Transient binding and jumping dynamics of p53 along DNA revealed by sub-millisecond resolved single-molecule fluorescence tracking

Characterization of the target search dynamics of DNA-binding proteins along DNA has been hampered by the time resolution of a standard single-molecule fluorescence microscopy. Here, we achieved the time resolution of 0.5 ms in the fluorescence microscopy measurements by optimizing the fluorescence excitation based on critical angle illumination and by utilizing the time delay integration mode of the electron-multiplying charge coupled device. We characterized the target search dynamics of the tumor suppressor p53 along nonspecific DNA at physiological salt concentrations. We identified a short-lived encounter intermediate before the formation of the long-lived p53–DNA complex. Both the jumps and the one-dimensional diffusion of p53 along DNA were accelerated at higher salt concentrations, suggesting the rotation-uncoupled movement of p53 along DNA grooves and conformational changes in the p53/DNA complex. This method can be used to clarify the unresolved dynamics of DNA-binding proteins previously hidden by time averaging.

Sequence-specific DNA-binding proteins bind to their respective target DNAs accurately and quickly and participate in the control and maintenance of cellular functions. To facilitate the search for target sequences among enormous lengths of DNA, these proteins utilize a strategy called facilitated diffusion, which involves a combination of various dynamics, such as one-dimensional (1D) diffusion and jumping along nontarget DNA, three dimensional (3D) diffusion between two separated sites of DNA, and intersegmental transfer at the contact points of two DNA strands [1][2][3][4][5][6] . Inhibiting the search for and binding to the target DNA by these proteins will lead to insufficient control of cell functions, which could result in disease 7,8 .
The prevailing method for the characterization of the target search dynamics of sequence-specific DNAbinding proteins is single-molecule fluorescence microscopy in combination with tethering and stretching of DNA on the surface of flow cells [9][10][11][12][13][14][15] . Typically, DNA-binding proteins labeled with a fluorescent dye or a quantum dot are introduced into the flow cell, allowed to interact with the stretched DNA, and excited selectively by highly inclined and laminated optical sheet (HILO) illumination or by total internal reflection fluorescence (TIRF). Fluorescent spots from single proteins are sequentially tracked using imaging detectors, such as electron-multiplying charge coupled devices (EM-CCDs), enabling the characterization of their target search dynamics. The time resolution of the method is determined by two factors. First, detection of fluorescent molecules at a spatial resolution of ~ 40 nm requires the collection of at least 50 photons, which in turn requires a certain period of data accumulation and sets the time resolution. Second, the frame rate of the imaging detectors (typically 10-50/s) also sets the time resolution. The shortest reported time resolution for localization of DNA-binding proteins along stretched DNA is 8 ms at a spatial resolution of 22-42 nm 16 . Thus, the standard setup of fluorescence microscopy Scientific RepoRtS | (2020) 10:13697 | https://doi.org/10.1038/s41598-020-70763-y www.nature.com/scientificreports/ can only provide spatial dynamics for single molecules blurred by time averaging over the period determined by the photon number and/or the frame rate. The time resolution may be improved using higher excitation power to increase the rate of photon emission and limiting the area of the imaging detector to increase the frame rate. The rate of photon detection from single fluorophores can be easily increased by increasing the excitation laser power at the expense of the total observation period owing to photobleaching. The imaging area can be reduced significantly by considering the one dimensionality of the stretched DNA and by restricting the region of interest by a slit. In the standard mode of EM-CCD, fluorescence photons from single molecules are accumulated as electrons in each pixel of the two-dimensional detector, which are sent and read out by an A/D converter one by one. However, by limiting the observation area to one stretched DNA, the time delay integration (TDI) detection mode of the EM-CCD, provided by Hamamatsu Photonics, can enhance the frame rate up to ~ 100 fold and achieve sub-millisecond detection of the dynamics of DNA-binding proteins.
p53 is a transcription factor that suppresses the cancerization of cells and has been investigated as a representative DNA-binding protein demonstrating facilitated diffusion mainly based on single-molecule fluorescence measurements 8,[17][18][19][20][21][22][23][24] . p53 binds to DNA nonspecifically and slides along DNA to search the target DNA sequence [17][18][19] . p53 possesses two sliding modes having different contacts with DNA by two DNA binding domains: core and C-terminal (CT) domains 20,21 . The disordered linker enables switching between the two sliding modes 22 . p53 slides along DNA rotationally following the DNA groove 15,25 . Target recognition by the sliding p53 is quite low and can be regulated by single mutations 8 . In addition to the sliding, p53 can utilize the ultrafast intersegmental transfer between two DNAs, which could help to skip obstacles bound to DNA during the target search in cells 23 . These dynamics of p53 were partly supported by molecular dynamics simulations [26][27][28][29] . Thus, single-molecule fluorescence studies have improved our understanding of the facilitated diffusion of p53.
Despite extensive studies on the facilitated diffusion of p53, the time resolution of these previous studies, several tens of milliseconds, hampers the detection and characterization of various events expected to occur in shorter time frames. First, the 1D diffusion of p53 in the presence of physiological salt concentrations could not be investigated at this time resolution, except in a single study 18 . Because DNA-binding proteins, including p53, dissociate from DNA rapidly at higher salt concentrations due to weakened electrostatic interactions, lower salt concentrations, such as 50 mM KCl, are typically used for the observation of p53 diffusion along DNA 20,22 . However, improvement of the time resolution may enable characterization of 1D diffusion under physiological salt conditions. Second, transient binding intermediates, which are expected to form after the collision of the DNAbinding proteins and DNA before the formation of the tight binding conformation, could not be characterized using the previous time resolution. Although such transient binding intermediates have sometimes been detected using two-protein systems interacting with each other, the intermediate in the DNA-protein systems has been reported only in one example, lac repressor 30 . Third, direct observation of the jumping of DNA-binding proteins along DNA, reported only for EcoRV 31 to date, is extremely difficult at the available time resolution. Accordingly, sub-millisecond detection will enable us to identify the unresolved dynamics of many DNA-binding proteins.
In this study, we optimized a single-molecule fluorescence detection method for DNA-binding proteins along DNA so as to achieve the sub-millisecond time resolution. Using this optimized setup, we characterized the dynamics of p53 at the time resolution of 500 μs. We succeeded in clarifying the salt-dependent 1D diffusion of p53 along DNA, the transient binding intermediate, and the jumping along DNA. The current setup will enable single-molecule characterization of the fast dynamics of other DNA-binding proteins.

Results
Optimization of a sub-millisecond detection setup for molecules moving along DNA. To increase the time resolution of single-molecule fluorescence detection, we combined high-power excitation based on the HILO and/or TIRF geometry of the fluorescence microscope and high-speed line detection based on the TDI mode of the EM-CCD (Fig. 1A). To detect a sufficient number of fluorescence photons in a submillisecond time period, we utilized an excitation laser power of 50 mW, corresponding to a power density of ~ 3,000 W/cm 2 in the epi-geometry with an observation radius of 23 μm. The illumination intensity was 100fold higher than that of our previous video-rate measurements 8,20 . The DNA was tethered on the optical substrate at one end using the DNA garden method and was stretched by a flow 32 . A rectangular slit in the detection pathway was used to select the fluorescence photons emitted from the labeled proteins bound to a single DNA of interest (Fig. 1B). The photons were detected within the rectangular area (600 × 10 ~ 19 pixels) of the EM-CCD operated in the TDI mode, in which the signal charges were continuously transferred and read out at submillisecond intervals (Fig. 1B). The slit prevented the incidence of unexpected photons from the area outside of the single DNA of interest. Therefore, movement of the molecules along the DNA could be directly recorded as a kymograph.
To test the performance of this setup, we measured p53 tetramers labeled with on average 3.2 fluorophores, ATTO532, interacting with the stretched nonspecific DNA 18,20 . Using HILO illumination at a laser power of 0.5 mW and the conventional detection mode of the EM-CCD operated at an interval of 33 ms, we obtained a series of two-dimensional images of the surface of the flow cell, in which more than 10 DNAs were tethered and into which the labeled p53 in the presence of 125 mM KCl was introduced. After the measurement, we chose one DNA area and constructed a kymograph by stacking the one-dimensional images in the order of the measurements. We detected many white dots, not traces, in the kymograph, indicating that many molecules of p53 dissociated from DNA within one frame (33 ms) after binding (Fig. 1C, left and middle panels). In contrast, using the increased laser excitation at 50 mW based on the illumination configuration close to the critical angle (explained below) and TDI image recording, we obtained kymographs at a resolution of 500 μs for p53 under the same solution conditions (Fig. 1C, right panel). In the sub-millisecond resolved kymograph, white traces, not Scientific RepoRtS | (2020) 10:13697 | https://doi.org/10.1038/s41598-020-70763-y www.nature.com/scientificreports/ dots, were observed that lasted from several milliseconds to several tens of milliseconds. Additionally, we found that p53 moved along DNA during the duration of its attachment. Accordingly, the optimized setup enabled us to detect the movement of p53 along DNA at sub-millisecond time resolution.
To determine the illumination suitable for ultrafast kymograph measurements of p53, we compared three illumination configurations: HILO, critical angle TIRF, and TIRF (Fig. 2). TIRF was defined as the configuration in which the incident angle of the excitation light was larger than the critical angle (60.7°), the conditions for the total internal reflection were satisfied, and the approach could selectively illuminate molecules bound to the tethered DNA; however, the excitation intensity decreased dramatically as a function of the distance from the surface. The distance between the tethered DNA and the substrate surface was estimated to be ~ 200 nm 33 . For the TIRF condition shown in Fig. 2, we chose 63.5° as the incident angle. In contrast, HILO was the configuration in which the incident angle (59.6°) was smaller than the critical angle, allowing molecules bound to DNA to be illuminated more effectively; however, the bulk molecules flowing in the excitation area would also be excited. Critical-angle TIRF was a variation of TIRF in which the incident angle (61.4°) was adjusted very close to the critical angle. Under these conditions, the penetration depth of the evanescent wave was 268 nm from the substrate surface and was significantly longer than 137 nm, i.e., that in the current TIRF condition at the incident angle of 63.5° (Supplementary text). The illumination intensity of molecules bound to DNA was 2.0-fold larger than that in the TIRF (Supplementary text). We used the same excitation laser intensity of 50 mW for the three measurements.
In the kymograph obtained by the TIRF setup in the solution containing 150 mM KCl, several vertical traces of p53 were observed only in the presence of DNA, confirming the detection of molecules bound to DNA (Fig. 2C). However, the fluorescence intensity of p53 was low owing to the limited excitation intensity by TIRF. In contrast, in the HILO kymograph, several vertical traces were also observed only in the presence of DNA, whose fluorescence intensity was higher than that obtained by TIRF ( Fig. 2A). However, many tilted traces were also detected both in the presence and absence of DNA, suggesting the detection of the flowing molecules. The An excitation laser at 532 nm was introduced through an objective lens into a flow cell using HILO, criticalangle TIRF, or TIRF geometry. The fluorescence from the molecules associated with a stretched DNA tethered in the flow cell was collected using the same objective, selected by a slit and optical filters, and detected using an EM-CCD operated at the TDI mode. (B) The TDI detection protocol for evaluation of fluorescence from DNAbinding proteins interacting with DNA. The fluorescence photons from a molecule bound to DNA selected by the slit (left) were recorded as charges stored in the rectangle area of the EM-CCD, and the data were transferred line by line and read out (middle). A kymograph was constructed by stacking the transferred 1D images sequentially (right). (C) Comparison of kymographs of p53 diffusing along DNA detected by the conventional system operated at a time resolution of 33 ms (left and middle) and by the newly developed system at a time resolution of 500 μs (right). The experiments were conducted in a solution containing 125 mM KCl.
Scientific RepoRtS | (2020) 10:13697 | https://doi.org/10.1038/s41598-020-70763-y www.nature.com/scientificreports/ critical-angle TIRF illumination maintained the high fluorescence intensity of molecules bound to DNA, similar to HILO, and significantly reduced the detection of flowing molecules compared with HILO ( Fig. 2B). Accordingly, we concluded that critical-angle TIRF illumination was the best approach for sub-millisecond fluorescence detection of molecules interacting with the tethered DNA.
Two binding components of p53 to DNA. In the sub-millisecond-resolved kymograph of p53 taken at the critical-angle TIRF, short-term traces were more frequently detected in the presence of DNA compared with that in the absence of DNA, suggesting the short-lived binding of p53 to DNA. To confirm the observation quantitatively, we tracked all traces in the kymograph obtained in the presence of DNA at 150 mM KCl and determined their residence times by developing an automated program. As expected, the residence time distribution of the tracked traces showed double exponential decay ( Supplementary Fig. S1A). The same tracking performed for the kymograph obtained without DNA gave a distribution whose occurrence was significant (> 25% of that obtained in the presence of DNA) only at the initial time bin from 2 to 3 ms ( Supplementary Fig. S1B). The time constants, obtained by fitting the residence time distribution on DNA except for the initial time bin with double exponentials, were 2.8 ± 0.5 ms (94% ± 1%) and 13 ± 3 ms (6% ± 1%), respectively, corresponding to the short-lived and long-lived binding components of p53 to DNA. The residence time distribution obtained after subtraction of the DNA-free data gave identical fitting parameters within the errors ( Supplementary Fig. S1C). Furthermore, it is unlikely that the short-lived component was artificially detected due to the blinking of the dye, because the labeled p53 tetramer possessed 3.2 dyes on average. These results suggested that both the short-and long-lived components could be attributed to the binding of p53 to DNA. To further elucidate the properties of the two binding components, we conducted sub-millisecond-resolved kymograph measurements of p53 at different salt concentrations. As the salt concentration decreased, traces of p53 having extended residence times increased (Fig. 3A), as clearly demonstrated in the residence time distribution (Fig. 3B). The residence time distributions obtained at all salt concentrations could be fitted well by the double exponential functions, whose time constants and amplitudes are presented in Fig. 3C,D, respectively. The time constant of the short-lived component did not depend on the salt concentration (Fig. 3C).  Fig. S3). Also, shorter residence times for 30-bp DNA in 125-150 mM KCl might be caused by the sliding of p53 off from the DNA ends 34 . Furthermore, the fraction of the two components was slightly dependent on the salt concentration when the concentration of KCl was greater than 100 mM (Fig. 3D)  Jumps of p53 along DNA. In addition to the short-lived binding component, we noticed another dynamic feature of p53 unresolved in previous studies of video-rate imaging. Specifically, there were sudden shifts in the traces of p53 in the sub-millisecond-resolved kymographs (Fig. 4A). The shifts occurred in the flow direction and were rarely against the flow, suggesting that these shifts represented the transient dissociation of p53 from DNA and its jumping along DNA. The result did not agree with the similar shift frequency in the two directions by assuming that a different molecule binds to DNA immediately after the dissociation of the molecule. The shifts were observed in kymographs obtained at all of the KCl concentrations examined in this study, suggesting that such jump events were a general feature of p53 (Fig. 4A).
To further understand this jumping motion of p53, we selected all jump events from the observed traces based on the following criteria: shifts having a jump distance larger than that expected from the 1D diffusion and shorter than that expected from the bulk flow. The jump distance distribution of the events selected from the kymograph obtained in 150 mM KCl demonstrated a distance-dependent decrease in the re-association probability of p53 (Fig. 4B). Under these conditions, the average jump time and average jump velocity were 2.2 ± 0.2 ms (Fig. 4C) and 0.291 ± 0.007 mm/s (Fig. 4D), respectively. Interestingly, these parameters were not dependent on the salt concentration ( Supplementary Fig. S4). By contrast, the jump frequency was dependent on the salt concentration and was enhanced by 3.1-fold in 150 mM KCl compared with that in 100 mM KCl (Fig. 4E). These results implied that the stronger electrostatic interaction between p53 and DNA at lower salt concentrations prevented the transient dissociation of p53 from DNA rather than affecting its re-association with DNA.
1D diffusion of p53 along DNA at physiological salt concentrations. The 1D diffusion of p53 along DNA at physiological salt concentrations has never been examined owing to the short residence time of several milliseconds, except in one pioneering study 18 . Accordingly, we next analyzed the 1D diffusion dynamics of p53 detected in the sub-millisecond-resolved kymographs. For all detected traces, we tracked the center of the  Fig. S5). The diffusion coefficient, D, obtained from the slope of the linear region of MSD, increased gradually as the salt concentration increased (Fig. 5B). The salt-dependent increase in D seemed to be coupled with that of the jump frequency (Fig. 4E). In fact, the D value was highly correlated with the jump frequency at various salt concentrations (Fig. 5C, r = 0.85). These results suggested that hops, not apparent even in the current sub-millisecond measurements, may occur during the 1D diffusion of p53 along DNA. We hypothesized that hops in DNA-binding domains occurred more frequently than the detectable larger jumps during the 1D diffusion, resulting in the enhancement of 1D diffusion at higher salt concentrations. To examine whether the 1D diffusion of p53 at physiological salt concentrations occurred along the DNA groove or not, we plotted the relationship between D and the molecular radii of p53 and other proteins, which could differentiate the rotation-coupled diffusion along the DNA groove and the rotation-uncoupled diffusion 14,25,35 (Fig. 5D). Many proteins were located within the group showing the rotation-coupled diffusion along the DNA groove (open circles). In contrast, the current D value for p53 (closed square) obtained in 150 mM KCl was much larger than those of the proteins showing the rotation-coupled diffusion and having the similar size, but was rather in line with those of TALE proteins, showing rotation-uncoupled diffusion (triangles). The results suggested that the 1D diffusion of p53 was not coupled with the major groove in DNA, consistent with our hypothesis that p53 moved along DNA more efficiently at higher salt concentrations by hopping of DNA-binding domains without strictly following the DNA groove.

Discussion
In this study, we optimized a single-molecule tracking method for DNA-binding proteins along DNA at the time resolution of 500 μs. The sub-millisecond time resolution was achieved using 1D detection based on the TDI mode of the EM-CCD, the slit for the selection of a single DNA of interest, and high-power laser excitation based on critical-angle TIRF. Using the optimized system, we clarified the presence of the short-lived encounter complex of p53 bound to DNA, the jumping of p53 along DNA, and the increased diffusion of p53 www.nature.com/scientificreports/ at near physiological salt concentrations. These newly characterized dynamics of p53 provide insights into our understanding of the facilitated diffusion of DNA-binding proteins. Improvement of the time resolution of the current system was achieved through consideration of the fluorescence photon numbers available within a short period of time and using the fast read-out mode of the imaging detectors. The TDI detection was originally developed to capture a moving object by transferring integrated signal charges with the object movement at the same speed so as to check the quality of products in factory. Because the movement of proteins is restricted within stretched DNA, we used the TDI mode of the EM-CCD, provided by Hamamatsu Photonics, and detected 1D images at a time resolution of 500 μs. The TDI mode could potentially reduce the time resolution further to 20 μs. Alternatively, a time resolution of up to ~ 2 ms could be achieved using the standard mode of an EM-CCD by setting a small region of interest.
The other optimized point for the increase in time resolution is the number of available photons in a short period of time. Using the current critical-angle TIRF excitation settings (intensity of 50 mW), we collected 50-200 photons during the time resolution of 500 µs. Currently available microscopes can achieve a spatial resolution of 16-24 nm for a spatially fixed molecule 36 . This estimate is smaller than the spatial uncertainly of the observed traces (27-72 nm), calculated from the intersection of the MSD plots of p53 at t = 0, but is reasonable considering the additional blurring of the current data caused by the fluctuations of DNA. The spatial resolution of the system is comparable to that of previous video rate measurements 16,20 . The increased fluorescent intensity in a short time can also be achieved by the HILO setup but the method detects the bulk molecules flowing in the relatively large excitation area as well as the molecules bound to DNA (Fig. 2). The critical-angle TIRF illumination can reduce the detection number of bulk molecules significantly because of the limited excitation area maintaining the high fluorescence intensity of the bound molecules. In contrast, the TIRF illumination decreases the fluorescence intensity significantly, because the penetration depth of the evanescent wave is smaller than the distance between the bound molecules and the surface. Thus, the critical-angle TIRF setup coupled with the high excitation power enables sub-millisecond fluorescence detection of molecules interacting with the tethered DNA.
In this study, we observed an encounter complex during the association process of p53 to a nonspecific sequence of DNA; this complex had a lifetime of several milliseconds before forming a long-lived complex. Our findings suggested that p53 interacted with DNA loosely in the encounter complex and that changes its conformation increased contacts of DNA-binding domains with the DNA and formed a more stable complex, as required for the target search along DNA (Fig. 6A). Because one p53 tetramer possesses four sets of two DNAbinding domains, the encounter complex could form contacts with DNA via some of the eight DNA-binding domains. Considering the higher affinity of the CT-disordered domain to DNA relative to the core domain, the CT-disordered domain likely participated in the encounter complex 21 . During the next step, the remaining DNA-binding domains may be recruited to form a stable long-lived complex. Interestingly, the conversion rate of the encounter complex to the long-lived complex was 6%, suggesting that the conformational change in p53 occurred rather slowly during the time frame of several milliseconds. Because many DNA-binding proteins possess multiple DNA-binding domains and flexible disordered regions, other DNA-binding proteins may also form encounter complexes similar to that formed by p53.
An encounter complex is an indispensable intermediate required for the formation of a stable complex in the association of two molecules, including protein/ligand, protein/protein, and protein/DNA pairs 37,38 . The encounter complexes were experimentally detected by measuring the concentration dependence of the reaction rate constant because the saturation of the association rate at the higher concentration represents the conversion of the encounter complex to the final product 37 . The R 2 dispersion experiments based on nuclear magnetic resonance (NMR) enabled detection of the encounter complex directly 39 . The observed lifetime of the encounter complex was less than several milliseconds 39,40 . In the p53/DNA system, the encounter complex had a longer lifetime of several milliseconds, as determined by the slow conformational change of p53 from the encounter complex to the long-lived stable complex described above (Fig. 6A).
The current sub-millisecond resolved data demonstrated the significant increase in the 1D diffusion coefficient of p53 along DNA at KCl concentrations higher than 100 mM; however, the data contradicted a previous report showing the independence of the diffusion coefficient against the concentration of monovalent ions 18 . The previous data were obtained using a video-rate system and by analyzing p53 sliding on DNA for extremely long periods, corresponding to rare events with a residence time more than tenfold longer than the ensemble data. The 1D diffusion of such rare molecules could be slower than that of the major populations.
To explain the salt-dependent enhancement of the 1D diffusion, we propose that p53 in the long-lived complex may change its conformation and move along DNA in the rotation-uncoupled manner at high salt concentrations (Fig. 6B). In fact, various physical parameters, including the diffusion coefficient and the jump frequency, changed significantly at 100 mM KCl, supporting the observed conformational changes in the p53/ DNA complex. At low salt concentrations, the DNA-binding domains interacted with DNA tightly, making p53 move following the phosphate backbone of DNA. In contrast, because high salt concentrations weaken the interaction between the domains and DNA, the domains may hop from one phosphate backbone of DNA to the other phosphate backbone separated by a half turn of the helix, resulting in the rotation-uncoupled movements of p53. Simultaneous hopping in the domains contacting the DNA may cause the dissociation of p53 from DNA and/or jumping of p53 along DNA.
This model is consistent with the following results by us and other researchers. Molecular dynamics simulations demonstrated that p53 moved along DNA in a rotation-uncoupled manner at high salt concentrations, likely because of weakened interactions between p53 and DNA 27 . The number of DNA-binding domains in contact with DNA decreased as the salt concentration increased 27 . In addition, hopping of the core domain or CT domain on DNA, observed in two independent simulations 26,27 , could enable p53 to transfer between different DNA backbones. This is consistent with the restricted hopping of the core domain in the sliding mechanism proposed based on single-molecule measurements 18 . The correlation between the diffusion coefficient and the Scientific RepoRtS | (2020) 10:13697 | https://doi.org/10.1038/s41598-020-70763-y www.nature.com/scientificreports/ jump frequency of p53 implied that simultaneous hopping of domains in contact with DNA may trigger the dissociation of p53 from DNA and may increase the observed jump frequency (Fig. 5C). The 1D diffusion caused by hopping of domains might be affected by the bulk flow (Fig. S6), and further investigation will be required using the stretched DNA in the absence of the flow, for instance, by tethering of two DNA ends to the surface or optical tweezers. Finally, we discuss the target search mechanism of p53 in cells. The search distance at which p53 moves along DNA per single binding is a key factor determining the search time for the target in cells. The average search distance of p53 was estimated to be 700 ± 100 bp using the diffusion coefficient and residence time in 150 mM KCl. The short residence time (18 ms, corrected by the photobleaching effect as explained in Supplementary text and Supplementary Fig. S1D) was compensated for by the fast 1D diffusion (1.2 × 10 7 bp 2 /s), demonstrating that the rotation-uncoupled motion promotes the 1D diffusion and contributes to the increased search distance. Interestingly, the estimated search distance was larger than the average distance between two molecules of DNAbinding proteins bound to DNA in cells (less than 100 bp) 41,42 . Furthermore, the large jumps of p53 along DNA may enable the skipping of the molecules bound to DNA and searching of the target located nearby, and the jumps may reduce the target search time to ~ 90% (Supplementary text). Accordingly, the rotation-uncoupled movement and jumps of p53 may contribute to the target search by extending the search distance.

Materials and methods
Fluorescence microscopy. A fluorescence microscope was constructed as described in our earlier report 20 , with some modifications. The output of the 532-nm laser (CL532-050-L; CrystaLaser, Reno, NV, USA) was magnified tenfold and was focused on the back focal plane of an oil-immersion objective lens (N.A. = 1.40; Nikon, Tokyo, Japan) using a spherical lens (f = 500 mm). A dichroic mirror (Di01-R405/488/532/635-25 × 36; Semrock, Inc., Rochester, NY, USA), located between the two lenses, was used to introduce the light to the objective lens. The flow cell was placed above the objective lens. In the back focal plane of the objective lens, the radial distances between the lens center and the excitation laser focus were 2.63, 2.68, and 2.73 mm for HILO, critical angle TIRF, and TIRF, respectively. The corresponding incident angle for HILO was 59.6°, which was smaller than the critical angle of the total internal reflection (60.7°). The incident angle for critical angle TIRF was 61.4°, which was close to the critical angle. The incident angle for TIRF was 63.5°, which was larger than the critical angle. The fluorescence from the sample was collected using the same objective lens, passed through the dichroic mirror, and then passed through the spatial filter unit composed of two multiple lenses (f = 200 and 70 mm) and a slit (Optonica Co., Kyoto, Japan). The slit width was set between 0.8 and 1.5 µm, such that a single DNA could be selected in the observation area (600 × 10 ~ 19 pixels). The width of the point spread function of the fixed fluorescent spot was ~ 200 nm. In the flow channel, DNA fluctuated ~ 64 nm along the perpendicular axis against the flow. A 532-nm notch filter, a 532-nm long pass filter, and a 590-nm short pass filter were placed in the fluorescence detection path. A spherical lens (f = 70 mm) was used to focus the fluorescence on the TDI-EM CCD camera (Hamamatsu Photonics, KK, Hamamatsu, Japan). The final magnification of the image was 100×.
Sample preparation. We used a thermostable and cysteine-modified mutant of human p53 (C124A, C135V, C141V, W146Y, C182S, V203A, R209P, C229Y, H233Y, Y234F, N235K, Y236F, T253V, N268D, C275A, C277A, and K292C) 20 . The expression and purification of p53 were conducted by following our reported method 20 . Briefly, p53 with the GST tag was expressed in Escherichia coli BL21 (DE3) pLysS cells. The cells were lysed by sonication, and the supernatants were loaded onto a GST column (GSTrap FF; GE Healthcare, Tokyo, Japan). The GST tag was cleaved using PreScission Protease (GE Healthcare), and samples were collected. The samples were purified further using a heparin column (HiTrap Heparin HP; GE Healthcare). DNA-binding ability of the purified sample was confirmed using a titration measurement based on fluorescence anisotropy 8 . The purified p53 was labeled with ATTO532 using maleimide chemistry, as reported in our previous study 20 . The p53 sample labeled with ATTO532 was purified using a cation exchange column (HiTrap SP HP; GE Healthcare). The labeling ratio was determined to be 0.8 dyes/monomer.
Tethering of DNA to flow cell. To tether DNAs in the flow cell, we used DNA garden methods to produce arrays of stretchable DNAs 32 . Briefly, NeutrAvidin (Thermo Fisher Scientific, Waltham, MA, USA) was microcontact-printed on coverslips coated using an MPC polymer (Lipidure-CM; NOF, Tokyo, Japan) with a custommade PDMS stamp (Fluidware Technologies, Saitama, Japan). Then, a flow cell was constructed by assembling double-sided tape, the coverslip, and the slide glass. The respective width and height of the flow path were ~ 3 and 0.1 mm, respectively. One of two holes of the slide glass was connected using a syringe through a tube 20 . For further coating of the flow cell, we used polyvinylpyrrolidone K15 (Tokyo Chemical Industry, Tokyo, Japan) and bovine serum albumin (BSA; Sigma-Aldrich, Tokyo, Japan). Finally, λDNA (New England Biolabs, Ipswich, MA, USA), annealed with 5′-GGG CGG CGA CCT -biotin-3′ (Sigma-Aldrich), was immobilized on the NeutrAvidin printed area of the inner surface of the flow cell.
Fast kymograph measurements of p53. We introduced the labeled p53 at 0.25-3 nM in a buffer containing 20 mM HEPES, 0.5 mM ethylenediaminetetraacetic acid (EDTA), 1 mM dithiothreitol, 0.5 mg/mL BSA, 2 mM Trolox, 2 mM MgCl 2 , and 25-150 mM KCl (pH 7.9) into the flow cell tethering DNAs using a syringe pump (Chemyx, Stafford, TX, USA). We first observed the larger area of the DNA array using two-dimensional imaging at an exposure time of 33 ms and a laser excitation power of 0.5 mW. Then, the slit was closed so as to detect only a single DNA, and fast kymograph measurements were conducted in TDI mode at an excitation power of 50 mW at 22 °C. Measurements were performed immediately after the dilution of labeled p53 from the stock solution at several tens of µM and completed within 50 min to prevent the dissociation of the tetramer into the dimers or monomers 43 . We obtained at least 600 kymographs consisting of 1,000 consecutive measurements of 0.5-ms exposures in each of the individual experimental conditions.
Tracking of p53 molecules in the kymographs. Single-molecule trajectories were obtained by tracking the center of the fluorescence intensity distributions at each time step for the kymographs. First, we picked peaks whose maximum fluorescence intensity was larger than 5 standard deviations of the background intensity at all time steps. Second, the selected peak detected at a time step was connected to the peak detected in the next time step if the two peaks were located within 2 pixels. If more than two peaks were detected at the next time step, the closest peak was connected. If there were no candidate peaks detected in the next time step, the procedure was repeated in the two subsequent time steps. Less than four missing time steps were allowed to connect traces considering the photoblinking of the fluorescence dye. Third, trajectories with at least five data points were selected. Finally, we determined the position of the molecule at every time step for each trajectory by fitting of the fluorescence distributions with a Gaussian function.

MSD analysis.
We calculated the MSDs of trajectories whose lengths were greater than 7 ms.