DNA thermal denaturation by polymer field theory approach: effects of the environment

We analyse the effects of the environment (solvent quality, presence of extended structures - crowded environment) that may have impact on the order of the transition between denaturated and bounded DNA states and lead to changes in the scaling laws that govern conformational properties of DNA strands. We find that the effects studied significantly influence the strength of the first order transition. To this end, we re-consider the Poland-Scheraga model and apply a polymer field theory to calculate entropic exponents associated with the denaturated loop distribution. For the d = 3 case, the corresponding diverging ε = 4-d expansions are evaluated by restoring their convergence via the resummation technique. For the space dimension d = 2, the exponents are deduced from mapping the polymer model onto a two-dimensional random lattice, i.e., in the presence of quantum gravity. We also show that the first order transition is further strengthened by the presence of extended impenetrable regions in a solvent that restrict the number of the macromolecule configurations.

(E)-(1-(4-Ethoxycarbonylphenyl)-5-(3,4-dimethoxyphenyl)-3-(3,4-dimethoxystyryl)-2-pyrazoline: Synthesis, Characterization, DNA-Interaction, and Evaluation of Activity Against Drug-Resistant Cell Lines

(E)-1-(4-Ethoxycarbonylphenyl)-5-(3,4-dimethoxyphenyl)-3-(3,4-dimethoxystyryl)-2-pyrazoline was synthesized via the cyclization reaction between the monocarbonyl curcuminoid (2E,6E)-2,6-bis(3,4-dimethoxybenzylidene)acetone and ethyl hydrazinobenzoate in high yield and purity (>95% by High-performance liquid chromatography (HPLC)). The compound has been fully characterized by 1H, 13C NMR, FTIR, UV-Vis and HRMS and its activity was evaluated in terms of its potential interaction with DNA as well as its cytotoxicity against resistant and non-resistant tumor cells. Both DNA thermal denaturation and DNA viscosity measurements revealed that a significant intercalation binding takes place upon treatment of the DNA with the synthesized pyrazoline, causing an increase in melting temperature by 3.53 ± 0.11 °C and considerable DNA lengthening and viscosity increase. However, neither re-sensitisation of Doxorubicin (DO X)-resistant breast cancer and multidrug resistance (MDR) reversal nor synergistic activity with DOX by potentially increasing the DOX cell killing ability was observed.

A class of individual-based models

We discuss a class of mathematical models of biological systems at microscopic level - i.e. at the level of interacting individuals of a population. The class leads to partially integral stochastic semigroups- [5]. We state general conditions guaranteeing the asymptotic stability. In particular under some rather restrictive assumptions we observe that any, even non-factorized, initial probability density tends in the evolution to a factorized equilibrium probability density - [4]. We discuss possible applications of the general theory such as redistribution of individuals - [2], thermal denaturation of DNA [1], and tendon healing process - [3]. [1] M. Debowski, M. Lachowicz, and Z. Szymanska, Microscopic description of DNA thermal denaturation, to appear. [2] M. Dolfin, M. Lachowicz, and A. Schadschneider, A microscopic model of redistribution of individuals inside an 'elevator', In Modern Problems in Applied Analysis, P. Drygas and S. Rogosin (Eds.), Bikhauser, Basel (2018), 77--86; DOI: 10.1007/978--3--319--72640-3.[3] G. Dudziuk, M. Lachowicz, H. Leszczynski, and Z. Szymanska, A simple model of collagen remodeling, to appear.[4] M. Lachowicz, A class of microscopic individual models corresponding to the macroscopic logistic growth, Math. Methods Appl. Sci., 2017, on--line, DOI: 10.1002/mma.4680[5] K. Pichor and R. Rudnicki, Continuous Markov semigroups and stability of transport equations, J. Math. Analysis Appl. 249, 2000, 668--685, DOI: 10.1006/jmaa.2000.6968

The relevance of nonlinear stacking interactions in simple models of double-stranded DNA

Single molecule DNA experiments provide interesting data that allow a better understanding of the mechanical interactions between the strands and the nucleotides of this molecule. In some sense, these experiments complement the classical ones about DNA thermal denaturation. It is well known that the original Peyrard–Bishop (PB) model by means of a harmonic stacking potential and a nonlinear substrate potential has been able to predict the existence of a critical temperature of full denaturation of the molecule. In the present paper, driven by the findings of single molecule experiments, we substitute the original harmonic intra-strand stacking potential with a Duffing type potential. By elementary and analytical arguments, we show that with this choice it is possible to obtain a sharp transition in the classical domain wall solution of the PB model and the compactification of the classical solitary wave solutions of other models for the dynamics of DNA. We discuss why these solutions may improve our knowledge of the DNA dynamics in several directions.