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This study offers a simulation of the stretching dynamics of a double-stranded DNA fragment in the high-gradient flow of fluid near collapsing cavitation bubbles. Calculated profiles of elastic tension along the model of a polymer fragment were used to estimate the rates of mechanochemical cleavage at different positions of DNA restriction fragments. The resulting cleavage rate profiles are qualitatively consistent with the experimentally observed profiles of ultrasonic cleavage rates of DNA restriction fragments, which are position-dependent. The proposed model also relates the sequence specificity of ultrasonic DNA cleavage, which was experimentally detected earlier, to the peculiarities of sequence-specific conformational dynamics of β-D-deoxyribose in the B-form double helix. A quantitative assessment of the ultrasonic DNA cleavage rates for different conformational states of β-D-deoxyribose derived from the proposed model qualitatively agrees with the experimental data.

The study reports a thermodynamic model describing microarray oligo-target hybridization. The relationship between hybridization signal intensity and Gibbs free energy change for oligo-target duplex formation was our function of interest. The behavior of this function that we called energetical hybridization isotherm in response to target concentration change was modeled considering different ratios of oligo-probes/target concentrations. The results of modeling were compared with the relevant and currently available from literature microarray adsorption experiment.

We investigated a phenomenon of ultrasonic cleavage of DNA complexed with transition metal cations Ag(I), Cu(II) and Hg(II). We found the statistically significant dependence of relative intensity of cleavage on cation type and concentration. Each cation may cause two different types of distortion in the DNA double-helix depending on whether it binds to major or minor DNA groove. The intensity of ultrasonic cleavage decreases if cation binds to the major DNA groove; the intensity of cleavage increases if cation binds to the minor DNA groove and disturbs the hydrogen bonds of complementary base pairs or it intercalates between bases. Both types of DNA distortion can affect the intensity of N-S interconversion of deoxyribose.

Ligand binding to DNA, as well as to microarrays, requires a system approach to description and analysis. This type of approach implies a fixed sequence of operations. Firstly, it is necessary to make a description of a binding scheme that realizes ligand and polymer in common spatial way. Secondly, a physical model of binding is required. Thirdly, a mathematical binding model should be constructed on the basis of the binding scheme and the physical model of binding. Every analysis of experimental data needs this preliminary work. A mathematical apparatus and classification of binding models have to follow on. Classification of different binding isotherms by different binding models is the direct problem. The inverse problem is a reconstruction of parameters of a binding model by experimental binding isotherm curves. The inverse problem can only be solved after solving the direct problem. An example of classification of binding models by oligonucleotides or proteins binding cooperativity and polymer properties like homo- or heteropolymer is presented.

The cleavage of dsDNA fragments in aqueous solution after irradiation with UV laser pulses at 193 nm has been studied. Samples were investigated using polyacrylamide gel electrophoresis. The intensity of damage of particular phosphodiester bond after hot alkali treatment was shown to depend on the base pair sequence. It was established that the probability of cleavage is twice higher for sites of DNA containing two or more successively running guanine residues. A possible mechanism of damage to the DNA molecule connected with the migration of holes along the helix is discussed.

A simple thermodynamic model describing the microarray oligo-target hybridization has been constructed. The relationship between the hybridization signal intensity and Gibbs free energy for oligo-target duplex formation has been considered. The behavior of this function, which we called energetical hybridization isotherm, in response to target concentration change was modeled at different ratios of oligo-probes/target concentrations. The results of modeling were compared with the relevant and currently available data from microarray adsorption experiments.

The regulation of the reporter gene activity in a single bacterial cell by means of lambda-phage C1 repressor has been described by the methods of statistical thermodynamics. The equations for the calculation of the mean production rate of the reporter protein and its standard deviation as a function of C1 repressor concentration in the cell have been obtained. The stochastic nature of C1 repressor binding with OR1 and OR2 operator sites becomes apparent when both repressor molecules and operators are present in the bacterial cell in a small number of copies. In this case, the number of repressor molecules that bind to OR1 and OR2 sites fluctuates considerably. The in vitro binding of C1 repressor to OR1 and OR2 sites, their mutant forms, and nonspecific DNA regions has been well studied. Using the binding constants of in vitro binding of C1 repressor to OR1, OR2 and nonspecific DNA regions and also the value of the cooperativity parameter for C1 repressor binding to OR1 and OR2 sites, we calculated the mean rate of synthesis of the reporter protein and its standard deviation as a function of repressor concentration in cell. The theoretical relations fit well the experimental results. The results of calculations confirm the assumption that gene expression noise in a single cell at a repressor concentration exceeding 100 nM is related to the stochastic nature of binding of repressor dimers to OR1 and OR2 sites. Other mechanisms of the generation of gene expression noise (for example, monomer-dimer balance) make a significant contribution at concentrations less than 100 nM.

A method for studying the local inhomogeneities of DNA and its dynamics is proposed. The method is based on the combination of two procedures, splitting the DNA molecules by ultrasound and analysis of DNA fragments obtained by gel electrophoresis. The frequency of cleavage of internucleotide bonds was found to depend on the type of nucleotides forming the bond and on their nearest neighbors. Estimates of cleavage frequencies in each of 16 dinucleotides showed that, in the 5'-d(CpG)-3', 5'-d(CpA)-3', and 5'-d(CpT)-3' dimers, the cleavage occurs considerably more frequently than in the rest, and the frequency of cleavage depends on the nearest neighbors. It was shown that the double-helix cleavage can occur with shifts by several nucleotides. Physical prerequisites were considered that can lead to this pattern of sequence - specific cleavage.

The binding of chitosan molecules to DNA in solutions of different ionic strength has been studied. The data were analyzed in terms of the model of ion condensation and the thermodynamic theory of the binding of protracted ligands to DNA. Combining these approaches made it possible to estimate the sterical and energetic characteristics of chitosan-DNA binding and establish the dependence of the chitosan-DNA binding constant on the ionic strength of solution.

The temperature stability of nanoconstructions formed by double-stranded DNA molecules fixed in the structure of their liquid crystalline dispersions and cross-linked by nanobridges was determined. It was shown that the heating of nanoconstructions is accompanied by a decrease in the amplitude of the negative bands in the CD spectrum both at lambda approximately 310 and lambda approximately 505 nm. Temperature "melting curves" were derived and characterzed by T(M) values. The T(M) values at lambda approximately 310 and lambda approximately 505 nm coincided with each other but differed from the T(M) value characteristic of the DNA cholesteric liquid crystalline dispersion.

The properties of nanoconstructions formed by double-stranded DNA molecules fixed in the structure of their liquid crystalline dispersions and cross-linked by nanobridges were described. The dependence of the optical properties of the nanostructures on various factors (DNA concentration, nanobridge components, etc.) was examined.

The regulation of gene expression is a basic problem of biology. In some cases, the gene activity is regulated by specific binding of regulatory proteins to DNA. In terms of statistical mechanics, this binding is described as the process of adsorption of ligands on the one-dimensional lattice and has a probability nature. As a random physical process, the adsorption of regulatory proteins on DNA introduces a noise to the regulation of gene activity. We derived equations, which make it possible to estimate this noise in the case of the binding of the lac repressor to the operator and showed that these estimates correspond to experimental data. Many ligands are able to bind nonspecifically to DNA. Nonspecific binding is characterized by a lesser equilibrium constant but a greater number of binding sites on the DNA, as compared with specific binding. Relations are presented, which enable one to estimate the probability of the binding of a ligand on a specific site and on nonspecific sites on DNA. The competition between specific and nonspecific binding of regulatory proteins plays a great role in the regulation of gene activity. Similar to the one-dimensional "lattice gas" of particles, ligands adsorbed on DNA produce "one-dimensional" pressure on proteins located at the termini of free regions of DNA. This pressure, an analog of osmotic pressure, may be of importance in processes leading to changes in chromatin structure and activation of gene expression.

Models of adsorption were considered, which describe the binding of biologically active ligands on DNA templates. The binding is described most comprehensively and in greatest detail by the distribution function, which determines the probability of detecting the preset number of adsorbed ligands on the template. In the case of noncooperative binding, this function corresponds to the Gaussian distribution and is characterized by two quantities: the mean value of the occupation of the template by ligands and the dispersion of occupation. The accuracy of the occupation of the template by ligands is inversely proportional to dispersion. As the length of the template and the number of reaction sites covered by one ligand upon binding increase, the accuracy of the occupation of the template by ligands increases. An important characteristic of binding is the degree of coverage of the template by ligands. This characteristic represents the portion of template reaction sites covered by all ligands adsorbed on the template. If polycations are bound to nucleic acid molecules, the coverage of the template determines the transition of nucleic acids to a compact state. The degree of template coverage for extended ligands depends only slightly on the binding constant in a wide range of concentrations of a free ligand in solution. Different adsorption models are considered from the unified point of view. The classification of cooperative interactions for a wide class of systems is given, from situations when several ligands are bound on nucleic acid templates to a situation when templates change by the action of ligands and begin to interact with each other.

Due to noncooperative binding of ligands to DNA molecules, DNA molecules are in equilibrium with different numbers of adsorbed ligands. This equilibrium for a given concentration of the free ligand in the solution is characterized by the distribution function, which describes the probability of revealing the DNA molecule with a definite number of adsorbed ligands. If polycations act as ligands, DNA molecules with the number of ligands sufficient for neutralizing the charges on phosphates may undergo a phase transition. One example of this transition is the formation of liquid-crystalline dispersions during the binding of DNA to chitosan. We analyzed the binding of chitosan to DNA on the assumption that this binding is due to equilibrium adsorption. At a definite concentration of chitosan in solution, DNA molecules are in equilibrium with different numbers of adsorbed molecules of chitosan. If the number of adsorbed ligands exceeds some critical value, the DNA molecule covered with chitosan becomes capable of interacting with other DNA molecules. As a result of this interaction (attraction), liquid-crystalline dispersions can form. Equations describing the dependence of the concentration of DNA molecules on the concentration of the ligand in solution were derived. It was shown that, at given parameters of the model, it is possible to describe experimental data characterizing the formation of cholesteric liquid-crystalline dispersions. The analysis of the data makes it possible to reconstitute both the size of the binding site occupied by chitosan on the DNA and the energy of interaction of chitosan with DNA.

Three variants of the model for the formation of "bridges" between the nucleic acid molecules fixed in the structure of particles of liquid-crystalline dispersions were considered. What the three variants have in common is that the bridges represent polymeric chelate cross-links consisting of alternating molecules of daunomycin and copper ions. The differences between the three variants are that in the first variant, the bridges begin and end with daunomycin molecules that form a complex by the mechanism of external binding with nucleic acids; in the second variant, the bridges begin and end with copper ions coupled with the pairs of bases of nucleic acids; and in the third variant, the bridges begin with the daunomycin molecule and end with the copper ion. For each variant, a mathematical model was constructed, which describes the formation of bridges, and equations of binding were derived. The results of calculations were compared with the experimental data. Within the framework of each variant, the values of the energy of interaction between the daunomycin molecule and the copper ion in the bridge, the energy of interaction of the daunomycin molecule with the nucleic acid, and the length of the bridge were varied. For all variants, those values of the parameters were chosen that fit best the experimental data. The theoretical curves obtained using the three variants of the model agree rather well with the family of experimental curves. The best agreement between the theoretical and experimental data was obtained when the polymeric chelate bridge includes more than two daunomycin molecules.

Formation of molecular construction that consists of double-stranded molecules of nucleic acids (or synthetic polynucleotides) located at the distance 30-50 A in the spatial structure of particles of their cholesteric liquidcrystalline dispersion and crosslinked by polymeric chelate bridges is described. The resulting superstructure, which possesses peculiar physicochemical properties, could be used as integral biosensor whose properties depend on temperature, the presence of chemical or biologically active compounds of different nature, etc.

The binding of daunomycin and copper ions to poly(I).poly(C) molecules fixed in a particle of a liquid-crystalline dispersion was studied. A thermodynamic model of adsorption was developed, which makes it possible to describe the formation of complexes of a particular kind, "bridges" that connect adjacent nucleic acid molecules fixed in a liquid crystal. The bridges represent chelate complexes, which incorporate the molecules of the antibiotic daunomycin and copper ions. Equations describing the dependence of the concentration of these bridges in solution on the concentration of their constituents were derived. The family of dependences of experimental amplitudes of bands in CD spectra typical of "bridge" structures on the concentration of copper ions represents a set of S-shaped curves, and, as the concentration of daunomycin in solution increases, the level of saturation of these curves increases. The analysis of experimental data with the use of this model suggests that the structures of this type compete with daunomycin molecules for the binding sites on poly(I).poly(C). By using this model, the energies of formation of bridge structures were calculated.

This study is a continuation of a series of papers dealing with topotecan interaction with double-stranded polydeoxyribonucleotides. We showed earlier that topotecan molecules form dimers in solution at concentration above 10(-5) (per base pair). Topotecan interaction with calf thymus DNA in solutions of low ionic strength was studied by fluorescence, circular dichroism, and linear flow dichroism. The data obtained indicate that topotecan forms two types of complex with DNA, DNA molecules combining with each other during formation of one of these complexes. The association constant of two topotecan-filled DNA molecules with each other was estimated at 10(4) M-1 (per base pair) in 1 mM sodium cacodylate buffer, pH 6.8, at 20 degrees C. A possibility of modulation of DNA topoisomerase I activity by topotecan due to complexation with several sites of a supercoiled DNA molecule is discussed.

A thermodynamic model of the formation of bridges consisting of alternating daunomycin molecules and copper ions and connecting neighboring nucleic acid molecules in a particle of a liquid crystalline dispersion was constructed. The model is based on the conception that ligands are adsorbed on lattices of reaction centers which are formed in a liquid crystal at a particular spatial arrangement of adjacent nucleic acid molecules (phasing). Equations were derived that describe typical experimentally obtained S-shaped dependences of bridge concentration on the concentration of copper ions and daunomycin molecules in an initial solution. It was shown that dependences of this kind take place in two variants of the adsorption model: when the binding of daunomycin with adjacent nucleic acid molecules is considered to be independent on the formation of bridges and when bridges compete with single daunomycin molecules for the sites on adjacent nucleic acid molecules.

In studies of interactions of ligands with nucleic acid molecules, S-shaped curves are often obtained. In this work we show that the sigmoidal shape of the curves is due to a competition of ligand molecules for DNA binding sites. If a ligand that binds to DNA can form two types of complexes with the binding constants K1 and K2 and binding site sizes L1 and L2, respectively, then in the event that K1 < K2 and L1 < L2, the dependence of the concentration of complexes of the first type on the concentration of the ligand added to solution can be S-shaped.

A model describing the interaction of a short oligonucleotide with long polynucleotide matrix has been developed. The model allows to calculate possibilities of oligonucleotide binding with different matrix sites on the basis of thermodynamic parameters of duplex formation. The model has been used for description of messenger RNA interaction with "clinger-fragment" sites on ribosomal RNA, which are potential sites of hybridization with mRNA. A possibility of rRNA interaction with mRNA by means of multiple duplex formation between "clinger-fragments" and numerous complementary short mRNA sites is discussed.

The influence of different types of long-range interaction of ligands adsorbed on DNA on the helix-coil transition was theoretically considered. The contact interaction was shown to differ significantly from the long-rang one. It was shown also that even weak dependence of a long-range potential on a degree of helicity resulted in the strong changes of a DNA melting curve. This result allowed to understand the different experimental data on DNA melting in the presence of different substances which reduced AT-and GC-base pairs thermostability difference.

The effect of finite fragment length on the distribution pattern of bound protein along the DNA fragment is considered. If the size of the binding site for a ligand on DNA is comparable with the length of the DNA fragment fluctuations in the amount of ligand bound to the fragment create some difficulties for evaluating the distribution pattern of ligand on DNA. A mathematical approach is developed which enables one to calculate the distribution pattern of ligand on DNA provided that the number of bound ligand on the DNA fragment is known. Expression are also obtained to treat the effects of fluctuations in the number of ligand molecules bound to the DNA fragment on the distribution pattern of ligand. A new procedure is proposed which may be useful for locating the preferable binding sites for ligand on DNA on the basis of footprinting experiments.

A model which permits the description of chromatosomes distribution along the DNA were developed. The experimental data on the spacing of chromatosomes on rat liver chromatin were analysed. It was shown that chromatosomes dimers spaced at less than 40 base pairs are encountered more rarely than might be expected on the basis of a random distribution of chromatosomes along DNA. We propose that between nearest neighbor chromatosomes in the fibre there exist interactions which hinder the rapprochement of chromatosomes. The data analysis put forth in this paper permits us to determine the energetic parameters of such anticooperative interactions.

Procedure was elaborated for recognizing potentials of paired interactions between ligand molecules adsorbed on the polymer. A method is proposed for describing such interactions by means of the potentials of simplest shapes, rectangular and trapezoidal ones. It is shown that when the interactions cover the distances much larger than the mean ones between the adsorbed molecules, the adsorption is described by the expression specific for noncooperative binding of the ligands. On this basis the method for analysing the experimental isotherms of adsorption is developed. It permits estimation of the interaction energy between the ligand adsorbed molecules and specific distance to which these interactions are distributed. This method is applied for analysing experimental isotherms of adsorption of antibiotic distamycin A on poly (dG) . poly (dC).

A model has been developed which allows description of the binding of antibiotics and dyes to a nucleic acid in which different regions are involved in the formation of a certain tertiary structure. Interactions between different segments of nucleic acid may contribute to the internal overall energy of the macromolecule. We consider the case when the tertiary structure and the internal energy of the macromolecule are altered upon binding of small molecules. These structural changes affect the shape of the binding isotherm of ligand to the nucleic acid. We obtain relations which permit to determine the dependence of the internal energy on the degree of binding of ligand to nucleic acid.

Cooperative effects arising upon binding of biologically active ligands to DNA are considered. Equations are derived which enable one to describe the binding of two different ligands to DNA. We also consider the case when ligand can form two type of DNA complexes. The cooperative binding of the ligand in the vicinity of saturation level of binding can be described with a good accuracy by equation derived for the non-cooperative adsorption of the same ligand with some effective binding constant Keff. It is shown that cooperative effects arising upon binding of proteins and other ligands to DNA can be divided into two groups depending on the symmetry of interactions between the bound ligand molecules. In particular, if such interactions favor the formation of dimeric ligand species on the DNA, Keff approximately a1/2, where a is the ligand-ligand interaction constant. If cooperative interactions favor the formation of aggregates of unrestricted size, then Keff approximately aL+Y, where L is the size of the binding site for the ligand on DNA.

The binding isotherms of CACCA(3'NHPhe----Ac) and CACCA(3'NHPhe) to E. coli ribosomes and 50S subunits were measured. A theoretical model of adsorption for the case of cooperative interaction between two ligands adsorbed on a ribosome was designated. The analysis of the experimental binding isoterms leads to the following conclusions. A ribosome (or subunit) binds one CACCA (3'NHPhe----Ac) molecule to donor site of the peptidyl transferase center, but two CACCA (3'NHPhe) molecules to both donor and acceptor sites. The binding of CACCA (3'NHPhe) to ribosomes (or subunits) is a cooperative process, characterized by the cooperativity coefficient tau = 40 +/- 5 or more. When model substrates CACCA-Phe, CACCA-Leu and CACCA-Val were taken instead of CACCA (3'NHPhe) in the incubation mixture with ribosomes, dipeptides were obtained even in the case, when ratio [model substrate]: [ribosome] (in moles) was much lower than 1. Puromycin binding to acceptor site with constant (1-2) X 10(4) M-1 also stimulates CACCA(3'NHPhe----Ac) adsorption to the donor site of ribosomes with cooperativity coefficient being equal to 1.5-2.5. It is also shown that cytidine 5'-phosphate binding to the donor site increases kappa cat of the reaction of minimal donors with CACCA-Phe by 1.5 orders of magnitude but has no effect on Km of this reaction. These facts point out that cytidine 5'-phosphate being adsorbed on the corresponding area of the donor site leads to the conversion of low-productive complex [ribosome + minimal donor substrate + acceptor substrate] into high-productive complex [ribosome + minimal donor substrate + acceptor substrate + cytidine 5'-phosphate].

A statistical analysis of occurrence of particular nucleotide runs (1 divided by 10 nucleotides long) in DNA sequences of different species has been carried out. There are considerable differences in run distributions in DNA sequences of prokaryotes, invertebrates and vertebrates. Distribution of various types of runs has been found to be different in coding and non-coding sequences. There is an abundance of short runs 1 divided by 2 nucleotides long in coding sequences, and there is a deficiency of such runs in the non-coding regions. However, some interesting exceptions from this rule exist: for run distribution of adenine in prokaryotes and for distribution of purine-pyrimidine runs in eukaryotes. This may be stipulated by the fact that the distribution of runs are predetermined by structural peculiarities of the entire DNA molecule. Runs of guanine or cytosine of three to six nucleotides long occur predominantly in the non-coding DNA regions in eukaryotes, especially in vertebrates.

The experimental binding isotherms of the distamycin A analog to 8 natural and synthetic DNAs were analyzed. The shapes of binding isotherms suggest that the bound ligand molecule induces transitions of DNA (B-form) into two perturbated conformation states. These transitions are responsible for the existence of positive and negative cooperative effects on binding of distamycin analogs to DNA. At low levels of binding positive cooperative effects play a dominating role whereas at high levels of binding negative cooperative effects are observed. These cooperative effects can be described by the aid of a potential of pairwise interactions between nearest neighbour bound antibiotic molecules. A detailed analysis of experimental binding isotherms shows that characteristic distances over which these interactions are extended depend on the AT content of DNA. The energetical and structural parameters characterising the allosteric transitions of DNA to the perturbated states are obtained.

Equations are derived to describe the cooperative binding of large ligands to DNA. A mathematical approach is developed which enables one to give a simple probabilistic interpretation of binding equations and to solve them in the general case when long-range interactions are allowed between bound ligands. These interactions can be mediated by conformation changes induced in the DNA in the course of binding process and transformed over some distances beyond the DNA region immediately covered by a bound ligand molecule (allosteric effect of DNA). Interactions between ligand molecules can be formally described in terms of model potential characterizing pairwise interactions between bound ligands. A procedure is developed which allows one to determined the form of such potential from experimentally measured binding isotherms. It is based on a comparison of experimental binding isotherms with the appropriate curves calculated for the case of non-interacting ligands.