The structural flexibility of DNA plays an important role in many biological functions, such as gene replication and expression, DNA-protein recognition, DNA repair and gene regulation. Using orientation quaternion technique via Adaptively Biased Molecular Dynamics (ABMD) method, we explore bending free energy of short DNA fragments including GC<sub>15</sub> in A-, B-, and Z- form, A-tract, as well as codon with mismatches and junctions. The orientation quaternion technique provides an effective method to induce rotational transformations or restrain the orientation of certain domains in a molecular system. This technique, in conjunction with ABMD method, which belongs to the general category of Umbrella sampling methods with a time-dependent potential, allows for an efficient and accurate estimation of the free energy as a function of bending angle and the direction. In addition, adopting various pulling and splitting protocols, we investigate global conformational changes, base-pairing and flipping, and relative stabilities of DNAs. The results are compared to those obtained using the Umbrella Sampling and Steered Molecular Dynamics method, and ultimately are used in order to gain insight into understanding the mechanics of global conformational deformability of DNA molecules.

Calculating bending free energies of different forms of DNA using orientation quaternion based enhanced sampling techniques

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