Nonlinear Schrödinger equation and DNA dynamics

We study a possible solitary wave solution of the nonlinear Schrödinger equation (NLSE). It is shown that the wave can be both modulated and nonmodulated depending on a ratio of the envelope and the carrier wave velocities. We also study the same type of the soliton solution in DNA dynamics. We show that the ratio of these two velocities is a measure of modulation and we conclude that the modulated wave is more stable than the nonmodulated one. Finally, we solved the problem concerning three parameters arising from the applied procedure for the solution of the NLSE.     

DNA dynamics - Experiment proposals

We argue that a breather wave, describing DNA dynamics, behaves like a real soliton. We rely on a Peyrard-Bishop-Dauxois (PBD) model. In addition, we propose a couple of experiments to confirm or reject this statement. These experiments should study solitonic interactions using micromanipulation technique. Also, we suggest how to measure a solitonic width and its amplitude.     

Temperature dependence of transport behavior of a short DNA molecule

DNA molecules may work as novel devices due to their interesting electronic transport properties. We here propose a theoretical method to deal with the temperature dependence of the transport behavior of a short DNA molecule, taking into account Coulomb interaction of electrons and the coupling between electrons and the two-level system in the DNA molecule. The nonlinear current-voltage curves are derived by using the Landauer formulae. We find that the voltage gap of the current-voltage curves is sensitive to the parameters of the two-level system. We also find that Coulomb blockade peaks can be controlled by varying the temperature, which relates to particular features of the DNA molecule.     

Thermal Vibration and Twist Induced Semiconducting Behaviour in Short DNA Wires

We study the transport properties of electrons in a short homogeneous DNA molecule where thermal vibrations and twist fluctuations of the base molecules are considered. The nonlinear current-voltage curves can be derived by using the equivalent single-particle multichannel network. The voltage gap is sensitive to the strength of thermal vibrations and twist fluctuations of the base molecules. Our results are in good agreement with the recent finding of semiconducting behaviour in short poly（G）-poly（C） DNA oligomers. The present method can also be used to calculate the other molecular wires.     

Non-monotonic swelling of a macroion due to correlation-induced charge inversion

It is known that a large, charged body immersed in a solution of multivalent counterions may undergo charge inversion as the counterions adsorb to its surface. We use the theory of charge inversion to examine the case of a deformable, porous macroion which may adsorb multivalent ions into its bulk to form a three-dimensional strongly-correlated liquid. This adsorption may lead to non-monotonic changes in the size of the macroion as multivalent ions are added to the solution. The macroion first shrinks as its bare charge is screened and then reswells as the adsorbed ions invert the sign of the net charge. We derive a value for the outward pressure experienced by such a macroion as a function of the ion concentration in solution. We find that for small deviations in the concentration of multivalent ions away from the neutral point (where the net charge of the body is zero), the swollen size grows parabolically with the logarithm of the ratio of multivalent ion concentration to the concentration at the neutral point.     

Current-voltage characteristics of double-strand DNA sequences

We use a tight-binding formulation to investigate the transmissivity and the current-voltage (I-V) characteristics of sequences of double-strand DNA molecules. In order to reveal the relevance of the underlying correlations in the nucleotides distribution, we compare the results for the genomic DNA sequence with those of artificial sequences (the long-range correlated Fibonacci and Rudin-Shapiro one) and a random sequence, which is a kind of prototype of a short-range correlated system. The random sequence is presented here with the same first neighbors pair correlations of the human DNA sequence. We found that the long-range character of the correlations is important to the transmissivity spectra, although the I-V curves seem to be mostly influenced by the short-range correlations.     

Lie Symmetries and Conserved Quantities for Super-Long Elastic Slender Rod

DNA is a nucleic acid molecule with double-helical structures that are special symmetrical structures attracting great attention of numerous researchers. The super-long elastic slender rod, an important structural model of DNA and other long-train molecules, is a useful tool in analysing the symmetrical properties and the stabilities of DNA. We study the Lie symmetries of a super-long elastic slender rod by using the methods of infinitesimal transformation. Based on Kirchhoff＇s analogue, generalized Hamilton canonical equations are analysed. The infinitesimal transformations with respect to the radian coordinate, the generalized coordinate, and the quasimomentum of the model are introduced. The Lie symmetries and conserved quantities of the model are presented.     

Strategies for the separation of polyelectrolytes based on non-linear dynamics and entropic ratchets in a simple microfluidic device

We perform Monte Carlo simulations of an existing electrophoretic microchannel device used for the size separation of large DNA fragments. This device is normally operated with a constant (dc) driving field. In contrast, we consider the case of a varying (ac) driving field, in the zero-frequency limit. We find that a time-asymmetric pulse can yield interesting migration regimes, in particular bidirectional transport for different molecular sizes. We also study a spatially asymmetric version of the device and show that it can rectify unbiased but non-equilibrium molecular motion, in agreement with previous predictions for entropic ratchets. Finally, at finite frequency we uncover a resonance for the molecular velocity in the channel which could lead to improved performance. Received: 16 November 2001 / Accepted: 11 February 2002 / Published online: 22 April 2002     

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.     

Further Discussion on Polaron Existence in Dry DNA

We study the interaction between holes and molecular vibrations on dry DNA by using the extended Firsov＇s model. The ground state energy, calculated by using two Hilbert spaces, Fock state space and coherent state space, is confirmed. The polaron binding energy, defined with the ground state energy, is 0.014eV, much less than the thermal energy 0.026eV at room temperature 300K, which means that polarons are difficult to form self-trapping at room temperature and Anderson localization will prevent a metallic state on dry DNA. The results are consistent with the available experiments.     

Using 3D fluid-structure interaction model to analyse the biomechanical properties of erythrocyte

This Letter presents a newly developed three-dimensional fluid-structure interaction model of the red blood cell (RBC). The model consists of a deformable liquid capsule modelled as Newtonian fluid enclosed by a hyperelastic membrane with viscoelastic property. Numerical results show that viscosity in the cytoplasm affects the deformed shape of RBC under loading. This observation is contrary to the earlier belief that viscosity of the cytoplasm can be neglected. Numerical simulations carried out to investigate large deformation induced on the RBC model using direct tensile forces show significant improvement in terms of correlation with experimental results. The membrane shear modulus estimated from the model ranges between 3.7 to compares well with results obtained from micropipette aspiration experiments.     

Modulational instability and exact soliton solutions for a twist-opening model of DNA dynamics

We study the nonlinear dynamics of DNA which takes into account the twist-opening interactions due to the helicoidal molecular geometry. The small amplitude dynamics of the model is shown to be governed by a solution of a set of coupled nonlinear Schrödinger equations. We analyze the modulational instability and solitary wave solution in the case. On the basis of this system, we present the condition for modulation instability occurrence and attention is paid to the impact of the backbone elastic constant K. It is shown that high values of K extend the instability region. Through the Jacobian elliptic function method, we derive a set of exact solutions of the twist-opening model of DNA. These solutions include, Jacobian periodic solution as well as kink and kink-bubble solitons.     

Effect of temperature on polaron dynamics in poly-DNA

We investigate the effect of temperature on polaron dynamics in the framework of a tight-binding model. The dissociation of a polaron will become fast with the increase of temperature. There exists a crossover of the charge localization time from strong to weak temperature-dependence. Instead of the uniform motion at zero temperature, a polaron moves un-uniformly under a driven field at a finite temperature, which indicates a discrete hopping between base pairs. It is also found that the polaron motion is thermally activated. A high temperature will result in a fast movement of a polaron under a deriving field.     

AFM, a tool for single-molecule experiments

Received: 27 March 1998     

Derivation of extremely slow dynamics of protein motion based on entropy invariance

It is a mysterious fact that protein systems often show an extremely slow dynamics of their molecular motions with time scales much longer than nanosecond order, although their characteristic frequencies obtained by the normal mode analysis fall in much shorter temporal regions. This Letter provides a heuristic account for why and how such extremely slow modes of protein motions naturally emerge from fast molecular modes on the basis of an idea of entropy invariance in the principal component analysis.     

Gap Caused by Strong Pairing in the Ladder Model of DNA Molecules

By directly diagonalizing the Hamiltonian of the ladder model of deoxyribonucleic acid （DNA） molecules, the density of states is obtained. It is found that DNA behaves as a conductor when the interchain hopping is smaller than twice the intrachain one, otherwise, DNA behaves as a semiconductor.     

Structural class tendency of polypeptide: A new conception in predicting protein structural class

Prediction of protein domain structural classes is an important topic in protein science. In this paper, we proposed a new conception: structural class tendency of polypeptides (SCTP), which is based on the fact that a given amino acid fragment tends to be presented in certain type of proteins. The SCTP is obtained from an available training data set PDB40-B. When using the SCTP to predict protein structural classes by Intimate Sorting predictive method, we got the predictive accuracy (jackknife test) with 93.7%, 96.5%, and 78.6% for the testing data set PDB40-j, Chou&Maggiora and CHOU. These results indicate that the SCTP approach is quite encouraging and promising. This new conception provides an effective tool to extract valuable information from protein sequences.     

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.     

Distinct conformational properties determined by implicit and explicit representation of protein-solvent interactions. An analytical and computer simulation study

In the protein folding problem, solvent-mediated forces are commonly represented by intra-chain pairwise contact energy. Although this approximation has proven to be useful in several circumstances, it is limited in some other aspects of the problem. Here we show that it is possible to achieve two models to represent the chain-solvent system, one of them with implicit and other with explicit solvent, such that both reproduce the same thermodynamic results. Firstly, lattice models treated by analytical methods, were used to show that the implicit and explicitly representation of solvent effects can be energetically equivalent only if local solvent properties are time and spatially invariant. Following, applying the same reasoning used for the lattice models, two inter-consistent Monte Carlo off-lattice models for implicit and explicit solvent are constructed, being that now in the latter the solvent properties are allowed to fluctuate. Then, it is shown that the chain configurational evolution as well as the globule equilibrium conformation are significantly distinct for implicit and explicit solvent systems. Actually, strongly contrasting with the implicit solvent version, the explicit solvent model predicts: (i) a malleable globule, in agreement with the estimated large protein-volume fluctuations; (ii) thermal conformational stability, resembling the conformational heat resistance of globular proteins, in which radii of gyration are practically insensitive to thermal effects over a relatively wide range of temperatures; and (iii) smaller radii of gyration at higher temperatures, indicating that the chain conformational entropy in the unfolded state is significantly smaller than that estimated from random coil configurations. Finally, we comment on the meaning of these results with respect to the understanding of the folding process.