Ludwig–Soret microscopy with the vibrational photothermal effect

Significance

We introduce vibrational photothermal-induced Soret (ViPS) imaging, an approach extending vibrational microscopy into the study of intracellular thermophoresis—the transport of biomolecules driven by temperature gradients. By combining steady-state optical heating via vibrational photothermal effects with high-resolution refractive index imaging, ViPS reveals previously inaccessible intracellular thermophoretic dynamics. We observed distinct thermophoretic behaviors between the nucleus and cytoplasm, including negative thermophoresis, potentially linked to diffusiophoretic processes. Remarkably, ViPS also captured a significant suppression of thermophoretic activity during the cellular dying process, offering insights into mechanisms of molecular aggregation and glass formation. ViPS imaging substantially enhances the analytical power of vibrational microscopy, opening avenues for investigating intracellular molecular transport.

Abstract

Vibrational microscopy provides label-free, bond-selective chemical contrast by detecting molecular vibrations, making it invaluable for biomedical research. While conventional methods rely on the direct detection of Raman scattering or infrared absorption, recently developed vibrational photothermal (ViP) microscopy achieves chemical contrast indirectly through refractive index (RI) changes. This indirect approach enables unique imaging capabilities beyond traditional chemical imaging. Here, we introduce an application of ViP microscopy: Label-free intracellular thermophoretic (Soret) imaging, which visualizes biomolecular transport driven by temperature gradients. ViP-induced Soret (ViPS) imaging leverages a steady-state temperature distribution generated by optical heating through vibrational photothermal effect, combined with time-resolved RI imaging via optical diffraction tomography. Using ViPS imaging, we measured thermophoretic behavior in living COS7 cells, determining intracellular diffusion and Soret coefficients. Notably, we observed a reversed direction of molecular transport (negative Soret effect) in the cytoplasm compared to the nucleus, possibly driven by thermophoresis-induced diffusiophoresis. Furthermore, time-lapse imaging under CO₂-depleted conditions revealed a remarkable reduction in thermophoretic activity, suggesting glass formation during the dying process, likely due to polymer aggregation. ViPS imaging represents a frontier in intracellular thermophoretic studies, expanding the capabilities of vibrational microscopy.

Vibrational microscopy is widely recognized as a powerful tool for biomedical research due to its label-free and bond-selective capabilities (1, 2). Conventional vibrational microscopy achieves chemical contrast by directly reading molecular vibrational information through Raman scattering or infrared absorption. In contrast, newly emerging vibrational microscopy techniques provide chemical contrast indirectly through intermediate phenomena. For example, vibrational photothermal (ViP) microscopy, such as mid-infrared photothermal microscopy, detects refractive index (RI) changes induced by the bond-selective ViP effect (3–8). In this approach, RI changes are not directly caused by molecular vibrations but rather result from thermal expansion due to heat dissipation from molecular vibrations. Recent advancements in ViP microscopy have led to intensive development, demonstrating chemical imaging capabilities in cells comparable to state-of-the-art techniques such as stimulated Raman scattering microscopy (9).

Vibrational microscopes that utilize intermediate phenomena, including ViP microscopes, have the potential to provide information beyond chemical contrast (10–12). For example, we have recently demonstrated that time-resolved ViP imaging enables the measurement of intracellular thermal properties by detecting ViP-induced heat diffusion (12). Since heat diffusion occurs on the microsecond timescale, time-resolved pump–probe ViP imaging made this experiment possible. RI changes can be induced not only by thermal expansion but also by other factors. As RI depends on molecular density (or cellular dry mass), RI image contrast varies with changes in molecular composition. We found that the ViP effect can drive directional molecular transport along a temperature gradient over a longer timescale. This phenomenon, known as thermophoresis or the Ludwig–Soret (or simply Soret) effect, has been widely studied in biophysics, primarily in vitro (13). Previous studies have explored biomolecular mobility, providing insights into molecular crowding and interactions via hydration and charge (14, 15). These in vitro studies have also highlighted the potential for opto-thermal manipulation or sorting of intracellular biomolecules at significantly lower laser power than optical tweezers (16, 17).

In this work, we propose and demonstrate intracellular label-free thermophoretic imaging of biomolecules using ViP microscopy, introducing an extended capability of vibrational microscopy. Our ViP-induced Soret (ViPS) imaging is enabled by two key factors: 1) the creation of a steady-state, Gaussian-like temperature distribution induced by seconds-long optical heating via bond-selective continuous absorption of water and 2) time-resolved imaging of spatiotemporal RI variations caused by molecular movements (changes in dry mass concentration) using optical diffraction tomography (ODT). The optically induced temperature distribution within a cell drives seconds-long, slow molecular transport (thermophoresis), modifying the RI. This effect can be distinguished from the faster RI variations caused by thermal diffusion, which occur on micro- to millisecond timescales. Using ViPS imaging, we measured the thermophoretic behavior in the nucleus of a living COS7 cell, determining the diffusion and Soret coefficients to be 4.6 μm² s⁻¹ and 0.01 K⁻¹, respectively. This indicates that a 1K inhomogeneous intracellular temperature distribution induces a 1% change in dry mass for molecules with a molecular weight of approximately 100 kDa. Additionally, we observed molecular transport in the cytoplasm occurring in the opposite direction to that in the nucleus, likely due to the combined effects of thermophoresis and diffusiophoresis. Furthermore, time-lapse imaging under CO₂-depleted conditions revealed a significant reduction in thermophoretic movement, suggesting that glass formation occurs in dying cells due to polymer aggregation.

Results

Working Principle of ViPS Imaging.

ViPS imaging is built upon a ViP microscope, where a visible microscope detects RI changes induced by the bond-selective photothermal effect using mid- or near-infrared light and its subsequent phenomena. Fig. 1 categorizes ViP-induced phenomena based on their respective timescales. The first observable phenomenon is an RI change caused by local thermal expansion (photothermal effect), which occurs on a nanosecond timescale (Fig. 1A). This mechanism forms the basis of conventional ViP imaging, where chemical contrast is achieved through bond-selective ViP excitation (3). The second phenomenon, thermal diffusion, occurs on a microsecond timescale (Fig. 1B). The dynamics of thermal diffusion can be visualized using time-resolved pump–probe imaging (12). The third phenomenon, and the focus of this work, involves thermophoresis and diffusiophoresis, occurring in milliseconds to seconds (Fig. 1C). Thermophoresis refers to molecular transport driven by a temperature gradient, which occurs under continuous ViP excitation. When a spatially focused continuous ViP excitation beam is applied to a sample, it quickly establishes a steady-state temperature distribution, inducing molecular movement along temperature gradients over seconds. This molecular transport redistributes molecular composition, leading to changes in the RI map. A detailed theoretical description of thermophoresis is provided in the Methods section, Thermophoresis (Soret Effect) and Diffusiophoresis.

Fig. 1.

Principle of ViPS imaging illustrated with ViP-induced phenomena. (A) ViP-induced thermal expansion on a nanosecond timescale, used in conventional ViP imaging to obtain chemical contrast. (B) ViP-induced heat diffusion on a microsecond timescale, visualized through time-resolved ViP imaging. (C) ViP-induced molecular transport occurring over milliseconds to seconds. Macromolecules migrate along temperature gradients, causing RI change. ViPS imaging captures thermophoresis (Soret effect) or thermophoresis-driven diffusiophoresis (negative Soret effect).

The principle of ViPS imaging is described as follows. An induced RI change ($\mathrm{\Delta }n$) under continuous heating can be expressed as

$$\mathrm{\Delta }n=\mathrm{\Delta }{n}_{\rho }+\mathrm{\Delta }{n}_{\sigma },$$ [1]

where $\mathrm{\Delta }{n}_{\rho }$ and $\mathrm{\Delta }{n}_{\sigma }$ represent the RI changes caused by density (ρ) changes due to thermal expansion and dry mass concentration (σ) changes, respectively. ViPS imaging specifically measures $\mathrm{\Delta }{n}_{\sigma }$. It is important to note that these two terms evolve on different timescales in cells. Our previous study experimentally revealed that the first term, $\mathrm{\Delta }{n}_{\rho }$, reaches a steady state within 5 ms after the initiation of heating, due to a balance between IR heat input and rapid thermal diffusion within the heated region (12). Because $\mathrm{\Delta }{n}_{\rho }$ can be considered constant at longer timescales, the temporal variation of the second term, $\mathrm{\Delta }{n}_{\sigma }$, can be separately extracted. In this work, we present 2D intracellular thermophoretic images based on depth-integrated dry mass concentration changes ($\mathrm{\Delta }\sigma$ [fg/μm²]) expressed as

$$\mathrm{\Delta }\sigma =\frac{\int \mathrm{\Delta }{n}_{\sigma }dz}{\alpha },$$ [2]

where α = 0. 2 × 10⁻³ [μm³/fg] is the reported RI increment relative to dry mass concentration in cells (18).

The ability to measure $\mathrm{\Delta }{n}_{\rho }$ at the onset of heating is crucial for precisely determining the induced temperature rise distribution, which is essential for quantitative analyses of diffusion and Soret coefficients. Under steady-state conditions, $\mathrm{\Delta }{n}_{\rho }$ can be expressed as

$$\mathrm{\Delta }{n}_{\rho }=\frac{\mathit{dn}}{\mathit{dT}} \mathrm{\Delta }{T}_s,$$ [3]

where dn/dT and $\mathrm{\Delta }{T}_s$ denote the thermo-optic coefficient and the steady-state temperature rise, respectively. Since the thermo-optic coefficient remains nearly constant within cells, the temperature rise distribution $\mathrm{\Delta }{T}_s$ can be determined by measuring a $\mathrm{\Delta }{n}_{\rho }$ image. By leveraging the time-resolved capability to distinguish thermal diffusion from molecular transport, ViPS microscopy enables the visualization of intracellular molecular thermophoresis from a single dataset of spatiotemporal RI variations.

ViPS Microscopy System.

Our ViPS microscopy system is based on a ViP-ODT microscope (12). A simplified schematic of the systems is shown in Fig. 2 (See Methods, ViP-ODT System for details). In this study, we set the IR wavelength to an overtone band of water molecules, which are nearly uniformly distributed within cells. Continuous-wave (CW) IR light generates a Gaussian-like heat distribution, corresponding to the IR beam spot, with a full-width at half-maximum (FWHM) diameter of ~5 μm. The induced RI change is quantitatively measured using an ODT microscope with visible light. The ODT system, based on off-axis digital holography (19) with an azimuthally scanned illumination scheme, provides 3-dimensional (3D) RI volumetric imaging with a spatial resolution of 250 nm laterally and 5 μm axially. The measurement temporal resolution is 20 ms, which is determined by the frame rate of the image sensor (50 Hz).

Fig. 2.

Schematic of ViPS microscopy system. BS: Beamsplitter, DM: Dichroic mirror.

Intracellular ViPS Imaging and Evaluation of Soret and Diffusion Coefficients.

We conducted intracellular ViPS imaging of living COS7 cells. First, a continuous 2.4-s heating was applied to the nucleus. The heating duration was chosen based on the characteristic diffusion timescales of intracellular biomolecules. Fig. 3A illustrates the temporal variations of RI change at the center and the periphery of the heating spot, as indicated by the blue and red squares in Fig. 3B. Both curves exhibit instantaneous changes at heating onset, attributed to thermal expansion ($\mathrm{\Delta }{n}_{\rho }$ in Eq. 1). Subsequently, gradual changes are observed, which can be explained by molecular transport ($\mathrm{\Delta }{n}_{\sigma }$ in Eq. 1). The latter exhibits opposing behaviors, a decrease at the center and an increase at the periphery of the heating spot, indicating that molecular transport redistributes dry mass density within a boundary while mostly conserving total mass.

Fig. 3.

Intracellular thermophoretic imaging and evaluation of Soret and diffusion coefficients. (A) Temporal variation in RI change ($\mathrm{\Delta }n$) at the center and periphery of the heating spot (corresponding to the blue and red square regions in Fig. 3B). (B) Steady-state temperature rise map ($\mathrm{\Delta }{T}_s$) derived from the $\mathrm{\Delta }{n}_{\rho }$ map, measured 10 ms after heating onset. The temperature rise was determined by averaging a 4.2 μm-thick volumetric layer along the z-axis within the cell. (C) Depth-integrated dry mass concentration change ($\mathrm{\Delta }\sigma$) measured 2.4 s after heating onset. (D) Comparison of time-resolved $\mathrm{\Delta }\sigma$ maps between experiment and simulation. The color scale matches that of Fig. 3C. The Inset shows cross-sectional profiles along the white dotted lines. (E) Comparison of experimental and simulated results for the temporal evolution of $\mathrm{\Delta }\sigma$ at the center of the heating spot (blue square region in Fig. 3B). (F) Depth-integrated dry mass concentration ($\sigma$) in cells with and without (control) Actinomycin D treatment, measured within a 2.2 μm × 2.2 μm area at the center of the heating spot. (G) Normalized depth-integrated dry mass concentration change ($-\mathrm{\Delta }\sigma /\mathrm{\Delta }{T}_s$) measured 2.4 s after heating onset. The number of measured cells was 14 for control and 12 for drug-treated.

As discussed above, thermal expansion occurs rapidly, reaching a steady state typically within milliseconds, before molecular transport begins. Thus, the $\mathrm{\Delta }{n}_{\rho }$ image can be extracted from the initial $\mathrm{\Delta }n$ image captured immediately after the beginning of heating. Using Eq. 3, we derived the temperature change distribution ($\mathrm{\Delta }{T}_s$), as shown in Fig. 3B, employing the thermo-optic coefficient of water (dn/dT = −1.0 × 10⁻⁴ K⁻¹). The $\mathrm{\Delta }{n}_{\sigma }$ images were obtained by subtracting the $\mathrm{\Delta }{n}_{\rho }$ image from the $\mathrm{\Delta }n$ images. Fig. 3C presents an image of depth-integrated dry mass concentration change ($\mathrm{\Delta }\sigma$), calculated using Eq. 2. The results clearly demonstrate that intracellular molecules migrate from higher to lower temperature regions, consistent with in vitro studies on biomolecular thermophoresis in aqueous environments (20). A notable feature is that molecular transport primarily occurs inside the nucleus. The expelled molecules (red-colored in Fig. 3C) remain within the nucleus, likely because they are physically blocked by the nuclear membrane. We quantified the positive and negative dry mass changes within the nucleus and found that 85% of the expelled molecules at the heating spot remain inside the nucleus (see SI Appendix, Supplementary Note 2 for details).

We evaluated the Soret ($S_T$) and diffusion (D) coefficients by comparing our experimental results with a numerical simulation of thermophoresis (see Methods, Numerical Simulation of Intracellular Thermophoresis for details on the calculation procedure). The temporal evolution of depth-integrated dry mass concentration change ($\mathrm{\Delta }\sigma$) was simulated using the experimentally determined temperature rise distribution ($\mathrm{\Delta }{T}_s$). Fig. 3D shows the $\mathrm{\Delta }\sigma$ maps at 0.1, 1, and 2.4 s after heating onset. Fig. 3E presents its temporal evolution of $\mathrm{\Delta }\sigma$ at the center of the heating region (averaged over the blue squared area shown in Fig. 3B). Through a systematic parameter search, we found that $S_T$ = 9.28 (± 0.10) × 10⁻³ K⁻¹ and D = 4.49 ± 0.10 μm²/s best reproduced the experimental results. The parameter search was performed in steps of 2 × 10⁻⁵ K⁻¹ for $S_T$ and 0.02 μm²/s for D, minimizing the sum of squared differences between the experimental and simulated data points. Errors were evaluated using CI based on a residual increase of 10%.

The Soret coefficient quantifies molecular migration induced by a 1 K temperature difference. The obtained value ($S_T$ = 9.28 × 10⁻³ K⁻¹) indicates that ~1% of the molecules migrate after 2.4 s of heating with a 1 K temperature difference. Notably, our method can evaluate multiple $S_T$ values corresponding to molecules of different sizes from a single temporal RI evolution dataset with extended heating. This is because longer heating durations facilitate the transport of less mobile, larger molecules, which generally exhibit higher $S_T$ values.

The diffusion coefficient provides insight into the molecular size of thermophoretic biomolecules. Previous studies using fluorescence-based techniques, such as fluorescence recovery after photobleaching, have reported intracellular diffusion coefficients for various biomolecules: 15 to 30 μm²/s for GFP (30 kDa) (21, 22), 5.5 μm²/s for IgG (160 kDa) (21), and 0.03 to 0.1 μm²/s for messenger ribonucleic acid (mRNA) (~1,000 kDa) (23). The diffusion coefficient obtained in our experiment (D = 4.6 μm²/s) is comparable to that of IgG, suggesting that the observed intracellular thermophoresis is primarily driven by biomolecules with molecular weights around 100 kDa or higher, such as proteins or small- to medium-sized RNAs. This inference aligns with prior knowledge of molecular confinement within the nucleus, where molecules larger than approximately 30 kDa cannot freely pass through the nuclear membrane (24).

To determine whether RNAs are dominant migrating molecules, we prepared RNA-reduced cells by treating them with Actinomycin D (See Methods, Preparation of Biological Samples for details). Fig. 3F presents the averaged intranuclear dry mass concentration at the center of the heating spot, comparing untreated and drug-treated cells. We observed a 13% reduction in dry mass following drug treatment. Given that ~10% of cellular dry mass is attributed to RNA in eukaryotic cells (22), this suggests that nearly all intracellular RNA was depleted, consistent with previous studies reporting a ~70 to 90% reduction in RNA levels following Actinomycin D treatment (25). Fig. 3G displays the thermophoresis-induced dry mass concentration change normalized by temperature increase ($-\mathrm{\Delta }\sigma /\mathrm{\Delta }{T}_s$), measured at the same region as Fig. 3F, with and without the RNA reduction. In RNA-reduced cells, thermophoresis signals decreased by 19%, indicating that approximately 20% of intracellular thermophoresis is driven by RNA migration. These results suggest that RNA is a major contributor to intracellular thermophoresis.

Site-Specific Intracellular Thermophoresis in the Nucleus and Cytoplasm.

We examined site-specific molecular transport by selectively heating different intracellular regions. In this study, we present the variation ratio of depth-integrated dry mass concentration ($\mathrm{\Delta }\sigma /\sigma$), calculated by normalizing $\mathrm{\Delta }\sigma$ with the RI image without heating ($\sigma$). Fig. 4A presents the $\mathrm{\Delta }{T}_s$ map, $\mathrm{\Delta }\sigma /\sigma$ image at 2 s after heating onset, and the temporal evolution of $\mathrm{\Delta }\sigma /\sigma$ at the center of the heating spot within the nucleus. For nuclear heating, we observed a reduction in dry mass at the center of the heating spot, while the surrounding region showed an increase in dry mass, consistent with the results shown in Fig. 3. Fig. 4B shows the corresponding results for cytoplasmic heating, where molecular transport occurred in the opposite direction, moving toward the higher temperature region. To quantify this difference, we measured 12 cells and evaluated the magnitude and direction of molecular transport using $-\mathrm{\Delta }\sigma /\sigma /\mathrm{\Delta }{T}_s$, which corresponds to the Soret coefficient ($S_T$) under spherical symmetry. Fig. 4C displays $-\mathrm{\Delta }\sigma /\sigma /\mathrm{\Delta }{T}_s$ at the center of the heating spot within the nucleus and cytoplasm, measured at 2.4 s, yielding values of 4.5 × 10⁻³ and −1.8 × 10⁻², respectively. These results clearly demonstrate a distinct difference in molecular transport direction between the nucleus and cytoplasm.

Fig. 4.

Site-specific thermophoretic behavior in the nucleus and cytoplasm. (A, Left) Steady-state temperature rise map ($\mathrm{\Delta }{T}_s$), (Middle Left) variation ratio of depth-integrated dry mass concentration ($\mathrm{\Delta }\sigma /\sigma$), (Middle Right) overlay image ($\mathrm{\Delta }\sigma /\sigma$ on RI), and (Right) temporal evolution of $\mathrm{\Delta }\sigma /\sigma$ at the center of the heating spot for nuclear heating. To visualize temporal evolution, $\mathrm{\Delta }\sigma /\sigma$ values were averaged within a 2.2 μm × 2.2 μm area. (B) Corresponding images and the temporal evolution curve for cytoplasmic heating. (C) Evaluated values of $-\mathrm{\Delta }\sigma /\sigma /\mathrm{\Delta }{T}_s$, corresponding to the Soret coefficient under spherical symmetry, measured at 2.4 s for 12 cells (nucleus) and 11 cells (cytoplasm). (D) $\mathrm{\Delta }\sigma /\sigma$ images at 0.04 and 0.08 s for cytoplasmic heating.

The opposite molecular transport observed in the cytoplasm, characterized by a negative Soret coefficient, can be explained by diffusiophoresis, which occurs in environments containing molecules of different sizes (26). Under such conditions, smaller molecules undergo thermophoresis earlier than larger molecules. The resulting spatial concentration gradient of small molecules generates a force that pushes larger molecules opposite to the thermophoretic direction. When this force exceeds the thermophoretic effect on larger molecules, a negative Soret effect arises. To verify the rapid thermophoresis of small molecules, we analyzed $\mathrm{\Delta }\sigma /\sigma$ images measured within the first 0.1 s of heating (Fig. 4D). At 0.04 s, molecules were expelled from the heating spot, exhibiting normal thermophoretic behavior. However, at 0.08 s, an opposite molecular transport toward the higher-temperature region began at the center of the heating spot. This observation suggests that early thermophoresis of small molecules triggers diffusiophoresis. Given that the cytoplasm contains a higher concentration of small molecules, such as metabolites, than the nucleus, it is reasonable that this effect was observed only in the cytoplasm.

An alternative explanation for the opposite molecular transport could be the optical tweezer effect; however, this was not the case in our experiment. To confirm this, we conducted the same experiment using a different IR wavelength (1,064 nm), which is off-resonance with water absorption. Under this condition, thermophoretic effects were suppressed, leaving only the optical tweezer effect. This experiment confirmed that the optical tweezer effect alone did not induce molecular transport. (see SI Appendix, Supplementary Note 3 for details).

Time-Lapse Observation of the Thermophoretic Reaction of Dying Cells.

The mobility of intracellular molecules is expected to vary depending on the cell’s vital state, as cellular viscosity is likely to change in dead cells due to molecular aggregation and other factors. To investigate these temporal changes, we conducted time-lapse imaging of cellular morphology and thermophoretic behavior under room temperature conditions without CO₂ supply. Fig. 5A presents RI and $\mathrm{\Delta }\sigma /\sigma$ images measured 2.4 s after heating onset within the nucleus, comparing representative images captured at the start of time-lapse measurement (0 h) and 5 h later. The RI image at 5 h reveals vivid contrasts, indicating localized regions of high dry mass concentration along intracellular structures, whereas the 0-h image exhibits smoother contrasts. Similarly, the $\mathrm{\Delta }\sigma /\sigma$ images show distinct differences: At 0 h, significant molecular mobility is observed, whereas at 5 h, thermophoresis is absent. Fig. 5B illustrates the temporal evolution of $\mathrm{\Delta }\sigma /\sigma$ at the center of the heating spot, clearly showing the absence of molecular transport in the 5-h image. Fig. 5C presents the time-lapse variations of $\mathrm{\Delta }\sigma /\sigma$ at 2.4 s after the heating onset within the nucleus for four different cells, all exhibiting a progressive decline in mobility over several hours. This observation, combined with the localized dry mass distribution visible in the RI image, suggests that glass-like formation may occur in dying cells, possibly due to polymer aggregation (27).

Fig. 5.

Time-lapse observation of intracellular thermophoretic behavior. (A) RI and $\mathrm{\Delta }\sigma /\sigma$ images captured at 0 h and 5 h. The $\mathrm{\Delta }\sigma /\sigma$ images were acquired 2.4 s after heating onset. (B) Temporal evolution of $\mathrm{\Delta }\sigma /\sigma$ at the center of the heating spot, averaged over a 2.2 μm × 2.2 μm region. (C) Time-lapse variations of $\mathrm{\Delta }\sigma /\sigma$, measured 2.4 s after heating onset within the nucleus for four different cells.

Discussion

To the best of our knowledge, intracellular thermophoresis has been previously explored in only one study, which utilized a fluorescence imaging technique (28). This study examined the reduction in the diffusion coefficient within the cellular environment compared to an aqueous environment by introducing fluorescent dyes (BCECF) and 21-mer DNA molecules into living cells. However, fluorescence imaging is limited to visualizing specific molecular species, making it challenging to obtain a comprehensive view of molecular density dynamics. Additionally, fluorescence imaging cannot directly measure temperature gradient maps, restricting the precise analysis of diffusion and Soret coefficients. In contrast, ViPS microscopy overcomes these limitations by simultaneously capturing intracellular molecular density changes and temperature rise distributions through RI changes, all within a single, label-free measurement. These advanced capabilities provide richer information and enable quantitative analyses of intracellular thermophoretic dynamics.

There is room for improvement in our current ViPS imaging system. One key area is enhancing the detectable minimum $\mathrm{\Delta }\sigma /\sigma$. Currently, this limitation is not due to RI noise in the ODT system (~10⁻⁵ without averaging, corresponding to $\mathrm{\Delta }\sigma /\sigma$ ~ 0.1%) but rather the random movement of small particles within the intracellular environment, particularly in the cytoplasm. This issue arises from taking RI differences between frames with a time interval exceeding 1 s. In our experiments, the noise values, evaluated as the SD of $\mathrm{\Delta }\sigma /\sigma$ images at 2 s without heating, were approximately 0.15% in the nucleus and 0.6% in the cytoplasm. A potential solution to reduce random molecular motion noise is to perform a correlation analysis of $\mathrm{\Delta }n$ images with and without IR heating. This approach takes advantage of the directional nature of thermophoretic transport, distinguishing it from random molecular movement and thereby improving measurement precision.

Thermophoresis of larger molecules can be captured by increasing the IR heating duration. However, slowly varying background drifts—caused by air fluctuations and sample-stage motion—begin to dominate the noise floor over longer timescales, limiting the sensitivity of RI measurements. This limitation may be addressed by implementing a more robust noninterferometric ODT configuration (29), which would allow for extended heating durations without compromising measurement stability.

Another promising direction is extending ViPS imaging beyond biological cells to more general sample systems. Quantitative determination of the Soret coefficient requires two parameters: the variation of the RI with temperature (dn/dT) and with dry-mass concentration (α). When these parameters are not available in the literature, they need to be independently obtained to determine the Soret coefficient (30, 31). Note that uncertainties in dn/dT and α propagate linearly into the Soret coefficient (e.g., a 10% error in dn/dT results in a 10% error in the Soret coefficient). In contrast, measurement of the diffusion coefficient does not require prior knowledge of these parameters, as it is determined solely from the temporal evolution of the RI profile and is independent of absolute temperature or dry-mass concentration changes.

A particularly exciting future direction is bond-specific thermophoretic imaging, which leverages the chemical contrast capability of ViP imaging. By incorporating bond-selective chemical imaging using MIR light, it would be possible to selectively observe the thermophoresis of specific molecular species, such as proteins, lipids, or DNA. This advancement would enable the spatiotemporal measurement of concentration changes for individual molecules, offering deeper insights into their thermophoretic behaviors.

Finally, we outline several future prospects in the context of cellular biology. Thermophoresis holds potential for regulating cellular functions through the controlled manipulation of biomolecules. Our study suggests that the primary contributors to the observed thermophoretic signals are likely proteins and small- to medium-sized RNAs. Thermophoresis-induced variations in molecular concentration may potentially trigger liquid–liquid phase separation (LLPS), which could potentially be visualized within cells using our microscope. Another intriguing possibility is the manipulation of mRNA or DNA via thermophoresis, potentially leading to modifications in cellular states. Monitoring this phenomenon through ViPS imaging could pave the way for precise control of cellular dynamics. However, the diffusion coefficients of these large molecules are two orders of magnitude lower than those examined in this study. Consequently, extended heating durations on the order of approximately 100 s may be necessary to detect such effects.

The reverse molecular transport observed in the cytoplasm may arise from more complex phenomena beyond simple thermophoresis-induced diffusiophoresis. In our experiment, approximately 0.5% of the total dry mass concentration migrated toward the lower temperature side during the initial heating stage within 0.08 s. This corresponds to a solute concentration of ~0.1% in water, calculated based on the cellular solute concentration of ~0.3 g/mL (22). This concentration is an order of magnitude lower than that observed in a previous in vitro study (26), where reverse molecular transport of DNA was induced by thermophoresis of PEG solutes with a solute concentration change of ~1%. However, the cellular environment differs significantly from in vitro dilute solutions due to factors such as the excluded volume effect, hydrophobic/hydrophilic interactions, and variations in chemical potential. Furthermore, other intracellular phenomena, such as LLPS or temperature-sensitive molecular reactions, may also contribute to thermophoresis-driven reverse molecular transport under relatively small solute concentration changes. To further investigate this phenomenon, molecular-specific thermophoretic imaging with ViP chemical contrast or simultaneous fluorescence imaging can be employed. These techniques can detect variations segregated by molecular size and species, offering greater specificity in identifying the underlying mechanisms and advancing our understanding of the complex cellular environment.

Our time-lapse thermophoretic imaging of dying cells has provided profound insights into the mystery of how living cells maintain fluidity without aggregation, despite being densely packed with proteins. It has been hypothesized that adenosine triphosphate (ATP) plays a critical role in sustaining intracellular fluidity in living cells (32). The random motion of intracellular particles, observed via 3D RI imaging with ODT, is believed to reflect this phenomenon (33). Investigating changes in thermophoretic behavior using our ViPS imaging could offer a clearer understanding of the mechanisms underlying intracellular fluidity. This approach may uncover the specific role of ATP and its impact on maintaining the dynamic nature of the intracellular environment.

Methods

Thermophoresis (Soret Effect) and Diffusiophoresis.

A spatial temperature gradient in a solution induces unidirectional molecular transport. The total flux J of molecules under the temperature gradient $\mathrm{\nabla }T$ can be described by molecular diffusion and thermophoretic transport, expressed as

$$J=-D\nabla c\left(\mathit{x},t\right)-D_T\nabla T\left(\mathit{x},t\right)c\left(\mathit{x},t\right),$$ [4]

where D, D_T, c, x, and t denote the diffusion coefficient, thermophoretic mobility, solute concentration, three-dimensional spatial coordinates, and time, respectively (20). The temporal variation of the solute concentration distribution $c\left(\mathit{x},t\right)$ is governed by

$$\frac{\partial c(\mathit{x},t)}{\partial t}=-\nabla \bullet J=D\nabla \bullet \left[\left(\nabla +S_T\nabla T\left(\mathit{x},t\right)\right)c\left(\mathit{x},t\right)\right],$$ [5]

where the Soret coefficient, defined as $S_T=D_T/D$, represents the magnitude and direction of $\mathrm{\nabla }c$ arising from the temperature gradient.

The transport of biomolecules, such as protein, DNA, and RNA (hereafter referred to as solute 1), within an aqueous environment is known to be directed toward the lower-temperature side ($S_T>\; >0$) (20). However, this direction reverses upon the introduction of another, smaller solute (hereafter referred to as solute 2) (26, 34). This phenomenon finds its origin in diffusiophoresis, which arises from the concentration gradient of solute 2 induced by thermophoresis. This gradient drives solute 1 in the opposite direction. In such case, the net flux of solute 1 can be expressed as

$$J_1=-D\nabla c_1\left(\mathit{x},t\right)-D_T\nabla T\left(\mathit{x},t\right)c_1\left(\mathit{x},t\right)+c_1\left(\mathit{x},t\right)u\left(\mathit{x},t\right),$$ [6]

where $c_1$ and u represent the concentration and diffusiophoretic velocity of solute 1, respectively. Note that u depends on the concentration gradient of solute 2. This phenomenon is treated as analogous to thermophoresis but with a negatively signed Soret coefficient.

ViP-ODT System.

A detailed schematic of the ViP-ODT system is presented in SI Appendix, Supplementary Note 1, Fig. S1. A homemade 10-ns Ti:Sapphire laser with a 1 kHz repetition rate generates visible probe pulses at 705 nm, which are introduced into a Mach–Zehnder interferometer via a single-mode optical fiber. In the interferometer’s sample arm, the probe pulses pass through beam-steering optics, consisting of a grating with a line density of 70 lines per millimeter (46-068, Edmund), an aperture, relay lenses, and a reflective objective lens (5007-000, Beck Optronic Solutions) positioned in a 4-f configuration. This setup illuminates the sample at an angled incidence with a numerical aperture of 0.58. The illumination angle can be adjusted in discrete steps by rotating the grating through 10 different angles, with the aperture synchronously rotating to transmit only the first-order diffraction beam. The FWHM illumination area on the sample is 110 μm, corresponding to a 1/11.8 times demagnification from the grating. For holographic measurement, the sample image is magnified by a factor of 167 onto the image sensor plane (Q-2HFW, Adimec) using an objective lens (LCPLFLN100XLCD, Olympus) and relay lenses. The reference light is directed to the image sensor in an off-axis configuration after matching the optical path length, beam size, and polarization to those of the object light.

We used a 1,456-nm CW laser diode (LD) (BL1456-PAG500, Thorlabs) for IR heating (CW-IR), which was electronically modulated using an LD driver (see SI Appendix, Supplementary Note 1 for the timing chart of ViPS imaging). The rise time of the IR laser is sufficiently short compared to the measurement frame rate, as shown in SI Appendix, Fig. S2. The CW-IR beam was spatially combined with the visible beam via a dichroic mirror and focused onto the sample through the reflective objective lens. The IR power used in ViPS imaging was ~2 mW.

Preparation of Biological Samples.

COS7 cells were cultured on a CaF₂ substrate (C20SQ-0.5, Pier Optics) using high-glucose Dulbecco’s modified Eagle medium containing L-glutamine, phenol red, and 4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid (FUJIFILM Wako). The medium was supplemented with 10% fetal bovine serum (Cosmo Bio) and 1% penicillin-streptomycin-L-glutamine solution (FUJIFILM Wako). The cells were maintained at 37 °C in a 5% CO₂ atmosphere. For imaging, the COS7 cells were sandwiched between the substrates with a 10-μm spacer (PCIMRS, MISUMI). The environmental temperature during measurements was 24 °C.

To reduce intracellular RNA levels for the experiment shown in Fig. 3 F and G, Actinomycin D (FUJIFILM Wako) was added to the cultured cells at a concentration of 2.0 μg/mL. Time-lapse imaging was then performed for 6 h following the treatment.

Numerical Simulation of Intracellular Thermophoresis.

To calculate the temporal evolution of the thermophoresis-induced change in depth-integrated dry mass concentration ($\mathrm{\Delta }\sigma$), we performed a two-dimensional diffusion simulation under a temperature gradient. A numerical program, implemented in Python with GPU acceleration, was developed based on the Forward Time Centered Space method. The pixel pitch was set to 207 nm to match the ODT measurement. For this calculation, a slightly modified version of Eq. 5 was used, expressed as

$$\frac{\partial \left(\mathrm{\Delta }\sigma \left(\mathit{x},t\right)\right)}{\partial t}=D{\nabla }^2\left(\mathrm{\Delta }\sigma \left(\mathit{x},t\right)\right)+D{S}_T\nabla \bullet \left[\nabla T_s\left(\mathit{x}\right)\{\sigma \left(\mathit{x}\right)+\mathrm{\Delta }\sigma \left(\mathit{x},t\right)\}\right].$$ [7]

Here, the diffusion term associated with the steady-state inhomogeneous dry mass distribution prior to heating (i.e., ${\mathrm{\nabla }}^2\left(\sigma \left(\mathit{x}\right)\right)$) is excluded, based on the assumption that the diffusion forces from this steady-state distribution are balanced by forces generated by factors other than the temperature gradient.

To ensure the conservation of the dry mass within the nuclear boundary, as evidenced by the experimental results shown in Fig. 3, the pixels at the edge of the nuclear region were constrained by the following equation

$$\nabla (\mathrm{\Delta }\sigma \left(\mathit{x},t\right))+S_T\nabla T_s\left(\mathit{x}\right)\{\sigma \left(\mathit{x}\right)+\mathrm{\Delta }\sigma \left(\mathit{x},t\right)\}=0.$$ [8]

Additionally, to prevent molecules from diffusing out of the region, the gradients of dry mass concentration and temperature were set to zero both inside and outside the boundary. The nuclear region was estimated from the raw RI image of the cell (see SI Appendix, Supplementary Note 2 for details).

Supplementary Material

Appendix 01 (PDF)

Data, Materials, and Software Availability

Custom code and experimental data are available at the repositories: https://github.com/Ideguchi-Lab/Ludwig-Soret-microscopy-with-vibrational-photothermal-effect (35) and 10.5281/zenodo.15877322 (36), respectively. No unique materials were generated in this study.