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Biomedical subjects

I Tobias

Publications and source records attributed to I Tobias.

12 recordsLinked to original sources
PubMed2000

Elastic stability of DNA configurations. I. General theory.

Results are presented in the theory of the elastic rod model for DNA, among which are criteria enabling one to determine whether a calculated equilibrium configuration of a DNA segment is stable in the sense that it gives a local minimum to the sum of the segment's elastic energy and the potential of forces acting on it. The derived stability criteria are applicable to plasmids and to linear segments subject to strong anchoring end conditions. Their utility is illustrated with an example from the theory of configurations of the extranucleosomal loop of a DNA miniplasmid in a mononucleosome, with emphasis placed on the influence that nicking and ligation on one hand, and changes in the ratio of elastic coefficients on the other, have on the stability of equilibrium configurations. In that example, the configurations studied are calculated using an extension of the method of explicit solutions to cases in which the elastic rod modeling a DNA segment is considered impenetrable, and hence excluded volume effects and forces arising from self-contact are taken into account.

Biophysical Phenomena↗
PubMed2000

Elastic stability of DNA configurations. II. Supercoiled plasmids with self-contact.

Configurations of protein-free DNA miniplasmids are calculated with the effects of impenetrability and self-contact forces taken into account by using exact solutions of Kirchhoff's equations of equilibrium for elastic rods of circular cross section. Bifurcation diagrams are presented as graphs of excess link, DeltaL, versus writhe, W, and the stability criteria derived in paper I of this series are employed in a search for regions of such diagrams that correspond to configurations that are stable, in the sense that they give local minima to elastic energy. Primary bifurcation branches that originate at circular configurations are composed of configurations with D(m) symmetry (m=2,3,...). Among the results obtained are the following. (i) There are configurations with C2 symmetry forming secondary bifurcation branches which emerge from the primary branch with m=3, and bifurcation of such secondary branches gives rise to tertiary branches of configurations without symmetry. (ii) Whether or not self-contact occurs, a noncircular configuration in the primary branch with m=2, called branch alpha, is stable when for it the derivative dDeltaL/dW, computed along that branch, is strictly positive. (iii) For configurations not in alpha, the condition dDeltaL/dW>0 is not sufficient for stability; in fact, each nonplanar contact-free configuration that is in a branch other than alpha is unstable. A rule relating the number of points of self-contact and the occurrence of intervals of such contact to the magnitude of DeltaL, which in paper I was found to hold for segments of DNA subject to strong anchoring end conditions, is here observed to hold for computed configurations of protein-free miniplasmids.

Biophysical Phenomena↗
PubMed1998

The elastic rod model for DNA and its application to the tertiary structure of DNA minicircles in mononucleosomes.

Explicit solutions to the equations of equilibrium in the theory of the elastic rod model for DNA are employed to develop a procedure for finding the configuration that minimizes the elastic energy of a minicircle in a mononucleosome with specified values of the minicircle size N in base pairs, the extent w of wrapping of DNA about the histone core particle, the helical repeat h(0)b of the bound DNA, and the linking number Lk of the minicircle. The procedure permits a determination of the set Y(N, w, h(0)b) of integral values of Lk for which the minimum energy configuration does not involve self-contact, and graphs of writhe versus w are presented for such values of Lk. For the range of N of interest here, 330 < N < 370, the set Y(N, w, h(0)b) is of primary importance: when Lk is not in Y(N, w, h(0)b), the configurations compatible with Lk have elastic energies high enough to preclude the occurrence of an observable concentration of topoisomer Lk in an equilibrium distribution of topoisomers. Equilibrium distributions of Lk, calculated by setting differences in the free energy of the extranucleosomal loop equal to differences in equilibrium elastic energy, are found to be very close to Gaussian when computed under the assumption that w is fixed, but far from Gaussian when it is assumed that w fluctuates between two values. The theoretical results given suggest a method by which one may calculate DNA-histone binding energies from measured equilibrium distributions of Lk.

Base Composition↗
PubMed1998

A theory of thermal fluctuations in DNA miniplasmids.

A recent analysis of the normal modes of vibration of a ring formed by bringing together and sealing, with or without the addition of twist, the ends of rods that are straight when stress free is taken as the basis for a theory of the statistical thermodynamics of a canonical ensemble of DNA minicircles with specified linking number difference deltaLk and number N of base pairs. It is assumed that N corresponds to a circumference in the range of one or two persistence lengths. For such an ensemble, the theory yields an expression for the average writhe (Wr), which can be employed to calculate the free energy, entropy, and enthalpy of supercoiling, deltaGsc, deltaSsc, and deltaHsc. The results obtained for the dependence of deltaGsc on deltaLk and N are in accord with experimental observations of equilibrium distributions of topoisomers of plasmids with N approximately 200 bp.

DNA, Superhelical↗
PubMed1995

Effects of localized bending on DNA supercoiling.

The DNA double helix is straight only in the idealized case. In reality, it bends, twists and stretches in response to local base sequence and to specific interactions with proteins and other bound ligands. Naturally occurring bends appear to promote the assembly of nucleosomes, and in some cases can effectively replace regulatory DNA-binding proteins in vivo. Recently, a computational method known as 'finite element analysis', which is used routinely by engineers to analyse the stability of buildings and bridges, has been applied to the quantitative assessment of natural curvature in supercoiled DNA structures, providing new insight into the relationship between local, sequence-dependent features and the overall topology of these chains.

Computer Simulation↗
PubMed1994

Computer simulation of protein-induced structural changes in closed circular DNA.

The effect of protein-induced wrapping on overall DNA folding is studied using Monte Carlo computer simulation techniques. A new modeling scheme is devised to represent configurations of closed circular DNA containing fragments of the double helix partially wrapped around a core of proteins. The DNA consists of two regions, a fragment wrapped in a left-handed superhelical path around a 'phantom' protein core and a free connecting loop. The loop has at least one single-stranded scission so that it can assume a torsionally relaxed state. The configuration of the loop is varied during the course of the computer simulations and the three-dimensional spatial arrangements of lowest total energy are identified. The axis of the DNA loop is represented by a finite three-dimensional Fourier series perturbation of an initial Bézier curve, making it possible to fix the position and orientation of the chain ends as well as the contour length of the free loop. The energy is approximated by elastic terms for the bending and twisting of the DNA and an excluded volume contribution that prevents the self-intersection of sequentially distant chain segments. The proportions of the protein-DNA complex, the number of superhelical turns, the chain length and the imposed linking number difference of the closed DNA are varied in the calculations. The resulting minimum energy structures are consistent with physical models and suggest new ways to think about how proteins add and remove supercoils from DNA. Of special note in this regard is the sudden collapse of three-dimensional structure that accompanies small incremental wrapping of the DNA around the idealized protein core. These observations offer new structural insight into the mechanisms of action of proteins which add or remove supercoils from DNA and provide a first step in thinking about the activity of such systems at the chemical level whereby small fluctuations in local molecular structure are translated into large-scale macromolecular changes. The configurations identified in the simulations can also be examined in the context of the well known "linking number paradox" associated with nucleosome formation on closed circular plasmids. The findings bear relevance to DNA with natural curvature as well as to protein-induced bending and deformations of the double helix.

Computer Simulation↗
PubMed1994

Electrostatic effects in short superhelical DNA.

We present Monte Carlo simulations of the equilibrium configurations of short closed circular DNA that obeys a combined elastic, hard-sphere, and electrostatic energy potential. We employ a B-spline representation to model chain configuration and simulate the effects of salt on chain folding by varying the Debye screening parameter. We obtain global equilibrium configurations of closed circular DNA, with several imposed linking number differences, at two salt concentrations (specifically at the extremes of no added salt and the high salt regime), and for different chain lengths. Minimization of the composite elastic/long-range potential energy under the constraints of ring closure and fixed chain length is found to produce structures that are consistent with the configurations of short supercoiled DNA observed experimentally. The structures generated under the constraints of an electrostatic potential are less compact than those subjected only to an elastic term and a hard-sphere constraint. For a fixed linking number difference greater than a critical value, the interwound structures obtained under the condition of high salt are more compact than those obtained under the condition of no added salt. In the case of no added salt, the electrostatic energy plays a dominant role over the elastic energy in dictating the shape of the closed circular DNA. The DNA supercoil opens up with increasing chain length at low salt concentration. A branched three-leaf rose structure with a fixed linking number difference is higher in energy than the interwound form at both salt concentrations employed here.

DNA, Superhelical↗
PubMed1993

The effect of intrinsic curvature on supercoiling: predictions of elasticity theory.

Elasticity theory of naturally curved rods is employed to study the effects of intrinsic curvature on the properties of the equilibrium conformations of supercoiled DNA. The results stand in sharp contrast to those obtained when the molecule is viewed as being straight in its relaxed form. Starting from very fundamental principles of the theory, we show that the torsion of an open segment with a curved duplex axis can vary when the temperature, and along with it, the intrinsic twist is changed. Conversely, an imposed helicity, such as might be associated with binding to a histone, can change the intrinsic twist. It is also shown that another consequence of the presence of naturally curved sequences is that the twist density will, in general, vary with position along the chain in all equilibrium states. Then portions of the molecule will be more or less susceptible to interaction with other agents sensitive to such a variation. Finally, some closed equilibrium global structures uniquely associated with intrinsic curvature are discussed.

DNA, Superhelical↗
PubMed1985

The twist, writhe, and linking number distributions in closed circular DNA.

We discuss the predictions which follow from the assumption of statistically independent twist and writhe distributions of given variances in circular DNA with single-strand nicks. The nature of the topoisomer distribution produced upon covalent closure of the nicks is described, as well as the nature of the twist and writhe distributions in the fully-closed molecules. In particular, we show how the distributions depend on the magnitudes of the given variances, and how the relative magnitudes of the variances can be deduced from experiment. One additional consequence of the theory is the prediction of a necessary difference between the temperature coefficient of the twist in nicked versus fully-closed circular DNA. The ratio of the two twist coefficients turns out to depend only on the ratio of the twist and writhe variances in nicked DNA.

DNA, Circular↗
PubMedDate not supplied

Flexing and folding double helical DNA.

DNA base sequence, once thought to be interesting only as a carrier of the genetic blueprint, is now recognized as playing a structural role in modulating the biological activity of genes. Primary sequences of nucleic acid bases describe real three-dimensional structures with properties reflecting those structures. Moreover, the structures are base sequence dependent with individual residues adopting characteristic spatial forms. As a consequence, the double helix can fold into tertiary arrangements, although the deformation is much more gradual and spread over a larger molecular scale than in proteins. As part of an effort to understand how local structural irregularities are translated at the macromolecular level in DNA and recognized by proteins, a series of calculations probing the structure and properties of the double helix have been performed. By combining several computational techniques, complementary information as well as a series of built-in checks and balances for assessing the significance of the findings are obtained. The known sequence dependent bending, twisting, and translation of simple dimeric fragments have been incorporated into computer models of long open DNAs of varying length and chemical composition as well as in closed double helical circles and loops. The extent to which the double helix can be forced to bend and twist is monitored with newly parameterized base sequence dependent elastic energy potentials based on the observed configurations of adjacent base pairs in the B-DNA crystallographic literature.

Base Composition↗