Theoretical Analysis of Disruptions in DNA Minicircles

Under sufficient bending stress, which appears in DNA minicircles and small DNA loops, the double helix experiences local disruptions of its regular structure. We developed a statistical-mechanical treatment of the disruptions in DNA minicircles, studied experimentally by Du et al. The model of disruptions used in our Monte Carlo simulation of minicircle conformations specifies these conformations by three parameters: DNA bend angle at the disruption, θ_d; local DNA unwinding caused by the disruption; and the free energy associated with the disruption in the unstressed double helix, G_d. The model is applicable to any structural type of disruption, kinks or opening of single basepairs. The simulation shows that accounting for both torsional and bending deformation associated with the disruptions is very important for proper analysis. We obtained a relationship between values of G_d and θ_d under which the simulation results are compatible with the experimental data. The relationship suggests that the free energy of basepair opening, which includes flipping out both bases, is significantly higher than the generally accepted value. The model is also applied to the analysis of j-factors of very short DNA fragments.     

Statistical Mechanical Approach for Predicting the Transition to Non-B DNA Structures in Supercoiled DNA

Abstract

Supercoiling causes global twist of DNA structure and the supercoiled state has wide influence on conformational transition. A statistical mechanical approach was made for prediction of the transition probability to non-B DNA structures under torsional stress. A conditional partition function was defined as the sum over all possible states of the DNA sequence with basepair 1 and basepair n being in B-form helix and a recurrence formula was developed which expressed the partition function for basepair n with those for less number of pairs. This new definition permits a quick enumeration of every configuration of secondary structures. Energetic parameters of all conformations concerned, involving B-form, interior loop, cruciform and Z-form, were included in the equation. The probability of transition to each non-B conformation could be derived from these conditional partition functions. For treatment of effects of superhelicity, supercoiling energy was considered, and a twist of each conformation was determined to minimize the supercoiling energy. As the twist itself affects the transition probability, the whole scheme of equations was solved by renormalization technique. The present method permits a simultaneous treatment of serveral types of conformations under a common torsional stress.

A set of energetic parameters of DNA secondary structures has been chosen for calculation. Some DNA sequences were submitted to the calculation, and all the sequences that we submitted gave stable convergence. Some of them have been investigated the critical supercoil density for the transition to non-B DNA structures. Even though the reliability of the set of parameters was not enough, the prediction of secondary structure transition showed good agreement with reported observation. Hence, the present algorithm can estimate the probability of local conformational change of DNA under a given supercoil density, and also be employed to predict some specific sequences in which conformational change is sensitive to superhelicity.     

Nucleic Acid Structure Analysis: A Users Guide to a Collection of New Analysis Programs

Abstract

Common nomenclature describing the geometry of nucleic acid structures was established at a 1988 EMBO Workshop on DNA Curvature and Bending (Diekmann, S. (1988) J. Mol. Biol. 208, 787–791; Diekmann, S. (1989) The EMBO Journal 8, 1–4; Sarma, RH. (1988) J. Biomol. Structure & Dynamics 6, 391–395; Dickerson, R.E. (1989) J. Biomol. Structured Dynamics 6, 627–634; Dickerson, RE. et al. (1989)Nuc. Acids Res. 17, 1979–1803). We have subsequently developed and incorporated sophisticated mathematics in a computer program to calculate the parameters described by the guidelines. The program calculates all the local parameters relating complementary bases and neighboring base and base pairs in both Cartesian and helical coordinate frames. In addition, the main mathematical property requested by the EMBO guidelines—that the magnitude of the parameters be independent of strand or direction of measurement—is accomplished without the use of a midway coordinate frame for the rotational parameters. The mathematics preserve the physical intuition used in defining the parameters; in particular, the rotational parameters are true rotations based on a simple physical model (rotation at constant angular velocity for a unit amount of time), not Euler angles or angles between vectors and planes as is the case with other approaches. As a result, the mathematical equations are symmetric with the property that a 5° tilt is the same as a 5° roll or a 5° twist, except that the rotations take place about different axes. In other approaches, a 5° tilt can mean a different amount of net rotation from a 5° roll or a 5° twist. In addition, a great deal of flexibility is built into the program so that the user has control over the analysis, including the input format, the coordinate frame used for the base pairing relationship, the point about which the rotations are performed, and which geometric relationships are analyzed. While there is a great deal of flexibility, the program is easy to use. Interactive queries and user accessible files make the options in the program very convenient to tailor to individual needs. In addition, there is also a program that calculates bond lengths, valence angles, and torsion angles along the nucleic acid backbone, and within the sugar and base rings. Another program ‘learns’ the identities of the bond lengths, valence angles, and torsion angles that the user would like to determine. This last program is especially useful for calculating the hydrogen bonds between atoms in complementary strands as well as the unusual hydrogen bonds found in recently determined nucleic acid NMR structures or within protein/nucleic acid complexes.     

Local sequential minimization of double stranded B-DNA using Monte Carlo annealing

A software algorithm has been developed to investigate the folding process in B-DNA structures in vacuum under a simple and accurate force field. This algorithm models linear double stranded B-DNA sequences based on a local, sequential minimization procedure. The original B-DNA structures were modeled using initial nucleotide structures taken from the Brookhaven database. The models contain information at the atomic level allowing one to investigate as accurately as possible the structure and characteristics of the resulting DNA structures. A variety of DNA sequences and sizes were investigated containing coding and non-coding, random and real, homogeneous or heterogeneous sequences in the range of 2 to 40 base pairs. The force field contains terms such as angle bend, Lennard-Jones, electrostatic interactions and hydrogen bonding which are set up using the Dreiding II force field and defined to account for the helical parameters such as twist, tilt and rise. A close comparison was made between this local minimization algorithm and a global one (previously published) in order to find out advantages and disadvantages of the different methods. From the comparison, this algorithm gives better and faster results than the previous method, allowing one to minimize larger DNA segments. DNA segments with a length of 40 bases need approximately 4 h, while 2.5 weeks are needed with the previous method. After each minimization the angles between phosphate–oxygen-carbon A₁, the oxygen–phosphate–oxygen A₂ and the average helical twists were calculated. From the generated fragments it was found that the bond angles are A₁=150°±2°and A₂=130°±10°, while the helical twist is 36.6°±2° in the A strand and A₁=150°±6° and A₂=130±6° with helical twist 39.6°±2° in the B strand for the DNA segment with the same sequence as the Dickerson dodecamer.Figure The final minimized DNA segment of the Dickerson dodecamer sequence represented by ball drawings and viewed (left) perpendicular and (right) down the helical axis     

Bounds on the total population for species governed by reaction-diffusion equations in arbitrary two-dimensional regions

Analysis based on the integration of differential inequalities is employed to derive upper and lower bounds on the total populationN(t) = ∫ _R θ(x ₁,x ₂,t) dx ₁ dx ₂ of a biological species with an area-density distribution function θ=θ(x ₁,x ₂,t) (≥0) governed by a reaction-diffusion equation of the form ∂θ/∂t =D∇²θ +fθ −gθ ⁿ⁺¹ whereD (>0),n (>0),f andg are constant parameters, θ=0 at all points on the boundary ∂R of an (arbitrary) two-dimensional regionR, and the initial distribution (θ(_{x 1},x ₂, 0) is such thatN(0) is finite. Forg≥0 withR the entire two-dimensional Euclidean space, a lower bound onN(t) is obtained, showing in particular thatN(∞) is bounded below by a finite positive quantity forf≥0 andn>1. An upper bound onN(t) is obtained for arbitrary bounded or unbounded)R withn=1,f andg negative, and ∫ _R θ(x ₁,x ₂, 0)² dx ₁ dx ₂ sufficiently small in magnitude, implying that the population goes to extinction with increasing values of the time,N(∞)=0. Forg≥0 andR of finite area, the analysis yields upper bounds onN(t), predicting eventual extinction of the population if eitherf≤0 or if the area ofR is less than a certain grouping of the parameters in cases for whichf is positive. These results are directly applicable to biological species with distributions satisfying the Fisher equation in two spatial dimensions and to species governed by certain specialized population models.     

Ni-Enhanced Charge Transport via π-π Stacking Corridor in Metallic DNA

The mechanism underlying DNA charge transport is intriguing. However, poor conductivity of DNA makes it difficult to detect DNA charge transport. Metallic DNA (M-DNA) has better conducting properties than native DNA. Ni²⁺ may chelate in DNA and thus enhance DNA conductivity. On the basis of this finding, it is possible to reveal the mechanisms underlying DNA charge transport. The conductivity of various Ni-DNA species such as single-stranded, full complement, or mismatched sequence molecules was systematically tested with ultraviolet absorption and electrical or chemical methods. The results showed that the conductivity of single-stranded Ni-DNA (Ni-ssDNA) was similar to that of a native DNA duplex. Moreover, the resistance of Ni-DNA with a single basepair mismatch was significantly higher than that of fully complementary Ni-DNA duplexes. The resistance also increased exponentially as the number of mismatched basepairs increased linearly after the tunneling current behavior predicted by the Simmons model. In conclusion, the charges in Ni²⁺-doped DNA are transported through the Ni²⁺-mediated π−π stacking corridor. Furthermore, Ni-DNA acts as a conducting wire and exhibits a tunneling barrier when basepair mismatches occur. This property may be useful in detecting single basepair mismatches.     

Modeling DNA Thermodynamics under Torsional Stress

Negatively twisted DNA is essential to many biological functions. Due to torsional stress, duplex DNA can have local, sequence-dependent structural defects. In this work, a thermodynamic model of DNA was built to qualitatively predict the local sequence-dependent mechanical instabilities under torsional stress. The results were compared to both simulation of a coarse-grained model and experiment results. By using the Kirkwood superposition approximation, we built an analytical model to represent the free energy difference ΔW of a hydrogen-bonded basepair between the B-form helical state and the basepair opened (or locally melted) state, within a given sequence under torsional stress. We showed that ΔW can be well approximated by two-body interactions with its nearest-sequence-neighbor basepairs plus a free energy correction due to long-range correlations. This model is capable of rapidly predicting the position and thermodynamics of local defects in a given sequence. The result qualitatively matches with an in vitro experiment for a long DNA sequence (>4000 basepairs). The 12 parameters used in this model can be further quantitatively refined when more experimental data are available.     

Modeling DNA Thermodynamics under Torsional Stress

Negatively twisted DNA is essential to many biological functions. Due to torsional stress, duplex DNA can have local, sequence-dependent structural defects. In this work, a thermodynamic model of DNA was built to qualitatively predict the local sequence-dependent mechanical instabilities under torsional stress. The results were compared to both simulation of a coarse-grained model and experiment results. By using the Kirkwood superposition approximation, we built an analytical model to represent the free energy difference ΔW of a hydrogen-bonded basepair between the B-form helical state and the basepair opened (or locally melted) state, within a given sequence under torsional stress. We showed that ΔW can be well approximated by two-body interactions with its nearest-sequence-neighbor basepairs plus a free energy correction due to long-range correlations. This model is capable of rapidly predicting the position and thermodynamics of local defects in a given sequence. The result qualitatively matches with an in vitro experiment for a long DNA sequence (>4000 basepairs). The 12 parameters used in this model can be further quantitatively refined when more experimental data are available.     

The ontogeny of the locomotor wave in sevruga fish (Acipenser stellatus Pall.)

Continuous filming of the swimming movements of sevruga prelarvae (Acipenser stellatus Pall.) was performed over the first to the fifteenth post-hatching days. These data were used to determine three locomotor characteristics: {f(v, θ), A(v, θ), w(v, θ)} where f is the frequency of the transverse oscillations; A is the amplitude of the tail fin movements; w is the speed of the locomotor wave; v is the speed of the locomotion; and θ is the number of days during which the filming was carried out. In addition, the comparison of two characteristics was performed. These are the step length L(v, θ) and the wavelength λ(v, θ), where L ≡ vT is the distance that a fish covers in time T ≡ 1/f and λ is λ ≡ wT. The results led to the conclusion that the prelarva swimming movements achieve the carangiform mode by the end of the second week. This is characteristic of adults and coincides with the beginning of external feeding. The mode is represented by an equation that follows from the generalized Bainbridge’s law: f = f ₀ + f ₁ v/H. The equation includes one anatomical parameter H of total length and two kinematic parameters f ₀ and f ₁, which can be calculated by the linear approximation method. These are the kinematic parameters that are changed in the early ontogenesis when 1 ≤ θ ≤ 15. However, the parameters become stable when θ ≥ 15. This means that the parameter values are constant and similar to those of adult fish. The similar properties of stabilization and variability have the kinematic parameters of other locomotor characteristics.

     

Consistency of the Asymptotic Quasi-Likelihood Estimate on Linear Models

Consider a model y_t = f_t(θ) + M_t, 0 ⩽ t ⩽ T where θ∈ Θ in an unknown parameter, f_t(θ) is a linear predictable process, M_t is a martingale difference, and the nature of E(M²_t/ℱ_t—1) is unknown. This paper presents an estimating procedure for θ based on the asymptotic quasi-likelihood methodology. Conditions under which the asymptotic quasi-likelihood estimate converges to the true parameter θ₀ are discussed. This method is applied to several simulated examples, and estimates of the unknown parameter are obtained by means of a two-stage technique. Comparison is made between the estimates obtained via this method and those obtained via the ordinary least squares method. Discussion is provided on the application of the model.     

Individual basepair stability of DNA and RNA studied by NMR-detected solvent exchange

In this study, we have optimized NMR methodology to determine the thermodynamic parameters of basepair opening in DNA and RNA duplexes by characterizing the temperature dependence of imino proton exchange rates of individual basepairs. Contributions of the nuclear Overhauser effect to exchange rates measured with inversion recovery experiments are quantified, and the influence of intrinsic and external catalysis exchange mechanisms on the imino proton exchange rates is analyzed. Basepairs in DNA and RNA have an approximately equal stability, and the enthalpy and entropy values of their basepair dissociation are correlated linearly. Furthermore, the compensation temperature, T(c), which is derived from the slope of the correlation, coincides with the melting temperature, and duplex unfolding occurs at that temperature where all basepairs are equally thermodynamically stable. The impact of protium-deuterium exchange of the imino hydrogen on the free energy of RNA basepair opening is investigated, and it is found that two A·U basepairs show distinct fractionation factors.     

Cy3-DNA stacking interactions strongly depend on the identity of the terminal basepair

We characterized the effect of the first basepair on the conformational dynamics of the fluorescent dye Cy3 attached to the 5′ end of double-stranded DNA using Gaussian-mixture adaptive umbrella sampling simulations. In the simulations, the sampling of all five dihedral angles along the linker was enhanced, so that both stacked and unstacked states were sampled. The affinity of Cy3 for a T·A basepair (with the dye attached to T) was found to be significantly less than for the other basepairs. This was verified experimentally by measuring the activation energies for cis-trans isomerization of the dye. The simulation and experimental results indicate the existence of partially unstacked conformations amenable to photoisomerization. The simulations also showed that stacking of Cy3 straightens the DNA while stabilizing the first basepair. Our findings indicate that fluorescence is modulated by Cy3-DNA interactions in a sequence-dependent manner.     

Oxidative stress induces the expression of the major histocompatibility complex in murine tumor cells

The effect of t-butyl hydroperoxide (t-BOOH) on the induction of the Major Histocompatibility Complex (MHC) class I genes has been studied in two cell clones (B9 and G2) of the methylcholanthrene-induced murine fibrosarcoma GR9. These two clones were selected based on their different biological and biochemical behavior specially related to their tumor induction capability when injected into a BALB/c mouse. t-BOOH (0.125mM) induced the expression of H-2 molecules in both cell clones. In B9 cell clone, in which MHC basal expression is very low or absent, t-BOOH significantly induced H-2K^d, H-2D^d and H-2L^d molecules. In G2 cell clone the expression of MHC class I genes was also enhanced by the xenobiotic, the effect being especially significant on the H-2L^d molecule which is not expressed under basal conditions. H-2 molecules expression was accompanied by the activation of the transactivator factor NFκB. These results suggest that oxidative stress may modulate the antigen expression of tumor cells and thus the immune response of the host organism.

Basal levels of oxidative parameters, such as anti-oxidant enzymes, malondialdehyde (MDA) and the DNA damaged base 8-hydroxy-2′-deoxyguanosine (8-OHdG), showed differences between the two fibrosarcoma cell clones.     

Determination of DNA base compositions from melting profiles in dilute buffers

Equations were determined for the dependency of the melting temperature (T_m) of DNA upon the logarithm of the sodium ion concentration, for four DNA samples of widely different base compositions (θ_GC). The slopes of these T_m versus log M equations wore found to decrease with increasing θ_{G C}of the samples. An empirical equation relating T_m, log M (Na⁺) and θ_{G C} was derived, which also accounts for differences in T_m versus log M slopes. Data from the literature for some synthetic polynucleotides and for the crab(Cancer pagarus) satellite poly AT are discussed in relation to the above finding. The changes in T_m versus log M slopes with θ_{G C} are interpreted in terms of changes in the thermodynamic parameters ΔS and ΔH with base composition.     

Acute modulation of myocardial function by angiotensin 1–7

Angiotensin 1–7 is a bioactive heptapeptide of the renin–angiotensin system. Its cardiovascular actions have recently acquired growing relevance, mainly due to its counter-regulatory actions in the angiotensin cascade. The aim of the present study was to evaluate the actions of angiotensin 1–7 on myocardial function. Increasing concentrations of angiotensin 1–7 (10⁻⁹ to 10⁻⁵ M) were added to rabbit right papillary muscles: (1) in baseline conditions with intact endocardial endothelium (EE); (2) after selective removal of the EE with Triton X-100 (1 s, 0.01%); (3) with intact EE in the presence of the Mas receptor antagonist A-779, the AT₁ receptor antagonist ZD-7155, the AT₂ receptor antagonist PD-123,319 or the nitric oxide synthesis inhibitor NG-nitro-l-arginine (l-NA). Concerning the effects on contractility, we observed a significant decrease on active tension, dT/dt_max, peak shortening and dL/dt_max of −10.5 ± 3.6%, −8.0 ± 3.0%, −5.3 ± 2.6% and −5.7 ± 2.3%, respectively. There was no change on relaxation parameters, namely dT/dt_min or dL/dt_min. Time to half relaxation was significantly decreased. The presence of ZD-7155 or PD-123,319 did not change these effects. However, angiotensin 1–7 effects on myocardial properties were abolished after selective EE removal and in the presence of A-779 or l-NA. In conclusion, in this animal species, angiotensin 1–7 through its binding to Mas receptor induces a negative inotropic effect modulated by the EE and nitric oxide and independent of AT₁ or AT₂ receptors activation. As the effects described in the present work were influenced by the endocardial endothelium, they may be disrupted in situations associated to endothelial dysfunction, as in heart failure or myocardial ischemia.     

Widespread Adaptive Evolution in the Human Immunodeficiency Virus Type 1 Genome

We investigated variable selective pressures among amino acid sites in HIV-1 genes. Selective pressure at the amino acid level was measured by using the nonsynonymous/synonymous substitution rate ratio ( = d_N/d_S). To identify amino acid sites under positive selection with > 1, we applied maximum likelihood models that allow variable ratios among sites to analyze genomic sequences of 26 HIV-1 lineages including subtypes A, B, and C. Likelihood ratio tests detected sites under positive selection in each of the major genes in the genome: env, gag, pol, vif, and vpr. Positive selection was also detected in nef, tat, and vpu, although those genes are very small. The majority of positive selection sites is located in gp160. Positive selection was not detected if was estimated as an average across all sites, indicating the lack of power of the averaging approach. Candidate positive selection sites were mapped onto the available protein tertiary structures and immunogenic epitopes. We measured the physiochemical properties of amino acids and found that those at positive selection sites were more diverse than those at variable sites. Furthermore, amino acid residues at exposed positive selection sites were more physiochemically diverse than at buried positive selection sites. Our results demonstrate genomewide diversifying selection acting on the HIV-1.     

Free-Energy Landscape and Characteristic Forces for the Initiation of DNA Unzipping

DNA unzipping, the separation of its double helix into single strands, is crucial in modulating a host of genetic processes. Although the large-scale separation of double-stranded DNA has been studied with a variety of theoretical and experimental techniques, the minute details of the very first steps of unzipping are still unclear. Here, we use atomistic molecular-dynamics simulations, coarse-grained simulations, and a statistical-mechanical model to study the initiation of DNA unzipping by an external force. Calculation of the potential of mean force profiles for the initial separation of the first few terminal basepairs in a DNA oligomer revealed that forces ranging between 130 and 230 pN are needed to disrupt the first basepair, and these values are an order of magnitude larger than those needed to disrupt basepairs in partially unzipped DNA. The force peak has an echo of ∼50 pN at the distance that unzips the second basepair. We show that the high peak needed to initiate unzipping derives from a free-energy basin that is distinct from the basins of subsequent basepairs because of entropic contributions, and we highlight the microscopic origin of the peak. To our knowledge, our results suggest a new window of exploration for single-molecule experiments.     

Application of modified ising model to the helix-coil transition of DNA molecules

Equilibrium properties of heterogeneous DNA near the melting temperature T_m are investigated using the grand partition function. The present approach gives exact and analytical solutions. The algebraic expressions enhance a more thorough understanding of the correlation among many observed equilibrium phenomena. The following quantities have been examined: melting temperature T_m, transition width W, partial melting curves θ_AT and θ_GC, mean length of a helical segment h, and correlation length γ.     

Continuum Percolation of 2D and 3D Simple Fluids

We use Monte Carlo and Molecular Dynamics computer simulations to investigate the percolation threshold, ρ _p , of d-dimensional Lennard-Jones LJ, and square-well fluids. We find that when the range of the potential well is small compared to the hard-core diameter (in the so-called ‘hard-core’ limit), an attractive well decreases ρ _p below the high temperature limiting value. In contrast, a hard shoulder potential produces the opposite trend. We investigate the structure of the 2D percolating clusters, in particular, the effects of periodic boundaries. We examine the shapes of the 3D clusters at the percolation threshold, resolved as a function of the number of particles in a cluster, s. The asphericity parameter, A₃ , describing the instantaneous shape of the cluster decays slowly from unity, typically only achieving ～ 0.3 by s ～ 100, close to the estimated universal value of 0.312.

We focus especially on the relationship between long and short range structural order as probed by the coordination numbers of the molecules. We also use a cluster-resolution of the co-ordination number to indicate the degree of branching in the clusters, and how it is influenced by the number of atoms in the cluster and temperature for the different potentials. We look forward to future directions for simulation in investigating physical properties in the vicinity of the percolation threshold.