Brownian Dynamics Simulation Of Nucleosome Formation In Microfluidic Chip

Chromatin being in the nucleolus is considered as the main organize carryingthe genetic information. The basic structure units of the chromatin are so-callednucleosomal core particles. The nucleosomal core particle is consist of 146 basepairs of negatively charged DNA (of approximate length 50 nm) wraps around apositively charged protein core of a diameter of roughly 8 nm (the histoneoctamer—two molecules of each of H2A, H2B, H3, and H4). The negativelycharged polymer wraps around a cationic protein core about 1.75 turns in acounter-clockwise fashion. It is expected that the manner of packing and thedynamics of nucleosomes are associated with gene activity in living cells.In eukaryotic cells, the diameter of the DNA molecule is about 2nm, but forhuman the length of the DNA is over 1 meter in a nucleus. How is the long DNApacked well-regulated in the mirco-cells?—It is the result of the interactionsbetween DNA and the histone octamer. The DNA is negatively charged and thehistone is a cationic, so the main interaction between them should be theelectrostatic interaction. The electrostatic interaction is not only very important tothe stability of the nucleosome, but the condensation of the chromatin fiber.In this paper, we have considered the electrical double layer into the electricalcharacteristics of nucleosome structural dynamics, and studied the salt-inducedelectrostatic interaction of the nucleosome. The main work of the paper includes:The electrostatic interaction between the DNA and the histone has beenstudied.Generally, the electrostatic charges exist when a solid surface is in contactwith an electrolyte solution. The electrostatic charges on the solid surface attractthe oppositely charged ions and influence the distribution of the nearby ions in theelectrolyte solution. Then an electrical field is established, this area which full ofthe oppositely charged ions is called the electrical double layer (EDL).The DNA is negatively charged while the histone is positively charged, sothere are groups of dissociated ions, which will lead to the electrical double layer.In this paper, the electrostatic interaction of the nucleosome is considered using theEDL theory.The mathematical model of the dynamic of the nucleosome has been founded.According to the EDL theory, the distribution equations of the ions will beobtained. The Poisson-Boltzmann equation obtained by adding the Poissonequation can calculate the potential. Considering different boundary conditions, therepulsion potential and the attraction potential can be calculated.In nucleosome, the free energy of the complex includes the bending potentialof the polymer (as DNA), the electrostatic repulsion potential between thepolymers, and the electrostatic attraction potential between polymer and protein (aspolymer and histone).All the calculated results can be visible by the plot function of the Matlab.The interaction potential energy has been showed.The result of the simulation showed that, the salt concentration influenced thenucleosomal potentials obviously. The electrostatic interaction can be modulated bychanging the salt concentration, and this is very important for the study of thenucleosomal dynamics.It indicates that the EDL effects may be significant in the low saltconcentrations solution, about 0.01M/L, and the repulsion potential may bedominant. Only few part of the DNA is absorbed on the surface of the histone, theDNA takes an extended form with the two strands extend straight away from thehistone because of the larger region controlled by the EDL.In the intermediate salt concentrations solution, about 0.1M/L, the repulsionpotential is lower than those in the low salt concentration, and the partial DNAwraps the histone tightly to keep the electrical balance. The DNA with 146 basepairs will wrap around the histone octamer in about 1.75 superhelical turns.In the high salt concentrations solution, about 1M/L, both of the interactionpotentials decrease. The degressive trend of attraction potential goes faster than therepulsion potential when the ionic concentration is higher than the threshold wherethe repulsion potential and the attraction potential reduce at same pace. Part orwhole of the DNA dewrap from the histone surface, free DNA is in equilibriumwith free histone particles.The Brownian dynamic simulation has been finished.By the Brownian dynamic simulation, the dynamic of the nucleosomeformation has been finished. The moving tracks of the DNA chain and the histoneare described by the Langevin equation.The wraped extend of the nucleosome has been studied. The relationship ofthe wraped extend with the changing of the salt concentration is obtained. The poltis showed that, with the changes of the concentration, the degree of the DNA wrapsaround the histone is different. The concentrations are changed from 0 to 500mM/L;it is found that the wraped extend coefficient is around 1 while salt concentration isaround 100mM/L.The moving of the nucleosome has been simulated by the Brownian dynamicsimulation. Through the figures of the nucleosome in three typical concentrations,it is showed that when the concentration is around 0.1M/L, the whole DNA chainwrapped around the histone, a stable histone/DNA complex is formed. At lower saltconcentrations, at roughly 0.01M/L, an expanded complex is found, only partialDNA wrapped around the sphere while the other extends straight away from thesphere. At higher salt concentrations, at roughly 1M/L, free DNA is in equilibriumwith free histone particles.