J. Phys. Chem. B 2008, 112, 1533-1539
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Role of Length-Dependent Stability of Collagen-like Peptides S. Sundar Raman,† R. Parthasarathi,† V. Subramanian,*,† and T. Ramasami‡ Chemical Laboratory, Central Leather Research Institute, Adyar, Chennai 600 020, India, and Department of Science and Technology, New Mehrauli Road, New Delhi 110 016, India ReceiVed: April 11, 2007; In Final Form: October 17, 2007
Understanding the structure, folding, and stability of collagen is complex because of its length and variations in the amino acid (AA) sequence composition. It is well known that the basic constituent of the collagen helix is the triplet repeating sequence of the form Gly-XAA-YAA. On the basis of previous models and with the frequency of occurrence of the triplets, the ((Gly-Pro-Hyp)n)3 (where n is the number of triplets) sequence replicate has been chosen as the model for the most stable form of the collagen-like sequence. With a view to understand the role of sequence length (or the number of triplets) on the stability of collagen, molecular dynamics simulations have been carried out by varying the number of triplet units on the model collagen-like peptides. The results reveal that five triplets are required to form the stable triple helix. Further analysis shows that the intermolecular structural rigidity of the imino acid residues, hydrogen bonding, and water structure around the three chains of the triple helix play the dominant roles on its structure, folding, and stabilization.
1. Introduction Structure, stability, and folding studies on mature type-I collagen are complicated because of the 300-nm-long triple helical domain consisting of homologous or heterologous R chains of collagen and variation in sequence.1-3 With a view to gain insight into the structure, stability, and folding of mature collagen,modelcollagen-likepeptides(CP)havebeensynthesized.4-10 Model CPs (Gly-Pro-Hyp)n where n is the number of triplets have been commonly used in most of the investigations, which is expected to adopt the stable triple helical structure.4-10 In synthetic designing, the guest amino acid residues have been included in the (Gly-Pro-Hyp)n host peptide. These peptides have been characterized using circular dichrosim (CD) spectroscopy (at different temperatures), NMR spectroscopy, and X-ray diffraction techniques.11-19 In this context, the group of Brodsky has made several noteworthy contributions on collagen stability and amino acid tendency to form collagen using model CPs.20-30 From these studies, it is possible to derive the interrelationship between sequence, structure, stability, folding, and the propensity for various amino acids to adopt collagen-like conformations. The nature of the interaction between collagen and integrin has been carried out using model CPs by X-ray diffraction methods.31 In addition to the various experimental studies on model CPs, molecular modeling studies have also been initiated to understand the interplay of the forces that are responsible for the stabilization of the triple helical structure. The effect of mutation in the model collagen and the cause for genetic disorders such as osteogenesis imperfecta (OI) have been investigated using the molecular dynamics (MD) method.32-37 Monti et al. have modeled the supramolecular structure of collagen and explained their interaction with various organic molecules.38,39 Increase in the thermal stability of collagen has also been investigated * Address correspondence to this author. Tel: +91 44 24411630. Fax: +91 44 24911589. E-mail:
[email protected]. † Central Leather Research Institute. ‡ Department of Science and Technology.
using molecular mechanics (MM) and quantum chemistry (QM) methods by Importa et al. 40,41 MD studies by Stultzs have revealed that the unfolding of imino-poor region leads to the interaction of collagen with collagenase.42 Docking of telopeptides with the triple helix has been attempted.43 Recent MD study on CPs has highlighted the role of aspartic acid (Asp) residues in the various positions in the collagen sequence. The differential stability of CP with Asp in the XAA and YAA positions has been attributed to the changes in the flexibility of the backbone and solvation.44 The presence of ion pairs in the collagen-like sequence has also been analyzed with the help of MD simulation.45 Despite the wealth of literature on the sequence-dependent stability of model CPs, studies on the inter-relationship between the sequence length and molecular stability have been limited. Particularly, the structural basis for the choice of the sequence length or number of triplets to form the stable model CP is not probed in detail. Hence, in this investigation MD simulation has been carried out to unravel the structural basis for the minimum number of triplets (sequence length) required to form the stable collagen-like triple helical motif. 2. Computational Details On the basis of the frequency of occurrence of the triplets in type-I collagen, the most stabilizing triplet Gly-Pro-Hyp was chosen to construct different model CPs.1-19 Sequences of different lengths, ((Gly-Pro-Hyp)n)3 where n ) 1-10 systems were constructed. These are some of the model CPs synthesized in previous studies.11-19 Triple helical structures of each system were built using the gencollagen package, which is a tool used to generate the three-dimensional coordinates for the triple helical structure of collagen for a given sequence.46 The model triple helical structures considered in this study were described schematically in Figure 1. All MD simulations were carried out using the AMBER 6.0 package following the standard protocols.32,47 Six nanosecond (ns) simulations were carried out with the NVT ensemble for all of the model CPs
10.1021/jp0728297 CCC: $40.75 © 2008 American Chemical Society Published on Web 01/11/2008
1534 J. Phys. Chem. B, Vol. 112, No. 5, 2008
Raman et al.
Figure 1. Schematic representation of amino acid composition of collagen-like peptides.
Figure 2. Schematic representation of the diameter (D) of the collagen triple helix encompassed by all three CR atoms where a, b, and c represent the distance between each chain’s CR atom. The Gly, Pro, and Hyp residues are represented in the ball and stick model. The red colored regions are the potential sites for water interaction.
with different sequence lengths. Each MD simulation was performed by employing periodic boundary conditions (PBC) and also in an explicit solvent (TIP3P) environment with 8.0 Å of solvent from the solute to the edge of the box.48 The force field developed by Park et al. were used for hydroxyl proline.49 The entire system was equilibrated for 1 ns. A production run period of molecular dynamics was performed for 5 ns at 300 K. The trajectories were saved at every 0.2 picoseconds (ps) for further analysis. The analyses of the trajectories were made using the PTRAJ package. To shed light on the role of length in the stability of CPs, we obtained various parameters from the MD trajectories. The definitions of various parameters used in this study to examine changes during MD simulations were described in the following analysis section.
Figure 3. Radius of gyration per triplet plotted as function of time for CPs.
3. Analysis 3.1. Root-Mean-Square Deviation (rmsd). The rmsd of each residue of all of the peptides was calculated with respect to initial conformation as a function of time using eq 1.
rmsd(t) )
[ ∑|| 1
N
N i)1
|| ]
ri(t) - ri(0)
1/2
2
(1)
where ri is the distance between atoms at time t is compared with the distance between the same atoms at time zero and N is total number of backbone atoms. The rmsd of the backbone
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J. Phys. Chem. B, Vol. 112, No. 5, 2008 1535
Figure 4. Average rms deviation of Gly, Pro, and Hyp residue in CPs.
in Figure 2. The diameter (D) of the triple helix was calculated as a function of time.
Di ) 2 × (a × b × c)
x(a + b + c) × (b + c - a) × (a + b - c) × (c + a - b) (2) where, a, b, and c are distance between each CR atom. The average diameter of the triple helix was calculated using the equation given below
Diameter ) average(D1,D2...Di)
Figure 5. Water accessibility per residue calculated from RDF peaks for CPs.
is presented in the Supporting Information, Figure 1. The residue-wise rmsd with time has averaged as Gly, Pro, and Hyp for the entire trajectory. 3.2. Measure of Diameter of the Triple Helix. During the MD simulation, the possibility of the winding and unwinding of the collagen superhelix is possible, which lead to changes in the diameter of the triple helix. To quantify variation in the diameter of the triple helix, we calculated the diameter of the circle encompassed by the three CR atoms of all the three chains as given in eq 2.50 The schematic representation of the definition of diameter is presented
(3)
where Di represents the diameter of a circle encompassed by the ith set of the three CR atoms of the chains. The average diameter of the triple helix over the entire trajectory is calculated. 3.3. Radial Distribution Function (RDF). The RDF or pair correlation function gab(r) between CP (designated as A) and water (designated as B) is defined in eq 4
gab(r) )
1
1
〈FB〉local NA
NA NB ∂(r
∑ ∑ i∈A j∈B
ij
- r)
4πr 2
(4)
where, 〈FB〉local is the water density averaged over all spheres around each electronegative atom in the CP model with radius rmax ) 10 Å. The schematic representation of water interacting regions were marked in red (Figure 2). The RDF data has been plotted against the distance and also given in the Supporting
1536 J. Phys. Chem. B, Vol. 112, No. 5, 2008
Raman et al. TABLE 3: Binding Energy of Each Collagen-like Peptide
triplet
binding energy (kcal/mol)
total number of hydrogen bonds
binding energy/ number of hydrogen bond (kcal/mol)
5 6 7 8 9 10
-59.39 -65.94 -73.61 -142.16 -175.87 -183.67
12 15 18 21 24 27
-4.94 -4.39 -4.08 -6.77 -7.32 -6.80
TABLE 4: Average Diameter of the Triple Helix of Each System
Figure 6. Average dihedral angle φ (N-CR) and Ψ (CR-C) plotted in a Ramachandran map for all collagen-like peptides.
TABLE 1: Average Puckering in Collagen-like Peptidesa triplets
Pro
SD
Hyp
SD
1 2 3 4 5 6 7 8 9 10
5.6 38.6 -16.4 -10.2 34.5 34.7 33.4 35.6 35.8 36.2
36.6 45.0 47.8 22.1 14.6 13.2 14.1 10.6 10.6 8.8
12.3 -6.7 -2.4 11.4 -20.5 -18.1 -19.3 -20.3 -17.8 -19.9
49.8 32.9 44.5 41.9 10.1 6.9 8.7 9.0 4.1 5.6
a
In degrees.
TABLE 2: Number of Hydrogen Bonds and Their % Occupancy of Each Collagen-like Peptide
triplets
by each hydrogen bond
in Å
in degrees
1 2 3 4 5 6 7 8 9 10
0 5 6 9 12 15 18 21 24 27
40.61 74.35 77.45 81.57 84.38 86.83 86.37 87.11 87.28
3.02 2.99 3.02 3.03 3.04 3.04 3.04 3.05 3.05
143.40 144.80 145.94 146.12 146.49 146.79 147.01 147.26 147.33
Information, Figures 2-6. From the RDF, variation in the solvent accessibility at different type of atoms in the CP with the chain length has been computed using eq 5.
Solvent accessibility at position I in the system ) Peak value in RDF at Ith position (5) Total number of such I positions in the model 3.4. Puckering Effect. CPs contain proline and hydroxy proline, which have five-membered rings. Changes in their ring conformation were determined using the PTRAJ analysis package. 3.5. Dihedral Angle Analysis. Conformational analysis during MD simulation was performed by looking at the changes in the Ramachandran angles with time. The average variation in these angles was computed in angstroms 3.6. Hydrogen Bond Analysis. The variation between the intermolecular hydrogen bonds present in the three R chains of
triplets
in Å
SD in Å
3 4 5 6 7 8 9 10
6.07 6.49 5.93 5.83 5.78 5.82 5.80 5.80
0.3 1.7 0.2 0.1 0.1 0.1 0.1 0.1
collagen with time was obtained from the trajectory using the geometrical criteria as given in eq 6. The lifetime of the hydrogen bonds was determined according to the expression in eq 6
Hi )
{
1, ((d(Hi - - Oi) e 3.5Å) and (140 o e angle (Oi - - Hi - Ni) e 180 o )) 0, otherwise
(6)
where Hi is the possible ith intermolecular hydrogen bond in the triple helix. The percentage of occupancy of the ith hydrogen bond is
Occupancy of hydrogen bond Hi in %
[
}
)
]
Total no. of Hi ) 1 state × 100 (7) Total no. of comformation
4. Results and Discussion To understand the effect of amino acid sequence length on the stability of CPs, we have carried out an MD investigation. Various structural parameters (defined in the analysis section) have been obtained from the trajectories collected during simulations. The rmsd of the backbone for each model is given as in the Supporting Information, Figure 1. Similarly, the radius of gyration per triplet has been plotted against time for each model in Figure 3. These two parameters are good indicators of the structure and stability. It can be found from the results that the model CPs that form the triple helix do not show any drastic change in the structure and there is no unfolding of these peptides from triple helical conformation. The residue-wise rmsd of each peptide has been averaged, and the same are shown in Figure 4. It can be seen from the rmsd results that the fluctuation of Gly is significantly high when compared to Pro and Hyp. Because Pro and Hyp are conformationally rigid residues due to the presence of five-membered rings; the sequence length does not influence the fluctuation of these amino acids. It can be observed from the rmsd results that the fluctuation in the Gly residue decreases with increase
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J. Phys. Chem. B, Vol. 112, No. 5, 2008 1537
Figure 7. Average structure of CPs at different lengths. Cyan color represents A chain, orange color represents B chain, and green color represents C chain.
in the sequence length. It is possible to note that the fluctuation in the Gly is minimum for (Gly-Pro-Hyp)5. It is interesting that from MD simulation a minimum of five triplets is necessary to form the stable triple helical motif of collagen. This result has profound implications in the amino acid composition of collagen. It is clear from the amino acid sequence data that every third residue in collagen is Gly and it is about 33% of the total amino acid content.51 It is well established that it is a primary structural requirement for the formation of the stable collagen triple helix. In addition, Gly residues are buried well inside the triple helix and the residues in the XAA and YAA positions are partially or fully exposed to the surroundings.52-54 Hence, the least fluctuation in the Gly residue leads to stabilization of CPs. It is well known that collagen has a characteristic Gly-XAAYAA repeating pattern. The architecture of collagen particularly reveals that the interaction of water with various amino acid residues is position-dependent. The residues in the XAA positions are highly accessible to water molecules, whereas the same in the YAA position are partially exposed to water.52-54 To understand the role of water interaction in the stabilization of model CPs, we calculated the position-dependent solvent interaction from the MD trajectory. The RDF for each possible water interacting atom is given in the Supporting Information, Figures 2-6. The peaks observed in the RDF have been used to understand the nature of solvent interaction with the model CPs. The backbone oxygen and side-chain hydroxyl atom of the Hyp residue, which can interact with the water molecules and their peaks, are at 1.75 and 1.85 Å, respectively. Gly nitrogen has a peak at 2.85 Å. Gly and Pro oxygen have peaks at 1.75 Å. A similar observation has been found from previous studies.44,45 Figure 5 depicts the average of the solvent interaction per residue for different model CPs corresponding to Gly, XAA, and YAA positions. The result directly reinforces that the solvent exposure of collagen is position-dependent. As the chain length increases, the residue-wise interaction with solvent decreases due to the formation of a compact triple helical structure. This is clearly evident from the results obtained for interaction of Gly with water molecules. For sequence lengths beyond five triplets, the water interaction with Gly residue is less when compared to the other positions because of the
formation of the compact triple helix in which Gly residue is accommodated well inside the triple helix as explained in the collagen model proposed by Ramachandran and others.55 The interaction of water molecules with residues in the XAA and YAA positions marginally decreases with sequence length, indicating the formation of a triple helix. The Ramachandran dihedral angles (φ and ψ) for Gly are -76° and 170°. The same for Pro residues in the XAA position are -76° and 168°. φ ) -75° and ψ ) 155° for the Hyp residue in the YAA position. The MD trajectory shows a deviation of (20° in the ψ angles. Figure 6 represents the variation in the average φ and ψ values for different model CPs with various sequence lengths. As mentioned earlier, because of the rigidity of the five-membered rings of imino acids, there is not much change in the φ values with increase in the sequence length. The deviation in the ψ values corresponding to the Hyp is more for the sequence length less than five triplets. However, the formation of a compact triple helix beyond four triplets decreases the fluctuation in the ψ values. Recent reviews on the factors that govern the stability of collagen highlight the significance of the puckering of imino acids.56-58 Pro in the XAA prefers up puckering, whereas the Hyp at the YAA prefers down puckering. The average puckering of Pro and Hyp for different model collagens is listed in Table 1 with the standard deviation. The number of triplets does not generally influence the puckering of Pro, whereas the puckering of Hyp is significantly dependent on the sequence length. Collagen models with less than four triplets prefer up puckering, whereas above four prefers down puckering, which is in accordance with the crystal structure data on CPs.18,19 This observation clearly reinforces that ring puckering plays a vital role in the formation as well as stabilization of collagen. Intermolecular hydrogen bonding is the most important interaction that seams the polypeptide chains together to form a exquisite stable triple helix. Modification of the hydrogen bonds leads to changes in the triple helical structure. N-H of Gly from one chain interacts with the OdC group of Pro at other chain in the same position to form a hydrogen bond. For every triplet in the collagen, one intermolecular hydrogen bond has been observed. Table 2 shows the number of hydrogen
1538 J. Phys. Chem. B, Vol. 112, No. 5, 2008 bonds observed in each system, their percentage of occupancy during the MD simulation, the average hydrogen-bond distance, and average bond angle over the period of 5-ns simulation. The geometrical nature of these hydrogen bonds is independent of the length of the triple helix. Although the length increases, the number of possible hydrogen-bonding sites in the structure and their percentage of occupancy increases. These results show the important role played by the intermolecular hydrogen bonds in the formation the stable triple helix. The triple helical association energy for each model was calculated using the following equation
Binding Energy) ETriple Helix (EchainA + EchainB + EchainC) (8) where ETriple Helix is the total energy of the triple helix and EchainA, EchainB, and EchainC are the energies of individual chains. For each model, the binding energy has been calculated for the last conformation of the trajectory by removing the solvent molecule and after minimization for 200 iterations using the conjugate gradient method to remove the kinetic energy component on the structure as in the standard practice. The binding energy for each model is given in Table 3. To understand the role of the hydrogen bond in the stability of the collagen structure, we calculated the binding energy/hydrogen bonds for each model. These results clearly predict the role of the hydrogen bond in the structure of the triple helix. Table 4 represents the average diameter of the collagen triple helix during the dynamics. It is evident from Table 4 that as the sequence length increases fluctuation in the diameter decreases and, hence, the stability of triple helix. Models containing more than five triplets have less fluctuation in the diameter because of the interaction of three R chains by hydrogen bonding and as consequence enhanced stability of the same. Figure 7 depicts the average structure of chosen models of collagen from the first 1 ns dynamics. Model peptides containing one triplet to four triples do not form the stable triple helix. The collagen models with more than five triplets form the stable triple helix, which is in agreement with the previous observation from melting temperature measurement on the model collagen with varying sequence length.59 The CPs with more than five triplets are also stable for 5 ns as revealed by the average structure obtained from the 5-ns trajectory. 5. Conclusions The MD simulation carried out on the model CPs has provided an interesting relationship between the length of the three R chains and stability. It is evident from the results that sequence length has a profound influence on the structure and stability. A minimum of five triplets is required to form the stable triple helix as evident from the beautiful variation in the rmsd, fluctuation in the diameter, water structure, energy, and intermolecular hydrogen-bonding interaction. It is important to note that CPs with less than four triplets prefer up puckering, whereas those with more than four prefer down puckering, which is in accordance with the crystal structure data. The average structure formed by the model CPs clearly shows that the stability of the triple helical domain increases with length. Acknowledgment. We acknowledge DST and CSIR, Government of India, New Delhi for financial support. R.P. and V.S. acknowledge the support under DST-DAAD project and
Raman et al. Prof. Dr. Gereon Niedner-Schatteburg, TU Kaiserslautern, Germany for his kind help during the visit and collaboration. Supporting Information Available: The rmsd of the backbone and RDF data. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Engel, J.; Ba¨chinger, H. P. Top. Curr. Chem. 2005, 247, 7. (2) Brodsky, B.; Persikov, A. V. AdV. Protein Chem. 2005, 70, 301. (3) Stultz, C. M. Protein Sci. 2006, 15, 2166. (4) Bachinger, H. P.; Bruckner, P.; Timpl, R.; Prockop, D. J.; Engel, J. FEBS J. 1980, 106, 619. (5) Babu, I. R.; Ganesh, K. N. J. Am. Chem. Soc. 2001, 123, 2079. (6) Sacca, B.; Renner, C.; Moroder, L. J. Mol. Biol. 2002, 324, 309. (7) Persikov, A. V.; Brodsky, B. Proc. Natl. Acad. Sci. 2002, 99, 1101. (8) Xu, Y.; Bhate, M.; Brodsky, B. Biochemistry 2002, 41, 8143. (9) Barth, D.; Kyrieleis, O.; Frank, S.; Renner, C.; Moroder, L. Chem.s Eur. J. 2003, 9, 3703. (10) Buevich, A. V.; Silva, T.; Brodsky, B.; Baum, J. J. Biol. Chem. 2004, 279, 46890. (11) Eberhardt, E. S.; Panasik, N.; Raines, R. T. J. Am. Chem. Soc. 1996, 118, 12261. (12) Lesage, A.; Penin, F.; Geourjon, C.; Marion, D.; van der Rest, M. Biochemistry 1996, 35, 9647. (13) Liu, X.; Kim, S.; Dai, Q. H.; Brodsky, B.; Baum, J. Biochemistry 1998, 37, 15528. (14) Buevich, A. V.; Dai, Q. H.; Liu, X.; Brodsky, B.; Baum, J. Biochemistry 2000, 39, 4299. (15) Kwak, J.; Capua, A. D.; Locardi, E.; Goodman, M. J. Am. Chem. Soc. 2002, 124, 14085. (16) Mohs, A.; Li, Y.; Doss-Pepe, E.; Baum, J.; Brodsky, B. Biochemistry 2005, 44, 1793. (17) Kawahara, K.; Nishi, Y.; Nakamura, S.; Uchiyama, S.; Nishiuchi, Y.; Nakazawa, T.; Ohkubo, T.; Kobayashi, Y. Biochemistry 2005, 44, 15812. (18) Schumacher, M.; Mizuno, K.; Bachinger, H. P. J. Biol. Chem. 2005, 280, 20397. (19) Schumacher, M. A.; Mizuno, K.; Bachinger, H. P. J. Biol. Chem. 2006, 281, 27566. (20) Mielewczyk, S. S.; Breslauer, K.; Anachi, R.; Brodsky, B. Biochemistry 1996, 35, 11396. (21) Shah, N. K.; Ramshaw, J. A. M.; Kirkpatrick, A.; Shah, C.; Brodsky, B. Biochemistry 1996, 35, 10262. (22) Liu, X.; Siegel, D. L.; Fan, P.; Brodsky, B.; Baum, J. Biochemistry 1996, 35, 4306. (23) Yang, W.; Battineni, M. L.; Brodsky, B. Biochemistry 1997, 36, 6930. (24) Shah, N. K.; Sharma, M.; Kirkpatrick, A.; Ramshaw, J. A. M.; Brodsky, B. Biochemistry 1997, 36, 5878. (25) Doss-Pepe, E.; Deprez, P.; Inestrosa, N. C.; Brodsky, B. Biochemistry 2000, 39, 14884. (26) Persikov, A. V.; Ramshaw, J. A. M.; Kirkpatrick, A.; Brodsky, B. Biochemistry 2000, 39, 14960. (27) Persikov, A. V.; Ramshaw, J. A. M.; Kirkpatrick, A.; Brodsky, B. J. Am. Chem. Soc. 2003, 125, 11500. (28) Silva, T.; Kirkpatrick, A.; Brodsky, B.; Ramshaw, J. A. M. J. Agric. Food Chem. 2005, 53, 7802. (29) Li, Y.; Kim, S.; Brodsky, B.; Baum, J. J. Am. Chem. Soc. 2005, 127, 10490. (30) Persikov, A. V.; Ramshaw, J. A. M.; Kirkpatrick, A.; Brodsky, B. Biochemistry 2005, 44, 1414. (31) Emsley, J.; Knight, C. G.; Farndale, R. W.; Barnes, M. J. J. Mol. Biol. 2004, 335, 1019. (32) Klein, T. E.; Huang, C. C. Biopolymers 1999, 49, 167. (33) Mooney, S. D.; Huang, C. C.; Kollman, P. A.; Klein, T. E. Biopolymers 2001, 58, 347. (34) Mooney, S. D.; Kollman, P. A.; Klein, T. E. Biopolymers 2002, 64, 63. (35) Mooney, S. D.; Klein, T. E. Mol. Cell. Proteomics 2002, 1, 868. (36) (a) Radmer, R. J.; Klein, T. E. Biochemistry 2004, 43, 5314. (b) Radmer, R. J.; Klein, T. E. Biophys. J. 2006, 90, 578. (37) Parthasarathi, R.; Raman, S.S.; Subramanian, V.; Ramasami, T. Unpublished results. (38) Bronco, S.; Cappelli, C.; Monti, S. J. Phys. Chem. B 2004, 108, 10101. (39) Monti, S.; Bronco, S.; Cappelli, C. J. Phys. Chem. B 2005, 109, 11389. (40) Improta, R.; Benzi, C.; Barone, V. J. Am. Chem. Soc. 2001, 123, 12568. (41) Improta, R.; Mele, F.; Crescenzi, O.; Benzi, C.; Barone, V. J. Am. Chem. Soc. 2002, 124, 7857.
Role of Length-Dependent Stability (42) Stultz, C. M. J. Mol. Biol. 2002, 319, 997. (43) Malone, J. P.; George, A.; Veis, A. Proteins: Struct., Funct., Bioinf. 2004, 54, 206. (44) Raman, S. S.; Parthasarathi, R.; Subramanian, V.; Ramasami, T. J. Phys. Chem. B 2006, 110, 20678. (45) Raman, S. S.; Vijayaraj, R., Parthasarathi, R.; Subramanian, V.; Ramasami, T. J. Mol. Struct. (THEOCHEM) In press (doi:10.1016/ j.theochem.2007.11.030). (46) Huang, C. C.; Couch, G. S.; Pettersen, E. F.; Ferrin, T. E.; Howard, A. E.; Klein, T. E. Pac. Symp. Biocomput. 1998, 349. (47) Pearlman, D. A.; Case, D. A.; Caldwell, J. C.; Seibel, G. L.; Singh, U. C.; Weiner, P.; Kollman, P. A. AMBER 6; University of California: San Francisco, CA, 1995. (48) Pearlman, D. A.; Case, D. A.; Caldwell, J. C.; Seibel, G. L.; Singh, U. C.; Weiner, P.; Kollman, P. A. Comput. Phys. Commun. 1995, 91, 1. (49) Park, S.; Radmer, R.; Klein, T.; Pande. V. S. J. Comput. Chem. 2005, 26, 1612.
J. Phys. Chem. B, Vol. 112, No. 5, 2008 1539 (50) Standard Mathematical Tables and Formulae; Zwillinger, D., Ed.; CRC Press: Boca Raton, FL, 1996; p 271. (51) Fietzek, P. P.; Kuhn, K. Int. ReV. Connect. Tissue Res. 1976, 7, 1. (52) Berisio, R.; Vitagliano, L. Biopolymers 2001, 56, 8. (53) Handgraaf, J. W.; Zerbetto, F. Proteins: Struct., Funct., Bioinf. 2006, 64, 711. (54) Mogilner, I. G.; Ruderman, G.; Grigera, J. R. J. Mol. Graphics Modell. 2002, 21, 209. (55) (a) Ramachandran, G. N.; Kartha, G. Nature 1955, 176, 593. (b) Rich, A.; Crick, F. H. C. Nature 1955, 176, 915. (56) Hodges, J. A.; Raines, R. T. J. Am. Chem. Soc. 2005, 127, 15923. (57) Shoulders, M. D.; Hodges, J. A.; Raines, R. T. J. Am. Chem. Soc. 2006, 128, 8112. (58) Jenkins, C. L.; Lin, G.; Duo, J.; Rapolu, D.; Guzei, I. A.; Raines, R. T.; Krow, G. R. J. Org. Chem. 2006, 71, 1754. (59) Long, C. G.; Braswell, E.; Zhu, D.; Apigo, J.; Baum, J.; Brodsky, B. Biochemistry 1993, 32, 11688.
