Torsional rigidity of DNA and length dependence of the free energy of DNA supercoiling

By analyzing the Boltzmann populations of DNA topoisomers that differ only in their linking numbers, the dependence of the free energy delta G tau of DNA supercoiling on the linking number alpha has been determined for DNA rings as small as 200 base-pairs (bp) in length. All experimental data can be fitted by the relation delta G tau = K (alpha-alpha)2, where alpha is a constant for a given DNA at a given set of conditions and K is a DNA length-dependent proportionality constant. For DNA rings with length N larger than 2000 bp, K is inversely proportional to N and the product NK is nearly a constant around 1150 RT X bp. For rings smaller than 2000 bp NK increases steadily with decreasing N; for a 200 bp ring NK is 3900 RT X bp. The increase in NK when N decreases can be interpreted as a result of the decrease in the contribution of the fluctuation in the writhing number to the equilibrium distribution in alpha. Assuming that the writhing contribution approaches zero for DNA rings 200 bp in size, the torsional rigidity of the DNA double helix is calculated to be 2.9 X 10(-19) erg cm. In addition, the large value of K for the small circles allows precise calculation of the helical repeat of DNA. For the 210 bp rings, the repeat is measured to be 10.54 bp.     

Torsional and bending rigidity of the double helix from data on small DNA rings

We have calculated the variance of equilibrium distribution of a circular wormlike polymer chain over the writhing number, [Wr)2), as a function of the number of Kuhn statistical segments, n. For large n these data splice well with our earlier results obtained for a circular freely jointed polymer chain. Assuming that [delta Lk)2) = [delta Tw)2) we have compared our results with experimental data on the chain length dependence of the [delta Lk)2) value recently obtained by Horowitz and Wang for small DNA rings. This comparison has shown an excellent agreement between theory and experiment and yielded a reliable estimate of the torsional and bending rigidity parameters. Namely, the torsional rigidity constant is C = 3.0.10(-19) erg cm, and the bending rigidity as expressed in terms of the DNA persistence length is a = 500 A. The obtained value of C agrees well with earlier estimates by Shore and Baldwin as well as by Horowitz and Wang whereas the a value is in accord with the data of Hagerman. We have found the data of Shore and Baldwin on the chain length dependence of the [delta Lk)2) value to be entirely inconsistent with our theorectical results.     

Topological distributions and the torsional rigidity of DNA. A Monte Carlo study of DNA circles

Distributions of the linking number of circular DNA molecules, defined as the sum of twist and the writhing number, are obtained by Monte Carlo simulations of small, randomly closed DNA circles. We estimate the relative contributions of fluctuations in twist and writhe to the linking number distribution, as functions of DNA size. Published experimental data on topoisomer distributions in circular DNA molecules are interpreted to estimate the torsional rigidity of DNA in solution. We show that ignoring the writhe component of the linking number distribution, even for DNA circles as small as 250 base-pairs, leads to an underestimate for the torsional stiffness of the double helix. The value of the torsional modulus obtained from this analysis, C = 3.4 X 10(-19) erg cm, is from 10 to 40% larger than that estimated by others and more than twice as large as the values obtained from fluorescence depolarization or other time-resolved spectroscopic measurements. We also develop further the theoretical treatment of ring closure probabilities for DNA described in the previous article. It is shown that the torsional part of the ring closure probability, phi 0,1 (tau 0) is a periodic function of DNA length that contributes strongly to the ring closure probability for short chains but makes negligible contributions for chains over 1000 base-pairs in length.     

Novel topologically knotted DNA from bacteriophage P4 capsids: studies with DNA topoisomerases.

DNA molecules isolated from bacteriophage P4 are mostly linear with cohesive ends capable of forming circular and concatemeric structures. In contrast, almost all DNA molecules isolated form P4 tailless capsids (heads) are monomeric DNA circles with their cohesive ends hydrogen-bonded. Different form simple DNA circles, such P4 head DNA circles contain topological knots. Gel electrophoretic and electronmicroscopic analyses of P4 head DNA indicate that the topological knots are highly complex and heterogeneous. Resolution of such complex knots has been studied with various DNA topoisomerases. The conversion of highly knotted P4 DNA to its simple circular form is demonstrated by type II DNA topoisomerases which catalyze the topological passing of two crossing double-stranded DNA segments [Liu, L. F., Liu, C. C. & Alberts, B. M. (1980) Cell, 19, 697-707]. The knotted P4 head DNA can be used in a sensitive assay for the detection of a type II DNA topoisomerase even in the presence of excess type I DNA topoisomerases.     

Untying a Protein Knot by Circular Permutation

Topologically knotted proteins are tantalizing examples of how polypeptide chains can explore complex free energy landscapes to efficiently attain defined knotted conformations. The evolution trails of protein knots, however, remain elusive. We used circular permutation to change an evolutionally conserved topologically knotted SPOUT RNA methyltransferase into an unknotted form. The unknotted variant adopted the same three-dimensional structure and oligomeric state as its knotted parent, but its folding stability was markedly reduced with accelerated folding kinetics and its ligand binding was abrogated. Our findings support the hypothesis that the universally conserved knotted topology of the SPOUT superfamily evolved from unknotted forms through circular permutation under selection pressure for folding robustness and, more importantly, for functional requirements associated with the knotted structural element.     

Type II DNA topoisomerases: enzymes that can unknot a topologically knotted DNA molecule via a reversible double-strand break

The T4 DNA topoisomerase is a recently discovered multisubunit protein that appears to have an essential role in the initiation of T4 bacteriophage DND replication. Treatment of double-stranded circular DNA with large amounts of this topoisomerase in the absence of ATP yields new DNA species which are knotted topological isomers of the double-stranded DNA circle. These knotted DNA circles, whether covalently closed or nicked, are converted to unknotted circles by treatment with trace amounts of the T4 topoisomerase in the presence of ATP. Very similar ATP-dependent enzyme activities capable of unknotting DNA are present in extracts of Drosophila eggs. Xenopus laevis eggs and mammalian tissue culture cells. The procaryotic enzyme, DNA gyrase, is also capable of unknotting DNA. We propose that these unknotting enzymes constitute a new general class of DNA topoisomerases (type II DNA topoisomerases). These enzymes must act via mechanisms that involve the concerted cleavage and rejoining of two opposite DNA strands, such that the DNA double helix is transiently broken. The passage of a second double-stranded DNA segment through this reversible double-strand break results in a variety of DNA topoisomerization reactions, including relaxation:super-coiling; knotting:unknotting and catenation:decatenation. In support of this type of mechanism, we demonstrate that the T4 DNA topoisomerase changes the linking number of a covalently closed double-stranded circular DNA molecule only by multiples of two. We discuss the possible roles of such enzymes in a variety of biological functions, along with their probable molecular mechanisms.     

Thermoelasticity of red blood cell membrane.

The elastic properties of the human red blood cell membrane have been measured as functions of temperature. The area compressibility modulus and the elastic shear modulus, which together characterize the surface elastic behavior of the membrane, have been measured over the temperature range of 2-50 degrees C with micropipette aspiration of flaccid and osmotically swollen red cells. In addition, the fractional increase in membrane surface area from 2-50 degrees C has been measured to give a value for the thermal area expansivity. The value of the elastic shear modulus at 25 degrees C was measured to be 6.6 X 10(-3) dyne/cm. The change in the elastic shear modulus with temperature was -6 X 10(-5) dyne/cm degrees C. Fractional forces were shown to be only on the order of 10-15%. The area compressibility modulus at 25 degrees C was measured to be 450 dyne/cm. The change in the area compressibility modulus with temperature was -6 dyne/cm degrees C. The thermal area expansivity for red cell membrane was measured to be 1.2 X 10(-3)/degrees C. With this data and thermoelastic relations the heat of expansion is determined to be 110-200 ergs/cm2; the heat of extension is 2 X 10(-2) ergs/cm2 for unit extension of the red cell membrane. The heat of expansion is of the order anticipated for a lipid bilayer idealized as twice the behavior of a monolayer at an oil-water interface. The observation that the heat of extension is positive demonstrates that the entropy of the material increases with extension, and that the dominant mechanism of elastic energy storage is energetic. Assuming that the red cell membrane shear rigidity is associated with "spectrin," unit extension of the membrane increases the configurational entropy of spectrin by 500 cal/mol.     

Knotted vs. Unknotted Proteins: Evidence of Knot-Promoting Loops

Knotted proteins, because of their ability to fold reversibly in the same topologically entangled conformation, are the object of an increasing number of experimental and theoretical studies. The aim of the present investigation is to assess, on the basis of presently available structural data, the extent to which knotted proteins are isolated instances in sequence or structure space, and to use comparative schemes to understand whether specific protein segments can be associated to the occurrence of a knot in the native state. A significant sequence homology is found among a sizeable group of knotted and unknotted proteins. In this family, knotted members occupy a primary sub-branch of the phylogenetic tree and differ from unknotted ones only by additional loop segments. These “knot-promoting” loops, whose virtual bridging eliminates the knot, are found in various types of knotted proteins. Valuable insight into how knots form, or are encoded, in proteins could be obtained by targeting these regions in future computational studies or excision experiments.     

Phage P1 Cre-loxP site-specific recombination. Effects of DNA supercoiling on catenation and knotting of recombinant products

Bacteriophage P1 contains a site-specific recombination system consisting of a site, loxP, and a recombinase protein Cre. We have shown that with purified Cre protein we can carry out recombination between two loxP sites in vitro. When that recombination occurs between two sites in direct orientation on the same DNA molecule, we observed the production of free and catenated circular molecules. In this paper we show that recombination between sites in opposite orientation leads to both knotted and unknotted circular products. We also demonstrate that the production of catenanes and knots is influenced by two factors: (1) supercoiling in the DNA substrate, supercoiled DNA substrates yield significantly more catenated and knotted products than nicked circular substrates; and (2) mutations in the loxP site, a class of mutations have been isolated that carry out recombination but result in a distribution of products in which the ratio of catenanes to free circles is increased over that observed with a wild-type site. A more detailed analysis of the products from recombination between wild-type sites indicates: (1) that the catenanes or knots produced by recombination are both simple and complex; (2) that the ratio of free products to catenanes is independent of the distance between the two directly repeated loxP sites; and (3) that for DNA substrates with four loxP sites significant recombination between non-adjacent sites occurs to give free circular products. These observations provide insights into how two loxP sites are brought together during recombination.     

Novel display of knotted DNA molecules by two-dimensional gel electrophoresis

We describe a two-dimensional agarose gel electrophoresis procedure that improves the resolution of knotted DNA molecules. The first gel dimension is run at low voltage, and DNA knots migrate according to their compactness. The second gel dimension is run at high voltage, and DNA knots migrate according to other physical parameters such as shape and flexibility. In comparison with one-dimensional gel electrophoresis, this procedure segregates the knotted DNA molecules from other unknotted forms of DNA, and partially resolves populations of knots that have the same number of crossings. The two-dimensional display may allow quantitative and qualitative characterization of different types of DNA knots simply by gel velocity.     

Effects of small neutral osmolytes on the supercoiling free energy and intrinsic twist of p30delta DNA

Both theory and experiments are employed to investigate the effects of small neutral osmolytes on the average intrinsic twist (l0), the torsion and bending elastic constants, and the twist energy parameter (ET) that governs the supercoiling free energy. The experimental data for ethylene glycol and acetamide at 37 degrees C suggest, and are interpreted in terms of, a model wherein the DNA exhibits an equilibrium between two distinct conformational states that possess different numbers of bound water molecules and exhibit different intrinsic twists and torsion and bending elastic constants. Expressions are derived to relate the effective ET and l0 to the equilibrium constant, water activity (aw), and number (n) of bound water molecules released per cooperative domain undergoing the two-state transition. The variations of l0 and ET with -ln(aw) are similar for acetamide and ethylene glycol at 37 degrees C. Fitting the theory to those data yields the range n = 103-125 for ethylene glycol and n = 71-113 for acetamide, depending on the assumed value of ET for the dehydrated state. The cooperative domain size of the two-state transition is estimated to exceed about 25-30 base pairs (bp). Between 0 and 19.4 w/v % ethylene glycol, the torsion elastic constant, measured by time-resolved fluorescence polarization anisotropy (FPA), increases by 1.37-fold, whereas the measured ET decreases by 1.15-fold over that same range. The implied decrease in bending rigidity over that range is by a factor of about 0.7. The variations of l0 and ET with increasing -ln(aw) due to added ethylene glycol at 37 degrees C are far smaller than the corresponding variations observed previously at 14 and 15 degrees C. However, at 21 degrees C, upon adding either ethylene glycol or acetamide, l0 and ET initially decline steeply with increasing -ln(aw), with slopes possibly comparable to those seen at 14 and 15 degrees C, but then flatten out and follow curves similar to those at 37 degrees C. Possible origins of such mixed behavior are discussed. The effects of betaine at both 37 and 21 degrees C differ qualitatively and quantitatively in various respects from those of ethylene glycol and acetamide. Upon adding sucrose, l0 initially jumps to higher plateaus at both 37 and 21 degrees C, but its effects on ET cannot be reliably assessed, due to the limited range of -ln(aw).     

Osmotic behavior of red blood cell as seen with an ultrasonic method

We have measured the density and ultrasonic velocity (usv) of swine red blood cell (RBC) suspensions in the wide osmolarity range from 300 mOsm to 1400 mOsm in saline solution. The cellular density and compressibility of RBC at each osmolarity were obtained using the fact that the density and the compressibility are additive by volume. The osmolarity dependence of hematocrit was also measured at a constant number concentration of RBC in the range of 300 mOsm to 1700 mOsm. The cellular density and the cellular compressibility of RBC as well as the inverse of hematocrit were expressed well into one unique exponential type equation f (pi) = a [1 - b exp (-c pi)] with a common value for the coefficient c = 0.0025 against the osmolarity pi. The results were analyzed with a simple consideration based only upon the contribution of free water inside the erythrocyte through the volume concentration phi of the free water in it. According to this theoretical analysis, the density and the compressibility of the free water were found to be 0.990 g/cm3 and 4.59 x 10(-11) cm2/dyne which agree closely with 0.998 g/cm3 and 4.59 x 10(-11) cm2/dyn of pure water at 20 degrees C within the experimental error.     

Effects of selective hypoglossal nerve stimulation on canine upper airway mechanics.

Electrical stimulation of the hypoglossal (XII) nerve has been demonstrated as an effective approach to treating obstructive sleep apnea. The physiological effects of conventional modes of stimulation (i.e., genioglossus activation or whole XII nerve stimulation), however, have yielded inconsistent and only partial alleviations of hypopneic or apneic events. Although selective stimulation of the multifasciculated XII nerve offers many stimulus options, it is not clear how these will functionally affect the upper airway (UAW). To study these effects, animal experiments in eight beagles were performed to investigate changes in the UAW resistance and critical pressure during simulated expiration (n = 4) and inspiration (n = 4). During expiration, nonselective XII nerve stimulation yielded the greatest improvement in UAW resistance (-0.66 +/- 0.11 cm H2O x l(-1) x min(-1)), compared with that for selective activation of the geniohyoid (-0.29 +/- 0.09 cm H2O x l(-1) x min(-1)), genioglossus (-0.31 +/- 0.12 cm H2O x l(-1) x min(-1)), and hyoglossus/styloglossus (0.37 +/- 0.06 cm H2O x l(-1) x min(-1)) muscles. For simulated inspiration, on the other hand, only whole XII nerve stimulation (-0.9 +/- 0.4 cm H2O) and coactivation of the genioglossus + hyoglossus/styloglossus muscles (-1.18 +/- 0.6 cm H2O) produced significant (P < 0.05) improvements in UAW stability (i.e., lowered critical pressure), compared with baseline (-0.52 +/- 0.32 cm H2O). The results of this study suggest that a multicontact nerve electrode can be used to achieve both UAW dilation and patency, comparable to that obtained with nonselective stimulation, by selectively activating the various branches of the XII nerve.     

Calibration of beam deflection produced by cellular forces in the 10(-9)--10(-6) gram range

An experimental procedure and method of analysis are presented for calibration of a thin-beam force transducer. The beam transducer can be produced and calibrated with a minimum coefficient of 10 ng (10(-5) dyne) force per micron (10(-4) cm) deflection, i.e., kB approximately 0.1 dyne/cm. Since beam deflections on the order of 0.1 micron can be detected, forces of a few nanograms can be resolved. Such forces are common in mechanical experiments on microscopic bodies, e.g., biological cells, artificial membrane capsules, droplets, etc.     

Light-scattering studies on supercoil unwinding

It has been shown previously that supercoiled [unk]X174 bacteriophage intracellular DNA (mol.wt. 3.2x10(6)) with superhelix density, sigma=-0.025 (-12 superhelical turns) at 25 degrees C is best represented as a Y shape. In this work two techniques have been used to unwind the supercoil and study the changes in tertiary structure which result from changes in the secondary structure. The molecular weights from all experiments were in the range 3.2x10(6)+/-0.12x10(6). In experiments involving temperature change little change in the Y shape was observed between sigma=-0.027 (-13 superhelical turns, 14.9 degrees C) and sigma=-0.021 (-10 superhelical turns, 53.4 degrees C) as evidenced by the root-mean-square radius and the particle-scattering factor P(theta). However, at sigma=-0.0176 (-8 superhelical turns, 74.5 degrees C) the root-mean-square radius fell to between 60 and 70nm from 90nm indicating a large structural change, as did alterations in the P(theta) function. In experiments with the intercalating dye proflavine from values of bound proflavine of 0-0.06mol of dye/mol equiv. of nucleotide which correspond to values of sigma from -0.025 to -0.0004 (-12 to 0 superhelical turns) a similar transition was found when the superhelix density was changed by the same amount, and the molecule was shown to go through a further structural change as the unwinding of the duplex proceeded. At sigma=-0.018 (-9 superhelical turns) the structure was compatible with a toroid, and at sigma=-0.0004 it was compatible with a circle but at no point in the sequence of structure transitions was the structure compatible with the conventional straight interwound model normally visualized as the shape of supercoiled DNA.     

Partial specific volume and adiabatic compressibility of G-actin depend on the bound nucleotide

We determined the partial specific volume and partial specific adiabatic compressibility of either ATP- or ADP-bound monomeric actin in the presence of Ca(2+) by measuring the density of and sound velocity in a monomeric actin solution at 18 degrees C. The partial specific volume of ATP-bound monomeric actin, equal to 0.744 cm(3)/g, which is exceptionally high among globular proteins, was reduced to 0.727 cm(3)/g when the tightly bound ATP was replaced with ADP. Associated with this, the adiabatic compressibility of ATP-bound monomeric actin, equal to 8.8 x 10(-12) cm(2)/dyne, decreased to 5.8 x 10(-12) cm(2)/dyne, which is a common value for globular proteins. These results suggested that an extraordinarily soft global conformation of ATP-bound monomeric actin is packed into a compact mass associated with the hydrolysis of bound ATP. When monomeric actin was limitedly proteolyzed at subdomain 2 with subtilisin, the nucleotide-dependent flexibility of the global conformation of monomeric actin was lost.     

DNA supercoiling inhibits DNA knotting

Despite the fact that in living cells DNA molecules are long and highly crowded, they are rarely knotted. DNA knotting interferes with the normal functioning of the DNA and, therefore, molecular mechanisms evolved that maintain the knotting and catenation level below that which would be achieved if the DNA segments could pass randomly through each other. Biochemical experiments with torsionally relaxed DNA demonstrated earlier that type II DNA topoisomerases that permit inter- and intramolecular passages between segments of DNA molecules use the energy of ATP hydrolysis to select passages that lead to unknotting rather than to the formation of knots. Using numerical simulations, we identify here another mechanism by which topoisomerases can keep the knotting level low. We observe that DNA supercoiling, such as found in bacterial cells, creates a situation where intramolecular passages leading to knotting are opposed by the free-energy change connected to transitions from unknotted to knotted circular DNA molecules.     

The presence of the region on pBR322 that encodes resistance to tetracycline is responsible for high levels of plasmid DNA knotting in Escherichia coli DNA topoisomerase I deletion mutant.

Plasmid pBR322 DNA isolated from Escherichia coli DNA topoisomerase I deletion mutant DM800 is estimated to contain about 10% of the knotted forms (Shishido et al., 1987). These knotted DNA species were shown to have the same primary structure as usual, unknotted pBR322 DNA. Analysis of the knotting level of deletion, insertion and sequence-rearranged derivatives of pBR322 in DM800 showed that the presence of the region on pBR322 encoding resistance to tetracycline (tet) is required for high levels of plasmid knotting. When the entire tet region is present in a native orientation, the level of knotting is highest. Inactivating the tet promoter is manifested by a middle level of knotting. For deletion derivatives lacking various portions of the tet region, the level of knotting ranges from lowest to high depending on the site and length of the tet gene remaining. Inverting the orientation of tet region on the pBR322 genome results in a middle level of knotting. Deleting the ampicillin-resistance (bla)gene outside of its second promoter does not affect the level of knotting, if the entire tet gene remains. A possible mechanism of regulation of plasmid knotting is discussed.