Monte Carlo simulation of melting transition on DNA nanocompartment

DNA nanocompartment is a typical DNA-based machine whose function is dependent of molecular collective effect. Fundamental properties of the device have been addressed via electrochemical analysis, fluorescent microscopy, and atomic force microscopy. Interesting and novel phenomena emerged during the switching of the device. We have found that DNAs in this system exhibit a much steep melting transition compared to ones in bulk solution or conventional DNA array. To achieve an understanding to this discrepancy, we introduced DNADNA interaction potential to the conventional Ising-like Zimm-Bragg theory and Peyrard-Bishop model of DNA melting. To avoid unrealistic numerical calculation caused by modification of the Peyrard-Bishop nonlinear Hamiltonian with the DNA-DNA interaction, we established coarse-gained Monte Carlo recursion relations by elucidation of five components of energy change during melting transition. The result suggests that DNA-DNA interaction potential accounts for the observed steep transition. 1.Introduction Studies on the physical chemistry of DNA denaturation have been lasted for almost forty years [1-3]. In 1964, Lifson proposed that a phase transition exists in one-dimensional polymer structure. He introduced several pivotal concepts, like sequence partition function, sequence generating function, etc., and established a systematic method to calculate the partition function [1]. These allow us to derive important thermodynamic quantities 1 of the system. In 1966, Poland and Scherage applied Lifson’s method to conduct research on amino acid and nucleic acid chains. They built PolandScherage (PS) model for calculating the sequence partition function and discussing the behavior of polymers in melting transitions. Another excellent progress would be the building of Peyrard-Bishop (PB) model [4,5] for DNA chains. In PB model, the Hamiltonian of a single DNA chain, which is constructed by phonon calculations, is given so that we can obtain the system properties through statistical physics method. The PB model has introduced mathematical formula of stacking energy, as well as the kinetic energy and potential energy of each base pair. By theoretical calculation, one can show the entropy-driven transition that leads DNA to shift from ordered state to disorder one [6,7]. However, all these works have not involved the DNA-DNA interactions because the subject investigated is DNAs in bulk solution, and the interaction between them has ever been neglected. The main idea of this paper is to inspect the influence of collective effect on the DNA melting process, primarily motivated by the experiment results of DNA nanocompartment [8,9]. Under the enlightenment of Poland-Scherage model and Zimm-Bragg model [10], we simplify Peyrard-Bishop model to meet a reasonable Monte Carlo simulation by the elucidation of five components of energy changes during melting transition. The result shows that the melting temperature and transition duration depend on whether we take into account the DNADNA interactions among columnar assemblies of DNA. 2.Experiment Recently, we found that specially designed DNA array can form a molecular cage on surfaces [8,9]. This molecular cage is switchable due to allosteric transformation driven by the collective hybridization of DNA. We named it ”active DNA nanocompartment (ADNC)”. Typical DNA motif designed to fabricate ADNC comprises two contiguous elements (inset to figure 1a): a double-stranded DNA (dsDNA) whose array is responsible for a compact membrane (figure 1a, right), and a single-stranded DNA (ssDNA) serving as skeleton supporting the dsDNA membrane, which is terminated on its 5 end by a surface linker such as an alkanethiol group that can be tethered to gold surface with a sulphur-gold bond [9] or an amino group that can be tethered to SiO2 substrate with specific surface attachment chemistry [11]. Because the diameter of ssDNA is much smaller than that of dsDNA, a compartment with designable effective height (heff, 5 ∼ 50nm, commensurate with the length of ssDNA skeleton) can form between the dsDNA membrane and substrate surface. Since ADNC is reversibly switchable, it is able to encage molecules with suitable size. We name this phenomenon molecular encaging effect. Both electrochemical methods [12] and fluorescent microscopy are used to substantiate the molecular encaging effect and the reversibility of switching. 2 Once the closed ADNC entraps some chemical reporters, the surface concentration (Γnc) of the encaged reporters can be determined by cyclic voltammetry or fluorescent microscopy. Figure 1b shows the isotherms of the molecular encaging effect for fluorescein (C20H10Na2O5). Figure 1c presents the melting curves of ADNC. Using the encaged molecules as indicator greatly sharpens the melting profiles for the perfectly complementary targets, and flattens denaturation profiles for the strands with a wobble mismatch. The observation shows that single-base mismatched strands are incapable of closing ADNC on surfaces. The result is highly consistent to our observation by electrochemical analysis [12]. These observations bring up an intriguing question: why the melting curves exhibit so steep transition compared to the case of DNA in bulk solutions or on a loosely packed microarray? We try to address this question in this paper. Worthy of mention is that the steepness of melting transition is useful when the ADNC is applied to DNA detection [8,9]. First, it greatly enhances the discrepancy of perfect targets and single mismatches. This provides much enhanced specificity in DNA recognition, 100 : 1 ∼ 105 : 1 of our system versus 2.7 : 1 of conventional system. Second, more sensitivity is obtained with optimally decreased ambiguity. Therefore, the clarification of the origin of the steep shape should help us to further extend the experience to related fields or generate new techniques. 3.Modeling Taking into account the directional specificity of the hydrogen bonds, the Hamiltonian of a single DNA chain is obtained as following form according to PB model [4-6], Hy = ∑ n [ 1 2 mẏn 2 + w(yn, yn−1) + V (yn) ] (1) where the yn is the component of the relative displacement of bases along the direction of hydrogen bond. The stacking energy w(yn, yn−1) corresponds to the interaction between neighboring base pair in one DNA chain w(yn, yn−1) = k 2 [