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Charge and Exciton Transport in DNA

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Charge and Exciton Transport in DNA Abstract Charge and Exciton Transport in DNA by Rajesh Shresth Doctor of Philosophy in Chemistry Tulane University Alexander L. Burin, Chair The rate of charge transfer and the degree of excited state delocalization in homogeneous DNA bases are investigated theoretically and computationally. In the first part molecular dynamics simulation is used to calculate the reorganization energy associated with charge transfer. The reorganization energy includes high frequency quantum vibrations only fractions of which contribute to charge transfer. Small polaron theory is used to rescale the quantum vibration contribution to reorganization energy and the subsequent charge transfer rate calculated using this quantum corrected reorganization energy is in some case in better agreement with the experiment. Also the RESP charges of AT and GC base pairs used in molecular dynamics is compared with the Mullikan charges obtained from DFT calculation. The RESP charges show that the oxidized AT base pair is more delocalized than oxidized GC base pair. This trend is opposite of what is observed for Mullikan charge obtained from DFT calculation. In the second part degree of excited state delocalization in homogeneous GC strand is calculated. Exciton coupling value between two adjacent GC base pairs that dictates the degree of delocalization is evaluated by fitting Van Vleck sum rule model to the experimental absorption and circular dichroism data. Furthermore the reorganization energy associated with exciton formation is calculated computationally and is used along with exciton coupling value to numerically obtain the degree of excited state delocalization in homogenous GC strand. Dedicated to my parents Acknowledgments I would like to express my deepest gratitude to my advisor, Dr. Alexander Burin for his excellent guidance and continuous encouragement during my time at Tulane University. I have been very fortunate to have a graduate advisor who gave me freedom to venture on my own. My development as a researcher and completion of this dissertation would not have been possible without his support. I would also like to thank the Department of Chemistry at Tulane University and especially the members of my dissertation committee. Furthermore, I would like to ac- knowledge my co-workers, John Leveritt and Arkady Kurnosov, Sarah Tesar and Gale Blaustein for insightful discussion and collaborating on research projects. I appreciate the financial support I received during my graduate studies at Tulane University. I thank Tulane University School of Science and Engineering and Department of Chemistry, the IBM Computational Science Fellowship Program and the National Science Foundation. I am fortunate to have a tight-knit extended family. They have helped me overcome setbacks and stay focused on my graduate study. I am forever indebted to them for their unending love and support. I am also grateful to all my friends for providing support and friendship that I needed. ii Contents I Molecular Dynamics Study of Charge Transfer in DNA 2 1.1 Background: . 3 1.2 Theoretical Model: . 4 1.3 Computational Model: . 9 1.3.1 Force Field: . 9 1.3.2 Numerical Algorithm: . 10 1.3.3 Solvent: . 11 1.3.4 Charge Derivation: . 12 1.3.5 Periodic Boundary Condition: . 13 1.3.6 Non-Bonded Interaction: . 13 1.3.7 Barostat: . 14 1.3.8 Thermostat: . 15 1.4 Calculation and Result: . 16 1.4.1 Monitoring MD simulation: . 17 1.4.2 Reorganization energy calculation: . 28 1.4.3 Decomposition of reorganization energy: . 29 1.4.4 Time Correlation Function: . 34 1.4.5 Rate of hole transfer: . 37 1.5 Conclusion: . 39 II Exciton Delocalization in DNA 41 2.1 Background: . 42 2.2 Theory: . 43 2.3 Experimental Data and Calculations: . 47 2.3.1 Exciton Coupling Calculations: . 51 iii 2.3.2 Inhomogeneous Broadening Calculation: . 52 2.3.3 Exciton Delocalization Length: . 57 2.4 Conclusion: . 61 A Charges for driving force calculations: 62 A.1 Neutral charges in GC and AT base pair used in MD: . 63 A.2 GC RESP charge used for driving force calculation: . 64 A.3 GC DFT charge used for driving force calculation: . 65 A.4 AT RESP charge used for driving force calculation: . 66 A.5 AT DFT charge used for driving force calculation: . 67 B Code for calculating hole transfer in identical adjacent DNA bases. 68 B.1 Fortran code to calculate driving force . 69 B.2 Matlab/Octave code for calculatin reorganization energy: . 74 B.3 Matlab/Octave code to calculate correlation function . 76 B.4 Matlab/Octave code to rearrange the charges. 77 C Detailed equation used for calculating driving force 79 D Program in Matlab to create a structure of GC dimer 82 E ZINDO spectrum of monomer and dimer GC Watson-Crick base pair 84 E.1 Excitation energies and oscillator strengths of GC base pair . 85 E.2 Excitation energies and oscillator strengths of stacked GC Dimer . 87 F Program in Scilab to calculate delocalization length 90 Bibliography 96 iv List of Tables 1.1 Reorganization energy . 29 1.2 Decomposition of reorganization energy different two frequency components 34 1.3 Decay Constants . 36 1.4 Characteristic relaxation time . 37 1.5 Classical rate of hole transfer . 37 1.6 Quantum corrected hole transfer rate . 38 1.7 Correlation between charge localization and reorganization energy . 39 2.8 Reorganization Energy associated with GC S0 − S1excitation. 55 2.9 Delocalization length and its dependence on site-energy. 60 A.1 Neutral charges in GC and AT base pair used in MD: . 63 A.2 GC RESP charge used for driving force calculation. 64 A.3 GC RESP charge used for driving force calculation. 65 A.4 GC RESP charge used for driving force calculation. 66 A.5 GC RESP charge used for driving force calculation. 67 v List of Figures 1.1 Convergence in time of the energy of the system . 18 1.2 Convergence in time of the temperature of the system . 19 1.3 Convergence in time of the pressure of the system . 21 1.4 Convergence in time of the volume of the system . 22 1.5 Convergence in time of the density of the system . 23 1.6 Convergence in time of the RSMD of the system . 25 1.7 Fluctuation in driving force in DNA . 26 1.8 Fluctuation in driving force in DNA . 27 1.9 The normalized spectral density functions J(ω). 30 1.10 The normalized spectral density functions J(ω). 31 1.11 The normalized spectral density functions J(ω). 32 1.12 The normalized spectral density functions J(ω). 33 1.13 Time Correlation Function . 35 1.14 Time Correlation Function . 35 2.15 Skeletal structure of C12−linked DNA hairpins. 48 2.16 Absorption spectra of C12−linked DNA hairpins . 49 2.17 Circular dichroism spectra of C12−linked DNA hairpins. 50 2.18 Schematic diagram of exciton coupling . 53 2.19 Electronic states of GC associated with absorption and fluorescence cycle. 54 2.20 Gaussian fitting of absorption of spectrum of a GC hairpin . 56 C.1 DNA base numbering convention used in our molecular dynamics simulation. 80 vi 1 Introduction In 1953, Waston and Crick showed that DNA has double helix spiral staircase like structure with base pairs acting as rungs. Soon after that discovery Eley and Spivey suggested that pi-stacking interaction between the adjacent bases could allow DNA to conduct charge [1]. However, subsequent experimental progress in the understanding of the electronic property of DNA languished due to difficulty in obtaining DNA in desired quantity and sequence from natural sources; and efficient synthesis of DNA was not pos- sible for two more decades until the breakthrough in phosphoramidite chemistry in early 1983 [2]. Interest in this field was rekindled after the pioneering work of Barton et al. in 1993, where she showed photoinduced long range DNA mediated charge transfer between non-covalently bound metallointercalators [3]. Since then there have been numerous the- oretical and experimental studies in charge and energy transfer property of DNA and the interest in the field is growing rapidly due the possibility of using it in nano-electronics [4], electrochemical biosensors [5], harnessing solar energy [6], repairing oxidative damage in DNA [7], economical DNA sequencing [8]etc. This dissertation “Charge and Energy transfer in DNA,” is a theoretical and computa- tional investigation of charge transfer rate and energy transfer parameter in homogenous DNA sequence. In part I, the quantum effect in the absolute rate of charge transfer between homogeneous adjacent DNA bases is examined. Understanding of hole transfer rate has application in desigining nanowires. In part II, the exciton coupling paramater is calculated by fitting our theroy to an exprimental data. Excion coupling paramater eluci- dates the excited state delocalization behavior of DNA and its understanding is important to use DNA for harnessing solar energy and repairing photodamage in DNA. 2 Part I Molecular Dynamics Study of Charge Transfer in DNA 3 1.1 Background: Theoretical studies of charge transfer in DNA are generally conducted using semi- classical Marcus’ theory [9], where coupling between donor and acceptor in the pre- exponential term is treated quantum mechanically and the reorganization energy in ex- ponential term is treated classically. Marcus equation has a form that looks very much like an Arrhenius equation for the temperature dependence of rate of chemical reaction. k = A.e−Ea/kbT (1.1) where Ea is the activation energy that needs to be overcome by thermal energy kbT for the reaction to occur. For the charge transfer reactions Marcus showed that the activation energy itself depends on solvent reorganization energy and Gibbs free energy difference between the reactant and the product 2 − (λ+4G) k = A.e 4λkbT (1.2) Here ∆G is the Gibbs free energy of reaction, the prefactor A depends upon the strength of the electronic interaction between donor and acceptor and the type of charge transfer, and λ is the reorganization energy that accounts for the structural reorganization of donor- acceptor molecules and the surrounding solvent molecules.
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