Modelling DNA loops using continuum and statistical mechanics

The classical Kirchhoff elastic-rod model applied to DNA is extended to account for sequence-dependent intrinsic twist and curvature, anisotropic bending rigidity, electrostatic force interactions, and overdamped Brownian motion in a solvent. The zero-temperature equilibrium rod model is then applied to study the structural basis of the function of the lac repressor protein in the lac operon of Escherichia coli. The structure of a DNA loop induced by the clamping of two distant DNA operator sites by lac repressor is investigated and the optimal geometries for the loop of length 76 bp are predicted. Further, the mimicked binding of catabolite gene activator protein (CAP) inside the loop provides solutions that might explain the experimentally observed synergy in DNA binding between the two proteins. Finally, a combined Monte Carlo and Brownian dynamics solver for a worm-like chain model is described and a preliminary analysis of DNA loop-formation kinetics is presented.     

A mathematical formulation of DNA computation

DNA computation is to use DNA molecules for information storing and processing. The task is accomplished by encoding and interpreting DNA molecules in suspended solutions before and after the complementary binding reactions. DNA computation is attractive, due to its fast parallel information processing, remarkable energy efficiency, and high storing capacity. Challenges currently faced by DNA computation are: 1) lack of theoretical computational models for applications and 2) high error rate for implementation. This paper attempts to address these problems from mathematical modeling and genetic coding aspects. The first part of this paper presents a mathematical formulation of DNA computation. The model may serve as a theoretical framework for DNA computation. In the second part, a genetic code based DNA computation approach is presented to reduce error rate for implementation, which has been a major concern for DNA computation. The method provides a promising alternative to reduce error rate for DNA computation.     

Modelling the biomechanical properties of DNA using computer simulation

Duplex DNA must remain stable when not in use to protect the genetic material. However, the two strands must be separated whenever genes are copied or expressed to expose the coding strand for synthesis of complementary RNA or DNA bases. Therefore, the double stranded structure must be relatively easy to take apart when required. These conflicting biological requirements have important implications for the mechanical properties of duplex DNA. Considerable insight into the forces required to denature DNA has been provided by nanomanipulation experiments, which measure the mechanical properties of single molecules in the laboratory. This paper describes recent computer simulation methods that have been developed to mimic nanomanipulation experiments and which, quite literally, 'destruction test' duplex DNA in silico. The method is verified by comparison with single molecule stretching experiments that measure the force required to unbind the two DNA strands. The model is then extended to investigate the thermodynamics of DNA bending and twisting. This is of biological importance as the DNA must be very tightly packaged to fit within the nucleus, and is therefore usually found in a highly twisted or supercoiled state (in bacteria) or wrapped tightly around histone proteins into a densely compacted structure (in animals). In particular, these simulations highlight the importance of thermal fluctuations and entropy in determining the biomechanical properties of DNA. This has implications for the action of DNA processing molecular motors, and also for nanotechnology. Biological machines are able to manipulate single molecules reliably on an energy scale comparable to that of thermal noise. The hope is that understanding the statistical mechanisms that a cell uses to achieve this will be invaluable for the future design of 'nanoengines' engineered to perform new technological functions at the nanoscale.     

DNA Molecules as Standard Reference Materials I: Development of DNA Identification Sequences and Human Mitochondrial DNA Reference Sequences

This paper describes the design, construction and characterization of two DNA molecules that function as prototype Standard Reference Materials for use in the determination of DNA sequences. The first prototype reference DNA molecule was constructed to function as a true reference DNA sequence encoding the human mitochondrial hypervariable region 1. The second DNA molecule was designed to be a molecular DNA “tag” for use in the identification of DNA Standard Reference Materials. DNA molecules were chemically and enzymatically synthesized, cloned in molecular cloning vectors and sequenced using manual and automated fluorescent DNA sequencing methods. The sequence of the cloned human mitochondrial HV1 DNA shows six base pair differences from the original published DNA sequence. The molecular DNA tag sequence uses the universal genetic code with one letter amino acid abbreviations to spell the words “NIST DNA STANDARD REFERENCE MATERIAL.” The need and utility of an expanded molecular code to uniquely identify DNA molecules is discussed. The use of these DNA molecules in the development of DNA Standard Reference Materials is also described.     

DNA capillary electrophoresis in entangled dynamic polymers of surfactant molecules

Aqueous solutions of monomeric nonionic surfactants, n-alkyl polyoxyethylene ethers (C16E6, C16E8, C14E6), can be used as sieving matrixes for the separation of DNA fragments by capillary electrophoresis. Unlike ordinary polymer solutions, these surfactant solutions behave as dynamic polymers. By combining the "reversible gel" theory of DNA electrophoresis and the static and dynamic properties of wormlike surfactant micelles, a model is developed for describing the migration behavior of DNA molecules in these solutions. According to the model, the separation limit can be extended at low surfactant concentrations. Surfactant solutions as a separation medium provide many advantages over ordinary polymers, such as ease of preparation, solution homogeneity, stable structure, low viscosity, and self-coating property for reducing electroosmotic flow. More importantly, the properties of wormlike micelles (micelle size, entanglement concentration) can be adjusted by simply changing the monomer concentration, denaturant, and temperature to allow the separation of different size ranges of DNA fragments. Fast separation is achieved for DNA fragments ranging from 10 bp to 5 kb by using bare fused-silica columns. DNA sequencing fragments of BigDye G-labeled M13 up to 600 bases were separated within 60 min.     

Comparison of Two Dimension-Reduction Methods for Network Simulation Models

Experimenters characterize the behavior of simulation models for data communications networks by measuring multiple responses under selected parameter combinations. The resulting multivariate data may include redundant responses reflecting aspects of a smaller number of underlying behaviors. Reducing the dimension of multivariate responses can reveal the most significant model behaviors, allowing subsequent analyses to focus on one response per behavior. This paper investigates two methods for reducing dimension in multivariate data generated from simulation models. One method combines correlation analysis and clustering. The second method uses principal components analysis. We apply both methods to reduce a 22-dimensional dataset generated by a network simulator. We identify issues that an analyst must decide, and we compare the reductions suggested by the methods. We have used these methods to identify significant behaviors in simulated networks, and we suspect they may be applied to reduce the dimension of empirical data measured from real networks.     

An investigation into the interactions between self-assembled adenine molecules and a Au(111) surface

Two molecular phases of the DNA base adenine (A) on a Au(111) surface are observed by using STM under ultrahigh-vacuum conditions. One of these phases is reported for the first time. A systematic approach that considers all possible gas-phase two-dimensional arrangements of A molecules connected by double hydrogen bonds with each other and subsequent ab initio DFT calculations are used to characterize and identify the two phases. The influence of the gold surface on the structure of A assemblies is also discussed. DFT is found to predict a smooth corrugation potential of the gold surface that will enable A molecules to move freely across the surface at room temperature. This conclusion remains unchanged if van der Waals interaction between A and gold is also approximately taken into account. DFT calculations of the A pairs on the Au(111) surface show its negligible effect on the hydrogen bonding between the molecules. These results justify the gas-phase analysis of possible assemblies on flat metal surfaces. Nevertheless, the fact that it is not the most stable gas-phase monolayer that is actually observed on the gold surface indicates that the surface still plays a subtle role, which needs to be properly addressed.     

组织建模及其分析方法研究

针对阶梯型ＣＩＭＳ体系结构,对组织视图建模的目的进行了探讨,企业了企业组织对企业经营过程的影响,提出了一种从组织结构和过程组织两个方面建立企业组织模型的方案,给出了组织框图的表述方法,并探讨了组织框架存在的现实意义,进而,针对经营过程,给出了组织单元到过程组织单元的转化方法,给出过程组织的分析依据,并研究了组织结构和过程组织之间的相互关系。     

Asymptotic Correlations Between Rotated Solutions in Factor Analysis

The asymptotic correlations between differently rotated solutions in exploratory factor analysis are derived. The solutions are orthogonally or obliquely rotated for unstandardized or standardized manifest variables. To obtain the asymptotic correlations between different solutions, the covariance models for manifest variables have been constructed so that two sets of solutions are involved in a single covariance structure. The asymptotic correlations can be used for the statistical test of the differences of rotated solutions. The correlation matrix between the rotated factors of the first solution and those of the second is also introduced in the models with appropriate restrictions to identify the models. The asymptotic standard errors of the estimates of the correlations between the factors in different solutions are simultaneously provided. A numerical example is presented with simulated values.

     

胃粘膜正常、肠化和腺癌组织基因组DNA的拉曼光谱分析

本文提出结合生物组织DNA提取技术和拉曼光谱技术来系统研究胃癌不同发生过程中的组织DNA空间结构的方法.实验中,首先提取涉及胃癌发病过程中的胃粘膜正常上皮组织、肠化组织和腺癌组织的基因组DNA,分别对其进行拉曼光谱检测,根据拉曼谱图特征,详细分析了基因组DNA的结构变化.实验结果表明,胃粘膜正常组织DNA中有稳定的磷酸骨架;肠化组织基因组DNA拉曼特征峰在1 090 cm~(-1)处谱峰强度低于1 050 cm~(-1)处谱峰强度,表明其磷酸骨架变得不稳定,其它位置的谱峰与正常组织相似;腺癌组织基因组DNA拉曼特征峰在1090 cm~(-1)附近出现双峰,其相对于1050 cm~(-1)处谱峰强度更强,提示DNA有可能出现断链并再次形成了稳定的磷酸骨架,在950 cm~(-1)、1 010cm~(-1),1 100～1 600 cm~(-1)波段的特征谱峰与正常组织DNA相比变化也较犬,说明脱氧核糖和碱基可能由于DNA断链也随之改变.这些结果提示胃癌的发生过程中DNA结构变化过程可能是:胃粘膜正常组织具有稳定的DNA磷酸骨架,在致病因素作用下发展为具有不稳定磷酸骨架DNA的肠化组织,最后组织DNA磷酸骨架断裂并重新形成稳定的DNA磷酸骨架,致胃癌发生.     

Maximum Likelihood and Restricted Likelihood Solutions in Multiple-Method Studies

A formulation of the problem of combining data from several sources is discussed in terms of random effects models. The unknown measurement precision is assumed not to be the same for all methods. We investigate maximum likelihood solutions in this model. By representing the likelihood equations as simultaneous polynomial equations, the exact form of the Groebner basis for their stationary points is derived when there are two methods. A parametrization of these solutions which allows their comparison is suggested. A numerical method for solving likelihood equations is outlined, and an alternative to the maximum likelihood method, the restricted maximum likelihood, is studied. In the situation when methods variances are considered to be known an upper bound on the between-method variance is obtained. The relationship between likelihood equations and moment-type equations is also discussed.     

Transient shell response by numerical time integration

In using the finite element method to compute a transient response, two choices must be made. First, some form of mass matrix must be decided upon. Either the consistent mass matrix prescribed by the finite element method can be employed or some form of diagonal mass matrix may be introduced. Secondly, some particular time integration procedure must be adopted. The procedures available divide themselves into two classes: the conditionally stable explicit schemes and the unconditionally or conditionally stable implicit schemes. The choices should be guided by both economy and accuracy. Using exact discrete solutions compared to the exact solutions of the differential equations, the results of these choices are displayed. Concrete examples of well-matched methods, as well as ill-matched methods, are identified and demonstrated. In particular, the diagonal mass matrix and the explicit central difference time integration method are shown to be a good combination in terms of accuracy and economy.     

The counter-current backmixing model for fluid bed reactors — computational aspects and model modifications

Numerical solution of differential equations describing the counter-current backmixing model of Fryer and Potter is very difficult due to the boundary value nature of the problem. Several numerical methods (shooting, superposition and finite difference) have been described and tested on a problem with a single first-order reaction in an isothermal fluid bed reactor. It was found that the finite difference method is the most stable method and provides accurate solution over the entire range of parameters that were investigated, while the shooting and the superposition methods could not produce accurate solutions for some parameter values. Also, some modifications of the Fryer and Potter model such as: compartment models and conversion to an initial value type of problem (Jayraman-Kulkarni-Doraiswamy model), have been described. Results obtained from compartment models are in close agreement with predictions obtained from the original Fryer and Potter model. This paper is dedicated to Dr L K Doraiswamy on his sixtieth birthday. Computations reported in this paper were carried out by N Nasif, J G Daly and S H Lane.     

The unsteady motion of two-dimensional flags with bending stiffness

The motion of a two-dimensional flag at a time-dependent angle of incidence to an irrotational flow of an inviscid, incompressible fluid is examined. The flag is modelled as a thin, flexible, impermeable membrane of finite mass with bending stiffness. The flag is fixed at the leading edge where it is assumed to be either freely hinged or clamped with zero gradient. The angle of incidence to the outer flow is assumed to be small and thin aerofoil theory and simple beam theory are employed to obtain a partial singular integro-differential equation for the flag shape. Steady solutions to the problem are calculated analytically for various limiting cases and numerically for order one values of a non-dimensional parameter that measures the relative importance of outer flow momentum flux and flexural rigidity. For the unsteady problem, the stability of steady solutions depends only upon two non-dimensional parameters. Stability analysis is performed in order to identify the regions of instability. The resulting quadratic eigenvalue problem is solved numerically and the marginal stability curves for both the hinged and the clamped flags are constructed. These curves show that both stable and unstable solutions may exist for various values of the mass and flexural rigidity of the membrane and for both methods of attachment at the leading edge. In order to confirm the results of the linear stability analysis, the full unsteady flag equation is solved numerically using an explicit method. The numerical solutions agree with the predictions of the linear stability analysis and also identify the shapes that the flag adopts according to the magnitude of the flexural rigidity and mass.     

Controlling the microadsorption structure of porphyrin dye assembly on clay surfaces using the "size-matching rule" for constructing an efficient energy transfer system

The microadsorption structure of two kinds of porphyrin molecules on an anionic clay surface was investigated by photochemical energy transfer reaction. Three procedures were examined for the preparation of the clay/porphyrin complexes: (i) coadsorption (CA) method, (ii) sequential adsorption (SA) method, and (iii) independent adsorption (IA) method as described in the text. Efficient and moderate energy transfer reactions were observed in the CA and SA complexes, respectively. On the contrary, the energy transfer did not occur in the IA complex. These results indicate that the microadsorption structure of the two kinds of porphyrin on the clay mineral surface resulting from the sample preparation methods, affects the energy transfer efficiency. As a result, it was revealed that (i) the adsorbed porphyrins can move on the clay mineral surface but cannot move from one clay surface to another clay sheet, and (ii) the integration structure of two kinds of porphyrin is more stable than the segregation structure in the present system. This unusual structure originated from an extremely strong electrostatic interaction between the porphyrin and the clay mineral as a result of a "size-matching rule". These unique strongly fixed dye assemblies on the clay mineral surface, in which the aggregation and segregation of dyes are suppressed, is very promising and attractive for constructing efficient photochemical reaction systems.     

An adaptive stabilization strategy for enhanced strain methods in non‐linear elasticity

This paper proposes and analyzes an adaptive stabilization strategy for enhanced strain (ES) methods applied to quasistatic non‐linear elasticity problems. The approach is formulated for any type of enhancements or material models, and it is distinguished by the fact that the stabilization term is solution dependent. The stabilization strategy is first constructed for general linearized elasticity problems, and then extended to the non‐linear elastic regime via an incremental variational principle. A heuristic choice of the stabilization parameters is proposed, which in the numerical examples proved to provide stable approximations for a large range of deformations, different problems and material models. We also provide explicit lower bounds for the stabilization parameters that guarantee that the method will be stable. These are not advocated, since they are generally larger than the ones based on heuristics, and hence prone to deteriorate the locking‐free behavior of ES methods. Numerical examples with two different non‐linear elastic models in thin geometries and incompressible situations show that the method remains stable and locking free over a large range of deformations. Finally, the method is strongly based on earlier developments for discontinuous Galerkin methods, and hence throughout the paper we offer a perspective about the similarities between the two. Copyright © 2009 John Wiley & Sons, Ltd.     

Identification of an extended Bouc–Wen model with application to seismic protection through hysteretic devices

In this paper is proposed an extended Bouc–Wen model for improving its capability to approximate experimental symmetric hysteretic loops. On the basis of the generalized equation there are defined integral and differential conditions that describe the essential geometric properties of a hysteretic curve. Next, a new method based on Genetic Algorithms is developed to identify the Bouc–Wen model parameters from experimental hysteretic loops obtained from periodic loading tests. The performance of presented approach is illustrated for two types of seismic protection devices with hysteretic characteristics: elastomeric base isolators and buckling restrained dissipative braces. The applicability of proposed method is highlighted by using the derived models to analyse by numerical simulation the efficiency of these devices for reducing seismic response of a three stories civil structure.     

Spectrophotometric and chemometric studies on the simultaneous determination of two benzodiazepines in human plasma

A numerical simple, accurate and precise method based on spectrophotometric data coupled with multivariate calibration methods, PLS and MLR, combined with GA was developed for the simultaneous determination of two benzodiazepines, Clobazam and Flurazepam. A data set of absorption spectra obtained from a calibration set of mixtures containing the compounds was used to build GA-PLS and GA-MLR models. The models were tested using a dataset constructed from the compound synthetic solutions. The better model was also applied to plasma samples. The proposed method requires no preliminary separation steps and can be used for these drugs analysis in quality control laboratories.     

Scanning Tunneling Microscopy and Spectroscopy of Novel Silver–Containing DNA Molecules

The quest for a suitable molecule to pave the way to molecular nanoelectronics has been met with obstacles for over a decade. Candidate molecules such as carbon nanotubes lack the appealing trait of self‐assembly, while DNA seems to lack the desirable feature of conductivity. Silver‐containing poly(dG)–poly(dC) DNA (E‐DNA) molecules have recently been reported as promising candidates for molecular electronics, owing to the selectivity of their metallization, their thin and uniform structure, their resistance to deformation, and their maximum possible high conductivity. Ultrahigh vacuum (UHV) scanning tunneling microscopy (STM) of E‐DNA presents an elaborate high‐resolution morphology characterization of these unique molecules, along with a detailed depiction of their electronic level structure. The energy levels found for E‐DNA indicate a novel truly hybrid metal–molecule structure, potentially more conductive than other DNA‐based alternatives.     

Sequence-specific detection of individual DNA polymerase complexes in real time using a nanopore

Nanoscale pores have potential to be used as biosensors and are an established tool for analysing the structure and composition of single DNA or RNA molecules. Recently, nanopores have been used to measure the binding of enzymes to their DNA substrates. In this technique, a polynucleotide bound to an enzyme is drawn into the nanopore by an applied voltage. The force exerted on the charged backbone of the polynucleotide by the electric field is used to examine the enzyme-polynucleotide interactions. Here we show that a nanopore sensor can accurately identify DNA templates bound in the catalytic site of individual DNA polymerase molecules. Discrimination among unbound DNA, binary DNA/polymerase complexes, and ternary DNA/polymerase/deoxynucleotide triphosphate complexes was achieved in real time using finite state machine logic. This technique is applicable to numerous enzymes that bind or modify DNA or RNA including exonucleases, kinases and other polymerases.