Quantification of native mRNA dynamics in living neurons using fluorescence correlation spectroscopy and reduction-triggered fluorescent probes

RNA localization in subcellular compartments is essential for spatial and temporal regulation of protein expression in neurons. Several techniques have been developed to visualize mRNAs inside cells, but the study of the behavior of endogenous and nonengineered mRNAs in living neurons has just started. In this study, we combined reduction-triggered fluorescent (RETF) probes and fluorescence correlation spectroscopy (FCS) to investigate the diffusion properties of activity-regulated cytoskeleton-associated protein (Arc) and inositol 1,4,5-trisphosphate receptor type 1 (Ip3r1) mRNAs. This approach enabled us to discriminate between RNA-bound and unbound fluorescent probes and to quantify mRNA diffusion parameters and concentrations in living rat primary hippocampal neurons. Specifically, we detected the induction of Arc mRNA production after neuronal activation in real time. Results from computer simulations with mRNA diffusion coefficients obtained in these analyses supported the idea that free diffusion is incapable of transporting mRNA of sizes close to those of Arc or Ip3r1 to distal dendrites. In conclusion, the combined RETF-FCS approach reported here enables analyses of the dynamics of endogenous, unmodified mRNAs in living neurons, affording a glimpse into the intracellular dynamics of RNA in live cells.

The transport and local translation of mRNA play crucial roles in synaptic functions in neurons (1)(2)(3). A variety of mRNAs are delivered to dendrites and axons and translated in response to synaptic activation (4). To date, genetic and biochemical approaches have been used to visualize mRNAs in living cells. Aptamer-based RNA imaging techniques have been widely applied (5). The MS2 system is the most popular one and enables highly sensitive and specific imaging of transcripts (6). However, this method requires genetic manipulation of the target RNA sequence by inserting multiple aptamer-binding sequences. Many studies using the MS2 system exogenously expressed abundant target RNAs containing the MS2-binding sequence, which can lead to biased results due to overexpression. Singer's group knocked in the MS2-or PP7-binding sequence to the 3Ј-UTRs of target RNAs (7,8), which avoids the exogenous overexpression effects but requires tedious efforts to produce knock-in animals.
Switch-on fluorogenic hybridization probes have been used to investigate the dynamics of unmodified mRNAs. The peptidic Pumilio homology domain RNA probe binds to RNA in a sequence-specific manner by recognizing eight conterminous bases, thus allowing spatiotemporal analysis of endogenous RNA localization (9,10). It requires optimization of the amino acid sequence for each target. Fluorescent oligonucleotide hybridization probes such as molecular beacons (11,12), in which internally quenched fluorescent antisense probes are used, and RNA-targeting Cas9 (13) enable the mapping of RNA localization with high versatility. Because of the weak signal and background fluorescence derived from unbound probes, the range of target mRNA species is limited. Turner-Bridger et al. (14) have succeeded in labeling native RNA in distal axons of neurons using molecular beacon probes with highly inclined and laminated optical sheet microscopy; however, it was difficult to detect mRNA signals in the soma and proximal axon owing to nonspecific signals derived from probes detached from mRNAs.
To label native mRNA, we used the reduction-triggered fluorescence (RETF) probe technique (15), which consists of a pair of oligonucleotides conjugated with a nonfluorescent azidomethyl fluorescein derivative as a fluorogenic tag and with triphenylphosphine as a reducing reagent (Fig. 1A). The RETF probe emits fluorescence after the pair of probes hybridize to the target mRNA side by side and a reducing reaction between them occurs. The RETF probe detected endogenous mRNA at the single-nucleotide-mismatched level in fixed bacterial and living human cells (15,16), and distinguished between prelariat and lariat RNA structures in the intron (17). Although the high signal-to-background ratio (S/B) of the RETF probe, reaching 2400:1 (15), stands out among RNA probes (e.g. the best S/B of FRET-based RNA probes reported was 50:1 (18)), background This article contains supporting information. * For correspondence: Takafumi Inoue, inoue.t@waseda.jp. cro ARTICLE fluorescence derived from reduced probes dissociated from target mRNA complicates quantitative analyses. We adopted the fluorescence correlation spectroscopy (FCS) method to overcome the background issue of the RETF probe. FCS allows quantification of the diffusion coefficient and concentration of fluorescently labeled biomolecules in living cells based on fluorescence fluctuation analysis within a tiny focal spot, which is small enough to measure molecular dynamics in not only neuronal dendrites (19), but also spines (20). Autocorrelation functions calculated from the fluorescence fluctuation are fitted with theoretical diffusion models, and quantitative parameters are deduced. With fluorescence fluctuation spectroscopy, which is closely related to FCS, quantitative measurements of MS2-labeled ␤-actin mRNA were performed (21), and protein-mRNA interactions were revealed (22). FCS discriminates diffusing molecule species of different diffusion coefficients, which are mainly influenced by the radius of gyration of the diffusion molecules and the viscosity of the medium. The radii of gyration of mRNA bound with RETF probes and free RETF probes were expected to be sufficiently different to be distinguished by diffusion coefficients.
Numerous mRNA types, such as activity-regulated cytoskeleton protein (Arc; also known as Arg3.1), inositol 1,4,5-trisphosphate receptor type 1 (Ip3r1), and Ca 2ϩ /CaM kinase II␣ (CaMKII␣), are distributed in the dendrites of central nervous system neurons. The immediate early gene, Arc, plays a role in activity-dependent synaptic modifications. Arc mRNA is robustly expressed by synaptic activity and then rapidly delivered throughout dendrites (23,24). After stimulation, Arc mRNA appeared in the cytoplasm within 15 min and translocated to the tips of distal dendrites within 1 h (25,26). Newly synthesized Arc mRNA transcripts are selectively localized at activated synapses by an activity-dependent mRNA degradation mechanism, which eliminates Arc mRNA from inactive dendritic regions (27). The localization and translation of Arc mRNA are associated with endocytosis of AMPA-type glutamate receptors, thus contributing to the regulation of synaptic efficacy (28,29). In addition to synaptic modification, Arc protein forms a retrovirus-like capsid structure and transfers mRNA between neurons (30,31). A previous study using the MS2 system reported that exogenously expressed RNA containing the 3Ј-UTR of Arc mRNA moved bidirectionally at a velocity of 6 -65 m/min in dendrites (32). Furthermore, the RNA localized at or near the base of dendritic spines with a high probability (33). A knock-in mouse line where Arc mRNA was labeled with an aptamer-binding cassette allowed visualization of the endogenous activity-induced transcription of individual mRNAs (8).
Ip3r1 is an intracellular Ca 2ϩ release channel expressed in central nervous system neurons, including cerebellar Purkinje cells and hippocampal neurons (34). It plays pivotal roles in synaptic plasticity in the hippocampus and cerebellum (35)(36)(37). Whereas the MS2 system was previously used to visualize the 3Ј-UTR of Ip3r1 mRNA, its use was limited to the detection of colocalization with RNA-interacting proteins (38,39). Thus, the dynamics of Ip3r1 mRNA is poorly understood.
In this study, we aimed to develop a technique to assess the dynamics of nonengineered endogenous mRNAs using the RETF probe together with FCS. We first tested whether RETF probes can detect Arc and Ip3r1 mRNAs in neuron. Subsequently, we employed FCS to discriminate mRNA-unbound and -bound probes by the difference in their diffusion coefficients. And finally, we tried out this approach by monitoring changes in the diffusion coefficient and concentration of Arc mRNA by neuronal activation. This combined RETF probe-FCS method, as demonstrated here, has a potential to distinguish RNA-bound and -unbound probes by diffusion patterns, providing semi-quantitative estimations of endogenous and unmodified mRNAs in living neurons.

Fluorescence derived from RETF probes increases after introduction by patch clamp
We designed two RETF probes targeting different mRNA locations, termed target 1 and target 2, for Arc mRNA and Ip3r1 mRNA, respectively. The target sequences were chosen from locations where successful in situ hybridization results were reported. To test whether the RETF probes can detect target RNAs in living neurons, we introduced sets of RETF probes targeting Arc mRNA or Ip3r1 mRNA into hippocampal neurons by the whole-cell patch-clamp method. The RETF probederived fluorescence signal started to increase after patchclamp formation in both soma and dendrites and was saturated within 40 min, whereas a mismatched probe pair consisting of the azidomethyl fluorescein (Az) probe of target 1 and the triphenylphosphine (TPP) probe of target 2 Arc RETF probes yielded no fluorescence signal more than autofluorescence (Fig. 1, B and C). Fluorescence signals derived from RETF probes targeting Arc or Ip3r1 mRNAs spread across the cytosol (Fig. 1D).

FCS measurement with RETF probe
Although the increase in fluorescence derived from the RETF probes was clear, there was a possibility that not all of the fluorescence signal was emitted from RETF probes bound to target mRNAs, as some of it may have been from RETF probes detached from target mRNAs. To test this, we performed FCS, which was expected to distinguish between the RNA-bound and -unbound forms of RETF probes by virtue of diffusion coefficients. As a control probe, we used a fluorescein-conjugated scramble probe: a 15-base ssDNA of a random sequence conjugated with fluorescein instead of reduced Az. The sequence was confirmed not to have a match in the rat RNA database.

Calibration of the FCS system
Laser power adjustment and focal volume calibration should be done periodically ( Fig. 2A). The irradiance of the 488-nm blue laser was adjusted to around 5 microwatts at the tip of the ϫ60 objective, which was determined not to saturate the absorption of the fluorophore within the focused laser spot (40). The focal volume was determined as horizontal and vertical radii (r xy and r z , respectively) by fitting an autocorrelation function of 10 nM rhodamine 6G in PBS buffer to a one-component three-dimensional (3D) diffusion model, with a fixed diffusion coefficient of 414 m 2 /s (41). The diameter of the detection pinhole built in the FV-300 confocal system, which also determines the effective focal volume for FCS, was fixed to 150 m for all FCS experiments, which was larger than the one optimal for confocality for the objective (100 m) due to the low signal condition in this study. The resultant r xy and r z were 0.34 and 3.26 m, respectively. The structure parameter (␥ ϭ r z /r xy ; 9.6) was larger than the benchmark values (ranging from 3 to 8) in optimally aligned systems, and ␥ was 5.6 with the 100-m-diameter pinhole in our system.

FCS measurement with RETF probes in vitro
In an in vitro condition, a RETF probe for Arc yielded autocorrelation functions after mixed with in vitro-transcribed Arc RNA (Fig. S1B), which were fitted well to a two-component diffusion model irrespective of the addition of the scramble probe. The addition of RNase A to the mixtures eliminated the slower diffusion components, leaving the faster diffusion component unchanged (Fig. S1C). The slower-diffusing component was thought to represent the RNA-RETF probe complex, because it was diminished by the RNase addition, and the concentration of it (C slow ) was decreased by the dilution with the scramble probe solutions (Fig. S1Dd). And we consider that the faster diffusion component observed in the RNA-RETF probe mixture without the addition of the scramble probe represented RETF probe molecules detached from RNA, because its diffusion coefficient (D fast ) was very similar to that of the scramble probe (Fig. S1Da). The concentration range of the fast and slow components (2-30 nM) indicates that our FCS system faithfully measures concentration at the low nanomolar range in cell-free conditions. Contribution of RETF probes that were

Quantification of mRNA dynamics by FCS and RETF probe
directly reduced by the triphenylphosphine-tagged probes without binding to RNA should be negligible, because the fluorescence signal was not detectable in an in vitro RETF experiment with RETF probes without RNA.

FCS measurement with RETF probe in neurons
In intracellular experiments, neurons were loaded with the target 1 and/or target 2 RETF probes or with the scramble probe together with Alexa Fluor 594 biocytin by whole-cell patch clamp (Fig. 2Ba) in a separate inverted microscope setup from the confocal/FCS microscope in this study. If the confocal/FCS microscope allows the patch-clamp experiment, the same microscope can be used. Substances may be alternatively loaded by microinjection, whereas it is much more difficult to apply to neurons than to cell lines because neurons are fragile. The success rate of the patch-clamp dye loading method was 80% (147 trials) in this study. If substance loading by patchclamp and FCS measurement are performed on a single microscope setup, keeping patch-clamping during FCS measurements is possible; however, that is not suggested because continuous exchange of contents between pipette and cytosol makes conditions complex.
The co-injected marker, Alexa Fluor 594 biocytin dye, was necessary to identify the target cell after changing microscope and to capture clear shapes of the cells, because the fluorescence intensity of RETF probes is too dim to identify easily and to capture confocal images of sufficient quality. Due to the high sensitivity of FCS, a scant cross-talk from the marker fluorescence channel to the FCS fluorescence channel would cause serious deformations of autocorrelation curves. There was no detectable contamination of the Alexa Fluor 594 fluorescence to the FCS recording channel.
A stainless chamber holding a coverslip with neurons was transferred from the microscope for patch-clamp to the confocal/FCS microscope, and FCS measurement was performed. Neurons injected with probes and the marker Alexa Fluor 594 biocytin were identified by epifluorescence microscopy with the Alexa Fluor 594 biocytin fluorescence, and confocal images were taken and stored (Fig. 2Bb). FCS recording was performed at the earliest 5 min after the patch-clamp loading to gain enough RETF signals (see Fig. 1C).
The recording point for FCS was located at the cytosol in the soma or locations in dendrites 30 -50 m away from the soma. The fluorescence intensity recorded at single points in cells often rapidly decayed during the first 2-3 s and then became relatively stable. We considered that this rapid decay of fluorescence signal derived from immobile fluorescence sources, which was not the subject of this study. Hence, at each recording point, we omitted the first 5 s of irradiance (Fig. 2Bc) and then started a series of FCS recordings ( Fig. 2Bd; 5-12 times for 20 s in each cell).
The waiting time for obtaining meaningful FCS results after loading RETF probe may depend on factors such as the concentration of target mRNA and the location of the recording point in the cell (e.g. cell body and distal or proximal dendrite). If an autocorrelation function is not smooth enough for fitting with diffusion models even after repeated records are averaged, the fluorescence signal is too weak for FCS analysis, and more time should be allowed (ϳ30 min; see the saturation of fluorescence signals in Fig. 1C). If acceptable signal intensity is not gained after trying several cells, it is possible that the target mRNA concentration in the target cell is not high enough for the RETF-FCS method or that the choice of target sequence is not Fluor 594 biocytin, were loaded to neurons with the whole-cell patch-clamp method (for details, see "Electrophysiology"). b, a confocal image of Alexa Fluor 594 biocytin was taken with a 561-nm laser for the determination of dendritic width. c, a recording point was chosen and irradiated with a 488-nm laser at the same laser power as used in FCS measurements for 5 s. d, 20-s FCS records were repeated for several times at the same point.
Step d was repeated in the neuron stimulation experiments, and steps c and d were repeated several times in other experiments (for details, see "FCS measurements and analysis"). C, FCS analysis. a, dendritic size of the measurement positions was determined using the confocal images, and parameters for the confined diffusion model were calculated for dendritic FCS measurements (for details, see "Size of dendrites"). b, photobleaching of raw fluorescence intensity traces was assessed and corrected. c, autocorrelation function (ACF) was calculated from each corrected intensity trace. ACFs taken from each cell were averaged. Diffusion parameters in each cell were obtained by fitting with diffusing models to the average of ACF of each cell (for details, see "FCS measurements and analysis").

Quantification of mRNA dynamics by FCS and RETF probe
appropriate. Although in cell-free FCS, longer recording time compensates for weak fluorescence signals, longer recording time, or more repetitions, results in too much photobleaching in intracellular FCS. Thus, the minimum limit of target RNA concentration is higher in intracellular FCS than cell-free FCS. More photostable fluorescence tags will be required for better sensitivity of intracellular FCS.

Dendritic shape and diffusion models
Knowing the dendrite size is necessary for choosing appropriate diffusion models (42). The dendritic width of target neurons for FCS measurement was measured at 30 -50 m away from the soma on Alexa Fluor 594 biocytin images ( Fig. 2Ca; see Experimental Procedures), where FCS measurements in the dendrite were performed. Accordingly, the dendrite diameter ranged from 1.9 to 3.0 m (2.5 Ϯ 0.3 m; Fig. 3B). The confinement degree is expressed as d/r i , using the dendritic diameter d and the focal radius r (42). Diffusion in the z-direction, perpendicular to the coverslip surface, is negligible because the d/r z value (0.75) was smaller than 0.833 (42). In the axial direction of the dendrite, the diffusion space was confined by the dendritic boundaries because the average d/r xy value was 7.2. Thus, we adopted a confined diffusion model to the autocorrelation functions recorded in dendrites with d z ϭ 2.5 m and the confinement parameter Y ϭ 7.2 (19). In the case of somata, a standard 3D diffusion model was used to fit to autocorrelation functions (19).

Photobleaching
Photobleaching of fluorescence molecules in the cytosol during single FCS recording led to an artifact, which gave rise to a very slow artifactual diffusion fraction (43). Thus, photobleaching was assessed by fitting each fluorescence trace to a doubleexponential equation, and deducing a photobleaching parameter, i 20 /i 0 , which represents fluorescence decay during the 20-s measurement period (Fig. S2). The photobleaching magnitude differed among the probe sets, and, in particular, those with the scramble probe and the combination of targets 1 and 2 of Arc and Ip3r1 probes were larger than those of singly loaded probes (Fig. S2A). There was a positive correlation between the photobleaching magnitude and the probe concentration (Fig. S2B), which is consistent with a previous study in which the photobleaching effect was smaller in weakly fluorescent cells (43). To minimize the photobleaching effect, we applied a photobleaching correction before the calculation of autocorrelation functions ( Fig. 2Cb; see "Experimental procedures").

Autocorrelation function and fitting with diffusion models
Autocorrelation functions calculated from each series of 20-s fluorescence recordings were averaged for each cell and fitted with one-and two-component diffusion models (Figs. 2Cc and 4 (B and C)). As the residual of the fitting of both RETF and scramble probes showed that the one-component model did not yield acceptable fitting, the two-component diffusion mod-

Quantification of mRNA dynamics by FCS and RETF probe
els were used in the rest of this study. Fitting to a two-component model is common in intracellular FCS studies because of the existence of slow diffusion fractions (19,43,44), which are thought to derive from autofluorescence, nonspecific binding of fluorescent probes to intracellular molecules that slowly diffuse, and other unknown factors affecting the shape of the autocorrelation function. In this study, the contribution of autofluorescence seems small, because no reasonable autocorrelation curves were obtained in neurons without loading fluorescent probes (data not shown).
The diffusion parameters were deduced by fitting averaged autocorrelation functions in each cell to the two-component model with triplet-state correction (Fig. 5). The faster-and slower-diffusing components of the scramble probe, therefore, represent freely diffusing ones and nonspecific binding of it to slowly diffusing molecules together with other unknown factors, respectively. The severalfold smaller D fast of the scramble probe in neurons (ranging from 62 to 68 m 2 /s in soma and dendrite) compared with its D value in cell-free medium (1.3 ϫ 10 2 Ϯ 5.0 m 2 /s, n ϭ 4 in water; Fig. S1) was consistent with

Quantification of mRNA dynamics by FCS and RETF probe
previous intracellular FCS studies (19,(43)(44)(45) showing much smaller D values in intracellular FCS recordings than those obtained in the cell-free FCS.
In the case of the RETF probes, the averaged autocorrelation functions of each cell show fluctuation at the shortest lag ranges (Ͻ0.01 ms). This fluctuation was presumably caused by low , the ratio of concentration of the slower component to that of the total concentration (C slow /C total ; C), and the ratio of particle brightness of the slower-diffusing component to that of the faster-diffusing component (⑀ slow /⑀ fast ; D) of the scramble probe (scr, green marks), target 1, target 2, and both target 1 and 2 of Arc RETF probes (represented as 1, 2, and 1&2 with red marks), and Ip3r1 RETF probes (represented as 1, 2, and 1&2 with blue marks) were calculated by fitting averaged autocorrelation functions in neurons with a two-component 3D diffusion model. In dendrite, a two-component confined diffusion model was also used (left) in addition to the 3D model (right). Autocorrelation functions of recording series in single neurons were averaged and are represented as single marks. Medians are indicated by black lines. For simplicity, not all statistical differences among groups are indicated. All data and statistical results are shown numerically in Table S1. *, p Ͻ 0.05; **, p Ͻ 0.01; ***, p Ͻ 0.001; assessed by Mann-Whitney U test.

Quantification of mRNA dynamics by FCS and RETF probe
occurrence of correlated events (i.e. the concentration of fluorophore was low). This notion is supported by the finding that the fluctuation at the same lag range of the scramble probe, of which fluorescence intensity, and thus concentration, was higher than those of RETF probes, was smaller than those of the RETF probes (Fig. 4A). The small event number may have manifested the stochastic nature of the triplet-state transition. To reduce this fluctuation of autocorrelation functions of the RETF probes, more repeat of recording was necessary, but photobleaching prevented it. This fluctuation at the shortest lags may be inevitable with the low concentration of endogenous mRNA. The impact of the fluctuation to the fitting result was investigated by swapping the shorter lag part of an autocorrelation function of a cell with those of other cells (Fig. S3). Fitting of the chimeric autocorrelation functions to the two-component 3D diffusion model resulted in varying D fast and diffusion coefficient of the slower component (D slow ), relatively steady concentration of faster component (C fast ), and very steady C slow values (Fig. S3C). Thus, the accuracy of the diffusion coefficients is impaired by the fluctuation of the shorter lag range of autocorrelation function for each cell, which requires enough cell number for reliable results, whereas the concentration values are not affected much.
Although the slower part of the autocorrelation functions (Ն0.01 ms) of the RETF probes look well-fitted to the twocomponent diffusion models (Fig. 4, B and C), diffusing molecule species may consist of not only the free RETF probes and RETF probes bound with full-length target mRNAs but also RETF probes bound with different-sized degraded target RNAs in addition to the nonspecific binding to intracellular molecules and other factors. Thus, the two-compartment diffusion models may reflect complex convolutions of such complicated diffusing molecular species, which is a shortcoming of FCS that it cannot handle many diffusion species precisely, but the FCS results should still reflect features of the binding of RETF probes to target RNA.
The range of D fast of the RETF probes in neurons (24 -73 m 2 /s, range of medians of cells of the same probe set) was close to that of the scramble probe (61-66 m 2 /s), implying that the faster component of the RETF probes in cells mainly reflects free RETF probes. The D fast values of the RETF probes in cells, especially in the soma, varied more widely than those of the scramble probe, and the unevenness differed among the RETF probe types (Fig. 5A), suggesting that the faster component of the RETF probes may consist of not only free RETF probes but also RETF probes bound to fragmented mRNAs. Free RETF probes may have derived from those once bound to the target RNA then detached, as was seen in the cell-free experiment (Fig. S1), whereas RETF probes that underwent a reduction reaction with reducing probes in the cytosol or in the patch pipette without binding target RNAs were negligible because, in a control experiment, Arc RETF probes introduced into HEK cells, which do not express Arc mRNA (31), did not show detectable fluorescence or reasonable autocorrelation curves (data not shown). C fast and C slow of the scramble probe had a positive correlation in both soma and dendrite (Fig. S4A), indicating that the slower-diffusing component of the scramble probe contains not only the background of unknown causes inherent in the intracellular FCS analysis (19,43,44), which rides on slow diffusing ranges of the autocorrelation curve, but also nonspecifically bound scramble probes with slowly diffusing molecules. In the case of RETF probes, such nonspecific binding should be much smaller because the overwhelming nonfluorescent RETF probes mask most of the nonspecific binding sites. Thus, C slow of RETF probes may represent binding to the target mRNAs in addition to the background inherent in the intracellular FCS analysis and nonspecific binding that is presumably much smaller than that of the scramble probe. This idea that the slower-diffusing component of the RETF probes reflected their binding to mRNAs is further supported by the following arguments. First, the ratios of C slow to the total concentration (C slow /C total , where C total ϭ C fast ϩ C slow ) of single Arc probes and of single and both IP3R probes together were much larger than that of the scramble probe and of both Arc probes together (Fig. 5C). Second, the brightness of particles in the slower-diffusing component relative to the faster-diffusing component (⑀ slow /⑀ fast ) was larger in cells loaded with targets 1 and 2 together than in those loaded with single RETF probes (Fig.  5Bc). This is because mRNA molecules bound to two RETF probes should be twice as bright as those bound to single RETF probes (Fig. 5D). However, the actual value of ⑀ slow /⑀ fast was not 2 but around 1.2-1.4, because not all target RNAs are bound by the two types of RETF probes: some target RNAs may have degraded and lost one of the RETF probe-binding sites, and some of the bound RETF probes may have been photobleached. Altogether, we consider that the slower component of the RETF probes contains an evaluable RNA-bound RETF probe fraction; however, it was not separable from nonspecific binding of RETF probes with slowly diffusing molecules, as seen with the scramble probe, which made quantitative evaluation of RNA-bound RETF probes difficult.
To evaluate the confined diffusion model applied to the dendrite, the autocorrelation curves obtained in the dendrite were also fitted with the 3D diffusion model (Fig. 5). As a result, the overall tendency did not differ, and the diffusion parameters, especially in D slow and ⑀ slow /⑀ fast , with the 3D diffusion model in the dendrite were closer to those in the soma than those with the confined diffusion model in the dendrite.

Arc mRNA increases upon TTX withdrawal
Although the slowly diffusing component of RETF probes in neuron possibly contains the mRNA-bound RETF probes, other slow components, as seen with the control scramble probe, are mingled with it and make interpretation of the mRNA-bound RETF probe diffusion difficult. To further characterize the mRNA-bound RETF probe fraction, we examined changes in the FCS properties during Arc transcription induction by neuronal activation. Neuronal activity was suppressed by incubation with 2 M tetrodotoxin (TTX) for 2 days, and then TTX was washed out, which induces rapid and robust Arc transcription (8,46,47). An RT-PCR assay showed that the Arc mRNA levels increased within 20 min and reached 4-fold within 40 min after TTX removal (Fig. 6A).
Neurons incubated with TTX were loaded with an Arc RETF probe (target 2) or the scramble probe by the whole-cell patch-

Quantification of mRNA dynamics by FCS and RETF probe
clamp method, and FCS was performed under HEPES-buffered saline (HBS) with 2 M TTX. Then the medium was washed with TTX-free HBS. Thereafter, FCS measurements were performed at the same locations in each cell every 20 min for 1 h. Two concentrations of the RETF probe, 2 and 10 M, were used to test the saturation level of the probe. In control experiments using the Arc RETF probe without TTX removal and the scramble probe with TTX removal, the C slow values were decreased rather than increased during the time course, which was interpreted as photobleaching of probes during the series of measurements. TTX withdrawal led to overall increases in C slow with the RETF probe in both soma and dendrites (Fig.  6Ba). In the soma, C slow slightly decreased 20 min after TTX withdrawal, possibly because of photobleaching during the series of measurements, and then it increased after 40 min (p Ͻ 0.05, paired t test between 20 and 40 min). The initial C slow values of the scramble probe were larger or about the same level as C slow of the Arc RETF probe 40 -60 min after TTX removal in soma and dendrite, respectively. It does not mean that C slow of the Arc RETF probe was below the background level: nonspecific binding is a major fraction of C slow of the scramble probe, whereas the nonspecific binding of fluorescent RETF probes should be very small because the overwhelming nonfluorescent RETF probes should mask the nonspecific binding sites. Therefore, C slow of RETF probes is smaller than that of the scramble probe. ⑀ slow /⑀ fast of the RETF probes was increased by the TTX removal, whereas it decreased in the control experiments (Fig. 6Bb). Although the increment of ⑀ slow /⑀ fast was not  Table S2.

Quantification of mRNA dynamics by FCS and RETF probe
large, there is a possibility that a small portion of RETF probetarget RNA complexes formed aggregates or incorporated in ribonucleoprotein particles (7,48). These results strongly suggest that the increase in C slow of the RETF probe reflected activation of Arc mRNA production by neuronal activation.
Because the absolute C fast values differed among the conditions owing to the difference in RETF probe concentration and the difference in the fluorescence emission nature of the RETF and scramble probes (Fig. 7A), normalized C fast time courses were plotted (Fig. 7B). In the control experiments (i.e. the RETF probe without TTX withdrawal or the scramble probe), C fast decreased, possibly because of photobleaching during the series of measurements. In the RETF probe with TTX withdrawal experiment, C fast increased in the dendrites, but not in the soma (Fig. 7B). Whereas D fast of the RETF probe fluctuated, it was larger than the intracellular diffusion coefficient of mGFP (D ϭ 13.8 Ϯ 0.9 m 2 /s, mean Ϯ S.E. (45)) throughout the measurement (Fig. 7C).

Simulation of RNA distribution
With the median diffusion coefficient of Arc mRNA (D slow ϭ 2.1 m 2 /s) obtained in this study, the time course of the distribution pattern of newly synthesized Arc mRNA by free diffusion along the dendrite was simulated using a one-dimensional (1D) diffusion model along a tapering cylindrical shape (Fig.  8A). The simulated translocation of diffusing RNA reached 100 m from the soma within 60 min, but it did not effectively reach 300 m even after 120 min under conditions with an Arc mRNA half-life of 47 min (46) (Fig. 8B). Because RNA protection from degradation has been proposed as a factor explaining uneven mRNA distribution within the cell (49, 50), a scenario without the RNA degradation term was also tested. We found that diffusing RNA still did not reach 300 m within 60 min (Fig. 8C). These simulation results indicate that the free diffusion of mRNAs is not sufficient for the distribution of mRNAs in distal dendrites within a reasonable time, and thus active transport mechanisms are necessary, as has been argued in previous reports (25,26).

Discussion
In this study, the dynamics and concentration of endogenous Arc and Ip3r1 mRNA in living neurons were investigated, using the RETF probe technique and the FCS method. The RETF probe has a high S/B ratio due to its very low leaky fluorescence before target binding, which makes it a unique RNA-labeling method among other methods such as molecular beacons (11,12) and RNA-targeting dCas9 (13). The fact that reduced and fluorescent RETF probes remain fluorescent after detachment  Table S2.

Quantification of mRNA dynamics by FCS and RETF probe
from the target RNA molecule is a shortcoming of this probe. The FCS method was able to constrain this issue by sorting the free detached RETF probes from mRNA-bound probes based on the different diffusion coefficients. However, as was seen with the scramble probe ( Fig. 4 (C and D), scramble), the autocorrelation function of intracellular FCS inherently accompanies slowly diffusing components (19,43,44), which overlap with the slowly diffusing component deriving from RETF probe-RNA complex and make it difficult to isolate pure diffusion parameters of RNA-bound RETF probes. Also, the possibility of the existence of different-sized degraded target RNAs makes the interpretation of the fitting results difficult. However, the increase in the slow component of the RETF probe after Arc mRNA induction by TTX removal indicated that the slower diffusion component of the RETF probes still reflects an increase in the RNA-bound RETF probes; hence, detection of changes in the Arc mRNA amount in single cells was achieved by the combination of RETF probe and FCS.
The total RNA concentration ([RNA total ]) is calculated as follows.
[ (See "Experimental procedures.") Because the C fast value of the scramble probe (61 (median, interquartile ranges (IQR): 56 -66) and 38 (median, IQR: 28 -78) nM in soma and dendrites, respectively) was about one-tenth of the probe concentration in the patch pipette (0.5 M), [RETF total ] is assumed to be 1000 nM, when we take the experiments in which patch pipette was filled with 10 M RETF into consideration here. K D is assumed to range from 0.01 to 200 nM, according to a study in which K D of RNA-DNA complex was measured using ␤-actin RNA and a series of 17-mer antisense DNAs targeting several locations in the RNA (51). [RNA bound ] is less than the C slow value (e.g. 7.1 nM at time 0) because C slow consists of [RNA bound ] and presumably the concentration of RETF probes nonspecifically binding to intracellular molecules. Because [RETF total ] is much higher than [RNA bound ] and K D , [RNA total ] can be approximated by the [RNA bound ] value with an error of at most 20%. The increase in C slow of the Arc RETF probe (10 M in pipette) was 3.0 (median, IQR: 1.7-3.1) and 4.9 (median, IQR: 3.6 -4.9) nM 60 min after the TTX withdrawal in soma and dendrite, respectively (Fig. 6), representing an actual increase in RNA concentration with permissible errors.
The faster-diffusing component of the RETF probes is considered to reflect the unbound reduced RETF probes deriving from RNA degradation of the RNA-RETF probe complex or from dissociation of the RETF probe from the RNA. Although the dissociation rate constant of DNA-RNA complex is unknown, if we assume that the dissociation rate constant between RETF probe and the RNA target is not very different

Quantification of mRNA dynamics by FCS and RETF probe
from that between RETF probe and DNA (10 Ϫ2 order s Ϫ1 ) (16), a non-negligible portion of RNA-bound RETF may detach from RNA constantly, as was observed in the in vitro experiment (Fig.  S1). The contribution of self-reduction of the RETF probe pair was negligible at the concentration ranges used in this study (15). The apparently large increase in C fast of the RETF probe upon TTX removal in dendrites may reflect activity-dependent Arc mRNA production and degradation (27), at least in the dendrite.
Reported diffusion coefficients of transcripts vary widely, possibly because of differences in the labeling and measurement methods; the diffusion coefficients of ␤-actin mRNA were 3.8 ϫ 10 Ϫ3 m 2 /s in neurons, 0.09 m 2 /s in mouse embryonic fibroblasts (7), 0.1 m 2 /s in the COS-7 cell line (52), and 5.3 ϫ 10 Ϫ3 m 2 /s in A549 lung carcinoma cells (53), using the single-particle tracking method. Moreover, the diffusion coefficient of ␤-actin/MS2 mRNA measured by FCS in mouse embryonic fibroblasts was 0.35 m 2 /s (21). Because the D slow values in the present study were higher than those in these previous reports, especially for the Arc RETF probes in the dendrite (Fig. 5B), the slower-diffusing component may include RETF probes bound to degraded RNAs, of which the diffusion coefficients were larger than those of probes bound to native RNAs.
In both soma and dendrite, C slow /C total of the double-probe cases, where both the target 1 and 2 RETF probes were loaded, was smaller than those of the single-probe cases for Arc, whereas it was not for IP3R1 (Fig. 5C). This difference between the double probe and the single probes seen for Arc can be explained by both detachment of RETF probes from target RNA and fragmentation of RNA: a single RNA molecule bound with both target 1 and 2 RETF probes yields two separate fluorescent particles when one of the probes detaches or when the RNA is broken into small pieces and the two bound probes are separated. In the former case, C total increases but C slow does not. In the latter case, C total increases as well, but C slow does not increase as much as C total does, because RETF probes bound with small RNA fragments may only contribute to increase in C fast . Thus, the apparent smaller C slow /C total with the double probe than those with the single probes observed only for Arc may reflect that the degradation rate of Arc mRNA is greater than that of IP3R1 mRNA, which is in good accordance with a report that Arc mRNA has an especially short half-life (44) (Fig.  9), together with the possibility that the dissociation rates of the Arc RETF probes from RNA were greater than those of the IP3R1 probes.
Activity-dependent rapid Arc transcription and transport have been reported with the in situ hybridization method; Arc mRNA appeared in the perikaryal cytoplasm within 15 min and propagated to proximal dendrites within 30 min (25,26). The RT-PCR assay in the current study showed that the Arc mRNA level was increased within 20 min after TTX withdrawal. In the RETF probe experiments, the concentration of Arc mRNA (C slow ) started to increase at 20 min after TTX withdrawal in the dendrite, whereas in the soma, this occurred at 40 min (Fig.  6). The delay in the C slow increase in the cell body may be explained by photobleaching during the series of measurements: the C slow time course curves of the Arc RETF probes may have been decreased by about 20% every 20 min as the time course of C slow of the scramble probe shows. RNA degradation also contributes to the decline in the C slow curve of the RETF probe. Thus, we consider that C slow of the RETF probe in the soma actually started to increase 20 min after the TTX wash. Additionally, the time lag of the RETF probe to become fluorescent after RNA binding (16) should be taken into account. The absolute increments in C slow in the soma and dendrites were almost the same; however, the rate of increase in the soma was smaller because the basal C slow value was larger in the soma than in the dendrites. Furthermore, the decrease in C slow of the scramble probe after TTX removal and that of the RETF probe without wash, both of which are attributed to photobleaching during the series of measurements, were larger at the soma than at the dendrite (Fig. 6Ba), showing that the tendency for a basal decrease was greater in the soma due to its larger irradiated volume. Thus, we consider that the true increase in C slow of the Arc RETF probe upon TTX removal in the soma was more dampened than that in the dendrite.
Whereas the simulation of mRNA diffusion showed that free diffusion of RNA was not sufficient to bring RNA molecules to distal dendrites within a reasonable time, newly synthesized Arc mRNAs appeared in distal tips of the dendrite, about 300 m from the soma, within 60 min (25,26). MS2-labeled ␤-actin mRNAs moved in various patterns, including stationary, corralled, diffusive, and directed motion (7). Indeed, the velocity of

Quantification of mRNA dynamics by FCS and RETF probe
actively transported exogenously expressed mRNA containing the 3Ј-UTR of Arc mRNA was sufficiently high to be translocated to distal dendrites rapidly (32). Given these findings, our results would support the idea that free diffusion is not capable of transporting mRNAs of sizes close to Arc or IP3R to distal dendrites (2,(54)(55)(56).
Through this study, shortcomings of the method, combination of RETF probe and FCS, have emerged as follows.
1) A non-negligible amount of fluorescent RETF probes is released from target mRNA, which prevents visualizing each mRNA as a dot by masking the RNA-bound RETF probe signal (Fig. 1). The MS2 and molecular beacon systems enable visualization of mRNA particles and thus single-particle tracking to quantify diffusion coefficients of labeled RNA by adding repeats of probe-binding sequence to target RNA (6,12). For the RETF probe method, FCS is necessary for analyzing diffusion properties of labeled RNA. The dissociation of RETF probe from target RNA may be minimized by optimizing the binding sequence length for better separation of RNA-bound RETF probes from free ones.
2) Intracellular FCS accompanies slowly diffusing components presumably due to nonspecific bindings and other unknown factors (19,43,44), as was also seen with the scramble probe in this study. These slow components overlap with the diffusion of the RETF probe-RNA complex, making estimation of the RNA diffusion parameters difficult. In this study, the rapid Arc mRNA production by neuronal activation helped to distinguish RNA diffusion from other diffusion fractions.
3) The RETF probe method requires turning-on of nonfluorescent fluorophores to fluorescent ones by chemical reaction. At present, only fluorescein is available for the mechanism. The weak photostability of fluorescein results in the apparent photobleaching in intracellular FCS measurement. Development of next-generation RETF probes with more photostable chromophores is awaited.
However, this method provides the following advantages.
1) The RETF probe technique enables observation of the native movement and amount of mRNA in living cells. Fluorescence in situ hybridization (FISH) enables observation of mRNA localization and estimation of copy number of mRNA (57,58); however, it cannot report temporal changes but only a snapshot of mRNA localization and quantity because of tissue fixation. Live RNA imaging techniques are superior to it in obtaining temporal insights into the RNA dynamics and regulation of RNA such as biosynthesis, processing, and intracellular transport. By combining with FCS, the behavior of the very low-concentration, low-nanomolar-order endogenous mRNA could be investigated, whereas precise measurement of the absolute concentration is hindered by the artifacts peculiar to intracellular FCS.
2) Endogenous mRNA can be monitored without alteration of the sequence by the RETF probe-FCS method, whereas other live RNA-imaging techniques require the addition of probebinding sequences to the target RNA sequence. In the MS2 system, aptamer-binding sequence is added to target RNA. The molecular beacon method requires the fusion of long probebinding sequence repeats to the target RNA sequence when visualizing single RNA molecules. The difficulty in quantitative control of exogenous RNA expression is another issue of these methods. Singer's group created knock-in mouse lines for endogenous ␤-actin and Arc mRNAs to contain aptamer-binding sequences to avoid this problem; however, this solution is expensive and time-consuming.
3) A pair of chromophore-and reducing reagent-conjugated oligonucleotide probes is sufficient for the quantification of RNA dynamics. To obtain sufficiently high S/B values, the other methods usually use multiple probes per RNA (12,59). In the MS2 and molecular beacon systems, a long repeat of probe-binding sequence is fused to the target RNA, and many fluorescent probes bind to it, which may affect the measurements of RNA dynamics, as the diffusion coefficient depends on the shape of molecule. Whereas these approaches have been successful in visualizing single mRNA molecules, it is better to minimize the number of tags per RNA molecule, as bound tags may disrupt the natural conformation of the target mRNA.
In summary, we combined the RETF probe technique and FCS to establish a method for analyzing the dynamics of endogenous unmodified mRNA in living neurons. This study demonstrates that free RETF probes can be segregated from RNAbound forms by the difference in the diffusion coefficient together with concentration estimation at the low-nanomolar range. And limitations of this method emerged, including the inability to estimate absolute RNA concentration, but rather only relative changes in RNA concentration, due to nonspecific binding of RETF probes.

Animal care and neuron culture
Animal care was in accordance with the guidelines outlined by the Institutional Animal Care and Use Committee of Waseda University. Throughout the experimental procedures, all efforts were made to minimize the number of animals used and their suffering. Primary cultured neurons were prepared from embryos of Wistar rats on embryonic day 18, in accordance with a standard protocol (60) with modifications. Triturated neurons were plated at a density of 1.7 ϫ 10 4 cells/cm 2 onto circular glass coverslips (12 mm in diameter; CD12001, Matsunami Glass, Osaka, Japan) coated with 4% polyethyleneimine (P3143, Sigma-Aldrich (Tokyo, Japan)), which were set in 24-well plastic dishes (92424, TPP Techno Plastic Products (Trasadingen, Switzerland)), in plating medium consisting of modified Eagle's medium supplemented with 2 mM L-glutamine, 1 mM sodium pyruvate, and 10% horse serum. After incubation for 3 days, the medium was changed to maintenance medium consisting of Neurobasal-A medium (12349-015, Gibco) supplemented with 2% B27 (17504-044, Gibco), 2 mM L-glutamine, and 0.05% penicillin/streptomycin. Primary cultured neurons at 15-20 days in vitro were used.
In the electrophysiology and FCS experiments, coverslips on which neurons adhered were mounted in a stainless chamber (SCC-D35, Tokai Hit (Fujinomiya, Japan)) that allows the bottom side of the coverslip to face the objective directly and the top side to be immersed with extracellular solution. Alternatively, disposable glass-bottomed plastic dishes can be used, where weight on the top of the dish may be necessary to gain Quantification of mRNA dynamics by FCS and RETF probe stable focus. HBS (20 mM HEPES, 115 mM NaCl, 5.4 mM KCl, 1 mM MgCl 2 , 2 mM CaCl 2 , and 10 mM glucose, pH 7.4) was used as an extracellular solution at room temperature throughout experiments, in which neurons were kept healthy within at least 2 h. If cells need to be kept for longer periods in experiment chambers, HEPES-supplemented Neurobasal-A with B27 is recommended (60).
In neuron activation experiments, neural activity was suppressed with 2 M TTX (L8503, Latoxan (Valence, France)) for 2 days before the experiment. For the induction of Arc mRNA, cells were washed five times with TTX-free HBS.

Electrophysiology
Probes were loaded with the whole-cell patch-clamp method at room temperature. HBS was used as the external solution. Patch pipettes (6 -9 M⍀) pulled from borosilicate glass capillaries (Sutter Instrument Co., Novato, CA, USA) were filled with the internal solution: 65 mM potassium gluconate, 65 mM cesium methanesulfonate, 10 mM KCl, 1 mM MgCl 2 , 4 mM Na 2 ATP, 20 mM HEPES, and 0.4 mM EGTA, pH 7.3, 295 mosM. On the day of the experiment, 2 or 10 M RETF probe or 0.5 M scramble probe and 5 M Alexa Fluor 594 biocytin (A12922, Life Technologies Japan (Tokyo, Japan)) were added to the internal solution. Whole-cell mode patch clamps were performed using an Axopatch 1D amplifier (Molecular Devices, Sunnyvale, CA, USA). Neurons were voltage-clamped at Ϫ60 mV for 20 min to allow the probes to fill the cell, and then the pipette was removed gently to let the hole on the plasma membrane reseal; pipettes were pulled up very slowly until the tip of pipette was visibly detached from the surface of target neuron.

Quantitative RT-PCR
Total RNA was extracted with the TRIzol method (Invitrogen Japan, Tokyo, Japan) at each time point after the TTX washout. Total RNA (0.2 g) was reverse-transcribed to complementary DNA using ReverTra Ace qPCR RT Master Mix with a genomic DNA remover (Toyobo, Osaka, Japan), in accordance with the manufacturer's protocol. Quantitative PCR was performed with the StepOnePlus system (Applied Biosystems, Foster City, CA, USA) using THUNDERBIRD SYBR qPCR Mix (Toyobo). The relative expression level of Arc mRNA was normalized by that of GAPDH mRNA. Primers used for amplification were the same as in a previous study (47): 5Ј-ATCCTGCAGATTGGTAAGTGCCGA-3Ј and 5Ј-GCAC-ATAGCCGTCCAAGTTGTTCT-3Ј for Arc mRNA and 5Ј-AGAGACAGCCGCATCTTCTTG-3Ј and 5Ј-GGTAACCAG-GCGTCCGATAC-3Ј for GAPDH mRNA.

Size of dendrites
The dendritic width was determined by the line profile of fluorescence intensity orthogonal to each dendrite taken from Alexa Fluor 594 biocytin confocal images of the target neurons of the FCS measurement. A theoretical line profile of cytosolic fluorescence intensity presupposing a circular cross-section of dendrite, S(y), was developed by Gennerich and Schild (19), with y ϭ y 0 and z ϭ 0 being the center of the circular crosssection, the radial radius of the confocal volume r xy ϭ 0.34 m, structure factor ␥ ϭ r z /r xy ϭ 9.6, where r z is the focal axial radius and the fitting parameter . Methods to deduce r xy and ␥ are described in the "Results" section. The dendritic radius R, y 0 , and were obtained by fitting the dendritic profile of Alexa Fluor 594 biocytin to the model. The measurement points on the dendrite were positioned 30 -50 m away from the soma to be orthogonal to the dendrites on confocal fluorescent images of Alexa Fluor 594 biocytin. Dendritic widths were measured at two or three points in each cell. Data analyses were implemented and performed in in-house software, TI Workbench, running on Mac computers (61).

FCS system
The confocal microscope mentioned above (FV-300, Olympus) was equipped with an additional GaAsP-type photomulti-Quantification of mRNA dynamics by FCS and RETF probe plier tube (PMT; H8631-40, Hamamatsu Photonics) for FCS, of which high sensitivity is preferred for intracellular FCS where high photobleaching prohibits long-duration recording. Fluorescence excited with the 488-nm laser was detected with the PMT through a 500 -550-nm band-pass filter in the photon counting mode, in which each detected photon was converted into a transistor-transistor logic (TTL) voltage signal. Photon counting is better than analog voltage output from PMT because the former is free from thermal noise. The shortcoming of the photon-counting mode is the saturation of photoncounting with high-frequency photon events; however, in the case of intracellular mRNA imaging with RETF probes, the low frequency of photon events did not lead to saturation. The photon events as TTL signals were fed into a counter port of a data acquisition card (PCIe-6363; National Instruments, Austin, TX, USA) running at 1 MHz, which was connected to a Mac computer running TI Workbench. TI Workbench stored the incoming photon signals as a time series of number of events per 1 s (61).

Intracellular FCS measurements and analysis
The recording point for FCS was positioned at the cytosol in the somata or dendrites 30 -50 m away from the soma, guided by the Alexa Fluor 594 biocytin fluorescence. The z-position was set to positions where the signal of Alexa Fluor 594 biocytin was maximal. The recording mode of the Fluoview software, running on a Windows PC, was switched from the 2D image acquisition mode to the point-scan mode, and the recording point was set on the 2D image on a computer screen. The light path for fluorescence was switched to the additional PMT for FCS, and the point-scan mode recording was started in the Fluoview software. TI Workbench on a Mac computer started recording through the additional PMT by receiving a TTL trigger from the FV-300 confocal system. FCS measurement was performed at a single point for 20 s, which was repeated 5-12 times at the same point. The autocorrelation function of each 20-s recording was calculated separately as described below, and autocorrelation functions recorded from the same recording point were averaged to avoid slow fluorescence decay of time constants longer than several seconds arising from photobleaching of diffusing molecules within the diffusion compartment, which would have occurred if the recording and autocorrelation calculation was not divided and then averaged but done continuously in living cells (43).
To further compensate for the photobleaching effects, intensity traces were corrected before calculating the autocorrelation function. The fluorescence intensity time course, I(t), was fitted to a two-component exponential function, which accounts for fast and slow photobleaching, i(t) ϭ i 0 ϩ i 1 ⅐exp(t/ t B1 ) ϩ i 2 ⅐exp(t/t B2 ). With these fitted parameters, bleach-corrected fluorescence intensity, I c (t) was calculated with the following formula.
Autocorrelation functions were calculated along an exponentially interleaved delay time progression, n ϭ 0 ⅐10 0.01n , where 0 is the sampling time (1 s). n ranged from 1 s to 10 s (i.e. integer n was in the range of 0 Յ n Յ 700 in this study).
The autocorrelation function, G() ϭ ͗F(t)⅐F(t ϩ )͘/͗F(t)͘ 2 Ϫ 1, where ͗F(t)͘ is the mean fluorescence intensity of each photobleaching-corrected recording (I c ), was calculated as follows. Here, M is an integer given by T/ n , where T is the total measurement duration (20 s).
Autocorrelation functions taken from each single cell were averaged and then fitted to a one-or two-component diffusion model, using the Levenberg-Marquardt algorithm (45,62), where C i and ⑀ i are the concentration of the ith species and the brightness of each diffusing particle in the ith component. Fitting the autocorrelation functions with the two-component model resulted in brightness of fluorescent particles in the second (slower-diffusing) component relative to that in the first (faster-diffusing) component, ⑀ slow /⑀ fast . The Trp i () term expresses triplet-singlet transitions (63,64). p T is the fraction of particles in the triplet state with a delay time of Ti . In the 3D free diffusion model, g Bi is given by the following (65).
The effective detection volume, V eff , for this 3D model is given by V eff ϭ 3 ⁄ 2 r xy 2 r z . In the case that diffusion is confined in axial and lateral directions, it is appropriate to apply a confinement diffusion model (19,42). When the dendritic diameter, d dend , is sufficiently smaller than the height of the detection volume, namely, d dend /r z Ͻ 0.833, the diffusion in the axial direction is negligible (42). Thus, g Bi is expressed by Equation 8 in such a case.
g Bi ͑͒ ϭ g xi ͑͒ ⅐ g yi ͑͒ (Eq. 8) If the confinement parameter Y ϭ d dend /r xy is smaller than 8, g yi is approximated as follows (42),

Quantification of mRNA dynamics by FCS and RETF probe
and V eff is given by V eff ϭ r xy 2 d dend . The singlet-triplet transition was corrected by setting a constant value T , which was deduced to be 23 s for intracellular measurements of the RETF probes, 18 s for intracellular measurements of the scramble probe, and 10 s for the scramble probe in cell-free measurements after fitting the averaged autocorrelation curves of each probe. The diffusion coefficient D i was calculated by the following.

Simulation
Diffusion simulation was performed based on the Fick-Jacobs equation (66), representing a 1D diffusion model in a cylindrical tube of varying cross-sectional area. Directing the x axis along the tube and denoting the cross-sectional area at x by S(x) with RNA degradation constant ␥ rna , the effective 1D concentration C(x, t) was given by the Fick-Jacobs equation, where D is the diffusion coefficient. To simplify the crosssectional change in the dendrite, S(x) was imposed according to Rall's 3/2 power law (67): DIA 3 ⁄2 ϭ Αdia 3 ⁄2 , which describes the relationship between the diameter of the parent (DIA) and daughter (dia) branches. When the cross-sectional area of the branch was calculated based on Rall's law, the sum of the daughter cross-sectional area was reduced by ϳ20% of the mother cross-sectional area at every bifurcation point. The change in cross-sectional area was formulated as S(x) ϭ 0.8 bn⅐x/L , where L is the dendrite length and bn represents the total bifurcation number. In this simulation, both parameters were set as L ϭ 300 m and bn ϭ 16. The degradation rate ␥ rna was log(2)/ht, where the half-life ht was set as 47 min (46). As the particles cannot escape from the tip of a dendrite, the boundary condition at x ϭ L was ∂C(L,͉t)/∂x ϭ 0. At the dendrite base (x ϭ 0), the concentration was increased linearly within 40 min to match the result of the gene induction experiment by the RT-PCR assay. In other words, C(0, t) ϭ 0.025t for 0 Յ t Յ 40 min and C(0, t) for 40 Ͻ t min. The simulation was performed on Python.

Concentrations of RNA and RETF probe in equilibrium
The equilibrium dissociation constant (K D ) of the RNA-RETF probe binding is calculated as follows, (Eq. 14)

Statistics
All offline analyses were performed using the in-house software, TI Workbench, running on a Mac computer (61) in combination with Microsoft Excel (Microsoft Japan, Tokyo, Japan), R (Vienna University of Economics and Business), and Igor Pro (Wavemetrics, Lake Oswego, OR, USA). The indicated data are given as average Ϯ S.D. unless otherwise indicated.

Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request