Determining Viscosity of the Nucleoplasm in U2OS Cells Using Fluctuation Correlation Spectroscopy

Foreword to the Reader

Hello future MXP II student! If you clicked on this project, there's probably a good chance that you have no idea what several of the words in the title of this project mean. Allow me to try to explain briefly: this is a biophysics project in which we measured biological cells (U2OS) and the fluid inside of them (specifically, the "nucleoplasm"). These cells were measured under living conditions in vitro (outside of the body). The technique we used to determine the viscosity of this fluid is called "fluctuation correlation spectroscopy", which is a cool technique in which we actually care about the "noise" (fluctuations) in our signal. This "noise" is generated by the underlying physical principle of Brownian motion. Because of Brownian motion, we can check the correlation between the signal at a certain time and a later time and actually determine physical properties of molecules suspended in solution.

If you are still curious about this project, read through the introduction to see a more indepth explanation. Additionally, reference [3] was the primary paper we referenced when looking for guidance, so that would be a good place to start too. The theory is a bit heavy, but try not to be too daunted, it took us a long time to understand the concepts ourselves (the autocorrelation function probably the most difficult concept).

One major warning when considering a project like this: both of us had experience working with biological cells before beginning this project. Additionally, we were fortunate to have Professor Jochen Mueller as an external adviser to help us through the project and use the equipment in his lab. What this means is that the scope of our project was probably bigger than a standard MXP project because we were able to work with biological cells (the university mandates training due to blood-borne pathogens) and Professor Mueller's latest research equipment. If you are interested in running a project similar to this one, I would recommend that you try to get into contact with Professor Mueller as soon as possible, as having an external adviser offers access to a lot of resources. If you have any questions about the project, feel free to contact me at finex080@umn.edu. I will most likely be active on this email for the next two years (Fall 2019-Spring 2021).

Best of luck in MXP II!

Sincerely,

Justyn Fine

Determining Viscosity of Nucleoplasm in U2OS Cells Using Fluctuation Correlation Spectroscopy

Justyn Fine and Shivani Mahajan

University of Minnesota, Minneapolis, MN, USA

(Published May 15, 2019)

Abstract

Fluctuation correlation spectroscopy was used to determine the viscosity of the nucleoplasm of U2OS biological cells by observing the fluctuations of diffusing enhanced green fluorescent protein molecules. The proteins were excited with laser light (488nm) and a small, femtoliter sized volume was observed through the application of confocal microscopy. The random diffusion of a countable number of fluorophores created measurable intensity fluctuations. These fluctuations were analyzed using a normalized autocorrelation function, from which a viscosity of 4.78 ± 0.24 cP at 20°C was obtained.

Introduction

Put simply, fluctuation correlation spectroscopy (FCS) is a method by which one analyzes the correlation between fluctuations in an electromagnetic signal; in essence, the fact that our signal is randomly changing (fluctuating) gives us information about the underlying properties in a system. The beauty of FCS is that we are taking what is typically thought of as "noise" and analyzing it to better understand how the particles emitting the "noise" are behaving. This method has wide reaching applications in thermodynamic and chemical kinetics studies of molecular systems (see this paper for a list of some of the more recent applications [1]). One of the most powerful applications of FCS is in biophysical studies of living systems. Since FCS only requires a signal generated by molecules, the corresponding fluorophores (essentially microscopic "light bulbs" we can turn on with laser light) can be generated inside of a living organism while avoiding crippling damage to the normal activity of the organism. This offers an advantage over some of the other biophysics techniques that involve UV and X-ray radiation since lasers in the visible light spectrum are sufficient for exciting the fluorophores and generating a signal such that the biological system remains unharmed during the measurement procedure. More specifically, FCS offers insights into molecular properties such as diffusion coefficients, viscosity of the solvent, and the radius of the fluorophores under study.

In this experiment, the system under study is the substance inside of the nucleus (the nucleoplasm) of U2OS biological cells (a type of human bone cell). The nucleus of the cell is sort of the "brain" of the most basic unit of eukaryotic organisms: it contains all of the genetic information (DNA) that codes for how the cell functions and behaves when exposed to environmental stimuli. Since the nucleus contains all of the instructions for how the cell functions, the cell also has an arsenal of machinery in order to access and translate this information into instructions, such as RNA polymerases and transcription factors. Think of this machinery sort of like a combination of databases, printers, and mail trucks that print and send out instructions to the rest of the cell. Although the majority of the cell fluid is made up of water, the viscosity inside the nucleus tends to be higher by a factor of approximately 2 to 8. This is because the crowded machinery within the nucleus creates an "effective" viscosity since diffusing particles have a chance of "bumping into" other larger molecules that makes the average medium feel "thicker". Because of this, different molecules in the medium (e.g. RNA polymerase) tend to move much more slowly than they otherwise would in water.

The viscosity of the cell nucleoplasm is a basic system parameter required for any biophysical model within the nucleus. As such, it is necessary for understanding and developing theories as to how the machinery inside the nucleus functions. One example is in the cell division process of mitosis. In mitosis, microtubules produced by centrioles attach to DNA chromosomes and pull them apart. Thus understanding viscosity allows one to develop an idea of how large the drag force pushing against the microtubules is, helping to develop a model for the process of mitosis.

Another interesting application of the viscosity of the nucleoplasm is in a model for DNA gene location. In order for DNA to be transcribed into instructions, the machinery of the nucleus needs to locate one specific base among many (3 billion in the human genome) in order to be functional. One proposed model for this random search is facilitated diffusion [2]. In a "random walk" search, the protein that is searching for the start site in the DNA is modeled as moving randomly in any direction until it reaches the correct location. In facilitated diffusion, however, the protein is modeled as switching between a 3D search (randomly moving around) and a 1D search ("sliding" along the DNA). The advantage of the 1D search is that the DNA structure can "shield" the protein from the surrounding medium, creating an effective viscosity that is equivalent to water rather than that of the nucleoplasm. This model couldn't be viable without a basic understanding of this inherent increase in viscosity in the nucleus, thus the viscosity is critical to understanding the DNA search process. Shown in Figure 1 is a cartoon depiction for how facilitated diffusion works.

Figure 1: A cartoon depiction of the random walk vs. facilitated diffusion model of the targeted DNA search problem. The target site (red) needs to be reached by the protein or other biological molecule (the green rectangular object) for gene expression.

To measure the viscosity, a microscope and laser system was used to study the diffusion of enhanced green fluorescent protein (EGFP), a biologically non-toxic fluorophore, inside the nucleus of U2OS cells. The setup itself utilized theoretical knowledge in Brownian motion, fluorescence, and confocal microscopy. The FCS analysis itself was carried out by means of calculating an autocorrelation function (ACF), from which a characteristic diffusion time can be obtained.

Theory

Brownian Motion

The physical principle that underlies FCS is Brownian motion. Brownian motion is the random, thermodynamic movement of particles suspended in a medium. In essence, particles in a medium move around randomly due to thermal fluctuations at the microscopic scale. It is from Brownian motion that the "useful noise" (the fluctuations) originates: without Brownian motion, there would be no biophysical fluctuation in our signal. One of the primary equations underlying our model for Brownian motion is the Stokes-Einstein equation for spherical particles

where D is the diffusion coefficient, k_B is the Boltzmann constant, T is the temperature of solution, R is the hydrodynamic radius of the molecule, and η is the viscosity of the solvent. This equation allowed us to relate the viscosity (η) to an experimentally determined parameter (D). The other parameters in the equation are constants that can be determined by literature values or a simple measurement.

Additionally, an equation relating the diffusion coefficient to the mean squared displacement can be derived for 2D using a random walk model:

This relates the average distance a particle travels and the time it takes to travel that distance to the diffusion coefficient. Thus, Brownian motion gives us a way to relate the observed movement of a particle to the viscosity of the solvent it is moving in.

Fluorescence

Fluorescence is the process we utilized in order to detect molecules in our observation volume. The concept of fluorescence involves the excitation of molecules via absorption of light at a certain wavelength which results in emission of light at a different wavelength. This concept is illustrated nicely in a Jablonski diagram, shown below.

Figure 2: A Jablonski diagram illustrating the process of fluorescence.

The molecule begins in a ground state (S0) that is the molecule's stable state. If an incident photon is within the absorption spectrum of the fluorophore, it will excite the molecule into a higher excited state (S2). The molecule then will undergo internal conversion in which it loses energy (typically thermal vibrations to the surrounding solvent) until it reaches its lower excited energy level (S1). From S1, the molecule then emits a photon to return to its ground state. Due to the internal conversion, the photon is emitted at a higher wavelength than the incident photon. This wavelength change is known as a Stokes shift. Since the light changes wavelength, the incident light can be distinguished from the emitted light with a dichroic filter. Thus, by measuring the number of photons of emitted light from the sample, we can get an accurate idea of how many molecules are present in the observation volume at a given time without directly observing the molecules.

Confocal Microscopy

An additional problem that arises is the size of cells. Since the nucleus of the cell is approximately 1-10μm in diameter, a small observation volume is required to analyze just the diffusion within the nucleus. Additionally, with sufficiently high concentrations of fluorophores, the number of molecules in a larger volume will be too high for fluctuation measurements (FCS requires a small number of particles, otherwise the fluctuations will be drowned out by the overall signal intensity). In a one-photon excitation setup (in which one incident photon causes fluorescence) the entire beam path that goes through the sample causes fluorophore excitation. As a result, the molecules that are diffusing above and below the nucleus will also be excited and a much larger volume overall will be excited away from the focal plane of the objective.

To solve this issue, we use an optical technique known as confocal microscopy. In confocal microscopy, the focal plane of the sample is the same as the focal plane of the detector. In essence, the light emitted from the sample is "beam walked" to the detector such that the light coming from the sample is focused when it reaches the plane of the detector. To utilize this property, a pinhole is placed in front of the detector so that the focused light (which is closer to the pinhole) will be sent to the detector while the out-of-focus light (which is spread out around the pinhole) will be rejected. This results in what we call "axial discrimination", in which we are able to discriminate the observation volume's signal from the signal coming from excited molecules away from the focal plane (i.e. along the axis perpendicular to the focal plane). Although this technique allows for good axial discrimination, it sacrifices a large portion of the intensity of the signal from the sample. Thus, the pinhole size must be balanced: a smaller pinhole means better axial discrimination, but also a lower signal. A larger pinhole means a higher signal, but worse axial discrimination.

To determine an appropriate size for our pinhole, we used the beam pattern emitted by the objective, which turns out to be an Airy pattern (you can look at the wikipedia page for an in depth explanation). A property of the Airy pattern is that the central ring (the Airy disk) contains the majority of the signal, so if we size our pinhole to be the same as the Airy disk, we can maximize our signal gain without sacrificing significant axial discrimination. The actual equation from geometric optics that gives us this size is given by

where d represents the diameter of the pinhole, λ is the wavelength of the input beam, f is the focal length of the lens, and r is the radius of the beam.

Assuming the pinhole is properly aligned, we expect the observation volume to follow the geometry of a point spread function (PSF). The PSF models the volume as a 3D Gaussian pattern in which the intensity of the laser decays as the distance from the focal "point" increases. This decay pattern occurs due to the diffraction limit of focusing light, as the minimum beam width (the most focused part of the laser) is limited by the finite size of the lens (i.e. the numerical aperture). Thus, although we model the focus of the light from a lens as a "point" in geometrical optics, we expect the actual "point" to "spread out" in the form of a Gaussian. Shown in the figure below is our model of the observation volume.

Figure 3: Our model for an observation volume, where z0 and r0 are the point spread function parameters.

The two parameters (r0 and z0) are determined by the optical setup: the pinhole (i.e. the axial discrimination) determines z0, while the objective (i.e. the numerical aperture) determines r0 (also known as the beam waist). Thus, confocal microscopy provides a means to limit the size of our observation volume to approximately a femtoliter.

Autocorrelation Function

To analyze the signal, we used an autocorrelation function (ACF). Since the particle diffusion is governed by Brownian motion, we expect a particle entering the observation volume to remain in the volume (on average) the amount of time it takes for the particle to diffuse randomly through it. This characteristic diffusion time is related to the mean squared displacement shown in the second equation in the "Brownian motion" section above. Thus, the overall signal (the number of photons received from the observation volume) should have a fluctuating signal whose "lifetime" is governed by the characteristic diffusion of any particular particle in the volume. That is to say that the signal should fluctuate randomly on longer time scales (due to the randomness of Brownian motion) but it should remain relatively constant for shorter time scales, or those close in magnitude to the characteristic diffusion time, since the amount of time it takes for the particles to enter or leave the volume (on average) is determined by a process with a finite time scale. This characteristic diffusion time can be mathematically determined from a signal by using a normalized autocorrelation function:

where G(τ) is the normalized correlation for a time-shift of τ and δF(t) is the deviation of the signal (F(t)) from its time average <F(t)> at time t.

In an ACF, the "lifetime" of the signal is determined by measuring the correlation between a signal and a time-shifted version of itself. By multiplying the deviations of the signal (δF(t)) by the deviations in a time shifted version of the signal (δF(t+τ)), we can determine an average correlation across the entire product. The more correlated the signals are (i.e. the more similar), the higher the positive correlation will be. This captures the idea that the signal is constant over time scales that are close to the characteristic diffusion time: if τ is less than or equal to the characteristic diffusion, then we expect the signal to remain relatively constant over the time length of τ and yield higher correlations. If the signal is the exact same as the time shifted version (i.e. the signal remains constant) then a perfect, positive correlation of 1 will be achieved (due to the normalization factor in the denominator). However, since the signal's "lifetime" is finite, we expect for sufficiently high τ values that the signal will be completely uncorrelated (due to the randomness of Brownian motion), and the correlation will be 0; a random signal will change randomly, thus a purely random process will be independent from another purely random process, averaging correlations to 0.

From knowledge of thermodynamic principles (such as Fick's law), Rieger, et al. demonstrated that the deviations in the intensity function can be modeled by spatial integration of the concentration fluctuation over the point-spread function (which represents the observation volume) [3]. This results in a theoretical autocorrelation function given by

However, the paper by Rieger, et al. makes some assumptions that we can't make for our apparatus and we assume for our setup that z0 >> r0, which allows us to drop the square root term. After these simplifications, our autocorrelation function simplifies to

Figure 5: A depiction of the apparatus setup, (not drawn to scale). The image includes the objective (O), filter cube (F), optical lenses (L1, L2, and L3), avalanche photodiode (APD), and multimode fiber (MMF).

Apparatus

The apparatus features a fiber coupled laser, a Nikon Ti2-e microscope, and an avalanche photodiode (APD). The laser emits at 488nm in the TEM00 mode, and is coupled into a fiber for alignment. Within the microscope, the laser enters a filter cube (F) which contains a dichroic filter that reflects the laser light (blue). The light is sent into a 60x water objective (O) from which it is focused into the sample. Any fluorophores within the beam path are then excited and reemit at a different wavelength (maximum at 509nm [4] for EGFP). Some of this light is then captured by the objective (green) and allowed to pass through the filter cube with the dichroic while a barrier filter within the filter cube blocks the remaining laser light. The light is then “beam walked” through a series of lenses (L1-L3) until it enters our multimode fiber (MMF) and is processed by the APD, a counting board, and the PC.

Data Collection and Sample Preparation

Samples were prepared in 8-well slide that was positioned on a slide holder above the objective lens of the microscope. The objective lens was focused into the solution, where we can see the signal of fluorescent particles. The signal was then sent to the bottom of the microscope and into the pinhole where it was read by the detector. We measured trials for around 30-60 seconds each with a low laser power determined by power characterization curves where the power is measured right above the sample. Note that the samples were kept at room temperature (20 ◦C) during the duration of the measurements.

Sample preparation involved four primary systems: Alexa488 in aqueous solution, Alexa488 in glycerol, EGFP in aqueous solution, and EGFP in U2OS cells.

To ensure proper alignment and setup of the system, a fluorescent dye, Alexa488, was measured for an ACF curve in aqueous solution (water). The Alexa solution was prepared by diluting a stock of Alexa488 provided by the lab. Diltuions ranging from 10x to 1500x were prepared by adding the corresponding amount of water to previous solutions. The solutions were then stored in an 8 well container to be placed on the objective stage.

Alexa488 was also measured in glycerol solutions. Glycerol solutions have well documented viscosities, thus observation of Alexa488 in glycerol solution provides a "pilot" trial for observing a viscosity change using FCS. Glycerol solutions of 50\% and 25\% were provided by the lab for study (the rest of the solution being water). 201x dilutions were made in 8 well containers since this level of dilution gave good ACF curves in control experiments.

To determine the viscosity of water according to EGFP, a provided sample of EGFP in aqueous solution was measured in the same way as Alexa488 dye, using the PSF parameters from the control (in this case a second control experiment was run with the two photon setup). A dilution of 100x was used due to the quality of the ACF curves it generated.

To determine the viscosity of the nucleoplasm, we used U2OS cells and transfected DNA plasmids for EGFP expression. Note that the DNA plasmids induced production of EGFP within the nucleoplasm and the surrounding cytoplasm, thus the nucleus and surrounding cytoplasm were both visible under laser excitation.

Data Analysis

The output file from the data acquisition card was a binary file containing the number of photon counts per microsecond of sampling time. A Matlab script was written and used to read in the output file and convert it to the intensity signal, F(t), by re-binning the data according to the sampling time and total time taken for the measurement. This signal was then split into 10 different segments of equal time length and an autocorrelation curve was generated for each of these 10 segments by implementing the normalized autocorrelation function definition (the first equation in the "Autocorrelation function" section) into the Matlab script. By splitting the signal into 10 different segments, an uncertainty can be found by taking the average of the ten measurements and finding the standard deviation between them (and dividing by the square root of 10). Assuming the population of ACF curve values is approximately normally distributed for each τ value, the standard deviation of each 10 sample averages divided by the square root of the sample size should give a rough approximation to the standard error of the population of 10 sample means (from statistical theory). Thus, the standard error can be used as an uncertainty in each data point along the ACF curve.

To determine the diffusion time, τD and the y-intercept, G(0), we use a non- linear least squares fitting analysis to fit the data to our simplified autocorrelation function. Note that the autocorrelation curve is found within the microsecond to a tenth of a second range on the semi-log plot and the ACF is observed and analyzed within this range to avoid after pulsing (an APD detector artifact which could skew our data).

Results

Figure 6: An example of one of the ACF curves generated by Alexa488. This particular curve was generated for a 100x dilution of Alexa488 in aqueous solution with binning of 1 μs over 30 s of data acquisition at a laser power of 3.8 μW.

Figure 7: A power characterization curve for Alexa488 at 706x dilution from stock. Counts are presented in kHz (thousand counts per second). A bend over was observed for laser powers above 10 μW.

We measured the laser power above the Alexa488 sample which was at a 706x dilution from stock solution. The observed intensity counts were then recorded. We can see that the linear regime of the laser is around 0-10 μW so that is our measuring range. Typically we used around 3-5 uW while taking measurements. Note that the power characterization curve helps us to determine when saturation starts to take effect. Saturation occurs when molecules are emitting photons at a rate limited by the process of fluorescence (i.e. maximum incident photons per molecule). Saturation occurs in the non-linear regime of the power characterization curve.

Figure 8: A plot of G(0) vs. dilution from stock solution for Alexa488. The data was taken under laser power of approximately 3.8 μW. From the linear fit in Excel, an R² value of 0.9942 was obtained, demonstrating a good fit to a linear relationship.

We took measurements with different concentrations of Alexa 488 (from the stock solution) and plotted our fitted G(0) values against the approximate dilution. The linear relationship is expected since G(0) is proportional to 1/N, where N is the average number of molecules in the observation volume.

Figure 9: An overlay of the ACF curves generated by Alexa488 in glycerol solutions. Note that the curves were normalized such that their G(0) values are equivalent. From the curves, it is apparent that an increasing glycerol percentage resulted in an increasing characteristic diffusion time (τ_D).

Adding different concentrations of Glycerol to an Alexa488 dye solution allows us to see the impact of viscosity on the autocorrelation curve. With a room temperature of ~20℃, we assume that water has an approximate viscosity of 1cP for simplicity. From the ratio calculations, a viscosity of 2.70±0.06 cP was measured for the 25% glycerol solution and a viscosity of 7.78±0.20 cP was measured for the 50% glycerol solution. The solutions were prepared as percentages by volume, so the conversion was made to by weight when compared to literature values [5]. The interpolated literature viscosities for our 25% and 50% glycerol solutions were ~2.5cP and ~8.8cP, respectively. Discrepancies may have been due to preparations of solution concentrations being imprecise and temperature value approximations.

Due to an experimental apparatus problem while taking EGFP measurements, we had to switch to a different apparatus, that utilized two-photon instead of one-photon FCS techniques, to get these EGFP measurements. The graph above shows an autocorrelation curve for EGFP in phosphate-buffered saline (PBS) solution, which is assumed to have the same viscosity as water.

Above is the autocorrelation curve for measuring EGFP in the cell nucleoplasm. When we took the ratio of the diffusion times we found that the viscosity of the nucleoplasm was approximately 4.78 ± 0.24 cP.

Figure 10: An overlay of the ACF curves generated by EGFP in PBS and U2OS (blue and black respectively). Note that the curves were normalized such that their G(0) values are equivalent. From the curves, it is apparent that the diffusion of EGFP in the nucleus resulted in an increasing characteristic diffusion time (τ_D).

Conclusion

Overall our viscosity measurements tend to be within range of the expected literature values. There are multiple ways to improve the accuracy of our measurements and there are multiple biophysical applications using FCS.

When looking at ways to improve the experiment, light shielding becomes an important factor. Most of our apparatus was enclosed in the microscope so it did not require further light shielding but as our signal passed under the microscope to the pinhole, background light did leak through. In the beginning of the experiment we had a temporary cardboard shielding that probably blocked most of the background signal but there were openings where light could leak through. We did not get around to finalizing the light shielding due to the apparatus malfunction while measuring EGFP but proper light shielding would probably give us more accurate results.

Further extensions of FCS could also be implemented. It is also possible to measure the cell cytoplasm viscosity using FCS and it might also shed light on how the cytoplasm and nulcleoplasm compare in terms of molecular crowding. There are also many ways to use the nucleoplasm viscosity to understand other biochemical path- ways like facilitated diffusion.

Further work could be done to improve this experiment. First, troubleshooting the initial setup for solutions to the technical difficulties would allow measurements of EGFP with a one photon apparatus. Additionally, U2OS cells could be measured in a temperature stage at 37°C to determine whether or not viscosity measurements would have better agreement with the literature. Since there is little information regarding U2OS nucleoplasm viscosity at 20°C in the literature, this experiment aimed to study a relatively novel property. As such, there are several factors such as the biological response at this temperature and the temperature dependence of the nuclear machinery that may have caused disagreement with the literature. Thus, this experiment provides a groundwork for setting up and calibrating an apparatus that can be used to test new systems. Further work could be done on different cells (such as HeLa) that are used more commonly in the literature with relative ease due to proof of concept through the calibration measurements for Alexa488.

In conclusion, fluctuation correlation spectroscopy is a useful tool in biophysics for obtaining important information about the properties of biological molecules.

Notes on Experimental Difficulties

Probably the most difficult part of the optical setup was aligning the pinhole. The pinhole alignment being off by a millimeter (depending on your pinhole size) is enough to completely lose the ACF curve, so it is imperative to have a good translational stage to mount your pinhole on in order to make fine-tuned adjustments.

The samples need to be relatively dilute, otherwise the G(0) value for your ACF curve will be too low and the background noise will drown it out. From Reiger et al, a concentration of approximately 1nM was used, but without a good optical setup the signal from this sample may be too low. Make sure your sample is somewhere between 1nM-1μM for initial testing for an ACF curve since anything higher will most likely give too low of a G(0) value.

Having access to a good optical dye is key for initial troubleshooting. We began with fluorescein dye, from which we had trouble getting a good ACF curve. We eventually used Alexa488 which had better optical properties, but is more expensive. Rhodamine 6G is the dye that Rieger et al. used, and we have good reason to believe it would work well too.

Acknowledgements

Special thanks to our external adviser, Jochen Mueller, who lent us the use of his lab and offered his expertise and guidance during the project and to the graduate students, Siddarth Reddy Karuka and John Kohler, who aided us during equipment troubleshooting.

References

[1] Macháň, Radek, and Thorsten Wohland. “Recent Applications of Fluorescence Correlation Spectroscopy in Live Systems.” FEBS Letters, vol. 588, no. 19, 2014, pp. 3571–3584.

[2] Mirny, Leonid, et al. \How a Protein Searches for Its Site on DNA: the Mechanism of Facilitated Diffusion." Journal of Physics A: Mathematical and Theoretical, vol. 42, no. 43, 2009, p.434013.

[3] Rieger, Robert, et al. \Fluctuation Correlation Spectroscopy for the Advanced Physics Laboratory." American Journal of Physics, vol. 73, no. 12, 2005, pp. 11291134.

[4] “Excitation and Emission of Green Fluorescent Proteins” BioTek, 20 Feb. 2001.

[5] Segur, J. B., and Helen E. Oberstar. “Viscosity of Glycerol and Its Aqueous Solutions.” Industrial & Engineering Chemistry, vol. 43, no. 9, 1951, pp. 2117–2120.