- Email: [email protected]
All-or-none folding transition in giant mammalian DNA
12 March 2002
Chemical Physics Letters 354 (2002) 354–359 www.elsevier.com/locate/cplett
All-or-none folding transition in giant mammalian DNA Kenichi Yoshikawa
a,*
, Yuko Yoshikawa b, Toshio Kanbe
c
a Department of Physics, Kyoto University & CREST, Kyoto 606-8502, Japan Department of Food and Nutrition, Nagoya Bunri College & CREST, Nagoya 451-0077, Japan Laboratory of Medical Mycology, Research Institute for Disease Mechanism and Control, Nagoya University School of Medicine, Nagoya 464-0064, Japan b
c
Received 7 November 2001; in final form 16 January 2002
Abstract Using fluorescence microscopy, we studied the folding transition induced by spermidine (3+) in individual giant DNAs isolated from pig liver, with an average size of 60 kbp varying between 15 and 150 kbp. We found that individual DNA chains undergo a large discrete transition, or switching, from an elongated coil state to a folded compact state. Interestingly, the width of the region of coexistence is rather narrow with respect to the spermidine concentration, despite the polydispersity of the DNA specimen. The weak dependence of the manner of the folding transition on molecular weight is discussed based on a simple mean-field theory. Ó 2002 Elsevier Science B.V. All rights reserved.
1. Introduction The compaction of DNA is a common feature in native genomes, e.g., in chromatin or phage heads. The manner of such packaging is expected to play an essential role in the biological functions of DNA, such as replication and transcription [1,2]. Many studies have shown that in vitro compaction of DNA can be generated by various chemical agents [3,4]. Polyamines [5–10], metal cations [11–15], neutral polymers [16–18], polypeptides [18] and basic proteins [19–21] have all been found to be very efficient condensing agents. However, most of these studies were performed
*
Corresponding author. Fax: +81-75-753-3779. E-mail address: [email protected] (K. Yoshikawa).
without a clear distinction between single-molecule packing and multi-chain aggregation. It seems to have been thought, at least until the mid-1990s, that a single-chain event could be realized only under idealized conditions with an infinitely dilute concentration of DNA [3,4]. We have recently made direct observations on the conformational change of long duplex T4 phage DNA molecules with a monodisperse size distribution (166 kbp, 57 lm in usual buffer [22]) using fluorescence microscopy. The common characteristics of the folding transition in single giant T4 DNA molecules induced by several kinds of condensing agents [23–27] can be summarized as follows: (1) Individual DNA molecules exhibit an all-or-none transition between an elongated coil and a compacted globule. (2) The transition diagram shows a region where the coil and globule states coexist. Thus, the folding transition appears
0009-2614/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 ( 0 2 ) 0 0 1 3 7 - 9
K. Yoshikawa et al. / Chemical Physics Letters 354 (2002) 354–359
355
to be steep but continuous for the ensemble average of DNA molecules. In the present study, the folding transition of mammalian DNA isolated from pig liver with a polydisperse size distribution was examined. We used a trivalent polyamine, spermidine, as the condensing agent. The polyamines putrescine, spermidine and spermine are present in millimolar concentrations in both eukaryotic and prokaryotic cells, where they stabilize compacted DNA molecules and also modulate the transcriptional activity of DNA [1,28,29]. The purpose of the present study is to determine (1) whether the manner of the transition at the level of individual molecules is the all-or-none type, (2) how the ensemble of mammalian DNAs behaves when treated with a condensing agent, and (3) whether there is any significant difference between mammalian and phage DNAs that might reflect the difference in the base composition (the GC content in T4 DNA (ca. 36%) [30] is considerably lower than that in mammalian DNA (ca. 42%) [31]).
2. Experimental 2.1. Isolation of DNA from pig liver To obtain a long DNA sample, we used a gentle procedure without centrifugation as follows. (i) Frozen pig liver was ground into pieces and then homogenized with a small amount of 10 mM Tris–HCl/1 mM EDTA buffer solution at pH 7.4. (ii) NaCl (2 M) was added to the homogenate and the suspension was heated at 60–70 °C in a water bath to denature protein components. (iii) Heat-denatured protein was removed by filtration. (iv) After filtering and cooling, the supernatant was mixed with two volumes of cold ethanol to precipitate DNA fibers. To purify the isolated DNA, steps (ii)–(iv) were repeated. The 260=280nm ratio of the final DNA samples was 1.85. The size of DNA was evaluated by fluorescence microscopy, where individual DNA molecules were stretched under shear stress and attached to a glass surface (Fig. 1c). The average full-stretch length was ca. 20 lm (60 kbp), and varied between 5 and 50 lm. These samples were stored in
Fig. 1. Fluorescence microscopic images of pig DNA. (a) Elongated coil state in bulk aqueous solution. (b) Folded compact state in solution with 1 mM spermidine. (a0 ) and (b0 ) Quasi-three-dimensional representations of (a) and (b), respectively. (c) Stretched and fixed specimen on a glass surface.
10 mM Tris–HCl buffer solution with 1 mM EDTA at pH 7.4 until use. 2.2. Fluorescence microscopic measurements For fluorescence microscopic measurements, DNA samples were dissolved in 10 mM Tris–HCl buffer solution with 50 mM NaCl, 10 mM MgCl2 and 1 mM dithiothreitol (DTT) at pH 7.5. The fluorescent dye 40 ,6-diamidino-2-phenylindole (DAPI) was added to the DNA solution at a final DNA concentration of 1 lM in nucleotide units. Compaction was induced by the addition of spermidine to the DNA solution. The concentration of spermidine varied from 0.3 to 6 mM. Fluorescence DNA images were obtained using an
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K. Yoshikawa et al. / Chemical Physics Letters 354 (2002) 354–359
Axiovert 135 TV microscope (Carl Zeiss, Germany) equipped with a 100 oil-immersion objective lens and a high-sensitivity Hamamatsu SIT TV camera, which allowed images to be recorded on videotape. The video images were analyzed with an Argus 20 image processor (Hamamatsu Photonics, Hamamatsu, Japan). Observations were performed at room temperature (ca. 20 °C). 2.3. Electron microscopic measurements Samples used for electron microscopy were mounted on carbon-coated copper grids (#200), negative-stained with 1% uranyl acetate, and observed with a transmission electron microscope (JEOL 1200EX, Tokyo) at 100 kV.
3. Results Fig. 1 shows fluorescence images of pig DNA molecules. Individual duplex DNA molecules exist as elongated random coils in the buffer solution (Fig. 1a) and transform into a collapsed globule in the presence of 1 mM spermidine (Fig. 1b). This experimental tool provides insight into the solution structure of DNA and reveals a clear difference between the coil and folded states in individual DNA molecules [23–27]. We examined the effect of the spermidine concentration on the higher order structure of DNAs at a fixed concentration of DNA (1 lM in nucleotide units). Fig. 2 shows the distribution of the long-axis length L at different concentrations of spermidine, together with a classification of the morphology (elongated coil or folded compact). L is the apparent long-axis length without correction for the blurring effect of the image in fluorescence microscopy [23]. All of the DNA molecules have an elongated conformation at up to 0.6 mM spermidine. At 0.8 mM spermidine, both the elongated and compact states coexist in the same solution. When the spermidine concentration is greater than 1 mM, all of the DNAs have a folded compact conformation. The change in the mean long-axis length is depicted in Fig. 3, indicating the large discreteness on the transition. Such tightly packed DNAs stay in solution and avoid both multi-chain aggregation and precipi-
Fig. 2. Distribution of long-axis length L of pig liver DNA dependent on the spermidine concentration.
Fig. 3. The mean long-axis length in coil and compact states, depending on the spermidine concentration.
K. Yoshikawa et al. / Chemical Physics Letters 354 (2002) 354–359
tation onto the glass surface, for at least several tens of minutes. Based on the experimental data, the long-axis length L of elongated DNAs is evaluated to be 2:4 lm, with a distribution between 1.4 and 4:0 lm. On the other hand, the long-axis length of the compact form is about 0:7–0:8 lm, indicating the formation of a tightly packed structure. By analyzing the Brownian motion of individual fluorescent objects of compact DNAs, we estimate that the compact DNA measures about 0:1–0:2 lm or even smaller. This means that there is a more than 10 000-fold change in the effective volume between the elongated and compact states. To characterize the morphology of pig liver DNA-spermidine complexes, we used electron microscopic observation at a DNA concentration of 80 lM. Fig. 4 shows that when the spermidine
Fig. 4. Transmission electron micrographs of pig liver DNA with 3 mM spermidine.
357
concentration is 3 mM, pig DNAs are condensed into compact structures, toroids or rods with end loops. The characteristic size of these compact structures, thus, corresponds to that evaluated from the Brownian motion observed by fluorescence microscopy.
4. Discussion Individual pig liver DNA undergoes a discrete conformational transition, or switching, between an elongated coil state and a folded compact state, similar to the conformational change observed in T4 phage DNA [23,24]. The folding transition for the ensemble of chains is rather narrow despite the polydispersity of DNA, indicating that the folding transition of giant DNAs is insensitive to the molecular size. Since polydispersity among giant DNA molecules is a rather common feature in specimens isolated from living cells, this finding of a rather narrow region of coexistence may be useful for the future development of an experimental technology in biological science. In the present study, we used spermidine, a trivalent cation, as the condensing agent. The mechanism of folding of long DNA chains induced by spermidine is explained as follows [24,26,32]: Before the folding transition, where the spermidine concentration is low (less than 0.8 mM), the degree of binding of spermidine to DNA is rather small. This is supported by the fact that the size distribution of elongated DNAs remains approximately the same for spermidine concentrations of 0, 0.3, and 0.6 mM, as shown in Figs. 2 and 3. In the coexistence region (e.g., at 0.8 mM), folded DNA exists in a compact state accompanied by the enhanced binding of spermidine. It is to be noted that the folded compact DNA molecules do not aggregate or condense each other at least during the period of observation on the order of several hours. In polymer science, it has been generally thought that a polymer chain has a compact form in a ‘poor solvent’; i.e., compact chains only exist in an infinitely diluted solution and they should aggregate and precipitate in a ‘poor solvent’ [33]. In contrast to this, the folded compact DNA behaves as a kind of solvable colloidal particle in a
358
K. Yoshikawa et al. / Chemical Physics Letters 354 (2002) 354–359
‘poor solvent’, due to the surviving negative charge on the surface [34]. Let us discuss why the nature of this transition is insensitive to the diversity in molecular size. Since we have given a rather detailed theoretical discussion elsewhere [24,26,35] including the effect of counter ions, we would like to discuss only the essence of the all-or-none folding transition, in relation to chain stiffness. We consider the difference in free energy, DF , between the elongated coil state, Fc , and the compact packed state, Fp , in a polymer chain with N segments:
From Eqs. (1), (2), (4), and (5) we get DF lnð8nN 1=2 Þ ðn ln H þ bÞN :
ð6Þ
We consider the case of DF ¼ 0, where the variables are N and H n ln H þ b ¼ N 1 lnð8nN 1=2 Þ:
ð7Þ
where ‘elas’ and ‘int’ indicate the elastic and interaction terms, respectively. We introduce the equilibrium swelling coefficient a, where a ¼ 1 corresponds to the ideal chain. By using the swelling ratio ap in the compact state, the elastic term in kT units can be approximated as [33]
Under the buffer conditions in the present study, the segment length ‘ 100 nm [22]. Since the effective radius of DNA, including the thickness of the ionic effect, is between 1 and 2 nm, we tentatively take r ¼ 1:5 nm. In our experiments, the size of DNAs is between 15 and 150 kbp, corresponding to N values between 50 and 500. We denote the ligand concentrations as H50 and H500 , where the free energies of the coil and compact states are the same for DNA chains with N ¼ 50 and 500, respectively. From the above discussion,
DFelas 3 ln ap :
n lnðH50 =H500 Þ 0:19:
DF ¼ Fp Fc ¼ DFelas þ DFint ;
ð1Þ
ð2Þ
Next, we introduce a stiffness parameter n as the ratio between the pseudo excluded volume vS of a sphere with a diameter of segment length ‘ and the effective excluded volume vK of a segment with radius r. n ¼ vS =vK ¼ ðp‘3 =6Þ=ðpr2 ‘Þ ¼ ‘2 =6r2 :
ð3Þ
For simplicity, we assume spherical symmetry for the folded compact state. While this assumption is strictly not precise, the following discussion is still valid at a semi-quantitative level. Since the volume in the compact state is given as vK N and the radius of an ideal chain is expressed as R ‘N 1=2 , a3p n1 N 1=2 =8:
ð4Þ
In the folded compact state, the segments exhibit ordered packing. Thus, the stabilization energy is considered to be roughly proportional to N. By introducing the concentration, H, of a ligand (spermidine in our case), the interaction term is [32,35] DFint ðn ln H þ bÞN ;
ð5Þ
where n and b reflect the number of binding ligands per segment and the degree of stabilization in the compact ordered sate, respectively.
ð8Þ
In double-stranded DNA, there are ca. 700 phosphate groups per segment. If we tentatively consider that n ¼ 10, the ratio of the concentrations is calculated as H50 =H500 1:02:
ð9Þ
This condition corresponds to the formation of ion-pairs for up to 4% of the phosphate moieties on the DNA chain. With a more plausible choice for this parameter, if n is larger than 10 [32], the relative ratio becomes smaller. Fig. 3 shows that the spermidine concentration in the region of coexistence between the coil and compact states ranges between 0.7 and 0.9 mM. Thus, the ratio between the minimum and maximum is 0:9=0:7 1:3. The width of the coexistence region almost corresponds to that observed for monodisperse T4 DNA [24], indicating that the effect of polydispersity of the DNA sample is minute on the diagram of the folding transition. As an additional remark, it is to be mentioned that the above theoretical framework does not hold for short oligomeric DNA molecules, i.e., the marked discrete nature of the folding transition should disappear for DNA less than several kbp.
K. Yoshikawa et al. / Chemical Physics Letters 354 (2002) 354–359
Acknowledgements This work was supported in part by a Grant-inAid for Science Research from The Ministry of Education, Science, Sports and Culture of Japan.
[17] [18] [19] [20] [21] [22]
References [1] I. Baeza, P. Gariglio, L.M. Rangel, P. Chavez, L. Cervantes, C. Arguello, C. Wong, C. Monta~ nez, Biochemistry 26 (1987) 6387. [2] J. Pelta, D. Durand, J. Doucet, F. Livolant, Biophys. J. 71 (1996) 48. [3] V.A. Bloomfield, Curr. Opin. Struct. Biol. 6 (1996) 334. [4] V.A. Bloomfield, Biopolymers 44 (1997) 269. [5] L.C. Gosule, J.A. Shellman, Nature 259 (1976) 333. [6] D.K. Chattoraj, L.C. Gosule, J.A. Shellman, J. Mol. Biol. 121 (1978) 327. [7] R.W. Wilson, V.A. Bloomfield, Biochemistry 18 (1979) 2192. [8] K.A. Marx, T.C. Reynolds, Biochim. Biophys. Acta 741 (1983) 279. [9] D. Porschke, Biochemistry 23 (1984) 4821. [10] D. Jary, J.-L. Sikorav, Biochemistry 38 (1999) 3223. [11] R.W. Widom, R.L. Baldwin, Biopolymers 22 (1983) 1595. [12] J.A. Schellman, N. Parthasarathy, J. Mol. Biol. 175 (1984) 313. [13] D.P. Gersanovski, C. Colson, C. Houssier, E. Fredericq, Biochim. Biophys. Acta 824 (1985) 313. [14] H.A. Tajmir-Riahi, R. Ahmad, M. Naoui, J. Biomol. Struct. Dyn. 10 (1993) 865. [15] C. Ma, V.A. Bloomfield, Biophys. J. 67 (1994) 1678. [16] Y.M. Evdokimov, N.M. Akimenko, N.E. Glukhova, A.S. Tikhonenko, Y.M. Varshavsky, Mol. Biol. 7 (1973) 151.
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[32] [33]
[34]
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L.S. Lerman, Cold Spring Harbor Sym. 38 (1974) 59. U.K. Laemmli, Proc. Natl. Acad. Sci. USA 72 (1975) 4288. D.E. Olins, A.L. Olins, J. Mol. Biol. 57 (1971) 437. D.J. Clark, J.O. Thomas, J. Mol. Biol. 187 (1986) 569. M. Garcia-Ramirez, J.A. Subirana, Biopolymers 34 (1994) 285. Y. Matsuzawa, K. Yoshikawa, Nucleosides Nucleotides 13 (1994) 1415. Y. Yoshikawa, K. Yoshikawa, FEBS Lett. 361 (1995) 277. M. Takahashi, K. Yoshikawa, V.V. Vasilevskaya, A.R. Khokhlov, J. Phys. Chem. B 101 (1997) 9396. S.M. Melnikov, V.G. Sergeyev, K. Yoshikawa, J. Am. Chem. Soc. 117 (1995) 2401. K. Yoshikawa, S. Kidoaki, V.V. Vasilevskaya, A.R. Khokhlov, Ber. Bunsenges. Phys. Chem. 100 (1996) 876. K. Yoshikawa, Y. Yoshikawa, Y. Koyama, T. Kanbe, J. Am. Chem. Soc. 119 (1997) 6473. C.W. Tabor, H. Tabor, Annu. Rev. Biochem. 53 (1984) 749. S. Sarhan, N. Seiler, Biol. Chem. H-S 370 (1989) 1279. Y. Matsuzawa, Y. Yonezawa, K. Yoshikawa, Biochem. Biophys. Res. Commun. 225 (1996) 796. G. Bernardi, B. Olofsson, J. Filipski, M. Zerial, J. Salinas, G. Cuny, M. Meunier-Rotival, F. Rodier, Science 228 (1985) 953. H. Murayama, K. Yoshikawa, J. Phys. Chem. 103 (1999) 10517. A.Yu. Grosberg, A.R. Khokhlov, Statistical Physics of Macromolecules, American Institute of Physics, New York, 1979. V.G. Sergeyev, S.V. Mikhailenko, O.A. Pyshkina, I.V. Yaminsky, K. Yoshikawa, J. Am. Chem. Soc. 121 (1999) 1780. Y. Yamasaki, K. Yoshikawa, J. Am. Chem. Soc. 119 (1997) 10573.
Chemical Physics Letters 354 (2002) 354–359 www.elsevier.com/locate/cplett
All-or-none folding transition in giant mammalian DNA Kenichi Yoshikawa
a,*
, Yuko Yoshikawa b, Toshio Kanbe
c
a Department of Physics, Kyoto University & CREST, Kyoto 606-8502, Japan Department of Food and Nutrition, Nagoya Bunri College & CREST, Nagoya 451-0077, Japan Laboratory of Medical Mycology, Research Institute for Disease Mechanism and Control, Nagoya University School of Medicine, Nagoya 464-0064, Japan b
c
Received 7 November 2001; in final form 16 January 2002
Abstract Using fluorescence microscopy, we studied the folding transition induced by spermidine (3+) in individual giant DNAs isolated from pig liver, with an average size of 60 kbp varying between 15 and 150 kbp. We found that individual DNA chains undergo a large discrete transition, or switching, from an elongated coil state to a folded compact state. Interestingly, the width of the region of coexistence is rather narrow with respect to the spermidine concentration, despite the polydispersity of the DNA specimen. The weak dependence of the manner of the folding transition on molecular weight is discussed based on a simple mean-field theory. Ó 2002 Elsevier Science B.V. All rights reserved.
1. Introduction The compaction of DNA is a common feature in native genomes, e.g., in chromatin or phage heads. The manner of such packaging is expected to play an essential role in the biological functions of DNA, such as replication and transcription [1,2]. Many studies have shown that in vitro compaction of DNA can be generated by various chemical agents [3,4]. Polyamines [5–10], metal cations [11–15], neutral polymers [16–18], polypeptides [18] and basic proteins [19–21] have all been found to be very efficient condensing agents. However, most of these studies were performed
*
Corresponding author. Fax: +81-75-753-3779. E-mail address: [email protected] (K. Yoshikawa).
without a clear distinction between single-molecule packing and multi-chain aggregation. It seems to have been thought, at least until the mid-1990s, that a single-chain event could be realized only under idealized conditions with an infinitely dilute concentration of DNA [3,4]. We have recently made direct observations on the conformational change of long duplex T4 phage DNA molecules with a monodisperse size distribution (166 kbp, 57 lm in usual buffer [22]) using fluorescence microscopy. The common characteristics of the folding transition in single giant T4 DNA molecules induced by several kinds of condensing agents [23–27] can be summarized as follows: (1) Individual DNA molecules exhibit an all-or-none transition between an elongated coil and a compacted globule. (2) The transition diagram shows a region where the coil and globule states coexist. Thus, the folding transition appears
0009-2614/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 ( 0 2 ) 0 0 1 3 7 - 9
K. Yoshikawa et al. / Chemical Physics Letters 354 (2002) 354–359
355
to be steep but continuous for the ensemble average of DNA molecules. In the present study, the folding transition of mammalian DNA isolated from pig liver with a polydisperse size distribution was examined. We used a trivalent polyamine, spermidine, as the condensing agent. The polyamines putrescine, spermidine and spermine are present in millimolar concentrations in both eukaryotic and prokaryotic cells, where they stabilize compacted DNA molecules and also modulate the transcriptional activity of DNA [1,28,29]. The purpose of the present study is to determine (1) whether the manner of the transition at the level of individual molecules is the all-or-none type, (2) how the ensemble of mammalian DNAs behaves when treated with a condensing agent, and (3) whether there is any significant difference between mammalian and phage DNAs that might reflect the difference in the base composition (the GC content in T4 DNA (ca. 36%) [30] is considerably lower than that in mammalian DNA (ca. 42%) [31]).
2. Experimental 2.1. Isolation of DNA from pig liver To obtain a long DNA sample, we used a gentle procedure without centrifugation as follows. (i) Frozen pig liver was ground into pieces and then homogenized with a small amount of 10 mM Tris–HCl/1 mM EDTA buffer solution at pH 7.4. (ii) NaCl (2 M) was added to the homogenate and the suspension was heated at 60–70 °C in a water bath to denature protein components. (iii) Heat-denatured protein was removed by filtration. (iv) After filtering and cooling, the supernatant was mixed with two volumes of cold ethanol to precipitate DNA fibers. To purify the isolated DNA, steps (ii)–(iv) were repeated. The 260=280nm ratio of the final DNA samples was 1.85. The size of DNA was evaluated by fluorescence microscopy, where individual DNA molecules were stretched under shear stress and attached to a glass surface (Fig. 1c). The average full-stretch length was ca. 20 lm (60 kbp), and varied between 5 and 50 lm. These samples were stored in
Fig. 1. Fluorescence microscopic images of pig DNA. (a) Elongated coil state in bulk aqueous solution. (b) Folded compact state in solution with 1 mM spermidine. (a0 ) and (b0 ) Quasi-three-dimensional representations of (a) and (b), respectively. (c) Stretched and fixed specimen on a glass surface.
10 mM Tris–HCl buffer solution with 1 mM EDTA at pH 7.4 until use. 2.2. Fluorescence microscopic measurements For fluorescence microscopic measurements, DNA samples were dissolved in 10 mM Tris–HCl buffer solution with 50 mM NaCl, 10 mM MgCl2 and 1 mM dithiothreitol (DTT) at pH 7.5. The fluorescent dye 40 ,6-diamidino-2-phenylindole (DAPI) was added to the DNA solution at a final DNA concentration of 1 lM in nucleotide units. Compaction was induced by the addition of spermidine to the DNA solution. The concentration of spermidine varied from 0.3 to 6 mM. Fluorescence DNA images were obtained using an
356
K. Yoshikawa et al. / Chemical Physics Letters 354 (2002) 354–359
Axiovert 135 TV microscope (Carl Zeiss, Germany) equipped with a 100 oil-immersion objective lens and a high-sensitivity Hamamatsu SIT TV camera, which allowed images to be recorded on videotape. The video images were analyzed with an Argus 20 image processor (Hamamatsu Photonics, Hamamatsu, Japan). Observations were performed at room temperature (ca. 20 °C). 2.3. Electron microscopic measurements Samples used for electron microscopy were mounted on carbon-coated copper grids (#200), negative-stained with 1% uranyl acetate, and observed with a transmission electron microscope (JEOL 1200EX, Tokyo) at 100 kV.
3. Results Fig. 1 shows fluorescence images of pig DNA molecules. Individual duplex DNA molecules exist as elongated random coils in the buffer solution (Fig. 1a) and transform into a collapsed globule in the presence of 1 mM spermidine (Fig. 1b). This experimental tool provides insight into the solution structure of DNA and reveals a clear difference between the coil and folded states in individual DNA molecules [23–27]. We examined the effect of the spermidine concentration on the higher order structure of DNAs at a fixed concentration of DNA (1 lM in nucleotide units). Fig. 2 shows the distribution of the long-axis length L at different concentrations of spermidine, together with a classification of the morphology (elongated coil or folded compact). L is the apparent long-axis length without correction for the blurring effect of the image in fluorescence microscopy [23]. All of the DNA molecules have an elongated conformation at up to 0.6 mM spermidine. At 0.8 mM spermidine, both the elongated and compact states coexist in the same solution. When the spermidine concentration is greater than 1 mM, all of the DNAs have a folded compact conformation. The change in the mean long-axis length is depicted in Fig. 3, indicating the large discreteness on the transition. Such tightly packed DNAs stay in solution and avoid both multi-chain aggregation and precipi-
Fig. 2. Distribution of long-axis length L of pig liver DNA dependent on the spermidine concentration.
Fig. 3. The mean long-axis length in coil and compact states, depending on the spermidine concentration.
K. Yoshikawa et al. / Chemical Physics Letters 354 (2002) 354–359
tation onto the glass surface, for at least several tens of minutes. Based on the experimental data, the long-axis length L of elongated DNAs is evaluated to be 2:4 lm, with a distribution between 1.4 and 4:0 lm. On the other hand, the long-axis length of the compact form is about 0:7–0:8 lm, indicating the formation of a tightly packed structure. By analyzing the Brownian motion of individual fluorescent objects of compact DNAs, we estimate that the compact DNA measures about 0:1–0:2 lm or even smaller. This means that there is a more than 10 000-fold change in the effective volume between the elongated and compact states. To characterize the morphology of pig liver DNA-spermidine complexes, we used electron microscopic observation at a DNA concentration of 80 lM. Fig. 4 shows that when the spermidine
Fig. 4. Transmission electron micrographs of pig liver DNA with 3 mM spermidine.
357
concentration is 3 mM, pig DNAs are condensed into compact structures, toroids or rods with end loops. The characteristic size of these compact structures, thus, corresponds to that evaluated from the Brownian motion observed by fluorescence microscopy.
4. Discussion Individual pig liver DNA undergoes a discrete conformational transition, or switching, between an elongated coil state and a folded compact state, similar to the conformational change observed in T4 phage DNA [23,24]. The folding transition for the ensemble of chains is rather narrow despite the polydispersity of DNA, indicating that the folding transition of giant DNAs is insensitive to the molecular size. Since polydispersity among giant DNA molecules is a rather common feature in specimens isolated from living cells, this finding of a rather narrow region of coexistence may be useful for the future development of an experimental technology in biological science. In the present study, we used spermidine, a trivalent cation, as the condensing agent. The mechanism of folding of long DNA chains induced by spermidine is explained as follows [24,26,32]: Before the folding transition, where the spermidine concentration is low (less than 0.8 mM), the degree of binding of spermidine to DNA is rather small. This is supported by the fact that the size distribution of elongated DNAs remains approximately the same for spermidine concentrations of 0, 0.3, and 0.6 mM, as shown in Figs. 2 and 3. In the coexistence region (e.g., at 0.8 mM), folded DNA exists in a compact state accompanied by the enhanced binding of spermidine. It is to be noted that the folded compact DNA molecules do not aggregate or condense each other at least during the period of observation on the order of several hours. In polymer science, it has been generally thought that a polymer chain has a compact form in a ‘poor solvent’; i.e., compact chains only exist in an infinitely diluted solution and they should aggregate and precipitate in a ‘poor solvent’ [33]. In contrast to this, the folded compact DNA behaves as a kind of solvable colloidal particle in a
358
K. Yoshikawa et al. / Chemical Physics Letters 354 (2002) 354–359
‘poor solvent’, due to the surviving negative charge on the surface [34]. Let us discuss why the nature of this transition is insensitive to the diversity in molecular size. Since we have given a rather detailed theoretical discussion elsewhere [24,26,35] including the effect of counter ions, we would like to discuss only the essence of the all-or-none folding transition, in relation to chain stiffness. We consider the difference in free energy, DF , between the elongated coil state, Fc , and the compact packed state, Fp , in a polymer chain with N segments:
From Eqs. (1), (2), (4), and (5) we get DF lnð8nN 1=2 Þ ðn ln H þ bÞN :
ð6Þ
We consider the case of DF ¼ 0, where the variables are N and H n ln H þ b ¼ N 1 lnð8nN 1=2 Þ:
ð7Þ
where ‘elas’ and ‘int’ indicate the elastic and interaction terms, respectively. We introduce the equilibrium swelling coefficient a, where a ¼ 1 corresponds to the ideal chain. By using the swelling ratio ap in the compact state, the elastic term in kT units can be approximated as [33]
Under the buffer conditions in the present study, the segment length ‘ 100 nm [22]. Since the effective radius of DNA, including the thickness of the ionic effect, is between 1 and 2 nm, we tentatively take r ¼ 1:5 nm. In our experiments, the size of DNAs is between 15 and 150 kbp, corresponding to N values between 50 and 500. We denote the ligand concentrations as H50 and H500 , where the free energies of the coil and compact states are the same for DNA chains with N ¼ 50 and 500, respectively. From the above discussion,
DFelas 3 ln ap :
n lnðH50 =H500 Þ 0:19:
DF ¼ Fp Fc ¼ DFelas þ DFint ;
ð1Þ
ð2Þ
Next, we introduce a stiffness parameter n as the ratio between the pseudo excluded volume vS of a sphere with a diameter of segment length ‘ and the effective excluded volume vK of a segment with radius r. n ¼ vS =vK ¼ ðp‘3 =6Þ=ðpr2 ‘Þ ¼ ‘2 =6r2 :
ð3Þ
For simplicity, we assume spherical symmetry for the folded compact state. While this assumption is strictly not precise, the following discussion is still valid at a semi-quantitative level. Since the volume in the compact state is given as vK N and the radius of an ideal chain is expressed as R ‘N 1=2 , a3p n1 N 1=2 =8:
ð4Þ
In the folded compact state, the segments exhibit ordered packing. Thus, the stabilization energy is considered to be roughly proportional to N. By introducing the concentration, H, of a ligand (spermidine in our case), the interaction term is [32,35] DFint ðn ln H þ bÞN ;
ð5Þ
where n and b reflect the number of binding ligands per segment and the degree of stabilization in the compact ordered sate, respectively.
ð8Þ
In double-stranded DNA, there are ca. 700 phosphate groups per segment. If we tentatively consider that n ¼ 10, the ratio of the concentrations is calculated as H50 =H500 1:02:
ð9Þ
This condition corresponds to the formation of ion-pairs for up to 4% of the phosphate moieties on the DNA chain. With a more plausible choice for this parameter, if n is larger than 10 [32], the relative ratio becomes smaller. Fig. 3 shows that the spermidine concentration in the region of coexistence between the coil and compact states ranges between 0.7 and 0.9 mM. Thus, the ratio between the minimum and maximum is 0:9=0:7 1:3. The width of the coexistence region almost corresponds to that observed for monodisperse T4 DNA [24], indicating that the effect of polydispersity of the DNA sample is minute on the diagram of the folding transition. As an additional remark, it is to be mentioned that the above theoretical framework does not hold for short oligomeric DNA molecules, i.e., the marked discrete nature of the folding transition should disappear for DNA less than several kbp.
K. Yoshikawa et al. / Chemical Physics Letters 354 (2002) 354–359
Acknowledgements This work was supported in part by a Grant-inAid for Science Research from The Ministry of Education, Science, Sports and Culture of Japan.
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