation studies are reported for the Soret coefficient of ions in various aqueous solutions under different concentrations and temperatures.^31,32 In our work, we use the values reported for ${\mathrm{Na}}^{+}$ and ${\mathrm{K}}^{+}$ ions in aqueous NaCl and KCl solutions at concentrations ranging from 5 to 125 mM, which approximate physiological conditions. The physical constants and parameters used in this study are summarized in Table 2.

Table 2.

Physical parameters used in this study

Parameter	Description	Value
$D_{{Na}^{+}}$	diffusion coefficient for ${Na}^{+}$	1.33 × 10−9 m2/s
$D_{K^{+}}$	diffusion coefficient for $K^{+}$	2 × 10−9 m2/s
$D_{{Cl}^{-}}$	diffusion coefficient for $C{l}^{-}$	2 × 10−9 m2/s
$D_{{Ca}^{2+}}$	diffusion coefficient for ${Ca}^{2+}$	0.7 × 10−9 m2/s
$\mathrm{F}$	Faraday’s constant	96,485.33 C/mol
${ϵ}_0$	vacuum permittivity	8.8 × 10−12 F/m
${ϵ}_r$	relative permittivity	80
$\mathrm{e}$	elementary charge	1.6 × 10−19 C
$\rho$	density	1,200 kg/m3
${\mathrm{C}}_{\mathrm{p}}$	heat capacity	4,200 J/kgK
$\mathrm{k}$	thermal conductivity	0.6 W/mK
${\mathrm{k}}_{\mathrm{B}}$	Boltzmann coefficient	1.3806 × 10−23 J/K
${\alpha }_T$	Soret coefficient	0.6
$T_{\mathit{ref}}$	reference temperature	34°C

Scale analysis

In order to provide a mechanistic insight into the significance of different ionic driving forces, we look into the dimensional analysis of the conservation equations. Therefore, the thermal diffusion equation can be scale analyzed in form of

$$\rho C_p\frac{\mathrm{\Delta }T}{\tau }\sim k\frac{\mathrm{\Delta }T}{L^2}\sim q$$ (5)

The timescale of temperature gradient (i.e., thermal diffusion time constant) is $\tau \sim \frac{\rho C_p{L}^2}{k}=200\mu s$ (for L = 5 μm), which means that the temperature change can travel 5 μm away from the focal point of the laser beam in less than 0.2 ms and hence can affect ionic diffusion in this space through thermophoresis. Therefore, when targeting the tissue 5 μm away from the cell, the timescale over which heat can diffuse into the cell can be shorter than 0.2 ms. This implies that the thermal event occurs on a timescale comparable to that of ion channel activation during action potentials (micro- to sub-millisecond).²⁸ Thus, thermophoresis associated with the heat shock may influence ionic redistribution in the vicinity of the membrane before significant ionic fluxes underlying processes such as action potential initiation are fully established. Therefore, the effect of thermal shock on the cell, as a thermodynamic system, is a highly transient effect, which makes the system thermodynamically irreversible, and the theories such as Gouy-Chapman-Stern cannot present an accurate model of the behavior of such a system. Here, we extend the scale analysis to the Nernst-Planck equation to obtain an estimation of the relative changes in the concentration upon the changes in temperature gradient. From the balance of temperature and diffusion driving, one can obtain

$$\frac{\mathrm{\Delta }\mathrm{C}}{{\tau }_D}\sim D{\alpha }_{T}C\frac{\mathrm{\Delta }T}{T{L}^2}$$ (6)

From the balance of ionic diffusion (first term on RHS of Equation 1) and the transient concentration term (LHS), one can obtain ${\tau }_D\sim \frac{L^2}{D}$. Substituting this diffusion time constant in Equation 6 we get $\frac{T}{\mathrm{\Delta }T}\frac{\mathrm{\Delta }C}{C}\frac{1}{{\alpha }_T}\sim 1$. If the degree of change in temperature is up to 20°–25°,¹⁶ $\frac{T}{\mathrm{\Delta }T}\sim 10$ and $\frac{\mathrm{\Delta }C}{\mathrm{C}}\sim 0.1{\alpha }_T$. Using ${\alpha }_T\sim 1-2$,^31,32 then $\frac{\mathrm{\Delta }C}{\mathrm{C}}\sim 0.1-0.2$. This indicates that the magnitude of ionic concentration change due to thermophoresis effect can be up to 20% which is significant for the cellular activity. In addition, given the nanoscale dimension we are dealing with, this can result in a substantial gradient in ionic flux in the vicinity of the membrane, influencing the electric capacitance of the membrane.

Numerical solution

We employ finite element analysis (COMSOL Multiphysics) to model the impact of a transient thermal shock on ionic thermodiffusion and redistribution near the cell membrane. As illustrated in Figure 1, our numerical model comprises three distinct domains: the intracellular space, the cell membrane, and the extracellular environment. To represent selective ion transport, the model includes two nanoscale ion channels—one for sodium ions and the other for potassium ions. To focus solely on the effects of thermophoresis, we assume that these channels are constitutively open during the thermal shock, omitting active gating dynamics. This simplification enables us to isolate the role of temperature gradients in driving ion migration and shaping charge density distributions at the membrane interface. The initial ion concentrations in the intracellular and extracellular domains were specified according to Table 3. Within the membrane region outside of ion channels, all ion concentrations were set to zero. For each ion channel, the concentrations of all nonpermeant ions were set to zero. To solve the model equations described in Section governing equations, we generate the grid using an explicit quadratic Euler discretization. First, the thermal diffusion equation is solved to obtain the temperature. This temperature is then used in the modified PNP formulation. In the vicinity of the membrane, the grid size is set to 0.1 nm up to 5 nm away from the membrane. The time step for the simulation is set at 1 × 10⁻⁵ ms.

Table 3.

Initial condition for ion concentration³³

Ion	Intracellular	Extracellular
${\mathrm{N}\mathrm{a}}^{+}$	12 mM	100 mM
${\mathrm{K}}^{+}$	125 mM	5 mM
${\mathrm{C}\mathrm{a}}^{2+}$	0.0001 mM	1.4 mM
${\mathrm{C}\mathrm{l}}^{-}$	137.0002 mM	107.8 mM

To ensure that the zero heat flux boundary condition at the top and bottom edges of the computational domain did not influence the temperature gradients near the membrane, we performed additional simulations using progressively larger computational domains. In these simulations, the height of the extracellular domain was varied between 10 μm and 60 μm while maintaining the same localized heat flux condition. Increasing the domain height beyond 30 μm resulted in less than 2.5% change in the temperature rise at the membrane surface (Figures S1A and S1B). To apply a physically meaningful boundary condition for the left side of intracellular thermal domain, we imposed a far-field temperature condition. Simulations were performed for intracellular thicknesses ranging from 1 μm to 10 μm, with all other parameters held constant. The results showed that both the membrane temperature and the membrane-normal temperature gradient (dT/dx), which are the parameters that control the thermophoresis, became insensitive to further increases in intracellular thickness beyond approximately 10 μm, with less than 0.5% variation in the membrane temperature (Figure S1C). Based on this analysis, a domain height of 30 μm and intracellular thickness of 10 μm were used in the thermal simulations. These results ensure that the temperature gradients near the membrane are insensitive to the exact location of the far-field boundaries once the computational domain exceeds these dimensions.

RESULTS AND DISCUSSION

We first confirmed the accuracy and sensitivity of our pipette-based temperature measurement approach. As the heated ACSF bath cooled over time, pipette resistance increased with a corresponding decrease in temperature, matching thermocouple readings (Figures 2A and 2B). The relationship between pipette resistance and temperature was found to be monotonic and fit well to a calibration curve (Figure 2C). Next, we used this calibrated pipette to measure temperature changes in acute cortical brain slices during localized NIR laser stimulation. A schematic of the measurement setup is shown in Figure 2D. Laser-induced temperature changes were recorded as a function of distance from the laser focal point at three different power levels (78 mW, 137 mW, and 216 mW). As expected, temperature increased with laser power and decreased sharply with distance from the laser spot (Figures 2E–2G). Glass micropipettes have been widely used as local thermometric probes, but their thermal response is inherently slower than the microsecond-scale dynamics of photothermal shock. Consequently, pipette measurements provide reliable estimates of temperature amplitude and spatial gradients but can underestimate the fastest components of the thermal transient. This limitation does not affect the main conclusions of the present study: the thermal diffusion model explicitly captures sub-millisecond temperature dynamics and provides the transient gradients that drive thermophoresis. The pipette therefore serves as a calibration tool for absolute $\mathrm{\Delta }\mathrm{T}$, while the temporal features most relevant for thermophoretic flux are obtained from simulation.

Figure 2.

Experimental measurement of thermally induced reversal potential shifts. (A) Schematic representation of the temperature measurement calibration, (B) an example of temperature (black, measured with a thermocouple) and glass pipette resistance (red) changing as the heated ACSF cools down, and (C) the relationship between pipette resistance and ACSF bath temperature. (D) Schematic representation of laser spot and calibrated glass pipette for measuring the temperature in the cortical region of brain slice, (E–G) The temperature measured as a function of distance for different laser intensities. (H) An example L5 pyramidal neuron patched with the calibrated glass pipette electrode next to the laser spot for temperature measurement. (I) Potassium currents resulted from the voltage steps. The laser pulse is applied once the current is steady to ensure the effect of voltage-clamp is not mixed up with the laser heating. (J) An example I-V curve for one cell with and without laser pulses. (K) Reversal potential results suggest statistically significant shift in reversal potential at different temperatures. The laser beam was positioned 5 μm from the soma. (L) Dependence of the laser-induced shift in reversal potential ($\mathrm{\Delta }{\mathrm{V}}_{\mathrm{R}\mathrm{e}\mathrm{v}}$) on the distance between the laser spot and the soma. Data are shown as mean ± SEM with individual neurons indicated by open circles; *p < 0.05, **p < 0.01 (unpaired t test).

To assess the physiological effects of these localized thermal changes, we patch-clamped L5 pyramidal neurons in the vicinity of the laser stimulation site (Figure 2H). We added TTX (1 μM; Tocris, USA) to the ACSF to block sodium channels and allowed 20 min to ensure uniform perfusion. Laser pulses were delivered after stabilization of membrane current to isolate thermal effects from voltage-induced responses (Figure 2I). Voltage-clamp recordings revealed a clear shift in the reversal potential of potassium currents at elevated temperature (44°C) compared with baseline (34°C), as shown in the example current-voltage (I-V) curve (Figure 2J). Across all recorded neurons, this depolarizing shift averaged +1.16 mV, which was statistically significant (n = 8, p = 0.007), confirming a temperature-dependent modulation of the ${\mathrm{K}}^{+}$ reversal potential (Figure 2K). However, according to the classical Nernst model derived from the electrochemical equilibrium, $E_{\mathit{RevK}}=\frac{k_{B}T}{e}Ln\left(\frac{C_{e{x}_K}}{C_{i{n}_K}}\right)<0$, a temperature jump as large as 10°C should result in a ~−3mV change (i.e., hyperpolarizing shift) in the reversal potential. This indicates that additional mechanisms, such as thermophoresis-induced ion redistribution, must be accounted for to balance fluxes under such quasi-equilibrium conditions. Since the scale analysis showed that the thermophoretic effect is significant in the balance of fluxes, we incorporate thermophoresis in Nernst-Planck flux (Equation 1) and integrate over x axis to obtain the following:

$$E_{Rev,K}=\frac{k_B{T}_{in}}{e{z}_K}\left(Ln\left(\frac{C_{e{x}_K}}{C_{i{n}_K}}\right)+2{\alpha }_{T}Ln\left(\frac{T_{ex}}{T_{in}}\right)\right)$$ (7)

The second term on the right-hand side represents the thermophoretic contribution. Since $T_{ex}>T_{in}$, this term adds a positive correction to $E_{\mathit{Rev,K}}$, producing a depolarizing shift in the reversal potential. For potassium ions, using ${\alpha }_T=0.6$ and $\mathrm{\Delta }\mathrm{T}={10}^{\circ }\mathrm{C}$, the thermophoretic term in the modified Nernst equation predicts a shift of approximately +1.02 mV. This value is close to the experimentally observed average shift of +1.16 mV in the reversal potential. For the integration, we assumed that the relative change in T is small compared with the change in $\mathrm{\Delta }\mathrm{T}/\mathrm{T}$ (e.g., $\mathrm{\Delta }\mathrm{T}=1^{\circ }\mathrm{C}$ and 10°C yields $\mathrm{\Delta }\mathrm{T}/\mathrm{T}=1/309$ and 10/318, respectively, with minimal variation in the denominator), allowing us to treat T as a constant in the flux terms. Equation 7 yields a quasi-steady approximation that explains how thermophoresis shifts the electrochemical potential balance before the system reaches steady state. To examine how stimulation geometry influences the thermophoretic contribution to membrane polarization, we next varied the distance between the laser spot and the soma. As shown in Figure 2L, increasing the stimulation distance from 5 μm to 10 μm and 20 μm results in a progressive reduction in the laser-induced shift in the reversal potential ($\mathrm{\Delta }{\mathrm{V}}_{\text{Rev}}$). This distance dependence is consistent with a weakening of the temperature gradient across the membrane as the heat source is moved farther from the cell. These results demonstrate that the magnitude of the thermophoresis-mediated effect is strongly dependent on the spatial relationship between the site of photothermal stimulation and the neuronal membrane.

It should be noted that in this experimental configuration, the temperature (T) and the temperature gradient ($\nabla \mathrm{T}$) cannot be independently controlled by simply moving the laser focus farther from the membrane. Increasing the stimulation distance reduces both quantities simultaneously. However, the experimentally measured thermal profiles (Figures 2E–2G) indicate that the spatial temperature gradient decreases much more strongly with distance than the absolute temperature itself. For example, in Figure 2G, the measured temperature near the cell decreases only from approximately 41.75°C at ~10 μm to ~40°C at ~40 μm (a change of ~2 K, corresponding to <1% change in absolute temperature), whereas the estimated temperature gradient–approximated from the measured temperature drop–decreases from roughly (45–41.75)/10 ≈ 0.325°C μm⁻¹ to (45–40)/40 ≈ 0.125°C μm⁻¹, corresponding to 2.6 times reduction. Because the measured temperature profile is not strictly linear, this estimate should be interpreted as a qualitative indicator of the spatial variation in the thermal field; the curvature of the profile further suggests that the local gradient decreases more rapidly with distance than implied by a linear approximation. This comparison indicates that increasing the stimulation distance primarily weakens the temperature gradient rather than substantially changing the absolute temperature. Since thermophoresis depends on the ratio ∇T/T, this geometry-dependent reduction in the gradient is expected to dominate the distance-dependent effect.

In principle, isolating the effect of absolute temperature from that of the temperature gradient would require directly heating the cell (i.e., placing the laser focus on the soma), where the temperature rise occurs with minimal spatial gradient across the membrane. However, in our experiments, positioning the laser directly on the cell resulted in rapid and large depolarization, leading to loss of the patch-clamp recording due to strong photothermal perturbation. As a result, stable measurements of reversal potential under these conditions were not possible.

To further investigate the role of stimulation geometry and compare the experimental observations with theoretical predictions, we performed simulations in which the distance between the heat source and the membrane was systematically varied. In the model, this distance is represented by the width of the extracellular domain (${\mathrm{L}}_{\mathrm{e}}$; see Figure 1B). As shown in Figures 3A–3C, increasing ${\mathrm{L}}_{\mathrm{e}}$ reduces the temperature gradient across the membrane and correspondingly decreases the thermally driven ionic flux through ${\mathrm{K}}^{+}$ channels. This reduction in flux leads to a monotonic decrease in the predicted shift in reversal potential with increasing ${\mathrm{L}}_{\mathrm{e}}$ (Figure 3D). The simulated dependence of $\mathrm{\Delta }{\mathrm{V}}_{\text{Rev}}$ on stimulation distance is in agreement with the experimental results in Figure 2L, providing further support for the strong geometry dependence of the thermophoretic mechanism.

Figure 3.

Geometry dependence of thermophoretic modulation of reversal potential. (A–C) Simulated ionic flux through ${\mathrm{K}}^{+}$ channels as a function of membrane voltage for increasing distances between the heat source and the membrane, represented by the width of the extracellular domain (L_e). Increasing L_e results in a reduced temperature gradient across the membrane. (D) Predicted shift in reversal potential ($\mathrm{\Delta }{\mathrm{V}}_{\text{Rev}}$) as a function of L_e, showing a monotonic decrease in the thermophoretic contribution with increasing distance from the heat source. These results demonstrate the strong dependence of thermophoresis on stimulation geometry and are consistent with the experimentally observed distance dependence in Figure 2L.

While the present model focuses on thermophoresis as a mechanism for modifying ionic distributions near the membrane and the reversal potential, other temperature-dependent effects on ion channels may also contribute to the experimentally observed response. For example, temperature changes can influence channel conformation, conductance, or gating kinetics, which may alter the magnitude of ionic currents and reversal potential. Such effects were not explicitly included in the present model, which isolates the contribution of thermophoretic ion redistribution. In addition, the thermophoretic coefficients used here are based on measurements in bulk electrolyte systems, whereas thermophoresis in the nanometer-scale ionic environment adjacent to biological membranes may differ due to strong electric fields, surface charge, and spatial confinement.^34,35 Therefore, the thermophoretic parameter used in this study should be interpreted as an effective coefficient describing ion transport in the membrane-adjacent ionic layer. Despite these simplifications, the model reproduces the direction and spatial dependence of the experimentally observed reversal potential shift, supporting thermophoresis as an important contributing mechanism.

Prior to investigating the effect of thermal shock on ion redistribution and diffusiophoresis through ion channels, we examined the temporal stability of thermal diffusion in the cellular medium. We assumed that the thermal properties of the domains and the membrane were close to those of water.³⁶ We first applied a heat flux consisting of three consecutive pulses with a Gaussian temporal profile (approximating the shape of a Gaussian laser pulse) at different time intervals ($\mathrm{\Delta }\mathrm{t}$) to examine how rapidly the temperature changes and recovers in the vicinity of the cell membrane (Figure 4). We call this effect inertia to thermal relaxation that can lead to the accumulated thermal stress inside the cell. For $\mathrm{\Delta }\mathrm{t}=0.2\mathrm{m}\mathrm{s}$, the temperature does not fully dissipate before the subsequent pulse is delivered, causing the temperature rise to accumulate (Figure 4A). This superposition of heat nonlinearly increases the cellular temperature and may contribute to the threshold for photothermal damage. By increasing the interval to 0.35 ms, the heat accumulation decreases (Figure 4B), and at $\mathrm{\Delta }\mathrm{t}=0.5\mathrm{m}\mathrm{s}$, this effect disappears, and the thermal stress inside the cell is not present anymore (Figure 4C). Proper design of the pulse interval can be useful in optimizing photothermal therapy. The effect of heat accumulation is also reflected in the charge density close to the membrane and in front of the sodium channel, potentially increasing the flux of sodium ions into the intracellular environment. This effect may contribute to optical and optothermal modulation of cells, depending on stimulation geometry and thermal gradients. As shown in Figure 4D, for a single pulse induced with the duration of 0.2 ms, the thermal relaxation time is about 0.9 ms. This implies that the time required for a laser-induced temperature rise to decrease to near-baseline values is 0.9 ms, and a pulse interval shorter than this can trigger heat accumulation and generate a nonlinear temperature rise. However, the diffusion timescale measured as the rising time in the temperature profile, which is the time that the thermal effect reaches the target point, is about 0.13 ms. The relaxation time here is almost an order of magnitude longer than the diffusion time (0.13 ms ≪ 0.9 ms), meaning that upon applying the pulse, heat propagates quickly within the cell. Still, it takes a relatively longer time for the cell to return to thermal equilibrium. This effect can modulate ionic transport across the membrane. Now, we turn our attention to the thermally induced ionic redistribution inside both intra- and extracellular domains.

Figure 4.

Temporal dynamics of thermal relaxation and charge redistribution. Triple thermal flux pulse applied on the extracellular boundary along with the temperature and charge density at the inlet of the ${\mathrm{Na}}^{+}$ channel (within 4 nm) for different pulse intervals: (A) 0.2 ms, (B) 0.35 ms, and (C) 0.5 ms. (D) A single pulse applied at the boundary of extracellular domain and its associated temperature profile generated at the inlet of the ${\mathrm{Na}}^{+}$ channel. (E) Maximum temperature rises as a function of pulse interval (left) and the pulse number (right).

Figure 5 illustrates the temporal gradient of charge density across the sodium and potassium channels, as well as the averaged charge density at the intracellular and extracellular sides of the membrane as a result of application of a single pulse (similar to Figure 4D) with a maximum temperature rise of 20°C. Since the charge density inside the channel is assumed to be negligible, the channel width is considered zero to avoid discontinuity in the curves. Therefore, x > 10 nm and x < 10 nm correspond to the right (extracellular) and left (intracellular) sides of the membrane (dashed line in Figures 5A and 5B), respectively. As it can be seen, before the thermal pulse is applied (t = 0.3 ms), there is no temporal gradient for charge density across the membrane, but, upon the temperature jump (t = 0.5 ms), a sharp increase in $d\rho /dt$ across the ${\mathrm{Na}}^{+}$ and ${\mathrm{K}}^{+}$ channels and on both sides of the membrane is triggered. This indicates a rising trend in charge on the left side of the membrane, whereas the opposite trend is observed on the extracellular side. At the times t > 0.5 ms, where the temperature is decreasing to reach the control condition ($dT/dt<0$), the sign of $d\rho /dt$ is reversed on both sides of the membrane. This implies that the temporal gradient of temperature dictates the sign of $d\rho /dt$ on the membrane, and a fast switch in temperature can trigger an abrupt change in the charge density across the membrane. To evaluate the direct effect of the thermal pulse on the membrane’s charge density, the average charge density is calculated by integrating the charge density across the intracellular and extracellular walls of the membrane (Figures 5C and 5D). As shown, increasing the temperature decreases the average charge on the extracellular surface of the membrane and increases it on the intracellular surface. For example, by increasing the temperature by 17°C (for 0.2 ms), the surface charge decreases by 35% on the extracellular surface, and it increases by 5.8% on the intracellular surface of the membrane. Since only cations can permeate the membrane here, the relative enhancement in intracellular charge density suggests that thermal shock depolarizes the cell by redistributing ions across the membrane. To further elucidate the origin of the surface charge redistribution, we examined the spatiotemporal evolution of ion concentration changes near the membrane. As shown in Figures S2 and S3, the thermally induced gradients drive transient ion fluxes localized around the channel regions, which give rise to the asymmetric charge accumulation on the intra- and extracellular sides of the membrane. This redistribution alters membrane capacitance, consistent with experimental observations of photothermal capacitance changes in simplified systems,¹⁶ although those studies did not address thermophoretic ion redistribution. These results indicate that thermal shock may exert an influence on excitability comparable to that of electrical stimulation.

Figure 5.

Thermally induced charge redistribution across the membrane. Temporal gradient of the charge density across the (A) sodium channel and (B) potassium channel, at the times before (0.3 ms), during (0.5 ms), and after thermal shock (t > 0.5 ms). Note: x > 10 nm and x < 10 nm correspond to the right (extracellular) and left (intracellular) sides of the membrane, respectively. Average charge density measured as a function of time at the (C) extracellular and (D) intracellular surfaces of the membrane for different temperature rises measured at the membrane surface.

To assess how closely thermal shock can mimic a given voltage induction, the charge density and ionic fluxes induced by both thermal and voltage stimuli are plotted as functions of time in Figure 6A. A single thermal pulse that generates a 11°C temperature rise at the membrane is applied to the extracellular boundary, and its effects on biophysical parameters are compared with those of voltage pulses with peak values of 2.5 mV, 5 mV, and 7.5 mV applied to the same boundary. As shown, a thermal stimulus corresponding to an 11°C temperature increase produces changes in charge density that are comparable in magnitude to those induced by a 5-mV voltage step, but with opposite sign (Figures 6B and 6C, left column). Specifically, the magnitude of the thermally induced change is similar on the extracellular side and larger on the intracellular side compared with the electrical stimulus. This suggests that a positive voltage applied to the extracellular domain can hyperpolarize the cell, whereas thermal stimulation at the same site can depolarize it by driving ions into the membrane via thermophoresis. The thermal stimulus also induces an increase in diffusion flux (Figures 6B and 6C, middle column) and in total ionic flux (Figures 6B and 6C, right column) at the inlets of both ${\mathrm{Na}}^{+}$ and ${\mathrm{K}}^{+}$ channels, reaching levels comparable to those produced by a 5-mV voltage pulse.

Figure 6.

Comparison of ionic redistribution induced by voltage versus thermal stimuli. (A) Schematic of the cell configuration showing the location of extracellular stimulus and ion channel inlets (${\mathrm{Na}}^{+}$ and ${\mathrm{K}}^{+}$), along with the profiles of electrical (red) and thermal (blue) stimuli applied extracellularly. (B) Time evolution of charge density (left), diffusion flux (middle), and total ionic flux (right) at the inlet of the ${\mathrm{Na}}^{+}$ channel in response to either thermal stimulus or voltage steps of 2.5, 5, and 7.5 mV. (C) Same variables as in (B) but measured at the inlet of the ${\mathrm{K}}^{+}$ channel.

The density and spatial organization of ion channels within a membrane patch can also influence the electrochemical response of the cell.³³ To investigate the effect of ion channel clustering on thermophoresis-driven charge redistribution, we simulated membrane patches with different channel cluster widths while keeping the separation between ${\mathrm{Na}}^{+}$ and ${\mathrm{K}}^{+}$ channel regions fixed. In these simulations, the cluster width $d_c$ represents groups of ion channels that form a localized conductive region within the membrane, and it was varied to represent groups of 5, 10, and 14 ${\mathrm{Na}}^{+}$ channels (corresponding to widths of 2.5, 5, and 7 nm, respectively). Increasing $d_c$ effectively increases the total ion transport capacity of the membrane patch. Figure 7 shows the thermophoresis-induced change in surface charge density on the extracellular (Figure 7A) and intracellular (Figure 7B) faces of the membrane as a function of the applied thermal stimulus. On both sides of the membrane, the magnitude of the surface charge variation increases monotonically with temperature rise. Larger channel clusters produce greater charge redistribution because the wider conductive region allows stronger thermophoretically driven cation transport across the membrane. On the intracellular side, this results in an increased accumulation of positive charge due to the inward thermophoretic flux of cations through ${\mathrm{Na}}^{+}$ and ${\mathrm{K}}^{+}$ channels. On the extracellular side, the surface charge becomes increasingly negative as temperature rises. Thermal stimulation drives cations toward the intracellular domain, while anions (i.e., ${\mathrm{Cl}}^{-}$) cannot cross the membrane because the modeled channels are selective for ${\mathrm{Na}}^{+}$ and ${\mathrm{K}}^{+}$ ions. Consequently, the depletion of cations near the extracellular membrane surface enhances the magnitude of the negative charge density. The larger relative variation observed on the extracellular side is due to the fact that the baseline surface charge density is much smaller in magnitude there than on the intracellular side; therefore, comparable absolute charge changes produce a larger normalized response extracellularly. These results indicate that the magnitude of thermally induced surface polarization depends not only on the applied temperature gradient but also on the effective size of the ion channel clusters.

Figure 7.

Effect of ion channel cluster size on thermophoresis-induced surface charge formation across the membrane. (A) Change in surface charge density ($\mathrm{\Delta }\mathrm{\rho }$, normalized to control) on the extracellular face of the membrane as a function of thermal stimulus intensity. (B) Corresponding surface charge change on the intracellular face of the membrane. Different curves represent varying channel cluster widths (2.5, 5, and 7 nm), corresponding approximately to clusters of 5, 10, and 14 ion channels, respectively. Increasing the cluster width increases the effective conductive area of the membrane patch, allowing stronger thermophoretically driven cation transport and thereby enhancing the magnitude of surface charge redistribution. Note that the direction of the charge change differs on the two sides of the membrane: the intracellular surface becomes more positively charged due to cation accumulation, whereas the extracellular surface becomes more negatively charged due to cation depletion near the membrane interface. Insets illustrate the schematic location of the measurement plane relative to the membrane.

Figure 8 shows the average ionic concentrations for (i) ${\mathrm{Na}}^{+}$, (ii) ${\mathrm{K}}^{+}$ and (iii) ${\mathrm{Cl}}^{-}$ ions on either side of the membrane in response to transient thermal pulses of varying intensity. Two membrane potentials (−75 mV and +80 mV) are considered to explore how the combined effects of temperature elevation and voltage polarity influence ion redistribution across the membrane. On the right (extracellular) side, when the membrane is hyperpolarized (−75 mV), both ${\mathrm{Na}}^{+}$ and ${\mathrm{K}}^{+}$ concentrations decrease with increasing temperature, indicating that thermophoresis drives ions from the extracellular to the intracellular domain. In contrast, ${\mathrm{Cl}}^{-}$ concentration slightly increases, suggesting a net accumulation of anions and possibly divalent cations. This divergent behavior between anions and cations indicates thermally driven charge separation, which contributes to transient changes in surface charge density and membrane capacitance, as discussed in Figure 5.

Figure 8.

Membrane potential modulates ionic concentration shifts under thermal gradients. Schematic shows (A) extracellular and (B) intracellular surfaces of the membrane (dashed lines) where the average ionic concentrations are computed. Each plot illustrates the steady-state concentrations of ${\mathrm{Na}}^{+}$, ${\mathrm{K}}^{+}$, and ${\mathrm{Cl}}^{-}$ ions as a function of temperature difference ($\mathrm{\Delta }\mathrm{T}$), comparing hyperpolarized (−75 mV) and depolarized (80 mV) membrane potentials. Stronger depolarizing conditions (80 mV) lead to distinct ionic redistribution patterns compared with hyperpolarized conditions (−75 mV), with ion-specific behaviors observed for ${\mathrm{Na}}^{+}$ and ${\mathrm{K}}^{+}$ (notable accumulation or depletion) and ${\mathrm{Cl}}^{-}$ (consistent trends). Dual-axis plots show both intra- and extracellular responses to temperature-driven stimuli.

Figure 9 presents the flux of potassium ions through the membrane as a function of membrane potential. When the membrane is hyperpolarized (e.g., <−50 mV), thermal stimulation reduces the outward flux of ${\mathrm{K}}^{+}$ ions. In contrast, under depolarized conditions, heating enhances ${\mathrm{K}}^{+}$ efflux.³⁷ This voltage-dependent modulation arises from the thermally induced ionic redistribution observed in Figure 8. Specifically, during hyperpolarization, intracellular ${\mathrm{K}}^{+}$ concentration increases (at the channel inlet) as a result of efflux decrease, while extracellular ${\mathrm{K}}^{+}$ decreases (at the outlet). Conversely, under depolarized conditions, thermal gradients enhance the outward driving force by depleting intracellular and accumulating extracellular ${\mathrm{K}}^{+}$. This is consistent with our experimental current-voltage (I-V) recordings, where elevated temperature increased potassium currents at depolarized voltages (see Figure 2J). These findings suggest that thermal modulation of ionic gradients, via thermophoresis and electrodiffusion, can influence ion channel currents regardless of temperature effects on proteins and the lipid bilayer, highlighting a novel mechanism by which photothermal stimulation affects membrane potential and excitability.

Figure 9.

Modulation of reversal potential by transient thermal shock. (A) Applied thermal stimulus at the extracellular boundary. (B) The ionic flux through ${\mathrm{K}}^{+}$ channels as a function of voltage difference across the membrane. The channels are assumed to be open regardless of the voltage.

CONCLUSION

This study provides direct experimental and theoretical evidence that photothermal shock alters the electrochemical behavior of neurons in ways not captured by previous models. Using whole-cell patch-clamp recordings combined with two-photon laser stimulation, we observed a depolarizing shift in the potassium reversal potential—a response opposite to that predicted by the standard Nernst equation (Figure 2). To explain this discrepancy, we developed a thermodynamic model that incorporated thermophoresis into the PNP framework and coupled it with transient thermal diffusion. Combined experimental and simulation results demonstrate that the magnitude of thermophoretic effects depends strongly on stimulation geometry, with both the ionic flux and the resulting shift in reversal potential decreasing as the heat source is moved farther from the membrane (Figure 3). This geometry dependence highlights the central role of spatial temperature gradients in determining the physiological impact of photothermal stimulation, indicating that laser heating does not affect all cells uniformly within the tissue, but preferentially impacts cells located closer to the stimulation site where temperature gradients are steepest. Importantly, the experimental thermal profiles indicate that increasing the stimulation distance reduces the temperature gradient much more strongly than the absolute temperature, highlighting that thermophoretic effects are governed primarily by spatial temperature gradients rather than bulk temperature changes.

Our simulations also demonstrate that laser-induced thermal gradients can rapidly redistribute ions within sub-millisecond timescales (Figures 5, S2, and S3), leading to asymmetric charge accumulation on either side of the membrane. These transient effects are strongly dependent on the temporal structure of the stimulus, with pulse interval shaping the magnitude and persistence of ionic polarization (Figure 4). This ionic polarization not only modifies reversal potential but also increases membrane capacitance via surface charge displacement—without requiring structural membrane deformation (Figure 5). We further show that thermally induced effects can emulate or exceed those produced by electrical stimulation, with a 20°C temperature jump as short as 0.2 ms generating capacitive and ionic responses comparable to the effects of several millivolts of extracellular voltage stimulus (Figure 6).

Although the depolarizing shift in reversal potential observed here is modest in absolute magnitude (~1 mV), even small changes on this scale can influence neuronal excitability. Notably, this empirical shift contrasts with the prediction of the classical Nernst model, which yields a change of approximately −3 mV for a 10°C temperature increase (and nearly −5 mV for a 20°C increase), underscoring that standard equilibrium assumptions fail to capture the ionic dynamics under photothermal perturbation. Such fine-scale shifts alter the driving force for ionic currents and may affect action potential threshold, firing probability, and dendritic integration, particularly in high-resistance compartments. Our results, therefore, suggest that thermophoresis-mediated ion redistribution provides a subtle but physiologically meaningful mechanism for modulating excitability under photothermal stimulation.

Additionally, our results highlight the role of channel clustering and spatial asymmetry in amplifying the thermophoretic response, especially on the extracellular side (Figure 7). We also show that this response is voltage dependent: under hyperpolarized conditions, thermal gradients reduce the outward potassium flux, while under depolarized conditions, the same thermal input enhances it (Figures 8 and 9). This polarity-dependent modulation of ion flow is consistent with experimental current-voltage recordings, where heating increased ${\mathrm{K}}^{+}$ currents selectively under depolarizing voltages (Figure 2). These findings further support the conclusion that thermal stimuli reshape ionic gradients and currents dynamically—without requiring channel gating changes—introducing a new layer of excitability control via thermal-electric coupling.

Together, these results point to thermophoresis as a fundamental biophysical mechanism underlying optothermal neuromodulation, capable of driving significant physiological responses through purely thermal means. This work bridges experimental observations with nonequilibrium thermodynamics and provides a quantitative framework for designing safer and more effective photothermal neural interfaces.

Supplementary Material

SUPPLEMENTAL INFORMATION

Supplemental information can be found online at https://doi.org/10.1016/j.bpj.2026.04.031.

SIGNIFICANCE.

Lasers are widely used to stimulate and study neurons, yet how rapid heating affects the ions that carry electrical signals in cells is not well understood. In this study, we combined patch-clamp experiments with mathematical modeling to demonstrate that brief thermal shocks alter the membrane ion balance in ways that classical theories cannot account for. We find that heating can drive ions to redistribute near the membrane, producing small but essential shifts in electrical properties that influence excitability. This work introduces a new framework for understanding how temperature affects ion transport and provides a foundation for designing next-generation approaches to control neural activity using light and heat.

APPENDIX: APPROXIMATE SOLUTION

Here we aim at deriving a simplified closed-form solution for the problem. To simplify the analysis, each of intra- and extracellular domains are divided into two regions.

• Debye layer ($0\le \mathrm{x}\le {\lambda }_{\mathrm{D}}$): A thin charged region near the membrane where electric potential and charge density vary rapidly.

• Bulk region ($\mathrm{x}>{\lambda }_{\mathrm{D}}$): A charge-neutral region dominated by diffusion and thermophoresis.

The Nernst-Planck equation delivers the net ionic flux due to variations in concentration, potential, and temperature, and can be generally written as follows^24,25:

$$J_i=D_i\frac{\partial c_i}{\partial x}+{\mu }_i{z}_{i}e{c}_i\frac{\partial \varphi }{\partial x}+D_i{S}_T{c}_i\frac{\partial T}{\partial x}$$ (A1)

We derive the Boltzmann distribution with thermophoresis and solve the PNP equations in the Debye layer first. In the Debye layer, the electric potential $\varphi (x,t)$ satisfies the Poisson equation (Equation 2). The charging time of the Debye layer, estimated as ${\lambda }_{\mathrm{D}}\mathrm{L}/\mathrm{D}\approx {10}^{-7}\mathrm{s}$ (where $L$ is the characteristic width of the region), is much shorter than other electrodiffusion timescales. This justifies assuming that ionic concentrations in the Debye layer reach a quasi-static state rapidly. Under this assumption, ion distributions follow Boltzmann equilibrium both inside and outside the cell. To obtain the equilibrium form ($J_i=0$), we set the net ionic flux to zero:

$$D_i\frac{\partial c_i}{\partial x}+{\mu }_i{z}_{i}e{c}_i\frac{\partial \varphi }{\partial x}+\frac{D_i{\alpha }_T{c}_i}{T}\frac{\partial T}{\partial x}=0$$ (A2)

Dividing through by $D_i{c}_i$, and using the Einstein Relation, ${\mu }_i=\frac{D_i}{k_{B}T}$, the above equation is simplified to

$$\frac{\partial c_i}{c_i}=-\frac{z_{i}e}{k_{B}T}\frac{\partial \varphi }{\partial x}-\frac{{\alpha }_T}{T}\frac{\partial T}{\partial x}$$ (A3)

For temperature, since the domain is thin (1 × 10⁻⁷m) and the thermal diffusion time constant $(\frac{L^2}{\alpha }\approx \frac{{10}^{-14}}{{10}^{-7}}={10}^{-7}s)$ is much shorter than the duration of the transient heat pulse (2 × 10⁻⁴s), heat diffusion occurs rapidly. Therefore, we can approximate the temperature distribution as a linear function of position across the domain, $T(x,t)=a\left(t\right)+b\left(t\right)\times x$. If the domain were significantly wider than the thermal diffusion length $\sqrt{\alpha t}\approx 5.5\times {10}^{-6}m$, the system could be treated as semi-infinite, and the corresponding temperature profile for that case would apply. In the Boltzmann formulation, T is typically treated as the average temperature of the system. To enable analytical integration, we assume that T remains constant in both thermally dependent terms. This approximation is valid when temperature variations are moderate. Here, we consider a temperature range from 308 K to 332 K (with an average temperature ${\mathrm{T}}_{\text{avg}}=320\mathrm{K}$) corresponding to a relative variation of approximately 3.7%. Hence, we treat $\mathrm{T}={\mathrm{T}}_0$ as constant while retaining $dT/dx$ as a nonzero gradient.

For the bulk electric potential, ${\varphi }_{\text{bulk}}$, and under the assumption of linear temperature profile, $T\left(x\right)=a\left(t\right)+b\left(t\right)x$, as stated above, Equation A3 can then be integrated to yield

$$\begin{gathered} c_i(x)=c_{i,\mathit{bulk}}\mathrm{e}\mathrm{x}\mathrm{p}\left(-\frac{z_{i}e}{k_B{T}_0}\left(\varphi (x)-{\varphi }_{\mathit{bulk}}\right)\right. \\ \left.-\frac{{\alpha }_T}{T_0}b(t)\left(x-x_{\mathit{bulk}}\right)\right) \end{gathered}$$ (A4)

This is a general form of the Boltzmann distribution inside the Debye layer, and we need to split it into two cases: (1) Debye layer in the extracellular domain; (2) Debye layer in the intracellular domain (Figure A1).

For simplicity, we consider a two-ion solution (NaCl) that satisfies the electroneutrality. Therefore, for a two-ion system, the Boltzmann expression for Debye layer inside the cell can be written as

$$\begin{gathered} C^{+}(x,t)=C_{in}(t)\mathrm{e}\mathrm{x}\mathrm{p}\left(\frac{e\left(\varphi (x,t)-{\varphi }_{in}(t)\right)}{k_B{T}_0}\right. \\ \left.+\frac{{\alpha }_T}{T_0}b(t)\left(x-{\lambda }_{in}\right)\right) \end{gathered}$$ (A5)

$$\begin{gathered} C^{-}(x,t)=C_{in}(t)\mathrm{e}\mathrm{x}\mathrm{p}\left(-\frac{e\left(\varphi (x,t)-{\varphi }_{in}(t)\right)}{k_B{T}_0}\right. \\ \left.+\frac{{\alpha }_T}{T_0}b(t)\left(x-{\lambda }_{in}\right)\right) \end{gathered}$$ (A6)

And for the extracellular Debye layer, it can be written as (bulk potential in extracellular domain ${\varphi }_{\mathit{out}}(t)=0$) follows:

$$C^{+}(x,t)=C_{\mathit{out}}(t)\mathrm{e}\mathrm{x}\mathrm{p}\left(\frac{e\varphi (x,t)}{k_B{T}_0}+\frac{{\alpha }_T}{T_0}b(t)\left(x-{\lambda }_{\mathit{out}}\right)\right)$$ (A7)

$$\begin{gathered} C^{-}(x,t)=C_{\mathit{out}}(t)\mathrm{e}\mathrm{x}\mathrm{p}\left(-\frac{e(\varphi (x,t))}{k_B{T}_0}\right. \\ \left.+\frac{{\alpha }_T}{T_0}b(t)\left(x-{\lambda }_{\mathit{out}}\right)\right) \end{gathered}$$ (A8)

We assumed electroneutrality in the bulk regions (inside and outside the cell), meaning that the bulk concentration for intracellular (for both ions) is $C_{\mathit{in}}(t)$ and for extracellular is $C_{\mathit{out}}(t)$. With this assumption, we can write the Poisson-Boltzmann equation for intracellular Debye layer as

$$\begin{gathered} \frac{\partial \varphi (x,t)}{\partial x^2}=\frac{e{C}_{in}(t)}{{ϵ}_0{ϵ}_c}\left(\mathrm{e}\mathrm{x}\mathrm{p}\left(-\frac{e\left(\varphi (x,t)-{\varphi }_{in}(t)\right)}{k_B{T}_0}\right.\right. \\ \left.+\frac{{\alpha }_T}{T_0}b(t)\left(x-{\lambda }_{in}\right)\right)-\mathrm{e}\mathrm{x}\mathrm{p}\left(\frac{e\left(\varphi (x,t)-{\varphi }_{in}(t)\right)}{k_B{T}_0}\right. \\ \left.\left.+\frac{{\alpha }_T}{T_0}b(t)\left(x-{\lambda }_{in}\right)\right)\right) \end{gathered}$$ (A9)

Figure A1.

Schematic representation of thermophoretic ion redistribution near a neural membrane under thermal stimulation. The membrane separates intracellular (left) and extracellular (right) regions, each containing a Debye layer of counter-ions. Red and blue curves represent the concentration profiles of cations (C⁺) and anions (C⁻), respectively. A rightward heat flux induces asymmetric ionic shifts, enhancing the cation accumulation on the extracellular side and altering the local electrostatic environment.

And, for the extracellular Debye layer, it can be written as

$$\begin{gathered} \frac{\partial \varphi (x,t)}{\partial x^2}=\frac{e{C}_{\mathit{out}}(t)}{{ϵ}_0{ϵ}_c}\left(\mathrm{e}\mathrm{x}\mathrm{p}\left(-\frac{e(\varphi (x,t))}{k_B{T}_0}\right.\right. \\ \left.+\frac{{\alpha }_T}{T_0}b(t)\left(x-{\lambda }_{\mathit{out}}\right)\right)-\mathrm{e}\mathrm{x}\mathrm{p}\left(\frac{e\varphi (x,t)}{k_B{T}_0}\right. \\ \left.\left.+\frac{{\alpha }_T}{T_0}b(t)\left(x-{\lambda }_{\mathit{out}}\right)\right)\right) \end{gathered}$$ (A10)

Since the relative permittivity of the membrane bilayer is significantly lower than that of the cytoplasmic fluid $\left({\mathrm{\epsilon }}_{\mathrm{m}}\ll {\mathrm{\epsilon }}_{\mathrm{c}}\right)$, the majority of the voltage drop occurs across the membrane rather than within the Debye layer. As a result, the potential inside the cell can be approximated as $\varphi (x,t)={\varphi }_{in}(t)$ for all $w_{in}<x<0$ inside the cell and $\varphi (x,t)\cong 0$ for extracellular $\left(0<x<w_{\mathit{out}}\right)$. This assumption allowed us to linearize the Poisson-Boltzmann equation:

$$\begin{gathered} \frac{\partial \varphi (x,t)}{\partial x^2}=1+\frac{e\varphi (x,t)}{k_B{T}_0}+\frac{{\alpha }_T}{T_0}b(t)\left(x-{\lambda }_{\mathit{out}}\right) \\ -\left(1-\frac{e\varphi (x,t)}{k_B{T}_0}+\frac{{\alpha }_T}{T_0}b(t)\left(x-{\lambda }_{\mathit{out}}\right)\right) \end{gathered}$$ (A11)

$$\begin{gathered} \frac{\partial \varphi (x,t)}{\partial x^2}=1+\frac{e\left(\varphi (x,t)-{\varphi }_{in}(t)\right)}{k_B{T}_0}+\frac{{\alpha }_T}{T_0}b(t)\left(x-{\lambda }_{in}\right) \\ -\left(1-\frac{e\left(\varphi (x,t)-{\varphi }_{in}(t)\right)}{k_B{T}_0}+\frac{{\alpha }_T}{T_0}b(t)\left(x-{\lambda }_{in}\right)\right) \end{gathered}$$ (A12)

That can be simplified as

$$\frac{{\partial }^2\varphi (x,t)}{\partial x^2}=-{\kappa }_{in}^2\left(\varphi (x,t)-{\varphi }_{in}(t)\right)$$ (A13)

$$\frac{{\partial }^2\varphi (x,t)}{\partial x^2}=-{\kappa }_{out}^2\varphi (x,t)$$ (A14)

Here, ${\kappa }_{\mathit{in}}^2=\frac{2e^2{C}_{\mathit{in}}(t)}{{ϵ}_0{ϵ}_c{k}_B{T}_0},{\kappa }_{\mathit{out}}^2=\frac{2e^2{C}_{\mathit{out}}(t)}{{ϵ}_0{ϵ}_c{k}_B{T}_0}$, and $\lambda =\frac{1}{\kappa }=\sqrt{\frac{{ϵ}_0{ϵ}_c{k}_B{T}_0}{2e^2{c}_{\mathit{out}}(t)}}$.

This leads to the well-known exponential profile for the potential (note that this is for Debye layer only).

Intracellular:

$${\varphi }_{in}(x,t)=C\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{h}\left({\kappa }_{in}x\right)+D\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{h}\left({\kappa }_{in}x\right)+{\varphi }_{in}(t)$$ (A15)

Extracellular:

$${\varphi }_{\mathit{out}}(x,t)=A\mathrm{e}\mathrm{x}\mathrm{p}\left(-{\kappa }_{\mathit{out}}x\right)+B\mathrm{e}\mathrm{x}\mathrm{p}\left({\kappa }_{\mathit{out}}x\right)$$ (A16)

Boundary conditions:

$$\begin{gathered} {\varphi }_{\mathit{in}}\left(-{\lambda }_{D,in},t\right)={\varphi }_{\mathit{in}}(t),{\left.\frac{\partial \varphi }{\partial x}\right|}_{-{\lambda }_{D,in}}=0 \\ {\varphi }_{\mathit{in}}(0,t)={\varphi }_{\mathit{out}}(0,t),{\left.{ϵ}_{\mathit{out}}\frac{\partial {\varphi }_{\mathit{out}}}{\partial x}\right|}_{x=0}={\left.{ϵ}_{\mathit{in}}\frac{\partial {\varphi }_{\mathit{in}}}{\partial x}\right|}_{x=0} \\ {\varphi }_{\mathit{out}}\left({\lambda }_{D,\mathit{out}},t\right)={\varphi }_{\mathit{out}}(t)=0,{\left.\frac{\partial \varphi }{\partial x}\right|}_{{\lambda }_{D,\mathit{out}}}=0 \end{gathered}$$ A17

After applying the boundary conditions, we get

$$C=D\cdot \mathrm{t}\mathrm{a}\mathrm{n}\mathrm{h}\left({\kappa }_{\mathit{in}}{\lambda }_{\mathit{in}}\right)$$ (A18)

$$A=-B\cdot e^{2{\kappa }_{\mathit{out}}{\lambda }_{\mathit{out}}}$$

$$C=A+B-{\varphi }_{\mathit{in}}(t)$$

$$D=\frac{{ϵ}_{\mathit{out}}}{{ϵ}_{\mathit{in}}}\frac{{\kappa }_{\mathit{out}}}{{\kappa }_{\mathit{in}}}(B-A)$$

Solving for A, B, C and D we obtain:

$$A=\frac{{\varphi }_{\mathit{in}}(t)}{1-\mathrm{e}\mathrm{x}\mathrm{p}\left(-2{\kappa }_{\mathit{out}}{\lambda }_{\mathit{out}}\right)+\frac{{ϵ}_{\mathit{out}}{\kappa }_{\mathit{out}}}{{ϵ}_{\mathit{in}}{\kappa }_{\mathit{in}}}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{h}\left({\kappa }_{\mathit{in}}{\lambda }_{\mathit{in}}\right)\left(1+\mathrm{e}\mathrm{x}\mathrm{p}\left(-2{\kappa }_{\mathit{out}}{\lambda }_{\mathit{out}}\right)\right)}$$ (A19)

$$B=-\mathrm{Aexp}\left(-2{\kappa }_{\mathit{out}}{\lambda }_{\mathit{out}}\right)$$

$$C=-\frac{{ϵ}_{\mathit{out}}{\lambda }_{\mathit{out}}}{{ϵ}_{\mathit{in}}{\lambda }_{\mathit{in}}}\tanh \left({\kappa }_{\mathit{in}}{\lambda }_{\mathit{in}}\right)\left(1+\exp \left(-2{\kappa }_{\mathit{out}}{\lambda }_{\mathit{out}}\right)\right)A$$

$$D=-\frac{{ϵ}_{\mathit{out}}{\lambda }_{\mathit{out}}}{{ϵ}_{\mathit{in}}{\lambda }_{\mathit{in}}}\left(1+\exp \left(-2{\kappa }_{\mathit{out}}{\lambda }_{\mathit{out}}\right)\right)A$$

We substitute the potentials in Equations 1, 2, 3, and 4 to obtain the concentrations in the Debye layer and then substitute the concentrations and potentials in the flux equation: We find the flux as a function of the gradients at the membrane surface $(\mathrm{x}=0)$:

$$J=-D\left(\frac{\partial C}{\partial x}+\frac{e}{k_B{T}_0}C\frac{\partial \varphi (x,t)}{\partial x}+C\frac{{\alpha }_T}{T_0}\frac{\partial T}{\partial x}\right)$$ (A20)

$$C^{+}(0,t)=C_{\mathit{out}}^{+}exp\left(\frac{e(A+B)}{k_B{T}_0}-\frac{{\lambda }_{\mathit{out}}{\alpha }_T}{T_0}b(t)\right)$$ (A21)

$$\begin{gathered} {\left.\frac{\partial C^{+}}{\partial x}\right|}_{x=0}=C_{\mathit{out}}^{+}(t)\left(\frac{e}{k_B{T}_0}\frac{\partial \varphi (0,t)}{\partial x}+\frac{{\alpha }_T}{T_0}b(t)\right)\mathrm{e}\mathrm{x}\mathrm{p} \\ \left(\frac{e\varphi (0,t)}{k_B{T}_0}+\frac{{\alpha }_T}{T_0}b(t)\left(0-{\lambda }_{\mathit{out}}\right)\right) \\ =C_{\mathit{out}}^{+}(t)\left(\frac{e{\kappa }_{\mathit{out}}}{k_B{T}_0}(-A+B)+\frac{{\alpha }_T}{T_0}b(t)\right)\mathrm{e}\mathrm{x}\mathrm{p} \\ \left(\frac{e(A+B)}{k_B{T}_0}-\frac{{\alpha }_T{\lambda }_{\mathit{out}}}{T_0}b(t)\right) \end{gathered}$$ (A22)

$${\left.\frac{\partial T}{\partial x}\right|}_{x=0}=b(t)$$ (A23)

$${\left.\frac{\partial {\varphi }_{\mathit{out}}(x,t)}{\partial x}\right|}_{x=0}={\kappa }_{\mathit{out}}(B-A)$$ (A24)

Also,

$${\left.J^{+}\right|}_{{\lambda }_{\mathit{out}}}=-D{C}_{\mathit{out}}^{+}(t)\cdot \frac{{\alpha }_T}{T_0}\cdot b(t)+\frac{D\cdot {\alpha }_T\cdot C_{\mathit{out}}^{+}(t)\cdot b(t)}{T_0}=0$$ (A25)

For extracellular, we can consider $C_{\mathit{out}}^{+}(t)=C_{\mathit{out}}=constant$, so the flux of ions at the boundary of Debye layer and bulk in the extracellular domain will be

$${\left.J^{+}\right|}_{{\lambda }_{\mathit{out}}}={\left.J^{-}\right|}_{{\lambda }_{\mathit{out}}}=D\cdot {\alpha }_T\cdot C_{\mathit{out}}\cdot b(t)\left(\frac{1-a(t)+b(t){\lambda }_{\mathit{out}}}{a(t)+b(t){\lambda }_{\mathit{out}}}\right)$$ (A26)

Also, for the intracellular at the boundary of Debye layer and bulk, we obtain

$${\left.J^{+}\right|}_{{\lambda }_{in}}={\left.J^{-}\right|}_{{\lambda }_{in}}=D\cdot {\alpha }_T\cdot C_{in}(t)\cdot b(t)\left(\frac{1-a(t)+b(t){\lambda }_{in}}{a(t)+b(t){\lambda }_{in}}\right)$$ (A27)

$C_{in}(t)$ is constant if the cell is in the rest. Also, the simulation confirms that $C_{in}(t)$ inside the cell, except the Debye length, does not change by time after applying the temperature jump.

DATA AVAILABILITY

All data supporting the findings of this study are available from the corresponding author upon reasonable request.