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The aim of this paper is to review some basic ideas, concepts, and questions of today's theoretical biology and stimulate reflection on them. Possible sources of misunderstanding, confusion, and disagreement in the discussion of the foundation of biology are outlined. Major attention is given to different interpretations (and implications) of the term “explanation” and “living system.” It is argued that the concepts of present day's physics are not general enough to describe biology. As examples of possible new concepts “complexity” and “creativity” are discussed. Different definitions of “living systems” and their flaws are reviewed. It is concluded that an explanation of a living system involves both, an understanding of its parts and of the organization of these parts. This leads to a discussion of the role of quantum mechanics and non-equilibrium statistical thermodynamics in biology. Finally, the implications of some philosophical points of view and the role of Godel's incompleteness theorem in a basic theory of biology are discussed.

The solid state physical approach is widely used for the characterization of electronic properties of DNA. In the simplest case the helical symmetry is explicitly utilized with a repeat unit containing only a single nucleotide or nucleotide pair. This model provides a band structure that is easily interpretable and reflects the main characteristic features of the single nucleotide or a nucleotide pair chain, respectively. The chemical variability of the different DNA chains is, however, almost completely neglected in this way. In the present work we have investigated the effect of the different sequences on the band structure of periodic DNA models. For this purpose we have applied the Hartree–Fock crystal orbital method for single and double stranded DNA chains with two different subsequent nucleotides in the repeat unit of former and two different nucleotide pairs in the latter case, respectively. These results are compared to simple helical models with uniform sequences. The valence and conduction bands related to the stacked nucleotide bases of single stranded DNA built up only from guanidine as well as of double stranded DNA built up only from guanidine–cytidine pairs showed special properties different from the other cases. Namely, they had higher conduction and lower valence band positions and this way larger band gaps and smaller widths of these bands. With the introduction of non-uniform guanidine containing sequences band structures became more similar to each other and to the band structures of other sequences without guanidine. The maximal bandwidths of the non-uniform sequences are considerably smaller than in the case of uniform sequences implying smaller charge carrier mobilities both in the conduction and valence bands.

The interactions of the PO 4 - groups of DNA and the positive parts of lysine/arginine were calculated in the nucleosomes using the ONIOM method. For the model system ( 3 H 2 O, K + ion, PO 4 - group, positive side chains of lysine, arginine, resp., Cl - ) a triple- ζ basis set with polarization functions was applied both at the HF and MP2 levels. For the real system two dezoxyriboses and two guanines were added, the calculations were performed with a double- ζ basis set at the HF level. The direct PO 4 - ⋯ Lys + / Arg + bonds are ∼5 eV strong. These decrease by ∼4 eV due to the Cl - ions. The water-mediated PO 4 - ⋯ H 2 O ⋯ Lys + / Arg + bonds are ∼1 eV strong and the Cl - -s hardly change their strength.

a b s t r a c t Using the ab initio Hartree-Fock crystal orbital method in its linear combination of atomic orbitals form we have calculated the band structures of poly( ˜ G-˜ and poly( ˜ A-˜ T). Here, besides the nucleotide bases, the sugar and phosphate parts of the nucleotide were also taken into account together with their first water shell and Na + ions. We use the notation with a tilde above the abbreviation of a base for the whole nucleotide; for instance poly( ˜ G) means a guanine base with the deoxyribose and PO − groups to which it is bound. The obtained band structures were compared with previous single chain calculations as well as with the earlier poly( ˜ G-˜ C) and poly( ˜ A-˜ calculation without water but in the presence of counterions.

The work presented here is the last step of our research plan to compute the band structure, the mobilities and finally the conductivities of simple, single-stranded DNA models, infinite homopolynucleotides. We have calculated the d.c. specific conductivities of three crystalline, rigid homopolynucleotides: poly(guanilic acid), poly(adenilic acid) and polythymidine in the presence of water and ions using a combined quantum chemical and solid state physical method (Hartree–Fock crystal orbital theory). The obtained specific conductivities are around 10 2 Ω − 1 cm − 1 . The results are compared to the available experimental values. The reliability of our method and the influence of static and dynamic disorder are also discussed. These results can pave the way to future computations, where the structural and dynamical disorder will gradually be introduced (of course in this case an appropriate form of hopping model has to be used).

In the Introduction of the paper the different theoretical models for the prediction of high Tc superconductivity, which were done before its discovery in ceramic materials, are reviewed. After this a number of models to interpret the experimentally found high superconductive transition temperature are mentioned. In the second part of the paper the results of Hartree-Fock and DODS band structure calculations on (Cu–O)x chains and on the 2-dimensional Cu–O plane are presented. We have found that in the 2D case the Fermi level is in a broad band due to O 2p orbitals, while there are narrow Cu 3d bands in the valence band region. This gives the possibility that the polarization of the localized electrons in the narrow bands provide an effective attraction between the mobile electrons in the broad band which can lead to formation of Cooper pairs and therefore also to a superconductive state. The DODS calculation of the (Cu–O)x chain leads to a spin alternation on the O atom in agreement with the experimentally found antiferromagnetic behavior of the ceramic materials. This gives rise to a spin-polaron (through a spin-flip) mechanism of superconductivity if positive holes are formed. Finally it is discussed how the band structures of the ceramic materials could be improved by taking into account charge transfer between the planes (via different cluster calculations), the effect of the Madelung potential of the crystal and last but not least correcting the bands for correlation effects using a generalized electronic polaron model.

As a first step in testing the possibility of correlation calculations of extended systems using localized orbitals, localization of the canonical Hartree-Fock orbitals of the four nucleotide bases was performed. The results show an excellent localization of the occupied orbitals and a rather good one for the virtuals (both for the σ- and π-orbitals). Interaction energy calculations of the stacked nucleotide bases show a few kcals/mol repulsion at the Hartree-Fock level, but they become attractive (again a few kcals/mol) if dispersion energy computed with the aid of London's formula is added. The internal charge transfer of ˜0.2 e from sugar to the nucleotide base (C, T, or A) found in large-scale ab initio homopolynucleotide calculations raises the question of whether there are free charge carriers in DNA B. Though in the Hartree-Fock level the answer is negative, one cannot rule out this possibility if, using a high-quality basis set, correlated band structures (using an unproved version of the electronic polaron model) will be computed. Interaction energy calculations between a polyglycine chain in different conformation and polynucleotide chains show a few kcals/mol attraction per base and glycine unit and a very small (a fraction of a kcal/mol) additional attraction due to the dispersion correction.

On the basis of Szent-Gyorgyi's recent suggestion that electron acceptors transform proteins from insulators to conductors, the possibility of charge transfer between proteins and electron acceptors and/or donors is discussed. Some problems arising in connection with the determination of the amount of charge transferred are mentioned. Afterwards possible methods to determine the correct positions and widths of partially filled bands in polymers are reviewed. Following this, the problem of interactions between charged polymers with partially filled bands is discussed. Finally the possible role of charge transfer in regulating the available (readable) part of the genetic information is pointed out.

As an illustration of the applicability of the coherent potential approximation (CPA) method to the treatment of aperiodic biopolymers (DNA and proteins) the results of a calculation with a k-dependent self-energy are presented in the case of the (SN)x and (SN—H)x mixed system. Further we give ab initio SCF LCAO band structures for polyglycine, which were corrected with the aid of the electron polaron model for long-range correlation and with the help of the OÂO method for excitonic effects. Finally, on the basis of the electronic structure of DNA and proteins, different possible mechanisms of chemical carcinogenesis are described.

A minimal basis set ab initio calculation has been performed for the four nucleotide bases and for the infinite polycytosine chain. The LEMO levels have been corrected using the ǑǍǑ procedure. Long-range correlation effects on the band structure of polyC have been computed using the electron polaron model. Using these calculated quantities and assuming that the other three homopolynucleotides have a similar band structure as polyC, the positions and widths of their valence and exciton bands have been approximated. Finally, by the superposition of the band structures of the homopolynucleotides the physically interesting bands of poly(G-C) and poly(A-T) have been estimated.

Ab initio supermolecule calculations have been performed for the glyoxal–formamide and for the H2S–formamide charge transfer complexes in their ground states. According to the results obtained with Mulliken's population analysis, glyoxal acts always as an electron acceptor against formamide which we have used as model compound for a peptide group. The results indicate also that the amount of transferred charge depends strongly on the intermolecular distance and on the relative orientation of the molecular planes. On the other hand we have found that H2S against our expectation acts at most relative geometrical positions as an electron acceptor with respect to formamidc.

Recently X-ray diffraction provided the structure of nucleosomes. External disturbances can unwrap DNA from the histone–protein and their genetic information becomes readable. This is strongly connected with cancer initiation. Therefore, first we performed charge transfer (CT) calculations between polythymidine and a periodic model-protein chain with a lysine or arginine and three glycines. The CT calculations were repeated between the infinite chains using combined solid state physical and quantum chemical methods. We found that the CT between the unit cells of an infinite polythymidine and poly(lysine-triglycine) is 0.04 e and 0.03 e for poly(arginine-triglycine). We investigated the influence of the basis set quality on the calculated CT values using a molecular model built of a thymidine and lysine or arginine. We have calculated also the bands of polythymidine and the two protein model chains. We have found that the differences between the highest level of the valence band of single polythymidine chain and the lowest level of the conduction bands of the model protein chains (6-11 eV depending on the basis set) are too large to assume a direct CT between these two bands.

The 1 Hartree-Fock crystal orbital (CO) method in its linear combination of atomic orbitals form was applied to determine the band structure of histone proteins taking 0.041e charge transfer per nucleotide base from the PO4 groups of poly(guanilic acid) to the arginine, and lysine side chains in histones (see text). Assuming that there are infinite COs, perpendicular to the main chain, formed by the amide groups of one segment of the protein chain bound together by H-bonds with the CAO groups of another segment of the chain, we have calculated the band structure. From this, we have determined the mobility using the deformation potential approximation. Multiplying this with the mobile electron concentration due to the charge transfer between the PO4 groups of DNA and the positive side chains in histones, we have obtained for the direct current (D.C.) electron conductivity fib 1.07 10 9 1 cm for a single fiber and after division by the cross-section of 9.10 10 16 cm 2 , spec 1.18 10 6 1 cm 1 for the specific conductivity. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem 109: 612- 617, 2009

Ab initio HF crystal orbital calculations were performed for a guanine–cytosine base pair stack at its equilibrium position and at 0.05 A dilatation and compression, respectively. The shifts of the conduction and valence band edges were used to determine the deformation potentials of the electrons and the holes. After performing an approximate calculation for the elastic constant, the mobilities of the electrons and holes were determined. They were combined with the mobilities belonging to the longitudinal and torsional motions at a stack in DNA.

In this work, the conformational behavior of ribonuclease Sso7d is studied as a function of chirality of its constituting amino acids. Both optimized structures (using molecular mechanics with the CHARMM force field) and dynamic behavior (obtained by molecular dynamic simulations) are compared.

We do not have a definition of the living and cancerous states; we can give only their main characteristics at the different levels of organization: cell, organ, and organism. A simple model is proposed for a normal eukaryotic cell based on Prigogine's equation of chemical kinetics with diffusion. In this model, possibly only a few hundred key biochemical reactions should be selected together with their rate and diffusion constants. To solve these coupled nonlinear partial differential equation systems, it is proposed that the model cell be subdivided into compartments and that the problem be worked out always for one compartment (finite element method). This is possible, since the most important biochemical reactions and reaction cycles occur in different parts of the cell. The solutions (concentrations) obtained in one compartment can be used as input to the other compartments (together with the components entering from the environment). As an example, the problem of 10 reactions and 3 compartments has been solved by discretizing the space coordinates and choosing time steps. The solutions obtained by solving the 10 differential equations directly and by the compartmentalization agree very well. The main obstacles to further progress lie in the right choice of reactions and compartments, as well as in the correct estimation of the rate and diffusion constants, which were measured in only a few cases. If such a model cell can be obtained, the solutions should be investigated to determine (i) for their stability (homeostasis); (ii) whether changing the input concentrations to a larger degree one would obtain a new stationary state showing the characteristics of a precancerous state; and (iii) a method of extracting those input concentrations, or functions of them, which are the most important regulatory parameters. If successful, this would provide a scientific definition of the living state in the normal and cancerous states, respectively, at least at the cell level. Finally, outline is provided showing how the model might be extended to multicellular cases, as well as the main difficulties of such a process. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006

The B3LYP DFT crystal orbital method was applied (with helical periodicity) to calculate the total energy per unit cell of a cytosine (C) molecule in a C stack. Applying afterwards the multidimensional metric method in its BFGS form, the geometry of a C molecule was optimized in the stack of DNA B (3.36 A stacking distance, 36° rotation). For comparison, we optimized also the geometry of a C trimer and pentamer (in DNA B form) using the Gaussian 03 program for the B3LYP molecular calculation and the default method for the geometry optimization. The results of the two completely different calculations agree quite well, which supports our confidence in the results of our C stack calculation. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

DFT crystal orbital (band structure) calculations have been performed for the nucleotide base stacks of cytosine, thymine, adenine, and guanine arranged in DNA B geometry. The band structures obtained with PBE, BLYP, and B3LYP functionals are presented and compared to other related experimental and theoretical results. The influence of the quality of the basis set on the fundamental gap values was also investigated using Clementi's double ζ, 6-31G and 6-31G* basis sets. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

Recent measurements of the frequency-dependent a.c. conductivity of aperiodic DNA double helices have provided results which are in good agreement with our theoretical findings based on the variable range hopping mechanism in the 1–1011 s−1 frequency range at room temperature. At the frequencies 100 GHz–1 THz it is probable that not the hopping mechanism, but dipole energy loss of the water helices surrounding DNA is the dominant cause of the conductivity, because the experiments have given nearly the same conductivites for single and double DNA strands. The theoretical temperature-dependence of the conductivity contrary to experiments, does not show a crossing point and the slopes of the theoretical curves do not become zero even below 60 K. This and the fact that at T≈125 K the experimental σ(ω) is by one order of magnitude larger than the theoretical value, indicates that at low temperatures not the hopping mechanism, but other ones (like multichannel tunneling, structural thermal fluctuations of the stack) become dominant.

First, the major steps in the progress of molecular biology of a single cell are summarized starting from the 1940s. This is followed by mentioning the major unsolved problems in this field. Afterwards, already existing applications of the main ingredients of a theory of a single cell (quantum theory, statistical mechanics in the most general sense, information theory and theory of regulation of non-linear systems) are briefly described. The further probable developments in these fields which will make it possible to solve the, until now unresolved, important problems of molecular biology (especially the regulation of reaction ensembles in the cell and the self-regulation of a cell) are briefly described. Finally, the possibilities of until now in biology unused other mathematical methods are mentioned. It is pointed out that all these theories most probably will grow to provide a general theoretical description of a single cell. In the conclusion, one has tried to describe the probable extension of the theory of a cell to cell ensembles, organs and organism. In the last case, the importance of the development of brain research is pointed out.

Static and dynamic (hyper)polarizabilities for polymers built up from HCCR with RH, OH, F have been calculated with the perturbed coupled Hartree–Fock method. At this level polyacetylene (PA) has the highest polarizability, but the inclusion of the electron correlation correction interchanges the ordering and the fluorinated system becomes the most polarizable one. This shows that these contributions cannot be neglected. We have investigated the series of polymers arising from the cyclic five-membered molecules pyrrole, furane, and thiophene and in addition polyparaphenylene (PPh) and polyaniline (PAn). The basis set dependence and the effect of the number of neighbors interaction have been studied. It turns out that polythiophene (PTh) is easier to polarize than polyparaphenylene, polypyrrole (PPy) and polyfurane (PFu). The correlation contribution does not change the sequence. Polyaniline in its neutral all- trans configuration shows the highest static and dynamic polarizabilities due to the very extended π-electron system of the elementary cell. In addition, the static and dynamic polarizabilities of the constituent molecules pyrrole, furane, thiophene and benzene have been calculated for comparison with the corresponding polymers.

Putting dipoles in different arrangements in the planes of the guanine molecules in a stack in DNA B conformation, in a model calculation the effect of the electric field on the ab initio Hartree–Fock band structure was studied. The calculations were performed at the stacking distances 3.12, 3.36, and 3.60 A, respectively. The electric fields of the dipoles decreased the very broad conduction band of a guanine stack, caused some shifts in the band structure, but hardly influenced the fundamental gap. The computed effective masses at the physically interesting band edges correspond to the bandwidth changes due to the electric field. The electric field significantly influences the deformation potentials at the band edges and with it the transport properties of the guanine stack. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

Ab initio B3LYP crystal orbital (CO) calculations have been performed on the 19 homopolypeptides (PolyGly, PolyAla, PolySer, PolyThre, PolyLeu, PolyiLeu, PolyVal, PolyAspAc, PolyAsp, PolyGlutAc, PolyGlut, PolyHist, PolyProl, PolyCyst, PolyMeth, PolyTyr, PolyPhenAla, PolyArg, and PolyLys) in their β pleated sheet conformation. Keeping the main chain conformation fixed as in PolyGly, the side chain geometries were optimized. For the calculation 2n+1 different k points were used with n = 8 for the case of simpler and n = 10 for more complicated side chains. The basis set applied was the double ζ one of Clementi. According to the results obtained, the conduction bands are shifted upward and the valance band downward, compared with the results of previous BLYP 1 and LDA 7 CO calculations. The bandwidths are similar to the previous cases. The band edges are in many cases not at the endpoints of the first Brillouin zones, causing nonmonotonous dispersion of both the conduction bands (CB) and the valance bands (VB), respectively. The fundamental gap values due to the upward shifts of the CB and downward shifts of the VB are substantially larger than in the case of our previous DFT CO calculations (values 6.0–7.0 eV). They are very close to the gap values, which can be estimated on the basis of experimental ultraviolet (UV) spectra of some homopolypeptides and on the basis of intermediate exciton theoretical calculations (6.5–7.5 eV). These surprisingly good results for the gaps are due to the compensation of errors (LDA or BLYP gives too small and simple HF provides too large gap values) in the B3LYP method. The admixture of the exact HF exchange with a weight of 0.19 obviously compensates the self interaction error occurring in the LDA or BLYP methods. This article discusses whether/how this result could be established by other B3LYP CO calculations on simple polymer chains and on stacked systems (e.g., nucleotide base stacks). Furthermore, a comparative analysis of the ground state DFT methods, the HF method and of the optimized effective potential method could throw more light on our successful theoretical results for the gaps of the homopolypeptides. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

A. Szent-Gyorgyi contributing so much to the citric acid (oxygen metabolism) cycle in which subsequent electron transfers occur in eight proteins has come to the idea already in 1941 that proteins have to be conductors. This hypothesis was first not accepted because of the too large gap and non-periodic nature of a protein chain. With the development of the theory of disordered systems and the occurrence of high-speed computers it was possible to show that both proteins and nucleotide base stacks are good hopping semiconductors, proving the correctness of Szent-Gyorgyi's original idea. Ab initio Hartree–Fock correlation corrected band structures were computed both for homopolypeptides and periodic nucleotide base stacks. On the basis of these band structures applying the intermediate exciton theory the UV spectra of different biopolymers were calculated. The results for a cytosine stack, polyglycine and polyalanine are in good agreement with experiments. Finally, the expected further development of the quantum theory of biopolymers are discussed.

First the correct expression of charge mobilities in the one-dimensional (1-D) case in the deformation potential approximation are derived in detail. They differ substantially from the usual 3-D expressions. Starting from an ab initio HF band structure of a guanine stack, the effective masses, the deformation potentials, and the 1-D electron and hole mobilities, respectively, were calculated. The mobility values obtained seem to bee quite reasonable. No attempt was made to calculate from the mobilities the conductivities because of the lack of reliable experimental data (the activation energies of the electron and hole conductivities and dopant concentrations).

An alternative method to solve the coupled-perturbed Hartree–Fock (CPHF) equations for infinite quasi–one-dimensional systems is presented. The new procedure follows a proposal made by Langhoff, Epstein, and Karplus to obtain perturbed wavefunctions free from arbitrary phase factors in each order of perturbation. It is based on the intermediate orthonormalization of the perturbed wavefunctions (which is different from the usual one) and a corresponding selection of the Lagrangian multipliers. In this way it is possible to incorporate the orthonormalization conditions into the set of CPHF equations. Moreover, a new, advantageous procedure to determine the derivatives of the wavefunction with respect to the quasimomentum k is presented. We report calculations of the dipole moment, the polarizability α, and the first hyperpolarizability β for different polymers (poly-HF, poly-H2O, trans-polyacetylene, polyyne, and polycarbonitrile) for different frequencies. These results are extensively compared with oligomer calculations. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 251–268, 2003

An alternative method to solve the coupled perturbed Hartree–Fock equations is presented. The new procedure follows a proposition made by Langhoff, Epstein and Karplus to obtain perturbed wave functions free from arbitrary phase factors in each order of perturbation. It is based on a different orthonormalization of the perturbed wave functions than the usual one and a correspondent selection of the Lagrangian multipliers. In this way it is possible to incorporate the orthonormalization conditions into the set of coupled perturbed Hartree–Fock equations. The equations are solved iteratively for each perturbation order. Calculations of dynamic NLO-properties for CH3F, CH2F2, CHF3, and water dimer are performed to verify the method.

We have calculated the static polarizabilities of polymers with small linear and medium-size cyclic elementary cells and their constituent molecules. The basis set dependence has been investigated for the average and the longitudinal polarizabilities. The influence on the results of the selected method for the calculation (finite field or coupled perturbed Hartree–Fock) was analyzed. The effect of the electron correlation for this property in these systems has been calculated for the first time in the frames of the crystal orbital approach. The results show that this correction amounts up to 35% of the ab initio Hartree–Fock values.

The frequency-dependent complex hopping conductivities of single nucleotide base stacks and base pair stacks were calculated on the following basis: (1) The determination of the density of states of these disordered systems with the help of the matrix block negative counting method. (2) Using the inverse iteration technique, the Anderson localization of the one-electron functions belonging to the physically interesting levels were computed. (3) With the help of the latter quantities the hopping frequencies corresponding to the relative motion of the base pairs with respect to each other (acoustic phonons) were determined. (4) Finally, using a random-walk theory the frequency-dependent complex conductivities (σ (ω)) were computed. The |σ (ω) |− ω curves show a saturation at ω ≈ 10 10 s −1 .T he|σ (ω)|'s have the values in the base pairs case (taking into account the role of the sugar-phosphate backbone, basis set, and correlation effects) are a few times 1 � −1 cm −1 for ω> 10 10 s −1 . This room temperature result is in excellent agreement with the energy loss (in a resonant cavity) experiment on lambda phage deoxyribonucleic acid (DNA) of Gruner and co-workers. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem 90: 838-847, 2002

Using the matrix block negative factor counting and inverse iteration methods, the electronic density of states (DOS) and wave functions belonging to the energy levels in the valence band regions of an aperiodic DNA base pair stack were determined. From these the hopping frequencies, and with the aid of the latter applying a random walk theory the frequency-dependent complex hopping conductivity of the stack was calculated. The calculations were performed for the frequency range 10 8 s −1 ≤ω≤10 11 s −1 and temperature range 60 K K . According to the results obtained at high frequencies and temperatures, the conductivity indicates variable range hopping (exponential temperature dependence, decrease of the conductivity with decreasing frequencies). The room-temperature conductivity value at high frequency is ∼5×10 −1 Ω −1 cm −1 which agrees well with recent experiments. The experimental and theoretical temperature-dependence at high frequencies also agrees well with each other. At lower frequencies (∼10 8 s −1 ), the conductivity at lower T values doesn't depend on the temperature. This indicates that in the 60 T ω≈10 8 s −1 the dominant mechanism of the conductivity is probably tunneling.

It is pointed out that periodic stacked systems, like TCNQ–TTF and the nucleotide base stacks, have comparatively broad energy bands (several tenths of an eV) despite that their stacking distance is over 3 A. The reason for this is that in such systems there are many σ-type interactions of their π orbitals. Comparing experimental and theoretical information, one can conclude that their room-temperature dc conductivity is in the order of 10 4 –10 6 Ω −1 m −1 . In the case of aperiodic DNA, the room-temperature hopping conductivity of the stack was found, both theoretically and experimentally, of the order of 100 Ω −1 m −1 at frequencies ω ≥10 10 s −1 .

We have used the matrix block negative factor counting method to calculate the density of states of an aperiodic single stack of DNA (a part of a human oncogene), consisting of 100 nucleotide bases in the DNA B conformation. The nearest water molecules were taken into account in the calculation. The work refers to the valence bands region of the stacks. Consequently the inverse iteration method was used to determine the Anderson localization of the physically interesting wave functions. The hopping frequencies between the units were determined from these. They have been used as input in a random walk theory. According to the results obtained, the real part and the absolute value of the complex hopping conductivity gets saturated at the frequency of 1012 s−1. Its value lies at ∼10−4 Ω−1 cm−1, which is by two orders of magnitude larger than the one obtained previously in the absence of water (∼10−6 Ω−1 cm−1). Different reasons for this rather large effect of water are discussed (e.g. basis set improvement by bases set superposition, the effect of the water dipoles).

First the reason for the 2–3 orders of magnitude difference in the Young modulus of a polymer chain in an ordered (crystalline) phase and in a macroscopic disordered sample is explained. This explanation points out: (1) that in a macroscopic sample the different chains are randomly oriented in respect to each other and (2) because of the polydispersity in the chain lengths, shorter chains will not be kept in the same position as in the crystalline phase. Consecutively, for nylon-11 a simple statistical mechanical calculation was performed for the total energy per unit cell, for the entropy term and for the free energy per unit cell in the case of free rotations around all the 11 single bonds of the unit cell. The results show a dominant role of the configurational entropy in accordance with C.F. von Weizsacker's general considerations back in 1958.

The Young's moduli of the linear chain polymers, polyethylene and six polyfluoroethylenes, constrained to the planar conformation, are calculated by means of the local density approximation (LDA) using the Perdew–Zunger (PZ) correlation potential and a linear combination of Gaussian-type orbitals (LCGTO).

Theoretical investigations of hopping conductivity across the base stacks and the theory of soliton generation by chemical carcinogens and by ionizing radiation in it have resulted in mechanisms of oncogene activation and a probable explanation of antioncogene inactivation through double strand breaks, respectively. Some ideas on how to counteract these events are also outlined. The same mechanisms can be used to explain damages on the apoptosis gene of a cell and on the genes which code the repair enzymes of DNA. It is further shortly discussed how a malignant transformation can start by carcinogen attacks on proteins and how the damage on regulatory proteins can become hereditary. Afterwards it is described how the self-regulation of a cell or cell ensembles could be modeled with the help of a comparatively few (a few hundred) correctly chosen biochemical reactions. Changes of the flows of the input compounds or of the reaction constants caused by carcinogens can bring the cell in a stationary state which is different from its original one (precancerous state) Such studies can lead to a physico-chemical definition of the cancerous cell. Next, some connections between the central nervous system and carcinogenesis are shortly described. Finally, in this paper the relations between the different events in carcinogenesis are summarized in a flow chart which contains also the possible points of counteractions (prevention of certain steps of cancer initiation).

Electronic density of states (DOS) histograms and of the nucleotide base stack regions of a segment of human oncogene (both single and double stranded, in B conformation) and of single-stranded random DNA base stack (also in B conformation), were calculated. The computations were performed with the help of the ab initio matrix block negative factor counting (NFC) method for the DOSs. The neglected effects of the sugar–phosphate chain and the water environment (with the counterions) were assessed on the basis of previous ab initio band structure calculations. Further, in the calculation of single nucleotide base stacks also basis set and correlation effects have been investigated. In the case of a single strand the level spacing widths of the allowed regions and the fundamental gap were calculated also with Clementi's double ς basis and corrected for correlation at the MP2 level. The inverse interaction method was applied for the study of Anderson localization.

The band structures of a formamide stack (in the DNA B stacking arrangement), as well of cytosine (C) and uracil (U) stacks were calculated at the ab initio Hartree‐Fock (HF) level using first a double basis set. The resulting valence and conduction bands were corrected for correlation on the basis of the inverse Dyson equation in the diagonal approximation with a MP2 selfenergy taking into account the relaxation effects. It has been found that if one supplements the double z basis with one belonging to a “phantom” molecule (a molecule without nuclear charges and electrons at the midway of the stacking distance, 3:36 A=2a 1:68 A and at half the rotation angle, 188) one obtains substantially larger correlation effects and the fundamental gap gets close to the values which can be estimated on the basis of the optical spectra. Most probably this finding will turn out to be important for other stacked systems. q 2000 Elsevier Science B.V. All rights reserved.

The effect of all types of ionizing radiations on higher organisms is nonspecific in the sense that all interactions occur through the agency of ionization and excitation processes. This, and the relative constancy of the amount of energy required to induce such processes, has led to the concept of absorbed dose as a quantifier for the amount of radiation delivered. However, equal doses of different radiations have different effects depending on the stopping power of the charged particles and on the temporal pattern of irradiation. Because individual energy transfers depend on neither one of these factors, it follows that the biological effectiveness of ionizing radiation depends on their spatial and temporal configuration. Microdosimetry is the study of the distribution in space and time of elementary energy deposits and their relation to subsequent damage. We discuss physico-chemical events that occur within the first microsecond following the interaction of charged particles with deoxyribonucleic acid (DNA) and argue that this particular time interval is uniquely important for understanding the biological effectiveness of radiation. Radiation biologists distinguish between direct hits and damage induced indirectly by radicals produced in the condensed medium surrounding the DNA target. The interaction and diffusion of these radicals (primarily OH) are described with the techniques of stochastic chemistry because—unlike “regular” chemistry—their initial spatial distribution is highly nonuniform. The information thus obtained is usually summarized in terms of proximity functions or microdosimetric distributions. The ultimate object of such studies is to obtain information on specific DNA alterations (e.g., strand breaks) or chromosomal damage and correlate them to such events as mutagenesis and carcinogenesis. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 80: 327–340, 2000

A finite field approach for the calculation of static vibrational polarizabilities of molecules is extended to polymers using the previously developed method for the calculation of the electronic contribution of periodic quasi-one-dimensional systems. The method has been applied to study the effect of the vibrations on the static polarizability of an infinite stack of alternating HF molecules and of poly(HF) in the experimentally determined hydrogen-bonded zig–zag structure. The results are discussed and compared with a calculation for the isolated HF molecule and studies in the literature.

The electronic density of states (DOS) of aperiodic nucleotide base and base pair stacks were calculated previously by the negative factor counting (NFC) procedure. Applying the inverse iteration method, the localized electronic wave functions of the first 100 filled levels were determined. As a third step the primary hopping frequencies between the localized electronic wave functions (at different sites) were computed assuming interactions via acoustic phonons. Finally using the hopping frequencies as input of a random walk theory of Lax and coworkers the complex, frequency-dependent hopping conductivities σ(ω) were determined. This procedure was performed for two different 100 base or base pair long sequences in the stack and for a 200 units long segment for a single stack. The influence of the application of a better basis set and that of correlation effects were also investigated. The results show an increase of σ(ω) as compared to the ones of different protein chains and at ω=10 10 s −1 they are close to 1 Ω−1 cm−1 in the case of 100 base pairs in the stacks. Further, the application of the better (double ζ) basis and of correlation corrections of the level schemes increase σ(ω). One can conclude that in aperiodic DNA there is hopping hole conduction (if its interaction with nucleoproteins generates holes via charge transfer) and its value is about 1 Ω−1 cm−1 at high frequencies. This result agrees well with the available experimental data.

Hartree–Fock and correlation corrected band structure calculation methods for periodic polymers are described together with many applications. The ionization potentials and gaps are in the second case in rather good agreement with experiment. Using the negative factor counting method the density of states, Anderson localization and hopping frequencies were computed for different proteins and nucleotide base stacks. Using a random walk theory their hopping conductivities were also determined. The results agree well with those of amorphous glasses. Applying the intermediate exciton theory the spectra of different polymers and of YBa2Cu3O7 (“123”) were computed again in good agreement with experiment. For “123” the effective interaction (screened Coulomb+excitonic) substituted into the BCS gap equation gives for T c =87 K (exp: 92 K), Δmax=19 meV (exp: 20 meV) and a dx2−y2 gap symmetry with a small s admixture (like in experiments). These successful calculations suggest applications (1) to predict polymers with several optimal properties, (2) to extend them to 3D periodic solids.

The coupled Hartree–Fock (CHF) equations in second order are derived to calculate dynamic polarizabilities and hyperpolarizabilities for infinite periodic chains. The analytical expressions for the second derivatives of the perturbed crystal orbitals with respect to the quasimomentum k are developed. The first and second derivatives are required on behalf of the definition of the perturbation operator describing the effect of the time-dependent electric field on the electronic structure of the polymer. The computer program has been applied to calculate the tensor elements of the second-harmonic generation and the optical rectification for the model chain poly(water) and the conjugated π-electron system poly(carbonitrile), respectively. The CHF-results are compared with uncoupled Hartree–Fock (UCHF) calculations.

We have calculated the charge transfer (CT) between the PO 4 - group of DNA and the lysine (Lys) and arginine (Arg) positive side chains of histones in presence of water and K + ions. The calculations were performed at the HF + MP2 level, using the TZVP basis set. The calculations were corrected for basis set superposition error and besides Mulliken’s population analysis we have introduced the – for charged systems more reliable – natural population analysis. The results show that the bare PO 4 - -Lys and the PO 4 - -Arg interactions become weaker, mainly, due to the presence of the K + ion. We have found 0.067 e CT for Lys and 0.050 e for Arg.

Using the HF + MP2 methods with full geometry optimizations the charge transfer (CT) from the PO 4 - groups of DNA to the arginine or lysine side chains of the proteins forming the nuclohistone cores were calculated. (X-ray investigation shows that in the nucleohistone core there are eight histones which are wrapped around by a DNA superhelix). We have found 0.21e and 0.26e CT, respectively. Knowing the structure of nucleohistones one can estimate a charge transfer at every fourth base pair. Taking as average 0.10e CT (there are also other attractive interactions) one can compute the concentrations of holes in DNA. From these one can obtain the dc conductivity for polyguanilic acid (the mobilities are known).