PROJECT MODEL

This model aims to establish a precise quantitative relationship between nitric oxide (NO) concentration and the ratio metric signal output from the fluorescent biosensor. The model directly draws upon and extends the classic ratiometric theory established by Grynkiewicz et al. for quantifying intracellular calcium concentration[1], innovatively applying its physicochemical principles to the field of nitric oxide sensing.

Regarding the measurement principle, quantitative analysis is achieved by detecting fluorescence signals at two wavelengths and calculating their ratio. Specifically, the ratio signal is defined as R = F₄₈₈ nm / F₄₀₅ nm, wherein F₄₈₈ nm originates from the NO-responsive channel, whose signal intensity changes significantly with NO concentration, and F₄₀₅ nm originates from the reference channel, whose signal remains largely unaffected by NO concentration and serves primarily as an internal standard to correct for non-specific interferences such as variations in probe concentration and sample thickness. This dual-channel ratiometric measurement design significantly enhances the accuracy and reliability of detection.

Based on this measurement principle, the core formula of the model is:

Among these, Kd represents the apparent dissociation constant of the probe with nitric oxide molecules, which is a key parameter reflecting the binding affinity between the probe and the ligand; Rmin denotes the theoretical ratio value when the probe is completely unbound; while Rmax refers to the theoretical ratio value when the probe is fully bound at saturating NO concentrations.

This paper will comprehensively and systematically elucidate the fundamental principles of this theoretical model, the physical meanings and definitions of each parameter, detailed fitting procedures, and provide a thorough explanation of how to determine the model parameters using experimental calibration data (i.e., the probe calibration process), as well as how to further apply the calibrated model to back-calculate the NO concentration in unknown samples.

The Grynkiewicz equation is a foundational theoretical framework for quantitative fluorescent indicator measurements. It describes the fluorescence response behavior of fluorescent indicators (I) when they bind to their specific ligands (L, nitric oxide in this study) and reach equilibrium. For the dual-wavelength ratiometric probe used in this study, its binding reaction with NO can be represented by the following reversible equilibrium:

I + NO ⇌ I-NO

The model's significant advantage and practical value lie in its ability to effectively eliminate or reduce interference from multiple common factors on measurement results—such as the actual concentration of the probe, optical path length of the sample cuvette, and fluctuations in excitation light intensity—by calculating the ratio (R) of fluorescence intensities at two wavelengths. This enables highly precise and reliable quantification of the target analyte concentration.

Through rigorous mathematical derivation, the core equation for calculating NO concentration is obtained as follows:

Where:

• .[NO]: The equilibrium concentration of nitric oxide, which is the target quantity to be determined.
• .Kd: The apparent dissociation constant of the complex formed between the probe and NO, expressed in μM. Its value reflects the binding affinity.
• .R: The fluorescence ratio value measured experimentally, calculated as R = F₄₀₅ ₙₘ / F₄₈₈ ₙₘ.
• .Rmin: The theoretical ratio value when no NO is present ([NO] = 0), i.e., all probe molecules are in the free state.
• .Rmax: The theoretical ratio value under saturating conditions where the NO concentration approaches infinity ([NO] → ∞), i.e., all probe molecules are bound to NO.
• .Sf₂: The fluorescence intensity factor of the free-state probe at the wavelength used in the denominator of the ratio (λ₂ = 488 nm).
• .Sb₂: The fluorescence intensity factor of the bound-state probe at the wavelength used in the denominator of the ratio (λ₂ = 488 nm).

Formula Simplification:

In many cases, particularly after probe optimization, it can be assumed that Sf₂ ≈ Sb₂. This ratio is approximately equal to 1, allowing the equation to be simplified into a form widely used in practice:

This formula serves as the core tool of the model for quantitatively determining the NO concentration in unknown samples.

This project aims to develop a novel genetically encoded fluorescent probe for nitric oxide (NO). The probe is constructed based on a fusion protein comprising the regulatory domain of the bacterial transcription factor NorR and a fluorescent protein. It will be systematically optimized through random mutation and directed evolution strategies to achieve a highly dependent and specific fluorescent response to NO concentrations.

Furthermore, by incorporating subcellular targeting signal sequences, the probe will be directed to specific regions such as the cytoplasm and mitochondria, enabling high-resolution in situ imaging of NO in living cells. This tool is expected to provide critical technical support for the early detection of subclinical cardiovascular pathologies, the evaluation of therapeutic efficacy, and the development of targeted drugs.

To accurately calculate [NO] in unknown samples using the above formula, a rigorous calibration experiment must first be performed using a set of standard NO solutions with precisely known concentrations. This experiment is designed to determine the three key parameters: Kd, Rmin, and Rmax.

3.1 Calibration Experiment and Data Processing

A 100 μL sample of 1 μmol/L NorR-YFP protein solution was added to each well of a 96-well black microplate. The plate was then placed in a microplate reader for fluorescence measurement. Fluorescence intensity was measured at an emission wavelength of 515 nm under two excitation wavelengths: 420 nm and 485 nm. It should be noted that the R₄₂₀/₄₈₅ nm ratio obtained from the microplate reader corresponds to the same fluorescence spectral band as the model-defined ratio R = F₄₀₅ nm / F₄₈₈ nm. Therefore, the two datasets are consistent and can be directly used in model calculations. The measured data are presented in Table 1.

3.2 Curve Fitting

Using the scientific data processing software GraphPad Prism, nonlinear regression fitting was performed on R and [NO] with the following equation. This equation is a rearranged form of the Grynkiewicz equation, describing how R varies with [NO]:

The fitted curve is shown in Fig. 1.

Fig.1 The fitted curve of the fluorescence ratio signal R as a function of the ligand concentration [NO]

Based on the fitted curve, the following parameters were obtained: Rmin = 1.0395，Rmax = 3.6255，Kd = 64.34μM. Thus, the mathematical model is derived as:

The model validation results show a fluorescence ratio of 3.3543 measured experimentally at 2000 μM NO concentration, while the model predicted a value of 3.5449. The relative error between these values is 5.68%, which falls within an acceptable range for biological experimental models and demonstrates the model's strong predictive capability under high-concentration conditions.

The observed deviation is mainly attributed to probe binding site saturation at elevated NO concentrations. Under such conditions, the fluorescence signal increase becomes less pronounced than theoretically expected, leading to a slight underestimation in experimental measurements. It's important to note that this saturation effect only occurs at concentrations significantly higher than the model's intended application range.

Considering the model's design purpose for blood NO detection, where physiological concentrations range from 100 to 500 nM - well below the saturation threshold - the model maintains high reliability and precision within its target operational range. These findings confirm the model's feasibility for practical blood NO detection applications.