Relaxation in biological macromolecules: Properties of some exact solutions

Sequence-dependent theory of oligonucleotide hybridization kinetics

A theoretical approach to the prediction of the sequence and temperature-dependent rate constants for oligonucleotide hybridization reactions has been developed based on the theory of relaxation kinetics. One-sided and two-sided melting reaction mechanisms for oligonucleotide hybridization reactions have been considered, analyzed, modified, and compared to select a physically consistent as well as robust model for prediction of the relaxation times of DNA hybridization reactions that agrees with the experimental evidence. The temperature- and sequence-dependent parameters of the proposed model have been estimated using available experimental data. The relaxation time model that we developed has been combined with the nearest neighbor model of hybridization thermodynamics to estimate the temperature- and sequence-dependent rate constants of an oligonucleotide hybridization reaction. The model-predicted rate constants are compared to experimentally determined rate constants for the same oligonucleotide hybridization reactions. Finally, we consider a few important applications of kinetically controlled DNA hybridization reactions.

The effect of sequence heterogeneity on DNA melting kinetics

We consider kinetics of the cooperative melting of DNA sections situated at the edge of the helix. Accurate calculations based on the real sequences of such sections demonstrate that their internal heterogeneity has a drastic effect on the melting kinetics. Allowance for the internal heterogeneity increases the relaxation time by several orders of magnitude as compared with a model based on the assumption of equal base-pair stability within a section. The relaxation times obtained are in good agreement with the experimental data of Suyama and Wada (A. Suyama and A. Wada, Biopolymers, 23, 409 (1984)). An analysis of the melting process revealed some simple sequence characteristics that determine its rate. An examination of the temperature dependence of the relaxation time led to a distinct interpretation of the apparent activation energies of the denaturation and renaturation. The relaxation time proved to reach its maximum near the equilibrium melting point of the section examined.

On the mapping of chains of first order chemical reactions on random walks

We present the transient solution to a random walk problem which characterizes chemical kinetic processes in which a particular state may have a finite number of internal states. While there are many chemical and physical examples, we introduce the solution through models of biophysical interest.