A note on graphing helical parameters of dynamics structure of DNA

A graphical procedure for analysis of helical parameters in dynamic structure of DNA is described. The performance of the procedure is illustrated by analysis of a 20 ps dynamics simulation of the non-self-complementary ninemer, 5'CAAACAGGA:5'TCCTGTTTG, which is a part of DNA from lacI gene. The dynamics trajectory of the duplex shows sequence-dependent fluctuations of helical parameters.     

Orientation by helical motion—II. Changing the direction of the axis of motion

We analyse the helical motion of organisms, concentrating on the means by which organisms change the direction in space of the axis of the helical trajectory, which is the net direction of motion. We demonstrate that the direction of the axis is determined largely by the direction of the organism's rotational velocity. Changes in direction of the rotational velocity, with respect to the organism's body, change the direction in space of the axis of the helical trajectory. Conversely, changes in direction of the translational velocity, with respect to the body of the organism, have little effect on the direction in space of the axis of the trajectory. Because the axis of helical motion is the net direction of motion, it is likely that organisms that move in helices change direction by pointing their rotational velocity, not their translational velocity, in a new direction.     

Molecular dynamics simulations of a nucleosome and free DNA

All atom molecular dynamics simulations (10ns) of a nucleosome and of its 146 basepairs of DNA free in solution have been conducted. DNA helical parameters (Roll, Tilt, Twist, Shift, Slide, Rise) were extracted from each trajectory to compare the conformation, effective force constants, persistence length measures, and fluctuations of nucleosomal DNA to free DNA. The conformation of DNA in the nucleosome, as determined by helical parameters, is found to be largely within the range of thermally accessible values obtained for free DNA. DNA is found to be less flexible on the nucleosome than when free in solution, however such measures are length scale dependent. A method for disassembling and reconstructing the conformation and dynamics of the nucleosome using Fourier analysis is presented. Long length variations in the conformation of nucleosomal DNA are identified other than those associated with helix repeat. These variations are required to create a proposed tetrasome conformation or to qualitatively reconstruct the 1.75 turns of the nucleosome's superhelix. Reconstruction of free DNA using selected long wavelength variations in conformation can produce either a left-handed or a right-handed superhelix. The long wavelength variations suggest 146 basepairs is a natural length of DNA to wrap around the histone core.     

Molecular Dynamics Simulations of a Nucleosome and Free DNA

Abstract

All atom molecular dynamics simulations (10ns) of a nucleosome and of its 146 basepairs of DNA free in solution have been conducted. DNA helical parameters (Roll, Tilt, Twist, Shift, Slide, Rise) were extracted from each trajectory to compare the conformation, effective force constants, persistence length measures, and fluctuations of nucleosomal DNA to free DNA. The conformation of DNA in the nucleosome, as determined by helical parameters, is found to be largely within the range of thermally accessible values obtained for free DNA. DNA is found to be less flexible on the nucleosome than when free in solution, however such measures are length scale dependent. A method for disassembling and reconstructing the conformation and dynamics of the nucleosome using Fourier analysis is presented. Long length variations in the conformation of nucleosomal DNA are identified other than those associated with helix repeat. These variations are required to create a proposed tetrasome conformation or to qualitatively reconstruct the 1.75 turns of the nucleosome's superhelix. Reconstruction of free DNA using selected long wavelength variations in conformation can produce either a left-handed or a right-handed superhelix. The long wavelength variations suggest 146 basepairs is a natural length of DNA to wrap around the histone core.     

Trajectory formation of arm movement by cascade neural network model based on minimum torque-change criterion

We proposed that the trajectory followed by human subject arms tended to minimize the time integral of the square of the rate of change of torque (Uno et al. 1987). This minimum torque-change model predicted and reproduced human multi-joint movement data quite well (Uno et al. 1989). Here, we propose a neural network model for trajectory formation based on the minimum torque-change criterion. Basic ideas of information representation and algorithm are(i) spatial representation of time,(ii) learning of forward dynamics and kinetics model and(iii) relaxation computation based on the acquired model. The model can resolve ill-posed inverse kinematics and inverse dynamics problems for redundant controlled object as well as ill-posed trajectory formation problems. By computer simulation, we show that the model can produce a multi-joint arm trajectory while avoiding obstacles or passing through viapoints.     

Effects of Geometric Parameters on Swimming of Micro Organisms with Single Helical Flagellum in Circular Channels

We present a computational fluid dynamics (CFD) model for the swimming of micro organisms with a single helical flagellum in circular channels. The CFD model is developed to obtain numerical solutions of Stokes equations in three dimensions, validated with experiments reported in literature, and used to analyze the effects of geometric parameters, such as the helical radius, wavelength, radii of the channel and the tail and the tail length on forward and lateral swimming velocities, rotation rates, and the efficiency of the swimmer. Optimal shapes for the speed and the power efficiency are reported. Effects of Brownian motion and electrostatic interactions are excluded to emphasize the role of hydrodynamic forces on lateral velocities and rotations on the trajectory of swimmers. For thin flagella, as the channel radius decreases, forward velocity and the power efficiency of the swimmer decreases as well; however, for thick flagella, there is an optimal radius of the channel that maximizes the velocity and the efficiency depending on other geometric parameters. Lateral motion of the swimmer is suppressed as the channel is constricted below a critical radius, for which the magnitude of the lateral velocity reaches a maximum. Results contribute significantly to the understanding of the swimming of bacteria in micro channels and capillary tubes.     

Effects of Geometric Parameters on Swimming of Micro Organisms with Single Helical Flagellum in Circular Channels

We present a computational fluid dynamics (CFD) model for the swimming of micro organisms with a single helical flagellum in circular channels. The CFD model is developed to obtain numerical solutions of Stokes equations in three dimensions, validated with experiments reported in literature, and used to analyze the effects of geometric parameters, such as the helical radius, wavelength, radii of the channel and the tail and the tail length on forward and lateral swimming velocities, rotation rates, and the efficiency of the swimmer. Optimal shapes for the speed and the power efficiency are reported. Effects of Brownian motion and electrostatic interactions are excluded to emphasize the role of hydrodynamic forces on lateral velocities and rotations on the trajectory of swimmers. For thin flagella, as the channel radius decreases, forward velocity and the power efficiency of the swimmer decreases as well; however, for thick flagella, there is an optimal radius of the channel that maximizes the velocity and the efficiency depending on other geometric parameters. Lateral motion of the swimmer is suppressed as the channel is constricted below a critical radius, for which the magnitude of the lateral velocity reaches a maximum. Results contribute significantly to the understanding of the swimming of bacteria in micro channels and capillary tubes.     

Electromagnetic field generation by ATP-induced reverse electron transfer

This paper describes a mechanism to explain low-level light emission in biology. A biological analog of the electrical circuitry, modeled on the parallel plate capacitor, traversed by a helical structure, required to generate electromagnetic radiation in the optical spectral range, is described. The charge carrier required for the emissions is determined to be an accelerating electron driven by an ATP-induced reverse electron transfer. The radial velocity component, the emission trajectory, of the moving charges traversing helical protein structures in a cyclotron-type mechanism is proposed to be imposed by the ferromagnetic field components of the iron in the iron-sulfur proteins. The redox systems NADH, riboflavin, and chlorophyll were examined with their long-wavelength absorption maxima determining the energetic parameters for the calculations. Potentials calculated from the axial velocity components for the riboflavin and NADH systems were found to equal the standard redox potentials of these systems as measured electrochemically and enzymatically. The mechanics for the three systems determined the magnetic moments, the angular momenta, and the orbital magnetic fluxes to be adiabatic invariant parameters. The De Broglie dual wave-particle equation, the fundamental equation of wave mechanics, and the key idea of quantum mechanics, establishes the wavelengths for accelerating electrons which, divided into a given radial velocity, gives its respective emission frequency. Electrons propelled through helical structures, traversed by biologically available electric and magnetic fields, make accessible to the internal environment the optical spectral frequency range that the solar spectrum provides to the external environment.     

Projected free fall trajectories

We are very adept at using the purely two-dimensional information we get from our retinae to manoever and react to the three-dimensional world: witness the tennis player returning a 100 mph serve. In another article (Saxberg 1987) we have shown how gravity can in theory be used as a constraint to determine the initial conditions of a three-dimensional free fall trajectory from the two-dimensional central projection of the trajectory. We have developed a simple video game to investigate what information is important to humans trying to solve a problem of this sort: predicting where a ball will fall. We show that humans do not seem to use the trajectory information suggested by the theoretical results in (Saxberg 1985), but rely on other sources of information, such as the size of the image on the projection surface.     

An interactive modeling program for DNA

An interactive program for modeling A-, B- and Z-DNA in a schematic and nonatomic representation has been developed for the Evans and Sutherland PS300. The program lets users display several molecules for which parameters determining the three-dimensional structure can be calculated either on the basis of theoretical models or inferred from experimental data. The calculation of the curvature and torsion of the helical axis, by a method based on Frenet's equations, makes it possible to quantify the effects of the parameters on the helical axis.     

A secondary and tertiary structure editor for nucleic acids

A major difficulty in the evaluation of secondary and tertiarystructures of nucleic acids is the lack of convenient methodsfor their construction and representation. As a first step ina study of the symbolic representation of biopolymers, we reportthe development of a structure editor written in Pascal, permittingmodel construction on the screen of a personal computer. Theprogram calculates energies for helical regions, allows user-definedhelices and displays the secondary structure of a nucleic acidbased on a user-selected set of helices. Screen and printeroutputs can be in the form of a backbone or the letters of theprimary sequence. The molecule can then be displayed in a formatwhich simulates its three-dimensional structure. Using appropriateglasses, the molecule can be viewed on the screen in three dimensions.Other options include the manipulation of helices and single-strandedregions which results in changes in the spatial relationshipbetween different regions of the molecule. The editor requiresan IBM or compatible PC, 640 kbyte memory and a medium or highresolution graphics card. Received on September 19, 1987; accepted on November 15, 1987     

The plasticity of a structural motif in RNA: Structural polymorphism of a kink turn as a function of its environment

The k-turn is a widespread structural motif that introduces a tight kink into the helical axis of double-stranded RNA. The adenine bases of consecutive G•A pairs are directed toward the minor groove of the opposing helix, hydrogen bonding in a typical A-minor interaction. We show here that the available structures of k-turns divide into two classes, depending on whether N3 or N1 of the adenine at the 2b position accepts a hydrogen bond from the O2′ at the −1n position. There is a coordinated structural change involving a number of hydrogen bonds between the two classes. We show here that Kt-7 can adopt either the N3 or N1 structures depending on environment. While it has the N1 structure in the ribosome, on engineering it into the SAM-I riboswitch, it changes to the N3 structure, resulting in a significant alteration in the trajectory of the helical arms.     

Systematic study of nuclear Overhauser effects vis-à-vis local helical parameters, sugar puckers, and glycosidic torsions in B DNA: insensitivity of NOE to local transitions in B DNA oligonucleotides due to internal structural compensations.

A method has been developed to solve structures of DNA oligomers in solution from the experimental NOE data. The method is a combination of two approaches: (1) full matrix NOESY simulations and (2) conformational calculations of DNA double helix based on generalized helical parameters. The process of the refinement of a solution structure does not involve NMR-derived interproton distance constraints; rather it consists of a direct fitting of a structure to the experimental NOE data, a weighted sum of energy, and R factor being under minimization. A helical parameters-based generation of DNA forms makes it possible to organize the search for the optimal structure more effectively, systematically varying starting conformations. The method has been used to calculate a structure for the self-complementary DNA hexamer GGATCC, which is consistent with the available experimental data. The structure belongs to the B family of forms, although the local structural heterogeneity is very strong. Sugar puckers vary from O4'-exo to C3'-exo; helical steps are open with different magnitudes toward the minor groove. Next, we have addressed the question of how uniquely the structure is defined by the existing NMR data. Different structural parameters have been systematically varied, and their effect on individual NOE's and the R factor has been studied. Two energetically conjugated parameters, sugar puckers and glycosidic angles, can be determined very reliably, because of the strong dependences of the intraresidue H6/H8 to H2'/H2'/H3' NOE's. In contrast, the local helical conformation of DNA and the geometry of base pairs proved to be underdetermined by the existing NOE information, because the effect of any helical parameter on interproton distances can be compensated by the concerted changes in other parameters.     

Swimming behaviour of the multicellular magnetotactic prokaryote ‘Candidatus Magnetoglobus multicellularis’ under applied magnetic fields and ultraviolet light

Magnetotactic bacteria move by rotating their flagella and concomitantly are aligned to magnetic fields because they present magnetosomes, which are intracellular organelles composed by membrane-bound magnetic crystals. This results in magnetotaxis, which is swimming along magnetic field lines. Magnetotactic bacteria are morphologically diverse, including cocci, rods, spirilla and multicellular forms known as magnetotactic multicellular prokaryotes (MMPs). ‘Candidatus Magnetoglobus multicellularis’ is presently the best known MMP. Here we describe the helical trajectories performed by these microorganisms as they swim forward, as well as their response to UV light. We measured the radius of the trajectory, time period and translational velocity (velocity along the helix axis), which enabled the calculation of other trajectory parameters such as pitch, tangential velocity (velocity along the helix path), angular frequency, and theta angle (the angle between the helix path and the helix axis). The data revealed that ‘Ca. M. multicellularis’ swims along elongated helical trajectories with diameters approaching the diameter of the microorganism. In addition, we observed that ‘Ca. M. multicellularis’ responds to UV laser pulses by swimming backwards, returning to forward swimming several seconds after the UV laser pulse. UV light from a fluorescence microscope showed a similar effect. Thus, phototaxis is used in addition to magnetotaxis in this microorganism.     

RNA secondary structures: comparison and determination of frequently recurring substructures by consensus

A method for assessing the preserved stem - loops of RNA secondarystructures is presented. Frequently recurring helical stemsin a set of secondary structures resulting from the simulatedfolding process of a given RNA are assessed and consensus structuralmotifs can then be selected to construct a secondary structureof the RNA. Alternatively, it can be applied to a series of‘optimal’ and ‘suboptimal’ secondarystructures computed using the dynamic program developed by Williamsand Tinoco. To demonstrate the power and the usefulness of theprogram we give examples of this procedure. Received on October 28, 1987; accepted on April 2, 1989     

Folding and catalysis by the hairpin ribozyme.

The hairpin ribozyme undergoes a site-specific transesterification cleavage of the phosphodiester backbone. The natural form of the ribozyme is a four-way helical junction, where two arms contain unpaired loops. This folds by pairwise coaxial stacking of helical arms, and a rotation into an antiparallel conformation in which there is close association between the loops. This probably generates the local conformation required to facilitate the trajectory into an in-line SN2 transition state. Folding is induced by the cooperative binding of at least two divalent metal ions, which are probably distributed between the junction and the loop-loop interface. The junction forms the structural scaffold on which the geometry of the ribozyme is built, and structural perturbation of the junction leads to impaired catalytic activity.     

A real time learning algorithm for recurrent analog neural networks

A new learning algorithm is described for a general class of recurrent analog neural networks which ultimately settle down to a steady state. Recently, Pineda (Pineda 1987; Almeida 1987; Ikeda et al. 1988) has introduced a learning rule for the recurrent net in which the connection weights are adjusted so that the distance between the stable outputs of the current system and the desired outputs will be maximally decreased. In this method, many cycles are needed in order to get a target system. In each cycle, the recurrent net is run until it reaches a stable state. After that, the weight change is calculated by using a linearized recurrent net which receives the current error of the system as a bias input. In the new algorithm the weights are changed so that the total error of neuron outputs over the entire trajectory is minimized. The weights are adjusted in real time when the network is running. In this method, the trajectory to the target system can be controlled, whereas Pineda's algorithm only controls the position of the fixed point. The relation to the back propagation method (Hinton et al. 1986) is also discussed.     

The study of helical distortions due to environmental changes: choice of parameters

Parameters like interhelical angles, helical parameters, levels of distortions, etc., have been analysed to test their sensitivity to environmental changes using a method developed in this laboratory. This analysis was done on protein structures solved under different environmental conditions like temperature and pH, and ligand binding. The study reveals that the helical parameters are not sensitive enough to study the effect of environmental changes on protein helices. On the other hand the helical distortions as well as changes in the interhelical angles are more sensitive to these changes. The study also provides with additional information like the origin of distortions in a helix when a ligand binds to a protein, bending in helical axis, identification and extent of domain movements, etc.