[Toroidal globular state of circular DNA]. / O toroidal'nom globuliarnom sostoianii kol'tsevoi zamknutoi DNK.

The influence of torsional elasticity of the double helix on compactization and structure of circular DNA in a compact form is studied in the case when the compact (globular) particle has a torus shape. For closed circular DNA the topological invariant, linking number of two strains, yields strict connection between conformation of double helix, considered as a unifilar homopolymer, and elastic energy of torsional twisting. The contribution of torsional elasticity to free energy of the toruslike globule is calculated. This contribution is shown to be proportional to the square of superturn's density. Torsional elasticity decreases the equilibrium radius of the toruslike globule formed by circular DNA in comparison with the case of linear DNA. Closure of linear DNA into a ring widens the stability range of the relatively short DNA compact form and tightens it for long DNA.

[A simple model of molecular construction]. / Prostaia model' molekuliarnoi konstruktsii.

The microscopic model illustrating the ideas of L.A. Blumenfeld about the role of slow conformational relaxation in the mechanism of action of enzymes is discussed.

[Several possible conformational states of a homogeneous elastic polymeric chain]. / O nekotorykh vozmozhnykh konformatisionnykh sostoianiiakh odnorodnoi uprugoi polimernoi tsepi.

A homogenous elastic macromolecule, the so-called persistent model is considered. Possible initiation of dense globular state in it with nematic orderliness of the chain elements is analysed. The entropy of such a system in an arbitrary state is calculated. It is shown that a relatively short rigid chain forms a thoroidal structure. With the chain elongation thor is increased, without changing its proportions. When the parameters are changed the thoroidal structure may turn into the conventional one-linkage one. Possible application of this model for solving the problem of trimeric package of nuclei acids is discussed in a few words.

[Theoretical model of homopolymer chain adsorption on a homogenous surface]. / Teoreticheskaia model' adsorbtsii gomopolimernoi tsepi na odnorodnoi poverkhnosti

On the basis of I. M. Lifshitz's theory the adsorption of the homopolymer on the homogenous surface is considered. It is shown that the attraction of monomers to the surface may lead not only to adsorption of the globule or coil but also to the emergence of a new peculiar phase--dislike globule without the fringe, all the monomers of which are stuck to the surface. A two-dimensional phase-diagram is plotted.

[Globule--substrate complex: several effects caused by the polymeric nature of the globule]. / Kompleks globuly s substratom: nekotorye éffekty obuslovlennye polimernoi prirodoi globuly

To anaylse possible role of globule polymeric nature in enzyme functioning, an equilibrium complex of homopolymeric liquidlike globule with a hard ball which models the substrate is considered. It is shown that the presence of linear memory in the globule may lead to an increase of the braking moment of forces affecting the substrate, to additional phase transitions concerned with a transition of the substrate of the globule centram to the perifery and vice versa etc. The shape of the globule surface adsorbed on the substrate is calculated.

[A community model of mutually learning neuronal nets]. / Model' soobshchestva iz vzaimno obuchaiushchikhsiia drug u druga neironnykh setei.

A model of a community is suggested whose members are formal neuron nets interacting by signals exchange. As a signal each net can emit an image formed by it when recognising the preceding signal. The emitted signal comes to the inputs of other nets and is used as their initial state for the recognition process. The collective dynamics of such model is discussed for the case of non-learning nets. Possible algorithm of mutual learning of the nets in them course of signals exchange is considered.

[Collective properties of the mutual-learned neuronal net systems in the information field]. / Kollektivnye svoistva sistemy vzaimoobuchaiushchikhsia neironnykh setei v informatsionnom pole.

Model of neural networks system, in which networks interact by transmission and associative recognition of signals, is studied by computer simulation and qualitative approach. System behavior depends on the value of learning parameter epsilon, which determines the weight of writing in memory of each network every transmissible signal. Two different regimes are found: regime of auto-governed behavior, which depends only on initial networks characteristics, and regime of collective recognition of initial signal in form of a certain stable signals cycle. Analogy of this model and Aigen's hypercycle, the problem of creation of some new information in this model are discussed, too.

[Bacteriophage DNA reptation]. / Reptatsiia DNK iz bakteriofaga.

The kinetics of reptation process of dsDNA leaving the phage head is analysed theoretically. It is assumed that the process is caused by DNA free energy decrease when it is leaving the head (DNA has to be in a globular state) for its surroundings where it is transformed into a coil state. For the analysis we have used the results of previous paper on equilibrium theory of DNA intraphage globule. Three possible cases for the ejection process friction are considered: friction in the tail-part channel, that of DNA segments with each other in the whole globule volume (it is essential for the collective way of the globule decondensation with simultaneous movement of all the loops--the first type way), the globule friction with internal capsid surface (it is most essential for the decondensation by the way of the globule rotation as a whole "spool"--the second type way). The first way would correspond to the greatest ejection time. The known experimental data on distinguishing ejection kinetics for phages with short and long tail-parts allow us to formulate arguments in favor of realization of the second way in nature.

[A theory of heteropolymers with frozen random primary structure: properties of the globular state, coil-globule transitions and possible biophysical applications]. / K teorii geteropolimerov s zamorozhennoi besporiadochnoi pervichnoi strukturoi: svoistva globuliarnogo sostoianiia, perekhod tipa klubok-globula, vozmozhnye biofizicheskie prilozheniia.

A new approach to the problem of correspondence between primary structures of polypeptides and their tertiary structures is presented. This approach is based on the following statement of the problem: what will be the statistical properties of tertiary structures provided that the statistical properties of primary structures (e. g. the ratio of polar and unpolar residues) are given? It is discussed whether such statement is useful for the investigation of the prebiological evolution and protein folding. It is emphasized that the basic point here is to determine the configurational entropy of the chain, i. e., the number of foldings which lead to a given density distribution space. Hence, the auxiliary problem of the ideal heteropolymer collapse in the external field is considered. This problem is investigated numerically in the case when the field is localized in the small region in space. It is shown that such geometrical characteristics as the size of a globule are not sensitive to the details of primary structure when the chain is a random coil, and become sensitive to such details in the opposite globular case. These characteristics in the globular state can be described by the stable probability distribution function which does not depend upon chain length. Geometric characteristics of the chain exhibit especially strong dependence upon the primary structure in the region of coil-globule transition which is of the second order for the ensemble of chains.

[The state of a toroid-like DNA globule: the persistent macromolecule in a low-molecular solvent]. / Sostoianie toroidal'noi globuly DNK: persistentnaia makromolekula v nizkomolekuliarnom rastvoritele.

Dimensions of a toroidal globule appearing at the compactization of DNA macro-molecule in a poor low-molecular solvent are estimated. Diagram of DNA molecule state was analysed in variables: contour length-concentration of the precipitating agent. Possible existence of the tricritical point in the joint of the regions of coil, isotropic globular and liquid crystalline globular states was suggested.

[Theory of the toroidal compact form of DNA in a polymer solution]. / K teorii toroidal'noi kompaktnoi formy DNK v polimernom rastvore.

A diagram of the states of single long rigid DNA macromolecule in solution of short flexible polymer was plotted. It has been shown that the compacting effect of the polymer solvent on DNA can be interpreted as hydrostatic pressure of coils gas on impermeable "walls" of the DNA globule. Conditions were found for the existence of compact (globular) states in the form of a sphere (stable for a very long DNA) and tore (for a relatively short one). Possibility of intramolecular liquidcrystalline orderliness of DNA segments in a globule was analyzed. Regions of realization of both regimes were studied: when compression with an added polymer was equalized by the forces of steric repulsion of DNA segments and when it was balanced by the elasticity of the DNA chain bendings.

[Elastic nature of a polymeric globule]. / O prirode uprugosti polimernoi globuly

Relative role of energetical and entropy contributions to the stresses which arise in the globule body after substrate absorption is considered. An integral solution is given for a simple model of the globule. An analysis of the result enables a conclusion that the entropy part is not small (it is large or of the same value) as compared with the energetical one, of only some peculiar globules have no evolutionary advantages.

[Solid interactions in statistical physics of biopolymers]. / Ob''emnye vzaimodeistviia v statisticheskoi fizike biopolimerov.

A short survey is presented of the development of statistical physics of biological macromolecules and its modern state. The main attention is paid to the analysis of the manifestation of scale invariance and fractal properties of biopolymers--DNA and proteins. Phase transitions related to the phase structure of DNA are briefly analysed. A more detailed account is given of phase transitions in globular proteins, denaturation problem, two phases of the melted globule and the theory of heteropolymers included. Some unsolved problems of this field of science and its prospects are discussed.

[The theory of double-helical DNA packing: globular state of a homogeneous elastic macromolecule in a small volume]. / K teorii upakovki dvukhspiral'noi DNK: globuliarnoe sostoianie odnorodnoi uprugoi makromolekuly v polosti malogo ob''ema.

Globular state of persistent chain modelling DNA double helix in the cavity with unpermeable walls was studied. The effect of excluded volume was accounted for by Onsager method. For the most interesting case when the cavity size is much smaller than the persistent length, the globule is like a hoop wound on the cavity walls on the inside. Depending on the molecule thickness four limiting regions with quantitatively distinguished properties of the globule are possible. For all the regions the thickness of " hoops " along and across the walls is found, as well as both characteristics widths of orientational distribution of the chain elements.

[Theory of DNA compactization in a polymer solution]. / K teorii kompaktizatsii DNK v polimernom rastvore.

A theory of DNA compactization is suggested. It is based on the concept about compact DNA globule as a polymeric one. The polymeric solution is considered as a strongly fluctuating system, and the double helical DNA as a rigid unifilar homopolymer. The globule is shown to appear in a diluted polymeric solution. The character of relative phase transition is analysed. With an increase of polymeric solution concentration the size of the DNA globule should decrease and the optic activity increase. Conditions are indicated under which the decompactization of DNA takes place at high concentrations of polymeric solution. This event is accompanied by an abrupt increase of DNA size and a decrease of optical activity.

[Self-similarity in the structure of DNA: why are introns needed?]. / Samopodobie v strukture DNK: zachem nuzhny introny?

Consequences of the hypothesis are analyzed that native spatial structure of DNA is the so-called crumpled globule, which is statistically free of knots. Since crumpled globule is self-similar fractal object in space, fixation of more or less unique chain fold, that is the case for eukaryotes, requires some self-similarity of the sequence. On this basis we explain quantitatively long-range power-law correlations in intron containing genes which have been discovered recently, predict some more detailed properties of correlations, which partly convinced already in experiment, and formulate a few more general hypotheses on the statistical properties of presently unassigned parts of DNA, on the role of intron as the instrument of fixation of DNA spatial structure and on the possible way of creation of such an apparatus in the evolution.

[On DNA compaction in diluted polymeric solutions]. / O kompaktizatsii DNK v razbavlennykh polimernykh rastvorakh.

Causes of compactization of double helical molecule of DNA in polyethylene glycol (PEG) solution are considered. The compactization mechanism is shown to be based on the displacement of PEG coil from the initiated globular DNA particle. An efficient virial coefficient of the interaction between DNA monomers through PEG chains is calculated. An efficient theta-point is found from PEG concentration. The experimental relationship between PEG critical concentration responding to the onset of compactization and PEG molecular weight is analysed. The absence of DNA compactization and PEG molecular weight is analysed. The absence of DNA compactization with PEG of low molecular weight is explained. Theoretical works on DNA compactization are reviewed.

[Polymer chain with eliminated volume in an exterior field]. / Polymernaia tsep' s iskliuchennym ob'emom vo vneshnem pole

The problem of the behaviour of a polymer chain with excluded volume in an external attractive potential field was considered. It was found that the phase transition (the capture of a polymer by a potential pit), is the phase transition of the second kind; the excluded volume affects neither the temperature, nor the kind of phase transition, but it influences essentially the structure of the system after capture. An analysis of this structure was undertaken; the dependence of the critical temperature on the parameters of the pit was calculated.

[The role of topological limitations in the kinetics of homopolymer collapse and self-assembly of biopolymers]. / Rol' topologicheskikh ogranichenii v kinetike kollapsa gomopolimera i v samoorganizatsii biopolimerov.

Fast collapse of a linear homopolymer after a spasmodic temperature decrease or deterioration of the solvent quality results in the initiation of folded nonequilibrium globule. The chain line in it is a fractal with the dimension mu less than or equal to 2 at small ranges and 3 at the large ones. This is provided by non-selfintersection of the chain and initiated therefore spatial segregation from each other at all the ranges of the chain regions, globulized each in itself. Further relaxation of the folded globule proceeds very slowly only at the expense of reptation (diffusion crawling) of the chain along itself, and results in the polymer knotting. The model of the folded globule permits explanation from a single viewpoint of a number of globular proteins properties. Predictions are formulated whose checking in a real or computer experiment should reveal the adequacy of our results.

[A theoretical model of DNA packaging in the phage head]. / Teoreticheskaia model' upakovki DNK v golovke faga.

Statistical model of dsDNA packaging to icosahedral bacteriophage capsid is presented. The model describes intraphage DNA as a globule, i.e. intramolecular liquid crystal. We analyse the free energy of DNA, which has a globulized part inside the phage capsid and coil-like tail outside it. Conditions when processes of DNA movement into capsid or back are thermodynamically favorable are investigated. These processes are not accompanied with any thermal effects. It is not "all or none" type process, i.e. intermediate stable states are possible. The role of DNA interaction with the capsid inner wall is considered. The essential model abilities for qualitative explanation of experimental data are exhibited.