A study of conformational response of DNA to nanoconfinement by monte carlo simulation

A Study of Conformational Response of DNA to Nanoconfinement by Monte Carlo Simulation NG SIOW YEE NATIONAL UNIVERSITY OF SINGAPORE 2012 A Study of Conformational Response of DNA to Nanoconfinement by Monte Carlo Simulation NG SIOW YEE (B.Sc. (Hons.), M.Sc. (Dist.)) University of Malaya Supervisor: Assoc. Prof. Johan R. C. van der Maarel Co-supervisor: Prof. Feng Yuan Ping A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF PHYSICS FACULTY OF SCIENCE NATIONAL UNIVERSITY OF SINGAPORE 2012 To my beloved mother, grandma, sister and brother and in the memory of our beloved father . Contents Contents i Summary v List of Publications vii Acknowledgements ix Introduction 1.1 Synopsis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1 About DNA . . . . . . . . . . . . . . . . . . . . . . . 1.3 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . 1.3.1 Supercoiling . . . . . . . . . . . . . . . . . . . . . . . 1.3.2 Linear DNA in nano-confinement . . . . . . . . . . . 1.4 Research Objectives . . . . . . . . . . . . . . . . . . . . . . . 12 Computer simulation 15 2.1 Synopsis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3 A Brief Review on Statistical Mechanics . . . . . . . . . . . 17 2.4 Methods of Computer Simulation . . . . . . . . . . . . . . . 21 2.4.1 Molecular Dynamics . . . . . . . . . . . . . . . . . . 22 2.4.2 Brownian Dynamics . . . . . . . . . . . . . . . . . . 23 2.4.3 Monte Carlo Method . . . . . . . . . . . . . . . . . . 25 i ii CONTENTS 2.5 Benchmarking . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.5.1 Random Number Generator . . . . . . . . . . . . . . 28 2.5.2 Computational Efficiency . . . . . . . . . . . . . . . . 31 Supercoiled DNA in a nanochannel 41 3.1 Synopsis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.2 Theory: Wormlike Chain Model . . . . . . . . . . . . . . . . 42 3.3 Simulation Protocol . . . . . . . . . . . . . . . . . . . . . . . 45 3.3.1 Closed-Circular DNA Model . . . . . . . . . . . . . . 45 3.3.2 CCDNA in a Cylindrical Confinement . . . . . . . . 47 3.3.3 Types of Monte Carlo Moves . . . . . . . . . . . . . . 47 3.3.4 Parameter Values . . . . . . . . . . . . . . . . . . . . 48 3.3.5 Benchmarking . . . . . . . . . . . . . . . . . . . . . . 50 3.3.6 Tests for Equilibration . . . . . . . . . . . . . . . . . 50 3.3.7 Reversible Work . . . . . . . . . . . . . . . . . . . . . 51 3.4 Results & Discussion . . . . . . . . . . . . . . . . . . . . . . 52 3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 A Quantitative Study: Simulation with SANS Experiment 61 4.1 Synopsis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 4.2 Theory of Small Angle Neutron Scattering . . . . . . . . . . 62 4.3 Materials and Methods . . . . . . . . . . . . . . . . . . . . . 65 4.3.1 Preparation of sample . . . . . . . . . . . . . . . . . 65 4.3.2 Neutron scattering . . . . . . . . . . . . . . . . . . . 65 Simulation Protocol . . . . . . . . . . . . . . . . . . . . . . . 67 4.4.1 Simulation Models . . . . . . . . . . . . . . . . . . . 67 4.4.2 Types of Monte Carlo Moves . . . . . . . . . . . . . . 70 4.4.3 Parameter Values . . . . . . . . . . . . . . . . . . . . 70 4.4.4 Benchmarking . . . . . . . . . . . . . . . . . . . . . . 72 4.4.5 Tests for Equilibration . . . . . . . . . . . . . . . . . 75 4.5 Results & Discussion . . . . . . . . . . . . . . . . . . . . . . 77 4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.4 iii CONTENTS Linear DNA confined in a nanochannel 85 5.1 Synopsis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 5.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 5.2.1 Cooperativity model (S-loop model) . . . . . . . . . . 87 5.2.2 Free energy cost of a hairpin formation and a S-loop growth 90 5.2.3 C-loop model . . . . . . . . . . . . . . . . . . . . . . 90 5.3 Simulation Protocol . . . . . . . . . . . . . . . . . . . . . . . 91 5.3.1 Simulation Model . . . . . . . . . . . . . . . . . . . . 91 5.3.2 Types of Monte Carlo Moves . . . . . . . . . . . . . . 93 5.3.3 Parameter Values . . . . . . . . . . . . . . . . . . . . 94 5.3.4 Benchmarking . . . . . . . . . . . . . . . . . . . . . . 94 5.3.5 Tests for Equilibration . . . . . . . . . . . . . . . . . 95 5.4 Results & Discussion . . . . . . . . . . . . . . . . . . . . . . 96 5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 Conclusions and Future Work 101 6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 6.2 Recommendations for Future Research . . . . . . . . . . . . 104 A Derivation of Scaling Laws 109 A.1 Odijk’s deflection regime . . . . . . . . . . . . . . . . . . . . 109 A.2 Daoud and de Gennes’s blob regime . . . . . . . . . . . . . . 111 B Writhe Evaluation 113 C Contrast variation in neutron scattering 117 D DNA in nematic potential 119 E Small Angle Light Scattering 121 E.1 Experimental Procedure . . . . . . . . . . . . . . . . . . . . 121 E.2 Simulation Protocol . . . . . . . . . . . . . . . . . . . . . . . 123 F Derivation of Relative Extension 125 iv CONTENTS G Derivation of ⟨Ns ⟩ and ⟨Nd ⟩ 127 H Derivation of u (fs , Ls , Dtube ) and s (fs , Ls , Dtube ) 129 I 131 Derivation of Orientational Order Parameter List of Figures 133 List of Tables 135 Bibliography 137 Summary In this thesis, the conformational response of DNA to cylindrical confinement is explored by using Monte Carlo computer simulation. Two types of DNA configurations are used in the present simulations. They are closedcircular/supercoiled and linear configurations. First, the Monte Carlo computer simulations were carried out to explore how the restriction of the configurational degrees of freedom by a cylindrical potential, which mimics confinement in a nanochannel, alters certain structural properties of the supercoil. The simulation results were used for interpretation of the emerging structure and energetics with the wormlike chain model, including the effects of the hard wall, charge, elasticity, and configurational entropy. The present simulation model was further employed to simulate a single supercoiled DNA molecule in a dense solution simply by modeling a test supercoiled DNA molecule confined within a cylindrical potential so as to mimic an effective dense surroundings. The form factors obtained from the simulations were compared with the form factors obtained from small angle neutron scattering experiment in zero-average contrast condition, which are freed from the complication by intermolecular interference. From the combination of scattering experiments and computer simulations, the interduplex distance of supercoiled DNA will then be derived and discussed, in terms of screened electrostatics and molecular interaction. The conformation of a linear DNA chain in the transition range between the deflection and blob regimes was explored by using the cooperativity model. In this range, the confined chain is neither in the full deflection v APPENDIX I. DERIVATION OF ORIENTATIONAL ORDER PARAMETER 132 Subsequently, Eq. (I.4) is substituted into Eq. (I.3) and ⟨φ2 ⟩ is expressed as the following ⟨ φ ⟩ ( = c0 Dtube Lp )2/3 (I.5) where c0 is the prefactor for the equation [34]. By substituting Eq. (I.5) into Eq. (I.2), the orientational order parameter for the strong confinement is then obtained: ( ⟨P2 (cos φ)⟩ = − 3c where c0 = 2c and c = 0.1701 [66]. Dtube Lp )2/3 (I.6) List of Figures 1.1 Tertiary structure of supercoiled DNA . . . . . . . . . . . . . . 1.2 Regular and irregular plectoneme . . . . . . . . . . . . . . . . . 1.3 A schematic figure of relative extension versus channel diameter 2.1 Trend of modern science advancement . . . . . . . . . . . . . . 16 2.2 Main body of Metropolis-Monte-Carlo algorithm . . . . . . . . . 35 2.3 Parking lot test part . . . . . . . . . . . . . . . . . . . . . . . 36 2.4 Parking lot test part . . . . . . . . . . . . . . . . . . . . . . . 37 2.5 Normalized histogram plot of uniformity test . . . . . . . . . . . 38 2.6 Graph ⟨Re2 ⟩ vs N lb2 and ⟨Rg2 ⟩ vs N lb2 . . . . . . . . . . . . . . . . 39 2.7 Benchmarking the algorithms . . . . . . . . . . . . . . . . . . . 40 3.1 Monte Carlo relaxation time profiles . . . . . . . . . . . . . . . 52 3.2 Snapshots of supercoiled DNA in nanotube . . . . . . . . . . . . 53 3.3 Writhe versus tube diameter . . . . . . . . . . . . . . . . . . . . 55 3.4 Inter-vertex distribution function . . . . . . . . . . . . . . . . . 55 3.5 Diameter of the supercoil . . . . . . . . . . . . . . . . . . . . . . 56 3.6 Free energy of bending, twisting, electrostatic and confinement . 58 4.1 Schematic diagram of the SANS experiment . . . . . . . . . . . 64 4.2 Schematic diagram of the SANS diffractometer D11 at ILL . . . 66 4.3 Form factor and structure factor vs momentum transfer . . . . . 68 4.4 Radii of gyration of open-circular DNA vs ionic strength . . . . 73 4.5 Snapshots of supercoiled DNA in nematic field . . . . . . . . . . 74 133 134 LIST OF FIGURES 4.6 Writhe and interduplex distance vs nematic strength . . . . . . 76 4.7 Distribution function vs the intervertex distance . . . . . . . . . 76 4.8 Normalized form factor vs momentum transfer . . . . . . . . . . 77 4.9 Cylinder diameter vs DNA concentration . . . . . . . . . . . . . 79 4.10 Interduplex distance vs DNA concentration . . . . . . . . . . . 80 5.1 Graph L∥ /Lc vs Dtube /Lp . . . . . . . . . . . . . . . . . . . . . 86 5.2 Identify S- and C-loop on a DNA conformation . . . . . . . . . 88 5.3 (a) Graph fs vs Dtube /Lp (b) Graph Ls vs Dtube /Lp . . . . . . . 96 5.4 (a) Graph Fu vs Dtube /Lp (b) Graph Fs vs Dtube /Lp . . . . . . . 97 A.1 Figure for two classical regimes . . . . . . . . . . . . . . . . . . 109 B.1 Construction of quadrangles on a unit sphere . . . . . . . . . . 114 List of Tables 2.1 Quantifying uniformity tests of pseudo-random number generator 30 3.1 Parameters setup for CCDNA in cylindrical confinement . . . . 49 3.2 Benchmark our result with available simulation data . . . . . . 51 4.1 Simulation parameters setup for SANS . . . . . . . . . . . . . . 72 5.1 Parameter setup for LDNA in cylindrical confinement . . . . . . 94 5.2 Benchmark our simulation result with theory . . . . . . . . . . . 95 5.3 Fitting parameters for Fs and Fu . . . . . . . . . . . . . . . . . 98 E.1 Simulation parameter setup for SALS . . . . . . . . . . . . . . . 124 135 Bibliography [1] R. 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INTRODUCTION 3 plementary bases A and T or C and G, as well as by van der Waals interactions between the stacked bases Each turn of the helix consists of 10 base pairs (bp) The helix has a distance of 3.4 nm repeated between each successive turn It has a width of 2.0 nm and the bases are perpendicular to the helical axis [4] For other configurations such as A- DNA and Z -DNA, the reader is referred to these references... freedom that a system has A group of microscopic states with the same values of macroscopic variables such as energy level, pressure, etc., defines a macroscopic state (or macrostate) To gain insight on the macroscopic properties of a physical system, data analysis is carried out on the ensemble by statistical means Such statistical tools are known as Statistical Physics (also known as Statistical Mechanics)... average of an macroscopic observable, A is defined by A = ∑ 1 ∑ Hn An exp(− )= An pn Q n kB T n (2.3) Similarly, the thermal average of the square of the macroscopic observable A is written as A2 ⟩ = ∑ 1 ∑ 2 Hn An exp(− )= A2 pn n Q n kB T n (2.4) The mean square fluctuation of observable A is then given by ⟨ A2 ⟩ = A2 ⟩ − A 2 (2.5) and is equal to variance of A for large system [83] • In a physical... Computer simulation is a computer program which is designed to simulate the behaviour of a real physical system via a simplified complex model It generates a vast amount of data that need to be statistically analyzed in order to gain insight into the system To validate and improve the simplified complex model used, simulation results are then gauged with available experimental and theoretical results... techniques and incorporation with existing biological techniques have made nanoconfinement a promising tool for studying single DNA molecules The results of DNA in nanoconfinement are also invaluable for the development of a better genome analysis platform [20, 55, 56] as well as the understanding of biological processes such as DNA packaging in viruses or segregation of DNA in bacteria [57, 58] Other applications... quantitative and systematic way List of Publications 1 Wilber Lim, Siow Yee Ng, Chinchai Lee, Yuan Ping Feng, and Johan R.C van der Maarel, Conformational Response Of Supercoiled DNA To Confinement In A Nanochannel, The Journal of Chemical Physics 129, 165102 (2008) 2 Xiaoying Zhu, Siow Yee Ng, Amar Nath Gupta, Yuan Ping Feng, Bow Ho, Alain Lapp, Stefan U Egelhaaf, V Trevor Forsyth, Michael Haertlein, Martine... that DNA itself is the genetic material [1] Then in 1953, James D Watson and Francis Crick successfully resolved the chemical structure of the DNA according to X-ray diffraction results by Rosalind Franklin and Raymond Gosling In fact, they knew in advance from Erwin Chargaff that DNA bases must exist in pairs [1, 3] Due to their discovery of the double-helix DNA model, major advancements have been made... Moulin, Ralf Schweins, and Johan R C van der Maarel, Effect of crowding on the conformation of interwound DNA strands from neutron scattering measurements and Monte Carlo simulations, Physical Review E 81 (Issue 6), 061905 (2010) 3 Siow Yee Ng, Liang Dai, Patrick S Doyle, and Johan R.C van der Maarel, Conformation model of back-folding and looping of a single DNA molecule confined inside a nanotube, ACS Macro... are useful when devising simulation methods and interpreting simulation results Besides that, a description on the standard simulation methods are reviewed in term of their formalism, advantages and limitations Last but not least, the benchmarking of the pseudo-random number generator employed and the efficiency of the simulation algorithms are demonstrated to illustrate the reliability of the simulations... SUMMARY conformation, nor a series of blobs representation Hairpins are expected to form along the chain due to thermal fluctuations The two-parameter cooperativity model was applied to describe the hairpin formations in term of S-loop formations and its growth along the chain The cooperativity model was then compared with Monte Carlo computer simulation in order to study the transition regime in a quantitative . A Study of Conformational Response of DNA to Nanoconfinement by Monte Carlo Simulation NG SIOW YEE NATIONAL UNIVERSITY OF SINGAPORE 2012 A Study of Conformational Response of DNA to Nanoconfinement. in a quantitative and systematic way. List of Publications 1. Wilber Lim, Siow Yee Ng, Chinchai Lee, Yuan Ping Feng, and Johan R.C. van der Maarel, Conformational Response Of Supercoiled DNA To. 3 plementary bases A and T or C and G, as well as by van der Waals inter- actions between the stacked bases. Each turn of the helix consists of 10 base pairs (bp). The helix has a distance of 3.4