Formation of collective conformational degrees of freedom during macromolecular chain folding dynamics in a viscous medium

Computational methods were used to study the dynamics of the formation of the collective conformational degrees of freedom in the relaxation folding of a model biopolymer chain of 50 nodes in a viscous medium; the model has been described previously. Collective conformational motions of the nodes were shown to arise due to friction forces in a viscous medium. The collective motions have several typical forms, including a wave of differently directed motions of chain nodes that propagates from one end of the chain to another (like a soliton) in response to a pertubation in terminal group position. Individual nodes located at the middle of the chain make approximately equal contributions to the total energy dissipation rate. The end nodes contribute approximately 2–4 times more than internal nodes to the total energy dissipation. The results of numerical experiments are consistent with the theoretical concept developed earlier to describe the dynamics of linear macromolecular chains in a viscous medium in the limit of a very large number of nodes.     

Harmonic dynamics of a DNA hexamer in the absence and presence of the intercalator ethidium

Vibrational normal mode calculations are presented for a DNA hexanucleoside pentaphosphate, d(CpGpCpGpCpG)2, and for its complex with the cationic intercalator ethidium. Two intercalation sites are modeled that differ in DNA backbone torsion angles. Normal mode frequencies for the DNA fragment itself are significantly lower than those reported earlier using different force fields, but an analysis of "effective" frequencies suggests that somewhat higher frequencies are more appropriate. Intercalation leads to significant lowering of mobility for the base pairs adjacent to the drug; in this sequence, the ethidium binding affects the guanosine atoms more strongly than the cytosine atoms. Motions of the bases and the intercalator are analyzed in terms of "twist" about the local helix axis and a "tilt" angle relative to this axis, and the results are compared to fluorescence studies of ethidium-DNA complexes.     

Harmonic and anharmonic aspects in the dynamics of BPTI: a normal mode analysis and principal component analysis.

A comparison is made between a 200-ps molecular dynamics simulation in vacuum and a normal mode analysis on the protein bovine pancreatic trypsin inhibitor (BPTI) in order to elucidate the dual aspects of harmonicity and anharmonicity in the dynamics of proteins. The molecular dynamics trajectory is analyzed using principal component analysis, an effective harmonic analysis suited for comparison with the results from the normal mode analysis. The results suggest that the first principal component shows qualitatively different behavior from higher principal components and is associated with apparent barrier crossing events on an anharmonic conformational energy surface. The higher principal components appear to have probability distributions that are well approximated by Gaussians, indicating harmonicity. Eliminating the contribution from the first principal component reveals a great deal of correspondence between the 2 methods. This correspondence, however, involves a factor of 2, as the variances of the distribution of the higher principal components are, on average, roughly twice those found from the normal mode analysis. A model is proposed to reconcile these results with those from previous analyses.     

Effects of viscous solvent on DNA polymer in a fiber

The viscous forces acting on a DNA macromolecule in a fiber are calculated. The DNA polymer is modeled as an infinite rod of elliptical cross section with a grooved surface. The viscous solvent is hydrodynamic water. Appropriate boundary conditions for determining the viscous forces on the acoustic vibrational modes are discussed. The viscous forces acting on each mode are then calculated as functions of both frequency and amount of water in the fiber. The mass loading of the DNA due to water in the grooves is shown to reduce the longitudinal acoustic velocity, which agrees with recent experimental results. The longitudinal modes are determined to be underdamped and correspondingly sharp over a range of frequencies and humidities appropriate to experimental conditions. The torsional and transverse acoustic modes are still strongly overdamped.     

A mathematical analysis for the Brownian dynamics of a DNA tether

In the single-particle tracking experiment, the internal motion of a single DNA or polymer molecule whose one end is attached to a microsphere (optical marker) and the other end is anchored to a substratum is studied (Finzi and Gelles, 1995). The stochastic Brownian dynamics of the sphere reflect the spontaneous fluctuations, thus the physical characteristics, of the DNA or polymer molecule (Qian and Elson, 1999, Qian, 2000). In this paper, two continuous models of polymer molecules, a flexible elastic string and a weakly bentable elastic rod, are analyzed. Both models are cast mathematically in terms of linear stochastic differential equations. Based on Fourier analyses, we calculate the mean square displacement (MSD) of the particle motion, the key observable in the experiment. We obtain for both models the short-time asymptotics for the MSD, as well as the long-time behavior in terms of the smallest non-zero eigenvalues. It is shown that: (i) the long-time dynamics of continuous elastic string model quantitatively agree with that of the discrete bead-spring model. (ii) The short-time MSD of both models are controlled by the tethered particle, with linear dependence on t. (iii) The two models show characteristic difference for long-time behavior: The longest relaxation time is proportional to L ² for long elastic string and to L for short elastic string, but is proportional to L ⁴ for both long and short weakly bentable rod. Received: 26 March 1998 / Revised version: 9 June 2000 / Published online: 14 September 2000     

Conformational motion correlations in the formation of polypeptide secondary structure in a viscous medium

The Langevin dynamics method and statistical correlation analysis were used to study the α-helical structure folding dynamics of the (Ala)₅₀, (AlaGly)₂₅, and (AlaGly)₇₅ polypeptides depending on the viscosity of the medium. Friction forces that arise when the effective viscosity of the medium is similar to the viscosity of water were found to result in strong correlations between the backbone torsion angles. The polypeptides under study folded mainly to produce α-helical structures. A structure of two contacting α-helices that were approximately equal in length and had a loop between them was observed for a longer chain of 150 residues. A method to visualize the correlation matrix of the dihedral angles of a polypeptide chain was developed for analyzing the effects of the dynamic correlation of conformational degrees of freedom. The analysis of the dynamics of the correlation matrix showed that rotations involving angles of the same type (φ–φ and ψ–ψ) occur predominantly in one direction. Rotations invoving different angles (φ–ψ) occur predominantly in opposite directions, so that the total macromolecule does not rotate. A significant reduction in the effective viscosity of the medium disrupts the correlation and makes the rotations stochastic, thus distorting the formation of the regular (helical) structure. The effects of correlated conformational motions are consequences of viscous friction forces. This conclusion agrees with our previous results that outlined the principle of the minimum rate of energy dissipation and the equipartition of energy dissipation rate between conformational degrees of freedom.     

Vibration of DNA polymer in viscous solvent

The problem of viscous damping of vibrating DNA polymer in solution is solved in the low-amplitude limit for all acoustic branches of the spectrum. The acoustic spectrum covers the microwave region of frequencies. Analytic solutions are obtained for a model describing the DNA polymer as a smooth circular cylinder. Numerical solutions are presented for a model describing the DNA polymer as a twisted cylinder of elliptical cross section. The amount of mass loading is determined for both models and the damped spectrum for the mass-loaded oscillator is calculated. The viscous damping is found to be a strong function of frequency, singular at very low frequencies for all modes except the torsional mode of the circular cylinder. All acoustic modes are overdamped, implying that the observation of well-defined resonances in DNA requires either highly structured water on the molecular level or very dry material.     

The propagation of acoustic waves along a DNA molecule in viscous environment

Low-frequency vibrations of the structural elements of the DNA molecule in a viscous solution were investigated. It was shown that shear, twist and extension waves can propagate along the axis of the molecule. The mutual influence of acoustic waves on each other was analyzed. Formulas for determining the sound velocity and the attenuation coefficients for these types of waves are obtained.     

Non-B DNA conformations analysis through molecular dynamics simulations

BackgroundNon-B DNA conformations are molecular structures that do not follow the canonical DNA double helix. Mutagenetic instability in nuclear and mitochondrial DNA (mtDNA) genomes has been associated with simple non-B DNA conformations, as hairpins or more complex structures, as G-quadruplexes. One of these structures is Structure A, a cloverleaf-like non-B conformation predicted for a 93-nt (nucleotide) stretch of the mtDNA control region 5′-peripheral domain. Structure A is embedded in a hot spot for the 3′ end of human mtDNA deletions revealing its importance in influencing the mutational instability of the mtDNA genome.MethodsTo better characterize Structure A, we predicted its 3D conformation using state-of-art methods and algorithms. The methodologic workflow consisted in the prediction of non-B conformations using molecular dynamics simulations. The conservation scores of alignments of the Structure A region in humans, primates, and mammals, was also calculated.ResultsOur results show that these computational methods are able to measure the stability of non-B conformations by using the level of base pairing during molecular dynamics. Structure A showed high stability and low flexibility correlated with high conservation scores in mammalian, more specifically in primate lineages.ConclusionsWe showed that 3D non-B conformations can be predicted and characterized by our methodology. This allowed the in-depth analysis of the structure A, and the main results showed the structure remains stable during the simulations.General significanceThe fine-scale atomic molecular determination of this type of non-B conformation opens the way to perform computational molecular studies that can show their involvement in mtDNA cellular mechanisms.     

Proofreading dynamics of a processive DNA polymerase

Replicative DNA polymerases present an intrinsic proofreading activity during which the DNA primer chain is transferred between the polymerization and exonuclease sites of the protein. The dynamics of this primer transfer reaction during active polymerization remain poorly understood. Here we describe a single‐molecule mechanical method to investigate the conformational dynamics of the intramolecular DNA primer transfer during the processive replicative activity of the Φ29 DNA polymerase and two of its mutants. We find that mechanical tension applied to a single polymerase–DNA complex promotes the intramolecular transfer of the primer in a similar way to the incorporation of a mismatched nucleotide. The primer transfer is achieved through two novel intermediates, one a tension‐sensitive and functional polymerization conformation and a second non‐active state that may work as a fidelity check point for the proofreading reaction.     

Base-flipping dynamics in a DNA hairpin processing reaction

Many enzymes that repair or modify bases in double-stranded DNA gain access to their substrates by base flipping. Although crystal structures provide stunning snap shots, biochemical approaches addressing the dynamics have proven difficult, particularly in complicated multi-step reactions. Here, we use protein–DNA crosslinking and potassium permanganate reactivity to explore the base-flipping step in Tn5 transposition. We present a model to suggest that base flipping is driven by a combination of factors including DNA bending and the intrusion of a probe residue. The forces are postulated to act early in the reaction to create a state of tension, relieved by base flipping after cleavage of the first strand of DNA at the transposon end. Elimination of the probe residue retards the kinetics of nicking and reduces base flipping by 50%. Unexpectedly, the probe residue is even more important during the hairpin resolution step. Overall, base flipping is pivotal to the hairpin processing reaction because it performs two opposite but closely related functions. On one hand it disrupts the double helix, providing the necessary strand separation and steric freedom. While on the other, transposase appears to position the second DNA strand in the active site for cleavage using the flipped base as a handle.     

A computational fluid dynamics model of viscous coupling of hairs

Arrays of arthropod filiform hairs form highly sensitive mechanoreceptor systems capable of detecting minute air disturbances, and it is unclear to what extent individual hairs interact with one another within sensor arrays. We present a computational fluid dynamics model for one or more hairs, coupled to a rigid-body dynamics model, for simulating both biological (e.g., a cricket cercal hair) and artificial MEMS-based systems. The model is used to investigate hair–hair interaction between pairs of hairs and quantify the extent of so-called viscous coupling. The results show that the extent to which hairs are coupled depends on the mounting properties of the hairs and the frequency at which they are driven. In particular, it is shown that for equal length hairs, viscous coupling is suppressed when they are driven near the natural frequency of the undamped system and the damping coefficient at the base is small. Further, for certain configurations, the motion of a hair can be enhanced by the presence of nearby hairs. The usefulness of the model in designing artificial systems is discussed.     

DNA helix-coil transition in alkaline medium

Dna helix-coil transition in th alkaline medium was considered theoretically and experimentally. On the basis of the theory and experimental comparison the DNA double-stranded form deprotonation was revealed.     

Cooperative dynamics of a DNA polymerase replicating complex

Engineered DNA polymerases continue to be the workhorses of many applications in biotechnology, medicine and nanotechnology. However, the dynamic interplay between the enzyme and the DNA remains unclear. In this study, we performed an extensive replica exchange with flexible tempering (REFT) molecular dynamics simulation of the ternary replicating complex of the archaeal family B DNA polymerase from the thermophile Thermococcus gorgonarius, right before the chemical step. The convoluted dynamics of the enzyme are reducible to rigid-body motions of six subdomains. Upon binding to the enzyme, the DNA double helix conformation changes from a twisted state to a partially untwisted state. The twisted state displays strong bending motion, whereby the DNA oscillates between a straight and a bent conformation. The dynamics of double-stranded DNA are strongly correlated with rotations of the thumb toward the palm, which suggests an assisting role of the enzyme during DNA translocation. In the complex, the primer–template duplex displays increased preference for the B-DNA conformation at the n ? 2 and n ? 3 dinucleotide steps. Interactions at the primer 3′ end indicate that Thr541 and Asp540 are the acceptors of the first proton transfer in the chemical step, whereas in the translocation step both residues hold the primer 3′ terminus in the vicinity of the priming site, which is crucial for high processivity.     

An analysis of the dynamics of mammalian mitochondrial DNA sequence evolution

The dynamics of the substitution process for mammalian mitochondrial DNA have been modeled. The temporal behavior of several quantities has been studied and the model's predictions have been compared with estimates obtained from recent mtDNA sequence data for an increasingly divergent series of primates, the mouse and the cow (Anderson et al. 1981, 1982; Bibb et al. 1981; Brown et al. 1982). The results are consistent with the hypothesis that the decrease in the proportion of transitions observed as divergence increases is a consequence of the highly biased substitution process. In addition, the results support the hypothesis that, although a portion of the mtDNA molecule evolves at an extremely rapid rate, a significant portion of the molecule is under strong selective constraints.      

Conformational dynamics of a transposition repressor in modulating DNA binding

The repressor of bacteriophage Mu functions in the establishment and maintenance of lysogeny by binding to Mu operator DNA to shut down transposition. A domain at its N terminus functions in DNA binding, and temperature-sensitive mutations in this domain can be suppressed by truncations at the C terminus. To understand the role of the C-terminal tail in DNA binding, a fluorescent probe was attached to the C terminus to examine its environment and its movement with respect to the DNA binding domain. The emission spectrum of this probe indicated that the C terminus was in a relatively hydrophobic environment, comparable to the environment of the probe attached within the DNA-binding domain. Fluorescence of two tryptophan residues located within the DNA-binding domain was quenched by the probe attached to the C terminus, indicating that the C terminus is in close proximity to this domain. Addition of DNA, even when it did not contain operator DNA, reduced quenching of tryptophan fluorescence, indicating that the tail moves away from the DNA-binding domain as it interacts with DNA. The presence of the tail also produced a trypsin hypersensitive site within the DNA-binding domain; mutant repressors with an altered or truncated C terminus were relatively resistant to cleavage at this site. Interaction of the wild-type repressor with DNA greatly reduced cleavage at the site. A repressor with a temperature-sensitive mutation in the DNA-binding domain was especially sensitive to cleavage by trypsin even in the presence of DNA, and the C-terminal tail failed to move in the presence of DNA at elevated temperatures. These results indicate that the tail sterically inhibits DNA binding and that it moves during establishment of repression. Such conformational changes are likely to be involved in communication between repressor protomers for cooperative DNA binding.     

Harmonic analysis of perfusion pumps

The controversy over the use of nonpulsatile versus pulsatile pumps for maintenance of normal organ function during ex vivo perfusion has continued for many years, but resolution has been limited by lack of a congruent mathematical definition of pulsatility. We hypothesized that the waveform frequency and amplitude, as well as the underlying mean distending pressure are all key parameters controlling vascular function. Using discrete Fourier Analysis, our data demonstrate the complexity of the pulmonary arterial pressure waveform in vivo and the failure of commonly available perfusion pumps to mimic in vivo dynamics. In addition, our data show that the key harmonic signatures are intrinsic to the perfusion pumps, are similar for flow and pressure waveforms, and are unchanged by characteristics of the downstream perfusion circuit or perfusate viscosity.