RecA plays a central role in homologous recombination of DNA. When RecA combines with dsDNA to form RecA-dsDNA nucleofilament, it unwinds dsDNA and changes its structure. The unwinding length extension of a DNA segment interacting with RecA has been studied by various techniques, but the dynamic differential stiffness of dsDNA conjugating with RecA has not been well characterized. We applied oscillatory optical tweezers to measure the differential stiffness of dsDNA molecules, interacting with RecA, as a function of time at a constant stretching force of 33.6pN. The values of the differential stiffness of DNA (for stretching force in the range of 20.0pN to 33.6pN) measured by oscillatory optical tweezers, both before and after its interaction with RecA, are consistent with those measured by stationary optical tweezers. In the dynamic measurement, we have shown that the association (or binding) rate increases with higher concentration of RecA; besides, we have also monitored in real-time the dissociation of RecA from the stretched RecA-dsDNA filament as ATPγS was washed off from the sample chamber. Finally, we verified that RecA (I26C), a form of RecA mutant, does not affect the differential stiffness of the stretched DNA sample. It implies that mutant RecA (I26C) does not bind to the DNA, which is consistent with the result obtained by conventional biochemical approach.
© 2009 OSA
The biological functions of double-stranded DNA (dsDNA) molecules are expected to correlate strongly with their conformation and mechanical properties [1,2]. Recently, the stiffness of DNA molecules has not only been measured by various techniques, such as atomic force microscopy (AFM) [3,4] or optical tweezers [5–9], but also been estimated theoretically . For example, the force-extension relation of a segment of λ−DNA was shown to be nonlinear while the DNA transforms from its B-form to its S-form until it reached a linear regime (or the enthalpic regime), with a differential stiffness independent of the stretching force in the range of 20pN to 65pN . Among a wide variety of DNA-binding proteins, RecA protein plays a critical role in homologous recombination. RecA can directly bind to dsDNA to form a nucleofilament through RecA polymerization on the dsDNA molecule in the presence of ATP or ATPγS or its poorly hydrolysable analog. During this process, the extension length of the dsDNA unwound by RecA at approximately 0.17nm per axial base pair had been observed [11–13]. The unwinding length extension of a DNA, interacting with RecA, has been studied by either fluorescence microscopy  or micro-manipulation techniques . The dynamic differential stiffness of a dsDNA associated with the structural change during the conjugation of RecA to a stretched DNA in the enthalpic regime, however, has not been well characterized. In this paper, we report our experimental results on how the interaction with RecA affects the structure of dsDNA, under a constant stretching force (of 33.6pN) in the enthalpic regime, in terms of the differential stiffness (dFstretch/dxDNA extension = kDNA) as a function of time. The sample preparation, experimental setup and procedures, theoretical model, and results are described in the following sections.
2. Experimental detail
2.1 dsDNA sample preparation
To hold and stretch a string of dsDNA sample with optical tweezers, two micron-size polystyrene particles were attached to the dsDNA sample, one at each end to serve as handles. The attachments were accomplished by a biotin-streptavidin link at one end and a DIG-antiDIG (digoxigenin and anti-digoxigen) link at the other, as is illustrated schematically below in Fig. 1 . The procedure for sample preparation is described in the following paragraphs.
Fragments of 3.0-kbp dsDNA, identical to that of ΦX174 DNA fragment (nucleotides #961 to 4032), were first generated using polymerase chain reaction (PCR). During PCR amplification, Pst I site was introduced on both ends of these DNA fragments. The products were then inserted into the pYES3/CT/LacZ vector (~8.9-kbp; Invitrogen) using Pst I site, resulting in plasmid Φ/Z. To label the end of DNA with biotin, 20μg of Φ/Z were digested with restriction enzyme EcoR I (the unique EcoR I site is at nucleotide #3532 of the pYES3/CT/LacZ). Then, it was treated with Klenow enzyme (New England Biolab) at room temperature for 1.5 hours in the presence of 0.1mM each for dGTP, dCTP, biotin-dATP, and biotin-dUTP.
To generate DIG-labeled fragments, 1.2-kbp DNA fragments, inserted in pGEMT vector, were amplified by using PCR with nucleotide mixtures containing DIG-dUTP (0.1mM DIG-dUTP, 0.1mM dTTP, 0.2mM dATP, 0.2mM dGTP and 0.2mM dCTP). SP6 and T7 were used as primers. After PCR amplification, the DIG-labeled products were digested with restricted enzyme Not I (New England Biolabs) and were ligated with the biotin-labeled Φ/Z fragments treated with the same restriction enzyme (Unique Not I site was 50 bases downstream of EcoR I site). The final dsDNA product (~4μm in length) was used without purification for subsequent attachment to two polystyrene particles, one at each end, according to the procedure described in Section 2.2.
2.2 Linkage of dsDNA with two polystyrene particles
To prepare the linkage of dsDNA with two polystyrene particles, 1μg of dsDNA sample, obtained by the procedure described above, was added into 10μl of the 0.5 w/v solution with 20μm diameter polystyrene particles pre-coated with streptavidin (Spherotech). The samples were allowed to interact for 60 minutes with gentle agitation every 5 minutes. The particles were then washed three times with de-ionized distilled water (DDW) and centrifuged at 3000rpm for 1 minute to remove the supernatant. Afterwards, 20μl of DDW was added to the sample to re-suspend the product; the resulting preliminary solution contained streptavidin-coated polystyrene particles conjugated to dsDNA via streptavidin-biotin links.
At the beginning of every experiment, 1μl of solution containing 0.1 w/v of 2μm diameter particles pre-coated with anti-digoxigenin (Spherotech) was mixed with 2μl of the preliminary sample solution into 147μl of 20mM Tris buffer (at pH7.0 with 1mM of MgCl2 and 50mM of KCl) to form the final sample solution. A 2μm particle in the final solution was trapped and manipulated to touch the surface of a 20μm particle repeatedly until a linkage of the two particles with a linkage distance on the order of a few microns was observed. The attachments of the particles to the ends of the dsDNA segment were facilitated by a biotin-streptavidin link at one end and a digoxigenin-anti-digoxigen (dig-anti-dig) link at the other end. The larger (20μm) particle sank and stably sat on the cover glass of the sample chamber due to its weight, while the smaller (2μm) particle remained suspended in the buffer solution allowing trapping by the optical tweezers.
In our DNA samples, the number of DNA molecules linked between the particles depends on the relative concentration of the DNA molecules and the streptavidin-coated particles in the solution. To minimize the number of DNA molecules linked between the two particles, we increased the relative concentration of streptavidin-coated particles in solution to a level when a linkage between two particles can still be obtained. Despite this compromise, from the experimental results discussed in Sections 4, it appeared that in our samples, the number of DNA molecules linked between two particles can be more than one.
2.3 Preparation of RecA proteins
Wild type E. coli RecA proteins were produced by an improved SUMO fusion protein system . Briefly, the pHD-RecA expression vector was transformed into BL21(DE3) host cells for production of His6-Smt3-RecA fusion proteins. Smt3 is the yeast SUMO protein. His6-Smt3-RecA was purified by Ni2+ resin. Removal of His6-Smt3 was performed on the Ni2+ resin by an engineered SUMO protease, His6-Ulp1403–621-His6. Because of its dual His6 tags, His6-Ulp14403–621-His6 exhibits a high affinity for Ni2+ resin and associates with Ni2+ resin after cleavage reaction. Both fusion protein purification and SUMO protease cleavage using one Ni2+-resin column were carried out. To produce I26C RecA mutant protein, pHD-RecA vector was subjected to site-directed mutagenesis to replace Ile26 with Cys. We verified that the I26C RecA mutant does not bind to ssDNA or dsDNA in the presence of Dithiothreitol (DTT) (Chien-Der Lee and Ting-Fang Wang, unpublished data).
2.4 Experimental setup
A schematic diagram of our experimental setup to stretch a dsDNA sample with oscillatory optical tweezers is shown in Fig. 2 . A linearly polarized laser beam (λ = 1064nm, 1W, cw laser) was expanded and collimated by a beam expander (BE) to slightly overfill the back aperture of an oil immersion objective (NA = 1.25, 100X). The beam was tightly focused to form optical tweezers inside a sample chamber, which contained the DNA samples suspended in a buffer solution. The trapping laser power was controlled by polarization rejection through the use of a half-wave plate (ΗW) and a polarizing beam splitter (PBS 1). A PZT mirror and a telescope (telescope 1) were used to control the trapping point to manipulate the trapped particle. A second laser beam (λ = 632.8nm, 10mW, cw laser) was used to track the position of the trapped particle. A spatial filter/ beam expander (SF/BE) unit expanded and collimated the tracking beam to a beam diameter of approximately 1cm. A second telescope (telescope 2) was used to adjust the relative position of the focal points of the two laser beams, (i.e., the trapping and the tracking beams), in the sample chamber. The two laser beams were combined by a polarizing beam splitter (PBS 2) and coupled into the back aperture of the oil-immersion microscope objective. The tracking beam diffracted by the trapped particle was collected by a condenser (NA = 0.42, 50X) and projected onto a quadrant photodiode (QPD) to track the motion of the particle in the transverse plane. A filter was used to block the trapping beam (λ = 1064nm) from entering the QPD. The electrical output signals from the QPD were recorded by a data acquisition system (DAQ) for data storage and for subsequent data analysis. The trapped particle was also illuminated by a lamp through the condenser, and wide-field images of the trapped particle were captured by a CCD camera for optical alignment of the trap and for image analysis of the trapped particle.
2.5 Experimental procedure
By adjusting the location of the focal spot of the trapping beam and hence the position of a trapped particle, the dsDNA sample was held approximately along the x axis, on the horizontal plane, as is illustrated in Fig. 3 .
With the smaller particle trapped by optical tweezers, the DNA sample can be stretched (or held loose) by translating horizontally the larger particle fixed to the cover glass mounted on a PZT-driven translational stage. The larger particle was moved in 50nm steps towards the smaller trapped particle until the smaller particle was pushed away to the right by about 50nm from the original equilibrium position “x0”. The sample stage was then stopped and moved backwards by about 50nm; the position of the stage at this point, where the two particles almost touched each other while the smaller particle was in the central position of the optical trap (i.e., x0 = 0), was taken as x1 = 0. At this point, the stretched length of DNA sample was assumed to be zero. This assumption affects the absolute stretched length of dsDNA shown in Fig. 5(a) but does not affect the measurements of the differential stiffness of DNA, described in the Section 4 and 5. As the larger particle was driven to the left, the stretched length of DNA was measured by x1 - x0 as is indicted in Fig. 3(c). The larger particle was displaced to stretch the dsDNA sample until the small particle was pulled away from the optical tweezers center by 200nm (i.e., x0 = 200nm). The position of the sample stage was fine-tuned on the y-z plane until the measured kDNA along x-axis reached a maximum value. This adjustment ensured that the DNA was stretched along a direction collinear with the oscillation direction. The measurement of kDNA is described in the following section.
3. Theoretical model
Consider a particle trapped in a viscous fluid balanced between the optical trapping force and the DNA stretching force as shown in Fig. 3(c). A schematic diagram indicating different forces acting on the particle, which is attached to a DNA sample and trapped in oscillatory optical tweezers, is shown in Fig. 4 . When the particle is driven by oscillatory optical tweezers, the one-dimensional equation of motion in the linear spring model can be expressed as .Fig. 3, defined such that x1–x0 is the DNA stretched length; η is the viscosity of surrounding viscous medium; kDNA is the differential stiffness (dFstretch/dxDNA extension) of the DNA sample (because the DNA samples have the same length, the value of kDNA is expected to be linearly proportional to the number of dsDNA molecules); A and ω are the amplitude and the angular frequency of the oscillatory trapping beam, respectively; kOT is the force constant of the optical trap which was deduced from the Boltzmann statistics by analyzing the Brownian motion of the trapped particle . Taking into account the very low Reynolds number of the system, the first term in Eq. (1) is ignored.
Solving Eq. (1) with a solution in the form ofEq. (3).Equations (3) can be solved to give 
4. Experimental measurements of kDNA by two approaches
The differential stiffness (kDNA) was measured, both before and after the interaction of DNA with RecA, by two approaches, the oscillatory optical tweezers method based on Eq. (4) and the stationary optical tweezers approach based on the steady-state force-extension curve of a stretched sample. In the stationary optical tweezers approach, the larger particle was displaced to stretch the dsDNA until the trapped small particle was pulled away from the trap center by 200nm. This experiment was repeated with different optical trapping powers ranging from 2mW to 20mW. For each optical trapping power, the position (x1) of the larger particle driven by the sample stage was readjusted to maintain the mean position of the trapped particle “x0” at 200nm. We verified that x0 = 200nm is within the linear regime of both the quadrant photodiode and the optical tweezers. From the pre-calibrated value of kOT as a function of optical power (data not shown), the corresponding stretching force on the DNA sample was determined to be in the range of 1.8pN to 33.6pN for optical trapping power varying from 2mW to 20mW. For each dsDNA sample stretched between two particles, the set of experiments described above was carried out in the absence of RecA proteins and repeated again 30 minutes after the injection of 200nM of RecA proteins to allow RecA to bind to the DNA sample.
For each stretching force, the stretched length of DNA between the two terminals was given by x1-x0, as is illustrated in Fig. 3(c). The steady-state force-extension relation obtained by stationary optical tweezers is shown in Fig. 5(a), where the data denoted by “■” represent the results for the bare DNA and those denoted by “◆” represent the results for the RecA-DNA complex.
In the oscillatory optical tweezers approach, the trapped particle was forced to oscillate around an equilibrium position by the trapping beam oscillating at a fixed frequency (f = 10Hz) and a fixed amplitude (A ≈33nm). The amplitude (D) and the relative phase (φ) of the oscillating particle with respect to that of the oscillating beam were measured by the QPD in conjunction with the lock-in amplifier. The differential stiffness (dFstretch/dxDNA extension) of the stretched DNA (kDNA) was determined from the oscillation amplitude (D) and the relative phase (φ) of the particle, the oscillation frequency (ω), the oscillation amplitude of a trapping beam (A), and the spring constant of optical tweezers (kOT) according to Eq. (4). The kDNA as a function of the stretching force measured by the oscillatory optical tweezers is shown in Fig. 5(b), where the data denoted by “■” represent the results for the bare DNA and those denoted by “◆” represent the results for the RecA-DNA complex. Although the hydrodynamic effect, due to the presence of the large stationary particle in the vicinity of the small particle, may affect the drag coefficient , for simplicity, we have ignored this factor in our results; its effect on the absolute value of kDNA in the enthalpic regime is estimated to be in the range of 4% to 8%.
The results in Fig. 5 show the transition of the stretched DNA from the entropic regime to the enthalpic regime as the stretching force increases. In this specific example, the steady-state stretch length of the dsDNA, at the same stretching force of 33.6pN, increased from 4.00μm (prior to the addition of RecA) to 5.75μm (after interacting with RecA) as shown in Fig. 5(a); Fig. 5(b) shows that for both samples (i.e., naked DNA and RecA-conjugated DNA) the differential stiffness (kDNA) increased monotonically with stretching force in the range of 1.8pN to 20.0pN. The differential stiffness (kDNA) reached a constant plateau value (~40.7pN/μm for naked DNA and ~47.1pN/μm for RecA-conjugated DNA) when the stretching force was in the range of 20.0pN to 33.6pN. These values can also be obtained from the slope of the linear regime (the last four data points in the enthalpic regime) of the force-extension relationship given in Fig. 5(a). The values of kDNA obtained from these two different approaches agree to better than 1%.
On one hand, our experimental data, shown in Fig. 5(a), indicate that for the same stretching force (at 25 pN, for example), the conjugation of RecA with DNA significantly increases the stretch length of DNA, and hence “RecA turns the DNA softer”. On the other hand, the experimental data shown in Fig. 5(a) and Fig. 5(b), also indicate that at the same stretching force (of 25pN) the differential stiffness of DNA increases from 41pN/μm to 47pN/μm after RecA proteins interact and conjugate with DNA. Despite the apparent conflict, there is no inconsistency in these results.
The values of the differential stiffness of bare DNA for 4 different sets of samples were determined to be 33.7, 35.6, 40.7 and 42.2pN/μm. The reason for the fluctuation in the value of kDNA from sample to sample is discussed below. According to the Modified Marko-Siggia worm-like chain (WLC) model :Eq. (5) can be approximated as
The approximation prescribed above was validated by the fact that FLA ~10−18J through out our experiments. From the data reported by Hegner et al in 1999 , the differential stiffness (kDNA) defined from Eq. (6) was approximately 3.7pN/μm which is about an order of magnitude smaller than our results. One possible explanation for this discrepancy is that the difference in the total number of base-pairs and the types of base-pairs may significantly affect the value of (kDNA). Although it is very unlikely, we do not have any solid evidence to completely exclude the possibility of having more than one DNA molecules linked between the two particles. This last statement is indirectly supported by the reproducibility of our results (to within ~ ± 2% for the same sample, and within ~ ± 10% from sample to sample). At this point, we do not have a definite answer to explain the difference; additional experiments will be required to resolve this dilemma. Despite this shortage, however, the measurement of the interaction of RecA with DNA in terms of the change in (kDNA) with time does provide useful information on the dynamics of the interaction.
5. The dynamics of RecA-DNA interaction quantified by its differential stiffness as a function of time
To study the dynamics of RecA-dsDNA interaction, we measured (via oscillatory optical tweezers approach) the differential stiffness of the stretched dsDNA sample as a function of time, at a constant optical stretching force of 33.6pN, as RecA solution was slowly injected into the sample chamber. During the experiment, the position of the larger particle attached to one end of the DNA sample was continually readjusted to keep the position of the small particle at 200nm from the trap center through a feedback system. This ensured that the DNA was stretched at a constant force of 33.6pN while binding with RecA through out the experiment. The trapped particle was oscillated with an oscillation frequency of 10Hz in a buffer solution (Tris buffer at pH7.0 with MgCl2 and KCl) while another solution containing RecA (200nM RecA, 1mM ATPγS, 1mM MgCl2, 50mM KCl, 1mM DTT, 20mM Tris, pH7.0) was injected into the sample chamber at a rate of 0.6ml/hr with a syringe pump. It has been reported that the activation barrier for RecA to bind to dsDNA was lowered when the dsDNA chain was stretched, leading to an acceleration of the polymerization (or binding) process [13,22,23].
The experimental results (denoted by “◆”) are shown in Fig. 6(a) ; at a constant stretching force of 33.6pN, the differential stiffness (kDNA = dFstretch/dxDNA extension) of the dsDNA sample increased from 40.5pN/μm to 47.1pN/μm in about 850s. From the observation of the length extension of dsDNA during the interaction with RecA, the binding rate of RecA proteins is estimated to be 2.02 proteins/s based on a model of the polymerization of a single fiber reported by Hegner et al. in 1999 . To study the dynamics of the dissociation of RecA from the RecA-DNA filament, de-ionized distilled (DDW) water was injected into the same chamber at a rate of 0.6ml/hr to dilute the ATPγS, and repeated the experiment described above. The differential stiffness, kDNA, of the dsDNA sample decreased from 47.1pN/μm to 40.9pN/μm in ~550s indicating the dissociation of RecA from the dsDNA in the absence of ATPγS. To further validate our experimental results, the experiment was repeated under identical condition with RecA (I26C), a RecA mutant which has been known to be incapable of binding to DNA. Our experimental result, denoted by “▲” in Fig. 6(a), shows that there was no change in the differential stiffness (kDNA) of DNA in this case. These results imply that the change in DNA stiffness was indeed resulted from the binding of RecA protein to the stretched DNA. The experiment described above was also repeated with different concentrations of RecA (100nM, 200nM, and 400nM). As shown in Fig. 6(b), the association rate of RecA with DNA, inferred from the change in kDNA with time, increased with increasing RecA concentration. In Fig. 6, the mean and the standard deviation were obtained by averaging the raw data (with a sampling rate of 1 data point per second) over 10s.
6. Summary and conclusion
We used oscillatory optical tweezers to trap and oscillate a small (diameter = 2μm) polystyrene particle attached to one end of the DNA while the other end of the DNA was attached to a larger polystyrene particle (diameter = 20μm) sat on the bottom of the sample chamber. The differential stiffness of the stretched DNA sample manifested its transition from the entropic regime to the enthalpic regime as the stretching force was increased from 1.8pN to 33.6pN. It reached a constant value for stretching force in the range of 20.0pN to 33.6pN (in the enthalpic regime). The values of differential stiffness (kDNA) of the DNA sample stretched in the enthalpic regime, both before and after its interaction with RecA, obtained by oscillatory optical tweezers and stationary optical tweezers agree to within 1%.
The association dynamics of dsDNA with RecA (in a solution containing ATPγS) was quantified in terms of the differential stiffness of the dsDNA sample as a function of time, and at a constant stretching force. The association rate of RecA-DNA, reflected from the change in kDNA with time, increased with increasing concentration of RecA. Although our samples may contain more than one DNA molecules, and the exact number of DNA molecules would alter the absolute value of the differential stiffness, the technique does provide useful information on the dynamic interaction of DNA with RecA proteins in the enthalpic regime. Besides, this technique is applicable to the study of the interactions of DNA with any other binding molecules in general.
This work is supported by the National Science Council (NSC) in Taiwan jointly under the following research contracts: (Contract Numbers: 96-2627-B-001-003, 96-2627-B-001-001), and a Grant from the Aim for the Top University Plan supported by the Ministry of Education of the Republic of China.
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