Design and Bio-Synthesis of Bionanoscale Self Assemblies and Nanotubes.
Abstract
I. One of our in phase I of this proposal is to design a palette of non-natural aminoacids with a broad range of desired
sticking properties ( both hydrophobic and hydrophilic) that would self assemble on a nanoscale. These non-natural
aminoacids are designed so that they can be incorporated into the protein machinery of living organisms to make welldefined protein based nanomaterials. These self-assembling nanoscale biomaterials can be used in nano-encapsulation, or
can be used in a biosensor. To this end we would continue the ongoing collaboration between the Goddard group at Caltech
(theory and design) and Tirrell group at Caltech for the biosynthesis. Nature encodes in proteins not only the chemical
architecture of the chain, but also the capacity for assembly into functional supramolecular systems. Artificial proteins
create analogous opportunities for the materials scientist and the materials engineer. We propose herein a coordinated
investigation of the design, synthesis and assembly of artificial proteins: we would start from the case of the “rod-coil-rod”
triblock copolymers that undergo reversible gel formation in response to changes in environmental parameters. The
reversible gelation would be used as a testing bed for the control of the properties of the artificial proteins designed at a
nanometer scale. We have promising preliminary results in the design and synthesis of fluorinated gcn4-pl leucine zippers
that leads to an increase in the temperature stability of the helix dimer motif. Tirrell introduced nonnatural aminoacids in
the sequence of native gcn4-pl leucine dimer zippers. Substitution of leucyl methyls by trifluoromethyl groups resulted in a
significant gain in helix thermal stability; the thermal melting transition temperature of the fluorinated peptide was elevated
from 49C to 62C. This extra stability has been explained by the simulations (Goddard) as due to the favorable
electrostatic interactions between fluorines and hydrogens. Simulations also explain that not all flourine substituted leucines
would have this stability. Here we propose:
 Design of non-natural aminoacid analogs that can be incorporated in protein synthesis by living organisms: To
begin with Vaidehi and Goddard would use simulations to alter the properties of leucine ( fluoroleucine- partially
fluorinated and perfluoro derivatives) to build temperature resistant stable helix dimers. Also study the variation
of the stability of these zipper dimers with the degree of fluorination and optical purity of the fluorinated dimers.
Substitution at other hydrophilic residue sites in the core of the dimer would also be performed. These results
would be used by Tirrell's group to synthesize ( in living organisms) these fluorinated leucines and other nonnatural aminoacid analogs to increase the stickiness or the strength of the dimers.
 Optimization of the length of the helices: The defining characteristic of the leucine-zipper motif is a heptad
periodicity, typically designated -(abcdefg)-, in which the a and d positions are occupied by hydrophobic groups
(often leucine), and e and g are acidic or basic (i.e., titratable) residues. We propose to study the variation of the
stability of the dimer with the length of the helices in the dimer. Also analogs of acidic and basic residues in the e
and g positions would be attempted to improve the stability of the dimers. Experiments would be done to
synthesize these fluorinated leucine dimers and measure its stability using Circular Dichroism (CD) variation with
temperature. Also we would use the gel-sol transition measurements to assess the properties of the dimers.
 Using simulations to design synthetic analogs of natural aminoacids with interesting functionality. This is also a
continuation of the ongoing collaboration in an effort to design various synthetic analogs of phenylalanine, by
calculating the binding energy of the phenylalanine to the phenylalanine t-RNA synthetase(PheRS). We would
continue these simulations for other analogs of phenylalanine and isoleucyl t-RNA synthetase.
Another major exploratory effort we propose between theory and experiment is in the design and fabrication of novel
polymeric nano-filaments drawn via a membrane-templating approach in aqueous systems. The diameters of such filaments
can be reduced to the nanometer size range. The changes in shape or in volume that are triggered by chemical or physical
signals are expected to occur on a timescale of milliseconds – faster from membrane templates. Towards this goal
 We would build and optimize the structures of the lipid bilayer nanotube of stearoyl-oleoyl phosphaidylcholine
and calculate the mechanical properties of these filaments including the bending modulus and "elastic" constants"
of these filaments and its variation with the concentration of polyethylene glycol that is used to strengthen the
nanotubes using first principles simulation techniques developed at the Goddard lab in the past 6 years as a part
of the NSF- Grand Challenge Group.
 Tirrell’s lab at Caltech will establish effective chemistries for filament preparation, develop mechanical testing
methods for accurate determination of the tensile and bending properties of nanometer-scale polymeric systems.
These filaments have potential utility as sensors and actuators in robotic and other devices.
II. Background, Preliminary and Proposed Work:
This section is partitioned into three parts: 1) a brief outline of the first principles simulation techniques that has
been derived by the Goddard group as a part of the NSF-Grand Challenge Application Group(NSF-ASC?) and NSFSGER-DBI-9708929(1996-1997?), 2) outlines the background and preliminary experimental and theoretical work for
the control self assembly of macromolecules or artificial proteins followed by the proposed work for this part and 3)
background and preliminary theoretical and experimental work on nanoscale polymer filaments and proposed work on
control design of nanofilaments of desired dimensions, tensile strength and mechanical properties.
II.1 First Principles Simulation Methods
This section describes briefly some first principles simulation methods developed in Goddard group
which provide new tools essential to the proposed project. As a part of the NSF-Grand Challenge
Application GroupNSF-ASC over the last five years we have developed various methods and computational
tools useful in describing and modifying the structures of complex bio macromolecules and materials. These
tools include:
II.1.1 Quantum Mechanical Methods
PS-GVB/Solvate (Tannor et.al 1994) (Pseudo Spectral Generalized Valence Bond) uses ab intio quantum
mechanical methods for predicting accurate structures and molecular properties including solvation effects [
at the Poisson Boltzmann level)]. This allows prediction of structures while including solvation effects. This
method is useful for accurate calculation of energies of small peptides with solvation and would be used for
predicting peptide energies with several mutations.
II.1.2 Fast Monte Carlo Methods
The Continuous Configurational Boltzmann Biased(CCBB) Monte Carlo method(Sadanobu and
Goddard 1997) is a highly efficient variant of the for direct evaluation of the partitio function, free energy,
and other configurational dependent physical properties for long polymer chains. This method (CCBB)
combines continuous configurational biased sampling with Boltzmann factor biased enrichment. To illustrate
the efficiency and to validate the bias correction for weighting the torsion and chain enrichments, we have
applied this model to isolated single chains using a united atom force field. For a 50 monomer polymer chain
CCBB with 400 chains leads to an accuracy of 0.1% in the free energy whereas simple sampling direct Monte
Carlo requires about 109 chains for this accuracy. This leads to cost savings by a factor of about 350 000.
CCBB is easily extended to multichain systems, to the condensed state, to more realistic force fields, and to
evaluating the mixing free energy for amorphous polymer blends. The CCBB method has been extended to
study the tertiary folding of proteins. The method uses double biasing to obtain an ensemble of compact
folded structures. Algorithmic filtering is needed through the ensemble for native like structures for further
study. We are currently developing such methods for deriving the loop structure of the outer membrane
protein A under the NIH/NIHCD project. The CCBB method has been tested in various proteins up to 75
residues(Debe and Goddard 1998). This method is a remarkable advancement that can be used for structure
based rationale studies where the native structure is not known. This method would be used in the proposed
study to calculate thermodynamic properties of polyglutamine aggregates.
1.
2.
3.
II.1.3. Molecular Dynamics(MD) Methods
We have developed the Massively Parallel Simulation (MPSim) program(Lim et. al 1997) to allow
simulations for systems with up to a million atoms or smaller systems for long time scales ( up to
microseconds). MPSim was developed for massively parallel computers and includes such important
algorithm developments as :
The Cell Multipole Method (Ding et. al 1992a) CMM, dramatically reduces the cost of long-range Coulomb
and van der Waals interactions while retaining high accuracy. The cost scales linearly with size, allowing
atomic level simulations for million atom systems(ref).
The Reduced Cell Multipole Method(Ding et. al 1992b) RCMM, handles the special difficulties with longrange Coulomb interactions for crystals by combining a reduced unit cell plus CMM for interaction of the
unit cell with its adjacent cells. The cost scales linearly with size retaining high accuracy, allowing simulation
of crystals with a million atoms per unit cell.
The Newton -Euler Inverse Mass Operator (NEIMO) method (Jain et. al 1993; Mathiowetz et. al 1995;
Vaidehi et. al 1996) for internal co-ordinate dynamics which treats some regions of the protein as rigid , while
2
4.
5.
6.
7.
others are treated with only torsional degrees of freedom. NEIMO allows use of large time steps which
enables long time dynamics. The cost of NEIMO is linear in the number of degrees of freedom , staying
much less than the other costs for million atom systems.
Heirarchical NEIMO(H-NEIMO) is a rigorous coarse grain MD method (Vaidehi and Goddard 1999) based
on atomic level forcefield. The dynamics can be performed at several levels of heirarchy ranging from all
torsion dynamics to coarse grain, domain dynamics. With fine-grain all-torsion NEIMO dynamics, we
normally treat double bonds, terminal single bonds, and rings (benzene) as rigid bodies. In H-NEIMO
dynamics we allow various levels of coarseness, keeping rigid during the dynamics various segments or parts
of a domain. This allows larger time steps and thus H-NEIMO dynamics allows one to simulate long time
scale domain motions in a protein in a shorter simulation timescale by focussing on those degrees of freedom
that bring about the large domain motions especially in enzymes.
Poisson-Boltzmann (PB) description (Tannor et al 1994) included in the dynamics to include solvent effects,
water or membrane, which are critical for simulation of bio-macromolecules. We have also recently included
a faster description of the solvent effects using the Surface Generalized Born(SGB) method(Ref). We have
also shown that the SGB method is as accurate as the PB method in describing the electrostatics of the
solvent.
Various thermodynamic ensembles like the constant temperature, constant volume, constant pressure and
constant energy (like the (T,V,N), (T,P,N) ensemble dynamics have been incorporated in the MPSim program.
This allows us to simulate the dynamics under experimental conditions.
Algorithms and methods suitable for massively parallel high performance (SGI-Origin-2000, IBM-SP2, Cray
T3D/T3E, HP/ Convex-Exemplar, and Intel Paragon).
II.1.4 Non-equilibrium Molecular Dynamics(NEMD) and Transport Properties
Recently we have made considerable progress in the theory of NEMD(Cagin et all?). We have developed
an approach to predict viscosity by including external shear rates directly into the Hamiltonian equations of
motion. The NEMD technique enables us to determine the transport coefficients from the response of the system
to finite applied fields. In NEMD the vicosity is calculated the same way the experimentalist would measure it.
The shear viscosity coefficient, , is obtained directly by evaluating the momentum flux in a system subject to a
known applied shear rate. Also NEMD can evaluate the pressure and viscometric function in addition to the shear
viscosity, enabling us to study the fluid microstructure in the nonequilibrium steady state.
II.2.1. Encoded Self-Assembly of Macromolecular Materials: Background and Preliminary Experimental work.
Nature encodes in proteins not only the chemical architecture of the chain, but also the capacity for
assembly into functional supramolecular systems. Artificial proteins create analogous opportunities for the
materials scientist and the materials engineer. We propose herein a coordinated investigation of the design,
synthesis and assembly of two classes of artificial proteins: i). “rod-coil-rod” triblock copolymers that undergo
reversible gel formation in response to changes in environmental parameters, and ii). uniform helical rod-like
polymers that form novel smectic liquid crystal phases. In each case, the capacity for self-assembly is encoded in
the chain sequence and is critically dependent upon the architectural control provided by the biocatalytic
polymerization process.
II.2.2 Reversible gels. Recent work from Tirrell’s laboratory has shown that rod-coil-rod triblock copolymers
containing leucine-zipper endblocks flanking a soluble polyelectrolyte domain undergo reversible gelation in
response to small changes in pH or temperature. The mechanism of gelation in these systems is unique, in that it
relies on controlled dimerization (or higher-order aggregation) of the leucine-zipper domains under conditions
where the polyelectrolyte “spacer” remains soluble (Figure II-1).
The leucine zipper is a common structural motif found in many eukaryotic transcription factors such as GCN4 (9).
The defining characteristic of the leucine-zipper motif is a heptad periodicity, typically designated -(abcdefg)-, in
which the a and d positions are occupied by hydrophobic groups (often leucine), and e and g are acidic or basic
(i.e., titratable) residues. Such periodic chains readily adopt helical conformations that place a and d on a single
hydrophobic face of the helix, where they are flanked by titratable residues e and g. The primary driving force for
protein dimerization is provided by formation of the hydrophobic interface of the dimer, but electrostatic forces
arising from e-g interactions can modulate dimer stability in response to changes in pH and stabilize heterodimeric
aggregates in preference to homodimers (10). The triblock design shown in Figure II-1 preserves the protein
dimerization function of the zipper domain, but turns that function toward entirely new objectives; protein-protein
recognition now leads not to DNA binding, but rather to the formation of switchable hydrogels. The mild
conditions under which gelation is reversible (near-neutral pH and near-ambient temperature) make these triblock
copolymer systems attractive candidates for use in molecular and cellular encapsulation and in controlled
3
reagent delivery (Figure II-2). This preliminary result is intriguing insofar as it illustrates the strong connection
between molecular structure and materials properties. Thus manipulations of the molecular structure would affect
the nanoscale properties of these hydrogels. At the same time, it highlights the need for precise, quantitative
descriptions of these connections, such that real materials design can be accomplished. GCN4-p1 is a leucine
zipper (shown in Fig?) peptide containing 33 residues in which four leucine-leucine interactions contribute to the
thermal stability of the coiled coil architecture.
Trifluoroleucine, an unnatural amino acid that has
been incorporated into proteins with high efficiency,
was substituted at all the leucine positions in GCN4p1. The choice of trifluoroleucine was based on two
factors. First it has been well documented that
fluorinated amino acids are nearly isosteric to their
natural analogs, and are equally (or more) inert
chemically (10). The second and the more crucial
factor in choosing trifluoroleucine is that it is accepted
by the endogenous leucyl-tRNA
Figure 1. Gelation of triblock artificial proteins.
synthetase (LeuRS) during biosynthesis of
recombinant proteins (11). When leucine auxotrophic
cells are shifted to a medium without leucine after
induction of protein synthesis, the host machinery will
charge trifluoroleucine in a highly efficient manner. In
fact, it has been observed that over 95% of leucine
positions in a recombinant protein can be substituted
by trifluoroleucine (12). Similar to wild type GCN4p1, the fluorinated peptide is essentially 100% helical as determined by circular dichroism (Fig.3A). Substitution of leucyl
methyls by trifluoromethyl groups resulted in a significant gain in helix thermal stability; the thermal melting transition
temperature of the fluorinated peptide was elevated from 49C to 62C(see Fig.3B). The thermal melting profiles of the
peptides were studied using circular dichroism (16). The ellipticity at 222 nm was monitored as a function of temperature
and converted to the fraction of peptide unfolded (Fig. 3B) (17). The difference in thermal behavior is most evident at
temperatures higher than 30C. Tfl-GCN4-p1 denatures to a lesser degree than leu-GCN4-p1 at the same temperature,
indicating a more stable coiled-coil aggregate. The fluorinated peptides are also more resistant to guanidine and urea
denaturation. Thus incorporation of non-natural aminoacids may provide proteins of enhanced stability.
100
[q] (103 deg cm2 dmol-1)
II.2.3 Preliminary Results from Theory
The collaboration between theory and experiment is ongoing
in this area of nanomaterials between Goddard’s group and Tirrell’s
group. Here we describe some of the preliminary results obtained on
the theoretical simulations that explain the strength of the fluorinated
zippers that have been synthesized by Tirrell’s group as compared to
the native triblock leucine zipper based polymers.
A
80
60
40
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0
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-40
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226
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254
258
Wavelength (nm)
1
0.9
Fraction Unfolded
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0.6
0.5
Quantum Mechanical and Molecular Dynamics Results for
Fluorinated Leucine Zippers.
We have an ongoing collaboration on the design of
temperature resistant fluorinated leucine based zippers described in
the previous section. In this section a brief description of the
simulation results on molecular level understanding of the binding
strength of the native gcn4 leucine dimer (fig 5A) and its fluorinated
derivatives(Fig5B) is presented. Constant temperature Nose-Hoover
dynamics was performed with a fast and accurate description of the
0.4
0.3
0.2
B
0.1
4
0
0
10
20
30
40
50
60
Temperature (C)
70
80
90
100
solvent using the SGB method using the MPSim code on an SGI-Origin 2000 parallel machine for the native gcn4 leucine
zipper. The starting structure for the dynamics was taken from the protein data bank for gcn4 leucine zipper. MD
simulations at 300K with DREIDII (Mayo et al 1984) and charges from CHARMM(ref) for the protein show a stable
structure with a net CRMS of <3.5 A, which is the experimental R factor. The binding energy (enthalpy) for this native
dimer was calculated to be –40.0Kcals/mole which is in good agreement with the experimental measurement of the
enthalpy of formation of the dimer which is 36.5 (?) Kcals/mole.
Fluorinated Zippers:
The charges on the fluorine of fluorinated leucine(Leu(F)) zippers are critical in determining the binding energy
of the dimers . These charges have been derived by performing a quantum mechanical(QM) calculation on the tripeptide,
Gly-Leu(F)-Gly using HF method with PB solvation and 6-31G** basis set. Using the QM charges on Leu(F) we built the
fluorinated dimer starting from the native dimer structures. Since substitution of one of the methyl groups on the side chain
of leucine leads to a chiral center at the -carbon there are several possible combinations of chirality in the dimer. There are
four leucine pairs that are selectively substituted with F. Considering that all the -carbons on a monomer helix is of the
same chirality we first studied the four possible dimers as shown below and in Fig. (6). The case where the carbon attached
to the fluorines in the side chain of fluoroleucine is closer as shown in Fig 6A ( the distance being 4.7A) is called "close".
When the flourines are as shown in Fig.6B where the distance between the carbons attached to the fluorines is 7.1A is
called the "far". The other case where one of the carbon attached to the fluorines is at 7.1A is called the "mixed" case.
There are obviously two possibilities here. It is experimentally tedious to synthesize these optically pure dimers but in such
a situation the theoretical simulations are very helpful in understanding the experimental results.
1.
R R
2. L L
3. R L
4. L R
R R
L L
R L
L R
R R
L L
R L
L R
R R
L L
R L
L R
"far"
"close"
"mixed1"
"mixed2"
Fig.4 The four possible conformers for which simulations were done presently.
Fig. 5. The native gcn4-pl dimer is shown in A and the
fluorinated dimer ( F atoms are red) is shown in B. A close up
view of the distances between the F atoms are shown in Fig.6
Using a one point energy of the minimized structures we
determined that the rotamer built using the native structure as the
template is of the lowest energy among the other possible
rotamers. We performed MD simulations on all four fluorinated
dimers for 200ps using MPSim with SGB solvation. The binding
energies were calculated by averaging the minimized energy of
the structures obtained over the last 10ps of the 200ps dynamics.
The helix monomer energies are obtained by averaging the same
way as the dimer, with minimization. The results for the
flourinated dimers show a separation into two cases. While the
energy of the "close" dimer is high due to the unfavorable
electrostatic repulsions between the fluorines the rest three
dimers "far", and the two "mixed" cases are similar as shown in
Fig. 7. Thus theory can clearly differentiate between the various
optical isomers of the fluorinated dimers using would aid the
design and control of experiments. This is a preliminary
demonstration of the strong collaboration that is in the heart of
this exploratory project.
Fig.6. The three possible conformers of fluorinated leucine
zippers . The fourth conformer showed in Fig.4 is the similar to
the “Mixed” case shown above but the fluorines switched
5
between the two helices. The larger distance shown in the picture is about 7A and the shorter one is about 4A.
Fig. 7 Potential energy(Kcals/mole) variation of the various dimers with time(ps).
II.2.4 Proposed Work: We propose herein a coordinated program of molecular molecular architecture, solution
properties, and gelation behavior of bioengineered block copolypeptides. The biocatalytic approach allows precise - and
independent - control of the length, composition and charge density of the polyelectrolyte domain, and of each of the
relevant architectural features of the associative endblocks. Such control is of real value in designing fluids and hydrogels
of predetermined physical properties.
Effect of Fluorine substitution at the molecular design level: Molecular modeling can provide immediate information for
two current approaches in gel engineering. First is the incorporation of even more hydrophobic residues such as
hexafluoroleucine at the d position. The increase in side chain size may cause even more hydrophobic driving force for
chain association in solution. However, as mentioned earlier, introduction of the cluster of fluorines in the hydrophobic
core might induce unfavorable electrostatic energy (i.e. repulsion). Molecular dynamics can be used to quantify the two
competitive energy contributions and predict the effects of such substitutions (or any other substitution at any position
within the peptide). Hence we would continue to study the effect of fluorination on the stability of the fluorinated zippers as
a function of the degree of fluorination of the side chains. In the simulations we are building optically pure isomers and
hence would compute the dimerization energy in terms of fundamental forces.
Prediction of the Effect of Length of the helical regions on the stability: The second approach that is underway in
our group is to lengthen the zipper domain so that it contains more leucine-leucine contacts at the hydrophobic
surface of the coil-coil. Lengthening the zipper domain requires meticulous recombinant DNA manipulation to
produce the protein in vivo since the wild-type GCN4 is already at the length limit of solid-phase peptide
synthesis. The structure of longer zippers is not known. Recent methods in the Goddard lab have yielded folded
structures of short polypetides to the experimental helical propensities(Bertsch et 1l 1998, Peng et al 1999). Hence
we would use the NEIMO MD methods with solvation to study the effect of length on the helical structure of the
zippers. These molecular dynamics results should provide insight into the amount of additional stability that might
be achieved before experiments are performed.
Experiments: The preliminary experiments were not done with optical purity at the chiral center of the fluorinated leucyl
methyl carbons. We propose to build optically pure fluorinated gcn4-pl dimers and measure its stability using Circular
Dichroism (CD) variation with temperature.
From the amino acid analysis and mass spectroscopy data, we will be able to determine the amount of
trifluoroleucine incorporation in the protein . Circular dichroism and DSC will be used to study the change in
energy associated with the different levels of substitution. Ultracentrifugation will not be used on these
macromolecules since disulfide linkages dramatically increase the aggregation order and distributions of coils.
6
Effects of Fluorination on the properties of hydrogels- Mesoscale Dynamics NEMD: Having studied the effect
of fluorine substitution and the effect of the length of the helical regions at the molecular level, the next step is the
mesoscopic simulations of the hydrogel. We would construct hydrogels at various levels of fluorine substitution
and optimal helical length. It is not known whether fluorination has other effects on the hydrogels in addition to
enhancing their thermal stability. To understand how the different levels of fluorination would affect the
properties of the hydrogel, such as the gel-sol transition we would perform the following simulations. The
hydrogels would be built as an infinite periodic system. We would then perform NEMD simulations on the
periodic system and apply a shear at a constant rate. The shear viscosity coefficient will be calculated using the
momentum flux caused by the shear rate. Now the sharp change in the viscosity coefficient with temperature
would depend on the level of fluorine substitution. Thus we would perform NEMD simulations at a given shear
rate at various temperatures and the temperature at which the viscosity changes sharply would be plotted vs the
level of fluorine substitution.
Experiments: First, proteins with different levels of fluorine incorporation will be synthesized by varying the level
of trifluoroleucine in the expression medium. After purification, amino acid analysis and mass spectrometry will
be used to determine the level of incorporation of fluorinated leucines. The pH responses of these hydrogels might
also be altered since the increased binding strength between the helical domains might require a higher level
deprotonation (i.e. higher pH) at the e and g positions to facilitate the transition from gel to solution. In fact, by
varying the level of fluorination, one might be able to obtain a collection of hydrogels with different pH dependent
behaviors. The results from the simulations of the previous section would be used for the design of experiments
for various level of fluorination. The optimum level of fluorination ( from theory) for which the transition
temperatures are higher would be chosen to study the effect of pH on the sol-gel transitions. This could be the first
time one can synthesize a series of pH sensitive proteins using the same amino acid sequences. On the other hand,
the free energy gain from entropy as a consequence of fluorination might be too small compared to the
electrostatic repulsion between residues e and g that the sol-gel transition behavior might not differ significantly
from the 100% leucine containing proteins. This competition in energy can be studied by monitoring the viscosity
change in gels as a function of pH. Rolling ball viscometry has been the method used to observe gelation
phenomena in our group. If necessary, commercial rheometers can be used to study the rheological change in
proteins upon fluorination.
III.1.1 Nanoscale Bionano-filaments- Background
Fig.8 Four views of the singlewall carbon nanotube along
and perpendicular tube axis.
Simulation capabilities for nanotubes and nanowires at
the Goddard group: We have performed extensive
molecular mechanics and molecular dynamics studies on
the energy, structure, mechanical and vibrational properties
of single wall carbon nanotubes (SWNT)(Gao et al 1998,
Che et al 1999) with different radius and chirality
(armchair (n,n), chiral (2n,n), and zigzag (n,0)). In this
study an accurate interaction potential derived from
quantum mechanics was used. The simulation studies were
primarily carried out using the MPSim Program. We
studied the mechanical properties and stabilities of the
carbon nanotubes as a function of radius and various forms
(circular and collapsed). In the bulk phase we determine
the specific packing, density, lattice parameters. Molecular
Dynamics and Molecular Mechanics studies led to a
triangular packing as the most stable form for all three
forms. More importantly, we determined the Young's
modulus along the tube axis for triangular-packed SWNTs
using the second derivatives of the potential energy. They
are Y = 640.30 GPa, Y = 648.43 GPa, and Y = 673.49
7
GPa, respectively. Normalized to carbon sheet these values are within a few percent of the graphite bulk value. Using
classical thin plane approximation and variation of strain energy as a function of curvature, we calculated the bending
modulus of the SWNTs. The calculated bending moduli are k (n,n) = 963.44(GPa), k (n,0) = 911.64(GPa), and k(2n,n) =
935.48(GPa). We also calculated the interlayer spacing between the opposite sides of the tubes and found d(n,n) = 3.38(Å),
d(2n,n) = 3.39(Å), and d(n,0) = 3.41(Å). In order to assess the tensile and compressive strength of the SWNTs, a series of
compressive and tensile loading experiments was performed by varying the c lattice parameter, along tube axis. With
respect to the optimum c lattice parameter, co, the strain can be defined as
 = c/co
The tubes are softer under compression due to buckling effect. Four different views along the tube axis and
perpendicular to the tube axis are presented in Figure (?). Based on those energy strain curves, "elastic constants",
as the second the derivative of energy with respect to applied strain was calculated.
III. 1.2 Simulation of lipid bilayers for membrane proteins :
Simulation Description
As a part of the ARO-MURI project on optimization of the structure of olfactory receptors, we carried out a
series of MD simulations (Floriano et al 1999) at constant temperature and pressure (NPT MD) for the 1,2dilauroyl-DL-phosphatidyl ethanolamine acetic acid (DPE), Disodium beta-glycerophosphate hydrate (GP0) and
L-alpha-glycerol phosphorylcholine (GPC) crystal structures (Elder et al., 1977; Lis & Starynowicz, 1985;
Abrahamsson & Pascher, 1966). The atomic coordinates were taken from the Cambridge Structural Database
(CSD). Figure ? shows the chemical diagrams for DPE, GP0 and GPC. The systems were chosen in order to
evaluate the performance of the force field and atomic charges progressively. Therefore we simulated a phosphate
group (GP0), a polar head group (phosphorylcholine) commonly present in membrane lipid bilayers (GPC), and
the same polar head group combined to alkane chains in the lipid bilayer DPE. The simulations started with the
CSD coordinates. The atomic coordinates and cell parameters were minimized using periodic boundary conditions
(PBC). The minimized crystals were submitted to 100 ps of NPT MD at 300K and 1atm, under PBC. All cell
parameters were flexible during simulations. The dynamics time step was 0.001 ps, the temperature relaxation
time was 0.01 ps, and the Rahman-Parrinello mass term was 0.1. The non-bonded interactions were calculated
using spline cutoffs (Rcut = 9 Å for GP0 and GPC; Rcut = 9 and 15 Å for DPE).
We used the Dreiding (Mayo et al 1984) force field combined with a set of charges derived from Charge
Equilibration. The results were compared to experimental cell parameters and densities (Elder et al., 1977; Lis &
Starynowicz, 1985; Abrahamsson & Pascher, 1966), and to previous theoretical studies (Willians & Stouch, 1993;
Tobias et al., 1997) available in the literature.
Results: Cell parameters, density and volume are listed in Table 1 for the DPE, GP0 and GPC crystal simulations.
Some results from the literature for GPC are also showed for comparison purposes. The first cited simulation
consist of a minimization using the force field CVFF (Dauber-Osguthorpe et al., 1988), with potential-derived
atomic charges calculated using the 6-31G basis set, fixed alpha and gamma angles, and rigid molecules (Williams
& Stouch, 1993). The second cited simulation reports two sets of 80 ps NPT MD at 300K and zero pressure, fully
flexible cells, periodic boundary conditions, and Ewald summation (ref) for the non-bonded interaction (Tobias et
al., 1997). The first set uses CHARMM22 (ref) force field and charges, and the second set uses a mixed flexible
Williams (Williams & Stouch, 1993) plus CHARMM22 potential and charges. All theoretical values are compared
to experimental data.
As seen in Table 2, the present simulations reproduce the experimental cell parameters and densities of the
DPE, GP0 and GPC crystals with more than 90% accuracy. The errors in density are 4% or less. The cell
parameters are very well reproduced, especially if we consider that both minimization and NPT MD calculations
had no restrictions on their values. The potential and charge scheme used by Tobias et al. (Tobias et al., 1997) also
give results in very good agreement with the experimental parameters for GPC, although it is somewhat worse
than ours in reproducing the density. On the other hand, those authors suggested based on their simulations results
of alkanes, that the alkane chains need more complicated potential forms than those used by them (data not
shown). Our results, on the contrary, are consistent for all three levels of complexity represented by the phosphate
(GP0), phosphorylcholine (GPC) and dilauroylphosphatidylethanolamine (DPE) molecules.
NPT simulations are useful tools for evaluating force field quality. Nevertheless, the present simulations are a
good indication that the combination Dreiding force field/Qeq polar groups is suitable for describing membrane
lipid bilayers. This combination is being currently use to simulate the purple membrane from Halobacterium
8
halobium, which is composed by lipid bilayers of diphosphatidyl glycerophosphate, in MD simulations of
transmembrane proteins. Figure 2 shows a schematic view of the simulated membrane.
Table 1. Cell parameters (a, b, c, alpha, beta, and gamma) and density (Dens) for (a) DPE, (b) GP0, and
(c) GPC crystals at 300K and 1 atm.
(a) DPE
a (Å)
b (Å)
c (Å)
Experimental (a)
Minimized-cell variable
NPT MD Spline/9A (g)
NPT MD Spline/15A (h)
47.70
48.12
56.98
49.29
7.77
7.21
7.05
7.23
9.95
10.4
10.49
10.63
(b) GP0
a (Å)
b (Å)
c (Å)
Experimental (b)
Minimized-cell variable
NPT MD (g)
8.85
8.74
8.67
8.85
8.78
8.64
32.77
32.86
33.01
alpha
(degrees)
90.00
89.77
88.88
90.55
beta
(degrees)
92.00
92.08
119.55
87.87
alpha
(degrees)
90.00
89.95
89.49
gamma
(degrees)
90.00
89.99
85.15
92.79
beta
(degrees)
97.17
95.66
94.64
(c) GPC
a (Å)
b (Å)
c (Å)
Experimental (c)
Williams & Stouch, 1993 (d)
Tobias et al., 1997 (S II) (e)
Tobias et al., 1997 (CHARMM22) (f)
Minimization-cell variable
NPT MD (g)
10.10
10.43
10.26
9.69
9.99
9.83
7.71
7.64
7.67
7.65
7.61
7.59
16.62
16.40
16.69
15.43
16.84
17.09
Dens
(g/cc)
1.1277
1.1789
1.1660
1.1232
gamma
(degrees)
90.00
90.10
89.28
alpha
(degrees
)
90.00
89.9
90.1
90.0
90.4
Volume (Å3)
3685.5
3604.8
3644.8
3783.7
Dens
(g/cc)
1.6448
1.6679
Volume (Å3)
2545.1
2509.8
2482.7
beta
(degrees)
gamma
(degrees)
Dens (g/cc)
102.70
102.8
103.1
99.7
106.8
106.0
90.00
1.35
90.0
90.4
90.0
89.8
1.30
1.47
1.39
1.39
(a) Elder et al., 1977; (b) Lis &.Starynowicz, 1985; (c) Abrahamsson &.Pascher, 1966; (d) CVFF force field,
potential-derived charges using the basis set 6-31G, minimization; (e) S II force field and charges, 80ps NPT,
300K, 0.0GPa; (f) CHARMM22 force field and charges, 80ps NPT, 300K, 0.0GPa (g) Dreiding force field, polar
groups Qeq charges, NPT at 300K, 1atm, 100ps, NB Spline/9Å; (h) same as (g) but NB Spline/15Å.
Table 2. Percentage of standard deviation from experimental values for calculated cell parameters (a, b, c, alpha,
beta, gamma) and density (Dens) of DPE, GP0 and GPC crystals at 300K and 1 atm
alpha
beta
gamma
Dens
(degrees)
(degrees)
(degrees)
(g/cc)
4
0
0
0
4
-1
0
0
-1
0
1
-1
-1
0
0
-1
0
1
3
-1
-1
NA
0
NA
NR
a (Å)
b (Å)
c (Å)
DPEa
1
-7
GP0a
-1
GPCa
Minimization
b
GPC
9
NPT MD
DPEa
3
-7
6
6
-4
3
GP0a
-2
-2
1
-1
-3
-1
-3
-1
3
0
3
0
3
1
0
0
0
0
0
-4
-4
-1
-7
0
-3
0
9
a
GPC
GPC S II
c
GPC
CHARMM22
a
c
present work
b
c
0
Williams & Stouch, 1993.
DPE
O
Tobias et al., 1997.
H
NA=not applicable (angles were kept
fixed).
NR=not reported.
O
H
O
O
O
P
N
O
O
O
H
GP0
O
O
P
O
OH
O
HO
GPC
CH3
O
3HC
OH
P
N
O
CH3
O
O
OH
10
Figure 2. Schematic view of a simulated membrane composed by bilayers of diphosphatidyl
glycerophosphate (DPG). The unit cell has 25 lipid bilayers corresponding to 15500 atoms.
In the two sections described above, Goddard group has demonstrated the capabilities to simulate the
strain in a nanotube and simulations of the lipid bilayer membranes for assembling membrane proteins.
Both of these components are vital for the proposal described below.
III.1.3 Nanotubes for Bio-Sensors: Recent developments in the fabrication of meso- and nanoscale
structures have included the self-assembly of carbon and other materials into nanotubes and quantum wires
(1) and the coalescence of lipid surfactants from solution into sub-micron tubules (2). Formation of bilayer
nanotubes from membrane capsules is a common occurrence in cell biology. For example, when a cell or
vesicle sticks to a foreign surface at a point and is then pulled away, an optically invisible bilayer tube
(diameter < 100 nm) usually connects the capsule to the surface even after displacements of many
diameters (4). Two physical conditions are requisite for nanotube formation from bilayer vesicles: (i) The
bilayer must be bonded to a spot on a rigid surface and (ii) there must be a reservoir of excess bilayer
surface beyond that sufficient to enclose the vesicle volume as a sphere. These two conditions are easily
attained and manipulated externally. First, vesicles after preparation are slightly dehydrated by increasing
the osmotic strength of the aqueous suspension. After aspiration into a micropipet, the excess surface of
the vesicle is drawn into a projection inside the pipet (Fig. 1 A), which provides the reservoir of bilayer for
nanotube production. By appropriate control of bilayer composition, strong attachments can be made when
11
the vesicle is touched to a surface. When the pipet holding the vesicle is withdrawn, a nanotube is formed
(Fig. 1 A and B).
Nanotubes and networks prepared in
this way are intrinsically unstable, and cannot
survive removal from the aqueous processing
medium. In the preliminary studies of Evans
and Tirrell (3), photoinitiated radical crosslinking of polyethylene glycol 1000
dimethacrylate (PEGDMA) confined to the
interior of the lipid assembly was chosen as a
A.
B.
prototype chemistry for stabilization of the
membrane template. Cross-linked
Fig. 1. Video microscope images of a lipid bilayer vesicle (~
multimethacrylates form elastic networks that 20 µm diameter) held by micropipet suction and tethered to
are widely used in applications where strength a solid microsphere (~ 4 µm diameter) by an invisible
and shape stability are required (7). PEGDMA nanotube of bilayer (~ 40 nm diameter) pulled from the
vesicle surface. (A) A bright field image shows only the
is soluble both in water and in organic
vesicle and microsphere. (B) Epi-illumination is used to
solvents, but after cross-linking, the
excite fluorescence from labeled lipids doped in the bilayer,
polymerized material forms a resilient and
revealing the 40-nm diameter tube of bilayer emanating
insoluble polyethylene glycol (PEG) gel. The from the vesicle.
PEG structure is attractive in the present
context for several reasons: (i) The capability
of swelling in aqueous and organic environments enables post-polymerization processing of patterns and
networks in a wide variety of solvents, (ii) PEG does not denature enzymes or other proteins of potential
interest in biosensor or biomaterials technology [PEG-modified enzymes are used currently in clinical
applications (8)], and (iii) PEG surfaces are relatively inert with respect to biological cells, suggesting that
cell viability and function should not be altered in cellular devices based on patterned PEGDMA networks.
Potential Uses for Lipid nanotubes: The nanotube techniques provide a basis for fabrication of functional
nanoscale conduit patterns and networks of various kinds. It has already been demonstrated that lipid
tubules can be used as precursors for formation of submicrometer silica tubes (10) and as templates for
deposition of metals (2) and metal oxides (11). The methods developed in these earlier approaches should
be directly applicable to the patterns made as described here, and should produce robust structures with
useful mechanical and electronic properties. Potentially more versatile, the porous core of a polymerized
nanotube provides unrestricted opportunity for elaboration of network properties. Photocrosslinking of
water-soluble conjugated polymers can lead to networks of organic conductors and impregnation of the
core with metal salts can be used to metallize the structure after reduction. A similar approach for
deposition of metals in carbon nanotubes has been reported by others (12). The cross-linked core of
nanotubes can serve to immobilize enzymes or other proteins capable of modulating electron transfer or
biochemical recognition processes, and it is conceivable that nanotube arrays might be used to link together
patterns of biological cells immobilized on substrates (13) to create integrated "cellular" biosensors and
devices. We plan ultimately to explore each of these directions, but the focus of the proposed work is on
fabrication and mechanical behavior of flexible, nanometer-scale polymeric filaments. Because of their
small size (and the associated property of rapid response to signals, such filaments show substantial
promise as sensors and actuators in robotic and other devices.
III.2 PROPOSED WORK
III.2.1. Control of Mechanical Properties
Molecular Modeling of the nanotubes-Variation of the length and concentration of the PEGDMA:
Engineering of the mechanical properties of nanometer-scale polymeric gels should be possible through
variation in the structure and concentration of the polymerizable component entrapped in the lumen of the
nanotube used as template. Goddard group has developed (Section III.1) the forcefields and simulation
methods required to simulate a lipid nanotube filled with various concentrations polyethylene glycol
dimethacrylate(PEGDMA). We also have previous experience in computing the strain in a nanotube caused
by bending forces or the ductility of the nanotube. As shown in Fig. (?) we would build and optimize the
structure of the bilayer nanotube and compute its ductility as a function of the length of the PEGDMA.
We would use dreidii forcefield with charges from charge equilibration method for the polar head of the
12
lipid(Floriano et al 1999) and for the polymer. It will also be important to examine the role of filament
diameter in determining mechanical properties. Because mechanical properties in these systems will
depend on the extent of covalent network formation within the nanotube template during
photopolymerization, the increase in surface-to-volume ratio in very small structures may become critical
in determining properties such as modulus if connectivity is reduced (or enhanced) by surface effects.
These are ideal situations for the study using molecular level simulations since the molecular level control
alters the properties of the nanostructure.
Measurement of Physical Properties:
Based on bulk measurements, the Young’s modulus E of the polymeric filaments could be
estimated to be between 0.1 and 1 MPa. Since the filament diameters will range from 10 nm to 1 micron,
we can estimate the spring constant k for a typical sample of length L=10 microns using the formula
k=EA/L, where A is the cross sectional area. We thus expect the filaments to have longitudinal spring
constants ranging from 1 pN/micron to 10 5 pN/micron (=100 pN/nm), depending on the diameter. Goddard
group would compute the effect of long range forces on the longitudinal spring constants since it is these
long range forces on the lipid and also the valence forces on the PEG molecules that govern the strain on
the walls of the nanotube. We would construct bilayer nanotubes ranging from 10nm to 100 nm in
diameter. The PEGDMA would be built along the walls of the nanotube as shown in Fig.(?). Both the
valence forces and the nonbond forces in PEGDMA along with the nonbond forces along the head of the
lipid and similar forces along the inner walls of the tube would account for the tensile strength along the
walls of the nanotube. Young's modulus and bending modulii along the tube axis and perpendicular to the
tube axis would be computed as described in the publication Gao et 1l 1999. These quantities would be
computed as a function of
 the length of the PEGDMA molecules
 cross-linking in the PEGDMA molecules
 concentration of the PEGDMA filling the nanotube starting from 10% .
 the tube diameter
13
Experiments : Preliminary experiments, PEGDMA 1000 at a concentration of 10% (w/v) was used by
Tirrell’s group to demonstrate the effectiveness of polymerization as a method of preparing nanometerscale filaments with some degree of toughness in the aqueous processing environment. In these
experiments the integrity and elasticity of the nanostructured polymeric gels could be readily demonstrated
by deforming the filament with a micropipet. The gels were observed to deform under tension, and then to
relax back to their initial state upon release. Early successes in experiments with methacrylate-functional
polyethyleneglycols (PEGs) prompt us to focus initially on this class of reactive polymers and oligomers.
Two kinds of structural variants are readily available, and will be explored: i). linear PEG dimethacrylates
of a variety of chain lengths, and ii). branched and star-shaped PEGs with up to approximately 100 arms
per chain. The results from the simulation study would offer the experiments insights into the role of
PEGDMA and the optimum concentration of PEGDMA for a desired strength of the nanotube. While the
latter class of PEGs is not available in methacrylated form, endgroup functionalization is straightforward
and preparation of multifunctional PEG methacrylates should present no substantial problems. Comparison
of the properties of gels produced from such polymers will allow us to establish the role of network
junction functionality in controlling the mechanical behavior of nanoscale gels.
A second variable to be explored in these studies is the concentration (or volume fraction) of the
prepolymer in the nanotube template. In general, one would expect the modulus and toughness of the gel
to increase with the volume fraction of (pre)polymer, but we anticipate that nanotube formation will not be
possible at very large prepolymer concentrations. Because the maximum concentration at which tube
formation occurs may be dependent on molecular architecture, it is not obvious a priori how one should
design the system to achieve maximum modulus and strength. Here the simulation techniques would offer
pathways by which the strength of the nanotube varies with the cocentration of the PEGDMA. We will
establish the minimum prepolymer concentrations that allow formation of continuous networks, as well as
the maximum concentrations at which tube formation can be achieved. Through systematic variation in
concentration we would study the mechanical strength of polymeric nanostructures. Once this variation and
molecular architecture is understood the experiments could be designed for understanding the relations
between fabrication conditions and the concentration of the polymer.
The Goddard group will examine this question in a systematic way, by computing the molecular
level stress in the nanotube as a function of the diameter of the nanotube( varying from microns to tens of
nanometers) and analyze the stress on bond and angle energies and other components of energy like the
electrostatic and van der Waal’s energy. This would throw light on the role of the filament diameter on its
mechanical strength which is difficult for experimentalists to optimize
14