| The studies of essence and heredity of DNA are of importance to the whole human being. Due to the inclusion of precious information about growth,evolution,disease and aging, the human genome project not only receives the assistance of the governments of America, United Kingdom, France, Japan Germany and China, but also attracts the plunge of many scientists in the fields of mathematics, physics, chemistry, computation, material and mechanics.In the early study, the averaged quantities can be obtained through the experiments of light scattering, birefringence and rheological stress, which represent a step forward to the understanding of DNA. But the strong heterogeneity of individual DNA chains can't be discovered. With the continuous development of science and technology, single DNA molecule can be manipulated by optical tweezers, magnetic tweezers and optical fiber. By the use of electron microscopy, fluorescence microscopy and scanning microscopy, conformational changes of DNA can be observed.Stretching and monitoring the single DNA offers advantages for gene mapping. The available methods are extending DNA combing on a surface, moving DNA through a nanochannel, stretching DNA through contraction, the unwinding of DNA in a uniform flow, the electrophoretical stretching of DNA, response of DNA to elongational flow and shear flow, single DNA molecule stretching in microcontractions, gels and hybrid gel-microcontraction devices. The above methods have provide a guarantee for the smooth implementation of human genome project, but there exist some shortcomings such as complicateion to operate and low efficiency to stretch DNA. To overcome these shortcomings, we propose a new microchannel which combines the hyperbolic contraction and a cylindrical obstruction. In this work, the Brownian dynamics and finite element method can be employed to simulate the stretching dynamics of T4 DNA in the combined microchannel as well as in the hyperbolic contraction.We model the T4 DNA as N beads with same radius connected by N-1 springs. Brownian dynamics simulation, which is introduced by Ermak and McCammon, can be used to obtain the trajectory of DNA. We use "Predictor - corrector method" to solve equations of motion, which promises high accuracy and less calculation time. The governing equation for the electrostatic potential is Laplace equation. In this work, we employ the finite element method with the Dirichlet conditions in the inlet and outlet, the Neuman conditions on the walls. In order to connect between the Brownian dynamics and the finite element method, we have developed a new two-time interpolation algorithm to address the electric field at each bead's position.The important parameters such as the length of the DNA chain, the number of spring, the Kuhn length, the radius of beads and the excluded volume parameter are set as: { }L = 70μm , N s = 34, N k ,s= 19.8, a = 77 nm ,υ= 0.0012μm. Thirty initial conformations are recorded Every period of the longest relaxation time, which include the kinked conformation, folded conformation, dumbbell conformation, and coiled conformation.By comparing the stretching process of T4 DNA in the single hyperbolic contraction and the new combined microchannel, the conclusion can be obtained as following:Firstly, because of the pre-stretching of the cylindrical obstruction, the ensemble average fractional extension in the combined microchannel is obvious higher than that in the single hyperbolic contraction. The location and the radius of the cylindrical obstruction may have effect on the pre-stretch.Secondly, the competitive effect of the strain rate (or Deborah number), the Brownian fluctuation and the conformation in the front of the entrance of the hyperbolic contraction can decide the stretching of DNA.In this study, the advantage of our new microchannel has proved. Moreover, the numerical simulation methods can be used to study the polymer behavior. Our work will provide the theoretical guidance and technical support for the design and development of biological chips.
|
PDF Full Text Request