Experiments on the bacterial nucleoid of Escherichia coli viewed as a physical entity

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(1)Experiments on the bacterial nucleoid of Escherichia coli viewed as a physical entity.

(2) Cover: Phase contrast and fluorescence images of Escherichia coli cells and nucleoids before and after cell lysis..

(3) Experiments on the bacterial nucleoid of Escherichia coli viewed as a physical entity. Proefschrift ter verkrijging van de graad van doctor aan de Technische Universiteit Delft, op gezag van de Rector Magnificus, prof. dr. ir. J. T. Fokkema, voorzitter van het College voor Promoties, in het openbaar te verdedigen op maandag 4 oktober 2004 om 10:30 uur door Sónia Maria DO MAR PEREIRA DA CUNHA Bioquímica, Universidade do Algarve, Faro, Portugal geboren te Porto, Portugal.

(4) Dit proefschrift is goedgekeurd door de promotor: Prof. dr. T. Odijk Samenstelling promotiecommissie: Rector Magnificus. voorzitter. Prof. dr. T. Odijk. Technische Universiteit Delft, promotor. Dr. C. L. Woldringh. Universiteit van Amsterdam, supervisor. Prof. dr. S. de Vries. Technische Universiteit Delft. Prof. dr. ir. M.-O. Coppens. Technische Universiteit Delft. Prof. dr. H. Lekkerkerker. Utrecht Universiteit. Prof. dr. D. Williams. Australian National University. Prof. dr. J.-L. Sikorav. CEA/ Saclay, France. ISBN: 90-77595-77-5.

(5) Contents I General Introduction 1.1 The bacterial nucleoid. 7. 1.2 Structure of the DNA. 9. 1.3 Factors contributing to DNA compaction in vivo. 11. II Macromolecular interactions 2.1 Brownian motion and the kinetic theory of gases. 19. 2.2 Brownian motion of colloids and osmotic pressure. 23. 2.3 Brownian motion of colloids in concentrated suspensions. 24. 2.4 Statistical properties of long polymers. 28. 2.5 Physical forces shaping the E. coli nucleoid. 32. 2.6 Outline and motivation. 38. III Isolation of the Escherichia coli nucleoid: an overview of nucleoid isolation. 41. methods IV Polymer mediated compaction and internal dynamics of isolated E. coli. 55. nucleoids V Expansion of Escherichia coli nucleoids released by osmotic shock. 97. VI Confined diffusion of DNA segments within the isolated Escherichia coli. 107. nucleoid VII Effects of magnesium on the hydrodynamic properties of supercoiled DNA. 121. Summary. 129. Samenvatting. 133. Acknowledgments. 137. Curriculum vitae. 139.

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(7) I General Introduction. In this thesis we focus on the compaction of DNA within Escherichia coli and aim to gain some understanding of the physical mechanism behind its spatial organization in the cell. In this introductory chapter we review current knowledge of the E. coli nucleoid. In chapter II we deal with a recent model that attempts to describe nucleoid formation in terms of an entropy-driven phase separation process and we provide a description of physical concepts necessary to understand the phenomenon of phase separation in binary mixtures. 1.1. The bacterial nucleoid. Being the carrier of the genetic information in all known living cells, DNA can be considered as one of the most essential polymers in life. DNA is a highly negatively charged polymer, so that strong repulsion between adjacent nucleotides may contribute to the DNA double helix locally adopting a straight rod conformation (Fig. 1.1).. 50 nm Fig. 1.1 Schematic drawing of the DNA double helix. Long DNA molecules can be represented as a slender polymer chain characterized by a persistence length C equal to 50 nm..

(8) DNA maintains more or less the same direction over a distance of 50 nm (Taylor and Hagerman, 1990) and belongs for that reason to the class of socalled semi-flexible polymers that show a fairly high resistance to bending. Nevertheless, in most biological systems DNA molecules are bent and folded into compact states, which are several orders of magnitude smaller than the contour length of the double helix (Table 1.1). The E. coli chromosome, for example, has a contour length of about 1.6 mm, yet the DNA is confined into a structure only about 1 µm long (Valkenburg and Woldringh, 1984). The DNA length in the bacterial virus (bacteriophage) T7 is circa 14 µm, yet the DNA is packed in a virus capsid of about 55 nm in diameter (Steven and Trus, 1986). In the case of human cells, a 1 m long genome is confined into a nucleus of about 10 µm diameter (Table 1.1). Table 1.1 DNA dimensions in biological systems.. DNA length (bp). DNA length (µm). Diameter confining compartment (µm). E. coli. 4.6*106. 1.6*103. 1. 1.61*103. Human. 2.91*109. 9.9*105. 10. 9.89*104. T7 bacteriophage. 4.0*104. 14. 5*10-2. 2.8*102. linear compaction factor. The mechanisms available to achieve similar degrees of DNA compaction in vitro are diverse (see for a review Bloomfield, 1996, 1997). Collapse of DNA into highly compact and organized structures such as toroids may be accomplished by the addition of natural polyamines including spermine4+ or spermidine3+ (Pelta et al, 1996). Likewise, basic proteins such as DNAbinding proteins and histones also promote DNA compaction (Dame et al, 2001; Garcia-Ramirez and Subirana, 1994). Moreover, under physiological concentrations of monovalent salts, addition of crowding agents such as polyethylene glycol (PEG) and albumin induce the collapse of DNA (Yoshikawa and Matsuzawa, 1995; Adrian et al, 1990; Vasilevskaya et al, 1995; Laemmli, 1975; Lerman, 1971; Cunha et al, 2001b, this thesis, Chapter IV).. 8.

(9) Although the mechanisms to achieve DNA compaction are diverse, each organism must have evolved by acquiring a DNA-packing mechanism adapted to its biological requirements. Within virus capsids, for instance, DNA is kept in such a tightly packed state that it is suggested that the DNA is present in a hexagonal crystalline phase (Cerritelli et al, 1997). Such a static picture of viral DNA is not unexpected if we take into account that much of virus biogenesis (DNA replication, capsid assembly etc.) occurs outside the capsid and at the cost of the biochemical machinery of the bacterial host. On the other hand, in eukaryotic and prokaryotic cells the genome is involved in cellular processes such as replication, transcription and segregation. Furthermore, sudden changes in environmental conditions require rapid modifications in the pattern of gene expression. In contrast to viruses, chromosomes have to be rapidly remodeled or organized according to the requirements of transcription. Obviously, these processes demand a very dynamic and flexible genome structure. In this thesis, we investigate the behavior of the E. coli chromosomal DNA from a physical point of view. Our objective is to present experiments and their analysis, which, we hope, will improve our comprehension of the mechanism behind DNA confinement within the bacterial cell. 1.2 Structure of the DNA DNA in the B-form is a non-branched polymer present in biological systems as two anti-parallel DNA strands that wind about a common axis to form a right-handed double helix (Fig. 1.2 A). In aqueous solutions the phosphate groups are dissociated conferring a characteristic highly negative charge to the DNA molecule. In 1953, Watson and Crick postulated the B-DNA conformation, characterized by a helical pitch (h) containing 10.5 bp or a rise of 3.5 nm per helical turn (Fig. 1.2 A). The linking number (Lk) is the variable that quantifies the number of times the two DNA strands are rotated about each other in a certain circularly closed configuration. The Lk of a relaxed DNA molecule (Lk0) is by definition positive. 9.

(10) #. $. PO CPO PO. Z. Fig. 1.2 Schematic representation of the right-handed B-DNA molecule (adapted from “The bacterial cell cycle”, Chapter 2 Woldringh, CL, to be found at http://wwwmc.bio.uva.nl/~conrad/cellcycle/book/chap2.pdf). A. The relaxed double helix has a 2 nm diameter, a pitch of 3.5 nm and a superhelical density Lk0. For simplicity long DNA chains can be represented as a slender rod, characterized by the persistence length C . Details such as base sequences are disregarded. B. Undertwisting the DNA molecule in a left-handed way results in the formation of righthanded supercoils: in this example 6 turns are introduced which is approximately equivalent to a writhe Wr=-6.. and equal to the total number of base pairs N, divided by the number of base pairs, γ, per turn of the double helix. For relaxed circularly closed DNA, the linking number is identical to the twist (Tw): Lk0= N/ γ = Tw. In many biological systems, DNA is in fact present as a circular double helix. In E. coli the DNA occurs in an underwound conformation so that Lk < Lk0. The DNA is then under internal torsional stress which it releases, in part, by adopting a so-called supercoiled conformation (Fig. 1.2 B). The Lk of a supercoiled DNA molecule is thus characterized by the sum of two disparate variables: the twist (Tw) or the number of times the strands are wound around each other and the writhe (Wr) reflecting the shape of the molecule as a whole: Lk = Tw+Wr. Since Wr is zero in the relaxed state, the excess linking number (∆Lk) equals:. 10.

(11) ∆Lk = Lk- Lk0 = ∆Tw, ∆Lk can be positive or negative depending on the over- or underwound state of the molecule. Dividing ∆Lk by Lk0 we define the relative difference in Lk between supercoiled and relaxed forms of DNA or the specific linking difference σ: σ = ∆Lk/ Lk0, a quantity that is independent of the contour length. For overwound DNA, σ is positive and for underwound DNA, σ is negative. Plasmid DNA isolated from E. coli often has a typical linking number deficit of about 5% and therefore a σ of –0.05 (Bauer, 1978). 1.3 Factors contributing to DNA compaction in vivo E. coli is a rod shaped Gram-negative bacterium and its genome consists of a closed circular DNA molecule with a contour length of 1.6 mm or 4.6*106 base pairs (Blattner et al, 1997). Being several hundred times longer than the cell the chromosome is folded into a so-called nucleoid occupying a fraction of the intracellular space (Mason and Powelson, 1956; Valkenburg and Woldringh, 1984). Already in 1976, Kavenoff and Bowen showed that right after its release from the cell envelope, the nucleoid expands reaching 10 times its initial size within a fraction of a second (see also Chapter V). One can therefore speculate about what kind of compacting forces cease to exist as soon as the cell is ruptured. The characterization of these forces has been a subject of attention for many years. During the past decades, several groups have developed protocols to isolate folded nucleoids in such a way that its structural integrity seems to be preserved. Much of what we know about nucleoid structure is based on biochemical studies performed on these isolated structures (for reviews see Pettijohn, 1996; Cunha et al, 2001a, this thesis, Chapter III). Considering the topology of the bacterial DNA, the macromolecular composition of the nucleoids, and the macromolecular. 11.

(12) composition of the cytoplasm, one suspects that three major factors could contribute to the structure of the nucleoid: 1) supercoiling, 2) binding of polyamines and DNA–binding proteins, 3) macromolecular crowding. Below, we explore the role of each of these three factors. 1.3.1 Supercoiling Isolated nucleoids are negatively supercoiled as evident from the biphasic behavior of their sedimentation rates to increasing concentrations of ethidium bromide (Stonington and Pettijohn, 1971; Worcel and Burgi, 1972; Sloof et al, 1983; Drlica and Worcel, 1975). The characteristic superhelical density σ of the nucleoid of about –0.05 (Bauer, 1978) results from the balanced action of two major topoisomerases: gyrase and topo I (Drlica and Woldringh, 1998). Gyrase inserts negative supercoils at the expense of ATP (Gellert et al, 1976) while topo I relaxes supercoils (Wang, 1971). About half of the negative supercoils are restrained after experiments involving DNA nicking and repairing in vivo while gyrase is inhibited, so that the effective σ is about – 0.025 (Pettijohn and Pfenninger, 1980; Sinden et al, 1980). These restraints are believed to result from the action of a group of low molecular weight and basic proteins, the so-called DNA binding proteins. They co-localize in vivo with the nucleoid (Talukder et al, 2000) and are also bound to isolated nucleoids (Murphy and Zimmerman, 1997). Evidence for their role in affecting DNA topology has been collected from both in vivo and in vitro experiments. For instance, H-NS binds to DNA templates in a more or less sequence independent manner and can both restrain and crosslink supercoils in vitro (Tupper et al, 1994; Dame et al, 2001). This finding is consistent with the fact that H-NS mutants have increased chromosomal negative supercoiling (Mojica and Higgins, 1997). Supercoiling forces DNA molecules to assume more compact interwound conformations (Boles et al, 1990) and for long supercoiled DNA molecules branching. occurs. for. entropic. reasons. (Marko. and. Siggia,. 1995).. Nevertheless, recent theoretical work shows that even taking branching into account, supercoiling alone cannot explain the tiny dimensions of the nucleoid inside the cell because of the excluded-volume effect (concept introduced in. 12.

(13) Chapter II) (Cunha et al, 2001b, this thesis, Chapter IV). That supercoiling is not the only factor contributing to nucleoid formation is apparent from the fact that the nucleoid volume increases only slightly after inhibition of gyrase (Stuger et al, 2002). Physiological levels of supercoiling are, however, essential for cellular processes such as DNA decatenation and nucleoid partitioning (Zechiedrich et al, 1997; Kato et al, 1989). Also computer simulations and in vitro experiments with 3.5 kb plasmids show that physiological levels of supercoiling decreases the probability of entanglement by a factor of 30 (Rybenkov et al, 1997). 1.3.2. Binding of polyamines and DNA–binding proteins DNA-binding proteins and natural polyamines (spermidine 3+ and spermine 4+) can be considered to be compacting agents because they decrease repulsive electrostatic interactions between DNA segments. With the exception of manganese 2+, condensation of supercoiled DNA can only be induced by cations with valence 3+ or greater (Bloomfield, 1997). However, the condensing effect of spermidine 3+ decreases considerably at Na+ concentrations greater than 100 mM, making its contribution to DNA compaction at intracellular ionic strengths less relevant (Pelta et al, 1996). DNA condensation by spermine on the other hand is not inhibited at physiological Na+ concentrations (Pelta et al, 1996), but its cellular concentration is believed to be low (Cayley and Record, 1991). Sedimentation analysis of isolated nucleoids supported the idea that the compact state of the isolated nucleoid is stabilized by protein and RNA molecules, as RNase and proteinase K treatments unfolded the isolated nucleoids (Stonington and Pettijohn, 1971; Drlica and Worcel, 1975; Worcel and Burgi, 1972, Pettijohn and Hecht, 1973). However, Sinden and Pettijohn (1981) could not observe any changes in the sedimentation properties in nucleoids isolated after treating the cells with rifampicin, an agent that inhibits RNA synthesis. Likewise, Sloof et al, (1983) confirmed that the compact structure of nucleoids isolated by osmotic shock was sensitive to proteinase K but found no evidence for the stabilizing role of RNA. The authors suggested that the previous observations could be an artifact of the nucleoid isolation procedure (see for a review Cunha et al, 2001a, this thesis, Chapter III). In 13.

(14) addition, our microscopy studies revealed that proteinase K is able to partially unfold the isolated nucleoids, suggesting that protein-DNA interactions do play an important role in the stabilization of the isolated nucleoid structure (unpublished observations). Previous studies have shown that the major proteins bound to the isolated nucleoid are FIS, HU, H-NS, IHF, and RNA polymerase (Murphy and Zimmerman, 1997). The fact that DNA-binding proteins can compact, bend and crosslink DNA in vitro (Dame et al, 2001; Teter et al, 2000; Tupper et al, 1994) led to the conclusion that this class of proteins could play a role in nucleoid compaction (see for review Pettijohn, 1996). Nevertheless, to date visualization of protein-DNA complexes resembling crosslinks in vivo or in isolated nucleoids have never been reported. On the contrary, most of the DNA-binding proteins seem to be uniformly distributed within the entire nucleoid (Talukder et al, 2000). Furthermore, nucleoids isolated from mutants lacking one of the major DNA binding proteins have the same domain organization as those in wild type cells (Brunetti et al, 2001). Therefore, based on the available experimental data, the contribution of DNA-binding proteins to nucleoid compaction both in vivo and in vitro is still elusive. In fact, DNA binding proteins are increasingly suggested to play the role of global regulators adjusting DNA topology to modulate gene expression to cellular physiological needs. The role of other proteins such as structural maintenance of chromosome (SMC) proteins has received much attention lately. In E. coli about 150 copies of the SMC protein MukB are present, which localize in the nucleoid region as discrete foci (Kido et al., 1996; den Blaauwen et al, 2001). The MukB protein consists of a N- (ATP-binding) and C- (DNA-binding) domain separated by a long coiled domain. In vitro it forms an anti-parallel dimer, which, when fully stretched, is about 100 nm long (Melby et al, 1998). It is thus plausible that MukB is able to bind two distant DNA chains and hence crosslink the DNA. Nevertheless, MukB mutants are repressed by topoisomerase I mutants that cause an increase in negative supercoiling resulting from gyrase A activity (Sawitzke and Austin, 2000). We may therefore conclude that, at least in vivo, the crosslinking action of MukB is not essential to DNA compaction. Instead, its role in maintaining chromosomal supercoiling levels seems to be more 14.

(15) relevant. To date no localization studies in isolated nucleoids have been performed. 1.3.3. Macromolecular crowding The phenomenon of phase separation in crowded suspensions containing at least two kinds of macromolecules has been the subject of many reports (Lerman, 1971; Laemlli, 1971; Wang et al, 2001; de Vries, 2001). A solution is called crowded if a significant fraction of the total volume is taken up by macromolecules (typically 20- 30%). The interior of E. coli can be considered to be crowded because besides DNA, proteins and RNA are present in concentrations of 300-400gl-1 that take up ~ 40% of the intracellular space (Zimmerman and Trach, 1991). In 1984 Valkenburg and Woldringh provided the first quantitative indication for the existence of a phase separation in vivo. Basing their inferences on differences in refractive indices, the authors showed that in E. coli a high (interpreted as being the cytoplasm) and a low protein-containing phase (interpreted to be DNA/ nucleoid phase) coexisted. More recently, analytical work based on excluded-volume and other interactions between proteins and DNA has led to quantitative predictions of the nucleoid dimensions inside the E. coli cell. To test this theory, we have explored the effects of excludedvolume interactions by monitoring the behavior of isolated nucleoids at various concentrations of the neutral polymer polyethylene glycol (PEG). We were able to estimate the free energy of the isolated nucleoid ( (P ) when compacted to intracellular dimensions (Cunha et al, 2001b, this thesis, Chapter IV), which turns out to be in good agreement with the (P calculated by Odijk (1998). Above we have introduced a number of physico-chemical concepts with which most of the readers in the bacterial field are not acquainted. The aim of the next chapter is to provide these readers with concepts bearing on the experiments presented in Chapters IV, V and VI. Chapter II is based on lectures given by Prof. Theo Odijk to Chemical Enginearing students during their second year of university.. 15.

(16) REFERENCES Adrian, M., ten Heggeler-Bordier, B., Wahli, W., Stasiak, A.Z., Stasiak, A. and Dubochet, J. (1990) Direct visualization of supercoiled DNA molecules in solution. EMBO J. 9, 4551-4554. Bauer, W. (1978) Structure and reactions of closed duplex DNA. Annu. Rev. Biophys. Bioeng. 7, 287–313. den Blaauwen, T., Lindqvist. A., Löwe, J. and Nanninga, N. (2001) Distribution of the Escherichia coli structural maintenance of chromosomes (SMC)-like protein MukB in the cell. Molec. Microbiol. 42, 1179- 1188. Blattner, F., Plunkett, G., Bloch, C., Perna, N., Burland, V., Riley, M., ColladoVides, J., Glasner, J., Rode, C., Mayhew, G., Gregor, J., Davis, N., Kirkpatrick, H., Goeden, M., Rose, D., Mau, B. and Shao, Y. (1997) The complete genome sequence of Escherichia coli K-12. Science 277, 14531474. Bloomfield, V. (1996) DNA condensation. Curr. Op. in Struct. Biol. 6, 334-341. Bloomfield, V. (1997) DNA condensation by multivalent cations. Biopolymers 44, 269-281. Boles, T., White, J. and Cozzarelli, N. (1990) Structure of plectonemically supercoiled DNA. J. Mol. Biol. 213, 931–951. Brunetti, R., Prosseda, G., Beghetto, E., Colonna, B. and Micheli. G. (2001) The looped domain organization of the nucleoid in histone-like protein defective Escherichia coli strains. Biochimie 83, 873-882. Cayley, S., Lewis, B. A., Guttman, H. J. and Record, M. T. Jr. (1991) Characterization of the cytoplasm of Escherichia coli K-12 as a function of external osmolarity. Implications for protein-DNA interactions in vivo. J. Mol. Biol. 222, 281-300. Cerritelli, M., Cheng, N., Rosenberg, A., McPherson, C., Booy, F. and Alasdair, S. (1997) Encapsidated Conformation of Bacteriophage T7 DNA. Cell 91, 271-280. Cunha, S., Odijk, T., Sueleymanoglu, E. and Woldringh, C. L. (2001a) Isolation of the Escherichia coli nucleoid. Biochimie 83, 149–154. Cunha, S., Woldringh, C. and Odijk, T. (2001b) Polymer-mediated compaction and internal dynamics of isolated Escherichia coli nucleoids. J. Struc. Biol. 136, 53-66. Dame, R., Wyman, C. and Goosen, N. (2001) Structural basis for preferential binding of H-NS to curved DNA. Biochimie 83, 231-234. Drlica, K. and Woldringh, C. (1998) Chromosomal organization: nucleoids, chromosomal folding, and DNA topology, in F. de Bruijn, J. Lupski, and G. Weinstock (Eds), Bacterial Genomes: Physical Structure and Analysis, pp 1222. Drlica, K. and Worcel, A. (1975) Conformational transitions in Escherichia coli chromosome: analysis by viscometry and sedimentation. J. Mol. Biol. 98, 393–411. Garcia-Ramirez, M. and Subirana, J. (1994) Condensation of DNA by basic proteins does not depend on protein composition. Biopolymers 34, 285–292.. 16.

(17) Gellert, M., Mizuuchi, M., O’Dea, M. and Nash, H. (1976) DNA gyrase: an enzyme that introduces superhelical turns into DNA. PNAS 73, 3872–3876. Kato, J., Nishimura, Y. and Suzuki, H. (1989) Escherichia coli parA is an allele of the gyrB gene. Mol. Gen. Genet. 217, 178-181. Kavenoff, R. and Bowen, B. (1976) Electron microscopy of membrane-free folded chromosomes from Escherichia coli. Chromosoma 59, 89-101. Kido, M., Yamanaka, K., Mitani, T., Niki, H., Ogura, T. and Hiraga, S. (1996) RNase E polypeptides lacking a carboxyl-terminal half suppress a MukB mutation in Escherichia coli. J. Bact. 178, 3917-3925. Laemmli, U. (1975) Characterization of DNA condensates induced by poly(ethylene oxide) and polylysine. PNAS 72, 4288-4292. Lerman, L. (1971) A transition to a compact form of DNA in polymer solutions. PNAS 68, 1886-1890. Marko, J. and Siggia, E. (1995) Statistical mechanics of supercoiled DNA. Phys. Rev. E 52, 2912-2938. Mason, D. and Powelson, D. (1956) Nuclear division as observed in live bacteria by a new technique. J. Bact. 71, 474–479. Melby, T., Ciampaglio, C., Briscoe, G. and Erickson, H. (1998) The symmetrical structure of structural maintenance of chromosomes (SMC) and MukB proteins: Long, antiparallel coiled coils, folded at a flexible hinge. J. Cell Biol. 742, 1595-1604. Mojica, J. and Higgins, C. (1997) In Vivo Supercoiling of Plasmid and Chromosomal DNA in an Escherichia coli H-NS Mutant. J. Bact. 179, 3528– 3533. Murphy, L. and Zimmerman, S. (1997) Isolation and characterization of spermidine nucleoids from Escherichia coli. J. Struct. Biol. 119, 321-335. Odijk, T. (1996) DNA in a liquid-crystalline environment: Tight bends, rings, supercoils. J. Chem. Phys. 105, 1270-1286. Odijk, T. (1998) Osmotic compaction of supercoiled DNA into a bacterial nucleoid. Biophys. Chem. 73, 23–29. Pelta, J., Livolant, F. and Sikorav, J.L. (1996) DNA aggregation induced by polyamines and cobalthexamine. J. Biol. Chem. 271, 5656–5662 Pettijohn, D. (1996) The nucleoid. In Escherichia coli and Salmonella, Cellular and Molecular Biology (ed. F.C. Neidhart et al) pp. 158-166. American society of Microbiology, Washington, D.C. Pettijohn, D. and Hecht, R. (1973) RNA molecules bound to the folded bacterial genome stabilize DNA folds and segregate domains of supercoiling. Cold Spring Harbor Symp. Quant. Biol. 38, 31-41. Pettijohn, D. and Pfenninger, O. (1980) Supercoils in Prokaryotic DNA restrained in vivo. PNAS 77, 1331-1335. Rybenkov, V., Vologodskii, A. and Cozzarelli, N. (1997) The Effect of Ionic Conditions on the Conformations of Supercoiled DNA. II. Equilibrium Catenation. J. Mol. Biol. 267, 312-323. Sawitzke, J. and Austin, S. (2000) Suppression of chromosome segregation defects of Escherichia coli Muk mutants by mutations in topoisomerase I. PNAS 97, 1671–1676. Sinden, R., Carlson, O. and Pettijohn, D. (1980) Torsional tension in the DNA double helix measured with trimethylpsoralen in living E. coli cells. Cell 21, 773-783.. 17.

(18) Sinden, R. and Pettijohn, D. (1981) Chromosomes in living Escherichia coli are segregated into domains of supercoiling. PNAS 78, 224-228. Sloof, P., Maagdelijn, A. and Boswinkel E. (1983) Folding of prokaryotic DNA: isolation and characterization of nucleoids from Bacillus licheniformis. J. Mol. Biol. 163, 277-297. Steven, A. and Trus, B. (1986) The structure of bacteriophage T7, in J. Harris and Horner (Eds), Electron Microscopy of Proteins: Viral Structures pp. 1–35. Stonington, G. and Pettijohn, D. (1971) The folded genome of Escherichia coli isolated in a protein-DNA-RNA complex. PNAS 68, 6-9. Stuger, R., Woldringh, C., van der Weijden, C., Vischer, N., Bakker, B., van Spanning, R., Snoep, J. and Westerhoff, H. (2002) DNA supercoiling by gyrase is linked to nucleoid compaction. Mol. Biol. Rep. 29, 79-82. Talukder, A., Hiraga, S. and Ishihama, A. (2000) Two types of localization of the DNA-binding proteins within the Escherichia coli nucleoid. Genes to Cells 5, 613-626. Taylor, W. and Hagerman, P. (1990) Application of the method of phage T4 DNA ligase-catalyzed ring-closure to the study of DNA structure. II. NaCldependence of DNA flexibility and helical repeat. J. Mol. Biol. 212, 363–376. Teter, B., Godman, S. and Galas, D. (2000) DNA bending and twisting properties of integration host factor determined by DNA cyclization. Plasmid 43, 73–84. Tupper, A., Owen-Hughes, T., Ussery, D., Santos, D., Ferguson, D., Sidebotham, J., Hinton, J. and Higgins, C. (1994) The chromatin-associated protein H-NS alters DNA topology in vitro. EMBO J. 13, 258–268. Valkenburg, J. and Woldringh, C.L. (1984) Phase separation between nucleoid and cytoplasm in Escherichia coli as defined by immersive refractometry. J. Bact. 160, 1151-1157. Vasilevskaya, V., Khokhlov, A., Matsuzawa, Y. and Yoshikawa, K. (1995) Collapse of single DNA molecule in polyethylene glycol solutions. J. Chem. Phys. 102, 6595–6602. de Vries, R. (2001) Flexible Polymer-induced condensation and bundle formation of DNA and F-actin filaments. Biophys. J. 80, 1186 - 1194. Wang, J. (1971) Interaction between DNA and an Escherichia coli protein. J. Mol. Biol. 55, 523–533. Wang, S., van Dijk, J., Odijk, T. and Smit, J. (2001) Depletion-induced demixing in aqueous protein-polysaccharide solutions. Biomacromolecules 2, 10801088. Worcel A. and Burgi E. (1972) On the structure of the folded chromosome of E. coli. J. Mol. Biol. 71, 127–147. Yoshikawa, K. and Matsuzawa, Y. (1995) Discrete phase transition of giant DNA: Dynamics of globule formation from a single molecular chain. Physica D 84, 220-237. Zechiedrich, E., Khodursky, A. and Cozzarelli, N. (1997) Topoisomerase IV, not gyrase, decatenates products of site-specific recombination in Escherichia coli. Genes Dev. 11, 2580-2592. Zimmerman, S. B., and Trach, S.O. (1991) Estimation of macromolecule concentrations and excluded volume effects for the cytoplasm of Escherichia coli. J. Mol. Biol. 222, 599-620.. 18.

(19) II Macromolecular interactions. 2.1 Brownian motion and the kinetic theory of gases The atoms and molecules in a liquid or gas are in constant thermal motion, continually colliding with each other. The net effect is that molecules move in incessant random motion. This thermal motion has been called Brownian motion after the botanist Robert Brown who in 1827 observed the movement of pollen grains suspended in water. The idea that particles are in incessant motion is the basis of the kinetic theory of gases developed in the 19th century by the physicists J.C. Maxwell and L. Boltzmann. According to this theory, the average kinetic energy < 'MKP > of a particle of mass O moving with a speed X equals:. < ' MKP >= O < X > . (2.1.1).. On the other hand, the kinetic energy is determined by the temperature of the system and given by the expression:. < ' MKP >= M$6 . (2.1.2),. where kB is Boltzmann’s constant ( M $ = 1.38066*10-23 JK-1) and 6 the absolute temperature. When we consider an ideal system consisting of. 0 particles occupying a volume 8 , the total free energy (KF (the subscript KF stands for ideal) may be written as:.

(20) 0  − 0 8. (KF = 0M$ 6 NP . (2.1.3).. We see that the free energy is extensive, i.e. proportional to 0 , but also depends on the particle number density or concentration 0 8 . If the accessible volume 8 increases, the free energy decreases because the number of degrees of freedom or the entropy ( 5 ) of the system increases. Entropy is related to the number of configurations 9 accessible to the system according to the expression:. 5 = M$ NP9. (2.1.4).. It can be shown that for an ideal gas 9 is proportional to its density so that (KF = − 65KF .. Maxwell and Boltzmann related the thermal motion of particles to the macroscopic properties of a gas (e.g. pressure, volume). As a result of their incessant movement, molecules continuously bombard the walls of the container exerting a pressure. The pressure 2 exerted by the particles can be deduced by differentiating the free energy with respect to the volume:. 2=−. ∂ (KF 0 = M $6 ∂8 8. (2.1.5).. This expression is the well-known equation of state of an ideal gas. It reflects the behavior of ideal gases whose molecules are modeled as point particles (having no volume) so that molecular interactions or collisions are neglected. The pressure of an ideal gas is simply proportional to the thermal energy M $6 and to the concentration of the gas particles 0 8 . This expression turns out to be a good approximation for the behavior of a real gas at very low particle density. Under these conditions, the volume taken up by gas particles is very small and the probability of collisions is almost zero. As the particle concentration increases, real gases start deviating from ideality because hard-. 20.

(21) core or excluded-volume interactions will place constraints on particle movement. Excluded-volume interactions come into play due to mutual steric exclusion between particles: two particles cannot occupy the same space at the same time. If gas particles are modeled as neutral hard spheres of radius. T , the distance of closest approach of their centers of mass is T (Fig. 2.1).. r. Fig. 2.1. Illustration of excluded volume between two hard spheres. When two spheres of radius T approach each other their centers of mass are excluded from a total volume given by the co-volume of the spheres β = π T (see text).. . By definition, excluded volume is the volume of solution within which the center of mass of one sphere may not be placed in the presence of another sphere and equals the co-volume. β = π T . β of the two spheres:. (2.1.6).. β (represented by the spherical shell around a test sphere) is related to pairs of interactions, so that the effective volume excluded to one gas particle equals β . A consequence of these hard-core interactions is that the volume available to a given particle of the gas (free volume of the solution) is reduced when compared to that applicable to an ideal gas. We readily anticipate that in a real system the decrease of the entropy 5 will result in an increase in the total free energy, which is proportional to the number of pairs of interactions. In a system consisting of 0 particles there will be 0 (0 − ) pairs of interactions, which for 0 >> can be approximated by 0 . Accordingly, the total excluded volume also referred to as self excludedvolume 8UGNH equals:. 21.

(22) 8UGNH = 0 β . (2.1.7).. After being scaled to the volume 8 occupied by the system and by the thermal energy M $6 , this final expression enters in the equation for the total free energy (VQV with a positive sign:. (VQV = (KF + (UGNH. 0 β 0 = 0M 6 NP( 8 )− 0 + 8 M $6 $. (2.1.8).. To account for higher order interactions (between 3, 4 etc particles) a virial expansion of the equation of state of a real gas in terms of particle number density 0 8 can be carried out. 0 2 0 = + $   M$6 8 8. .  + $  . 0  8. . (2.1.9).. + . Here, $ , $ etc, are the second and third virial coefficients associated with two, three, etc body interactions. Because the probability of collision between 3 or more particles is very small, it follows that the contribution of the different terms of the virial expansion to the total pressure can usually be approximated by considering only the first two terms: ideal + two particle contributions. For spherical particles interacting via excluded volume, $ can usually be set equal to half the excluded-volume. 2 0 β  0  = +   M 6 8 8 . β: (2.1.10).. $. An expression for the total energy (VQV of the system analogous to equation 2.1.8 may be written in terms of 8UGNH :. (VQV = (KF + (UGNH. 22. 8UGNH 0 = 0M 6 NP( 8 )− 0M $6 + 8 M$6 $. (2.1.11)..

(23) 2.2 Brownian motion of colloids and osmotic pressure. A colloidal suspension consists of mesoscopic particles of sizes ranging from about. O. (1 nm) to. O. (103 nm) suspended in a solvent. These size limits. ensure that the particles are much larger than the solvent molecules but are small enough so that gravitational sedimentation does not influence their Brownian motion appreciably. Following the line of reasoning of the kinetic theory of gases, Albert Einstein developed in 1905 the first quantitative theory of Brownian motion for colloidal particles. He argued that as colloidal particles move through a fluid, they are subject to an incessant random bombardment of solvent molecules and thus experience a randomly fluctuating force. As a result, colloids are forced to wander about in all directions, i.e. they execute a random walk or Brownian motion. Since the force exerted by the solvent is random and has no preferred direction, the average displacement in time is zero. The simplest quantity characterizing the motion of a non-interacting Brownian particle is its mean square displacement as a function of time.. < T V − T >= &V. (2.2.1),. where & denotes the colloid diffusion coefficient, a variable commonly used to describe the mobility of particles. Einstein also derived the connection between the diffusion coefficient & and physical quantities such as the absolute temperature, viscosity (η ) and the particle radius. As a particle diffuses through the fluid, it induces a long-range velocity field through the fluid. Viscous drag forces will arise due to shearing between “layers” of the fluid and the particle experiences a retarding frictional force H given by:. H = πηTJ. (2.2.2),. 23.

(24) known as the Stokes relation. In this expression TJ is the hydrodynamic radius of the particle in solution,. η is the viscosity describing the friction or the. resistance to motion felt by a particle. Therefore, a Brownian particle diffusing through a fluid experiences an accelerating force arising from the thermal motion of the solvent molecules, which is balanced by a frictional retarding force H or viscous drag. The balance of these two forces leads to the socalled Stokes-Einstein relation:. &=. M 6 $. (2.2.3).. πη T. J. In non-dilute suspensions, colloidal particles will collide and interact with each other in the course of diffusion. These interactions can be modeled in terms analogous to the kinetic theory of gases. To estimate the osmotic pressure ( π ) exerted by 0 colloidal particles suspended in a solution of volume 8 we make use of the virial equation:. π  0  0 = + $  8  + M 6 8. (2.2.4).. $. This equation is the analogue of eq. (2.1.10) in the kinetic theory of gases. Therefore, the free energy of a colloidal suspension consisting of one species of colloidal particles can be estimated by applying equation 2.1.11 analogously.. 2.3 Brownian motion of colloids in concentrated suspensions In. concentrated. suspensions,. colloidal. particles. interact. through. hydrodynamic, van der Waals, electrostatic and excluded-volume interactions. The dynamic properties of the colloid suspension are then determined by the interplay between Brownian motion and particle-particle interactions, which are now briefly introduced.. 24.

(25) Hydrodynamic interactions Brownian particles influence neighboring particles because, as they diffuse through the solvent, they create a fluid flow. By being perturbed by the sum total of these flows, colloidal particles experience hydrodynamic interactions. Hydrodynamic interactions usually lead to long-range correlations because the fluid velocity decays as 1/r (inverse interparticle distance). Entrapment of a particle between several flow fields works in general as a frictional force and contributes to a decrease in the diffusion rate of the particles. As every particle is influenced by the flow field caused by its neighbors, they will move in concert and with a similar speed on average. However, in highly congested suspensions hydrodynamic interactions are screened. The exact nature of this screening is still under investigation. Some authors argue that the particles themselves function as hard barriers canceling the propagation of flow fields. Others argue that interference of several flow fields could cancel each other. Given the fact that within E. coli DNA is confined into a small structure, and thus highly congested, it is conceivable that hydrodynamic screening takes place under certain conditions. Hence, hydrodynamic screening can have a major impact on the dynamics of the bacterial nucleoid. In Chapter IV, V and VI of this thesis we address this problem. Electrostatic interactions When immersed in polar solvents, colloids such as proteins and DNA are often charged due to the ionization of surface groups. In the presence of added electrolytes such as NaCl, electrical double layers of counterions will screen the charges. Overlap of the electrical double layers for similar charges results in repulsive electrostatic interactions, which have the form of a screened Coulomb potential. 7 T =. Where. S S. . πεε T. GZR− κ F. (2.3.1).. ε and ε are the dielectric permitivities of air (vacuum) and of the. medium respectively, S and S the interacting charges (1.6*10-19 Coulomb) and F the distance between particles.. κ − is the Debye-Hückel screening 25.

(26) length and is inversely proportional to the square root of the salt concentration:. κ− =. S S. . π ε ερK M$ 6 . ions/ dm3.. , with ρ the density of monovalent salt in K. κ − is related to the distance beyond which electrostatic. interactions are << M$ 6 . The higher the ionic strength, the smaller. κ − and. hence the more effectively the potential is screened. Accordingly, in suspension charged particles are characterized by an effective radius − approximately given by TJCTF − EQTG + κ . At low ionic strengths. κ − is large. and the electrical double layer will overlap at distances many times greater than the particles radius. At room temperature and at a salt concentration of 1 M NaCl. κ − ≈ PO , meaning that at a distance larger then 0.3 nm the. electric field of a point charge will be felt only slightly by other particles. Reducing the ionic strength to physiological concentrations we obtain:. ρK = ⋅ × . . = × ions/ dm3,.        × −     −  κ =   × × × × × × × − ×   . . . ≈ PO .. Therefore, within E. coli a charged particle such as a globular 40 kDa protein having a hard core radius of about 2.3 nm will in reality have an effective radius TGHH = TJCTF − EQTG + κ − ≈ 3 nm. Van der Waals interactions Van der Waals interactions are very often attractive forces, which arise from instantaneous charge fluctuations between neighboring particles so that induced dipole-dipole interactions occur. For interparticle distances larger then the particle radius r, van der Waals interactions decay as 1/ r6. In suspensions consisting of charged particles electrostatic repulsions at low ionic strength overwhelm van der Waals interactions.. 26.

(27) Depletion In biological systems, such as the E. coli cytoplasm, a mixture of particles with different shapes, sizes and charges coexist. In addition to self excludedvolume interactions, cross terms also occur. We first consider the cross interaction in a mixture of hard spheres of two different sizes. In dilute solutions the small spheres are excluded from a layer of thickness r around the big spheres called the depletion zone (Fig 2.3 A). In analogy to equation 2.16, the volume excluded to a small sphere (cross excluded-volume X ETQUU KU IKXGPD[ X ETQUU =. π (4 + T) . (2.3.2).. At high concentrations, when two large spheres approach to a distance D smaller than 2r, the depletion zones start to overlap (Fig 2.3 B) so that the small spheres are depleted from the void between the two big particles.. A. D. B. C. Fig. 2.3. Description of depletion forces in a binary mixture of hard-spheres. AWhen moving a small sphere and a big sphere towards each other, the center of mass of the small sphere is excluded by a total volume given by equation 2.3.2. B- At concentrations where the gap between the two spheres is smaller than 2r, the depletion zones start overlapping and the small particles are expelled from the space between the large particles. C- Phase separation results in an overlap of depletion areas (dashed area) that are shared by several big spheres and therefore in a decrease in the volume excluded to the small particles.. A consequence of these so-called depletion interactions is that the small spheres experience a decrease in their freedom of motion or translational. 27.

(28) entropy. Moving the big spheres together (Fig. 2.3 C) results in an overlap of the depletion layers and thus in a decrease in the volume excluded to the small spheres. This gain in entropy reduces the total free energy of the system, which we can express as. (VQV = (KF + (ETQUU + (UGNH =. 0 ⋅ 0 8 0 0 β0 = 0 M 6NP T − 0 M 6 + 0 M 6 NP 4 − 0 M 6 + T 4 ETQUU M 6 + M6 4 $ T $ 4 $ T $ $ 8 $ 8 8 8. (2.3.3).. Where 0 T is the number of small spheres and 0 4 the number of large spheres. If (ETQUU > (KF + (UGNH , cross excluded-volume interactions could drive the formation of two distinct phases. The final equilibrium state will result from a balance between the intervening forces ( (KF favors mixing so that some small particles are allowed to enter the phase overwhelmingly containing the big spheres). An equilibrium state can be computed by ensuring that the chemical potential and the osmotic pressure of the small spheres are identical in the two phases. In section 2.5 we briefly review calculations of Odijk (1998), pertaining to the phase separation of DNA-proteins within E. coli.. 2.4. Statistical properties of long polymers. Modeling and theoretically defining the statistical properties of DNA is an important step towards modeling the E. coli nucleoid. Theoretical models are used to predict and describe observed macroscopic properties in terms of polymer configurational properties. Freely jointed chain model One popular idealized model to describe a polymer is the freely jointed chain, which does not consider the contribution of self-interactions such as excludedvolume and electrostatic repulsions. Here, polymer chains of contour length . are made up of 0 or . C identical subunits linked together and freely. 28.

(29) r rotating. The subunits are represented by vectors TK of length C , running from position K to K + along the chain (Fig. 2.4.1).. Fig. 2.4.1 Illustration of a polymer modeled as a freely jointed chain consisting of subunits of equal length C , the Kuhn segment length of the polymer. The subunits r are represented by vectors T , which go from position K to K + of the chain taking a random orientation. The dimensionsr of each chain configuration can be characterized by the end-to-end vector 4. As the interactions between the monomers are ignored, each vector adopts a random orientation independent of its neighbors. In analogy to the random walk, such a flexible polymer is called a random coil. Each segment (the step size of the walk) is a step taken in a random direction. We now introduce the mean-square end-to-end distance as a measure of the polymer size (see Fig. 2.4.1).. r 4G ≡< 4 >=. 0. 0. ∑ ∑ K = L= =. → → TK ⋅ TL. = 0C. (2.4.1).. r r The average is computed by making use of the fact that TK ⋅ TL = C if K = L ; r r and TK ⋅ TL = if K ≠ L . Thus, 4G increases as 0 1/2. The continuous buffeting of solvent molecules against the polymer chain induces continuous. r. fluctuations in the adopted conformation and thus 4 fluctuates around the . average 4G . The probability function of finding a polymer composed of 0. r. segments with an end-to-end vector equal to 4 is.   r  2 4 0 =    π 0C . . .  r  4  GZR −   0C   . (2.4.2).. 29.

(30) The configurational entropy 5EQPH of the coil is by definition r 5EQPH = M$ 6 NP Y 4 0 . (2.4.3),. r where Y 4 0 is the number of possible trajectories or conformations of the r r r random-walk starting at the origin and ending between 4 and 4+ + F4  r  r r r  4  Y 4 0 = 2 4 0 F4` GZR− −     0C . (2.4.4).. r. We see that the number of conformations decreases exponentially with 4 and thus stretched configurations are highly unfavorable. This entropic effect will drive the polymer to adopt a coiled conformation with 4 much smaller. r. then . . In terms of entropy, substituting Y 4 0 in expression 2.4.3 we find. 5EQPH = −. M $ 4 0C. . . + EQPUV. (2.4.5).. Because segment interactions are neglected, the configurational entropy is the only factor contributing to the free energy ( of the polymer chain, which is given by. ( 04 = −65 = −M $ NP Y 40 =. 4 0C. . M $6. (2.4.6).. Excluded-Volume Effect In reality, polymers rarely behave as ideal because their subunits interact through hard-core collisions and electrostatic repulsion. Furthermore, the orientation of consecutive infinitesimal segments is often not random but constrained. Because the 0 segments are now interacting, two effects will balance in a calculation of the magnitude of 4 : the configurational entropy that favors folded conformations and the excluded-volume that favors more expanded conformations. In the case of DNA where C >> F ( F = 2nm is the diameter of the double helix) the subunits are approximated by hard cylinders. 30.

(31) of length C and diameter F (Fig. 2.4.2). The excluded-volume between two such segments is proportional to the C F and given by:. β=. π . C F. (2.4.7). a. d. Fig. 2.4.2 Illustration of excluded volume between two hard cylinders. When the two rods approach each other their centers of mass are excluded from a total volume given by. β=. π. . C F. (see text).. For a polymer chain consisting of 0 segments, the free energy (UGNH arising from excluded-volume interactions equals:. (UGNH ≈. $ 0 β M $6 = U M$6 8 4. (2.4.8).. The ratio of the total self excluded-volume $U to the volume 8 occupied by the chain gives the magnitude of ( . The total free energy of the polymer UGNH. (VQV now results from two different parameters: the self-interaction energy (UGNH and the configurational entropy 5EQPH :. (VQV (R, N) = (UGNH – 65EQPH `. $U 8. M $6 +. 4 0C. M 6. $. (2.4.9).. Minimizing (VQV with respect to 4 , the magnitude of the end-to-end distance can be estimated:. ∂(VQV 0 β 4 =− + =, ∂4 4 0C. 31.

(32) . 4 ≈ 0 β. . C .. If we make use of the worm-like chain model to estimate the dimensions of a DNA molecule with the size of the E. coli chromosome, we see that 4 is at least one order of magnitude larger than the E. coli diameter (see Table 2.1). Table 2.1 Dimensions of a linear DNA molecule according to the worm-like chain model. 3. contour length (µm) diameter (nm) persistence length (µm) Kuhn length (µm). 1.6*10 2 0.05 0.1. b (µm ) number of Kuhn seg. R (µm). 3.1 *10. 3. -5. 4. 1.6*10 16. Theoretical work of Odijk (1998) shows that excluded-volume interactions between DNA and soluble proteins are fairly high and overwhelm ( of the UGNH DNA. Accordingly, a phase separation between DNA and proteins and the formation of a compact nucleoid is foreseen (Odijk, 1998). In the next section this theory is briefly reviewed. 2.5 Physical forces shaping the E. coli nucleoid Our system consists of one long supercoiled DNA molecule (L= 1600µm, hard-core radius. D = F = 1 nm) and many soluble proteins ( O = 1.6*106;. hard-core radius TRTQV = 2.3 nm). The DNA effective superhelical density. σ is. about -0.025 so that we can derive the contour length of the superhelix. .5 = . UKP α (α = 52° is the superhelical pitch angle), the persistence length of the superhelix 2U ( 2U = 2 UKP α = 78.8 nm) and the supercoil diameter &U = 32 nm (Boles et al, 1990; Odijk, 1996; Ubbink and Odijk, 1999). The proteins and DNA coexist in a compartment of volume 8 = 0.37µm3 equal to the cell volume. DNA and proteins were modeled as hard impenetrable. 32.

(33) particles interacting by hard-core repulsion. Electrostatic repulsion was incorporated into the hard-core model and the effective radius of the two interacting particles was computed precisely. A convenient approximation for the effective radius of a particle is TGHHGEV = TJCTF − EQTG + κ − , where. κ − is the. Debye screening length, which at 0.2 M NaCl equals 0.68nm (see section 2.3). Our objective is to determine the free energy of the system ( , which takes VQV into account self and cross excluded-volume interactions and has the form:. (VQV = (RTQV + (ETQUU + ( &0#. (2.5.1).. We start by considering the system in the absence of phase separation or when both DNA and protein are confined to a volume 8 = 8EGNN (Fig. 2.5.1). To estimate (. &0#. , the superhelix was modeled as a closely packed coil. consisting of .U C = 630/ 0.158 ≈ 4000 negatively charged supercoiled DNA segments (also called Kuhn segments) interacting mainly via excludedvolume. Interactions arising from electrostatic repulsion can be ignored because &U = nm which is >> κ − .. Fig. 2.5.1 Schematic drawing of an E. coli cell where only the cell envelope, soluble proteins and the supercoiled DNA are represented. In the absence of a phase separation both DNA and proteins are evenly distributed throughout the cell.. The excluded-volume between two Kuhn segments is given by equation 2.4.7 and equals. β=. π #U &U = ×− µm3 . (2.5.2).. 33.

(34) The total self excluded-volume $U is proportional to the number of pairs of interacting segments and equals:. $U = 0 β = × µm3 . (2.5.3).. The DNA segments are thus subjected to strong self excluded-volume interactions. Proper scaling to the confinement volume 8 gives us an estimate of the free energy of the nucleoid (&0# :. $ (&0# ≈ U M $6 ≈ × M $6 8. (2.5.4).. To obtain an estimate of ( , the proteins are modeled as negatively RTQV charged hard spheres with a radius T = TRTQV + κ − =2.97 nm. Because the proteins volume fraction in the cytoplasm is fairly low, interactions between the proteins can be neglected to a zeroth-order approximation. Hence, the consists of an ideal term: free energy of the proteins ( RTQV. .   O  − O  M 6  8  $. (RTQV =  O NP . (2.5.5).. While diffusing, proteins collide with the DNA double helix itself (proteins are much smaller then the superhelix dimensions) and experience for that reason cross excluded-volume interactions (Fig. 2.5.2). The volume $E excluded to one protein is proportional to the contour length of the DNA double helix . and to a depletion radius ' , which is computed exactly but may be viewed approximately as the sum of the radii of the two interacting particles corrected for κ − .. $E ≈ π.' ≈ µm3. (2.5.6),. with ' ≈ TRTQV + D + κ − ≈ + + × ≈ nm. 34.

(35) E. L. Fig. 2.5.2 Illustration of the volume $ excluded to one protein by a DNA supercoil. E. $E. is proportional to the contour length of the DNA double helix . and to a. depletion radius ' , which is the sum of the radii of the two interacting particles corrected for κ. −. .. The total cross excluded-volume 8ETQUU is proportional to the number of proteins O and equals: 3 8ETQUU ≈O$E ≈× × ≈× µm. (2.5.7).. (ETQUU is then given by: (ETQUU ≈. O$E 8. M$6 ≈ × M $6. (2.5.8).. We may now write the expression representing the total free energy of the system ( VQV. (VQV. O$E $U O = O NP − O + + M$6 8 8 8. (2.5.9). ( The magnitude of the depletion interactions is large so that ETQUU ( ≈ 10. &0#. From this simple argument we may infer that the macromolecular composition of E. coli is such that the occurrence of a phase separation due to depletion interactions may be feasible. In order to find out if it is possible to thermodynamically define an equilibrium state where (ETQUU (. &0#. ≈ 1, we. 35.

(36) ensure that the chemical potential ( µ = ∂(VQV ( π = −∂(VQV. ∂O ) and the osmotic pressure. ∂8 ) exerted by the proteins are identical in the respective. nucleoid ( P ) and protein cytoplasm ( E ) phases. This leads to the coexistence equations.   µ = µ ⇒NPX = NPX + $E  E P E P 8  P   π TRTQV $U  π = π ⇒ X = X + $EXP + P E P  E 8P 8P     X 8 = X 8 − 8 + X 8  VQV E P P P. Here XE and XP are the protein volume fractions in the cytoplasm and in the nucleoid, respectively. The third equation ensures that the total protein volume fraction XVQV is constant and equals the experimentally measured value of 0.143. The solutions for this system are:. 8P = 0.098 µm3; XE = 0.168 and XP = 0.0548. Compare with experimental values:. 8P = 0.080 µm3; XE = 0.166 and XP = 0.06. A phase separation is predicted that leads to confinement of the DNA into a nucleoid (Fig. 2.5.3).. Fig. 2.5.3 Schematic drawing of an E. coli cell where only the cell envelope, soluble proteins and the supercoiled DNA are represented. Taking into account that (ETQUU. (&0#. ≈ 10,. cross interactions can induce the formation of a phase separation. between DNA and proteins or the formation of the nucleoid.. 36.

(37) From the coexistence equations we can estimate at which point the phase separation within E. coli no longer exists and the DNA will occupy the entire cell. By eliminating XP from the coexistence equations we obtain the expression:. −. π TRTQV $U XE $E. −$ $E  $E  E 8P × =  +  G 8P  8P . (2.5.10).. Phase separation will prevail as long as the left side of the equation equals the right side. If we rewrite this expression as:. − − S ×7 = + + 7 G− 7. (2.5.11),. where. π TRTQV $U S= = XE $E XE. and. 7=. $E 8P. and look for equilibrium states where:. − − S ×7 − + + 7 G− 7 = 0. (2.5.12),. Fig. 2.5.4 Theoretical prediction of the point of phase transition of the E. coli nucleoid.. 37.

(38) we see that (Fig. 2.5.4) 7 ≈ 0 (or 8P → ∞ ) when S > , so that the phase separation holds until XE = = 0.083.. 2.6 Outline and motivation In this thesis we study the nature of the DNA compaction mechanism responsible for the nucleoid formation within E. coli. Chapter III is devoted to a literature review and new results on nucleoid isolation procedures. We then focus on the experimental studies performed with isolated nucleoids. In Chapter IV we monitor the volume of isolated nucleoids in the presence of a neutral crowding agent PEG. We show that polymer crowding may compact isolated nucleoids into dimensions comparable to the intracellular ones. A discussion of these results with reference to the phase separation theory discussed in Chapter II is also given and we conclude that depletion can be the force behind the formation of the bacterial nucleoid. Furthermore, based on dynamic light scattering (DLS) experiments we show that at least within isolated nucleoids, screening of hydrodynamic interactions occur rendering the supercoil segments a fast dynamics. In Chapter V we study the mechanism of expansion of a nucleoid right after being released from a bacterial cell. Our aim is to verify if the dynamics of expansion of a liberated nucleoid conform to scaling-theory predictions where the DNA self-interaction energy is the force driving the nucleoid volume increase. This chapter shows that although the observed dynamics is on average characterized by a subdiffusive exponent, excluded volume arguments alone do not fully explain the process of nucleoid expansion. In Chapter VI we directly monitor the movement of DNA segments within isolated nucleoids. We conclude that the isolated nucleoid has a gel-like structure where supercoil segments show confined Brownian motion. The observed diffusion constant substantiates the DLS experiments preformed in Chapter IV.. 38.

(39) REFERENCES Boles, T., White, J. and Cozzarelli, N. (1990) Structure of plectonemically supercoiled DNA. J. Mol. Biol. 213, 931–951. Bauer, W. (1978). Structure and reactions of closed duplex. DNA. Annu. Rev. Biophys. Bioeng. 7, 287–313. Elbaum, M. Fygenson, D. and Libchaber, A. (1996) Buckling Microtubules in Vesicles. Phys. Rev. Let. 76, 4078-4081. Hagerman, P. (1988) Flexibility of DNA. Ann. Rev. Biophys. Chem. 17, 265-286. Odijk, T. (1998) Osmotic compaction of supercoiled DNA into a bacterial nucleoid. Biophys. Chem. 73, 23–29. Odijk, T. (1996) DNA in a liquid-crystalline environment. tight bends, rings, supercoils. J. Chem. Phys. 105, 1270-1286. Odijk, T. (1998) Osmotic compaction of supercoiled DNA into a bacterial nucleoid. Biophys. Chem. 73, 23–29. Odijk, T. (1997) Diktaat Thermodynamica voor Biotechnologen: “DNA in waterige oplossing”. TU Delft faculteit der Scheikundige Technologie en der Materieelkunde. Odijk, T. (1997) Diktaat Thermodynamica voor Biotechnologen: “Depletie”. TU Delft faculteit der Scheikundige Technologie en der Materieelkunde. Odijk, T. en Frens, G.- Cahiers voor Fysische 4: “Polymeren”. TU Delft, Faculteit der Scheikundige Technologie en der Materieelkunde. Ubbink,. J.. and. Odijk,. T.. (1999). Electrostatic-. undulatory. theory. of. plectonemically supercoiled DNA. Biophys. J. 76, 2502-2519.. 39.

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(41) III. Isolation of the Escherichia coli nucleoid**. Sónia Cunhaa,b, Theo Odijkb, Erhan Süleymanoglua and Conrad L. Woldringha,*. a. Swammerdam Institute for Life Sciences, BioCentrum Amsterdam,. University of Amsterdam, Kruislaan 316, 1098 SM Amsterdam, The Netherlands b. Section Theory of complex fluids, Kluyver Institute for Biotechnology, Delft. University, 2600 GB Delft, The Netherlands. Running title: Isolation of E. coli nucleoids *. Corresponding author: Tel. +31 20 525 6219; fax: +31 20 525 6271. Email: woldringh@bio.uva.nl (C.L. Woldringh) **Published in Biochimie (2001) 83, 149–154.

(42) ABSTRACT Numerous protocols for the isolation of bacterial nucleoids have been described based on treatment of cells with sucrose-lysozyme-EDTA and subsequent lysis with detergents in the presence of counterions (e.g. NaCl, spermidine). Depending on the lysis conditions both envelope-free and envelope-bound nucleoids could be obtained, often in the same lysate. To investigate the mechanism(s) involved in compacting bacterial DNA in the living cell, we wished to isolate intact nucleoids in the absence of detergents and high concentrations of counterions. Here, we compare the general lysis method using detergents with a procedure involving osmotic shock of Escherichia coli spheroplasts that resulted in nucleoids free of envelope fragments. After staining the DNA with DAPI (4',6-diamidino-2-phenylindole) and cell lysis by either isolation procedure, free-floating nucleoids could be readily visualized in fluorescence microscope preparations. The detergent-salt and the osmotic-shock nucleoids appeared as relatively compact structures under the applied ionic conditions of 1 M and 10 mM, respectively. RNase treatment caused no dramatic changes in the size of either nucleoid. INTRODUCTION Ever since it was realized that DNA occurred as a confined structure within the bacterial cell (Mason and Powelson, 1956) one has tried to isolate it. Isolation of this entity was expected to provide information on the mechanism of folding of DNA within the cytoplasm. The visualized DNA has been called chromatin body (Robinow, 1956), nucleo- or DNA-plasm (Kellenberger et al, 1958), or nucleoid (Ryter et al, 1958). The term nucleoid or bacterial chromosome is generally used to describe the packaged DNA structure in situ, including associated protein and RNA components. Isolated nucleoids may have lost or gained certain associated components during the lysis procedure. Ideally, an isolated nucleoid should be as identical as possible to the intracellular chromosome in. 42.

(43) vivo. Because in actively growing cells the chromosome is involved in coupled transcription/translation (Miller et al, 1970) and in replication, repair and recombination, isolated nucleoids could also comprise the components involved in these processes. In early isolation procedures (see for reviews Hirschbein and Guillen, 1982; Pettijohn and Sinden, 1985) it was experienced that the bacterial DNA spontaneously unfolded upon cell lysis using lysozyme and detergents. In most studies, therefore, counterions (Stonington and Pettijohn, 1971; Worcel and Burgi, 1972) or spermidine (Kornberg et al, 1974) were added to prevent this unfolding. In addition, it was found that depending on the lysis conditions, either envelope-free or envelope-bound nucleoids could be obtained (Hirschbein and Guillen, 1982; Pettijohn and Sinden, 1985). To understand the presence of an in vivo phase separation between DNA and cytoplasm as indicated by microscopic observation (review Woldringh and Odijk, 1999) and as predicted on the basis of physical consideration (Zimmerman and Murphy, 1996; Odijk, 1998), we wish to analyze nucleoid compaction in vitro using crowding agents like polyethylene glycol (PEG 20,000) or proteins. Because the use of detergents or high salt conditions may induce the dissociation of DNA binding proteins and may generate nucleoids attached to envelope fragments and RNA (see below), we used an osmotic shock method (Sloof et al, 1983). Here we compare the detergentsalt (or detergent–spermidine) method with that of osmotic shock for obtaining isolated nucleoids. We describe some properties of both types of nucleoids stained. with. DAPI. (4',6-diamidino-2-phenylindole). as. visualized. by. fluorescence microscopy. Nucleoid isolation by the detergent-salt or detergent-spermidine method Nucleoids and envelope fragments. Nucleoids isolated by the detergent method have been given various names depending on the applied conditions. For instance, “low- and high-lysozyme nucleoids” are obtained after incubation with 0.4 and 4 mg/ml lysozyme, respectively (Murphy and Zimmerman, 1997a). It should be noted that lysozyme concentrations above 0.8 mg/ml can lead to artificial and secondary associations between DNA and 43.

(44) envelope remnants as emphasized by Silberstein and Inouye (Silberstein and Inouye, 1974). Also, “high-salt nucleoids” (Stonington and Pettijohn, 1971) and “low-salt spermidine nucleoids” (Kornberg et al, 1974) can be distinguished. As an example of the detergent-spermidine method we consider a relatively recent protocol given by Murphy and Zimmerman (1997a). The various steps of their procedure will be discussed briefly below (see summary in the first column of Table 3.1). In the first step, intact cells (figure 3.1A) are plasmolyzed in sucrose buffer containing lysozyme and EDTA to obtain detergent-sensitive cells with a partly digested peptidoglycan layer (figure 3.1B). In the second step, the cells are treated with detergents such as Brij, deoxycholate and/or Sarcosyl to disrupt the plasma membrane and allow extrusion of the DNA (see hypothetical schemes in figure 3.1C, D).. Fig. 3.1 Schematic representation of the hypothetical behavior of cell structures during detergent-salt lysis (see also Table 1, first column). A. The intact cell is represented by the cell wall (outer membrane plus peptidoglycan layer), the plasma membrane, soluble proteins, polyribosomes and the nucleoid. The DNA is drawn as branched plectonemic supercoils, compacted in the cell center by depletion forces (molecular crowding; see Woldringh and Odijk, 1999). The polyribosomes extend 44.

(45) from the DNA to the plasma membrane. B. Plasmolyzed cell with a partly digested peptidoglycan layer obtained by incubation in a sucrose-lysozyme-EDTA buffer. C. Detergent lysis at low temperature (0 – 10 °C). The plasma membrane is largely dissolved and the polyribosomes have dissociated causing strands of nascent RNA (drawn as short, thick lines; RNA strands remain connected to the DNA via RNA polymerase) to entangle with DNA segments. Most DNA binding proteins have also dissociated. Free loops of supercoiled DNA are expelled through several gaps in the cell envelope resulting in an “envelope-bound nucleoid”. D. Detergent lysis at high temperature (20 – 25 °C). Similar to C except that the nucleoid is expelled through a single gap in the cell envelope, resulting in an “envelope-free nucleoid”.. It should be noted that in all protocols the lysis of E. coli cells includes lysozyme to digest the peptidoglycan layer. An exception is the protocol of Hinnebusch and Bendich (1997) in which E. coli cells are lysed within agarose blocks by incubation in buffer containing only sodium dodecyl sulfate (SDS) and proteinase K. The ultrastructural changes occurring in E. coli cells during SDS-lysis have been reported previously (Woldringh and Iterson, 1972). Murphy and Zimmerman (1997a, 1997b) used high-lysozyme-spermidine nucleoids (Table 3.1). These nucleoids have a much higher protein and RNA content than the high-salt nucleoids. Cells lysed under the high-salt condition, usually 1M NaCl, can either give rise to envelope-bound (figure 3.1C) or envelope-free nucleoids (figure 3.1D), depending on the temperature of lysis [20], which may vary the degree of disruption of the peptidoglycan layer. The “low-salt spermidine nucleoids” (Murphy and Zimmerman, 1997a) are presumably always attached to membranous fragments derived from the cell envelope (see figure 9 in Murphy and Zimmerman, 1997b) As discussed by Materman and Van Gool (1978) cell lysis has to proceed at higher temperatures (20 – 25 °C) to obtain the release of the nucleoid purportedly through a single gap in the cell envelope (figure 3.1D; see also Meijer et al, 1976). Less or more extensive digestion of the peptidoglycan layer may lead to the extrusion of the DNA through many gaps in the still rodshaped remnant of the envelope (figure 3.1C) or to trapping of vesicular envelope fragments, respectively. In both cases the "binding" of the nucleoid to envelope fragments is probably due to entanglement rather than to specific DNA-envelope attachment sites, as frequently suggested in early studies (e.g. Dworsky and Schaechter, 1973).. 45.

(46) Nucleoids and RNA. Numerous reports have described the occurrence of indirect attachments of DNA to the plasma membrane via coupled transcription, translation and translocation of membrane proteins (Kleppe et al, 1979; Vos-Scheperkeuter and Witholt, 1982). These observations led to the formulation of the transcription/translation-mediated segregation model (Woldringh et al, 1995) or the transertion model (Norris, 1995) in which the nascent RNA functions as an expansion factor shaping the nucleoids into rodlike structures and moving them during segregation. This idea of transcription/translation-mediated expansion of the nucleoid was based on electron microscope observations showing that treatment with rifampin (Dworsky, P., M. Schaechter) or chloramphenicol (Morgan et al, 1967) causes compaction of the nucleoid. This suggested that nascent RNA represents an expansion factor counteracting the compaction force exerted through macromolecular crowding (Woldringh and Odijk, 1999; Zimmerman and Murphy, 1996). When considering this behavior of isolated nucleoids with respect to RNA there seems to occur a reversal in the role of nascent RNA concerning compaction of the nucleoid. However, in the case of isolated high-salt or -spermidine nucleoids it is the same nascent RNA which can now be considered to represent a compaction or stabilizing factor, as RNAse treatment of these nucleoids causes their unfolding as indicated by sucrose-gradient analyses (Pettijohn and Hecht, 1973; Murphy and Zimmerman, 2000).. Nucleoid isolation by osmotic shock In the osmotic-shock method (Table 3.1, second column) cells are incubated in a sucrose-containing buffer with lysozyme and EDTA until all cells have converted to spheroplasts (figure 3.2B) or, in the case of Gram-positive cells, to protoplasts (Sloof et al, 1983). In our hands, a 100-fold dilution of the suspension in 10 mM NaCl resulted in empty, spherical ghosts (as visible in phase contrast) and in expanded nucleoids resembling globules with a radius of 2 to 3 µm. We suspect that the nucleoids are released through a single. 46.

(47) gap; otherwise they would remain entangled with the ghost as in the hypothetical figure 3.1C. Table 3.1 Comparison of lysis-protocols for the isolation of nucleoids using either the detergentsalt or the osmotic shock method.. Procedure steps. Detergent-salt. Osmotic shock. Incubation buffer. 10 mM Tris, pH8. 10 mM Naphosphate pH7.4. 10 mM EDTA. 10 mM EDTA. 100 mM NaCl. 100 mM NaCl. 20% sucrose. 0.8 M sucrose (~30%). low: 0.4 mg/ml. 0.4 mg/ml. Lysozyme concentration. high: 4 mg/ml Incubation time and. 40 sec at 0°C. 30 min at 20°C. 0.5% Brij58. (no detergent). 0.2% DOC. osmotic shock by. low salt:. 5 mM spermidine or. 100 x dilution in 10 mM NaCl. high salt:. 1 M NaCl. temperature Treatment. lysate after 3 min at 10°C. In a theoretical analysis, Odijk (2000) calculated that liberated nucleoids would swell within 10 min to a radius of 9 µm. Taking branching of supercoils into consideration, preliminary calculations show that the average radius of gyration would be about 3 µm. The swelling does not seem to continue as all nucleoids in the lysate have similar sizes after standing for 4 h at room temperature. The nucleoids we measure thus appear smaller than our theoretical estimates. We hope to explain this discrepancy in future work. The complexes liberated by osmotic shock can be described as “lowlysozyme. low-salt”. nucleoids.. Preliminary. ethidium-bromide. titration. experiments indicated that the nucleoids are supercoiled. By what constraints the size of the isolated nucleoids is maintained is presently unknown, but it is unlikely caused by RNA entanglements as suggested for the detergent-salt nucleoids (see figure 3.3 C, D).. 47.

(48) Fig. 3.2. Schematic representation of the hypothetical behavior of cell structures during lysis by osmotic shock (see Table 3.1, second column). A. Intact cell as in figure 3.1A. B. Prolonged incubation in a sucrose-lysozyme-EDTA buffer results in the conversion of a plasmolyzed cell (figure 3.1B) into an osmotically sensitive spheroplast. C. 100-fold dilution of the spheroplast suspension results in the liberation of the nucleoid from a large, spherical envelope ghost. It is not known to what extent the polyribosomes do remain intact.. Sloof et al. (1983) reported that nucleoids isolated from Bacillus licheniformis protoplasts by osmotic shock are unaffected by treatment with 10 µg/ml RNAse as analyzed by sucrose-density centrifugation. Because of the low salt concentration used in this procedure, ribosomes are not expected to dissociate from the mRNA. Consequently, they may still persist in the form of polyribosomes and no artificial stabilization of the nucleoid by DNA-RNA associations is to be expected.. Microscopic observation of isolated nucleoids Nucleoids isolated from DAPI-stained cells can readily be observed by fluorescence microscopy. Both methods of isolation (Table 3.1) resulted in globular, sometimes elongated complexes that did not aggregate. They showed similar sizes when prepared in a liquid layer of about 10 µm thick and photographed as free-floating complexes (figure 3.3A and B). However, upon excitation of the DAPI fluorochrome (using a dichroic filter cube containing a band pass filter with transmission between 300-400 nm), the nucleoids disintegrated rapidly and disappeared within about 10 sec. The nucleoids 48.