Method for Improved Fluorescence Corrections for Molar Mass Characterization by Multi-Angle Light Scattering

Abstract

Multi-angle light scattering (MALS) was used to determine the absolute molar mass of fluorescent macromolecules. It is standard protocol to install bandwidth filters before MALS detectors to suppress detection of fluorescent emissions. Fluorescence can introduce tremendous error in light scattering measurements and is a formidable challenge in accurately characterizing fluorescent macromolecules and particles. However, we show that for some systems, bandwidth filters alone are insufficient for blocking fluorescence in molar mass determinations. For these systems, we have devised a post-collection correction procedure to calculate the amount of fluorescence interference in the filtered signal. By determining the intensity of fluorescent emission not blocked by the bandwidth filters, we can correct the filtered signal accordingly and accurately determine the true molar mass. The transmission rates are calculated before MALS experimentation using emission data from standard fluorimetry techniques, allowing for the characterization of unknown samples. To validate the correction procedure, we synthesized fluorescent dye-conjugated proteins using an IR800CW (LI-COR) fluorophore and Bovine Serum Albumin protein. We successfully eliminated fluorescence interference in MALS measurements using this approach. This correction procedure has potential application toward more accurate molar mass characterizations of macromolecules with intrinsic fluorescence, such as lignins, fluorescent proteins, fluorescence-tagged proteins, and optically active nanoparticles.

Graphical Abstract

INTRODUCTION

When light propagates through a medium, it creates an oscillating electric field that induces oscillating dipoles in molecules that it passes through. The oscillating dipoles within molecules create electromagnetic fields – thus emitting light, a phenomenon known as light scattering (LS). Our focus lies with elastic light scattering (Raleigh scattering), where there is no change in the wavelength of the emitted light from the incident light. Most importantly, Raleigh scattering can be used to determine the molar mass of a molecule. The relationship between molar mass and scattered light of molecules in a dilute solution when using the Raleigh-Gan-Debye approximation¹ (RGD) is given.

$$R_{\theta }=K^{*}McP\left(\theta \right)\left[1-2A_{2}McP\left(\theta \right)\right]$$ (1a)

$$K^{*}=4{\pi }^2{n}_0^2\frac{{(dn/dc)}^2}{{\lambda }^4{N}_A}$$ (1b)

Where R_θ (cm⁻¹) is the excess Raleigh ratio as measured by a detector at angle θ M is the weight average molar mass (g/mol), P(θ) is the form factor, K* is the optical constant, and c is the concentration. Elaborations on RGD can be found elsewhere in the literature^1,2. For large molecules R_g ≥ about 10nm for a 658nm laser)¹, the scattered light intensity will have an angular dependence, represented in P(θ). Theoretically, all size and shape effects vanish (P(θ) → 1) when intensities are measured at the same angle as the incident beam (θ = 0°), however, measuring scattering at θ = 0° cannot be done in practice without also measuring the intensity of the incident light¹. Instead, multiple angles about the illuminated sample can be measured and then extrapolated to 0° to arrive at a size and shape independent of molar mass – this is called multi-angle light scattering (MALS). By examining the angular dependence and angular variation of scattered light, we can also determine the radius of gyration and shape, respectively. However, shape information is limited to very large macromolecules. A combination of MALS with an online fractionation technique such as size-exclusion chromatography (SEC-MALS), is often used to characterize disperse solutions and is employed in this study. This technique allows for the additional determination of the number -average molar mass (M_n) and dispersity (Đ, M_w/M_n).

Fluorescent macromolecules and nanoparticles are prevalent in biological, chemical, and medical fields where fluorescent light is emitted and can significantly obscure scattered light measurements, resulting in a many times over-estimation of molar mass if fluoresced photons are measured as scattered photons^3,4. Modifications of light scattering instruments to suppress the detection of fluorescent light most commonly involve altering the incident laser wavelength to reduce absorption/fluorescence and installing bandwidth filters on the detectors to filter out red-shifted fluoresced light^3,4. However, these standard mitigation and suppression techniques are limited in that too narrow of filters block light scattering signal, thus significantly reducing the instrument’s sensitivity⁴. Also, the intensity of scattered light scales with the incident laser wavelength on the order of λ⁻⁴, drastically reducing the sensitivity at higher wavelengths. As a result, for most SEC-MALS systems found in literature, bandwidth filter widths range from 10–20nm⁴ and incident wavelengths are not larger than 1000nm⁵. For some systems, these precautions are sufficient to reduce fluorescence to negligible intensities. In systems where these precautions are insufficient, there is no other ubiquitous techniques for fluorescence removal from light scattering signal.

All detectors (filtered and unfiltered) will yield the same measured intensity for non-fluorescing, isotropic scatterers, such as a low molecular weight polystyrene. By comparison, a fluorescing isotropic scatterer of similar molar mass will yield two different intensities between the filtered and unfiltered detectors. We observe these effects for fluorescent hybrid poplar lignin as compared to polystyrene in Figure 1, where the Raleigh ratio is proportional to the measured light intensity reaching the detectors.

Figure 1.

Plot of the Raleigh ratio vs. elution time of detectors 3–16 for A) 30 kDa polystyrene standard (non-fluorescing) and B) hybrid poplar lignin sample (fluorescing). Both samples are dissolved in dimethylformamide (DMF) at 3.0 mg/mL. Due to noise, the high and low angle detectors (1,2,17,18) were excluded. The blue region in B) indicates the difference due to fluorescence between the filtered (even numbered) and unfiltered (odd numbered) detectors.

The difference in Raleigh ratio observed between the filtered and unfiltered detectors is due to fluorescence interference. Fluorescence, in general, has been a recurring challenge observed in light scattering characterization of various biomolecules including lignin since before 1980^3,6–11. The most recent and comprehensive work for lignin characterization using various incident laser wavelengths and bandwidth filters by Zinovyev et al.³ found that the highest wavelength laser (785nm) with bandwidth filters yielded the most accurate results, albeit transmitted fluorescence was still detected. It is presumed that emitted fluorescence close to the incident beam’s wavelength is transmitted and subsequently measured as scattered light. Figure 2 illustrates this phenomenon, where we simulated the transmitted emission for an infrared fluorophore, IR800CW (LI-COR), using a MALS incident beam wavelength of 784nm and ± 10nm bandwidth filters. The IR800CW is the same fluorophore used throughout this study and was chosen for its well-defined, narrow emission characteristics.

Figure 2.

The image shows the overlap between the absorption peak (red) and the emission peak (blue) of the IR800CW fluorophore provided by the manufacturer (LI-COR). The MALS central wavelength of 784 nm (green, dashed) is shown. The blue-shaded regions indicate the blocked wavelengths via the bandwidth filters. The dotted region indicates the transmitted emissions. The transmitted wavelengths are between 774 and 794nm.

Current practice does not account for transmitted fluorescence, however, shown in this work and suggested elsewhere^3–5, even with filters installed, fluorescence interference can still introduce significant error. In pursuit of more accurate molar mass determination, we address the transmitted fluorescence problem directly. Herein we develop a methodology for precisely determining the contribution of residual fluorescence in light scattering signals that neither bandwidth filters nor laser wavelengths can eliminate and correct accordingly.

For areas of research investigating materials with tunable optical properties, where emission and excitation spectra are subject to change, correcting for transmitted fluorescence may be a convenient means of obtaining accurate molecular information without altering instrumentation. Common examples include optically active nanoparticles that exhibit size and shape-dependent emission characteristics^12–14. Additionally, experiments using multiple fluorescent probes¹⁵ or similar labeling techniques will find it easier to simply correct for fluorescence rather than carefully designing experiments around the limitations of the MALS instrument. MALS techniques traditionally have been poorly suited for optically active materials due to interference phenomena; however, this method expands the range and versatility of MALS techniques in investigating optically interfering materials.

EXPERIMENTAL

FLUORESCENCE INTERFERENCE CORRECTION (FIC) PROCEDURE.

Depending on the sample and how intensely it fluoresces, transmitted fluorescence can result in significant over-estimations of molar mass despite suppression and blocking precautions. In this case, we propose the following method to correct for the fluorescence that reaches the filtered detectors, denoted by the transmission factor, T_f.

We assume there exists a distinct component of the measured light intensity given by R_θ that only represents contributions from fluorescence, R_θF, because of increased detector voltage, V_θF. Similarly, there also exists a component of R_θ is due to light scattering, R_θS measured by increased detector voltage, V_θS. The laser monitor (LM) measures the intensity of the incident beam as a relative voltage, V_FM.

$$R_{\theta }=R_{\theta S}+R_{\theta F}$$ (3a)

$$R_{\theta F}=N_{\theta }{A}_{\mathit{\text{CSCC}}}\left[\frac{\left(V_{\theta F}-V_{\theta ,\mathit{\text{baseline}}}\right)}{V_{LM}}\right]$$ (3b)

$$R_{\theta S}=N_{\theta }{A}_{\mathit{\text{CSCC}}}\left[\frac{\left(V_{\theta S}-V_{\theta ,\mathit{\text{baseline}}}\right)}{V_{LM}}\right]$$ (3c)

N_θ is the normalization coefficient for a detector at angle θ, and A_CSCC is the system configuration constant and contains corrections specific to the instrumentation. For the filtered and unfiltered detectors, the observed R_θ is a combination of the two components, R_θS and R_θF.

$$R_{\theta ,\mathit{\text{unfiltered}}}=R_{\theta S}+R_{\theta F}$$ (4a)

$$R_{\theta ,\mathit{\text{filtered}}}=R_{\theta S}+T_f{R}_{\theta F}$$ (4b)

R_{θ,unfiltered} measures all the fluorescence emitted in the plane of the detectors at angle θ plus scattering. R_θ,filtered measures the scattering plus a fraction of the fluorescence component that passes through the filter given by a transmission factor, T_f. Therefore, at every θ where there is a filtered detector and an unfiltered detector, we can solve for R_θS. R_θS is the pure scattering component that corresponds to the correct molar mass. Algebraic rearrangement of Eq. 4a and 4b yields the solution for R_θS (Eq. 5).

$$R_{\theta S}=\left(\frac{R_{\theta ,\mathit{\text{filtered}}}}{1-T_f}\right)-\left(\frac{T_f{R}_{\theta ,\mathit{\text{unfiltered}}}}{1-T_f}\right)$$ (5)

A generalized form of Eq. 5 for SEC analysis can be found in SI.1. Table 1 lists the fixed angles and the viewing angles of each detector. We match each filtered detector to the nearest-angle unfiltered detector. In systems exhibiting angle-dependent intensities, the anisotropy will be symmetric about the laser axis and cancel between the filtered and unfiltered detectors. Consequently, for a purely scattering signal, if the angular dependence on intensities is extreme, as is the case for very large macromolecules (>10⁶ g/mol) or highly anisotropic geometries, the 7° ± 2 difference between the matched unfiltered and filtered detectors could introduce error. If necessary, this limitation could be overcome by double interpolation of the unfiltered detectors to match the angles of the filtered detectors; however, samples used in this experiment scatter isotropically at 784nm, and this precaution is not needed.

Table 1.

Angles retrieved from Wyatt DAWN user manual. For FIC, each filtered detector is “matched” with an unfiltered detector based on proximity in angle with respect to the incidence beam direction. Angles “seen” by the detector are functions of the refractive index of the flow cell and solvent. “Fixed angle” refers to the physical angle of the detector with respect to the center of the scattering volume and direction of the laser. “Scattering angles” are the “seen” angles of the detectors due to refraction effects in a PBS water solution and fused silica flow cell.

Matched Detectors Set	Unfiltered Detectors (Odd)			Filtered Detectors (Even)
	Channel #	Fixed Angles (°)	Scattering Angles (°)	Channel #	Fixed Angles (°)	Scattering Angles (°)
1	1	22.5	N/A	2	28.0	13.0
2	3	32.0	20.7	4	38.0	29.6
3	5	44.0	37.5	6	50.0	44.8
4	7	57.0	53.1	8	64.0	61.1
5	9	72.0	70.1	10	81.0	80.1
6	11	90.0	90.0	12	99.0	99.9
7	13	108.0	109.9	14	117.0	120.1
8	15	126.0	130.4	16	134.0	140.0
9	17	141.0	149.0	18	147.0	157.7

For reference, the even detectors are equipped with bandwidth filters, and the odd detectors are left unmodified, as shown in Figure 3. In the case of highly absorbing samples (change in forward monitor signal > 5%), absorption corrections are required, and the Raleigh ratios are divided by the intensity measured by the forward monitor instead of the laser monitor.

Figure 3.

Diagram of Wyatt MALS instrument. Odd detectors do not have filters, and even detectors do have filters (red). Before the laser enters the flow cell, it passes through a beam splitter that targets the laser monitor (LM) detector. After the flow cell, the laser passes through a second window and a neutral density filter (blue) before hitting the forward monitor (FM) detector. Each detector is positioned θ degrees with respect to the direction of the MALS laser.

We are directly measuring the angle-dependent emitted light intensities of the solution. To determine molar mass, we convert raw voltage readings into Raleigh ratios, R_θ. Specific to the MALS instrumentation, there are reflection and geometry corrections that are dependent on the refractive indexes of the cell and solvent, laser wavelength, and the geometry of the cell. Wyatt nomenclature refers to the collection of the corrections as the “Configuration Specific Calibration Constant, “ A_CSCC. Included in A_CSCC are corrections for each detector:

$$R_{\theta }=N_{\theta }{A}_{\mathit{\text{CSCC}}}\left[\frac{V_{\theta }-V_{\theta ,\mathit{\text{baseline}}}}{V_{\mathit{\text{laser}}}}\right]$$ (6)

The normalization coefficient, N_θ compensates for the slight variations in resistivity and sensitivity between detectors. An absolute R_θ can be derived from detector voltages for each detector at angle θ using Eq (6). Additionally, Eq. (6) shows that changes in ΔV_θ correspond to linearly proportional changes in R_θ While it is more intuitive to consider the intensity differences caused by fluorescence by examining voltages, it is more convenient to apply corrections to R_θ directly. Eq (6) tells us that this is a valid approach if corrections are applied proportionally.

ESTIMATING TRANSMITTANCE, T_f.

The only unknown in Eq (5) is the transmission factor of the bandwidth filters concerning the fluorescence. We conduct two methods to estimate the transmission value of our system.

1. This value can be estimated by fluorescence measurements and calculating the fraction of intensity from the emission spectrum that falls within the bandwidth filter range when excited at the wavelength of the MALS laser.

2. If the actual molar mass of the sample is known beforehand, we choose a transmission factor such that the inflated molar mass corrects to the known molar mass.

Our MALS instrument employs a vertically polarized light source, and Cehlinik et al.¹⁶, among others^17,18, show theoretically and experimentally that fluorescence emissions are isotropic in the plane of the incident beam when exciting with vertically polarized light. Assuming that all the bandwidth filters are identical in their transmission properties, every detector experiences the same degree of fluorescence transmission. Thus, a single transmission value for a given fluorophore applies to every detector. As a result, for a unique sample, only its transmission factor is needed to find the true scattering component of the signal and its corresponding true molar mass.

LABELING BOVINE SERUM ALBUMIN

A protocol for labeling protein with fluorescent molecules, developed by McCarthy et al.¹⁵, was used to design a well-characterized fluorescing standard derived from BSA and a near-IR fluorophore (IR800CW – LI-COR Inc.). In short, dibenzocyclooctyne-PEG5-NHS ester (10 mM in DMSO; Click Chemistry Tools Cat: 1378531-80-6), referred to as the “linker,” is reacted with BSA in 60 molar excess and allowed to incubate for 30 minutes at room temperature. The NHS ester group of the linker reacts with the multiple free amine sites on the surface of the BSA. The unreacted linker is removed from the solution using Amicon Ultra 100 kDa molecular weight cut-off filters (Fisher Scientific Cat: UFC5100BK). The BSA-linker conjugate is then reacted with a 55 bp DNA oligo containing a 5′ azide modification (Integrated DNA Technologies), referred to as the docking strand, for 16 hours at 4°C. The resulting product is a macromolecule that is a BSA-linker-docking strand-conjugate (BSA-I). For the low signal required of this set of experiments, the docking strand was added at a molar ratio of only 1:3 docking strand to BSA. The BSA-I solution is concentrated to $0.5\frac{mg}{mL}$ by weight of initial BSA. Finally, we load the IR800CW-conjugated fluorescent oligo (that is complementary to the docking strand) into a 0.5 mL BSA-I solution. The fluorophore is successfully bound to the BSA-linker-docking strand complex and is confirmed by observing the presence of fluorescence in SEC-separated samples within the elution window, as shown in Figure 4.

Figure 4.

Elution spectra for A) BSA-I (no fluorophore) and B) BSA-II (0.03μM fluorophore) with the Raleigh ratios (left axis) of Detector 11 (red) and 12 (blue). The RI trace (black, right axis) overlays the relative concentration.

The fluorophore that was chosen (IR800CW) strongly fluoresces within the bandwidth filter’s transmission range and the BSA protein was chosen as it is a common standard in SEC-MALS characterization. The BSA solution before fluorophore conjugation is labeled BSA-I. All BSA solutions after fluorophore conjugation are labeled BSA-II. To ensure consistency, the same solution is used for every injection. We injected our sample four times at fluorophore concentrations of 0, 0.03, 0.06, and 0.10 μM. The first injection is the BSA-I solution with no fluorophore as a reference for the fluorophore experiments. Next, we added fluorophore to the same solution (now a BSA-II solution), then injected it. We repeated the fluorophore addition two more times, adding more fluorophore after each injection. We calculated the number of fluorophore molecules added to the solution and found that the estimated theoretical changes in molar mass moments were negligible, as shown in Table 2. Further details regarding these calculations can be found in SI.2.

Table 2.

The molar mass moments of BSA-I and BSA-II conjugates based on theoretical increases in molar mass with increased dye conjugation, the molar mass moments as measured by the MALS filtered detectors with no correction, and the molar mass moments corrected by FIC given a transmission value. Details on the “theoretical” values can be found in SI.2.

Sample	Theoretical			No Corrections (Filtered Detectors)			Fluorescence Interference Correction
	Mn (kDa)	Mw (kDa)	Đ (Mn/Mw)	Mn (kDa)	Mw (kDa)	Đ (Mn/Mw)	Mn (kDa)	Mw (kDa)	Đ (Mn/Mw)	Trans % (Tf)
BSA-I	109.2*	129.9*	1.19*	109.2	129.9	1.19	-	-	-	-
BSA-II 0.03	109.2	129.9	1.19	284.9	321.3	1.13	109.2	130.5	1.2	23.77
BSA-II 0.06	109.3	130.0	1.19	675.8	752.1	1.11	109.3	129.1	1.19	23.56
BSA-II 0.10	109.3	130.1	1.19	1149	1276	1.11	109.3	127.5	1.17	23.45

CHROMATOGRAPHY-SEC-UV-MALS_IR-dRI

A Dawn MALS detector (Wyatt Technologies) equipped with a 784.2nm laser and ±10nm bandwidth filters is plumbed into an ultraviolet-visible spectroscopy (UV-Vis) instrument, at 280nm (1200 Series Agilent, G1311-A), and a differential refractive index (dRI) detector (Optilab, WREX-08) at 658nm. Previous work³ calculated that differences in the 785nm MALS laser and the 658nm RI laser results in only a marginal error (1 – 3%) as it pertains to the specific refractive index, dn/dc, used in Eq (1a and 1b). Molar mass estimations and calculations are performed in ASTRA 7.3. Raw data and system properties are exported, and custom corrections and data analysis are performed in MATLAB software and can be found in SI.6. A dn/dc value of 0.185 mL/g was used for all experiments.

For BSA protein analysis, a mobile phase of HPLC-grade phosphate buffer solution (PBS) is made at 100 mM NaCl with standard ratios, degassed (1100 Series Degasser, Agilent, G1310), and pumped (1100 Series Quaternary Pump, Agilent, G1310-A) into an online autosampler (1200 Agilent Autosampler, G1323-A) at 0.30 mL/min through an AdvancedBio SEC column (Agilent, PL1580–1301) at 23°C.

RESULTS AND DISCUSSION

FLUORESCENCE INTERFERENCE CORRECTION (FIC) PROCEDURE VALIDATION

This work demonstrates the ability to correct for fluorescence that cannot be entirely blocked or mitigated by conjugating a well-defined protein (BSA) with fluorophores using a protocol developed in a prior study¹⁵ to synthesize the conjugated protein. BSA readily aggregates in solution, and as expected, the BSA-I (no fluorophore added) sample exhibits populations of monomer, dimer, trimer, and higher-order aggregates, as seen by the multiple peaks in Figure 4 and labeled in Figure 5A. The BSA-I solution in Figure 4A has no fluorophores or chromophore moieties, and as expected, no difference in scattered light intensity between the filtered and unfiltered detectors at similar viewing angles is observed.

Figure 5.

A) molar mass (left axis, red) and relative concentration (right axis, black) vs. elution trends of BSA-I (red). Elution region of BSA monomer, dimer, trimer, and higher order aggregates are labeled I, II, III, and IV, respectively. B) BSA-II solutions with increasing degrees of fluorophore complexation. Orange, yellow, and purple traces correspond to IR800CW fluorophore loading concentrations of 0.03, 0.06, and 0.10 μM, respectively. C) the corresponding Zimm plot evaluated at 3.5 minutes (dashed line, Image B) using detectors 4, 6, 8, 10, 12, 14, and 16 (all filtered) for each experiment.

In contrast, as shown by the BSA-II experiment (fluorophore addition to BSA-I) in Figure 4B, the two detectors measure significantly different intensities due to fluorescence interference. No fluorophore is detected past the elution of the BSA-II proteins, indicating that we successfully annealed all the fluorophore to the BSA-I linker sites.

Despite the presence of bandwidth, injections of the BSA-II solutions result in drastic increases in estimated molar mass. Figure 5C highlights this effect, where extreme changes in intensity occur when fluorophore loading increases. In addition to the upwards shifting of the molar mass, fluorophore conjugation drastically changes the elution behavior. The BSA-I oligomer molar mass peaks, indicated by the roman numerals in Figure 5A, transitioned from monodisperse “steps” – typical for protein seperations¹⁹ – to increasingly erratic elution behavior with increasing fluorophore conjugation of the BSA-II experiments, as seen in Figure 5B. Importantly, the elution behavior defies SEC principles, further suggesting that our observations are an artifact of fluorescence interference. The molar mass moments, M_n and M_w, calculated from Figure 5B are given in Table 2.

It is important to note that only filtered detectors are used to calculate the molar masses shown in Figure 5A–C. We would expect if the filters were effective, that all measurements would be nearly identical given that the fluorophore adds negligible amounts of mass to the BSA molecules as shown in Table 2. Therefore, for the BSA-II experiment the differences in measured molar mass are entirely due to fluorescence interference and that the bandwidth filters are insufficient in preventing large over-estimations and errors in M_n, M_w, and dispersity.

To correct for transmitted fluorescence, we apply FIC using a single transmission factor, T_f. T_f is found through an iterative golden-section search algorithm²⁰ such that the FIC-corrected signal yields molar masses whose M_n matches the M_n of the theoretical calculation. Alternatively, M_w values can be used if performing batch experiments and molar mass distribution data is not available. A detailed discussion on matching methods can be found in SI.3. We repeat this procedure for each loading condition and for the whole elution window. Figure 6 shows the resulting molar mass elution trends.

Figure 6.

Molar mass vs. elution trends of BSA-I (red) and BSA-II solutions with increasing degrees of fluorophore complexation after applying FIC. Orange, yellow, and purple traces correspond to IR800CW fluorophore loading concentrations of 0.03, 0.06, and 0.10 μM, respectively.

Despite the incredible differences observed in molar mass traces of the uncorrected signal in Figure 5B, the FIC-corrected traces overlap the original BSA-I curve in Figure 6. As shown in Table 2, the transmission values found are nearly identical at every loading condition, at approximately 23.5%. The agreement in transmission values supports the assumption that every filtered detector experiences a single transmission value for a given excitation beam and fluorescent species. Also, the universal transmission factor for all BSA-II shows that the FIC procedure is independent of the total fluorescence intensity. Notably, fluorescence interference has the potential to inflate apparent molar masses, but it also obscures true elution behaviors. The successful corrections show how FIC can be used to correct for nearly all transmitted fluorescence and its subsequent errors, provided that the transmission factor for the system is known or inferred. The FIC procedure is robust as it is independent of overall fluorescent intensity, which allows for the characterization of heterogeneous and complex samples. Importantly, FIC does not depend on how the sample is delivered to the MALS instrument. This provides the ability to perform accurate MALS characterizations for fluorescent materials using any means of chromatography-based separations or field-flow fractionation – not just SEC.

DETERMINATION OF TRANSMISSION FACTORS

Applying FIC in non-model systems with unknown molar mass requires MALS-independent determination of the transmission factors. Here we used spectrofluorimetry to estimate the emission spectra experienced by the MALS instrument during elution that was combined with the known transmission properties of the bandwidth filters. The supplier (Wyatt Technologies) quotes the transmission properties of the bandwidth filters at ±10nm, centered about the wavelength of the laser. However, more precise transmission properties are required as the bandwidth filters do not perfectly filter at ±10nm. To determine the transmission properties more accurately, we use a spectrometer (StellarNet, BLACK-Comet) with a tungsten halogen light source (StellarNet, SL5 Tungsten Halogen + Deuterium Lamp). The broad-spectrum intensities from the halogen light source are measured with no filter in the beam path and with a filter in the beam path. The ratio between the filtered and unfiltered intensities is the effective transmission, as shown in Figure 7.

Figure 7.

Transmission vs. wavelength of the bandwidth filters installed in the even detectors of the MALS instrument.

The manufacturer (LI-COR) provided an emission profile of the IR800CW fluorophore, which we have corrected to account for photon energy, shown in Figure 8. Numerical integration of the entire normalized emission peak starting from the MALS laser wavelength yields arbitrary emission energy. The transmission factor, T_f, or the fraction of the energy intensity transmitted by the bandwidth filter compared to the total emitted energy, as follows:

$$T_f=\frac{{\int }_{{\lambda }_{\mathit{\text{MALS}}}}^{\infty }{I}_f\left(\lambda \right)\cdot T_B\left(\lambda \right)}{{\int }_{{\lambda }_{\mathit{\text{MALS}}}}^{\infty }{I}_f\left(\lambda \right)}$$ (7)

Where, λ_MALS is the central wavelength of MALS laser, T_B (λ) is the transmission of the bandwidth filter at every wavelength, and I_f (λ) is the energy intensity measured at every wavelength. The transmission calculated assuming perfect blocking starting at 794.2nm (MALS wavelength + 10nm) was found to be upwards of 1.2 times larger than the transmission calculated using the real transmission properties found through fluorimetry and highlights the need for precisely characterized filters. The Fabry-Perot style laser employed in the MALS has a very narrow linewidth and is highly coherent, thus we assume all light detected at wavelengths higher than 784.2nm is due to fluorescence.

Figure 8.

A) emission spectra data of IR800CW fluorophore provided by the manufacturer. Intensity photon counts have been converted to energy intensity and normalized. The blue shaded region indicates the intensity transmitted by the bandwidth filters. B) changes in calculated transmission as a function of the MALS laser wavelength. The red diamond indicates a transmission factor of 23.5% at an excitation wavelength of 784.2nm.

Plotted in Figure 8A is the normalized emission spectrum of the IR800CW fluorophore. The shaded region represents the transmitted energy to the filtered detectors. The unfiltered detectors block none of the wavelengths, and all the energy emitted via fluorescence is measured. The ratio between the transmitted energy and total energy is the effective transmittance of the bandwidth filters, as shown in Eq (7). This analysis yields a transmission value of 23.5%. This value agrees exceptionally well with the transmission values calculated using the FIC method of the BSA-II series experiments, indicating that fluorimetry techniques can determine the transmission values of samples independent of MALS characterization. As shown in Figure 8b, the transmission value determined by fluorimetry techniques is sensitive to the chosen central wavelength of the MALS laser. A central laser wavelength of 784.2nm is used for all analyses (provided by the manufacturer) and confirmed by spectroscopy (StellarNet, BLACK-Comet).

CONDUCTING FIC SUMMARY

Table 3 is given to provide a summary of the additional parameters needed in transmission factor calculation and conducting FIC. Once the instrument wavelength and bandwidth filter characteristics are known, then only the samples emission spectrum is needed to apply FIC. These system parameters apply to all samples, mobile phases, and configurations. The emission spectra (I_f (λ)) can be determined for each unique sample by standard fluorimetry although many common fluorophore spectrums are readily available in literature and from manufacturers. Here, we have shown that the transmission factors obtained through fluorimetry (and subsequently obtaining the emission spectra) agrees well with the true transmission factor obtained using the BSA standard. For single fluorophores, it can be reasonably assumed that the emission profile is independent of excitation wavelength. In the case of fluorophore mixtures that absorb and emit in varying intensities at different excitation wavelengths, the emission spectrum is a convolution that will change shape depending on excitation wavelength. In these cases, a representative emission profile can be obtained by measuring emissions when exciting precisely at the wavelength of the MALS laser. Importantly, because the wavelength dependence of the emission profile is included into the transmission factor calculation, this methodology is not limited to the instrumentation employed in this study; FIC has the potential to be used broadly with any combination of MALS laser and bandwidth filter.

Table 3.

Required system and sample parameters required for transmission factor determinations and Fluorescence Interference Corrections (FIC).

Required System Parameters	Description	Required Sample Parameters	Description
TB(λ)	The representative transmission profile of intensities versus wavelength for the installed bandwidth filters.	If (λ)	Emission spectra of your sample in your mobile phase, obtained through fluorimetry. Used in combination with TB (λ) and λMALS to obtain the transmission factor (Tf), according to Eq. 7.
λ MALS	The central wavelength of the MALS laser. Already necessary for standard MALS characterization.

While this work is shown using the IR800CW fluorophore, this methodology can be applied to any fluorescent sample containing a fluorophore or combination of fluorophores if fluorimetry analysis is available and its emission spectra can be obtained. To aid in the data reduction and application of FIC to light scattering signal, we have built a MATLAB-based graphical user interface titled “FIGMENT”, that works in tandem with ASTRA (Wyatt Technologies, version 7.3.2) to automatically perform the transmission factor and FIC calculations for light scattering data and emission spectra data, respectively. Within FIGMENT you can find a database of emission spectrums of 30 different fluorophores and two types of bandwidth filters. Additional information and instructions can be found in SI.6.

ABSORBANCE AND ANISOTROPY

Absorbance corrections (AC) are often necessary for highly absorbing samples, however, the BSA-II conjugates are weakly absorbing. This is possible due to the low concentrations of the fluorophore present in the BSA-II experiments. As a result, the total amount of absorbed incident light is negligible throughout the entire elution profile (change in signal < 0.5%) as measured by the forward monitor. Regardless, we performed AC on all experiments and found no significant changes to the final molar mass results. However, absorbance may not be negligible for other species, and AC procedures should be applied followed by FIC to obtain accurate molar mass measurements.

Slight variation in detectors’ absorbance, among other phenomena, can introduce noise and anisotropy into the results. There is consideration of anisotropic effects in the context of FIC, and an in-depth discussion can be found in SI.4. In short, anisotropic effects had a negligible impact on final molar mass estimations. However, we did detect very small anisotropic contributions from fluorescence interference that could make it difficult to extract accurate molecular information that relies on studying the anisotropy of the scattering, such as radius of gyration and shape parameters. The BSA proteins used in these experiments were too small for measurable anisotropic behaviors at near-IR wavelengths; however, such effects may become significant for lower incident wavelengths, larger molecules, and molecules with anisotropic geometry. Improvements towards correcting anisotropic systems is the target for future work. Regardless, we show that this method is still exceptionally accurate in providing corrected molar mass estimations for macromolecules up to the order of ${10}^5\frac{g}{mol}$ and thus can be applied widely to typical polymer and protein characterizations. Moreover, this technique can be used in both static and online (flow) light scattering systems, both of which are standard in any macromolecule characterization lab.

CONCLUSIONS

In this work, we demonstrate a system where bandwidth filters do not effectively mitigate fluorescence in light scattering signals and additional procedures are employed for accurate molar mass estimations. To address this, we developed a novel methodology to retrieve accurate molar mass information from SEC-MALS experiments, despite significant fluorescence interference. In doing so, we define a “transmission factor” as the fraction of fluorescent intensity that escapes past the bandwidth filter to the light scattering detector. Using a BSA-fluorophore conjugated protein, we have shown that once the transmission factor is known, the Fluorescence Interference Correction (FIC) method can remove all fluorescence contributions from detector signals, obtain accurate molar mass, and restore true elution behavior. Also, we have shown that the transmission factors can be easily obtained through simple fluorimetry techniques. Fluorimetry is ubiquitous making this technique accessible in most characterization laboratories. Overall, this methodology can be applied to correct for fluorescence interference in any sample as long the emission spectrum is well characterized. This methodology bolsters MALS-based characterization to include a much broader and diverse array of materials that contain fluorophore moieties or may be otherwise optically active. Potential applications include fluorescent polymers, proteins, macromolecules, and optically active nanoparticles.

ABBREVIATIONS

AC

absorbance correction

BSA-I

Bovine Serum Albumin-linker-docking strand-conjugate

BSA-II

Bovine Serum Albumin-linker-docking strand-IR800CW-conjugate

dRI

differential refractive index detector

FIC

fluorescence interference correction

FM

forward monitor

IR

infrared

MALS

multi-angle light scattering

PBS

phosphate buffer solution

SEC

size-exclusion chromatography

UV-vis

ultraviolet-visible light spectrum detector