Slow nucleic acid unzipping kinetics from sequence-defined barriers

Recent experiments on unzipping of RNA helix-loop structures by force have shown that ≈40-base molecules can undergo kinetic transitions between two well-defined “open” and “closed” states, on a timescale ≈1 sec [Liphardt et al., Science 297, 733-737 (2001)]. Using a simple dynamical model, we show that these phenomena result from the slow kinetics of crossing large free energy barriers which separate the open and closed conformations. The dependence of barriers on sequence along the helix, and on the size of the loop(s) is analyzed. Some DNA and RNA sequences that could show dynamics on different time scales, or three(or more)-state unzipping, are proposed. Our dynamical model is also applied to the unzipping of long (kilo-basepair) DNA molecules at constant force. Received 29 July 2002 / Received in final form 5 February 2003 Published online: 16 April 2003 RID="a" ID="a"e-mail: cocco@ldfc.u-strasbg.fr RID="b" ID="b"e-mail: jmarko@uic.edu RID="c" ID="c"e-mail: monasson@lpt.ens.fr     

The secondary structure of RNA under tension

We study the force-induced unfolding of random disordered RNA or single-stranded DNA polymers. The system undergoes a second-order phase transition from a collapsed globular phase at low forces to an extensive necklace phase with a macroscopic end-to-end distance at high forces. At low temperatures, the sequence inhomogeneities modify the critical behaviour. We provide numerical evidence for the universality of the critical exponents which, by extrapolation of the scaling laws to zero force, contain useful information on the ground-state (f = 0) properties. This provides a good method for quantitative studies of scaling exponents characterizing the collapsed globule. In order to get rid of the blurring effect of thermal fluctuations, we restrict ourselves to the ground state at fixed external force. We analyze the statistics of rearrangements, in particular below the critical force, and point out its implications for force-extension experiments on single molecules. Received 18 June 2002 and Received in final form 23 September 2002 RID="a" ID="a"e-mail: muller@ipno.in2p3.fr     

Optimized Monte Carlo analysis for generalized ensembles

We present a new, maximum-likelihood based method to combine data from a multiple number of Monte Carlo simulations performed within any type of ensemble. The method offers an efficient iterative scheme to obtain the density of states of a wide range of energies as well as of other macroscopic variables. It should in particular be useful for the study of systems with a rough energy landscape. Received 4 June 2002 Published online 14 October 2002 RID="a" ID="a"e-mail: borg@alf.nbi.dk     

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.     

Ground state and glass transition of the RNA secondary structure

RNA molecules form a sequence-specific self-pairing pattern at low temperatures. We analyze this problem using a random pairing energy model as well as a random sequence model that includes a base stacking energy in favor of helix propagation. The free energy cost for separating a chain into two equal halves offers a quantitative measure of sequence specific pairing. In the low temperature glass phase, this quantity grows quadratically with the logarithm of the chain length, but it switches to a linear behavior of entropic origin in the high temperature molten phase. Transition between the two phases is continuous, with characteristics that resemble those of a disordered elastic manifold in two dimensions. For designed sequences, however, a power-law distribution of pairing energies on a coarse-grained level may be more appropriate. Extreme value statistics arguments then predict a power-law growth of the free energy cost to break a chain, in agreement with numerical simulations. Interestingly, the distribution of pairing distances in the ground state secondary structure follows a remarkable power-law with an exponent -4/3, independent of the specific assumptions for the base pairing energies.     

A DFT study of electron or hole localization in a peptide containing asparagin

The mechanisms of protein degradation induced by ionisation are of great interest for radiobiology, improvement of mass spectroscopy and industrial processes such as radio sterilisation. Sequences containing asparagin are very sensitive especially if surrounded by glycine. Very few techniques allow a satisfying understanding of the processes induced by creation of an anionic or cationic site in a peptide. We used the methods of quantum chemistry (DFT/B3LYP with 6-31G^* basis set) to characterise the geometry modifications induced in the cations or in the anions derived from peptide Gly Asn Gly. The cationic sites are localised mostly close to the first peptidic bond and induce a lengthening of the Ca-C(O) bond. Conversely the anionic sites are localised on a carbonyl function. Implications are discussed considering the radiolytic products and the proposed mechanisms. Received 21 January 2002 Published online 13 September 2002     

Transition from coherence to bistability in a model of financial markets

We present a model describing the competition between information transmission and decision making in financial markets. The solution of this simple model is recalled, and possible variations discussed. It is shown numerically that despite its simplicity, it can mimic a size effect comparable to a crash localized in time. Two extensions of this model are presented that allow to simulate the demand process. One of these extensions has a coherent stable equilibrium and is self-organized, while the other has a bistable equilibrium, with a spontaneous segregation of the population of agents. A new model is introduced to generate a transition between those two equilibriums. We show that the coherent state is dominant up to an equal mixing of the two extensions. We focus our attention on the microscopic structure of the investment rate, which is the main parameter of the original model. A constant investment rate seems to be a very good approximation. Received 7 August 2000 and Received in final form 10 September 2000     

Sphere packing, helices and the polytope {3, 3, 5}

The packing of tetrahedra in face contact is well-known to be relevant to atomic clustering in many complex alloys. We briefly review some of the structures that can arise in this way, and introduce methods of dealing with the geometry of the polytope {3, 3, 5}, which is highly relevant to an understanding of these structures. Finally, we present a method of projection from S₃ to E₃ that enables coordinates for the key vertices of the collagen model of Sadoc and Rivier to be calculated. Received 27 March 2001     

Co-ion dependence of DNA nuclease activity suggests hydrophobic cavitation as a potential source of activation energy

The source of the activation energy that allows cutting of DNA by restriction enzymes is unclear. A systematic study of the cutting efficiency of the type-II restriction endonuclease EcoRI, with varying background electrolyte ion pair and buffer reported here, shows only a modest dependence of efficiency on cation type. Surprisingly, efficiency does depend strongly on the presumed indifferent anion of the background salt. What emerges is that competition between the background salt anion and the buffer anion for the enzyme and DNA surfaces is crucial. The results are unexpected and counterintuitive from the point of view of conventional electrolyte theory. However, taken together with recent developments in surface chemistry, the results do fall into place and could also suggest a novel mechanism for enzyme activity as an alternative to metal-activated hydrolysis: microscopic cavitation in a hydrophobic pocket might be the source of activation energy. Received 19 June 2000 and Received in final form 17 October 2000     

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     

Comparison of the measured phase diagrams in the force-temperature plane for the unzipping of two different natural DNA sequences

In this work, we consider the critical force required to unzip two different naturally occurring sequences of double-stranded DNA (dsDNA) at temperatures ranging from 20 ^°C to 50 ^°C, where one of the sequences has a 53% average guanine-cytosine (GC) content and the other has a 40% GC content. We demonstrate that the force required to separate the dsDNA of the 53% GC sequence into single-stranded DNA (ssDNA) is approximately 0.5 pN, or approximately 5% greater than the critical force required to unzip the 40% GC sequence at the same temperature. In the temperature range between 20 and 40 ^°C the measured critical forces correspond reasonably well to predictions based on a simple theoretical homopolymeric model, but at temperatures above 40 ^°C the measured critical forces are much smaller than the predicted forces. The correspondence between theory and experiment is not improved by using Monte Carlo simulations that consider the heteropolymeric nature of the sequences.     

Modeling of recognition sites of nucleic acid bases aaand amide side chains of amino acids. Combination of experimental and theoretical approaches

A combined experimental-theoretical approach to modeling of building blocks of recognition complexes formed by nucleic acid bases and the amino-acids side-chain amino group is reviewed. The approach includes the temperature dependent field-ionization mass spectrometry and ab initio quantum chemical calculations. The mass spectrometric technique allows determination of interaction enthalpies of biomolecules in the gas phase, and the results it produces are directly comparable to the results obtained through theoretical modeling. In our works we have analyzed both thermodynamic and structural aspects of the recognition complexes of four canonical nucleic acid bases and acrylamide, which models the side chain of asparagine and glutamine. It has been shown that all bases can interact with amide group of the amino acids via their Watson-Crick sites when being incorporated into a single strand DNA or RNA. Stability of the complexes studied, expressed as - ΔH (kJ mole^-1) decreases as: m⁹Gua (- 59.5) > m ¹Cyt (- 57.0) > m ⁹Ade (- 52.0) ≫m ¹Ura (- 40.6). We have determined that in the double stranded DNA only purine bases can be recognized. Received 5 February 2002 and Received in final form 14 March 2002 Published online 13 September 2002     

Deformation in cooperative molecular motors

We implement a model to represent the effect of the deformation of the backbone of a system of motor proteins while sliding on a track filament. This model incorporates a nearest neighbor interaction term among the motors for the deformation energy. Correlations induced by this term result in increased motor force for inter-particle distances small compared to the ratchet period. Received 20 February 2001 and Received in final form 31 May 2001     

Models for the size distribution of businesses in a price driven market

A microscopic model of aggregation and fragmentation is introduced to investigate the size distribution of businesses. In the model, businesses are constrained to comply with the market price, as expected by the customers, while customers can only buy at the prices offered by the businesses. We show numerically and analytically that the size distribution scales like a power-law. A mean-field version of our model is also introduced and we determine for which value of the parameters the mean-field model agrees with the microscopic model. We discuss to what extent our simple model and its results compare with empirical data on company sizes in the US and debt sizes in Japan. Finally, possible extensions of the mean-field model are discussed, to cope with other empirical data. Received 10 January 2001 and Received in final form 12 March 2001     

Monte Carlo simulations of electron dynamics in N2/CO2 mixtures

Motivated by experimental investigations of electrical discharges in N₂/CO₂/H₂O, Monte Carlo (MC) electron dynamics simulations in atmospheric N₂/CO₂ mixtures were performed. The goal was to obtain electron energy distribution functions (EEDFs), mean free path, drift velocity, collision frequency and mean energy of electrons, rate coefficients of electron-impact reactions, ionisation and attachment coefficients, as functions of the reduced electric field strength (E/N) and of the concentration of individual gas components. The results obtained by MC simulations were fitted with polynomials of up to the 3rd order with reasonable accuracy for E/N above 80 Td. The studied parameters below 80 Td were strongly non-linear as functions of E/N. This is mostly due to the influence of elastic collisions of electrons with CO₂ molecules prevailing in CO₂-dominant mixtures for E/N < 40 Td, and vibrational excitation collisions of N₂ species prevailing in N₂-dominant mixtures for E/N from 40 to 80 Td. The effect of these electron-impact processes was specific for each of the studied parameters.     

Solute effects on the helix-coil transition

We discuss the effects of the solvent composition on the helix-coil transition of a polypeptide chain. We use a simple model to demonstrate that improving the hydrogen-bonding ability of the solvent can make the transition less cooperative, without affecting the transition temperature. This effect is very different from other solvent effects which primarily influence the melting transition rather than the cooperativity. Received 10 December 2001 and Received in final form 22 March 2002     

Connecting cluster dynamics and protein folding

The relaxation dynamics of clusters can be interpreted in terms of the topographies of their potential surfaces. Systems with short-range potentials have sawtooth-like potential surfaces with small drops in energy from one local minimum to the next and few-body motions as the clusters move from one minimum to another; such systems readily take on amorphous structures. These are called “glass-formers". Systems with long-range forces have potentials whose topographies are like rough staircases, with some large drops in energy from one minimum to the next; their well-to-well passages involve very collective motions and such systems are excellent structure-seekers. They find their way to well-ordered, highly selective structures under almost all circumstances. These characteristics generalize to describe the potential surfaces and folding behavior of polypeptides and proteins. The forces are effective long-range forces due to the polymer chain. Staircase topographies emerge both from direct sampling of potential surfaces and from the inversion of the kinetics generated by a much more aaabstract topological model, from which folding pathways can be inferred. Received 4 December 2000     

Fibril stability in solutions of twisted -sheet peptides: a new kind of micellization in chiral systems

The problem of fibril (fibre) formation in chiral systems is explored theoretically being supported by experiments on synthetic de novo 11-mer peptide forming self-assembled -sheet tapes. Experimental data unambiguously indicate that the tapes form fibrils of nearly monodisperse thickness ca . 8-10 nm. Fibril formation and stabilisation are attributed to inter-tape face-to-face attraction and their intrinsic twist, correspondingly. The proposed theory is capable of predicting the fibril aggregation number and its equilibrium twist in terms of molecular parameters of the primary tapes. The suggested novel mechanism of twist stabilisation of finite aggregates (fibrils) is different to the well-known stabilisation of micelles in amphiphilic systems, and it is likely to explain the formation and stability of fibrils in a wide variety of systems including proteinaceous amyloid fibres, sickle-cell hemoglobin fibres responsible for HbS anemia, corkscrew threads found in chromonics in the presence of chiral additives and native cellulose microfibrillar crystallites. The theory also makes it possible to extract the basic molecular parameters of primary tapes (inter-tape attraction energy, helical twist step, elastic moduli) from the experimental data. Received 7 May 1999 and Received in final form 15 February 2000