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construction of model of plating of DNA

2.2.3.1. Transferring from real objects to the modelling

The conclusions received in item 2.2.2, have been used for construction of some self-assemblage models nanoprovoda on a matrix of DNA with participation nanochastits gold.

Models on the basis of electrostatic and polarising mechanisms on the basis of a Monte-Carlo technique with use of identical principles of configuration of systems have been developed.

It is supposed, that the fragment of a molecule of DNA is in a colloidal dispersion nanochastits gold with a diameter from 0.5 to 3.5 nanometers. For maintenance of the electrostatic mechanism of self-assemblage nanoprovoda on DNA matrix it is necessary to attach to a surface nanochastits the chemical groups getting positive charge in water solution. It is necessary to note, what even without special cationic modification nanochastitsy can possess big enough positive charge, and aggregation of the charged LF on DNA can cause significant conformational changes of this molecule, up to it kompaktizatsii [126]. However now various ways of fixing of a molecule of DNA, interfering its conformational changes are developed.

DNA is zhestkotsepnoj a macromolecule c persistentnoj in the length of ~150 pairs the bases (distance between the bases of 0.34 nanometers). To reproduce characteristic structure of metalloorganic aggregate, it is necessary to carry out modelling on scales of order 100 And. In case of systems of such size use atomisticheskogo modelling is connected with the big computing expenses since it is necessary to consider the systems containing ~1,000,000 atoms. For reduction of time of calculations use of coarse-grained models is necessary. It assumes a choice of adequate display of real objects on modelling representation and models of interparticle interaction.

Charted representation of all a component of models is presented on fig. 2.10. For DNA two models - "simplified" and "detailed" have been constructed to find out influence of degree of coarsening of model of polyanion on plating structure. For LF two variants of modelling representation have been constructed also, each of which reflects specificity of the studied mechanism of plating - electrostatic and polarising. In some variants of models low molecular weight counterions for research of influence of mobile charges on structure of metalloorganic aggregate were used.

In case of the "simplified" representation DNA fragment is constructed in a kind
sterzhneobraznoj sequences from Adna = 100 overlaped spherical links of diameter 2 σ, where σ = 10 And (fig. 2.10, system Ia see).rasstojanie centre to centre spheres equally 0.34 σ. It is supposed, that the molecule is completely dissociated. Distribution of charges of a double spiral of DNA is modelled as follows. On a surface of each sphere two spherical power centres of diameter 0.3 σ with a charge-1 e are located. The piece connecting these centres, is perpendicular polyanion axes, and its length is equal to diameter of sphere. At transferring from one sphere to another charged STS turn on angle 2 π∕ 10, modelling spiral structure of DNA.

Dimensional distribution of charges in the "detailed" model of DNA is under construction the same as and in the "simplified" representation. Difference of models consists in construction neutral STS.

The distance between pair charges is filled by overlaped spheres of diameter 0.4 σ with step 0.2 σ. Such construction allows to model as a first approximation features of two-spiral structure of DNA (fig. 2.10, system 1б see).

Drawing 2.10 - Components of models of plating of a fragment of DNA of LF of gold in coarse-grained representation

LF were considered as unstructured spherical particles of diameter D as their intrinsic energy under studied conditions practically does not change. It is in details discussed in following point. Charges funktsionalizirovannyh nanochastits

Are modelled by the additional power centres of diameter 0.34 σ and charge Z∖e ∖, where Z - an integer. Induced charges Zindэлектронейтральных LF are modelled by two additional power centres of diameter 0.34 σ and two charges ∖qina ∖, located on a LF surface. Orientation of the centres is fixed by a direction of a straight line connecting them which crosses a matrix axis at right angle. Diameter and a charge nanochastits are key parametres of calculations.

The monovalent ions formed at dissociation of DNA and functional groups nanochastits, are modelled by spheres of diameter 0.3 σ. Number of positive counterions to equally number of individual charges on DNA matrix. The quantity of negative counterions corresponds to total number of elementary charges of all nanochastits. Thus in system the electroneutrality condition is observed. Solvent is considered as the continuous environment with inductivity ε = 79.

2.2.3.2. Approximating of metal potential Gupta

At research by methods of computer modelling of the systems containing neutral atoms of metals and metal nanochastitsy, it is necessary to use the potential adequately describing their interaction. The big number of works [127-129] is devoted a problem of restoration of such potential. The Most known is so-called potential Gupta [127; 130] which parametres are picked up on the basis of experimental data for cohesive energy of atoms of a metal body. This potential is often used at studying of properties nanochastits [130; 131].

Carrying out of calculations with use of potential Gupta demands the big expenses of time owing to it neadditivnosti and multiincompleteness. Meanwhile in separate problems, such as modelling of processes with participation zolej metals, are not present necessity to calculate full potential energy of system taking into account contributions of all atoms. It is caused by that under normal conditions intrinsic energy of colloid particles remains practically invariable and all processes in system are defined by interparticle interactions. Therefore in most cases for situation simplification it is possible to neglect internal structure nanochastits and to replace with their spheres of the set diameter. It considerably simplifies computer model, but demands alternative to potential Gupta of the description of interaction of two unstructured metal nanochastits.

Let's consider interaction nanochastits, consisting of Aатомов gold. Value of potential energy of i th atom of metal with co-ordinates ri is defined by means of G potential upta [130]:

In 77 potential of pushing away, and the second summand is attraction potential. Apparently from (2.2), nonlinearity of potential Gupta is caused by the second summand.

Potential Gupta has short-range character. Calculations of potential energy of one atom of gold depending on radius for various arrangements of atoms have shown scraps Rcutпотенциала, that potential energy leaves on saturation at Rcut ≈ 6 And (see 2.11). It means, that essential influence on potential energy of each atom of metal is rendered only by neighbours from the proximate environment. Hence, at rapprochement nanochastits their interaction will be defined not by all atoms, but only what are located in a contact zone. To a contact zone the atoms located on a surface nanochastits belong, the distance between which does not exceed radius of saturation of metal potential. Thus, potential energy of interaction of two nanochastits gold can be as a first approximation presented in the form of the simple formula:

Where N - a median number of atoms on a surface nanochastits in a contact zone, Δr - distance between surfaces of particles (fig. 2.12 see). Number Nможет to be easily positioned from the relation of the areas falling to a zone of contact nanochastits. The distance between surfaces is defined as a distance between the proximate external atoms belonging to different particles.

For the purpose of check (2.3) numerical experiment on studying of interaction of two nanochastits has been made the various size. For this purpose granetsentrirovannaja cubic (GTSK) the lattice of the big size with length of a rib of an unit cell 0.40782 nanometers and angle between ribs 90o in the beginning was under construction. Then co-ordinates of those atoms which entirely belong to sphere of diameter D.Такой algorithm inevitably got out result ins to facet occurrence nanochastits. We will notice, that real nanochastitsy gold also possess a facet [130; 132].

Drawing 2.11 - Potential

Energy of one atom of gold depending on radius "scraps" of metal potential: atoms are built in an one-dimensional chain, located in one plane, form the continuous environment

Drawing 2.12 - Examples atomisticheskih models nanochastits gold with number of atoms N1 = 55 and N2 = 177, used in a problem of restoration of potential of interaction between LF. Equivalent unstructured LF have been presented by spheres of diameter D1 = 15 And and D2 = 21 And V.Oblast who has been led round by a fat dotted line, charted represents the interreacting atoms which are on a distance, not exceeding Rcut = 6 A ∆r/DAu - distance between nanochastitsami

Moreover, in a case nanochastits GTSK the lattice not always is most energetically favourable under normal conditions. The internal structure of LF can be unequal and belong to the various stable states, one of which is streamlining as GTSK [132]. Interactions of two nanochastits with diameters D1и D2 have been considered, and also single atom and nanochastitsy at T = 298 K.Poskolku of LF in atomisticheskoj models have not spherical form, their launching orientation was generated in a random way by means of the task of three angles of Euler. For construction of configurations of the system possessing the least potential energy depending on distance between LF, the computing schema on the basis of a Monte-Carlo technique [69] has been used (see podp. 1.3.3.1). In expression (1.7), for calculation ∆U the difference full energy, calculated on the basis of 1) potential Gupta (2.2) in a case atomisticheskoj models of LF and 2) expressions (2.3) in case of unstructured LF was used. Periodic boundary conditions to a modelling cell were not applied, as interaction energy only two nanochastits was a studying subject, and position of the centre of one of them has been fixed. For each chosen set of parametres of calculation it has been executed at least 100,000 MK steps of the settlement schema (carried on each power centre) after the system passed in an equilibrium state. Transferring in an equilibrium state was defined on stabilisation of full energy
Systems. For each fixed distance Δrпросчитывались 250 cases answering to casual mutual orientations on which averaging of amplitude of the operating potential was made.

On fig. 2.13 the reduced specific potentials of interaction between nanochastitsami and their approximating under the formula (2.3) are shown various diameters. Apparently from the graphs, the reduced and modelling potentials are in good enough conformity.

Drawing 2.13 - Specific potential energy of interaction nanochastitsy diameter 15 And with (7) atom of gold, (2) nanochastitsej diameter 15 And, (3) nanochastitsej diameter 18 And: and - potential

Drawing 2.14 - Instant pictures of two LF from 55 atoms Au in initial and final conditions at various temperatures: 298 K, 894 K

It is reduced on the basis of numerical modelling, - approximating. DAu = 2.88 And

Stability nanochastits has separately been studied at their direct contact. The received results have shown, that at ambient temperature collision of two nanochastits result ins their aggregations only in the event that their sides are parallel. Full merge nanochastits occurs at T> 600 K, the example of interaction of two nanochastits at various temperatures is shown on fig. 2.14. With approach to melting point of gold the internal structure of LF loses distant order [132; 133]. These results allow to use the spherical power centres of constant diameter as LF model.

Thus, rather simple approach for interaction energy of two nanochastits is received. Use of the formula (2.3) allows to save essentially time in problems of numerical modelling of colloidal dispersions and to execute transferring with atomisticheskogo on mezoskopichesky consideration level at modelling of process of plating.

2.2.3.3. The settlement schema

Let's pass to a statement of a technique of modelling. For studying of the electrostatic mechanism of self-assemblage and influence of levels of detailed elaboration of systems following models (fig. 2.10 see) have been constructed:

For studying of the polarising mechanism of self-assemblage one model of following composition has been constructed:

PR) sterzhneobraznyj polyanion to with neutral LF II δ (contains subsystems with, dlи d2) and the implicit account of counterions, NtotaI = 3Ndna+3Nnp.

Potential energy. For all models identical expression for calculation of full potential energy of system has been used:

Thus the stroke in the sum means, that interactions between the power centres belonging to one subsystem are not considered. The full number of power centres Nt0ta ι is defined by composition of model. The first summand of expression (2. 4) is potential of excluded volume for the power centres:

For calculation of electrostatic energy in case of the implicit account of counterions expression for ekranirovannogo kulonovskogo potential has been used

81 where ε = 79, p  - density of mobile counterions in a solution. For T = 298K G = 7.14А, thus 1/к = 2.7 σ. In case of the obvious account of counterions it was used usual kulonovsky potential

The size of the induced charges ±Zindявляется to polyanion also is calculated by function of distance under known formulas of an electrostatics

Where P - electrical dipole moment nanochastitsy in electric field of a matrix of DNA of intensity E, r - the shortest distance from the centre of LF to a matrix axis.

The potential of interaction of two nanochastits Umetрассчитывался under the formula (2.3) and at rapprochement nanochastits joined with probability 0.001. As the basis results of modelling of two blizkoraspolozhennyh (on distance of less diameter of atom of gold) nanochastits have served (see podp. 2.2.3.2). The physical sense of introduction of probability of inclusion of potential Umetзаключается that real LF has a facet, instead of is theoretically spherical as in used model. Accordingly number of atoms in a contact zone and consequently, and interaction energy will differ from collision to collision. Therefore only the small number of collisions can lead to formation of aggregate from two nanochastits. Thus near to polyanion where concentration nanochastits becomes big owing to an electrostatic attraction to the charged groups, matrixes and collisions nanochastits become extremely frequent event, potential Umetобеспечивает "pasting" nanochastits in aggregate.

Method and modelling technique. At the heart of the computing schema of modelling the Monte-Carlo technique has been used. Solution components were seated in a cubic cell with periodic boundary conditions. The size of a rib of a cell was fixed and equal to length of polyanion, i.e. 34 σ. All calculations were made at T = 298 K. The sequence of microconditions of the system answering to set initial ensemble, was generated by a method of essential sample, as well as in case of research

Gels-grids solution cysteine-silver (podp. 1.3.3.1). Thus each new configuration built on the basis of previous by moving and rotation casually chosen nanochastitsy (with equal probability). The size of displacement of particles did not exceed 0.288 σ. The power centres forming polyanion, were motionless. Electrostatic interaction was calculated under schema Evalda [66; 67]. Initial co-ordinates nanochastits got out in a random way. Duration of calculations averaged Nmc = 500,000 MK steps at use of models Э1 and П1 and 4,000,000 MK steps to other cases to a stage of approach of an equilibrium state which was defined from the analysis of potential energy of system. To exclude influence of a choice of initial conditions on an end result for each set of parametres a series from 10 calculations with the subsequent averaging of results was made.

2.2.4.

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A source: Komarov Pavel Vyacheslavovich. MULTISCALE MODELLING NANODISPERSNYH of POLYMERIC SYSTEMS. The dissertation on competition of a scientific degree of the doctor of physical and mathematical sciences. Tver - 2014. 2014

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