Loops in DNA: An overview of experimental and theoretical approaches

DNA loop formation plays a central role in many cellular processes. The aim of this paper is to present the state of the art and open problems regarding the experimental and theoretical approaches to DNA looping. A particular attention is devoted to the effects of the protein bridge size and of protein induced sharp DNA bending on DNA loop formation enhancement.     

Comment on the paper “Comparison of the measured phase diagrams in the force-temperature plane for the unzipping of two different natural DNA sequences” by C.H. Lee, C. Danilowicz, V.W Coljee, and M. Prentiss

The paper by Lee et al. describes the experiments on the unzipping of λ DNA sequences as a function of force and temperature. This comment aims to stress that the unzipping takes place out of equilibrium due to high sequence-dependent free-energy barriers. The force at which a heterogeneous sequence is unzipped therefore depends on the experimental waiting time.     

Dynamics of intramolecular recognition: Base-pairing in DNA/RNA near and far from equilibrium

The physics of the base-pairing interaction in DNA and RNA molecules plays a fundamental role in biology. Past experimental and theoretical research has led to a fairly complete and quantitative understanding of the equilibrium properties such as the different phases, the melting behavior, and the response to slow stretching. The non-equilibrium behavior is even richer than might be expected on the basis of thermodynamics. However, the non-equilibrium behavior is also far less understood. Here, we review different theoretical approaches to the study of base-pairing thermodynamics and kinetics, and illustrate the rich phenomenology with several examples that use these approaches.     

Counterion vibrations in the DNA low-frequency spectra

The vibrations of univalent metal cations with respect to phosphate groups of the DNA backbone are described using the four-mass model approach (S.N. Volkov, S.N. Kosevich, J. Biomol. Struct. Dyn. 8, 1069 (1991)) extended in this paper. The force constant of the counterion-phosphate interaction is determined by considering the DNA with counterions as a lattice of ion crystal. For such ion-phosphate lattice the Madelung constant and the dielectric constant are estimated. The obtained value of the Madelung constant is lower than for the NaCl crystal, and its value is about 1.3. The dielectric constant is within 2.3-2.7 depending on the counterion type and form of the double helix. The calculations of the low-frequency spectra show that for the DNA with metal cations Na⁺ , K⁺ , Rb⁺ and Cs⁺ the frequency of ion-phosphate vibrations decreases from 174 to 96cm^-1 as the counterion mass increases. The obtained frequencies agree well with the vibrational spectra of polynucleotides in a dry state which prove our suggestion about the existence of the ion-phosphate lattice around the DNA double helix. The amplitudes of conformational vibrations for DNA in B -form are calculated as well. The results demonstrate that light counterions ( Na⁺ do not disturb the internal dynamics of the DNA. However, heavy counterions ( Cs⁺ have effect on the internal vibrations of the DNA structural elements.     

Effect of the Carbon-Nanotube Length on Water Permeability

Effect of the carbon nanotube （CNT） channel length on the water flow through the CNT is studied using molecular dynamics simulations. The water flow is found to decay with the channel length （-1/N^2.3, N is the number of carbon rings along the nanotube axis）, much faster than that predicted by a previous continuous-time random walk （CTRW） model （-1/N）. This unexpected decay rate of flow is found to result from the weakening of the correlation of the concerted motion of the water molecules inside the ONT. An improved CTRW model is then proposed by taking into account of this effect. Meanwhile, the diffusion constant of water molecules inside CNTs with various lengths is found to be relatively invariant, which results in a relatively constant hopping rate.     

Statistical theory of force-induced unzipping of DNA

The unzipping transition under the influence of external force of a dsDNA molecule has been studied using the Peyrard-Bishop Hamiltonian. The critical force F_c(T) for unzipping calculated in the constant force ensemble is found to depend on the potential parameter k which measures the stiffness associated with a single strand of DNA and on D, the well depth of the on-site potential representing the strength of hydrogen bonds in a base pair. The dependence on temperature of F_c(T) is found to be (T_D - T)^1/2 (T_D being the thermal denaturation temperature) with F_c(T_D) = 0 and F_c(0) = . We used the constant extension ensemble to calculate the average force F(y) required to stretch a base pair a y distance apart. The value of F(y) needed to stretch a base pair located far away from the ends of a dsDNA molecule is found twice the value of the force needed to stretch a base pair located at one of the ends to the same distance for y 1.0 . The force F(y) in both cases is found to have a very large value for y 0.2 compared to the critical force found from the constant force ensemble to which F(y) approaches for large values of y. It is shown that the value of F(y) at the peak depends on the value of k which measures the energy barrier associated with the reduction in DNA strand rigidity as one passes from dsDNA to ssDNA and on the value of the depth of the on-site potential. The effect of defects on the position and height of the peak in the F(y) curve is investigated by replacing some of the base pairs including the one being stretched by defect base pairs. The formation and behaviour of a loop of Y shape when one of the ends base pair is stretched and a bubble of ssDNA with the shape of an eye when a base pair far from ends is stretched are investigated.     

Effect of spermine and DNase on DNA release from bacteriophage T5

Bacterial viruses (bacteriophages) consist of nucleic acid protected by a protein envelope called capsid. At the start of infection, the phage genome is translocated into the bacterial cytoplasm. In vitro (and also in vivo), this DNA release can be triggered by binding a specific receptor protein to the phage tail. The force responsible for the release arises from energy stored in the capsid due to strong confinement of the DNA. We show that this force can be modified by adding molecules like spermine that affect DNA conformation. The tetravalent cation spermine can reduce the pressure inside the capsid and induce condensation of the released DNA. We examine the effect of spermine on DNA ejection from phage T5 by using light scattering and gel electrophoresis to measure the amount of DNA remaining in the capsid at the end of ejection. We discuss the results in terms of free energy minimization and we demonstrate that the presence of a DNA condensate outside the phage generates an additional force pulling passively on the DNA remaining inside the capsid.     

Fluctuating semiflexible polymer ribbon constrained to a ring

Twist stiffness and an asymmetric bending stiffness of a polymer or a polymer bundle is captured by the elastic ribbon model. We investigate the effects a ring geometry induces to a thermally fluctuating ribbon, finding bend-bend coupling in addition to twist-bend coupling. Furthermore, due to the geometric constraint the polymer's effective bending stiffness increases. A new parameter for experimental investigations of polymer bundles is proposed: the mean square diameter of a ribbonlike ring, which is determined analytically in the semiflexible limit. Monte Carlo simulations are performed which affirm the model's prediction up to high flexibility.     

Unfolding designable structures

Among an infinite number of possible folds, nature has chosen only about 1000 distinct folds to form protein structures. Theoretical studies suggest that selected folds are intrinsically more designable than others; these selected folds are unusually stable, a property called the designability principle. In this paper we use the 2D hydrophobic-polar lattice model to classify structures according to their designability, and Langevin dynamics to account for their time evolution in the presence of shear flow. We demonstrate that, among all possible folds, the more designable ones are easier to unfold due to their large number of surface-core bonds.     

Topological and geometrical entanglement in a model of circular DNA undergoing denaturation

The linking number (topological entanglement) and the writhe (geometrical entanglement) of a model of circular double stranded DNA undergoing a thermal denaturation transition are investigated by Monte Carlo simulations. By allowing the linking number to fluctuate freely in equilibrium we see that the linking probability undergoes an abrupt variation (first-order) at the denaturation transition, and stays close to 1 in the whole native phase. The average linking number is almost zero in the denatured phase and grows as the square root of the chain length, N, in the native phase. The writhe of the two strands grows as in both phases. Received 8 May 2002 Published online 13 August 2002     

Tautomery and H-bonding characteristics of 2-aminopurine: a combined experimental and theoretical study

An experimental and theoretical RHF, MP2 and DFT/6-31++G^** study is described of the matrix FT-IR spectra of monomer 2-aminopurine and H-bonded complexes of 2-aminopurine with water. 2-aminopurine occurs in Ar predominantly as the amino-N9H tautomer, but small amounts of the amino-N7H tautomer are also present. An approximate K_T value for this tautomeric equilibrium is found to be 0.016 (RHF) and 0.015 (DFT) using the infrared intensity measurement. Four H-bonded complexes of the abundant amino-N9H form with water are detected in the experimental FT-IR spectrum by their characteristic predicted absorptions, i.e. the three closed complexes N3 ^... H-O ^... H-N9, N1 ^... H-O ^... H-NH, N3 ^... H-O ^... H-NH and the open complex N7 ^... H-OH. From the experimental results, the proton affinity of the N7 atom in 2-aminopurine can be estimated. The dependence of the H-bond strength on the H-bond linearity is demonstrated by a correlation between the N ^... H distance and the N ^... H-O angle in closed N ^... H-O ^... H-N complexes. Received 10 December 2001 Published online 13 September 2002     

Model for DNA hairpin denaturation

We investigate the thermal denaturation of DNA hairpins using molecular dynamics simulations of a simple model describing the molecule at a scale of a nucleotide. The model allows us to analyze the different interacting features that determine how an hairpin opens, such as the role of the loop and the properties intrinsic to the stem.     

Microgels and fractal structures at interfaces and surfaces

The behavior of microgels near surfaces and their adsorption is studied by simple scaling theory. Two different types of microgels can be studied, i.e., fractal type microgels and randomly crosslinked polymer chains. In the first case the gel can be described mainly by introducing a spectral dimension. The second type requires more attention and uses the number of crosslinks as parameter. The main result is that soft gels with weakly coupled crosslinks and a low number of crosslinks adsorb much better than hard gels, with many crosslinks. Similar results for fractal gels and branched polymer are presented. Fractal gels with low connectivity adsorb easier than gels with a large connectivity dimension. We discuss also consequences on surface protection by microgels. Received: 11 August 1997 / Received in final form: 20 November 1997 / Accepted 22 January 1998     

Folding of lattice protein chains with modified Gō potential

We propose a modified Gō model in which the pairwise interaction energies vary as local environment changes. The stability difference between the surface and the core is also well considered in this model. Thermodynamic and kinetic studies suggest that this model has improved folding cooperativity and foldability in contrast with the Gō model. The free energy landscape of this model has broad barriers and narrow denatured states, which is consistent with that of the two-state folding proteins and is lacked for the Gō model. The role of non-native interactions in protein folding is also studied. We find that appropriate consideration of the contribution of the non-native interactions may increase the folding rate around the transition temperature. Our results show that conformation-dependent interaction between the residues is a realistic representation of potential functions in protein folding. Received 10 April 2002 / Received in final form 20 August 2002 Published online 19 December 2002 RID="a" ID="a"e-mail: wangwei@nju.edu.cn     

Specific heat spectra for quasiperiodic ladder sequences

We performed a theoretical study of the specific heat C(T) as a function of the temperature for double-strand quasiperiodic sequences. To mimic DNA molecules, the sequences are made up from the nucleotides guanine G, adenine A, cytosine C and thymine T, arranged according to the Fibonacci and Rudin-Shapiro quasiperiodic sequences. The energy spectra are calculated using the two-dimensional Schr?dinger equation, in a tight-binding approximation, with the on-site energy exhibiting long-range disorder and non-random hopping amplitudes. We compare the specific heat features of these quasiperiodic artificial sequences to the spectra considering a segment of the first sequenced human chromosome 22 (Ch22), a real genomic DNA sequence.     

Kinetics of protein-release by an aptamer-based DNA nanodevice

A recently introduced DNA nanodevice can be used to selectively bind or release the protein thrombin triggered by DNA effector strands. The release process is not well described by simple first or second order reaction kinetics. Here, fluorescence resonance energy transfer and fluorescence correlation spectroscopy experiments are used to explore the kinetics of the release process in detail. To this end the influence of concentration variations and also of temperature is determined. The relevant kinetic parameters are extracted from these experiments and the kinetic behavior of the system is simulated numerically using a set of rate equations. The hydrodynamic radii of the aptamer device alone and bound to thrombin are determined as well as the dissociation constant for the aptamer device-thrombin complex. The results from the experiments and a numerical simulation support the view that the DNA effector strand first binds to the aptamer device followed by the displacement of the protein.     

A simple atomistic model for the simulation of the gel phase of lipid bilayers

In this paper we present the results of a large-scale numerical investigation of structural properties of a model of cell membrane, simulated as a bilayer of flexible molecules in vacuum. The study was performed by carrying out extensive Molecular Dynamics simulations, in the (NVE) micro-canonical ensemble, of two systems of different sizes ( 2×32 and 2×256 molecules), over a fairly large set of temperatures and densities, using parallel platforms and more standard serial computers. Depending on the dimension of the system, the dynamics was followed for physical times that go from few hundred picoseconds for the largest system to 5-10 nanoseconds for the smallest one. We find that the bilayer remains stable even in the absence of water and neglecting Coulomb interactions in the whole range of temperatures and densities we have investigated. The extension of the region of physical parameters that we have explored has allowed us to study significant points in the phase diagram of the bilayer and to expose marked structural changes as density and temperature are varied, which are interpreted as the system passing from a crystal to a gel phase. Received 6 July 2000 and Received in final form 28 December 2000     

Vectorial representation of single- and multi-domain protein folds

We discuss a vectorial representation applicable to both single- and multi-domain protein folds. This generalized vectorial representation is essentially identical to the previously described vectorial representation for single-domain proteins folds when applied to these, but allows for the additional consistent representation of multi-domain structures. We show that the generalized vectorial representation enables the accurate analytical prediction of site-specific amino acid distributions for both single- and multi-domain protein folds, similarly as the previously described vectorial representation does for single-domain folds.