Lattice model on the rate of DNA hybridization

We develop a lattice model on the rate of hybridization of the complementary single-stranded DNAs (c-ssDNAs). Upon translational diffusion mediated collisions, c-ssDNAs interpenetrate each other to form correct (cc), incorrect (icc), and trap correct contacts (tcc) inside the reaction volume. Correct contacts are those with exact registry matches, which leads to nucleation and zipping. Incorrect contacts are the mismatch contacts which are less stable compared to tcc, which can occur in the repetitive c-ssDNAs. Although tcc possess registry match within the repeating sequences, they are incorrect contacts in the view of the whole c-ssDNAs. The nucleation rate (k_{N}) is directly proportional to the collision rate and the average number of correct contacts (〈n_{cc}〉) formed when both c-ssDNAs interpenetrate each other. Detailed lattice model simulations suggest that 〈n_{cc}〉∝L/V where L is the length of c-ssDNAs and V is the reaction volume. Further numerical analysis revealed the scaling for the average radius of gyration of c-ssDNAs (R_{g}) with their length as R_{g}∝sqrt[L]. Since the reaction space will be approximately a sphere with radius equals to 2R_{g} and V∝L^{3/2}, one obtains k_{N}∝1/sqrt[L]. When c-ssDNAs are nonrepetitive, the overall renaturation rate becomes as k_{R}∝k_{N}L, and one finally obtains k_{R}∝sqrt[L] in line with the experimental observations. When c-ssDNAs are repetitive with a complexity of c, earlier models suggested the scaling k_{R}∝sqrt[L]/c, which breaks down at c=L. This clearly suggests the existence of at least two different pathways of renaturation in the case of repetitive c-ssDNAs, viz., via incorrect contacts and trap correct contacts. The trap correct contacts can lead to the formation of partial duplexes which can keep the complementary strands in the close proximity for a prolonged timescale. This is essential for the extended 1D slithering, inchworm movements, and internal displacement mechanisms which can accelerate the searching for the correct contacts. Clearly, the extent of slithering dynamics will be inversely proportional to the complexity. When the complexity is close to the length of c-ssDNAs, the pathway via incorrect contacts will dominate. When the complexity is much less than the length of c-ssDNA, pathway via trap correct contacts would be the dominating one.