Marcin Molski

On the holistic approach in cellular and cancer biology: nonlinearity, complexity, and quasi-determinism of the dynamic cellular network.

A keystone of the molecular reductionist approach to cellular biology is a specific deductive strategy relating genotype to phenotype—two distinct categories. This relationship is based on the assumption that the intermediary cellular network of actively transcribed genes and their regulatory elements is deterministic (i.e., a link between expression of a gene and a phenotypic trait can always be identified, and evolution of the network in time is predetermined). However, experimental data suggest that the relationship between genotype and phenotype is nonbijective (i.e., a gene can contribute to the emergence of more than just one phenotypic trait or a phenotypic trait can be determined by expression of several genes). This implies nonlinearity (i.e., lack of the proportional relationship between input and the outcome), complexity (i.e. emergence of the hierarchical network of multiple cross‐interacting elements that is sensitive to initial conditions, possesses multiple equilibria, organizes spontaneously into different morphological patterns, and is controled in dispersed rather than centralized manner), and quasi‐determinism (i.e., coexistence of deterministic and nondeterministic events) of the network. Nonlinearity within the space of the cellular molecular events underlies the existence of a fractal structure within a number of metabolic processes, and patterns of tissue growth, which is measured experimentally as a fractal dimension. Because of its complexity, the same phenotype can be associated with a number of alternative sequences of cellular events. Moreover, the primary cause initiating phenotypic evolution of cells such as malignant transformation can be favored probabilistically, but not identified unequivocally. Thermodynamic fluctuations of energy rather than gene mutations, the material traits of the fluctuations alter both the molecular and informational structure of the network. Then, the interplay between deterministic chaos, complexity, self‐organization, and natural selection drives formation of malignant phenotype. This concept offers a novel perspective for investigation of tumorigenesis without invalidating current molecular findings. The essay integrates the ideas of the sciences of complexity in a biological context. J. Surg. Oncol. 1998;68:70–78.

Quantum-chemical investigation of the structure and the antioxidant properties of α-lipoic acid and its metabolites

Quantum-chemical computations were used to investigate the structure–antioxidant parameter relationships of α-lipoic acid and its natural metabolites bisnorlipoic acid and tetranorlipoic acid in their oxidized and reduced forms. The enantiomers of lipoic and dihydrolipoic acid were optimized using the B3LYP/6-311+G(3df,2p), B3LYP/aug-cc-pVDZ and MP2(full)/6-31+G(d,p) levels of theory as isolated molecules and in the presence of water. The geometries of the metabolites and the values of their antioxidant parameters (proton affinity, bond dissociation enthalpy, adiabatic ionization potential, spin density, and the highest occupied molecular orbital energy) were calculated at the B3LYP/6-311+G(3df,2p) level of theory. The results obtained reveal similarities between these structures: a pentatomic, nonaromatic ring is present in the oxidized forms, while an unbranched aliphatic chain (as found in saturated fatty acids) is present in both the oxidized and the reduced forms. Analysis of the spin density and the highest occupied molecular orbital energy revealed that the SH groups exhibited the greatest electron-donating activities. The values obtained for the proton affinity, bond dissociation enthalpy and adiabatic ionization potential indicate that the preferred antioxidant mechanisms for α-lipoic acid and its metabolites are sequential proton loss electron transfer in polar media and hydrogen atom transfer in vacuum.

ON THE MODIFICATION OF FRACTAL SELF-SPACE DURING CELL DIFFERENTIATION OR TUMOR PROGRESSION

A novel parameter called expansion coefficient has been defined to measure both connectivity and collectivity in a population of cells conquering the available space and self-organizing into tissue patterns of the higher order. Connectivity (i.e. interconnectedness) denotes that there are complex dynamic relationships, not just structural, static ones, in a population of cells enabling the emergence of global features in the system that would never appear in single cells existing out of the system. Collectivity denotes that all interconnected cells interact in a common mode. Evolution of this coefficient during differentiation or tumor progression was investigated by the box-counting method. The population of control or retinoid-treated primary cancer cells cultured in the monolayer (i.e. quasi-2D) system possessed fractal dimension and self-similarity. However, the expansion coefficient was close to zero, indicating that connectivity was low, and no collective state emerged. A significant change of the coefficient occurred when primary cells formed aggregates, quasi-3D systems with increased connectivity, and during treatment of the aggregates with retinoid resulting in a collective state (i.e. in differentiation of cells). Those statistical features were lost during tumor progression. All populations of the secondary cancer cells possessed integer dimension and the expansion coefficient was equal to zero.

Non-Born-Oppenheimer calculations of the pure vibrational spectrum of HeH +

Very accurate calculations of the pure vibrational spectrum of the HeH(+) ion are reported. The method used does not assume the Born-Oppenheimer approximation, and the motion of both the electrons and the nuclei are treated on equal footing. In such an approach the vibrational motion cannot be decoupled from the motion of electrons, and thus the pure vibrational states are calculated as the states of the system with zero total angular momentum. The wave functions of the states are expanded in terms of explicitly correlated Gaussian basis functions multipled by even powers of the internuclear distance. The calculations yielded twelve bound states and corresponding eleven transition energies. Those are compared with the pure vibrational transition energies extracted from the experimental rovibrational spectrum.

SELF-SIMILARITY, COLLECTIVITY, AND EVOLUTION OF FRACTAL DYNAMICS DURING RETINOID-INDUCED DIFFERENTIATION OF CANCER CELL POPULATION

From the reductionist perspective of molecular biology, proliferation or differentiation of eucaryotic cells is a well-defined temporal, spatial, and cell type-specific sequence of molecular cellular events. Some of those events, such as passing of the restriction point in the cell cycle, are of a stochastic nature. Results of this study indicate that, in spite of the intracellular stochasticity, cancer cells can form collective structures with fractal dimension and self-similarity. A transition from the monolayer culture to the aggregated colony facilitated interconnectedness between P19 cells, altered constitutive expression of randomly chosen retinoid-responsive genes, and increased fractal dimension of the entire population. Retinoid-induced emergence of neuron-like phenotype decreased fractal dimension significantly, slowing down dynamics of gene expression. Since the differentiated P19 cells retained both their cancer phenotype and a number of gene defects, we conclude that the appropriate dynamics of intracellular events is neccessary for the proper course of differentiation. Owing to self-similarity, dynamics of cellular expansion can be measured by a fractal dimension in a single cell or in the entire population.

Orbit-orbit relativistic corrections to the pure vibrational non-Born-Oppenheimer energies of H2

We report the derivation of the orbit-orbit relativistic correction for calculating pure vibrational states of diatomic molecular systems with sigma electrons within the framework that does not assume the Born-Oppenheimer (BO) approximation. The correction is calculated as the expectation value of the orbit-orbit interaction operator with the non-BO wave function expressed in terms of explicitly correlated Gaussian functions multiplied by even powers of the internuclear distance. With that we can now calculate the complete relativistic correction of the order of alpha(2) (where alpha=1/c). The new algorithm is applied to determine the full set of the rotationless vibrational levels and the corresponding transition frequencies of the H(2) molecule. The results are compared with the previous calculations, as well as with the frequencies obtained from the experimental spectra. The comparison shows the need to include corrections higher than second order in alpha to further improve the agreement between the theory and the experiment.

Dipole moment of ArH+X1Σ+ from analysis of pure rotational and vibration-rotational spectra

Abstract By a direct fit to 431 experimental wave numbers of pure rotational and vibration-rotational transitions of ArH + X 1 Σ + in six isotopic variants, 16 coefficients of radial functions defining the Born–Oppenheimer potential energy, adiabatic and nonadiabatic effects have been determined at σ =0.885 and F =4.07×10 15 . Using a relation between nonadiabatic rotational effects and electric and magnetic properties of the molecule, a permanent dipole moment of 40 Ar 1 H + is estimated as μ 0 =2.12(55) D which agrees both with the ab initio value 2.2(1) D and the experimental result μ 0 =3.0(6) D within quoted error limits.

Electric and magnetic properties of LiH X1Σ+ from analysis of pure rotational and vibration–rotational spectra

Abstract Pure rotational and vibration–rotational transitions (1530 lines) of LiH X 1 Σ + in four isotopic variants are analyzed with a deformationally self-consistent procedure in an analytic version. Using a relation between nonadiabatic rotational effects and electric and magnetic properties of the molecule, we estimate a permanent dipole moment of μ 0 =1.933(76)×10 −29 Cm, electric polarity + LiH − and rotational g -factor g 0 =−0.253(14) for 7 Li 2 H and g 0 =−0.618(28) for 7 Li 1 H. They conform acceptably with magnitudes from published experiments on Stark and Zeeman effects and from quantum-chemical calculations of electronic structure.

Reduction of wavenumbers of pure rotational and vibration-rotational transitions of KrH+ X1Σ+ to parameters of radial functions

From the 352 wavenumbers of the assigned pure rotational and vibration—rotational transition of KrH+ X1Σ+ in 11 isotopic variants, 10 coefficients of radial functions defining the Born—Oppeneheimer potential energy, adiabatic and non-adiabatic effects have been determined at = 0.982. From the radial coefficients representing non-adiabatic rotational effects the rotational g factor g 0 = 0.576(12) and electric dipole moment μ0 = 1.967(40) D of 84KrH+ are estimated at polarity [−KrH+]+. The latter conforms acceptably with the ab initio result μ0 = 1.944D, whereas the former differs from the absolute experimental value |g 0| = 0.5545 by about 3%, and from the relativistic ab initio value g 0 = 0.6082 by about 5%.

A comparison of approaches for reduction of vibration-rotational spectra of NaCl X 1Σ+ to parameters of radial functions

We compare applications of a deformationally self-consistent procedure and of hypervirial perturbation theory, as embodied in a computer programme Radiatom, to spectral data of 23 Na 35 Cl and 23 Na 37 Cl in the electronic ground state X 1 Scomprising 1210 vibration‐rotational transitions. From a marginally evaluated value of a parameter related to nonadiabatic rotational effects we predict rough values of electric dipolar moment and rotational g-factor; the former is near a known experimental value. Comparison is also made with values transformed from results obtained with a potential-energy function of exponential form.