Aqueous hydration of nucleic acid constituents: Monte Carlo computer simulation studies

Monte Carlo computer simulations were performed on dilute aqueous solutions of thymine, cytosine, uracil, adenine, guanine, the dimethyl phosphate anion in the gauche-gauche conformation and a ribose and deoxyribose derivative. The aqueous hydration of each molecule was analysed in terms of quasi-component distribution functions based on the Proximity Criterion, and partitioned into hydrophobic, hydrophilic and ionic contributions. Color stereo views of selected hydration complexes are also presented. A preliminary discussion of the transferability of functional group coordination numbers is given. The results enable to comment on two current problems related to the hydration of nucleic acids: a) the theory of Dickerson and coworkers on the role of water in the relative stability of the A and B form of DNA and b) the idea of water bridges and filaments emerging from the computer simulation results on the hydration of DNA fragments by Clementi.     

Monte-Carlo simulation of hydration of nucleic acid fragments

Monte-Carlo simulation of the systems containing a stack of 6 complementary base pairs and 180 water molecules has been performed. Characteristic of the hydration shell structure in major and minor grooves has been found for the stacks of repeating A : U and G : C base pairs as well as alternating (A : U, U : A) and (G : C, C : G) ones. Probabilities of the formation of bridges, formed by 1, 2 and 3 water molecules, between hydrophilic centres of the bases have been estimated. One water molecule forms an H-bonded bridge between two adjacent hydrophilic centres with high probability if N...N, N...O or O...O distance between these centres is close to 4.3 A. Hydration shell structure was found to depend significantly on the stack sequence and configuration, while global hydration characteristics (average energy, the number of water-water and water-base H-bonds) are only slightly dependent on the stack sequence and configuration. For the stacks in A conformation the number of water molecules forming more than one H-bonds with the bases is greater in comparison with the stacks in B-like conformation. This result is discussed in connection with the concept of hydration economy during B to A transition.     

Modeling of hydration of incorrect nucleic acid base pairs by the Monte Carlo method

The hydration of water bridged base pairs of nucleic acids have been simulated via the Monte Carlo method. The simulation have shown that water molecules forming H-bonds with both bases preserve this H-bonding with large probability in the water surrounding. This fact supports the supposition about the important role of water molecules in wrong base pair formation and about the role of these base pairs in the structure and functioning of nucleic acids.     

Nature of the stacking of nucleic acid bases in water: a Monte Carlo simulation

The results of a Monte Carlo simulation of the hydration of uracil and thymine molecules, their stacked dimers and hydrogen-bonded base pairs are presented. Simulations have been performed in a cluster approximation. The semiempirical atom-atom potential functions have been used (cluster consisting of 200 water molecules). It has been shown that the stacking interactions of uracil and thymine molecules in water arise mainly due to the increase in the water-water interaction during the transition from monomers to dimer. It has been found out that stacked base associates are more preferable than base pairs in water. This preference is mainly due to the energetically more favourable structure of water around the stack.     

Ring closure probabilities for DNA fragments by Monte Carlo simulation

The rate of ligation of DNA molecules into circular forms depends on the ring closure probability, commonly called the j-factor, which is a sensitive measure of the extent to which thermal fluctuations contribute to bending and twisting of DNA molecules in solution. We present a theoretical treatment of the cyclization equilibria of DNA that employs a special Monte Carlo method for generating large ensembles of model DNA chains. Using this method, the chain length dependence of the j-factor was calculated for molecules. in the size range 250 to 2000 base-pairs. The Monte Carlo results are compared with recent analytical theory and experimental data. We show that a value of 475 A for the persistence length of DNA, close to values measured by a number of other methods, is in excellent agreement with the cyclization results. Preliminary applications of the Monte Carlo method to the problem of systematically bent DNA molecules are presented. The calculated j-factor is shown to be very sensitive to the amount of bending in these fragments. This fact suggests that ligase closure measurements of systematically bent DNA molecules should be a useful method for studying sequence-directed bending in DNA.     

A Monte Carlo simulation of hydration of xanthine-derivatives and their stacked forms.

Results on a Monte Carlo simulation of the hydration of monomer and possible stacked dimer forms of a purine alkaloid series in 200- and 400-water molecule clusters are presented. Investigation of different purine stacked dimers in a 200-water molecule cluster reveals that for caffeine there exists one, for theophylline two and for theobromine four dimers are energetically favorable. For caffeine, the same energetically favored stacked dimer form is observed in both the 200- and 400-water molecule cluster. The main factor stabilizing the preferred dimer stacks is the change in the interaction between water molecules of the monomer cluster and those water molecules in the dimer cluster.     

Monte Carlo computer simulation of the aqueous hydration of the glycine zwitterion at 25 degree C

Monte Carlo computer simulation on a dilute aqueous solution of the glycine zwitterion are reported. The results are presented in terms of the Quasi-Component Distribution Functions (QCDF) of Ben Naim and partitioned into atomic and functional group contributions using the Proximity Criterion. The Proximity Criterion analysis has been extended to orientational properties and a new normalization procedure has been introduced for the radial distribution functions obtained by the Proximity Criterion. The solvation environment of the glycine zwitterion is found to contain, on the average, 14.4 water molecules out of which 3.2 belong to the ammonium group, 6.1 to the methylene group and 5.1 to the carboxyl group. The importance of the many-body statistical mechanical approach to hydration is emphasized by our finding that the configuration corresponding to the absolute minimum of the glycine zwitterion-water potential surface was found to have negligible statistical weight in the aqueous simulation.     

Monte Carlo simulation of biospecific interactions

Numerical simulations of the stochastic time evolution of biospecific interactions are described and show that when molecular populations are large, time course predictions match those obtained using a deterministic expression. When population size is decreased the effects of stochastic noise become apparent. The significance of stochastic noise in sensitive binding-based assay systems suggests an immediate need for models of this type.     

Monte Carlo simulation program for ecosystems

A Monte Carlo computer simulation program is designed in orderto describe the spatial and time evolution of a population ofliving individuals under preassigned environmental conditionsof energy. The simulation is inspired by previous techniquesdeveloped in physics — in particular, in molecular dynamicsand simulations of liquids — and it already provides somenew insights regarding macroscopic deterministic models in ecologyand concerning eventual control of artificial biomass productionplants. Received on July 15, 1986; accepted on October 9, 1986     

Monte Carlo simulation of intercalated carbon nanotubes

Monte Carlo simulations of the single- and double-walled carbon nanotubes (CNT) intercalated with different metals have been carried out. The interrelation between the length of a CNT, the number and type of metal atoms has also been established. This research is aimed at studying intercalated systems based on CNTs and d-metals such as Fe and Co. Factors influencing the stability of these composites have been determined theoretically by the Monte Carlo method with the Tersoff potential. The modeling of CNTs intercalated with metals by the Monte Carlo method has proved that there is a correlation between the length of a CNT and the number of endo-atoms of specific type. Thus, in the case of a metallic CNT (9,0) with length 17 bands (3.60 nm), in contrast to Co atoms, Fe atoms are extruded out of the CNT if the number of atoms in the CNT is not less than eight. Thus, this paper shows that a CNT of a certain size can be intercalated with no more than eight Fe atoms. The systems investigated are stabilized by coordination of 3d-atoms close to the CNT wall with a radius-vector of (0.18–0.20) nm. Another characteristic feature is that, within the temperature range of (400–700) K, small systems exhibit ground-state stabilization which is not characteristic of the higher ones. The behavior of Fe and Co endo-atoms between the walls of a double-walled carbon nanotube (DW CNT) is explained by a dominating van der Waals interaction between the Co atoms themselves, which is not true for the Fe atoms.     

A Monte Carlo simulation of chemical reactions

A computer-based algorithm to solve complex chemical rate equations is introduced. A simple Monte Carlo sampling method is used to generate chemical reactions in numbers proportional to reaction probabilities, and a second-order Runge-Kutta method is used to calculate time. The method is compared with a closed form mathematical solution for a simple chemical system, and it is compared with a numerical integration of the rate equations for a more complicated system.     

A Monte Carlo simulation of Auger cascades

The energy imparted to biological tissue after the decay of incorporated Auger emitters stems from two sources: (a) energy deposition by the Auger and Coster-Kronig electrons and (b) the charge potential which remains on the multiple ionized atom after the end of the cascade. For the numerical assessment of both the kinetic energy of the released electrons and the charge potential, a new and--for purposes of microdosimetry--precise method is presented. Based on relativistic Dirac-Fock calculations and a rigorous bookkeeping, this method provides a perfect energy balance of the considered atomic system when applied to Monte Carlo simulations of Auger cascades. By comparing the results for charge distribution for krypton and iodine with experimental data and the electron spectrum of 125I with theoretical data, it can be shown that the approach followed in this work is reasonable and appropriate for the determination of the energy deposited by incorporated Auger emitters in small volumes of condensed matter. The total energy deposited by 125I in a volume of 20-nm diameter is 2.03 keV which is made up by multiple ionization (1.07 keV) and energy deposition by the emitted Auger electrons (0.96 keV).     

Monte Carlo simulation of the enzymatic lysis of yeast

The overall reaction in the enzymatic lysis of yeast takes place in three major steps: (i) the two-layer wall is digested, (ii) the cell bursts under the osmotic pressure difference to release its intracellular material, and (iii) the intracellular material is digested by the enzymes still present in the solution. The first and third steps are continuous processes, adequately described by Michaelis-Menten kinetic models. The second step is a discrete event, statistical in nature. A model of engineering value should effectively bridge the gap between the two continuous processes (first and third steps). In this work, Monte Carlo simulations are used to identify a suitable function that captures the statistical nature of cell rupture and represents the rate of release of intracellular material. It is shown that the two-parameter beta distribution function serves this purpose most effectively. Comparisons with experimental results indicate that the cell rupture ratio is a widely distributed statistical function. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 53: 290-295, 1997.     

Monte Carlo simulation studies on the prediction of protein folding types from amino acid composition

A number of methods to predicting the folding type of a protein based on its amino acid composition have been developed during the past few years. In order to perform an objective and fair comparison of different prediction methods, a Monte Carlo simulation method was proposed to calculate the asymptotic limit of the prediction accuracy [Zhang and Chou (1992),Biophys. J. 63, 1523–1529, referred to as simulation method I]. However, simulation method I was based on an oversimplified assumption, i.e., there are no correlations between the compositions of different amino acids. By taking into account such correlations, a new method, referred to as simulation method II, has been proposed to recalculate the objective accuracy of prediction for the least Euclidean distance method [Nakashimaet al. (1986),J. Biochem. 99, 152–162] and the least Minkowski distance method [Chou (1989),Prediction in Protein Structure and the Principles of Protein Conformation, Plenum Press, New York, pp. 549–586], respectively. The results show that the prediction accuracy of the former is still better than that of the latter, as found by simulation method I; however, after incorporating the correlative effect, the objective prediction accuracies become lower for both methods. The reason for this phenomenon is discussed in detail. The simulation method and the idea developed in this paper can be applied to examine any other statistical prediction method, including the computersimulated neural network method.     

Monte Carlo simulation of diffusion of adsorbed proteins

We present the results of three-dimensional lattice Monte Carlo simulations of protein diffusion on the liquid-solid interface in a wide temperature range including the most interesting temperatures (from slightly below T(f) and up to T(c), where T(f) and T(c) are the folding and collapse temperatures). For the model under consideration (27 monomers of two types), the temperature dependence of the diffusion coefficient is found to obey the Arrhenius law with the normal value (approximately 10(-2)-10(-3) cm(2)/s) of the preexponential factor. Proteins 2000;39:76-81.     

Monte Carlo simulation of denaturation of adsorbed proteins

Denaturation of model proteinlike molecules at the liquid–solid interface is simulated over a wide temperature range by employing the lattice Monte Carlo technique. Initially, the molecule containing 27 monomers of two types (A and B) is assumed to be adsorbed in the native folded state (a 3 × 3 × 3 cube) so that one of its sides is in contact with the surface. The details of the denaturation kinetics are found to be slightly dependent on the choice of the side, but the main qualitative conclusions hold for all the sides. In particular, the kinetics obey approximately the conventional first-order law at T > T_c (T_c is the collapse temperature for solution). With decreasing temperature, below T_c but above T_f (T_f is the folding temperature for solution), deviations appear from the first-order kinetics. For the most interesting temperatures, that is, below T_f, the denaturation kinetics are shown to be qualitatively different from the conventional ones. In particular, the denaturation process occurs via several intermediate steps due to trapping in metastable states. Mathematically, this means that (i) the transition to the denatured state of a given molecule is nonexponential, and (ii) the denaturation process cannot be described by a single rate constant k_r. One should rather introduce a distribution of values of this rate constant (different values of k_r correspond to the transitions to the altered state via different metastable states). Proteins 30:168–176, 1998. © 1998 Wiley-Liss, Inc.     

The Monte Carlo simulation of pearl chain formation

Summary The phenomenon of pearl chain formation (PCF) is investigated by means of a statistical model using the Monte Carlo method. Fifteen particles (cells) interacting with simple dipole-dipole potential are shown to form chains under the influence of an external field with a threshold potential significantly lower than the two particle estimate. A possible overlap between PCF and the thermal effects of an electric field is suggested.     

All-atom Monte Carlo simulation of GCAA RNA folding

We report a detailed all-atom simulation of the folding of the GCAA RNA tetraloop. The GCAA tetraloop motif is a very common and thermodynamically stable secondary structure in natural RNAs. We use our simulation methods to study the folding behavior of a 12-base GCAA tetraloop structure with a four-base helix adjacent to the tetraloop proper. We implement an all-atom Monte Carlo (MC) simulation of RNA structural dynamics using a Go potential. Molecular dynamics (MD) simulation of RNA and protein has realistic energetics and sterics, but is extremely expensive in terms of computational time. By coarsely treating non-covalent energetics, but retaining all-atom sterics and entropic effects, all-atom MC techniques are a useful method for the study of protein and now RNA. We observe a sharp folding transition for this structure, and in simulations at room temperature the state histogram shows three distinct minima: an unfolded state (U), a more narrow intermediated state (I), and a narrow folded state (F). The intermediate consists primarily of structures with the GCAA loop and some helix hydrogen bonds formed. Repeated kinetic folding simulations reveal that the number of helix base-pairs forms a simple 1D reaction coordinate for the I-->N transition.     

Monte Carlo simulation of bifurcation in the intracellular viral kinetics

Intracellular viral kinetics are of special interest because the virion population inside an infected cell is well known to tend to grow exponentially and the corresponding kinetics may be unstable. To clarify the special features of such kinetics, we present Monte Carlo simulations taking into account the key steps of virion formation and competition of the host and viral mRNA for the host translation apparatus. Asymptotically, the model employed predicts either a stable steady state or 'ignition' with the unlimited viral growth. Under steady-state conditions, the mean square fluctuations of the viral genome and virion numbers are found to be appreciably larger than those expected on the basis of the Poissonian distribution. In the case of unstable kinetics, the simulations show the type of deviations from the corresponding mean-field results.