Relationships between interaction energy (E
) and electron density properties at the X···X bond critical point or the d(X···X) distance were established for the large set of structures (A)
...Y-X···X-Z(B)
bearing the halogen bonds Cl···Cl, Br···Br, and I···I (640 structures in total). The best estimator of E
is the kinetic energy density (G
), which reasonably approximates the whole set of the structures as -E
= 0.128G
- 0.82G
+ 1.66 (R
= 0.91, mean absolute deviation 0.39 kcal/mol) and demonstrates low dispersion. The potential and kinetic energy densities, electron density, and the d(X···X) distance behave similarly as estimators of E
for the individual series Cl···Cl, Br···Br, and I···I. A number of the E
(property) correlations are recommended for the practical application in the express estimates of the strength of the homo-halogen bonds.
Bond energy is the main characteristic of chemical bonds in general and of non-covalent interactions in particular. Simple methods of express estimates of the interaction energy, E
, using ...relationships between E
and a property which is easily accessible from experiment is of great importance for the characterization of non-covalent interactions. In this work, practically important relationships between E
and electron density, its Laplacian, curvature, potential, kinetic, and total energy densities at the bond critical point as well as bond length were derived for the structures of the Z-I···Hal
and Z-Hal···I
types bearing halogen bonds and involving iodine as interacting atom(s) (totally 412 structures). The mean absolute deviations for the correlations found were 2.06-4.76 kcal/mol.
Relationships between the Y•••X bond critical point (BCP) properties or the Y•••X distance and the halogen bond interaction energy were analyzed in detail by theoretical methods for the series of ...structures (A)nZ—Y•••X− (X,Y = F, Cl, Br; totally 441 structures). No relationship was found for the whole set of structures or for the series (A)nZ—F•••X−, (A)nZ—Cl•••X−, and (A)nZ—Br•••X−. The interaction energies may be roughly estimated from the BCP properties for the series (A)nZ—Y•••F−, (A)nZ—Y•••Cl−, and (A)nZ—Y•••Br− as well as for (A)nZ—Y•••X− (when (A)nZ is variable, X and Y are constant) with the mean absolute deviation values 2.04‐4.38 kcal/mol. The corresponding recommended relationships are provided and they are significantly different from the popular dependencies deduced previously for other types of noncovalent interactions. Tremendous effect of the computational method and basis set on the relationships under analysis was discovered. Computational results clearly indicate that, for practical purposes, the Eint(BCP property) dependencies should be established not simply for each global type of interactions (hydrogen bond, halogen bond, chalcogen bond, etc.) but for each combination of the first and second order atoms taking into account also the computational method and basis set.
Relationships between the Y•••X interaction energy and electron density based properties at the bond critical point were analyzed in detail for the large statistically significant set of the halogen bond structures (A)nZ—Y•••X− (Y, X = F, Cl, Br, 441 structures). The tremendous effect of the computational method and basis set on the relationships under analysis was discovered.
A continuous mathematical model of non-invasive avascular tumor growth in tissue is presented. The model considers tissue as a biphasic material, comprised of a solid matrix and interstitial fluid. ...The convective motion of tissue elements happens due to the gradients of stress, which change as a result of tumor cells proliferation and death. The model accounts for glucose as the crucial nutrient, supplied from the normal tissue, and can reproduce both diffusion-limited and stress-limited tumor growth. Approximate tumor growth curves are obtained semi-analytically in the limit of infinite tissue hydraulic conductivity, which implies instantaneous equalization of arising stress gradients. These growth curves correspond well to the numerical solutions and represent classical sigmoidal curves with a short initial exponential phase, subsequent almost linear growth phase and a phase with growth deceleration, in which tumor tends to reach its maximum volume. The influence of two model parameters on tumor growth curves is investigated: tissue hydraulic conductivity, which links the values of stress gradient and convective velocity of tissue phases, and tumor nutrient supply level, which corresponds to different permeability and surface area density of capillaries in the normal tissue that surrounds the tumor. In particular, it is demonstrated, that sufficiently low tissue hydraulic conductivity (intrinsic, e.g., to tumors arising from connective tissue) and sufficiently high nutrient supply can lead to formation of giant benign tumors, reaching tens of centimeters in diameter, which are indeed observed clinically.
It has been hypothesized that solid tumors with invasive type of growth should possess intrinsic resistance to antiangiogenic therapy, which is aimed at cessation of the formation of new blood ...vessels and subsequent shortage of nutrient inflow to the tumor. In order to investigate this effect, a continuous mathematical model of tumor growth is developed, which considers variables of tumor cells, necrotic tissue, capillaries, and glucose as the crucial nutrient. The model accounts for the intrinsic motility of tumor cells and for the convective motion, arising due to their proliferation, thus allowing considering two types of tumor growth—invasive and compact—as well as their combination. Analytical estimations of tumor growth speed are obtained for compact and invasive tumors. They suggest that antiangiogenic therapy may provide a several times decrease of compact tumor growth speed, but the decrease of growth speed for invasive tumors should be only modest. These estimations are confirmed by numerical simulations, which further allow evaluating the effect of antiangiogenic therapy on tumors with mixed growth type and highlight the non-additive character of the two types of growth.
The efficacy of antitumor radiotherapy can be enhanced by utilizing nonradioactive nanoparticles that emit secondary radiation when activated by a primary beam. They consist of small volumes of a ...radiosensitizing substance embedded within a polymer layer, which is coated with tumor-specific antibodies. The efficiency of nanosensitizers relies on their successful delivery to the tumor, which depends on their size. Increasing their size leads to a higher concentration of active substance; however, it hinders the penetration of nanosensitizers through tumor capillaries, slows down their movement through the tissue, and accelerates their clearance. In this study, we present a mathematical model of tumor growth and radiotherapy with the use of intravenously administered tumor-specific nanosensitizers. Our findings indicate that their optimal size for achieving maximum tumor radiosensitization following a single injection of their fixed total volume depends on the permeability of the tumor capillaries. Considering physiologically plausible spectra of capillary pore radii, with a nanoparticle polymer layer width of 7 nm, the optimal radius of nanoparticles falls within the range of 13-17 nm. The upper value is attained when considering an extreme spectrum of capillary pores.
In this work, four new ruthenium complexes Ru(η
6
-
p
-cymene)(L1)Cl
1
, Ru(η
6
-
p
-cymene)(L2)Cl
2
, Ru(η
6
-
p
-cymene)(L3)Cl
3
and Ru(η
6
-
p
-cymene)(L4)Cl
4
HL1 = (2-cyanophenyl)glycine; HL2 = ...(5-chloro-2-cyanophenyl)glycine; HL3 = (2-cyano-3-fluorophenyl)glycine; HL4 = (4-cyanophenyl)glycine were synthesized and well characterized by several spectroscopic and analytical techniques. Complexes
1
and
3
were found to be fluorescent in most of the solvents; however,
2
and
4
were found to be fluorescent mostly in EtOAc, DMF and ethanol. Amongst these four complexes,
3
has shown selective sensing against CO
3
2−
and SO
4
2−
anions by quenching of fluorescence. The LOD values are found to be in the sub-micromolar range. Investigations of the sensing mechanism performed by computation and NMR studies indicate a possible adduct formation between the NH group of the ligand and the anion(s) through hydrogen bond formation, which ultimately might lead to proton transfer to the bi-negative anion. The quantum yield of the complex
3
was found to decrease on addition of CO
3
2−
and SO
4
2−
anions from 0.46 to 0.13 and 0.12, respectively. The Job's plot indicates the binding between the probe and anion in a 1 : 1 ratio for both CO
3
2−
and SO
4
2−
anions. Along with that, all the complexes were found to be biocompatible when tested against several cell lines showing very high IC
50
values. It can also be observed that
1
is capable of penetrating within the cells and can act as a cell imaging agent showing fluorescence, and thus can be used for bio-imaging purposes.
Four new ruthenium(
ii
)-arene amino acid complexes were synthesised and characterized by spectrophotometric, analytical and computational techniques. Further evaluation for their sensing, bio-compatibility, and bio-imaging abilities were carried out.
In contrast to V(V) complexes with various organic ligands, a simple vanadate without any additive is inactive in neutral medium toward the oxidation of alkanes with H
O
. In this work, we discovered ...that the insufficient activation of H
O
upon coordination to the simple vanadate - the commonly accepted reason for the low catalytic activity of the vanadate - cannot explain this phenomenon. Two main findings are reported here on the basis of DFT calculations. First, the generally accepted Fenton-like mechanism of the generation of the active oxidizing species (HO˙) in a vanadate/H
O
/MeCN system was revisited. A new mechanism based on the tremendous activation of the OOH ligand in the intermediate V(OO)
(OOH)(H
O) toward the homolytic O-O bond cleavage is not only feasible but significantly more favourable than the Fenton-like pathway. The surprisingly low activation barrier calculated for the HO˙ generation (15.4 kcal mol
) demonstrates the efficiency of this process. The presence of easily oxidizable non-innocent OO ligands in this intermediate explains such an activation. Second, it was found that the generated HO˙ radicals may be easily captured by the V atom soon after their formation followed by the elimination of the molecular oxygen. This side reaction of the H
O
dismutation efficiently consumes the produced HO˙ radicals decreasing their concentration in the reaction mixture and preventing the following oxidation of alkanes.
A new continuous spatially-distributed model of solid tumor growth and progression is presented. The model explicitly accounts for mutations/epimutations of tumor cells which take place upon their ...division. The tumor grows in normal tissue and its progression is driven only by competition between populations of malignant cells for limited nutrient supply. Two reasons for the motion of tumor cells in space are taken into consideration, i.e., their intrinsic motility and convective fluxes, which arise due to proliferation of tumor cells. The model is applied to investigation of solid tumor progression under phenotypic alterations that inversely affect cell proliferation rate and cell motility by increasing the value of one of the parameters at the expense of another.It is demonstrated that the crucial feature that gives evolutionary advantage to a cell population is the speed of its intergrowth into surrounding normal tissue. Of note, increase in tumor intergrowth speed in not always associated with increase in motility of tumor cells. Depending on the parameters of functions, that describe phenotypic alterations, tumor cellular composition may evolve towards: (1) maximization of cell proliferation rate, (2) maximization of cell motility, (3) non-extremum values of cell proliferation rate and motility. Scenarios are found, where after initial tendency for maximization of cell proliferation rate, the direction of tumor progression sharply switches to maximization of cell motility, which is accompanied by decrease in total speed of tumor growth.
Intramolecular chalcogen bonding in arylhydrazones of sulfamethizole is strengthened by conjugation in the π‐system of a noncovalent five‐membered ring. The S⋅⋅⋅O distance in the sulfamethizole ...moiety of these compounds ranges from 2.698(3) to 2.806(15) Å, which indicates its strong dependence on the attached arylhydrazone fragments. Information on the nature of the intramolecular chalcogen bond was afforded by DFT calculations.
A new synthon: Three new arylhydrazone dyes have been synthesized and characterized by single‐crystal X‐ray diffraction to investigate the effect of attached substituents on the aromatic moiety of the molecules, highlighting the role of the resonance assisted chalcogen bond synthon in the structural features of these dyes.
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