Quantum Mechanical Modeling of Self-Reproducible Living PNA Chip Immersed in the

Lipid Bilayer Vesicle Controlled by Quantum Computing Logic Gates

Arvydas Tamulis, Vykintas Tamulis, Jelena TamulieneInstitute of Theoretical Physics and Technology of Vilnius University

A. Gostauto 12, Vilnius 2600, Lithuania; http://www.itpa.lt/~tamulis/

1. Theoretical methods and original software

In order to better understand the origin of life and the production of artificial living

organisms and programmable nano-biorobots we used ab initio quantum mechanical (QM)Hartree-Fock (HF), density functional theory (DFT), QM semiempirical PM3 [1, 2} andmolecular dynamics (MD) NAMD, GROMACS and CHARMM simulations [3-5] toinvestigate various bioorganic systems of artificial minimal living organisms based onpeptide nucleic acid (PNA), photo-sensitizer, lipid precursor and SH anion molecules [6].Quantum modeling of nano-structures self-assembly in PNA based minimal living organismswere performed using our developed software for building PNA double helix [7] andadditionally our implemented code in quantum chemical program packages for thecalculations of extended DFT [8-10] for accurate descriptions of hydrogen bonding and Vander Waals interactions. Our originally developed codes for electron charge and spin densitytunneling calculations and visualization in electronic and magnetic excited states we used forquantum mechanical search of new light harvesting sensitizers in artificial living organismsand for quantum modeling of molecular electronics and spintronics logical elements in PNAbased minimal living organisms [11, 12].

2. Research stages of quantum mechanical modeling of self-reproducible and logically

controlled living PNA chip

Quantum mechanical modelings of self-reproducible and logically controlled living PNAchips were divided into five research stages:

1) Elementary acts of PNA chip computing are self­assembling of supramoleculesadenine::thymine and guanine::thymine. Systematic exact QM investigations of self-assemblyenergy of formation for supramolecules adenine::thymine and guanine::thymine were

performed using ab initio HF and non local gradient and extended DFT models includingelectron correlations: B3PW91, B3LYP, PBELYP, PBEPBE [1, 2], X3LYP [9] in additionwith base set superposition error methodology [10]. The best result for G-C pair energy offormation was obtained using X3LYP model using diffusion and polarization basis sets isequal to 61 kcal/mol [13].

2) Self-formation of large fragments of PNA suitable for construction of PNA chipspossessing the protogene information was done by Vykintas Tamulis developed software forbuilding PNA double helix [13].

3) Self-assembly of fragment of PNA chip: twelve nucleobases PNA double helix -tree 1,4-bis(N,N-dimethylamino)naphthalene sensitizers and lipid precursor molecules surrounding by

QUANTUM MECHANICAL MODELING OF SELF-REPRODUCIBLE LIVING PNA CHIP IMMERSED IN THE LIPID BILAYER VESICLE

CONTROLLED BY QUANTUM COMPUTING LOGIC GATES

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water molecules immersed in lipid molecules bilayer was modeled by QM HF, DFT, PM3methods and MD NAMD, GROMACS and CHARMM simulations (see figure bellow) [14].

Water molecules in this image are omitted for the better seeing all details.The lipid bilayer vesicles surrounding the PNA chip possessing artificial photo-synthetic system

including 1,4-bis(N,N-dimethylamino)naphthalene sensitizer and lipid precursor moleculeswere modeled by DFT, PM3 and molecular dynamics NAMD and GROMACS methods. Vesicle

composed from around 100000 atoms was built starting from exact quantum mechanical studies ofseparate molecules, later were performed DFT investigations of self-assembling to nucleobases

dimers and photosynthetic supramolecules and finally was done molecular dynamics processing ofself-formation of entire artificial minimal living vesicle [13].

4) Quantum mechanical processes of self-reproduction of PNA chip possessing artificialphotosynthetic system were systematically investigated using time dependent (TD) DFTmethod. Absorption spectra and relative positions of the HOMO and LUMO eigenvalues oflipid precursor and sensitizers: 1,4-bis(N,N-dimethylamino)naphthalene, 1,4-dihydroquinoxaline and 7,8-dimethylisoalloxazine molecules show that our new investigatedsensitizers 1,4-dihydroquinoxaline and 7,8-dimethylisoalloxazine molecules are good forusage them in the PNA chips because their HOMO are enough high relatively LUMO of lipidprecursor molecule and absorption spectra are in the visible region [15]. It was calculated andvisualized electron tunneling in our optimized self-assembled supramolecule: cytosinePNAfragment-sensitizer 1,4-bis(N,N-dimethylamino)naphthalene and lipid precursor moleculesusing TD DFT method. HOMO-LUMO (first excited state) transition is equal to 439.21 nmwavelength in absorption spectrum of this supramolecule. HOMO-LUMO transition leadswith 0.988 electron tunneling from sensitizer molecule to lipid precursor molecule. The sameelectron tunneling is in the third excited state [13]. The applying of extended TD DFT for

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TNT2005 29 August - 02 September, 2005 Oviedo-Spain

accurate descriptions of hydrogen bonding and Van der Waals interactions, the usage ofdiffusion basis set and surrounding this self-assembled supramolecule by water moleculesgives the HOMO-LUMO (first excited state) transition equal to 573.33 nm [13].

5) We have also explored the possibility of using programmable PNA chip possessingphotosynthetic systems in molecular electronics and spintronics installing classical Booleanand quantum logics gates and logically controlled molecular machines. For this were donedetailed quantum mechanical investigations of electronic and spintronic structure and NMRspectra of biliverdin Cu, Co, Zn dimers and ESR spectra of endohedral fullerene ErSc2@C80

and neutral radical molecules: beta-diketone and dodecyl syringate [16]. It was suggestedrecently that self-assembling systems could be used to create a macroscopic ensemble ofquantum entangled 3-spin groups, as a first step in quantum information processing. Thespins of such a group could be connected by dipole-dipole interaction. Application of anonuniform external magnetic field would allow selective excitation of every spin inside thegroup. The proper sequence of resonant electromagnetic pulses would drive all spin groupsinto the 3-spin entangled state. In the suggested proposal the spins were associated with asingle unpaired electron spin of a neutral radical molecule in the self-assembled systems. Oneof the key elements of this strategy is the proper choice of molecules for experimentalimplementation of the proposal. Involved in this choice are four criteria for the chemicalstructure of these molecules:

1) A specific group or structural elements to provide self-organization characteristics;2) A specific group to provide an attachment of the molecule to a substrate in SAM;3) An unpaired, spatially localized electronic spin representing an elementary qubit;4) Strong non-compensated valence bonds, which are responsible for the unpaired electron

spin, to provide the chemical stability of a qubit.Modern quantum chemical methods provide powerful tools for theoretical modeling and

analysis of molecular electronic structure and may be used to guide the synthetic effort. Inparticular, the small carbon-centered π-radical molecules (8-14 atoms) possessing a β-

diketone structure have been investigated in the scope of unrestricted Hartree-Fock (UHF)and unrestricted density functional theory (UDFT) methods. It was shown that an unpaired,spatially localized electronic spin representing an elementary qubit and strong non-compensated valence bonds, which are responsible for the unpaired electron spin, to providethe chemical stability of a quantum bit (qubit). Electronic g-tensor shift along the long axis ofour investigated β-diketone neutral radical molecule is close to free-electron g-factor and

therefore entirely determined by first order contributions to electronic g-tensor shift, i.e. canbe influenced only slightly by environment due to the fact that first order contributions to g-tensor shift solely determined by spin density distribution in radical. Rotation of the radicalaround the long axis will not change g-factor of molecule along the long axis as well due tothe orientation of it g-tensor principal axes.

The neutral dodecyl syringate radical molecule is suggested as a candidate for molecularESR quantum computers. First principles quantum chemical calculations indicates that thismolecule with a stable delocalized electron spin may represent a qubit in quantuminformation processing. The spin density analysis exhibits that unpaired spin of radicalmolecule is delocalized in the region of entire hexagonal ring where the non-compensated

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valence bond is delocalized. The spin density shifts are investigated in five electronic excitedstates using configuration interaction (CI) unrestricted Hartree-Fock (UHF) time dependent(TD) method with EPR-II basis. The spin density shifts are more essential in first, fourth andfifth excited states that might be used for designing of controlling gates in quantuminformation processing. It was found that exist internal local spin density flips in the first andfifth electronic excited states. Isotropic Fermi contact couplings constants and anisotropicspin dipole couplings were investigated and indicated the largest hyperfine splittings (HFS)of electron spin resonance (ESR) spectra on atoms of above mentioned region of delocalizednot-compensated valence bonds.

The investigated qubits in biliverdin dimers, endohedral fullerene and neutral radicalmolecule allowed us to design and implement a set of molecular electronics AND, OR, XOR,ControlNOT logically controlled molecular machines to the PNA in order to controlprocesses of self-replication and photosynthesis in the artificial living organisms.

References

1. M. J. Frisch, et al, Gaussian 03, RevC.01, Gaussian, Inc., Pittsburgh PA, 2005

2. GAMESS­US license agreement: M.W. Schmidt, K.K. Baldridge, J.A. Boatz, S.T. Elbert,M.S. Gordon, J.H. Jensen, S. Kosecki, N. Matsunaga, K.A. Nguyen, S.J.Su, T.L. Windus, M.Dupuis, J.A. Montgomery, J. Comput. Chem. 14, 1347­1363 (1993.3. http://www.ks.uiuc.edu/Research/namd/4. http://www.csar.cfs.ac.uk/user_information/software/chemistry/namd.shtml

5. http://www.netsci.org/Resources/Software/Modeling/MMMD/6. S. Rasmussen, L. Chen, M. Nilsson, and S. Abe; Artificial Life, vol 9, 267-316, 2003).

7. Vykintas Tamulis developed software for building PNA double helix.

8. Perdew, J. P., Burke, K. & Ernzerhof, M. (1996) Phys. Rev. Lett. 77, 3865-3868.9.Xin Xu, William A. Goddard III, "The X3LYP extended density functional for accuratedescriptions of nonbond interactions, spin states, and termochemical properties",www.pnas.org/cgi/doi/101073/pnas.0308730100 PNAS, March 2, 2004, vol. 101, no. 9,2673-2677.10. A. Bende, A. Vibok, J. Halasz, S. Suhai, “BSSE-Free Description of the FormamideDimers”, International J. Quantum Chemistry”, vol. 84, 617-622 (2001).11. A. Tamulis, J. Tamuliene, V. Tamulis, "Quantum Mechanical Design of Photoactive Molecular

Machines and Logical Devices", 11th chapter in "Handbook of Photochemistry and Photobiology",Vol. 3 "Supramolecular Photochemistry", Ed. H.S. Nalwa, American Scientific Publishers, p.p. 495-

553, 2003.12. J. Tamuliene, A. Tamulis, J. Kulys, “Electronic Structure of Dodecyl Syringate Radical Suitable

for ESR Molecular Quantum Computers", Nonlinear Analysis: Modelling and Control, Vol. 9, No. 2,2004, p. 185-196.

13. Arvydas Tamulis, Vykintas Tamulis, Andrzej Graja, “Quantum mechanical modelling ofphotosynthetic system self-assembly in PNA based artificial living organisms”, article prepared for

publication to the Journal of Structural Chemistry, March 2005.14. Arvydas Tamulis, Vykintas Tamulis, Steen Rasmussen, “Quantum Molecular Dynamics Self-

Assembly of PNA Artificial Photosynthetic System on Lipid Bilayer”, paper completing for

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publication.15. J. Tamuliene, A. Tamulis, “Quantum Mechanical Investigations of 1,4-dihidrochinoksaline and

7,8-dimetilizoaloksazine for sensibilization of self-assembled system consist of PNA and LipidMolecules”, article submitted to the Journal of Structural Chemistry, November 2004.

16. Arvydas Tamulis, Jelena Tamuliene, Vykintas Tamulis, “Quantum Mechanical Investigations ofElectronic Structure, Spectra, Electron Charge and Spin Density Transfer and Magnetically Features

of Syringate Radical Molecule Based Logical Gates of ESR Molecular Quantum Computers”, articleprepared for publication in the Journal of Structural Chemistry, March 2005.

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TNT2005 29 August - 02 September, 2005 Oviedo-Spain