FLIM quantification of temperature-dependent enzyme-NADH binding dynamics

Abstract

Metabolic enzyme-coenzyme interactions are temperature-dependent; yet, conventional biochemical assays lack the temporal and spatial resolution to resolve rapid thermal effects on cellular metabolism and cellular binding equilibria. Here, fluorescence lifetime imaging microscopy (FLIM) of the metabolic coenzyme nicotinamide adenine dinucleotide (NADH) was used to quantify steady-state and rapid temperature-dependent changes in enzyme-coenzyme binding dynamics through estimation of dissociation constants (K _D ) and corresponding fractions of free NADH (α₁). A computational model describing the temperature dependence of enzyme-coenzyme binding affinity was constructed to relate changes in K _D to temperature-dependent shifts in α₁. This model was validated in LDH-NADH solutions, MCF-7 cells, and primary murine hippocampal neurons using FLIM. Both steady-state and rapid temperature increases induced increases in free NAD(P)H across all samples, consistent with a reduction in binding affinity (increased K _D ). Rapid thermal gradients induced by short pulses of infrared light produced greater increases in free NADH in LDH-NADH solutions than in cells. These results establish FLIM of NADH as a non-contact, quantitative method to evaluate the temperature-dependence of enzyme-coenzyme binding at millisecond timescales. Additionally, integration of temperature-dependent dissociation constant modeling with FLIM provides a generalizable framework for studying dynamic enzymatic binding processes within living cells that are otherwise inaccessible using conventional assays.

1. Introduction

Cellular metabolism governs energy production through enzyme-mediated reactions that support essential cellular processes such as cell proliferation, DNA replication, cell function, and cell signaling [1,2]. Metabolic reactions are mediated by redox coenzymes, including reduced nicotinamide adenine dinucleotide (NADH) and flavin adenine dinucleotide (FAD). Enzyme-coenzyme interactions are sensitive to environmental factors such as temperature, which can alter binding affinity and dissociation constants [3,4]. However, quantification of rapid metabolic dynamics in living systems remains a significant experimental challenge.

Conventional biochemical approaches for measuring reaction dynamics generally require cell lysis, pooling of substrates from many cells, and acquisition times of seconds to minutes [5–7]. Live-cell metabolic flux assays, such as the Seahorse XF-96, provide measurements of oxygen consumption and extracellular acidification rates [8]. Plate-reader enzyme based assays require seconds to minutes for measurements and lack spatial resolution to detect individual cells or localized changes. Similarly, mass spectrometry-based proteomics and protein assays, such as ELISA, require cell lysis and pooling of materials from many cells, which is incompatible with real-time, live-cell analysis [9,10].

Fluorescence lifetime imaging microscopy (FLIM) of metabolic coenzymes provides a non-invasive approach to measure cellular metabolism with high spatial and temporal resolution [11]. NADH and its phosphorylated form (NADPH) exhibit autofluorescence with similar spectral characteristics; therefore, by convention, NAD(P)H is used to denote the combined signal from both fluorophores [12]. Free and enzyme-bound NAD(P)H exhibit distinct fluorescence lifetimes [13–15]. Time-domain FLIM via time-correlated single photon counting (TCSPC) resolves the fluorescence lifetime decay at each pixel, allowing the two lifetimes and their relative fractions within cells to be quantified [13,15,16]. Since enzyme-coenzyme binding and dissociation occur concurrently with enzymatic activity, FLIM measurements provide an indirect readout of enzyme-coenzyme interaction dynamics [17]. While FLIM has been widely used to study steady-state cellular metabolism, the temporal structure of laser-scanning FLIM acquisition enables evaluation of fluorescence lifetime metrics at pixel and line scan timescales, providing a framework to probe rapid, transient changes in binding equilibrium within living cells.

The temperature-dependence of dissociation constants provides a controlled system for investigating temperature-induced changes in binding affinity. Infrared (IR) light is strongly absorbed by water, generating spatially and temporally confined thermal gradients that produce localized temperature increases up to 25^∘C over micro- to millisecond durations [18–22]. These rapid, transient thermal gradients provide a localized, non-contact method to manipulate cellular environments [19,21,22] and have been shown to induce changes in neural activity [20,23–25]. However, the contribution of thermally driven metabolic processes to these infrared responses remains unexplored, perhaps due to the lack of available metabolic assays to evaluate metabolic changes due to millisecond IR exposures [26].

Here, a thermodynamic binding model based on temperature-dependent dissociation constants was combined with FLIM of NADH to quantify temperature-dependent changes in metabolic enzyme-coenzyme binding under steady-state and transient thermal perturbations. A computational model based on equilibrium dissociation constants was developed to describe the temperature dependence of lactate dehydrogenase (LDH)-NADH binding and the corresponding fraction of free NADH, α₁. The model was validated through fluorescence lifetime imaging of LDH-NADH solutions held at steady-state temperatures via a stage-top incubator or exposed to thermal gradients induced by a short IR light pulse. Additionally, the relationship between temperature and NADH binding dynamics was characterized via FLIM for MCF-7 cells and primary murine hippocampal neurons. The laser-scanning nature of TCSPC FLIM was exploited to obtain FLIM measurements at 0.8 ms, rather than the whole image frame rate, enabling rapid NADH binding measurements. A consistent increase in the free fraction of NADH was observed with increased temperature in the model results, LDH-NADH solutions, and cells for both steady-state and dynamic temperature perturbations, establishing FLIM of NADH, together with equilibrium binding analysis, as a quantitative approach to evaluate rapid, temperature-dependent changes in metabolic enzyme-coenzyme interactions.

2. Methods

2.1. Computational model to relate dissociation constants, temperature, and NADH free fraction

First, a computational model was developed to describe the temperature dependence of LDH-NADH binding equilibrium and the resulting fraction of free NADH (FLIM parameter α₁). NADH was modeled as shifting between free and LDH-bound states according to a reversible binding reaction (Eq. (1)).

$$\text{LDH}+\text{NADH}\rightleftharpoons \text{LDH-NADH}$$ (1)

The model calculates the fraction of free NADH, α₁, as a function of temperature and time for thermal gradients such as those produced by short pulses of IR light. In this model, α₁ is defined as a dimensionless fractional quantity representing the proportion of total NADH that is free, such that (α₁ + α₂ = 1), where α₂ represents the enzyme-bound fraction. Therefore, the FLIM-derived free NADH fraction was defined by Eq. (2),

$${\alpha }_1=\frac{[{\text{NADH}}_{\mathit{\text{free}}}]}{[{\text{NADH}}_{\mathit{\text{total}}}]}$$ (2)

where $[{\text{NADH}}_{\mathit{\text{free}}}]$ is the concentration of free NADH and $[{\text{NADH}}_{\mathit{\text{total}}}]$ is the total NADH concentration. Because α₁ represents a normalized fractional quantity, its value was constrained between 0 and 1.

A previously published equilibrium occupancy model [17] was used to estimate the relationship between NADH binding and the free NADH fraction. The enzyme concentration can be calculated with Eq. (3),

$$[\mathit{\text{Enzyme}}]=\frac{[\mathit{\text{NADH}}]-({\alpha }_1)}{F\ast s}$$ (3)

where [NADH] is the total NADH concentration, [Enzyme] is the concentration of LDH, α₁ is the desired fraction of free NADH, s is the number of binding sites LDH possesses, and F is the fraction of binding sites that NADH will occupy, which can be calculated via Eq. (4) [17].

The fractional occupancy of LDH binding sites by NADH was described using a Langmuir isotherm approach with Eq. (4),

$$F=\frac{{\alpha }_1[\text{NADH}]}{{\alpha }_1[\text{NADH}]+K_D}$$ (4)

where F is the fraction of occupied LDH binding sites, [NADH] is the total NADH concentration, α₁ is the desired fraction of free NADH, and K_D is the temperature-dependent equilibrium dissociation constant.

The temperature dependence of the dissociation constant was modeled using the van’t Hoff relationship in Eq. (5),

$$K_D=K_{D0}\text{exp}\left(\frac{\mathrm{\Delta }H}{R}(\frac{1}{T}-\frac{1}{T_0})\right)$$ (5)

where $K_{D0}$ is the dissociation constant $(4.2\times {10}^{-6}\mathrm{M})$ at the reference temperature $T_0$ (24^∘C), $\mathrm{\Delta }H$ is the enthalpy change of binding (-4.75 kJ ⋅ mol⁻¹), R is the universal gas constant (8.314 J ⋅ K⁻¹ ⋅ mol⁻¹), and T is the absolute experimental temperature changes in Kelvin [27,28]. To verify appropriate temperature-dependent dissociation constants, K_D values were simulated using transient temperature profiles induced by IR pulses. The IR pulses were delivered at 1470 nm using pulse durations of 2 ms and 4 ms, corresponding to radiant exposures of 0.8 J/cm² and 1.7 J/cm², respectively. The resulting temperature gradients were imported into MATLAB and converted from Celsius to Kelvin. Equation (5) was then used to compute the dissociation constant, K_D, as a function of time and temperature.

To relate the fraction of free NADH $\left({\alpha }_1\right)$ and the temporally-varying dissociation constant K_D, Eq. (4) was substituted for F in Eq. (3), resulting in Eq. (6).

$$\left(\frac{{\alpha }_1\ast [\mathit{\text{NADH}}]}{{\alpha }_1\ast [\mathit{\text{NADH}}]+K_D}\right)\ast s\ast [\mathit{\text{Enzyme}}]=[\mathit{\text{NADH}}]-{\alpha }_1[\mathit{\text{NADH}}]$$ (6)

Equation (6) was then simplified and solved for α₁ using an s parameter of 4 as LDH possesses 4 binding sites per enzyme molecule [27,29]. Only the real component of the resulting quadratic equation (Eq. (7)) was used in the model simulation.

$${\alpha }_1^2[\mathit{\text{NADH}}]+{\alpha }_1([\mathit{\text{NADH}}]s[\mathit{\text{Enzyme}}]-{[\mathit{\text{NADH}}]}^2+k)-k[\mathit{\text{NADH}}]=0$$ (7)

For the simulations, an NADH concentration of 50 µM was used to minimize self-quenching [17]. Equation (5) was computed at room temperature (20 ^∘C) to obtain a dissociation constant, K_D, of 4.1 µM. An LDH concentration of 14.03 µM was determined with Eq. (7) for an NADH concentration of 50 µM, α₁ of .60 (60%), s of 4, and K_D of 4.1 µM. Equation (7) was used to calculate NADH α₁ for the K_D values determined as a function of time and temperature for the IR-thermal gradients. The free NADH, α₁, fractions were then expressed as percentages (%) and plotted as a function of time and temperature.

2.2. Solution and cell preparation

An LDH-NADH solution corresponding to an initial NADH free fraction, α₁, of approximately .60 (60%) was prepared based on concentrations determined from the computational model. First, a 1000x stock solution (50 mM) of NADH was prepared by dissolving 354.9 mg of NADH disodium salt (Sigma, #481913) into 10 mL of 1x phosphate-buffered saline (PBS) (Gibco, #10010023). The 1000x NADH stock was then diluted with 1x PBS to create a 100x (5 mM) NADH stock. The final working solution of 50 μM NADH and 14.03 μM LDH was prepared by mixing 0.801 mL of LDH (Sigma, #SAE0049), 10 μL of the 100x NADH solution, and 189 μL of 1x PBS. Solutions were gently vortexed to ensure homogeneity. The NADH and LDH concentrations were chosen to achieve an initial α₁ value of 60% and to minimize self-quenching, consistent with prior studies [17]. Two 35 mm glass-bottom imaging dishes were prepared with 200 μL of solution, one with the 100x NADH stock and the other with the 50 μM LDH-NADH solution (Mattek, #P35G-1.5-14-C). To minimize photobleaching in the presence of room light, the stock solutions were wrapped with aluminum foil and stored at 2-8^∘C in a refrigerator.

The MCF-7 mammary adenocarcinoma cell line (HTB-22^TM, ATCC) was cultured in high glucose Dulbecco’s Modified Eagle’s Medium (DMEM) (Gibco, #11965092) supplemented with 10% fetal-bovine serum (FBS) (Gibco, #A5256701) and 1% antibiotic-antimycotic (Corning, #45000-616). The cells were maintained within an incubator at 37^∘C and 5% CO₂ environmental conditions. Upon reaching confluence, the cells were passaged and plated 48 hours prior to imaging at a density of approximately 1 x 10⁵ cells per 35 mm glass-bottom imaging dish (Mattek, #P35G-1.5-14-C).

The primary neuron cell cultures were established by dissociating embryonic day 18 (E18) hippocampal murine tissues (TransnetYX Tissue, C57EHP) into single neurons. To facilitate the attachment of neurons, 35 mm glass-bottom imaging dishes were coated with a 300 μL mixture containing 50 μg Poly-D-Lysine and 8.5 pH borate buffer solution. Neurons were plated at 45,000 cells/dish and maintained in NbActiv1 +Glutamate (TransnetYX Tissue, NB1+GLU500) for four days. After 4 days, half of the media was exchanged for NbActiv4 (TransnetYx, NB4), and subsequent media changes were performed every 3-4 days. Neurons were imaged after one week of growth.

2.3. FLIM of solutions and cells

Fluorescence lifetime images were captured using a custom-built inverted multi-photon fluorescence microscope (Marianas, 3i) with a 40x water-immersion objective (NA 1.1) that provides a field of view (FOV) of approximately 270x270 μm. NADH fluorescence was excited with a tunable titanium:sapphire femtosecond laser (COHERENT: Chameleon Ultra II) set at 750 nm with a laser power between 8 mW to 12 mW for the LDH-NADH solution, MCF-7, and neuron cell cultures. The fluorescence emission signals were detected with a photomultiplier tube (PMT) and a 447/60 nm filter was used to refine the NAD(P)H emission. TCSPC electronics (SPC-150N, Becker & Hickl) were used to capture lifetime information. The second harmonic generation (SHG) of urea crystals was stimulated at 900 nm and captured with the same 40x water-immersion objective and PMT to measure the instrument response function (IRF) of the FLIM system.

For the steady-state temperature experiments, a stage-top incubator was used to maintain the samples at 5% CO₂ and the environmental temperature was varied to obtain images at 20^∘C, 29^∘C, 33^∘C, 37^∘C, and 43^∘C. To maintain equilibrium, the samples were maintained for at least five minutes at each temperature before imaging. These discrete temperature values were selected to encompass the peak temperatures of the IR-induced thermal gradients used in the computational model. FLIM images of 256x256 pixels were acquired at 5 or more different locations within the imaging dishes at a pixel dwell time of 50 μs and 3 frame integration for a total image acquisition time of approximately 30 s.

For the dynamic temperature experiments, a 1470 nm laser diode (LUMICS: LuOcean Mini 4) was introduced with a 200 μm optical fiber to deliver short pulses of infrared light to the samples. The optical fiber was positioned with a micro-manipulator at 45^∘ and approximately 0, 100, or 250 μm above the samples. A function generator (Berkeley Nucleonics Corporation: Model 525) and the corresponding BNC25 software were used to induce a single IR pulse. The pulses were modulated at discrete millisecond durations to generate IR exposures at 0-4 ms. To limit the FOV to a cell and minimize background pixels during IR exposure, the 256x256 pixel image was cropped to fit a single cell for the primary hippocampal neurons. A pixel dwell time of 100 μs with single-frame integration was used, so each pixel represents 100 μs of acquisition time. This approach allows the temporal dynamics of IR-induced changes to be resolved directly from the laser scan position across the image. A total of at least 5 images were captured per infrared pulse duration for each sample: LDH-NADH solutions, MCF-7 cells, and primary hippocampal neurons.

2.4. FLIM analysis

The fluorescence lifetime decays for the steady-state temperature experiments were analyzed in SPCImage (Becker & Hickl) to extract the fluorescence lifetime parameters. The fluorescence lifetime decays for each pixel were deconvolved from the IRF produced from the SHG of the urea crystals. To exclude background pixels, a decay peak threshold value of 50 was set. To determine the differences in free and protein-bound NADH, the pixel decays were fit to a two-component exponential model. The fluorescence intensity as a function of time (I(t)) was calculated based on the fractional contributions, α₁ and α₂, and their corresponding lifetimes, ${\tau }_1$ and ${\tau }_2$ , of free and protein-bound NADH, respectively (Eq. (8)). The C parameter was used to account for background signal. The short lifetime parameter, ${\tau }_1$ , was measured from the FLIM images of 50 µM NADH solutions using a one-component fit at each discrete temperature and set as the ${\tau }_1$ parameter for the LDH-NADH solutions. The mean ${\alpha }_1$ value was then computed across the pixels for each image.

$$I(t)={\alpha }_1{e}^{-\frac{t}{{\tau }_1}}+{\alpha }_2{e}^{-\frac{t}{{\tau }_2}}+C$$ (8)

For the FLIM images acquired during IR stimulation, the raw data was set to a spatial bin of 0 in SPCImage to preserve the temporal resolution of each pixel. The exponential decays at each pixel were exported for custom analysis in MATLAB. Customized data analysis software (MATLAB) was developed to analyze the fluorescence decay curves and identify when the laser pulse was delivered from the IR-induced thermal lensing artifact. The fluorescence decay matrix was first filtered to remove an image artifact present in the spatial y-dimensions 249-256 of the 256x256 image by setting the corresponding pixel values to 0. Cell masks were created to spatially define the boundaries of individual cells, or groups of cells, isolating them from background signals that would interfere with the data analysis. The 100 μs pixel dwell time was used to correlate pixel positions to time values. The pixel decays were summed in groups of 8 sequentially within a line scan to improve the SNR of the decay curves and to calculate ${\alpha }_1$ at a temporal resolution shorter than the image duration of approximately 7 s. After summation, the decays were deconvoluted from the urea-measured IRF, starting at the maximum peak of each decay. To extract the ${\alpha }_1$ parameter, the decays were fit to a two-component exponential model (Eq. (8)). To reduce noise, a moving average filter with a sliding window of 24 data points was applied to the free NADH parameter.

To assess the reliability of the extracted ${\alpha }_1$ values for the dynamic experiments, representative FLIM fitting quality-control metrics were evaluated from four representative images. Photon counts averaged 1710 ± 369 photons. Less than 17% of fits failed to converge for the solution images, and less than 0.7% failed to converge for the cell images. R-squared values, as a metric of goodness of fit, averaged 0.79 ± 0.05. The mean 95% confidence interval half-width for ${\alpha }_1$ was ± 0.07. The root mean square (RMS) residual average was 6.38, which represents a relative fitting error of 0.37% based on the mean photon counts. The filtered and unfiltered ${\alpha }_1$ traces exhibited a correlation coefficient of 0.80, indicating that the moving average filter preserved the overall temporal behavior of the signal, while reducing high-frequency fluctuations.

2.5. Infrared laser characterization and measurement of thermal gradients

To measure the peak temperatures induced by the infrared light pulses, Europium (III) thenoyltrifluoroacetonate trihydrate (Eu-TTA), a thermosensitive dye, was imaged with a 40x water-immersion objective (NA 1.2) on a customized widefield fluorescence microscope previously described [30]. The powdered Eu-TTA dye (#AC423190010, FSH) was diluted with dimethyl sulfoxide (DMSO) to a 50 mM working solution. In preparation for imaging, 35 mm glass-bottom imaging dishes were filled with 3 mL of the 50 mM Eu-TTA dye. For imaging, a white-light LED source (#XT720S, X-Cite Xylis) was filtered with a 357/44 nm excitation filter (#FF01-357/44, Brightline). To reduce photobleaching during image acquisition, a 0.5 neutral density filter was placed within the excitation path, which reduced the illumination power to 4.32 mW. The emission was then isolated with a 607/70 nm filter and captured with an sCMOS camera (Prime BSI Express Scientific CMOS, Teledyne Photometrics). Images were cropped to a FOV of 333x333 pixels to achieve a camera exposure time of 0.44 ms (2,272 frames per second (FPS)).

To approximate the thermal conditions present during FLIM imaging, the Eu-TTA temperature experiments were configured to replicate the FLIM optical geometry as closely as possible. Both the FLIM and widefield systems used an inverted microscope configuration with the infrared delivery fiber positioned above the sample at the same fiber-to-sample distances and incident angles used during the FLIM acquisition (Table 1). Although Eu-TTA measurements were performed in DMSO rather than aqueous media, the sample plane and fluid layer thickness were maintained as consistently as possible between imaging configurations to preserve similar thermal diffusion conditions. Therefore, the measured temperatures should be interpreted as estimates of local thermal trends rather than absolute temperatures directly experienced by the FLIM sample during acquisition. Temperature uncertainty values were calculated from repeated measurements and are reported as mean ± standard deviation.

Table 1. Table of experimental parameters and laser characterization values for the 1470 nm laser. Pulses were delivered at a height of 0 μm (LDH-NADH solution), 100 μm (MCF-7 cells), and 250 μm (neurons), corresponding to spot sizes of $7.0\times {10}^{-3}{\mathrm{cm}}^2,1.1\times {10}^{-3}{\mathrm{cm}}^2$ , and $1.9\times {10}^{-3}{\mathrm{cm}}^2$ , respectively. RE denotes radiant exposure.

Laser Characterization Measurements
Duration (ms)	Power (W)	Energy (J)	Fiber Tip RE (J/cm2)	Sample Plane RE (J/cm2)	ΔT (∘C)
LDH-NADH Solution
0	0	0	0	0	0 ± 0.6
0.5	2	$1.0\times {10}^{-3}$	1.4	1.4	2.1 ± 0.1
1.0	2	$2.0\times {10}^{-3}$	2.8	2.8	3.7 ± 3.0
2.0	2	$4.0\times {10}^{-3}$	5.7	5.7	8.9 ± 3.4
3.0	2	$6.0\times {10}^{-3}$	8.5	8.5	14 ± 1.0
4.0	2	$8.0\times {10}^{-3}$	11.4	11.4	26 ± 1.2
MCF-7 Cells
0	0	0	0	0	0 ± 1.0
1.0	2.5	$2.5\times {10}^{-3}$	2.2	1.8	4.7 ± 2.1
2.0	2.5	$5.0\times {10}^{-3}$	4.5	3.5	6.6 ± 1.1
3.0	2.5	$7.5\times {10}^{-3}$	6.7	5.2	11 ± 2.2
4.0	2.5	$1.0\times {10}^{-2}$	9.0	7.0	22 ± 3.3
Neuron Cells
0	0	0	0	0	0 ± 0.7
1.0	1.5	$1.5\times {10}^{-3}$	0.8	0.4	4.1 ± 0.5
2.0	1.5	$3.0\times {10}^{-3}$	1.6	0.8	10 ± 0.7
3.0	1.5	$4.5\times {10}^{-3}$	2.4	1.3	14 ± 1.2
4.0	1.5	$6.0\times {10}^{-3}$	3.1	1.7	22 ± 3.6

A calibration curve established the relationship between temperature and Eu-TTA mean fluorescence intensity. A stage-top incubator was used to maintain the samples at discrete temperature values ranging from 25^∘C to 45^∘C, and a total of 30 images were acquired. Data analysis was performed in ImageJ [31] to extract the mean fluorescence intensity values as a function of temperature. A linear regression was performed (Excel) to relate the Eu-TTA fluorescence to temperature.

For estimating the IR-induced temperatures, the 1470 nm laser was placed in the Eu-TTA sample and imaged on the widefield microscope in the same method described for the FLIM experiments (Table 1). To capture the fluorescence intensity before, during, and after the infrared pulses, the function generator was used to introduce the laser pulse 500 ms after the camera was triggered. A stack of 4,000 images at a frame rate of 2,272 fps was used to acquire a total of 8 fluorescence image stacks per laser pulse duration (0-4 ms). Data analysis was then performed in ImageJ to extract the mean fluorescence intensity for each image. The Eu-TTA calibration curve (Fig. 4) was used to relate the mean fluorescence values to temperatures. Temperatures were plotted over time, and the peak temperature following the laser pulse was extracted for each trial. Peak temperatures were reported as mean ± standard deviation.

Fig. 4.

Calibration curve for a 50 mM Eu-TTA solution showing fluorescence intensity (a.u.) as a function of temperature (^∘C). A total of 30 images were acquired over temperatures ranging from 25^∘C to 45^∘C. Linear regression analysis yielded an equation of Intensity (a.u)= -6.48xTemperature (^∘C)+708.55 with an R-squared value of 0.97 (red line). The 95% confidence bounds are shown in dashed red lines.

To estimate the radiant exposure for each laser pulse duration, the power (W) was calculated from the measured output of the laser (LUMICS). The laser spot size (cm²) was calculated for the 200 μm optical fiber at an angle of 45^∘ and 0, 100, and 250 μm sample distances. The energy (J) was calculated by multiplying the power (W) with the pulse duration (s). The radiant exposure values at the fiber tip were then calculated by dividing the energy (J) by the spot size (cm²) for each pulse condition. The IR radiant exposure at the sample plane was estimated using Beer’s law (Eq. (9)) to account for absorption over the distance between the fiber and the sample,

$$I(t)=I_0{e}^{-{\mu }_{a}z}$$ (9)

where z represents the fiber-to-sample distance, and μ_a is the absorption coefficient of 24.9 cm⁻¹ for water at 1470 nm [32].

2.6. Statistical analysis

Statistical comparisons were performed using one-sample t-tests to assess whether the experimentally measured free NADH fraction, ${\alpha }_1$ , differed from the corresponding model prediction at each temperature and radiant exposure. Experimental measurements were obtained from individual FLIM images, with each image yielding a single ${\alpha }_1$ value. Additionally, the slope and y-intercept coefficient from the linear regression fits were compared between the experimental data and model results using z-tests via (Eq. (10)), where ${\beta }_1$ and ${\beta }_2$ are the coefficients being compared and SE ${\beta }_1$ and SE ${\beta }_2$ are their associated standard errors [33]. The z-scores were then used to find the corresponding p-values. For all figures with boxplots, the central line denotes the median, the box edges represent the first and third quartiles (25th and 75th percentiles), and the whiskers extend to 1.5× the interquartile range.

$$Z=\frac{{\beta }_1-{\beta }_2}{\sqrt{{(SE{\beta }_1)}^2+{(SE{\beta }_2)}^2}}$$ (10)

3. Results

3.1. Modeling indicates IR-induced thermal gradients increase K_D and free NADH, ${\alpha }_1$

Equations (1)–(7) were used to relate the dissociation constant, K_D, temperature, T, and the fraction of free NADH, ${\alpha }_1$ , to simulate thermal gradient effects on LDH-NADH binding dynamics. A temperature increase resulted in a corresponding increase in the dissociation constant, K_D, which rose rapidly during the thermal gradient and exponentially decayed as the temperature decayed (Fig. 1(A)). A higher IR radiant exposure resulted in higher peak temperatures and higher dissociation constants (Fig. 1(A)). The 1.7 J/cm² IR-light pulse resulted in a peak temperature of 42^∘C and a peak dissociation constant of 4.7 µM (Fig. 1(A)). In comparison, the 0.8 J/cm² pulse reached a peak temperature of 31^∘C and a dissociation constant of 4.4 µM (Fig. 1(A)).

Fig. 1.

The simulated dissociation constant, $K_D$ , (A) and free NADH, ${\alpha }_1$ , (B) for a LDH-NADH solution are dependent on the thermal gradient produced by short pulse IR light. Two thermal gradients were used in the simulations: red (1470 nm, 1.7 J/cm², 4 ms) and blue (1470 nm, 0.8 J/cm², 2 ms).

The simulated dissociation constants were then related to the fraction of free NADH, ${\alpha }_1$ , through Eq. (7). As the temperature increased, the fractional amount of NADH, ${\alpha }_1$ , also increased, indicating a reduction in protein-bound NADH (Fig. 1(B)). Following the peak temperature, the free NADH values returned to baseline as temperatures decreased. Higher radiant exposures resulted in an increased proportion of free NADH. The 1.7 J/cm² pulse resulted in an ${\alpha }_1$ of 68% (Fig. 1(B)), while the 0.8 J/cm² pulse resulted in an ${\alpha }_1$ of 64% (Fig. 1(B)). The simulations demonstrate that transient thermal perturbations are predicted to induce rapid increases in the fraction of free NADH, ${\alpha }_1$ , during the period of temperature elevation.

3.2. Steady-state relationship between temperature and free NADH, ${\alpha }_1$

A steady-state temperature experiment was conducted on LDH-NADH solutions, MCF-7 cells, and primary hippocampal neurons to assess the influence of temperature on the fraction of free NADH, ${\alpha }_1$ . Representative FLIM images, false colored to free NADH fraction, ${\alpha }_1$ , show a shift to red-tones indicating an increase in ${\alpha }_1$ with an increase in temperature (^∘C) (Fig. 2).

Fig. 2.

Representative images false-colored to free NADH fraction, ${\alpha }_1$ , of LDH-NADH solutions, MCF-7 cells, and neurons at 20^∘C, 33^∘C, and 43^∘C. Scale bar: 85.3 µm.

Quantitative analysis across multiple images and technical replicates demonstrated an increase in free NADH, ${\alpha }_1$ , with increased temperature in the LDH-NADH solutions, MCF-7 cells, and neurons (Fig. 3). For the LDH-NADH solution, the ${\alpha }_1$ value increased from a baseline value of 62% (20^∘C) to 74% at 43^∘C, which corresponded to a percent change of 20% (Fig. 3(A)). The experimental LDH-NADH solution ${\alpha }_1$ values followed the same trend as the model-calculated values. The percent differences between model and experimental ${\alpha }_1$ values were below 27.2% across all temperature groups (Fig. 3(A)). Statistically significant differences were observed at 33^∘C (*** p < 0.001) and 37^∘C (*** p < 0.001) (Fig. 3(A)). The experimental data for the MCF-7 cells and neurons also showed an increase in free NADH, ${\alpha }_1$ , with an increase in temperature (Fig. 3(B), C). The MCF-7 cells had an ${\alpha }_1$ of 77% at 43^∘C, which was a percent change of 20% from the control (20^∘C) ${\alpha }_1$ of 65% (Fig. 3(B)). The neurons exhibited an ${\alpha }_1$ of 79% at 43^∘C, which was a 15% increase from the free NADH amount of 69% at 20^∘C (Fig. 3(C)).

Fig. 3.

Effects of temperature on free NADH, ${\alpha }_1$ , for (A) LDH-NADH solutions, (B) MCF-7 cells, and (C) primary hippocampal neurons. In (A), the black circles correspond to the model-predicted values and the numbers represent the percent difference between the computational model and experimental results for each temperature group (n ≥ 5 images per temperature, *** p < 0.001, one-sample t-test). (D) Slope coefficients of the linear regression fits for LDH-NADH solutions, MCF-7 cells, and neuron cells. (E) Y-intercept coefficients of the linear regression fits for LDH-NADH solutions, MCF-7 cells, and neuron cells. Error bars represent the standard error of the coefficients (** p < 0.01, *** p < 0.001, z-test).

For all three samples, linear regression models of the relationship between free NADH, ${\alpha }_1$ , and temperature yielded a positive slope ranging from 0.5%/^∘C to 0.6%/^∘C (Fig. 3(D)). The computational model-predicted slope coefficient of 0.3%/^∘C aligned more closely with the neuron cells than with the slope observed for the LDH-NADH solution and MCF-7 cells (0.6%/^∘C) (Fig. 3(D)). The linear regression fits yielded y-intercept values between 50.5% and 60.4% for all samples (Fig. 3(E)). The computational model-predicted y-intercept coefficient of 52.9% aligned more closely with the MCF-7 cells than with the slope observed for the LDH-NADH solution (50.5%) and neuron cells (60.4%). Statistically significant differences were found between the LDH-NADH solution and neuron cells (** p < 0.01) and between the MCF-7 cells and neuron cells (*** p < 0.001).

3.3. Characterization of IR pulse energy and peak temperature

To characterize the IR laser pulses, the 1470 nm laser radiant exposures were computed, and the IR-induced temperatures were measured (Fig. 4, Table 1).

Longer pulse durations resulted in higher energy (Table 1), with the radiant exposure $\left(J/{\text{cm}}^2\right)$ increasing proportionally with pulse duration. The fluorescence intensity of the 50 mM Eu-TTA solution was determined as a function of temperature (^∘C) (Fig. 4), and the resulting linear equation, Intensity (a.u)= -6.48xTemperature (^∘C)+708.55, was used to compute temperature from fluorescence intensity image stacks for each IR pulse width and fiber height (Table 1). Slight differences in fiber height across samples resulted in different peak temperatures across experiments. Overall, the 0-4 ms IR pulses applied to the samples corresponded to 0-12 J/cm² radiant exposures and peak $\mathrm{\Delta }T$ values of 22^∘C to 26^∘C.

3.4. IR-induced thermal gradients increased free NADH, ${\alpha }_1$

FLIM was performed on LDH-NADH solutions and cells during exposure to a single pulse of 1470 nm light to evaluate IR-induced thermal gradient effects on free NADH. Representative fluorescence intensity images of LDH-NADH solutions show a decrease in fluorescence caused by the infrared laser pulse (Figs. 5(A)). Representative line plots of ${\alpha }_1$ , as a function of time, show no change with mock (0 ms) IR exposure, whereas ${\alpha }_1$ increases with increasing peak temperatures of 22^∘C (0.5 ms, 1.4 J/cm²) and 34J/cm²) IR pulses (Fig. 5(B)). The free NADH, ${\alpha }_1$ , increased to 78% for the 1.4 J/cm² IR-pulse and 96% for the 8.5 J/cm² IR-pulse, corresponding to a percent change of 35% and 66%, respectively (Fig. 5(C)). When repeated and quantified over multiple trials, the free NADH, ${\alpha }_1$ , of the LDH-NADH solutions increased with increasing peak temperature (^∘C), indicating a temperature-dependent shift toward free NADH with higher IR-induced thermal gradients (Fig. 5(D)). Experimental results were then compared with model predictions (y = 0.4x + 52.9), revealing statistically significant differences between the model and experiment at 20^∘C (**** p < 0.0001), 29^∘C (* p < 0.05), 34^∘C (** p < 0.01), and 46^∘C (** p < 0.01).

Fig. 5.

(A) Representative fluorescence intensity images of the LDH-NADH solution exposed to peak temperatures of 20^∘C (0 ms, 0 J/cm² pulse), 22^∘C (0.5 ms, 1.4 J/cm² pulse), and 34^∘C (3 ms, 8.5 J/cm² pulse). Scale bar= 85 µm. (B) Fraction of free NADH before, during, and after peak temperatures of 20^∘C (0 ms, 0 J/cm² pulse), 22^∘C (0.5 ms, 1.4 J/cm² pulse), and 34^∘C (3 ms, 8.5 J/cm² pulse), derived from the data in panel A. (C) The percent change in free NADH before, during, and after peak temperatures of 20^∘C (0 ms, 0 J/cm² pulse), 22^∘C (0.5 ms, 1.4 J/cm² pulse), and 34^∘C (3 ms, 8.5 J/cm² pulse), derived from the data in panel B. (D) Peak free NADH, ${\alpha }_1$ , of LDH-NADH solutions due to 20^∘C, 22^∘C, 24^∘C, 29^∘C, 34^∘C, and 46^∘C peak temperatures of 1470 nm light as determined experimentally (boxplots) and through model-simulations (black circles, text values). The percent difference is computed between the mean of the experimental data and the simulated value. Stars indicate significance with a t-test of means (n ≥ 5 peak values (one per image) per peak temperature, * p < 0.04, ** p < 0.01, and ****p < 0.0001).

Representative fluorescence intensity images of MCF-7 and neuron cells show constant intensity values over time in control samples (0 J/cm²) and decreases in fluorescence intensity during infrared exposures (Fig. 6(A)). The fractional contribution of free NADH, ${\alpha }_1$ , shows minimal modulation in control (20^∘C) (Fig. 6(B)). Slight increases in ${\alpha }_1$ were observed, including a 7% increase at a peak temperature of 27^∘C (2 ms, 3.5 J/cm² pulse) for the MCF-7 cells and a 9% increase at 30^∘C (2 ms, 0.8 J/cm² pulse) in neurons (Fig. 6(B)). Higher IR-induced peak temperatures (^∘C) led to greater increases of the fractional amounts of free NADH, ${\alpha }_1$ , for the MCF-7 cells and the neurons (Figs. 6(D)).

Fig. 6.

(A) Representative fluorescence intensity images of MCF-7 cells and neuron cells exposed to peak temperatures of 20^∘C (0 ms, 0 J/cm² pulse), 27^∘C (2 ms, 3.5 J/cm² pulse) for the MCF-7 cells, and 30^∘C (2 ms, 0.8 J/cm² pulse) for the neuron cells. Scale bar= 85 µm for the MCF-7 cells and 19 µm for the neuron cells. (B) Fraction of free NADH before, during, and after 1470 nm IR exposure, derived from the data in panel A. (C) The percent change in free NADH before, during, and after IR exposure, derived from the data in panel B. (D) Peak free NADH, ${\alpha }_1$ , for the MCF-7 cells due to 20^∘C, 25^∘C, 27^∘C, 31^∘C, and 42^∘C peak temperatures of 1470 nm light. Boxplots computed from 5-8 images. (E) Peak free NADH, ${\alpha }_1$ , for the neuron cells due to to 20^∘C, 24^∘C, 30^∘C, 34^∘C, and 42^∘C peak temperatures of 1470 nm light. Boxplots computed from 7-9 images.

4. Discussion

Cellular metabolism is governed by enzyme-mediated reactions that are governed by temperature [3,4]. This study combined a temperature-dependent binding model with FLIM measurements of NADH to quantify how steady state and transient thermal perturbations modulate enzyme-coenzyme binding dynamics. The model predicted that increased temperatures would increase the LDH-NADH dissociation constant, $K_D$ , resulting in increased free fractions of NADH and a shift in binding equilibrium. Consistent with these model predictions, both steady-state temperatures and IR-induced thermal gradients produced rapid, reversible increases in NADH free fraction as measured by FLIM in LDH-NADH solutions, MCF-7 cells, and primary hippocampal neurons (Figs. 5, 6). The magnitude of the modulation in free NADH scaled with the peak temperature and was largest in the LDH-NADH solutions (Fig. 5).

To simplify the model, the temperature-dependence of the LDH-NADH dissociation constant, $K_D$ , was assumed to follow the van’t Hoff relationship across all temperatures (Eq. (5)). The LDH-NADH reaction was selected as a simplified system because NADH is autofluorescent, enabling direct experimental validation of free and bound fractions through FLIM quantification. The Eu-TTA calibration curve (Fig. 4) provided a relationship between Eu-TTA fluorescence intensity and temperature, allowing experimentally measured thermal gradients generated by IR pulses to be incorporated directly into the model. The measured temperature gradients were used to estimate temperature-dependent changes in $K_D$ (Eq. (5)), which were then used to predict the fraction of free NADH (α₁) (Eq. (7)). Although the enthalpy change of binding, $\mathrm{\Delta }H$ , is often considered constant across a small range of temperatures, high temperature ranges can lead to temperature-dependent changes in $\mathrm{\Delta }H$ . This occurs because the bound states (the LDH-NADH complex) and unbound states (free LDH and NADH molecules) of the LDH-NADH reaction may have different heat capacities at large temperature ranges, causing the enthalpy change of binding to vary with temperature [28,34]. According to the van’t Hoff relationship, a value higher than the selected $\mathrm{\Delta }H$ of $-4.75\mathrm{kJ}\cdot {\mathrm{mol}}^{-1}$ will increase the dissociation constant, $K_D$ , while a $\mathrm{\Delta }H$ lower than $-4.75\mathrm{kJ}\cdot {\mathrm{mol}}^{-1}$ will decrease $K_D$ (Eq. (5)). Compared with LDH-NADH solution experimental values, the model underestimates free NADH at higher peak temperatures, suggesting that the enthalpy change of binding, $\mathrm{\Delta }H$ , may increase under these conditions, leading to higher dissociation constants than predicted (Fig. 3(A), 5(D)).

The use of FLIM to detect changes in free NADH in response to rapid temperature change presents a unique approach for estimating variations in the dissociation constants, $K_D$ , governing LDH-NADH binding. Pixel-wise analysis of FLIM images enabled quantification of free-to-bound NADH ratios at 0.8 ms temporal resolution, achieved through high-speed TCSPC acquisition. This approach allows transient thermal effects on NADH-enzyme binding to be resolved at sub-image frame timescales. Since NADH binding to enzymes is directly governed by equilibrium dissociation constants (Eqs. (3) and (4)), FLIM was leveraged as an indirect reporter of temperature-dependent binding equilibria underlying metabolic activity. In contrast to conventional methods for assessing cellular metabolism activity, such as spectrophotometry and stopped-flow techniques, which often require large sample sizes, homogeneous environments, and the use of exogenous labeling [35,36], FLIM offers label-free, spatially resolved measurements under dynamic conditions (Figs. 3, 5, 6). However, the extraction of α₁ values relies on bi-exponential fitting of fluorescence decay curves and is sensitive to photon counts and signal-to-noise ratios, which can be limited for autofluorescent molecules and fast measurements. While fluorescence lifetime is relatively robust to intensity fluctuations [11,37], IR exposure may introduce transient optical effects such as thermal lensing and scattering changes that reduce photon counts and increase fitting uncertainty, potentially contributing to variability in α₁. Additionally, computed α₁ values represent spatial averages over selected regions of interest, which may contribute to variability in cellular measurements (Fig. 6). Nevertheless, control datasets processed using the identical fast-FLIM reconstruction pipeline exhibited minimal transient changes in α₁ in the absence of infrared stimulation, suggesting that spatial heterogeneity alone did not generate the observed transient dynamics (Fig. 5, 6).

The amount of free NADH remained broadly comparable across samples under both steady-state and IR-induced thermal conditions (Figs. 3, 5). However, measurements obtained under IR-induced thermal gradients exhibited greater variability relative to controlled heating with the stage-top incubator. For the LDH-NADH solution, the maximum deviation between the model and experiment was $27.2\mathrm{\%}$ under steady-state heating at 43^∘C, whereas IR-induced heating (peak 29^∘C) produced a larger deviation of 41.8% (Figs. 3, 5). This difference likely reflects the rapid millisecond heating timescale, which may be too fast for activation of slower regulatory responses such as heat shock mechanisms [38,39]. In contrast, controlled heating allows partial metabolic adaptation up to 45^∘C, where temperatures past this threshold can result in protein denaturation [40–42]. Importantly, thermal injury depends on both peak temperature and exposure duration. The infrared-induced temperature elevations examined in this study were transient, and therefore the thermal dose may be substantially lower than that associated with sustained heating known to produce cellular damage. Despite this increased variability, the overall magnitude of the free NADH response remained similar across conditions. This suggests that temperature is the dominant factor governing NADH binding fractions, and the rate of heating contributes to variability.

Greater changes in free NADH were observed in the LDH-NADH solutions compared to MCF-7 and neuronal cells (Fig. 5(D), 6(D), 6(E)). This is likely due to the homogeneity of the solution which only contained NADH and LDH molecules, whereas cellular samples contain multiple metabolic pathways and additional endogenous fluorophores, including NADPH, flavin adenine dinucleotide (FAD), FMN-binding fluorescent protein (FMN), and dihydrolipoamide dehydrogenase (lipDH), which can buffer NADH dynamics and introduce background fluorescence signals [43–45]. While temperature alters enzyme-coenzyme binding dynamics, system complexity contributes to heterogeneity in the metabolic response.

5. Conclusion

Here, a computational model was developed to simulate temperature-dependent metabolic enzyme-coenzyme binding dynamics in response to transient thermal perturbations generated by infrared (IR) light. Model predictions were compared across FLIM experiments on LDH-NADH solutions, MCF-7 cells, and primary hippocampal neurons. Increases in temperature lead to higher fractions of free NADH, indicating reduced binding of NADH to partner enzymes and an increase in dissociation constants, $K_D$ . FLIM provides an indirect measure of metabolic state by resolving free and protein-bound NADH, enabling inference of dynamic changes in enzyme-coenzyme binding that are difficult to capture using conventional techniques due to limited temporal resolution. High-speed TCSPC FLIM combined with pixel-wise analysis enabled the extraction of free-to-bound NADH ratios on sub-millisecond timescales (0.8 ms), resolving transient thermal effects on binding interactions within a single image frame. Together, the computational model and FLIM measurements establish a framework for quantifying temperature-driven changes in enzyme-coenzyme binding dynamics and demonstrate that rapid thermal perturbations can modulate intracellular metabolic reactions through shifts in binding affinity.

Funding

United States Air Force Office of Scientific Research https://ror.org/011e9bt93 ( FA9550-20-1-0078, FA9550-23-1-0441); National Institutes of Health https://ror.org/01cwqze88 ( R35 GM142990).

Disclosures

The authors declare no conflicts of interest.

Data Availability

All code is freely available at [46].