QUANTUM SELF-ASSEMBLY AND PHOTOINDUCED ELECTRON TUNNELING IN
PHOTOSYNTHETIC SYSTEM OF MINIMAL LIVING CELL
Arvydas Tamulis and Vykintas Tamulis
Vilnius University Institute of Theoretical Physics and Astronomy, A. Gostauto 12,
LT-01108 Vilnius, Lithuania
E-mail: tamulis@itpa.lt(Received :August 17, 2006
Abstract
We used quantum mechanical (QM) electron
correlation interactions density functional theory(DFT) methods (i.e. high precision quantum
mechanical calculations) to investigate self-assembled
photoactive bioorganic system of artificial minimalliving cell. The cell system studied is based on
peptide nucleic acid (PNA) and consists of 333 atoms(not including the associated water solvent shells)
and is 3.0 nm in diameter. The electron correlations
interaction originating the hydrogen bonds and Van
der Waals weak chemical bonds that increase due tothe addition of a polar solvent (water) molecules,
fatty acid (FA), precursor fatty acid (pFA) molecules
and waste pieces of the pFA molecules play a criticalrole in the QM interaction based self-assembly of thephotosynthetic center and functioning of thephotosynthetic processes of the artificial minimalliving cell. The distances between the separated
sensitizer, precursor fatty acid, and water molecules
are comparable to Van der Waals and hydrogenbonding radii. As a result these nonlinear quantum
interactions compress the overall system resulting ina smaller gap between the HOMO and LUMO
electron energy levels and photoexcited electron
tunneling occurs from the sensitizer a 1,4-bis(N,Ndimethylamino) naphthalene to pFA molecules. The
electron tunneling and associated light absorption ofmost intense transition as calculated by the timedependent density functional theory (TD DFT)
method differs from spectroscopic experiments byonly 0.3 nm, which is within the value of experimenterrors. This agreement implies that the quantum
mechanically self-assembled structure of minimal cellvery closely approximates the realistic one.

Accepted: March 13, 2007)
The artificial minimal living cells or protocells [4,5] are based on PNA (see Figure 1). PNA is similar
to DNA but has a peptide-based backbone, as
opposed to DNA’s sugar-phosphate backbone. PNA
is able to form very stable duplex structures with thesame complementary Watson-Crick pairing between
the nucleobases (B).
The diameter of the experimentally madeFigure 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.

Keywords
quantum self-assembly of photosynthetic centers,
measure of the complexity of artificial minimalliving cell
1. Introduction
The main features of regular and artificial
bioorganic life based on DNA, RNA and PNA are
growing, multiplying and information processing.
Modern quantum mechanical methods provide
powerful tools for theoretical modeling and analysisof biomolecular electronic and spectra structure [1-3]and may be used to guide the synthetic effort of more
effective photosynthetic systems providing the lightharvesting and growth.
Viva Origino 35 (2007) 66 - 72
© 2007 by SSOEL Japan- 66 -

minimal living cell is only 5 nm [4, 5]. Therefore all
their processes including self-assembly andabsorption of light could be investigated using
quantum (wave) theory.
The main difference from classical (Newtonian)
theory is that quantum particles including thebioorganic supramolecules which self-organize into
the minimal cells, behave as waves rather than
discrete particles with definitive positions andmomenta. For example, valence electrons ofsupramolecules (which mainly determine features ofnano-size protocells) possess strict quantum statesand discrete quantum electronic UV-VS, vibrational,
NMR, EPR, etc. spectra. The entire minimal cellmight be considered to be a molecular electronics
device that self-assembles according to quantum
correlated electron interaction potentials and thatabsorbs light and carries on its metabolism according
to quantum electron excitation and tunneling
equations.
The main purpose of this article is to find thegeneral rules of quantum mechanical self-assemblyand charge transfer in the artificial minimal living
cells that are being synthesized [4, 5], and to predict
the new trends of more effective synthesis ofphotosynthetic centers. The current work uses larger
supramolecular systems and more exact quantum
mechanical methods than our earlier works [1-3].
This article provides a collection of quantumViva Origino 35 (2007) 66 - 72

mechanical tools and their application to a variety ofminimal cell photosynthetic processes, while thisarticle also provides a perspective of the requirements
for success in the synthesis of new forms of livingorganisms.

sets of valence triple zeta quality. Generally, in thebasis sets derived by Pople's group, the s and pcontractions 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
the same, and they have identical exponents.
However, the coefficients for the s- and p-type
contractions are different. The symbol “*” is used toindicate when Pople's basis sets are augmented withd- or f-type polarization functions: n-ijG* or nijkG* when this is done only for heavy atoms; and nijG** or n-ijkG** when done for all atoms together
with p-functions for hydrogen atoms.
The basis sets are also frequently augmented withthe so-called diffuse functions. These are very
shallow Gaussian basis functions, which moreaccurately represent the "tail" portion of the atomic
orbitals, which are distant from the atomic nuclei.
These gaussians have very small exponents and decay
slowly with distance from the nucleus. The diffuse
gaussians are usually s- and p-type, thoughsometimes diffuse polarization functions are also
used. Diffuse functions are necessary for a correct
description of anions and weak bonds (e.g. hydrogenbonds) and are frequently used for calculation ofproperties suchas dipole moments,
andpolarizabilities, 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 gaussianwith the same exponent is added to a standard basis
set for heavy atoms; and n-ij++G or n-ijk++G when
one diffuse s-type and p-type Gaussian is added forheavy atoms together with one diffuse s-type
gaussian for hydrogen atoms. Table 1 lists theavailability of diffuse and polarization functions andthe range of applicability for each built-in Gaussian03[6] and ORCA [8, 9] program packages basis set weuse.

2. Procedure/Methodology
Our quantum simulations of single bioorganic
molecules possessing closed electronic shells startfrom a trial geometry (Cartesian coordinates of thenuclei). Using restricted Hartree-Fock (HF) and adensity functional theory (DFT) approached by theGaussian 03 [6], GAMESS-US [7] or ORCA [8, 9]
program packages, we obtain the lowest molecularenergy, which depends on these coordinatesparametrically. A subsequent standard geometry
optimization procedure [6-11] minimizes the energy
with respect to the nuclear positions. Special care isrequired to verify that the obtained optimal molecular
structure is a global minimum in the phase space ofthe nuclear (3n-6, n being 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 of the molecular orbitals (extent of the phasespace of the single-electron states). For simple
covalently bonded molecules we chose Becke's 3
parameter exchange functions [12] with non-local
Lee-Yang-Parr electron correlations [13] (DFTB3LYP), and PBEPBE [6, 8, 9, 14], and PBELYP[7, 14] models. Currently, the B3LYP method is
considered to be the most appropriate method to take
into account electron correlations in large closed-shellsupermolecules of which atoms are linked bycovalent bonds (i.e., there are no Van der Waals norhydrogen bonds between atoms in a single molecule)[15, 16]. For simulations of the self-assembly of
bioorganic supramolecules in which the separate
molecules are associated by hydrogen bonds or Van
der Waals forces we used PBEPBE [6, 8, 9, 14], andPBELYP [7, 14] methods. In these two methods,
exchange functionals include some electron
correlation effects at larger distances that provide
relatively good descriptions of the Van der Waals
forces and hydrogen bonds. To obtain accurate
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
orbitals of the 6-31++G** basis set (the standard
tables [17] give the appropriate basis set description).
The above-mentioned 6-311++G** basis set
convention was adopted by John Pople andcoworkers. The basis set structure is given for thewhole molecule, rather than a particular atom. The
notation also emphasizes the split valence (SV)nature of these sets. Symbols like n-ijG or n-ijkG are
encoded as follows: n – the number of primitives forthe inner shells; ij or ijk - the number of primitives
for contractions in the valence shell. The ij notation
describes sets of valence double zeta quality and ijk,

Table 1 The function availability and range of applicability
for each built-in basis set in Gaussian03 [6] and ORCA [8, 9]
program packages.

- 67 -

Basis set

Applies to
atoms

Polarization
functionsDiffusefunctions

3-21G

H-Xe

* or **

+

6-31G

H-Kr

(3df,3pd)++

6-311G

H-Kr(3df,3pd)++

The chemical formulas of the molecules used in
the simulated version of minimal cell are 1) 1,4bis(N,N-dimethylamino)naphthalene – (CH3)2-NC 8H6-N-(CH3)2, and 2) cytosine – C 4H5N3O, and 3)
precursor of fatty acid – C 6H5-CO-(CH2)-O-CO(CH2)3-CH3, and 4) head (the waste piece) of the
precursor of fatty acid – C 6H5-CO-CH3, 5) and fatty
acid – HO-CO-(CH2)3-CH3 (see Figure 2).

Viva Origino 35 (2007) 66 - 72

was comparing enough well with the experimental
value of 450.0 nm [5]. It was possible that theremaining small (450.0-440.0=10 nm) difference
understood by the greater number of water and fatty
acid molecules found in the real system incomparison with the previous models [2, 3]. The
slightly shorter wavelength given by the model was
also consistent with our finding that the inclusion of
more water and fatty acid molecules in the models
resulted in longer wavelengths for the absorption
spectrum.
All figures were created by Molekel software [20]in this article.

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, and2) cytosine molecules, and 3) precursor of fatty acid, and
4) head (the waste piece) of the precursor of fatty acid, 5)
and fatty acid molecules. Carbon atoms and theirassociated covalent bonds are shown as green sticks,
hydrogens are in light grey, oxygens – red, nitrogens –blue.

Quantum modeling of the self-assembly of nanostructures in PNA based minimal living cells was
performed using the software we developed forbuilding PNA double helices.
The geometries of the constituent molecules andtheir pairs were individually optimized using the
PBELYP [7, 14] method with the 6-311++G** basis
set implemented in the GAMESS-US program
package which is installed in dual processor Opteronservers Linux cluster of our Theoretical MolecularElectronics and Spintronics research group and with
the PBEPBE method [6, 14] using the 6-311++G**
basis set [17] implemented via the Gaussian03
program package on the Los Alamos National
Laboratory (LANL) SGI Altix 3000 supercomputer.
We used TD DFT PBEPBE method [6] with the
6-31G basis set together with COSMO water solvent
method [18] in the ORCA program package which isinstalled on our dual processor Opteron servers Linuxcluster to calculate the absorption spectra and therelative positions of the HOMO and LUMO
eigenvalues of Schroedinger equation of the pFA andvarious separate sensitizer molecules, that is to say,
1,4-bis(N,N-dimethylamino)naphthalene, and 1,4dihydroquinoxaline, and 7,8-dimethylisoalloxazine[2]. Analysis of the results showed that thesesensitizers were good candidates for use in artificial
minimal cells because their HOMO electron energy
levels were energetically high enough relative to the
LUMO electron energy level of the pFA moleculeand their absorption spectra were in the visible region[2]. These investigations were performed without thepresence of surrounding water molecules. Therefore
the absorption spectra were strongly shifted to theblue region. Thus the resulting analysis was valuable
only for comparison of HOMO and LUMO
eigenvalues relationships, but not for obtaining thereal wavelengths of the absorption spectra.
By investigating a number of different models [2,3, 20] of the photosynthetic systems and eachsubsequent model including more water and fatty
acid molecules, we were able to quantify this effect.
The rather good model shown in the paper [19] gave
an excitation photon wavelength of 440.0 nm, which

3. Quantum modeling of self-assembly andphotoinduced electron transfer in PNA based
artificial minimal cell3.1. Quantum modeling of self-assembly of
minimal living cell.
We have investigated geometry optimization of aminimal cell section containing a cytosine bearing
PNA fragment with an attached 1,4-bis(N,Ndimethylamino)naphthalene sensitizer, six fatty acid,two pFA, two the waste pieces of the pFA molecules,
and 18 water molecules constituting the micellar
container’s inner monolayer, using the electron
correlated PBEPBE method with the 3-21G basis set(see Figure 3). The cell system studied is consistedof 333 atoms (not including the associated water
solvent shells) and is 3.0 nm in diameter.

Figure 3. Image of the geometric and electronic structure of asystem consisting of 333 atoms and containing fragment ofPNA
molecule
withattached
1)
1,4-bis(N,Ndimethylamino)naphthalene, 2) cytosine molecules, andtwo, 3) precursor of fatty acid molecules (in the left and in
the top-right), and two, 4) head the waste pieces of the
precursor of fatty acid molecules (in the bottom and in theright), and six, and 5) fatty acid molecules and watermolecules that were optimized using the PBEPBE/3-21G
model. Carbon atoms and their associated covalent bonds
are shown as green sticks, hydrogens are in light grey,
oxygens – red, nitrogens – blue. Hydrogen bonds are
depicted by dashed lines.

- 68 -

Viva Origino 35 (2007) 66 - 72

The water molecules, which surrounded the entire
bioorganic photosynthetic complex were found tostabilize the system. Thereby all the interatomic
distances were reduced (all H-bonds are marked indash lines in Figure 3). The water molecules
organized into nano ice-like substructures. One ofsuch a nano ice-like substructures is self-organized in
the right-bottom in Figure 3, and another in the topright. It is only because of the hydrogen and Van der
Waals bonds among the cytosine-PNA, fatty acid,
pFA, waste pieces of the pFA molecules and watermolecules that this system with 3.0 nm larger
diameter exists. The distances among the separated
sensitizer, fatty acid, pFA, waste pieces of the pFA
molecules and water molecules are comparable to Van
der Waals and hydrogen bonding radii, and therefore
we may regard the minimal cell as single electron
conjugated supramolecule that we can deal with using
an electron correlated model. Since cytosine-PNA
fragment interacts with fatty acid, and pFA, andwaste pieces of the pFA molecules and with watermolecules through their correlated electrons,intermolecular distances and surface area calculations
are critical in understanding the time dependent
electron tunneling processes associated with thevarious excited states of this minimal cell. These
nonlinear quantum interactions compress the overallsystem resulting in a smaller gap among the HOMO
and LUMO electron energy levels.
It is important to say that only quantum
mechanical electron correlation TD-DFT experimentswith minimal protocells gives results to be exactlycomparable with spectroscopic results and all othermore simplyfied QM methods such as local gradient
DFTor ab initio Hartree-Fock gives structures andspectra far from the experimentaly measured.

also consistent with our finding that the inclusion of
more molecules in the models resulted in longer
wavelengths for the absorption spectrum. The shift of
the absorption spectrum to the red for the artificial
protocell photosynthetic center might be consideredas the measure of the complexity of this system.
This our found method of designing ofphotosynthetic centres of minimal cells makes
possible to search for new sensitizers [21].
3.3. Quantum modeling of electron tunneling in
excited states of minimal living cell.

of

We have performed calculations using TD DFTPBEPBE method [8, 9] with the 6-31G basis set
together with COSMO [18] water solvent method of
the difference of electron charge density (excited-state- ground-state) for the conjugated cytosine-1,4bis(N,N-dimethylamino)naphthalene supermolecule,six fatty acid, two pFA molecules, and two waste
pieces of the pFA molecules, and visualized theelectron charge tunneling associated with certain
excited state transitions (see examples in the Figures
4-6).
The calculation indicated that the most intenseelectron charge transition from the conjugatedcytosine-PNA
fragment-1,4-bis(N,Ndimethylamino)naphthalene supermolecule to one ofthe pFA molecules was for the eighth excited state(HOMO-1→LUMO+1) transition and had an energy
and wavelength of 2.753 eV and 450.3 nm
respectively (see Table 2 and Figure 4).
The electron cloud hole in Figures 4, 5 and 6 isindicated by the dark blue color while the transferred
electron cloud location is visualized by the grey color.
We have also found a relative intense electron
charge transition for the tenth excited state mainly
from the 1,4-bis(N,N-dimethylamino)naphthalene

The absorption spectrum (see Table 2) of thisphotosynthetic system was calculated optimizing
geometry by using the TD DFT PBEPBE method [8,9] with the 6-31G basis set together with COSMO[18] water solvent method.
This latest and indeed the most realistic model
shown in the present paper gave an excitation photon
wavelength of 450.3 nm, which was comparing
exactly with the experimental value of 450.0 nm [5].
The small (10 nm) difference obtained in the previous
paper [19] was compensated for including to theprevious rather good system by two waste pieces ofthe pFA molecules in addition to the water, fatty acid,and pFA molecules. The waste piece of the pFA
molecule possesses the aromatic ring (see Figure 2)
therefore conjugated electrons strongly interact withother molecules in this system generating Van der
Waals forces. These additional Van der Waals
interactions of the introduced two waste pieces of thepFA molecules with the water, fatty acid, and pFA
molecules shortened all the inner micelle diameterand resulted in a even smallest gap between the
HOMO and LUMO electron energy levels. This was

Figure 4. Visualization of the electron charge tunnelingassociated with the eighth excited state. The transition isfrom the conjugated cytosine-PNA fragment-1,4-bis(N,Ndimethylamino)naphthalene supermolecule (in the leftbottom) to the one of the pFA molecules (in the left).
Carbon atoms and their associated covalent bonds areshown as green sticks, hydrogens are in light grey,
oxygens – red, nitrogens – blue.

3.2. Quantum mechanical calculations
absorption spectrum of minimal living cell.

- 69 -

Viva Origino 35 (2007) 66 - 72
Table 2 Excitation transitions energies of a cytosine-PNA fragment covalently bonded to a 1,4-bis(N,N-dimethylamino)
naphthalene sensitizer, six fatty acid, two pFA molecules, two the waste pieces of the pFA molecules and 18 watermolecules, as calculated using the TD PBEPBE method with the 6-31G basis set together with water solvent COSMO
method [18]. The weight of the individual excitations are given if larger than 0.01. Arrow → indicates the direction ofindividual electron transition from ground state HOMO-m to certain excited state LUMO+n.
ExcitedState #

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15

Individual t r a n s i t i o n s
HOMO-m → LUMO+n
HOMO
LUMO
→
HOMO
LUMO+1→HOMO
LUMO+2→HOMO
LUMO+3→
HOMO-1LUMO→
HOMO-2LUMO→
HOMO
LUMO+4→
HOMO-1
LUMO+1→HOMO-1
LUMO+2→
HOMO-2
LUMO+1→HOMO-2
LUMO+2→
HOMO-1
LUMO+3→
HOMO-2
LUMO+3→HOMO
LUMO+5→
HOMO-3
LUMO→

Weight o f
individualtransition
0.99
0.99
0.99
0.99
1.00
0.99
0.99
0.99
0.99
0.99
1.00
0.99
0.99
0.01
0.99

Energy( e V)

Wavelength
(nm)

2.161
2.362
2.371
2.520
2.549
2.571
2.711
2.753
2.759
2.773
2.781
2.908
2.930
3.004
3.009

573.7
524.8
522.9
491.9
486.3
482.2
457.4
450.3
449.3
447.1
445.8
426.3
423.1
412.7
412.1

Oscillator
strength(arbitrary
0.000016
0.000022
0.000000
0.000221
0.000000
0.000006
0.000080
0.000902
0.000000
0.000409
0.000000
0.000002
0.000061
0.000732
0.000065

molecule to the same pFA molecule (HOMO2→LUMO+1) equal to 447.1 nm (2.773 eV) (seeTable 2 and Figure 5).
We have also found a relative intense electron
charge transition for the fourteenth excited state(412.7 nm or 3.004 eV) from the 1,4-bis(N,Ndimethylamino)naphthalene molecule to the secondof pFA molecules (weight of individual transition
HOMO→LUMO+6 is equal to 0.99) (see Table 2
and Figure 6).

Figure 6. Visualization of the electron charge tunnelingassociated with the fourteenth excited state. The transition
is
from
the
sensitizer
1,4-bis(N,Ndimethylamino)naphthalene molecule to the second ofpFA molecules (in the top-right).

Figure 5. Visualization of the electron charge tunnelingassociated with the tenth excited state. The transition ismainlyfromthesensitizer
1,4-bis(N,Ndimethylamino)naphthalene molecule to the one of pFA
molecules (in the left).

- 70 -The electron tunneling intense transitions of the
8th, 10th and 14th excited states should induce
metabolic photodissociation of pFA molecule
because the transferred electron cloud is located on
the head (the waste piece) of pFA molecule (seeFigures 4, 5 and 6). The new fatty acid from
dissociated pFA molecule will join to minimal cell,and therefore this minimal cell will grow and later
spontaneously break in two new minimal cells andViva Origino 35 (2007) 66 - 72

once again will use pFA molecules during the photoexcitation processes for generation the new FA
molecules, etc. This photoinduced autocatalytic
bioorganic system was experimentaly proved in thepapers [4, 5], and called in LANL "Protocell
Assembly" project as minimal artificial living cell.
Our last two quantum self-assembled models of
the photosynthetic systems includes a PNA fragment
which is covalently bonded to a Ru(bipyridine)32+[21]
orbis(4-dimethylamino-2dihydroxyphenyl)squarine sensitizer, and pFA andwater molecules. It was confirmed by the small
differences (0.2 nm) of the experimental absorption
spectra peaks [5] in comparison with our QM
calculated that our chosen method of designing single
electron nano photocells might be useful not only for
artificial organisms but also for wide implementationin the nano photodevices and molecular computers[22].
Conclusions
An important finding of our investigation of thequantum self-assembly of photosynthetic centers andthe functioning of the photosynthetic process is thecritical role played by the nonlinear quantum electron
correlated hydrogen bonds and Van der Waals
interactions that result from the addition of water andfatty acid molecules. The distances between theseparated sensitizer, fatty acid precursor (pFA) andwater molecules are comparable to Van der Waals andhydrogen bonding radii, and therefore we may regard
minimal cells as single electron conjugatedsupramolecules that we can deal with using anelectron correlated TD DFT methods. These nonlinear
quantum interactions compress the overall system
resulting in a smaller gap among the HOMO andLUMO electron energy levels and photoexcitedelectron tunneling from sensitizer to pFA molecules.
Our presenting quantum self-assembled model ofthe photosynthetic systems includes a cytosine-PNA
fragment which is covalently bonded to a 1,4bis(N,N-dimethylamino) naphthalene sensitizer, andsix fatty acid, two pFA molecules, and two heads(the waste pieces) of the pFA molecules of
constituting the 3.0 nm size micellar container’s
inner monolayer with water. The correspondence ofour calculated absorption spectra peak 450.3 nm withthe experimental one indicate that we obtained
realistic structure of photosynthetic center of minimalcells reported in [4, 5], and makes possible to search
for new sensitizers [21].
Quantummechanicalelectroncorrelation
experiments of self-assembly of above describedartificial minimal living cells show that these cells
are complex systems because only entire ensembl of
PNA, sensitizer, pFA, FA and water molecules isstable and performs quantum photosynthetic
processes. Removing the small part of nucleobase,
FA and water molecules leads to the structuralchanges in comparison with realistic structures andthe difference from the spectroscopic values ofphotoexcited electron tunneling from sensitizer (1,4- 71 -bis(N,N-dimethylamino)naphthalene
topFA
molecules. QM electron correlation experiments ofself-assembly of artificial minimal cells removing themain part of nucleobase, FA and water molecules
lead to the degradation of these cells. We can statethat the inclusion of ever more water, fatty acid, pFA
molecules, waste pieces of the pFA molecules andnucleobase molecules in the different artificial
minimal cells results in a shift of the absorption
spectrum to the red for the artificial protocell
photosynthetic center, leading to an ever closer
approach to the real experimental value, and indicatesthe measure of the complexity of this quantum
complex system, i.e. a minimal protocell. It is
important to say that only QM electron correlation
TD-DFT experiments with minimal protocells give
results to be exactly comparable with spectroscopic
results and all other more simplyfied QM methods
such as local gradient DFTor ab initio Hartree-Fockgives structures and spectra far from theexperimentaly measured.
The correspondence of experimental absorption
spectra peaks and our QM calculated confirmed that
our chosen method of designing single electron nano
protocells might be useful not only for artificial
minimal living cells but also for wide
implementation in the nano photodevices, andmolecular computers [22].
Acknowledgments
The work was funded via the PACE
(Programmable Artificial Cell Evolution), theEuropean Integrated Project in the EU FP6-IST-FET
Complex Systems Initiative, and partially by the
Agency for International Science and Technology
Development Programmes.
The authors also thank the Los Alamos National
Laboratory Protocell Assembly LDRD DR project foruse of the LANL SGI Altix 3000 machine and theirinstalled Gaussian 03 program package.
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