Influence of Media Disorder on DNA Melting: A Monte Carlo Study

We explore the melting of a lattice DNA in the presence of atmospheric disorder, which mimics the crowded environment inside the cell nucleus, using Monte Carlo simulations. The disorder is modeled by randomly retaining lattice sites with probability $p$ while diluting the rest, rendering them unavailable to the DNA. By varying the disorder over a wide range from $p=1$ (zero disorder) up to the percolation critical point $p_c=0.3116$, we show the melting temperature $(T_m)$ to increase nearly linearly with disorder up to $p\approx 0.6$, while strong non-linearity enters for $p\lesssim 0.6$. Associated changes in the bubble statistics have been investigated, showing a substantial change in the bubble size exponents at corresponding melting points for $p\leq 0.5$. Based on these findings two distinct disorder regimes showing weak and strong effects on melting are identified. For simulations, we use the pruned and enriched Rosenbluth method in conjunction with a depth-first implementation of the Leath algorithm to generate the underlying disorder.