Simulations Of Counterions Around Dna With Explicit Account Of Solvent

Molecular Dynamics of DNA

The studies of the ionic environment of DNA discussed above have been carried out within continuum solvent models. The effects of solvent and hydration can be taken into account rather straightforwardly in computer simulations by introducing explicit solvent (water) molecules. However, an all-atom description makes the simulations very time-consuming and reduces the size of the system that can be considered. At the present level of computer power, the maximum number of atoms that can be simulated long enough to obtain meaningful results is on the order 104, which corresponds to a simulation box size of 50-60 A. This size is not enough to study polyelectrolyte aspects of ion distribution. Still, all-atom simulations are extremely important for understanding ion-DNA interactions in close proximity to the DNA.

The preferable method in all-atom simulations is MD, although the first attempt to simulate such model was performed by the MC method.[60] Earlier MD simulations of DNA[61-63] were too short to produce information on ionic distribution. Given the diffusion of counterions around DNA on the order 10~6cm/ sec2, at least nanosecond time scale is needed for the counterions to sample the space around DNA. Such simulations became possible from the second part of 1990s, when a large number of works on MD simulations of DNA, with full-atomic description of solvent and ions, appeared.[64-71] In the majority of these studies, the main interest was in the DNA molecule itself, investigating DNA backbone structure and dynamics, base stacking, phosphate orientation, overall nucleic acid structure, and so on. (For more information on these issues, the reader is referred to recent reviews.)[3,72] Below, we shall concentrate on works dealing with MD simulations of ion distributions around DNA. Note first that results on MD simulations are dependent on the force field used. The force fields used in macromolecular simulations are usually empirically parameterized to reproduce some set of experimental results. At present, the most often used force fields for DNA simulations are AMBER[73] and CHARMM.[74] It was found that these force fields may give somewhat different DNA structures.[70] However, the hydration structure and ion distribution are very similar in AMBER and CHARMM simulations.[71,75] This is because of the fact that these force fields differ mainly by parameters describing intramolecular DNA interactions, whereas parameters describing forces between water, ions, and DNA are almost the same.

Specific Binding of Ions

A major issue in molecular dynamic studies of the ionic environment of DNA is the problem of specific ion binding to different sites on the DNA surface. Whether this binding is sequence-specific or purely electrostatic is still to be determined. X-ray experiments carried out in the 1980s have suggested that there exists a ''spin of hydration'' of DNA,[76] which is a sequence of water molecules in the minor and major grooves that is impenetrable to cations. Cations, according to this picture, form a diffuse cloud around, which is defined by electrostatic interactions. However, MD simulations, made in the 1990s, have shown that Na+ counterions may intrude the spin of hydration of DNA and substitute for water molecules.[66-68,77] This was also confirmed by newer, high-resolution X-ray data.[78]

The question of sequence-specific counterion binding to DNA has a principal importance to our understanding of mechanisms of DNA recognition. When counterions bind to DNA in a sequence-specific manner, they form a mosaic of non-uniform charge distribution depending on the DNA sequence. Moreover, it was supposed that direct ion binding to DNA affects the DNA structure,[78] although this point of view is under debate.[79] Molecular computer simulation can provide valuable information to this discussion.

Most of the mentioned MD simulations of DNA have been carried out with Na+ counterions. In some works, other counterions were also studied. In Ref.[68], a comparative study of Li+, Na+, and Cs+ around DNA was performed. It was found that these monovalent alkali ions interact with DNA in a very different manner. Li+ ions bind almost exclusively to the phosphate groups of DNA. Na+ ions bind prevailing bases in the minor groove through one water molecule, although a smaller fraction of ions binds directly to the bases at some specific sites (AT step in the minor groove and guanine bases in the major groove). Cs+ ions bind directly to sugar oxygen in the minor groove. It was shown also that the specific character of ion bonding is, to a large extent, determined by the hydration structure of water around DNA. A stronger binding of Li+ ions to DNA was also confirmed by NMR studies of the diffusion of Li+ and Cs+ ions in oriented DNA fibers.[80]

DNA oligomers d(TpA)12 in the presence of K+ counterions were simulated in Ref.[81]. Comparing with Na+ counterions, a stronger preference of K+ ions to the major groove has been observed.

MD of DNA with divalent ions Mg2+ and Ca2+ was performed in some recent works.[63,64,82] However, the slow diffusion of Mg2+ ions makes it difficult to perform a reliable estimation of distribution of these ions around the DNA.

Recently, some works appeared on the distribution of multivalent polyamine ions around DNA.[83-85] It was found that flexible polyamine molecules (spermine or spermidine) have several binding modes, interacting with different sites on the DNA in an irregular manner. That is why polyamine molecules are not seen in X-ray diffractions of DNA. Spermine4+ ions compete with Na+ ions and water molecules in binding to bases in the minor groove, and they influence the structure of the DNA hydration shell in different ways.[85]

Comparison with Continuum Solvent Models

An interesting question that MD simulation could answer is: How reliable are computations within the continuum solvent model, for example, in the prediction of overall ion density around DNA? The angularly averaged density profile of counterions (Na+ mostly) has been calculated in some recent works.[66-68] At short distances (within 5 A from the DNA surface), these density profiles are defined mainly by the details of DNA structure and hydration forces. Naturally, the distributions are very different from the density profiles calculated for the cylindrical model of DNA within the continuum solvent model (both in analytical approaches and MC simulations). Such comparison, from Ref.[68], is shown in Fig. 5, where angularly averaged distributions of different monovalent counterions around the DNA are displayed, together with the PB theory result. Introducing details of the DNA structure within the continuum dielectric model may make the counterion distribution closer to

Fig. 5 Density profile of different ions around DNA obtained in all-atom MD simulations. The results marked with (*) are from a simulation with a larger simulation cell than the other data. The thin dotted line shows the PB results with a cell radius corresponding to the system marked (*). Source: From Ref.[68]. Adenine Press.

Fig. 5 Density profile of different ions around DNA obtained in all-atom MD simulations. The results marked with (*) are from a simulation with a larger simulation cell than the other data. The thin dotted line shows the PB results with a cell radius corresponding to the system marked (*). Source: From Ref.[68]. Adenine Press.

Fig. 6 Integral charge for Na+ and CF ions per phosphate obtained in all-atom MD simulations and PB approximation. Source: From Ref.[68]. Adenine Press.

that obtained in MD simulations. For example, a maximum in ion density is observed at about 8 A from the DNA axis, corresponding to a high probability for counterions to be inside the DNA grooves.[38]

On larger distances from the DNA, the ion distribution, computed in MD simulations, became more similar to that calculated in the PB theory, or obtained in continuum solvent simulations. In addition, the integral charge for Na+ ions turned out to be very similar already on distances greater than 12 A from the DNA surface (Fig. 6). This means that cylindrical PB equation, despite many inherent approximations, is still able to evaluate amounts of ions that are attracted (or "non-specifically'' bound) to DNA.

In Refs.[33] and [34], an approach was suggested to link together the two levels of simulations of electrolyte or polyelectrolyte systems (i.e., the all-atom MD simulations and the MC simulations without explicit solvent). The main idea is that detailed all-atom MD simulations provide information on how to parameterize parameters for the continuum solvent model. In practice, as a first step, an MD simulation of size as large as can be afforded is performed. From this simulation, the radial distribution function (RDF) between ions as well as between ions and some sites of DNA is determined. Then, an inverse MC procedure is performed,[34,86] which finds the effective interaction potentials that match the RDF obtained in the MD simulations. The great benefit of effective potentials is that they can be used for simulation of the very same system but of substantially larger scale because the solvent molecules are not included. The typical behavior of the effective potentials is that they have a few oscillations at short distances, reflecting the molecular structure of the solvent, and then—at distances of more than 10 A—approach the Coulombic potential with the dielectric constant of water.[33,34] The short-range part of the effective potentials is rather ion-specific, thus the specific features of ion-DNA interactions are automatically included in the model.

In Ref.[34], the effective potentials between different alkali ions and DNA have been determined and used for MC simulations of the ion environment of DNA. The computed ion distributions are shown in Fig. 7. One can notice clear similarities with the ion distribution obtained in all-atom MD simulations in Fig. 5. Another interesting observation is that for Na+ and K+ ions, the density profiles follow very closely the

Multiscale Simulation Approach

However, direct simulation of ion density in MD simulation is a tedious task and can be performed only at relatively small distances from the DNA surface. These distances do not include the true "bulk'' phase, where neither water nor ions are affected by the electrostatic field of DNA. On the other hand, the problem of finding the ion distribution in the whole range (from the DNA surface to the bulk solution) is the important one. The "bulk'' ion concentration in the living cell is determined by the work of ion channels in the membrane; however, only ions that are in close proximity to DNA affect their properties. Although continuum solvent models allow to compute for the ion distribution in the whole range, they contain adjustable parameters, such as the effective ion radius, and are unable to describe the effects of specific ion binding (e.g., specific binding of Li+ ions to the phosphate groups).

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