Design and Bio-Synthesis of Bionanoscale Self Assemblies and Nanotubes.

AbstractI. 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 well-defined 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 49C to 62C. 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 non-natural 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 NSF-SGER-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 MethodsPS-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 MethodsThe 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.

II.1.3. Molecular Dynamics(MD) MethodsWe 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 :

1. 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).

2. The Reduced Cell Multipole Method(Ding et. al 1992b) RCMM, handles the special difficulties with long-range 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.

3. 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 others are treated with only torsional degrees of freedom. NEIMO allows use of large time steps which

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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.

4. 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.

5. 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.

6. 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.

7. 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 PropertiesRecently 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 reagent delivery (Figure II-2). This preliminary result is intriguing insofar as it illustrates the strong connection

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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 GCN4-p1. 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 GCN4-p1, 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 49C to 62C(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 30C. 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.

II.2.3 Preliminary Results from TheoryThe 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.

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 solvent using

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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 RR 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

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the “Mixed” case shown above but the fluorines switched 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

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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. 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.

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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 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 andperpendicular 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 1,2-dilauroyl-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

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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 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) alpha (degrees)

beta (degrees)

gamma (degrees)

Dens (g/cc)

Volume (Å3)

Experimental (a) 47.70 7.77 9.95 90.00 92.00 90.00 1.1277 3685.5Minimized-cell variable 48.12 7.21 10.4 89.77 92.08 89.99 1.1789 3604.8NPT MD Spline/9A (g) 56.98 7.05 10.49 88.88 119.55 85.15 1.1660 3644.8NPT MD Spline/15A (h) 49.29 7.23 10.63 90.55 87.87 92.79 1.1232 3783.7

(b) GP0 a (Å) b (Å) c (Å) alpha (degrees)

beta (degrees)

gamma (degrees)

Dens (g/cc)

Volume (Å3)

Experimental (b) 8.85 8.85 32.77 90.00 97.17 90.00 1.6448 2545.1Minimized-cell variable 8.74 8.78 32.86 89.95 95.66 90.10 1.6679 2509.8NPT MD (g) 8.67 8.64 33.01 89.49 94.64 89.28 2482.7

(c) GPC a (Å) b (Å) c (Å) alpha (degrees)

beta (degrees)

gamma (degrees)

Dens (g/cc)

Experimental (c) 10.10 7.71 16.62 90.00 102.70 90.00 1.35 Williams & Stouch, 1993 (d) 10.43 7.64 16.40 102.8Tobias et al., 1997 (S II) (e) 10.26 7.67 16.69 89.9 103.1 90.0 1.30Tobias et al., 1997 (CHARMM22) (f) 9.69 7.65 15.43 90.1 99.7 90.4 1.47Minimization-cell variable 9.99 7.61 16.84 90.0 106.8 90.0 1.39NPT MD (g) 9.83 7.59 17.09 90.4 106.0 89.8 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

a (Å) b (Å) c (Å)alpha

(degrees)

beta

(degrees)

gamma

(degrees)

Dens

(g/cc)

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Minimization

DPEa 1 -7 4 0 0 0 4

GP0a -1 -1 0 0 -1 0 1

GPCa -1 -1 0 0 -1 0 1

GPCb 3 -1 -1 NA 0 NA NR

NPT MD

DPEa 3 -7 6 6 -4 3 0

GP0a -2 -2 1 -1 -3 -1

GPCa -3 -1 3 0 3 0 3

GPC S IIc 1 0 0 0 0 0 -4

GPC

CHARMM22c

-4 -1 -7 0 -3 0 9

apresent workbWilliams & Stouch, 1993.cTobias et al., 1997.

NA=not applicable (angles were kept

fixed).

NR=not reported.

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NO

P

O O

O

O

O

O

O

H

H

H

DPE

GP0

GPC

OP

O

OO

OH

HO

NO

P

O O

OH

O

CH3

CH3

3HCOH

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

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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 cross-linking of polyethylene glycol 1000 dimethacrylate (PEGDMA) confined to the interior of the lipid assembly was chosen as a prototype chemistry for stabilization of the membrane template. Cross-linked multimethacrylates form elastic networks that are widely used in applications where strength and shape stability are required (7). PEGDMA is soluble both in water and in organic solvents, but after cross-linking, the polymerized material forms a resilient and insoluble polyethylene glycol (PEG) gel. The 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

A. B.

Fig. 1. Video microscope images of a lipid bilayer vesicle (~ 20 µm diameter) held by micropipet suction and tethered to a solid microsphere (~ 4 µm diameter) by an invisible nanotube of bilayer (~ 40 nm diameter) pulled from the vesicle surface. (A) A bright field image shows only the vesicle and microsphere. (B) Epi-illumination is used to excite fluorescence from labeled lipids doped in the bilayer, revealing the 40-nm diameter tube of bilayer emanating from the vesicle.

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III.2.1. Control of Mechanical PropertiesMolecular 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 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 105 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

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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 nanometer-scale 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

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