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A low-cost pulsed laser is used in conjunction with a homebuilt laser confocal-scanning epifluorescence microscope having submicron lateral and axial spatial resolution to determine cytoplasmic viscosity at specific intracytoplasmic locations in J774 mouse macrophage cells. Time-dependent fluorescence anisotropy measurements are made at each location and global deconvolution techniques are used to determine rotational correlation times. These rotational correlation times are related to the hydrated volume of 8-hydroxyperene-1,3,6-trisulfonic acid (HPTS) to calculate viscosity at specific points inside the cell. In the cytoplasmic areas measured, rotational correlation times of HPTS ranged from 0.186 ns to 0.411 ns, corresponding to viscosities ranging from 1.00 +/− 0.03 cP to 2.21+/− 0.05 cP.
©2010 Optical Society of America
1. Introduction
In our previous work [1] we have described the use of time-dependent fluorescence anisotropy as an important tool for understanding the state of biological samples being processed for storage in a dry state. This approach was used to estimate the molecular mobility in small samples (10-20 µL) at various stages of dehydration, to identify heterogeneity in water contents and/or mobility distributions that manifest on a macroscopic scale. This is a potential problem for achieving appropriate samples for long-term storage in a dry state. In addition to understanding the nature of the sample on a macroscopic level, it is also desirable to understand the localized state of samples on a sub-micron to nanoscale level.
Storage in a dry or anhydrous state involves removing water from the cellular samples so that the intracellular molecular mobility decreases and degradative biochemical processes are slowed. Glass forming sugars such as trehalose are generally introduced into the intracellular space to decrease mobility of molecules within the cell and encourage the formation of a glassy state at low moisture contents thereby minimizing adverse reactions that can lead to degradation of the cell. Sugars can also provide specific protection to biomolecules and membranes during processing for dry preservation [2–5]. One of the challenges to achieving this level of protection is the difficulty in attaining suitable levels of protectants inside the cell. A variety of methods are frequently employed to transport trehalose across the cell membrane, including fluid phase endocytosis [2] and various poration techniques [3,4]. Unfortunately the methods for assessing trehalose uptake generally yield average values in a population, as opposed to a specific distribution within a population or within a cell. If the change in intracellular mobility can be effectively measured as trehalose is loaded into the intracellular space, an experimental relationship can be established between the intracellular viscosity and intracellular trehalose concentration. This relationship is highly relevant in determining the nature of cellular protection, as methods are developed to protect cells against desiccation stresses during dry processing. In this paper, we demonstrate an approach for determining the localized intracellular viscosity with high resolution time-dependent laser-scanning confocal microscopy.
There are two broad approaches to determining intracellular viscosity: the first makes use of mechanical techniques [6]. Indirect mechanical methods are mostly based upon manipulating the extracellular membrane (i.e., deforming the membrane) and the intracellular viscosity is measured indirectly by examining the response of the cell to the deformation. While these techniques are useful to characterize cellular membranes, they do not provide a direct way to measure viscosities at specific points within the cell. Early direct mechanical methods of observing cell viscosity utilized the insertion of magnetic beads into the cell. The beads were magnetically dragged through the cell, the shear rates of the molecules were observed through a microscope objective and the shear rate of the beads were analyzed. The measured viscosity of the cell in these experiments varied widely, from 10 cP to as much as 108 cP [7–11].
The second approach to measuring cell viscosity is the use of optical methods. These methods work by inserting fluorescent probes into the cell, and then exciting the fluorophores. One technique for using fluorescence to determine viscosity is fluorescence ratio imaging. In this technique, a selected fluorophore is excited at two excitation wavelengths, and the ratio of the resulting emission from the fluorophore at the different excitation wavelengths give information about the viscosity of the solution in which the fluorophore is located. For this technique to work, the fluorophore must be sensitive to intramolecular charge transfer, which is in turn sensitive to the environment of the solute. In addition, the emission from the fluorophore should be outside the range of autofluorescent emission from the cell when measuring cell viscosity. Finally, the technique requires specialized spectrofluorimeters which are capable of more than one excitation wavelength while measuring single emission wavelengths [12,13]. Another optical technique also relies on the excitation of a fluorescent probe in a cell. The resulting fluorescent signal has a time dependence which carries information about the local viscosity. Measured fluctuations in the photon counts result from translational and rotational Brownian diffusion of the fluorophores in the sample volume. If the viscosity of the sample volume increases, then we expect that the translational or rotational diffusion time across the sample volume will be higher. There are two ways to obtain these measurements. First, fluorescence correlation spectroscopy (FCS) can be used to measure the translational diffusion kinetics of particles in solution. The diffusion coefficient is then related to the viscosity [14–20]. The other method of probing the cell optically is to use time-dependent fluorescence anisotropy, which measures the rotational diffusion of the fluorophore in the sample. There have been previous attempts at using anisotropy techniques for examining viscosity within the cell, but they have either been wide-field methods which have provided an average of the cytoplasmic viscosity in the entire cell, macroscopic intercellular viscosity, without sub-cellular resolution [21–24], or have concentrated on cellular membranes [25]. In this work, we use time-dependent fluorescence anisotropy techniques to measure intracellular cytoplasmic viscosity on a sub-micron level, and to look at variations within a live cell following endocytosis of the fluorescent probe 8-hydroxyperene-1,3,6-trisulfonic acid (HPTS) into the intracellular space by incubation. Since part of the focus of our work is to develop low-cost measurement methods which may be used in a wide variety of labs, we prefer techniques which do not depend upon specialized probes and employ equipment which is relatively low-cost, and which can be used for a variety of measurements. Time dependent anisotropy measurements fit that criterion. We show the details of our quantitative analysis towards the development of further implementation as an imaging modality for high spatial resolution viscosity mapping.
Fluorescence emission in general has different horizontal and vertical components. We define the time-resolved fluorescence anisotropy as
where is the polarized component of fluorescence parallel to the polarized excitation beam, and is the polarized component of fluorescence perpendicular to the polarized excitation beam. For a spherical rotator, these two components may be shown to beHere is the fundamental anisotropy of the fluorophore, θis the rotational correlation time of the fluorophore in solution, represents the peak intensity of the fluorescent signal, andτrepresents the radiative fluorescent lifetime of the fluorophore. When we substitute Eqs. (2) into Eq. (1), we find that the time-dependent anisotropy may be written asThe rotational correlation time is directly related to the rotational diffusion of the fluorophore in the solution. Once we determine the rotational correlation time, we can then use the Stokes-Einstein and Perrin equations to relate rotational correlation time to local viscosity:where η is the viscosity, V is the hydrated volume of the molecular fluorophore, R is the gas constant, and T is the temperature in K [26].In the laboratory, the measurement of fluorescence anisotropy is complicated by the efficiency of the detection channel for horizontally polarized light relative to vertically polarized light. This efficiency effect is usually accounted for by the g-factor. The g-factor can be taken into account by modifying Eq. (1) so that we write
We can measure the g-factor experimentally by measuring the polarized emission components parallel and perpendicular to the vertically polarized excitation beam, and then measuring the polarized emission components relative to a horizontally polarized excitation beam. We then compute a value for g under the assumption that r(t) should be the same for both excitation polarizations, provided that the sample has no preferential alignment of the ensemble excitation dipoles. This is a valid approach for our samples. The results of this computation depend on the experimental geometry. For our experimental arrangement, we find that the g-factor iswhere is the maximum intensity of the vertically polarized emission parallel to vertically polarized excitation, is the maximum intensity of the horizontally polarized emission perpendicular to vertically polarized excitation, is the maximum intensity of the vertically polarized emission parallel to horizontally polarized excitation, and is the maximum intensity of the horizontally polarized emission parallel to horizontally polarized excitation. Determining g by this method is preferred, but in our cell imaging experiments we found that it was not always practical, due to the need to make large numbers of measurements quickly. We chose to include the g-factor in our fitting algorithm as a fitting parameter. We checked this assumption by measuring the g-factor using the experimental method described above, and then comparing that measurement with the fitted value of g. In one experiment, we found that the calculated value of g was 0.552, while the fitted value of g was 0.541. This gives an error of around 2.5%. This was a typical result. We did find that g varied from coverslip to coverslip, but multiple measurements on one coverslip yielded similar values for g. We attribute this to positional variations in coverslips.In this work, we present an instrument, experimental data collection method, and data deconvolution method for mapping intracellular viscosity with sub-micron lateral and axial spatial resolution. In order to effectively determine quantitative viscosity of the intracellular region, we first calibrate the molecular rotational correlation time of our chosen fluorophore (HPTS, or pyranine) with known viscosity solutions of trehalose in water. We then construct a calibration curve which is used to generate a value for intracellular viscosity using the rotational behavior of the same fluorophore.
2. Current experimental setup
A schematic diagram of our experimental setup is shown in Fig. 1 . The sample is placed on a homebuilt scanning stage described in a previous paper [27] driven by a Digital Instruments Nanoscope III controller. The excitation laser for the confocal imaging system is a 470 nm diode laser (PicoQuant) with a 0.03 nanosecond pulse-width driven at 10 MHz. We adjust the laser power so that the photon count rates remain between 1 to 5% of the excitation rate of the laser. This ensures that single photon counting statistics are valid. The laser is coupled into a single-mode optical fiber for spatial filtering, after which it is passed through a 470/20nm bandpass filter so that unwanted fluorescence and Raman scattering from the fiber can be removed. The light then passes through a sheet polarizer so that the sample illumination is linearly polarized. A dichroic beam splitter whose reflection cut-off is around 500 nm then directs the polarized light into a 1.25NA 100x oil-immersion objective lens, which focuses the excitation beam onto the sample. The objective lens also gathers the fluorescence emission from the excited sample (epifluorescence mode). The dichroic beam splitter in the detection path then rejects the excitation laser signal and enables measurement of emitted fluorescence only.
For the calibration phase of our study, the emitted fluorescence passes through a 535/40nm bandpass filter and then through a polarizing beam splitter, which allows us to measure polarized emission components parallel and perpendicular to the excitation beam. These polarized components are focused onto two MPD-series single photon avalanche diodes (SPAD), allowing us to measure the polarized emission components simultaneously using a TimeHarp 200 card (PicoQuant). Neutral density filters are used in front of the detector to prevent detector saturation (only for calibration purposes), and the optical path and detectors were optically shielded to prevent scattered light from the laser or from the emission to enter the detectors, causing a depolarization artifact.
For cell imaging and anisotropy measurements, a motorized flip mirror is added in the detection path, which deflects the emission beam to an EG&G SPAD. Photon counts from the SPAD are collected by the Nanoscope III controller, which is used to image the cells. Once we identified areas of interest within the cell, we park at the regions of interest, and the flip mirror is rotated to allow the beam to pass into the polarizing beam splitter and from there into the MPD detectors to measure fluorescence anisotropy.
We prepared samples of various viscosities of aqueous α-α-trehalose solutions by using a solution of 10 mM HPTS in deionized (DI) water. To make each sample, we weighed specific amounts of α-α-trehalose dihydride powder, dissolved that into the HPTS DI water, and weighed the resulting solution. We then determined the weight-weight% ratio of trehalose in the sample.
To determine the local mobility in the intracellular space of trehalose-loaded mouse J774 cells, the cells were incubated in loading buffer (0.7mM CaCI2, 1.1 mM MgC12, 2.7 mM KCI, 1.5 mM KH2PO4, 138 mM NaCI, and 8.1 mM Na2HPO4) containing 10 mM HPTS probe for 15 min. Cells were then washed 5 times and resuspended in the buffer. A droplet of cells in solution (20 μL) was placed on a glass cover slip and incubated for 15 min to allow cells to loosely attach before imaging. The cover slip was placed in a sample holder and was covered in buffer solution to prevent cell dehydration while measurements were made.
3. Experimental results
We first calculated the viscosity of the various aqueous trehalose solutions we made. The area number of published references giving viscosity measurements for aqueous α-α-trehalose [28–32], and this data has been fit to the Génotelle equation to determine the viscosity of trehalose as a function of temperature and mole fraction of sugar [33]. The Génotelle equation is empirically written as
whereis an empirically determined correction factor for temperature, is the viscosity of water, x is the mole fraction of trehalose, t is the temperature in degrees Centigrade, and a1, a2, b1, b2,and n are fitting coefficients with values of −0.159, 26.4, 1.31, 30.9, and 1.2 respectively, as given in [34]. Our samples ranged from 0 wt/wt% to 40.19 wt/wt%. Figure 2 shows a calculated calibration curve based on the Genotelle equation that we will use to relate measured rotational correlation times of HPTS with actual viscosity of known solutions. This will then allow us to measure rotational correlation times in cells and directly relate them to local environmental viscosity.
Fig. 2 Calculated viscosity of trehalose samples as a function of the ratio of the weight of trehalose to the weight of the solution.
We then determined the rotational correlation times for HPTS is each of our aqueous trehalose samples. This analysis is complicated by the instrument response function (IRF) of the laser, confocal microscope, and detectors. The intensities shown in Eq. (2) assume that the sample is excited instantaneously. In the lab, the excitation pulse from the laser is not a delta function (in time); there is always a finite temporal broadening of the pulse, and likewise, there is a measurable response time for the SPADs. This means that the lifetimes we measure in the lab are a convolution of the instrument response function of our system with the actual fluorescence lifetimes of the sample. It is necessary to measure the IRF of our microscope in order to recover the non-convolved fluorescent lifetimes of the sample.
We measure the IRF by scattering the laser off a clean cover slip and into our detectors, using neutral density filters in the detection sample to avoid damaging the detectors and to prevent photon pile-up. We then measure the time-resolved intensity from this scattered light. This allows us to determine the time-resolved IRF of our microscope as shown in Fig. 3 . One potential problem with this method is that it is possible to get reflections of the initial IRF in the data, and in fact, we do see some evidence of that in the perpendicular trace of the IRF. The amplitude of these reflections is minor, barely above the background, so we chose to accept this IRF.
It would be tempting at this point to do a simple deconvolution of the measured fluorescent lifetimes and the measured IRF. Unfortunately, the measured photon counts also include noise from the detectors, so a simple deconvolution of the IRF and the measured photon counts is not sufficient to recover the decay curves of Eqs. (2). A better technique is iterative reconvolution: we start with initial seed values for the coefficients in Eqs. (2) and construct model decay equations. These model decay functions are convolved with the measured IRF of our system. These convolved model functions are fit simultaneously to the parallel and perpendicular measured lifetime component photon counts with a nonlinear least-squares method in MATLAB to obtain the rotational correlation times of the fluorophore in the sample [35–37]. This iterative reconvolution process is essential to obtaining accurate rotational correlation times, particularly for rotational correlation times less than the width of the IRF.
Figure 3 shows the IRF measured for both channels for the calibration phase of our experiment. Before the data analysis is performed, the background (measured as the average number of counts for each channel in the first 50 bins) is subtracted from the relevant channel. This adjusted IRF is convolved with decay curves modeled on Eqs. (2) with initial estimated values for the amplitude, g, θ, ro and τ. After reiterative convolution and global fitting, the fitted fluorescence anisotropy curves are plotted, and values for g, θ, ro and τ are obtained. In order to provide a clearer picture of our deconvolution method, we show measured data in Fig. 4 . This particular measured data is from a sample of 4.61 wt/wt% aqueous trehalose, with θ = 0.174 ns, ro = 0.25, and τ = 5.38 ns. The 95% confidence intervals for θ, and τ are 0.171 ns to 0.177 ns and 5.371 ns to 5.385 ns, respectively, with a χ2 = 1.41.
Fig. 4 Deconvolved fluorescene anisotropy curve showing measured data (green and blue curves) and fitted anisotropy curves.
Background fluorescence, for example from autofluorescence from the cell, is ignored based on the following evidence. First, for this set of experiments we attempted to image cells in the same spectral region that were not loaded with HPTS fluorophore and had little to no success locating the cells using the same imaging parameters as used in the experiments above. Further, the radiative lifetime of the measured fluorescence (5.38 ns as quoted above) is very close to the 5.4 ns radiative lifetime of HPTS in water, thus indicating that the measured fluorescence of our experiments is dominated by the HPTS fluorophore. We must be clear in our discussion of background fluorescence. In our experiments presented with this data, autofluorescence was negligible. However, this is not always the case. Variations in cell nutrients and other reagents used in cell culturing lead to variations in observed fluorescence background.
In our calibration experiments we made a fluorescence anisotropy measurement at three different locations within each sample, determined the rotational correlation time at each location, then averaged the result for each sample. We found that the best fits for HPTS in an aqueous trehalose solution were obtained using a single-exponential decay function for the rotational correlation time decay. This indicates that the HPTS molecule can be modeled as a spherical rotator. The results are summarized in Table 1 . Finally, we fit rotational correlation time to the trehalose viscosity (Fig. 3) and find the linear relationship we expected from Eq. (4) for this range of viscosities.
Table 1. Calculated viscosity and rotational correlation times for different wt/wt% samples of aqueous trehalose.
Imaging was accomplished by utilizing our microscope in the imaging mode discussed earlier. Endosomes could clearly be identified by monitoring the intensity of HPTS emission. We selected non-endosomal areas of interest within each cell, then zoomed in on those specific areas and parked on those regions. We shifted our microscope to the fluorescence anisotropy configuration and measured the fluorescence anisotropy in the selected regions and then collected high-resolution anisotropy data in this region. Because we are no longer scanning when we collect the data, the sample volume of the measurement is determined by the diffraction limit of our microscope. We then determined the rotational correlation time at each location, using the Einstein-Stokes equation to determine the local viscosity at the measured points.
Fitting the results in Fig. 5 to a linear model, we find that the slope of the line (our value for ) is 0.186 +/− 0.0.0049 ns/cP, with a y-intercept of 0.00219 ns. The r-squared value is 99.65%. Since we need to find the viscosity from the rotational correlation time, we divide the measured value of the rotational correlation time by this amount to obtain the viscosity.
A fluorescence image of a live J774 microphage is shown in Fig. 6 . As expected the viscosities at different locations within the cell were not uniform. In the cell imaged in Fig. 6, the measured viscosities range from 1.00 +/− 0.03 cP, which is close to the viscosity of water, up to 2.21+/− 0.05 cP in other areas. We found that single exponential decay functions gave the best fits for fluorescent anisotropy in the regions we examined. This indicates that in those regions cytoplasmic structures are not binding on or otherwise influencing the rotation of the fluorophore. A full study of intracellular viscosity of cells with different concentrations of trehalose is currently underway and will be reported later.
4. Conclusions
We have demonstrated a well-calibrated method for measuring the viscosity of cells at different locations within the cell by using fluorescence anisotropy measurements, using a low-cost laser, and a home-built stage. We have provided a detailed qualitative and quantitative description of our methods and algorithms that result in high resolution measurements of TDFA for the determination of intracellular viscosity with submicron spatial resolution. The cell samples were placed on the stage of a home-built confocal laser-scanning microscope, imaged, particular locations within the cell were identified, and fluorescence anisotropy measurements were made. The viscosity for each location was determined from the Stokes-Einstein equation, using the molar volume of the HPTS molecule which was measured by the use of a calibration curve relating rotational correlation time to predicted viscosity for specific weight-weight percent solutions of trehalose over a range for which the Stokes-Einstein equation was valid.
Our results indicate that fluorescence anisotropy measurements are a practical technique for the measurement of micro- and nano-viscosities within cells. This technique, combined with automation of the data collection and data analysis phase, will allow us to present high spatial resolution maps of the internal viscosities of the cell, providing another important tool in the analysis of intracellular processes.
Our measured values of intracellular viscosity under our conditions varied from 1.0 cP to 2.2 cP. This range is fairly narrow relative to some other reported studies. We believe that our intracellular environment remains very water-like under our conditions. Further, the fact that we are measuring molecular rotations makes our measurements sensitive to localized environments. Utilization of mechanical methods such as magnetic beads and extracellular probes are much larger and the inhomogeneity of cellular constituents can lead to much larger apparent viscosities. For example, intracellular features could constrict the movement of the larger beads thus leading to a very large apparent viscosity while the medium is still very water-like. Hence, this method also has the advantage of measuring viscosity on a localized (molecular) level.
Acknowledgments
The authors would like to acknowledge financial support from the Department of Defense and The University of North Carolina at Chapel Hill via the project entitled “Collaborative Initiative in Biomedical Imaging to Study Complex Diseases”. We would also like to thank Dr. Ana Jofre of the Department of Physics and Optical Science at The University of North Carolina at Charlotte for help with the lifetime deconvolution algorithms.
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