John H. Maddocks

Conformational analysis of nucleic acids revisited: Curves+

We describe Curves+, a new nucleic acid conformational analysis program which is applicable to a wide range of nucleic acid structures, including those with up to four strands and with either canonical or modified bases and backbones. The program is algorithmically simpler and computationally much faster than the earlier Curves approach, although it still provides both helical and backbone parameters, including a curvilinear axis and parameters relating the position of the bases to this axis. It additionally provides a full analysis of groove widths and depths. Curves+ can also be used to analyse molecular dynamics trajectories. With the help of the accompanying program Canal, it is possible to produce a variety of graphical output including parameter variations along a given structure and time series or histograms of parameter variations during dynamics.

On the Kinematics of Wheeled Mobile Robots

A wheeled mobile robot is here modelled as a planar rigid body that rides on an arbitrary number of wheels. The rela tionship between the rigid body motion of the robot and the steering and drive rates of wheels is developed. In particular, conditions are obtained that guarantee that rolling without skidding or sliding can occur. Explicit differential equations are derived to describe the rigid body motions that arise in such ideal rolling trajectories. The simplest wheel configura tion that permits access of arbitrary rigid-body motions is determined. Then the question of slippage due to misalign ment of the wheels is investigated by minimization of a non- smooth convex dissipation functional that is derived from Coulombs Law offriction. It is shown that this minimization principle is equivalent to the construction of quasi-static motions. Examples are presented to illustrate the models.

A systematic molecular dynamics study of nearest-neighbor effects on base pair and base pair step conformations and fluctuations in B-DNA

It is well recognized that base sequence exerts a significant influence on the properties of DNA and plays a significant role in protein–DNA interactions vital for cellular processes. Understanding and predicting base sequence effects requires an extensive structural and dynamic dataset which is currently unavailable from experiment. A consortium of laboratories was consequently formed to obtain this information using molecular simulations. This article describes results providing information not only on all 10 unique base pair steps, but also on all possible nearest-neighbor effects on these steps. These results are derived from simulations of 50–100 ns on 39 different DNA oligomers in explicit solvent and using a physiological salt concentration. We demonstrate that the simulations are converged in terms of helical and backbone parameters. The results show that nearest-neighbor effects on base pair steps are very significant, implying that dinucleotide models are insufficient for predicting sequence-dependent behavior. Flanking base sequences can notably lead to base pair step parameters in dynamic equilibrium between two conformational sub-states. Although this study only provides limited data on next-nearest-neighbor effects, we suggest that such effects should be analyzed before attempting to predict the sequence-dependent behavior of DNA.

A continuum rod model of sequence-dependent DNA structure

Experimentally motivated parameters from a base‐pair‐level discrete DNA model are averaged to yield parameters for a continuum elastic rod with a curved unstressed shape reflecting the local DNA geometry. The continuum model permits computations with discretization lengths longer than the intrinsic discretization of the base‐pair model, and, for this and other reasons, yields an efficient computational formulation. Obtaining continuum stiffnesses is straightforward, but obtaining a continuum unstressed shape is hindered by the ‘‘noisy’’ small‐scale structure and rapid helix twist of the discrete unstressed shape. Filtering of the discrete data and an analytic transformation from the true normal‐vector field to a natural (untwisted) frame allows a stable continuum fit. Equilibrium energies of closed rings predicted by the continuum model are found to match the energies of the underlying discrete model to within 0.5%. The model is applied to a set of 11 short DNA molecules (≊ 150 bp) and properly distinguis...

Hamiltonian Dynamics of a Rigid Body in a Central Gravitational Field

This paper concerns the dynamics of a rigid body of finite extent moving under the influence of a central gravitational field. A principal motivation behind this paper is to reveal the hamiltonian structure of the n-body problem for masses of finite extent and to understand the approximation inherent to modeling the system as the motion of point masses. To this end, explicit account is taken of effects arising because of the finite extent of the moving body. In the spirit of Arnold and Smale, exact models of spin-orbit coupling are formulated, with particular attention given to the underlying Lie group framework. Hamiltonian structures associated with such models are carefully constructed and shown to benon-canonical. Special motions, namely relative equilibria, are investigated in detail and the notion of anon-great circle relative equilibrium is introduced. Non-great circle motions cannot arise in the point mass model. In our analysis, a variational characterization of relative equilibria is found to be very useful.Thereduced hamiltonian formulation introduced in this paper suggests a systematic approach to approximation of the underlying dynamics based on series expansion of the reduced hamiltonian. The latter part of the paper is concerned with rigorous derivations of nonlinear stability results for certain families of relative equilibria. Here Arnolds energy-Casimir method and Lagrange multiplier methods prove useful.

Stability of nonlinearly elastic rods

This paper describes previously unknown stabilities and instabilities of planar equilibrium configurations of a nonlinearly elastic rod that is buckled under the action of a dead-load. The governing equations are derived from variational principles, including ones of isoperimetric type. Properties of stability are accordingly determined by study of the second variation. Stabilities to deformations both in the plane and out of the plane are considered.Among the newly discovered properties are: secondary bifurcation from the first buckled mode, marked differences between stability to two-dimensional and to three-dimensional variations, and the stabilizing influence of resistance to twist. In the isoperimetric examples, the analysis makes crucial use of a novel device to account for the dependence of the second variation on constraints.

Stability and Folds

It is known that when one branch of a simple fold in a bifurcation diagram represents (linearly) stable solutions, the other branch represents unstable solutions. The theory developed here can predict instability of some branches close to folds, without knowledge of stability of the adjacent branch, provided that the underlying problem has a variational structure. First, one particular bifurcation diagram is identified as playing a special role, the relevant diagram being specified by the choice of functional plotted as ordinate. The results are then stated in terms of the shape of the solution branch in this distinguished bifurcation diagram. In many problems arising in elasticity the preferred bifurcation diagram is the loaddisplacement graph. The theory is particularly useful in applications where a solution branch has a succession of folds.The theory is illustrated with applications to simple models of thermal selfignition and of a chemical reactor, both of which systems are of Émden-Fowler type. An analysis concerning an elastic rod is also presented.

μABC: a systematic microsecond molecular dynamics study of tetranucleotide sequence effects in B-DNA.

We present the results of microsecond molecular dynamics simulations carried out by the ABC group of laboratories on a set of B-DNA oligomers containing the 136 distinct tetranucleotide base sequences. We demonstrate that the resulting trajectories have extensively sampled the conformational space accessible to B-DNA at room temperature. We confirm that base sequence effects depend strongly not only on the specific base pair step, but also on the specific base pairs that flank each step. Beyond sequence effects on average helical parameters and conformational fluctuations, we also identify tetranucleotide sequences that oscillate between several distinct conformational substates. By analyzing the conformation of the phosphodiester backbones, it is possible to understand for which sequences these substates will arise, and what impact they will have on specific helical parameters.

Hamiltonian Formulations and Symmetries in Rod Mechanics

This article provides a survey of contemporary rod mechanics, including both dynamic and static theories. Much of what we discuss is regarded as classic material within the mechanics community, but the objective here is to provide a self-contained account accessible to workers interested in modelling DNA. We also describe a number of recent results and computations involving rod mechanics that have been obtained by our group at the University of Maryland. This work was largely motivated by applications to modelling DNA, but our approach reflects a background of research in continuum mechanics. In particular, we emphasize the role that Hamiltonian formulations and symmetries play in the effective computation of special solutions, conservation laws of dynamics and integrals of statics.

Second-Order Comparison of Gaussian Random Functions and the Geometry of DNA Minicircles

Given two samples of continuous zero-mean iid Gaussian processes on [0,1], we consider the problem of testing whether they share the same covariance structure. Our study is motivated by the problem of determining whether the mechanical properties of short strands of DNA are significantly affected by their base-pair sequence; though expected to be true, had so far not been observed in three-dimensional electron microscopy data. The testing problem is seen to involve aspects of ill-posed inverse problems and a test based on a Karhunen–Loève approximation of the Hilbert–Schmidt distance of the empirical covariance operators is proposed and investigated. When applied to a dataset of DNA minicircles obtained through the electron microscope, our test seems to suggest potential sequence effects on DNA shape. Supplemental material available online.