QUANTUM SELF-ASSEMBLY OF ARTIFICIAL MINIMAL LIVING CELLS AND MOLECULAR
ELECTRONICS CONTROL
Arvydas Tamulis
Vilnius University Institute of Theoretical Physics and Astronomy,
A. Gostauto 12, Vilnius, Lithuania.
E-mail: tamulis@itpa.lt(Received November 14, 2007; Accepted March 12, 2008)(Abstract)
Artificial minimal living cells and their substructuresare quantum mechanically self-assembling due tocompetition of weak electrostatic forces and weak
attraction Van der Waals dispersion forces, and hydrogenbonds originated due to electron correlation interactions
among biological and water molecules. The best
available method to simulate in minimal cells these weakelectrostatic and Van der Waals dispersion forces, andhydrogen bonds is to perform quantum mechanical nonlocal density functional potential calculations of artificial
minimal living cells consisting of around 400 atoms. The
cell systems studied are based on peptide nucleic acidand are 3.0 – 4.5 nm in diameter. The electron tunnelingand associated light absorption of most intensetransitions as calculated by the time dependent density
functional theory method differs from spectroscopic
experiments by only 0.3 nm, which are within the valueof experiment errors. This agreement implies that thequantum mechanically self-assembled structure ofartificial minimal living cells very closely approximate
the realistic ones.
Analysis of time dependent density functional theory
method calculated absorption spectrum and images ofelectron transfer trajectories in the different excitedstates allow to separate two different logically controlled
functions of molecular device consisting of guaninecytosine-PNA-1,4-dihydroquinoxaline-1,4-bis(N,Ndimethylamino)naphthalene supermolecule and Van der
Waals bonded precursor of fatty acid molecule. These
two different logically controlled functions of artificial
minimal living cells are: 1) initiation of metabolic fatty
acid production in five excited states or 2) initiation ofgene dehybridization in one excited state. This designed
supermolecule works in the artificial minimal cell as
molecular electronics classic OR logic function (Boolean
logics OR gate).
(Keywords)
quantum self-assembly of supramolecules; artificial
minimal living cells; photoexcited electron tunneling;
molecular electronics logical gate
1. Introduction
Artificial living technologies are rapidly developing
in several laboratories around the world: in USA (Steen
Rasmussen, James Bailey, Hans Ziock, Los Alamos
National Laboratory (LANL) [1]; Liaohai Chen, Argone
National Laboratory), in Italy (Pier Luigi Luisi’s groupat RomaTre University), in Germany (John S. McCaskill,
Guenter von Kiedrowski, Ruhr-Universitaet Bochum;
Patrick Wagler, Protostreem GmbH), and in European
Center for Living Technology (headquarter in Venice).

Viva Origino 36 (2008) 10 - 19
ⓒ 2008 by SSOEL Japan

New creating nano biorobots are planed to be used fornanomedicine, nanoecology, and for future emerging
new information technologies. Despite of really useful
benefits of these artificial living technologies one canforesee also some possible dangerous events in the caseif these new creating artificial living cells might selfmutate and escape to the natural biospheres. We are
creating molecular electronics logic gates regulating thephotosynthesis, growing and dividing of artificial living
cells and nanobiorobots in the order to prevent thenegative affects of these new emerging artificial living
information technologies. The molecular electronics andspintronics logical devices which regulate photosynthesis,
self-assembling to the mobile computing structures,
selectively capturing and transporting nuclear, chemical
and microbial pollutions already were quantum
mechanically designed [3-8].
The artificial minimal living cells (LANL scientists
call them as protocells) that are synthesized in USA Los
Alamos National Laboratory (LANL) [1, 2] are only afew (4-6) nanometers in size. In their simplest form,
these cells consist of a micelle which acts as thecontainer, a light driven metabolism, and a genetic
system, whose functions are all very tightly coupled. The
container consists of amphiphilic fatty acid (FA)molecules that self-assemble into a micelle. The
hydrophobic interior of the micelle provides analternative thermodynamic environment from theaqueous (in [1] and this paper) or methanol (in paper [2])exterior and acts as a sticking point for thephotosensitizer, fatty acid precursors (pFA) (food), andthe genetic material. Peptide nucleic acid (PNA) is
chosen as the genetic material as it is far less polar thanRNA or DNA and therefore should stick to the micelle,
especially if hydrophobic chains are added to the PNA
backbone. It is also capable of undergoing the same
Watson-Crick pairing and replication as RNA and DNA(see Figure 1). PNA is similar to DNA but has a peptidebased backbone, as opposed to DNA’s sugar-phosphatebackbone.
The first main goal of this article is to report theresults of quantum mechanical (QM) modeling of theself-assembly and charge transfer in a minimal protocell[1] that might have implications for the first livingorganism on the Earth [2] arround 3.8-3.5 bilion years
ago. The climate in the Earth at that time was hot withintense UV radiation therefore PNAs might were themost suitable for genome of minimal living cells incomparison with RNA or DNA. This article uses acollection of quantum mechanical tools and applies them
to a variety of protocell photosynthetic problems, while
also providing a perspective of the requirements for
success in the synthesis of new forms of livingorganisms.

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Viva Origino 36 (2008) 10 - 19
Figure 1 and other figures in this article was done by
Molekel software [9].
The metabolism involves the photoexcitation of anelectron in various photosensitizers which are stabilized
by the donation of an electron from non–canonical PNA
bases (for example, 8-oxo-guanine). The excited electron
is in turn used to cleave a fatty acid precursor to yield
another fatty acid molecule, thereby allowing thecontainer to grow until it reaches an unstable size anddivides. The artificial minimal cell could be fed PNA
monomers or use an essentially identical metabolism toconvert a PNA precursor monomer into a true monomer,
thereby also providing the material to allow the doublestranded PNA “gene” to replicate when it undergoes arandom dehybridization to yield two complementary
single-stranded templates [1, 2]. Finally, as the different
nucleobases have different electron donor and electron
relay capabilities, there is also a mechanism for natural
selection, with some bases and base orderings being
superior to others in their ability to facilitate themetabolism.
The artificial minimal living cell contains on theorder of 103 atoms. Due to its small size, all its processes,
including its self-assembly from component molecules,
its absorption of light, and its metabolism should in
principle be investigated using quantum mechanical(wave) theory [10-14].
Usually self-reproducing artificial living cells that are
creating in LANL and in other laboratories (see forexample, http://www.istpace.org/index.html) do not havethe nanosize electronics tools which might be able toregulate the growth and multiplication. It is important tohave possibility to stimulate or prevent uncontrolled
multiplication of artificial living organisms by installing
different molecular electronics devices. The second main
goal of this paper is by using quantum mechanicalexperiments to predict the possibility of biochemical
experimental synthesis of molecular electronics
controlled artificial minimal living cells or nanobiorobots
which might be used for nanomedicine and nanoecology.
It is presented in this paper the quantum mechanicallydesigned molecular electronics OR logical gate for thethe regulation of artificial minimal living cell functions.

Figure 1. PNA has a peptide-based backbone. Carbon atoms
and their associated covalent bonds are shown as green spheres
and sticks, hydrogens are in light grey, oxygens – red, nitrogens– blue. B means attached nucleobase molecule.

2. Procedure/Methodology
We used quantum mechanical electron correlationinteractions density functional theory (DFT) methods (i.e.
high precision quantum mechanical simulations) toinvestigate
variousself-assembled
photoactive
bioorganic systems of artificial minimal living cells [4-8].
The cell systems studied are based on peptide nucleic-11-

acid (PNA) and consisted of up to 400 atoms (notincluding the associated water solvent shells) and are up
to 3.0-4.2 nm in diameter.
The chemical formulas of the molecules used in thesimulated version of minimal cell are sensitizers: 1) 1,4bis(N,N-dimethylamino)naphthalene – (CH3)2-N-C8H6N-(CH3)2 and 1,4-dihydroquinoxaline -C8N2H7 , canonic
nucleobase 2) cytosine – C4H5N3O, 3) precursor of fatty
acid – C6H5-CO-(CH2)-O-CO-(CH2)3-CH3, 4) head (thewaste piece) of the precursor of fatty acid – C6H5-COCH3, 5) and fatty acid – HO-CO-(CH2)3-CH3 (see Figure
2).

Figure 2. The molecules used in the simulated version ofminimal cell are fragment of PNA supermolecule with
attached 1) 1,4-bis(N,N-dimethylamino)naphthalene, and 2)
cytosine molecules, and 3) precursor of fatty acid, and 4)
head (the waste piece) of the precursor of fatty acid, 5) andfatty acid molecules. Carbon atoms and their associatedcovalent bonds are shown as green sticks, hydrogens are inlight grey, oxygens – red, nitrogens – blue.

Our quantum simulations of single bioorganic
molecules possessing closed electronic shells start from a
trial geometry (Cartesian coordinates of the nuclei).
Using restricted Hartree-Fock (HF) and a density
functional theory (DFT) approaches in the Gaussian 03[15], GAMESS-US [16] or ORCA [17, 18] program
packages, we obtain the lowest molecular energy, which
depends on these coordinates parametrically. A
subsequent standard geometry optimization procedure[15-20] minimizes the energy with respect to the nuclear
positions. Special care is required to verify that theobtained optimal molecular structure is a global
minimum in the phase space of the nuclear (3n-6, nbeing the number of atoms) degrees of freedom.
In order to obtain accurate results in investigatingsupermolecules, two factors need to be accounted for: i)the quality of the density functional and ii) the quality ofthe molecular orbitals (extent of the phase space of thesingle-electron states). For simple covalently bonded
molecules we chose Becke's 3 parameter exchange
functional [21] with non-local Lee-Yang-Parr electron
correlations [22] (DFT B3LYP), and PBEPBE [15, 17,
18, 23], and PBELYP [16, 23] models. Currently, theB3LYP method is considered to be the most appropriate
method to take into account electron correlations in large
closed-shell supermolecules of which atoms are linked
by covalent bonds (i.e., there are no Van der Waals norhydrogen bonds between atoms in a single molecule) [24,25]. For simulations of the self-assembly of bioorganic
supramolecules in which the separate molecules areassociated by hydrogen bonds or Van der Waals forces
we used PBEPBE [15, 17, 18, 23], and PBELYP [16, 23]
methods. In these two methods, exchange functionals
include some electron correlation effects at larger

Viva Origino 36 (2008) 10 - 19
distances that provide relatively good descriptions of the
Van der Waals forces and hydrogen bonds. To obtainaccurate optimal molecular geometries for single
molecules, we use the 6-311G** basis set which includes(5d, 7f) polarized atomic orbitals. For self-assembly ofpairs of bioorganic molecules we add diffusion orbitalsof the 6-31++G** basis set (the standard tables [26] givethe appropriate basis set description).
The above-mentioned 6-311++G** basis set
convention was adopted by John Pople and coworkers.
The basis set structure is given for the whole molecule,rather than a particular atom. The notation alsoemphasizes the split valence (SV) nature of these sets.
Symbols like n-ijG or n-ijkG are encoded as follows: n –the number of primitives for the inner shells; ij or ijk the number of primitives for contractions in the valenceshell. The ij notation describes sets of valence double
zeta quality and ijk, sets of valence triple zeta quality.
Generally, in the basis sets derived by Pople's group, thes and p contractions belonging to the same "electron
shell" (i.e. corresponding formally to the same principal
quantum number n) are folded into an sp-shell. In thiscase, the number of s-type and p-type primitives is thesame, and they have identical exponents. However, thecoefficients for the s- and p-type contractions aredifferent. The symbol “*” is used to indicate when
Pople's basis sets are augmented with d- or f-type
polarization functions: n-ijG* or n-ijkG* when this isdone only for heavy atoms; and n-ijG** or n-ijkG**
when done for all atoms together with p-functions forhydrogen atoms.
The basis sets are also frequently augmented with theso-called diffuse functions. These are very shallow
Gaussian basis functions, which more accurately
represent the "tail" portion of the atomic orbitals, which
are distant from the atomic nuclei. These additional basis
functions can be important when considering anions andother large, "soft" molecular systems. These gaussians
have very small exponents and decay slowly with
distance from the nucleus. The diffuse gaussians areusually s- and p-type, however sometimes diffuse
polarization functions are also used. Diffuse functions
are necessary for a correct description of anions andweak bonds (e.g. hydrogen bonds) and are frequently
used for calculation of properties such as dipole
moments, polarizabilities, etc. The inclusion of diffuse
functions is indicated with the “+” sign: n-ij+G or nijk+G when one diffuse s-type and p-type gaussian withthe same exponent is added to a standard basis set forheavy atoms; and n-ij++G or n-ijk++G when one diffuse
s-type and p-type Gaussian is added for heavy atoms
together with one diffuse s-type gaussian for hydrogenatoms. Table 1 lists the availability of diffuse andpolarization functions and the range of applicability foreach built-in Gaussian03 [15], GAMES-US [16] andORCA [17, 18] program packages basis set we use.
Quantum modeling of the self-assembly of nanostructures in PNA based minimal living cells was
performed using the software we developed for building
PNA double helices.
The geometries of the constituent molecules and theirpairs were individually optimized using the PBELYP [16,23] method with the 6-311++G** basis set implemented

in the GAMESS-US program package which is installedin dual processor Opteron servers Linux cluster of ourTheoretical Molecular Electronics and Spintronics
research group and with the PBEPBE method [16, 23]
using the 6-311++G** basis set [26] implemented via theGaussian03 program package on the LANL SGI Altix
3000 machine.
Table 1: The function availability and range ofapplicability for each built-in basis set in Gaussian03 [15],GAMESS-US [16] and ORCA [17, 18] program packages.

Applies to Polarization
Basis set atoms
functions
3-21G
H-Xe
* or **
6-31G
H-Kr(3df,3pd)
6-311G H-Kr
(3df,3pd)

Diffusefunctions+++++

3. Quantum Mechanical Self-Assembly of Artificial
Minimal Living Cell
For the reasons of better understanding of the selfassembling process of artificial minimal cell it wascalculated electronic structure of fatty acid HO-CO(CH2)6-CH3 (see Figure 3) by PBEPBE method usingrather wide basis set 6-311++G*. Sum of Mulliken
charges on the hydrophilic head of fatty acid and on thefirst -CH2 chain (HO-CO-(CH2-) is equal to -0.14 ofelectron charge. Since this molecule is neutral (total sumof Mulliken charges = 0.00) therefore on the rest part of
the hydrophobic tail of this fatty acid charge will beequal to +0.14 of electron charge due to a small quantum
mechanical internal shift of whole conjugated valence
electron cloud from electron-donor tail to electronacceptor head. Additional factor for the repulsion of tailsof fatty acids is that this tail is covered by positively
charged hydrogens. The Van der Waals radii spheres of
all atoms in this fatty acid are drawn in the Figure 3
below.
The summary of our detailed investigations ofquantum mechanical self-assembly of various micelles
and artificial minimal cells models [8] is that fatty acidsin the vacuum are not able to perform self-assembly due
to the quantum dispersion forces and due to thealternating charge of the different groups -CH2- in thetails because really these two kinds of attraction forces
are small. Dispersion forces are weak Van der Waals
intermolecular forces that arise from the attractive force
between quantum multipoles. The more competitiveelectrostatic repulsion forces which destroy micelles andartificial cells in the vacuum due to the negative charges
on the heads of FA and small positive charges on the FA

Figure 3. Van der Waals radii spheres of all atoms in fatty
acid HO-CO-(CH2)6-CH3. The Van der Waals spheres ofcarbon atoms and their associated covalent bonds areshown as grey spheres and sticks, hydrogens are in light
grey, oxygens – red.

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Viva Origino 36 (2008) 10 - 19
tails, and additionally because the tails of fatty acids arecovered by positively charged hydrogen atoms.
The electron correlations interactions among polar
solvent (water) molecules, PNA, fatty acid, precursor
fatty acid, and waste ends of precursor fatty acidmolecules leads to appearing the additional attraction
dispersion forces and hydrogen bonds. A hydrogen bondis a special type of quantum attractive interaction thatexists among an electronegative atom and a hydrogen
atom bonded to another electronegative atom and thishydrogen atom exist in two quantum states. The
hydrogen bonds and Van der Waals weak chemicalbonds (dispersion forces) play a critical role in thequantum mechanical electron correlations interaction
based self-assembly of the photosynthetic center andfunctioning of the photosynthetic processes of theartificial minimal living cells.
The best available method to simulate in minimalcells these Van der Waals dispersion forces andhydrogen bonds is to perform quantum mechanical nonlocal density functional potential calculations [3-8].
Other approaches, such as lowest level of correction(MP2), multiconfiguration self consistent field (MCSCF)
or complete active space SCF (CASSCF), in principle
more suited to model dispersion forces, would not beapplicable for minimal cells due to the huge
computational cost.
The distances between the separated sensitizer,
precursor fatty acid, and water molecules are comparable
to Van der Waals and hydrogen bonding radii. As aresult these nonlinear quantum interactions compress theoverall system resulting in a smaller gap between the
HOMO and LUMO electron energy levels andphotoexcited electron tunneling occurs from thesensitizer(eithera1,4-bis(N,N-dimethylamino)
naphthalene or 1,4-dihydroquinoxaline) to pFA
molecules [6-8]. For example, the average distanceamong photoelectron donor and photoelectron acceptor
fragments in the modeled photosynthetic system withoutwater molecules is approximately equal to 5.6 Å (thesmallest interatomic distance is equal to 4.83 Å) while
the average distance among photoelectron donor andphotoelectron acceptor is equal to 3.5 Å in the minimal
cell with real water molecules presented in the Figure 4(the smallest interatomic distance is equal to 2.58 Å).
It have been done quantum mechanical PBEPBE/321G [23] method geometry optimization (i.e. selfassembly) procedure using GAMES-US [16] package
starting from randomly displaced various molecules
shown in Figure 2 that are components of LANL
minimal cell [1, 2]. As one can see in the Figure 4 aftergeometry optimization these molecules self-organized to
the regular structure due to accounting the quantum
electron correlations interactions, i. e. due to the balanceof weak electrostatic, hydrogen bonding and weak
dispersion Van der Waals forces :1) the cytosine-PNA hydrophilic fragment
covalently
bondedtoa
1,4-bis(N,Ndimethylamino)naphthalene sensitizer molecule
are in the center;2) six 5-carbon fatty acid molecules are oriented bytheir hydrophilic ends to the cytosine-PNA
fragment covalently bonded to a 1,4-bis(N,N-dimethylamino)naphthalene sensitizer molecule;3) two precursor fatty acid molecules (pFA) (in the
top-left and top-right) are oriented by theirhydrophilic ends the cytosine-PNA fragment
covalently
bondedtoa
1,4-bis(N,Ndimethylamino)naphthalene sensitizer molecule;4) two the waste pieces of the pFA molecules areoriented by their hydrophilic ends to thecytosine-PNA fragment covalently bonded to a
1,4-bis(N,N-dimethylamino)naphthalene
sensitizer molecule;5) most of the water molecules self-organize into
clusters of nano ice-like substructures.
Furthermore, all the interatomic distances
betweenthe
1,4-bis(N,N-dimethylamino)naphthalene sensitizer and the pFA molecule
become reduced, i.e. the photosynthetic system
become more compressed due to the presence of
the water molecules;
All the macromolecular living systems (not only
these our investigating artificial minimal cells) are selfassembling based on competition of weak electrostaticforces (due to small internal shift of whole conjugatedvalence electron cloud from electron-donor tail toelectron-acceptor head) and other quantum (dispersion,
H-bonding) fine effects. Emergency of natural life or
artificial life is a priory predicted due to the existence of
these weak quantum mechanical electron correlations
interactions.
It have been performed calculations of optimal
electronic structure and spectra of this photosynthetic
center using time dependent (TD) DFT PBEPBE method[23] with the 6-31G basis set together with COSMO
water solvent model using ORCA package [17, 18, 27]
installed on our research group dual processor Opteronservers Linux cluster. It was taken from thesecalculations the difference of electron charge density(certain excited-state - ground-state) for thephotosynthetic center of artificial minimal living cell [1,2] which consists of conjugated cytosine-PNA-1,4bis(N,N-dimethylamino)naphthalene supermolecule, six
fatty acid, two pFA molecules, and two the waste piecesof the pFA molecules and performed the visualized theelectron charge tunneling associated with certain excitedstate transitions (see Figure 4).
Electron charge tunneling energy equal to 2.753 eV(450.3 nm) associated with the eighth excited state
shown in Figure 4 correspond to experimental value
equal to 450.0 nm of the most intense absorption line [2].
This agreement implies that the quantum mechanically
self-assembled structures of minimal living cells very
closely approximate the realistic ones.
Quantummechanicalelectroncorrelation
experiments of self-assembly of above describedartificial minimal living cells show that these cells arecomplex systems because only entire ensemble of PNA,
and sensitizer, and pFA, and FA and water molecules isstable and therefore it is able to perform quantum
photosynthetic processes. Removing the small part ofnucleobase, FA and water molecules leads to thestructural changes in comparison with realistic structuresand difference in comparison with the spectroscopic
values of photoexcited electron tunneling from sensitizer-13-

Viva Origino 36 (2008) 10 - 19
living cells gives results exactly comparable with
spectroscopic results and all other more simplified
quantum mechanical methods such as local gradient DFT
or ab initio Hartree-Fock gives structures and spectra far
from the experimentally measured.
The corresponding of experimental absorption
spectra peaks and our quantum mechanically calculated
confirm that our chosen method of designing single
electron nano photocells might be useful not only for
artificial living organisms but also for wide
implementation in the nano photodevices, and molecular
computers.
4. Quantum Mechanical Design of MolecularElectronics OR Gate for the Regulation of Artificial
Minimal Living Cell Functions
We used TD DFT PBEPBE method [23] with the 631G basis set together with COSMO water solvent
method [27] in the ORCA program package which isinstalled on our Linux cluster to calculate the absorption
spectra and the relative positions of the HOMO andLUMO eigenvalues of Schroedinger equation of various
separate different sensitizer molecules: 1,4-bis(N,Ndimethylamino)naphthalene, and 1,4-dihydroquinoxaline,
and 7,8-dimethylisoalloxazine that were previously ourinvestigated by less accurate DFT methods [4]. Analysis
and comparison of the results showed that thesesensitizers are good candidates for use in artificial
minimal cells because their HOMO electron energy
levels are energetically high enough relative to the
LUMO electron energy level of the pFA molecule andtheir absorption spectra are in the visible region.
Geometry optimization of artificial logicallycontrolled photosynthetic system consisting of guaninecytosine-PNA fragment (left-bottom of Figure 5) withcovalently
bondedtwo
sensitizers:
1,4dihydroquinoxaline
and1,4-bis(N,Ndimethylamino)naphthalene molecules and Van der
Waals dispersion forces bonded precursor of fatty acidmolecule (in the right-top of figure), and surrounded byhundreds of real water molecules was performed bysemiempirical quantum mechanical PM3 method. Later
most of water molecules are removed and geometry ofthis minimal cell was reoptimized by DFT PBEPBE/631G methods ORCA package [17, 18] on our researchgroup Linux cluster.
It have been performed calculations using TD DFTPBEPBE method [23] with the 6-31G basis set together
with COSMO water solvent model using ORCA package[17, 18, 27] installed on our Linux cluster of thedifference of electron charge density (excited-state ground-state) for the photosynthetic center of logicallycontrolling artificial minimal living cell which consistsof
conjugatedguanine-cytosine-PNA-1,4dihydroquinoxaline-1,4-bis(N,N-dimethylamino)
naphthalene supermolecule and Van der Waals
dispersion forces bonded pFA molecule, and surroundedby real water molecules.
The absorption spectrum of this photosynthetic
system is detailed placed in the Table 2 and electron
charge transfer trajectories in different excited states areshown in the Figures 6-12).

Figure 4. Image of a photosynthetic system consisting of acytosine-PNA fragment covalently bonded to a 1,4-bis(N,Ndimethylamino)naphthalene sensitizer molecule (in thecenter), six 5-carbon fatty acid molecules, two pFA
molecules (in the left and top-right), and two the waste
pieces of the pFA molecules and water molecules that were
optimized using the PBEPBE/3-21G method. Visualizationof the electron charge tunneling associated with the eighth
excited state. The transition is from the conjugated cytosinePNA
fragment-1,4-bis(N,N-dimethylamino)naphthalene
supermolecule (in the center-left) to the one of the pFA
molecules (in the left). The electron cloud hole is indicatedby the dark blue color while the transferred electron cloud
location is designated by the grey color.

(1,4-bis(N,N-dimethylamino)naphthalene
topFA
molecules. Quantum mechanical electron correlation
experiments of self-assembly of artificial minimal living
cells removing the main part of nucleobase, and FA andwater molecules leads to the degradation of these cells.
We can state what the inclusion of ever more water, andfatty acid, and pFA molecules, and waste pieces of thepFA molecules and nucleobase molecules in the different
artificial minimal living cells results in a shift of theabsorption spectrum to the red for the artificial protocell
photosynthetic center, leading to an ever closer approachto the real experimental value and indicates the measureof the complexity of this quantum complex system, i.e. aminimal protocell.
As it was underlined before, the second main goal ofthis article is to demonstrate the ab initio quantum
mechanical processes of minimal cells such as
photoexcited electron tunneling from photoelectron
donor molecule to photoelectron acceptor molecule. The
most general quantum mechanical theory reality of thiscomplex nonlinear bioorganic system is that according ofquantum uncertainty the cloud of photoelectron holepossesses some asymmetrical delocalization whilemainly is localized on conjugated with sensitizer
supermolecule. Electron cloud also due to quantum
uncertainty is partially delocalized while the largest
probability to find this photoelectron is on the waste endof pFA molecule.
The quantum reality of nanometer size bioorganic
systems is different in comparison with our meter size
world and even in comparison with micrometer size
bacteria world.
It is important to say that only quantum mechanicalelectron correlation TD-DFT experiments with minimal-14-

Viva Origino 36 (2008) 10 - 19

Figure 5. Molecular electronics OR logic gate installed inphotosynthetic center of minimal cell consists of: guaninecytosine-PNA–1,4-dihydroquinoxaline-1,4-bis(N,Ndimethylamino)-naphthalene supermolecule and Van der
Waals dispersion forces bonded pFA molecule (in the topright, between the sensitizer molecules) surrounded by realwater molecules environment. The 1,4-dihydroquinoxaline
and1,4-bis(N,N-dimethylamino)-naphthalene
arecovalently bounded to the PNA via a molecular insulator
bridges.

Figure 6. Geometrical structure of pFA molecule. There
are numerated heavy C and O atoms in the waste end of
this molecule and in the part of FA fragment.

pFA molecule are equal to +0.282 of electron charge (e)while the sum on the same atoms in anion pFA molecule
is equal to -0.632 e (see Table 3). It means that almost
entire (-0.914 e) additional electron after self-consistent
field procedure localizes on the waste end of pFA
molecule while only -0.086 e charge localizes on FA
fragment of this molecule.
Chemical bond orders in quantum chemistry are
equal to values of non diagonal elements of condensed tochemical bonds all electrons matrix multiplied by two.
Data of selected chemical bonds of neutral and anion
pFA molecules are presented in Table 4.
Analysis of selected bond orders of neutral and anion
pFA molecules shows that the most weakness chemicalbond order is between ninth and 10th atoms in the neutralpFA molecule. The additional electron which is placedon the waste end of pFA molecule decrease the bondorder from 0.297 to 0.260 between ninth and 10th atoms.
It is known in molecular physics that additional
electron which fall down on the molecular fragment
initiate the vibrations and rotations of all chemical bondsin this fragment and it is large probability that the mostweakness chemical bond between ninth and 10th atoms

The electron tunneling transitions of the 13th, 17th,and 23th, 24th, 26th excited states should induce metabolic
photodissociation of pFA molecule because thetransferred electron cloud is located on the head (thewaste piece) of pFA molecule (see Figures 7, 8 and 1012).
In order to understand process of photodissociationof pFA molecule but reduce expenses of computations it
was investigated the electronic structure of single neutralpFA molecule (see Figure 6) by using B3LYP/6-311G
method. After geometry reoptimization procedure it was
obtained the electronic structure of negative ion of thismolecule using unrestricted B3LYP/6-311G method
Atomic Mulliken charges in Table 3 are withhydrogens summed into carbon atoms. i.e. the atomic
charges of hydrogens are already added to the atomic
charge of neighboring carbon atom. The sum of
Mulliken charges of atoms from No 1 to 9 of neutral

Table 2. Excitation transitions energies of a photosynthetic center of logically controlling artificial minimal living cell which consistsof conjugated guanine-cytosine-PNA-1,4-dihydroquinoxaline-1,4-bis(N,N-dimethylamino)naphthalene supermolecule and Van der
Waals dispersion forces bonded pFA molecule, and surrounded by real water molecules were calculated using TD DFT PBEPBE
method with the 6-31G basis set together with COSMO water solvent method in the ORCA program package. Arrow → indicates the
direction of individual electron transition from ground state HOMO-m to certain excited state LUMO+n.
Weight of
ExcitedIndividual transitions
EnergyWavelength
Oscillator strength
individualState #
(eV)
(nm)
(arbitrary units)
HOMO-m → LUMO+ntransition

13

HOMO-1→ LUMO

0.999

2.176

569.7

0.00015

16

HOMO→ LUMO+12

0.999

2.320

534.4

0.00011

17

HOMO-4→ LUMO

0.999

2.370

523.2

0.00006

19

HOMO→ LUMO+13

0.998

2.427

510.9

0.00032

23

HOMO-6→ LUMO

0.999

2.542

487.7

0.00029

24

HOMO-7→ LUMO

0.999

2.561

484.2

0.00022

26

HOMO→ LUMO+14

0.986

2.606

475.7

0.00010-15-

Viva Origino 36 (2008) 10 - 19
will be broken. This photodissociation process of pFA
molecule is observing experimentally in LANL
"Protocell Assembly" project.
The new fatty acid from dissociated pFA molecule
will join to minimal cell, therefore this minimal cell willgrow and later spontaneously break in two new minimalcells and once again will use pFA molecules during thephoto excitation processes for generation the new FA
molecules, etc. This photoinduced autocatalytic
bioorganic system was experimentaly proved in the
Table 3. Atomic Mulliken charges with hydrogens summed
into carbon atoms of neutral and anion pFA molecules
calculated by B3LYP/6-311G method.
Number of atom
Neutral pFA
Anion of pFA

1 C
2 C
3 C
4 C
5 C
6 C
7 C
8 O
9 C
10 O
11 C
12 C
13 O

0.048
0.001
0.100
-0.141
0.099-0.0140.280-0.3400.249-0.4670.534-0.022-0.391-0.108-0.086-0.028-0.124-0.030-0.1040.183-0.4860.151-0.461
0.531-0.039-0.411

Sum of charges on 19 atoms

0.282-0.632

Figure 8. Electron charge transfer transition for theseventeenth excited (523.20 nm) state is from the guaninecytosine-PNA–1,4-bis(N,N-dimethylamino)naphthalene
supermolecule HOMO-4 to the pFA molecule LUMO
calculated by TD-DFT PBEPBE/6-31G method.

Table 4. Bond orders of selected chemical bonds of neutral
and anion pFA molecules calculated by B3LYP/6-311G
method.
Neutral pFA
Chemical bonds
Anion of pFA
9-10

C-O

0.297

0.260

7-8

C-O

1.322

1.277

10-11

O-C

0.376

0.455

Figure 9. Electron charge transfer transition for thenineteenth excited (510.9 nm) state is from the guaninecytosine-PNA–1,4-dihydroquinoxaline
supermolecule
HOMO to the cytosine and pFA molecules LUMO+13
calculated by TD-DFT PBEPBE/6-31G method.

Figure 7. Electron charge transfer transition for the thirteenth
excited (569.7 nm) state is from the guanine-cytosine-PNA–
1,4-bis(N,N-dimethylamino)naphthalene
supermolecule
HOMO-1 to the pFA molecule LUMO calculated by TDDFT PBEPBE/6-31G method. The electron cloud hole isindicated by the dark blue color while the transferred
electron cloud location are designated by the grey color.

Figure 10. Electron charge transfer transition for the twenty
third excited (487.7 nm) state is from the guanine-cytosinePNA–1,4-dihydroquinoxaline supermolecule HOMO-6 tothe pFA molecule LUMO calculated by TD-DFTPBEPBE/6-31G method.

-16-Viva Origino 36 (2008) 10 - 19
papers [1, 2], and called in LANL "Protocell Assembly"
project as minimal artificial living cell.
The electron tunneling transition of the 19th excitedstate should induce metabolic photodissociation of pFA
molecule and photodissociation of hydrogen bonds ofnucleotide base pair in the guanine-cytosine-PNA
fragment in the same time because the part of transferred
electron cloud is located on the head (the waste piece) ofpFA molecule and another part of transferred electron
cloud is located on the cytosine molecule of cytosinePNA fragment (see Figure 9). The phenomenon when
the part of transferred electron cloud is located on thehead (the waste piece) of pFA molecule and another partof transferred electron cloud is located on the cytosine
molecule might be explained by quantum uncertainity ofwave function of entire supramolecule but this case (19thexcited state) is not interesting for the reasons of theconstruction of molecular electronics classic logic
function (Boolean logics gate) while might be used forthe construction of molecular quantum computing gate.
The electron tunneling transition of the 16th excitedstate should induce photodissociation of hydrogen bondsof nucleotide base pair in the guanine-cytosine-PNA

fragment because the transferred electron cloud islocated on the cytosine molecule of guanine-cytosinePNA fragment (see Figure 13).
Quantummechanical
B3LYP/6-31+G*andPBEPBE/6-31+G* calculations of model system
consisting of guanine-cytosine surrounded by 101 watermolecule (see Figure 14) shows that the placement ofadditional negative electron charge leads to theenlargement of interatomic distances of hydrogen bonds
and to the reducing of the bond orders of the guaninecytosine hydrogen bonds [28].
The additional electron located on cytosine in thesixteenth excited (534.4 nm) state should destroy thehydrogen bonds of nucleotide base pair guanine-cytosine
and initiate the PNA gene dehybridization in the artificial
minimal living cells. The geometry reoptimization ofnegatively charged model system guanine-cytosine in thesurrounding 51 water molecules cluster in the excitedstates were done by using Turbomole program package[29] and leaded to the breaking of hydrogen bonds ofFigure 13. Electron charge transfer transition for the
sixteenth excited (534.4 nm) state is from the guaninecytosine-PNA–1,4-dihydroquinoxaline
supramolecule
HOMO to the cytosine molecule LUMO+12 calculated by
TD-DFT PBEPBE/6-31G method.

Figure 11. Electron charge transfer transition for the twenty
fourth excited (484.2 nm) state is from the guaninecytosine-PNA–1,4-dihydroquinoxaline HOMO-7 to thepFA molecule LUMO calculated by TD-DFT PBEPBE/631G method.

Figure 14. The hydrogen bonds of nucleotide base pairguanine-cytosine and among 101 water molecules cluster
are marked by dashed lines. Carbon atoms and theirassociated covalent bonds are shown as green sticks,
hydrogens are in light grey, oxygens – red, nitrogens –blue.

Figure 12. Electron charge transfer transition for thetwenty sixth excited (475.7 nm) state is from the guaninecytosine-PNA–1,4-dihydroquinoxaline
supermolecule
HOMO to the pFA molecule LUMO+14 calculated by
TD-DFT PBEPBE/6-31G method.

-17-Viva Origino 36 (2008) 10 - 19
electronics classic OR logic function, i.e. Boolean logics
OR gate (see Figure 15).
This OR molecular electronics logical gate is forselected stimulation of the photosynthesis or the selfreproduction of artificial minimal living cells whichshould be ease to synthesize it and install in these
artificial minimal living cells for investigations of theefficiency of their functionality. Our research is on theway for total prevention of the photosynthesis and selfreproduction of artificial minimal living cells by
installing molecular electronics AND logic gate andusing external magnetic fields with molecular spintronics
ControlNot gate [30].

guanine-cytosine [28] while the geometry optimizationin the sixteenth excited (534.4 nm) state of entire
supermolecule shown in the Figure 13 is still too
expensive. This PNA gene photoinduced dehybridizationin the minimal cells not yet experimentally done in
LANL "Protocell Assembly" project.
Analysis of digits of 6th column in Table 2 showsthat most oscillator strengths of photoexcited electrontransitions (in 13th, 23th, 24th excited states) initiating
metabolic lipid production are more intense incomparison with the oscillator strength photoexcitedelectron transition (in 16th excited state) initiating gene
dehybridization.
Analysis of TD DFT calculated absorption spectrum
characteristics in the Table 2 show that in thissupramolecule all the weights of individual transitions
are approximately equal to 1. It means that enough todraw only one figure for the representation of certaintransition because the superposition of anotherelementary transition with significantly small weight
does not significantly affect on this transition. Images ofelectron transfer trajectories (see Figures 10, 11, 13-15
and 16) in the different excited states allow to separate
two different logically controlled functions of moleculardevice consisting of guanine≡cytosine-PNA-1,4dihydroquinoxaline-1,4-bis(N,Ndimethylamino)naphthalene supermolecule and Van der
Waals bonded pFA molecule. These two different
logically controlled functions of artificial minimal living
cells are:1) initiation of metabolic fatty acid production in
the excited states 13th, 17th and 23th, 24th, 26th or2) initiation of gene dehybridization in the
16thexcited state.
In other words one should be able to initiate themetabolic fatty acid production illuminating this artificial
minimal cell by wavelengths: 569.7 nm, 523.2 nm, 487.7
nm, 484.2 nm, 475.7 nm or one should be able initiate
the gene dehybridization illuminating this artificial
minimal cell by wavelength equal to 534.4 nm.
It can be stated that our quantum mechanicallyinstalled guanine-cytosine-PNA-1,4-dihydroquinoxaline1,4-bis(N,N-dimethylamino)naphthalene supermolecule
works in the artificial minimal living cell as molecular

5. Conclusions
Artificial living cells and their substructures are selfassembling due to electron correlation interactions
among biological and water molecules which leads toappearing of the quantum mechanical repulsion weakelectrostatic forces (due to internal shift of whole
conjugated valence electron cloud from electron-donor
tail to electron-acceptor head) and the quantum
mechanical attraction Van der Waals dispersion forces
and hydrogen bonds. Dispersion forces are weakintermolecular forces that arise from the attractive force
between quantum multipoles. A hydrogen bond is a
special type of quantum attractive interaction that exists
between an electronegative atom and a hydrogen atom
bonded to another electronegative atom and thishydrogen atom exist in two quantum states.The best
method to simulate these Van der Waals dispersion
forces and hydrogen bonds is to perform quantum
mechanical non-local density functional potential
calculations of artificial minimal living cells consistingof around 400 atoms. The cell systems studied are basedon peptide nucleic acid and are 3.5 – 4.5 nm in diameter.
The electron tunneling and associated light absorption ofmost intense transitions as calculated by the timedependent density functional theory method differs fromspectroscopic experiments by only 0.3 nm, which arewithin the value of experiment errors. This agreement
implies that the quantum mechanically self-assembled
structure of artificial minimal living cells very closely
approximate the realistic ones.
Analysis of TD DFT calculated absorption spectrum
and images of electron transfer trajectories in the
different excited states allow to separate two different
logically controlled functions of molecular device
consistingofguanine-cytosine-PNA-1,4dihydroquinoxaline-1,4-bis(N,Ndimethylamino)naphthalene supermolecule and Van der
Waals dispersion forces bonded pFA molecule. These
two different logically controlled functions of minimalcells (protocells) are:1) initiation of metabolic lipid production in the
excited states 13th, 17th and 23th, 24th, 26th or2) initiation of gene dehybridization in the
16thexcited state.
It is possible to initiate the metabolic lipid
production illuminating this artificial minimal cell bywavelengths: 569.7 nm, 523.2 nm, 487.7 nm, 484.2 nm,
475.7 nm or it is possible to initiate the gene
dehybridization illuminating this artificial minimal cell

Figure 15. The summarizing picture of the OR molecularelectronics logical gate for selected stimulation of thephotosynthesis or the self-reproduction of artificial minimalliving cells.

-18-Viva Origino 36 (2008) 10 - 19
14.

by wavelength equal to 534.4 nm.
Our quantum mechanically installed guaninecytosine-PNA-1,4-dihydroquinoxaline-1,4-bis(N,Ndimethylamino)naphthalene supermolecule works in theartificial minimal cell (protocell) as molecularelectronics classic OR logic function (Boolean logics ORgate).
Acknowledgments
The work was funded via the PACE (Programmable
Artificial Cell Evolution), the European Integrated
Project in the EU FP6-IST-FET Complex Systems
Initiative, and partially by the Agency for International
Science and Technology Development Programmes(Lithuania).
Author also thanks the Los Alamos National
Laboratory Protocell Assembly LDRD DR project foruse of the LANL SGI Altix 3000 machine and theirinstalled Gaussian 03 program package.

15.

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