The continuum limit of the Poland-Scheraga DNA denaturation model

Abstract

Using a field theory equivalent to a lattice version of the Poland-Scheraga (PS) model, the phase diagram for a long DNA molecule is derived in closed form. A one-loop renormalization group calculation for the generalized PS model with excluded volume interactions shows that there are two stable fixed points. At both fixed points, the excluded volume effect plays a role. At the fixed point reached when the original excluded volume effect is weak, the phase transition is continuous. At the other fixed point, the phase transition is first order.

Figures (4)

• Figure 1: Two DNA single strands can pair only at same distance $s$ from the endpoints. The length is measured from $3'$ to $5'$ on the template strand and from $5'$ to $3'$ on the other strand. The only allowed conformations then are a sequence of loops.
• Figure 2: Single strand mass $m_{\varphi}$ as a function of pairing energy $r_{0}=c_{\varphi}-\beta E_{\varphi}$ with $\Lambda^{-1}$ as length unit for fixed total length 200, $W=1$ and various coupling constant values $\lambda^{2}$.
• Figure 3: One loop renormalizations due to the excluded volume interactions (wiggly line). The heavy lines in the diagrams A, B and C can be a single strand or a double strand. The wavevector $k$ indicates the symmetry point used in the renormalization.
• Figure 4: The flow of $u_{\psi}$, $u_{\varphi\psi}$ and $\lambda$ projected into the $u_{\varphi\psi}$-$\lambda$-plane. The initial value for $u_{\psi}$ is $1/8$. There are two stable fixed points: the usual excluded volume fixed point with $\lambda=0$ and a DNA-specific fixed point with $\lambda\neq0$ and $u_{\varphi}\neq0$.