arXiv subjects

Alexey K. Mazur

Publications and source records attributed to Alexey K. Mazur.

26 records · Page 2Linked to original sources

arXiv2000

Molecular Dynamics Studies of Sequence-directed Curvature in Bending Locus of Trypanosome Kinetoplast DNA

The macroscopic curvature induced in the double helical B-DNA by regularly repeated adenine tracts (A-tracts) plays an exceptional role in structural studies of DNA because this effect presents the most well-documented example of sequence specific conformational modulations. Recently, a new hypothesis of its physical origin has been put forward, based upon the results of molecular dynamics simulations of a 25-mer fragment with three A-tracts phased with the helical screw. Its sequence, however, had never been encountered in experimental studies, but was constructed empirically so as to maximize the magnitude of bending in specific computational conditions. Here we report the results of a similar investigation of another 25-mer B-DNA fragment now with a natural base pair sequence found in a bent locus of a minicircle DNA. It is shown that the static curvature of a considerable magnitude and stable direction towards the minor grooves of A-tracts emerges spontaneously in conditions excluding any initial bias except the base pair sequence. Comparison of the bending dynamics of these two DNA fragments reveals both qualitative similarities and interesting differences. The results suggest that the A-tract induced bending obtained in simulations reproduces the natural phenomenon and validates the earlier conclusions concerning its possible mechanism.

physics.bio-ph↗

arXiv2000

The Physical Origin of Intrinsic Bends in Double Helical DNA

The macroscopic curvature induced in the double helical B-DNA by regularly repeated adenine tracts (A-tracts) is a long known, but still unexplained phenomenon. This effect plays a key role in DNA studies because it is unique in the amount and the variety of the available experimental information and, therefore, is likely to serve as a gate to the unknown general mechanisms of recognition and regulation of genome sequences. We report the results of molecular dynamics simulations of a 25-mer B-DNA fragment with a sequence including three A-tract phased with the helical screw. It represents the first model system where properly directed static curvature emerges spontaneously in conditions excluding any initial bias except the base pair sequence. The effect has been reproduced in three independent MD trajectories of 10-20 ns with important qualitative details suggesting that the final bent state is a strong attractor of trajectories form a broad domain of the conformational space. The ensemble of curved conformations, however, reveals significant microscopic heterogeneity in contradiction to all existing theoretical models of bending. Analysis of these unexpected observations leads to a new, significantly different hypothesis of the possible mechanism of intrinsic bends in the double helical DNA.

physics.bio-ph↗

arXiv2000

A-Tract Induced DNA Bending is A Local Non-Electrostatic Effect

The macroscopic curvature induced in double helical B-DNA by regularly repeated adenine tracts (A-tracts) is a long known, but still unexplained phenomenon. This effect plays a key role in DNA studies because it is unique in the amount and the variety of the available experimental information and, therefore, is likely to serve as a gate to the unknown general mechanisms of recognition and regulation of genome sequences. The dominating idea in the recent years was that, in general, macroscopic bends in DNA are caused by long range electrostatic repulsion between phosphate groups when some of them are neutralized by proximal external charges. In the case of A-tracts this may be specifically bound solvent counterions. Here we report about molecular dynamics simulations where a correct static curvature in a DNA fragment with phased adenine tracts emerges spontaneously in conditions where any role of counterions or long range electrostatic effects can be excluded.

physics.bio-ph↗

arXiv1999

A Minimal Model of B-DNA

Recently it has been found that stable and accurate molecular dynamics (MD) of B-DNA duplexes can be obtained in relatively inexpensive computational conditions with the bulk solvent represented implicitly, but the minor groove filled with explicit water (J. Am. Chem. Soc. 1998, 120, 10928). The present paper further explores these simulation conditions in order to understand the main factors responsible for the observed surprisingly good agreement with experimental data. It appears that in the case of the EcoRI dodecamer certain sequence specific hydration patterns in the minor groove earlier known from experimental data are formed spontaneously in the course of MD simulations. The effect is reliably reproduced in several independent computational experiments in different simulation conditions. With all major groove water removed, closely similar results are obtained, with even better reproducibility. On the other hand, without explicit hydration, metastable dynamics around a B-DNA like state can be obtained which, however, only poorly compares with experimental data. It appears, therefore, that a right-handed DNA helix with explicitly hydrated minor groove is a minimal model system where the experimental properties of B-DNA can be reproduced with non-trivial sequence-dependent effects. Its small size makes possible virtually exhaustive sampling, which is a major advantage with respect to alternative approaches. An appendix is included with a correction to the implicit leapfrog integrator used in internal coordinate MD.

physics.comp-ph↗

arXiv1998

A Rational Approach to Ring Flexibility in Internal Coordinate Dynamics

Internal coordinate molecular dynamics (ICMD) is an efficient method for studying biopolymers, but it is readily applicable only to molecules with tree topologies, that is with no internal flexible rings. Common examples violating this condition are prolines and loops closed by S-S bridges in proteins. The most important such case, however, is nucleic acids because the flexibility of the furanose rings always plays an essential role in conformational transitions both in DNA and RNA. There are a few long-known theoretical approaches to this problem, but, in practice, rings with fixed bond lengths are closed by adding appropriate harmonic distance restraints, which is not always acceptable especially in dynamics. This paper tries to overcome this handicap of ICMD and proposes a rational strategy which results in practical numerical algorithms. It gives a unified analytical treatment which shows that this problem is very close to the difficulties encountered by the method of constraints in Cartesian coordinate dynamics, and certain ideas of the latter appear helpful in the context of ICMD. The method is affordable for large molecules and generally applicable to all kinds of rings. A specific implementation for five-membered rings is described and tested for a proline-rich polypeptide and a decamer DNA duplex. In both cases conditions are found which make possible time steps around 10 fsec in ICMD calculations.

physics.comp-ph↗

arXiv1998

The Hierarchy of Fast Motions in Protein Dynamics

For many biological applications of molecular dynamics (MD) the importance of good sampling in conformational space makes it necessary to eliminate the fastest motions from the system in order to increase the time step. An accurate knowledge of these motions is a necessary prerequisite for such efforts. It is known that harmonic vibrations of bond lengths and bond angles produce the highest frequencies in proteins. There are also fast anharmonic motions, such as inter-atomic collisions, which are probably most important when bond lengths and bond angles are fixed. However, the specific time scales corresponding to all these limitations are not known precisely. In order to clarify the above issue this paper analyses time step limiting factors in a series of numerical tests by using an internal coordinate molecular dynamics approach, which allows chosen internal coordinates to be frozen. It is found that, in proteins, there is a rather complicated hierarchy of fast motions, with both harmonic and anharmonic effects mixed together at several close time scales. Non-bonded interactions, notably strong hydrogen bonding, create locally distributed normal modes with frequencies similar to those of bond stretching between non-hydrogen atoms. They also impose ubiquitous anharmonic limitations starting from rather small step sizes. With fixed standard amino acid geometry, rotations of hydrogen bonded hydroxyl groups limit time steps at the 5 fsec level. The next important limitation occurs around 10 fsec and is created by collisions between non-hydrogen atoms.

physics.comp-ph↗

arXiv1997

Common Molecular Dynamics Algorithms Revisited: Accuracy and Optimal Time Steps of Stoermer-Leapfrog Integrators

The Stoermer-Verlet-leapfrog group of integrators commonly used in molecular dynamics simulations has long become a textbook subject and seems to have been studied exhaustively. There are, however, a few striking effects in performance of algorithms which are well-known but have not received adequate attention in the literature. A closer view of these unclear observations results in unexpected conclusions. It is shown here that contrary to the conventional point of view, the leapfrog scheme is distinguished in this group both in terms of the order of truncation errors and the conservation of the total energy. In this case the characteristic square growth of fluctuations of the total energy with the step size, commonly measured in numerical tests, results from additional interpolation errors with no relation to the accuracy of the computed trajectory. An alternative procedure is described for checking energy conservation of leapfrog-like algorithms which is free from interpolation errors. Preliminary tests on a representative model system suggest that standard step size values used at present are lower than necessary for accurate sampling.

physics.comp-ph↗

arXiv1997

Quasi-Hamiltonian Equations of Motion for Internal Coordinate Molecular Dynamics of Polymers

Conventional molecular dynamics simulations macromolecules require long computational times because the most interesting motions are very slow compared with the fast oscillations of bond lengths and bond angles that limit the integration time step. Simulation of dynamics in the space of internal coordinates, that is with bond lengths, bond angles and torsions as independent variables, gives a theoretical possibility to eliminate all uninteresting fast degrees of freedom from the system. This paper presents a new method for internal coordinate molecular dynamics simulations of macromolecules. Equations of motion are derived which are applicable to branched chain molecules with any number of internal degrees of freedom. Equations use the canonical variables and they are much simpler than existing analogs. In the numerical tests the internal coordinate dynamics are compared with the traditional Cartesian coordinate molecular dynamics in simulations a 56 residue globular protein. It is shown that the traditional and internal coordinate dynamics require the same time step size for the same accuracy and that in the standard geometry approximation of amino acids, that is with fixed bond lengths, bond angles and rigid aromatic groups, the characteristic step size is 4 fsec, that is two times higher than with fixed bond lengths only. The step size can be increased up to 11 fsec when rotation of hydrogen atoms is suppressed.

physics.chem-ph↗