Molecular Dynamics Simulations of DNA and ProteinâDNA

Chapter 26

Molecular Dynamics Simulations of DNA and Protein—DNA Complexes Including Solvent

Downloaded by UNIV OF CALIFORNIA SAN DIEGO on February 2, 2016 | http://pubs.acs.org Publication Date: September 29, 1994 | doi: 10.1021/bk-1994-0568.ch026

Recent Progress D. L. Beveridge, K . J. McConnell, R. Nirmala, M. A . Young, S. Vijayakumar, and G . Ravishanker Department of Chemistry and Program in Molecular Biophysics, Wesleyan University, Middletown, C T 06459

The results of three new molecular dynamics (MD) trajectories for the d(CGCGAATTCGCG) double helix in water, including one of 1 nanosecond (ns) duration, and an M D study of the λ repressor -operator complex are described. The D N A simulations form the basis for a detailed analysis of the progress of the trajectory over time and the dynamics of axis bending. The results indicate that the ns dynamical trajectory progresses through a series of three substates of Β form D N A , with lifetimes of the order of hundreds of picoseconds (ps). Evidence for an incipient dynamical structure is presented. To validate the simulation, the calculated axis bending is compared with that observed in corresponding crystal structure data. The results indicate that, for this system at least, significant new dynamical behavior is introduced in the ns regime, that previously reported calculations at the ps level did not reveal. Simulation of the protein - D N A complex and the independent components thereof have been carried out for 100-320 ps to date. Some preliminary results from the protein-DNA complex and indications of the extent of structural reorganization on complex formation are presented.

Molecular Dynamics (MD) computer simulations have been used in a number of recent studies (1) to investigate the nature of D N A fine structure, axis bending and helical flexibility implicated in important protein-DNA interactions (2). We report herein progress in the development of an accurate theoretical model of the structure and motions of the D N A double helix in water in the unbound state, and in a complex with a regulatory protein. The systems under consideration are the oligonucleotide duplex of sequence d(CGCGAATTCGCG), which contains the target sequence for the restriction enzyme Eco RI endonuclease, and the λ repressoroperator protein-DNA complex. The results are being compared in detail with experimental data from X-ray crystallography to validate the theoretical model.

0097-6156/94/0568-0381S08.00/0 © 1994 American Chemical Society

In Structure and Reactivity in Aqueous Solution; Cramer, Christopher J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1994.


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STRUCTURE AND REACTIVITY IN AQUEOUS SOLUTION

Previous studies from this laboratory have addressed various aspects of water structure around D N A (3), in particular the spine of hydration in the minor groove (4) and comparison with crystallographic ordered water sites (5). These studies suggest considerable localization of ordered water in the minor groove and a more disordered water in the major groove, and that both effects could contribute to the overall energetics of stabilization. It must be noted that the thermodynamics for the * spine of hydration* is not unequivocally established but there is increasing evidence suggesting a stabilizing role (5). Here, we consider the influence of solvation on the behavior of the structural dynamics of D N A and of protein-DNA complexes, including waters explicidy. M D on the d ( C G C G A A T T C G C G ) Duplex M D on D N A including solvent is computationally quite intensive, and trajectories published to date consider time scales of only a few hundred ps (6,7). In order to examine the sensitivity of results to trajectory length and choice of starting structure, we have recently performed a series of three simulations on the d(CGCGAATTCGCG) duplex, two for 500 ps and one extended to 1000 ps, or 1 ns (8). These simulations are based on the GROMOS86 force field (9), which has been setup for the simulation of biomolecules in aqueous environment (10), and the SPC model of water (21). The GROMOS force field has been extensively employed for simulation of proteins and D N A in this laboratory (6,12,13) and others (14-17). The SPC model of water is a non-polarizable effective pair potential for liquid water and is similar to other widely used models such as SPC/E (18), F3C (19), TIPS (20,21) and its variants, in terms of geometrical and nonbonded properties (22). A l l of the above models are rigid with the exception of F3C, which is flexible. The water models vary in their ability to reproduce experimentally observed properties of water. The radial distribution function agrees well up to the first solvation shell for all of these models and up to the third (~ 7 Â) for SPC and F3C (22). Calculated diffusion constant (Â /ps) for the SPC model (0.36) is comparable to that of TIP3P (0.40) but slightly higher than the experimental value (0.23) at 300 Κ (22). The dipole moment for the SPC model is 2.27 D , compared to 1.85 for the isolated molecule and the density at 300 K, and at 1 atmosphere pressure turns out to be 0.97 g/cm compared to an experimental value of 0.995 at 305 Κ (18). Overall, it is apparent that the SPC model of water and the GROMOS force field provide a reasonable model for simulation of proteins, D N A and protein-DNA complexes. Using GROMOS unmodified, irreversible base pair opening events were observed. Such behavior was subsequendy noted in M D studies of D N A based on other force fields as well (23,24). Base pah* opening is observed experimentally in D N A via N M R spectroscopy (25). However, the experiments are carried out on the ms time scale and the results indicate the phenomena to be infrequent. This led us to suspect that the opening events seen in our previous M D are deficiencies in the potentials and not accurate theoretical descriptions of the phenomena. A subsequent simulation employed a harmonic restraint function with GROMOS86 to assure that Watson-Crick base pairing was maintained intact. The results were found to be consistent with available experimental data within reasonable limits of expectation, 2

3



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both in comparisons with crystal structure data (6), and with 2D-N0ESY build up curves obtained from N M R spectroscopy (26,27). Subsequent studies of hydrogen bond interaction energies in Watson-Crick base pairs revealed that GROMOS underestimates the magnitude of these interactions. A hydrogen bond potential in the form proposed by Tung et al. (28) was then added to our implementation of the GROMOS force field. The resulting base pair interaction energies compared closely with corresponding experimental data and corresponding ab initio quantum mechanical calculations(Gould, I.; Kollman, P., submitted). The simulations described herein are based on the GROMOS force field with this modification. Unlike the hydrogen bonds, no additional potential has been applied for stacking interactions. The current studies also utilize a longer range switching function, which feathers the truncation of potentials over the length scale from 7.5 to 11.5 Â, which eliminates the tendency of charged groups to cluster at the cutoff limit when potentials are truncated too abruptly, a behavior recently noted by Auffinger et al. (29). Further concerns about the accuracy of force field in ionic interactions and the convergence in the dynamical behavior of mobile counterions have led us to follow Tidor et al. (30) to treat the effect of counterions implicitly in this set of studies, using reduced charge of -0.24 eu on the phosphate groups, consistent with Manning's theory of counterion condensation (31). Solvation is carried out by placing the solute in a box of a given shape and filling with water to obtain an overall density of 1 gm/cc. The shape of the box is chosen, that requires the least number of waters for solvation of a given thickness. The box is then divided into uniform grids and a water molecule is placed in each grid that has no solute atoms. The initial placement is relaxed by a Monte Carlo (MC) simulation employing the Metropolis algorithm, wherein the solute is held rigid and waters are allowed to equilibrate around the solute. The M C simulations are carried out until the total and solute-solvent interaction energies converge. The simulations on the dodecamer duplex D N A are carried out using free M D , surrounded by -3500 water molecules in a hexagonal prism elementary cell of constant volume, treated under periodic boundary conditions to model dilute aqueous solution. Velocities are re scaled when necessary (owing to conformational transitions) to produce an average kinetic energy corresponding to 300 K . The three new simulations on the d(CGCGAATTCGCG) duplex were performed under protocols identical except for starting structure and length. The starting configurations were a) the canonical B80 (32) fiber form of D N A (500 ps trajectory), b) the Drew-Dickerson (33) crystal form (500 ps trajectory) and c) the protein bound form observed in the complex of d(CGCGAATTCGCG) with the restriction enzyme Eco RI endonuclease (34) (1 ns trajectory). The canonical form is a regular Watson-Crick double helix with a straight axis. The crystal form shows axis bending at or near the interfaces of the C G and A T tracts, and the Eco RI form shows, in addition to deformations at nearly the same positions as in the uncomplexed form, an extreme kink in the middle region of the structure at the A 6 and T7 steps. The simulations were performed using the program W E S D Y N (35) and analyzed by means of various utilities available in M D Toolchest (36). A l l three simulations were found to converge to essentially similar M D behavior, indicating the results, at least for this system, are not sensitive to the choice of starting



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structure. The extreme kink in the Eco RI dodecamer was found to relax within the first 20 ps of M D , indicating the protein-bound form to be a strained conformation rather than a metastable intermediate. This results support those of a current study by Rosenberg and coworkers (37) based on the A M B E R force field. The M D based on the Eco RI form was extended to 1 ns, and forms the basis for this more detailed analysis. The stability and convergence behavior of the simulation was monitored by one-dimensional (ID) and two-dimensional (2D) root mean square deviation (RMS) maps. The latter is especially informative, since the extent of similarity among all structures in the trajectory is depicted graphically (Figure 1). Essentially, the 2-D RMS provides a measure of the deviation of every structure in the trajectory with respect to all others. Thus, a square matrix of RMS values are generated wherein the upper and bottom halves are symmetrical and, therefore, only one half of the matrix is presented. The diagonal elements represent deviation of a structure with respect to itself and consequently have an RMS value of zero. The off-diagonal elements provide a measure of the similarity of any two structures from different time points in the trajectory and their gray scaling reflects the extent to which they are similar. The results indicate that after an initial equilibration period, the M D structure resides for -300 ps in a form -4.5Â RMS from canonical Β form D N A . The dynamical structure then makes a distinct transition to a new form, still in the Β family but somewhat more distant (-7.5À RMS) from the canonical form, where it remains for 180 ps. A rapid (-1.5 ps) reversible base pair opening event occurs in this structure at the T7 step, concomitant with displacements in hélicoïdal roll and twist. Then the dynamical structure transits to a third form, where it resides at the termination of the run. The third form, as evidenced by a cross peak in the 2-D RMS map, bears a strong resemblance to the first, indicating that the M D results appear to describe an incipient dynamical equilibrium among putative dynamical substates of the Β family. The lifetime for a given structural form of D N A suggests that a minimal trajectory length of at least 200-300 ps would be necessary in order to fully relax the D N A in solution, given our methods and protocol. Validation of the M D results was pursued by a comparison of calculated and observed helix bending characteristics. To analyze axis bending in a given structure, the magnitude β and angular direction of bending α are computed from deviations in the hélicoïdal parameters roll and tilt. The values of β and α for a given step can be projected onto a polar plot or "bending dial", seen in perspective at the bottom of Figure 2a. The detailed analysis of multiple sequences can be carried out by superimposing results from individual structures on a single bending dial for each base pair step in a D N A sequence. The use of bending dials to analyze D N A crystal structures and M D simulations has been described previously by Young et al. (38). The bending dials for 20 reports of d(CGCGAATTCGCG) duplex structures in the Nucleic Acids Data Bank (39) are shown in comparison with the M D results in Figure 2b. The results show graphically that bending towards the minor groove occurs at the G2-C3 step, followed in the succeeding step C3-G4 by a bend towards the major groove. The origin of the bending in the hélicoïdal parameters is inter-base pair roll. A similar effect is seen in the other flanking sequence; these are the upper and lower roll points identified by Dickerson and coworkers (40). The axis deformations from the 1 ns M D trajectory are shown in Figure 2c, and indicate that



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Figure 1. ID RMS map (top) and 2D RMS map (center) for base pairs in the 1 ns M D simulation of the d(CGCGAATTCGCG) duplex. Shaded areas in the 2D RMS map indicate regions of RMS deviation < 2 Â. The diagonal elements represent the RMS deviation of a given structure with respect to itself (at each time point) and the off-diagonal elements represent similarity of structures from different time points in the trajectory, the gray scale reflecting the extent of the RMS deviation between them. Average M D structures for each of three putative substates are shown at bottom.




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(b)

(c)

Figure 2. Bending dials analysis [Young, 1994 #762] of the crystal structures of the d(CGCGAATTCGCG) duplex resident in the NDB[Berman, 1992 #745], compared with corresponding results from a 1 ns M D simulation[Ravishanker, 1994 #809]. a) Definition of bending dial (seen in perspective view at bottom) in terms of base pair roll and twist; b) Bending dials analysis for 20 crystal structures, and c) Bending dials analysis for the M D structures. Each ring represents a 5° increment in axis deflection. To make trends in the analysis more discernible, crystal structure dials extend to 25°, while M D dials extend to 45°. In Structure and Reactivity in Aqueous Solution; Cramer, Christopher J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1994.


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the natural roll points are found at G2-C3 steps and the C9-G10 steps. The deformation in each case is a bend towards the major groove. The adjoining step does not distinctly show the corresponding roll into the minor groove as observed crystallographically, a discrepancy between the calculated and observed results. The effect of crystal packing, which can be significant in D N A oligonucleotides (41-43), is not considered in the calculations. Thus roll bends corresponding to experiment are found in the M D at the agreement level indicated, and not unreasonable considering the calculated results are for an aqueous solution model. The interesting question of the role of crystal packing effects on axis bending will the subject of a forthcoming paper in which we describe an M D performed on the crystallographic unit cell. Analysis of the water structure in this system will also be the subject of a subsequent paper. We find that M D models of D N A are increasing in their accuracy and utility in investigating the fundamental nature of D N A structure and motions. Detailed analysis of the progress of the simulations reveals that the trajectories progress through a series of substates with lifetimes of several hundred ps, and provides evidence for the presence of an incipient dynamic equilibrium among substates on the ns time scale. The stability of the M D calculations over such a long duration suggest our model of D N A is reasonable and is encouraging to note the feasibility of studying dynamical processes occurring in the ns regime. It is likely that further detail will emerge as M D simulations are extended to successive decades of time and new motional regimes are encountered. M D Simulation Studies of the λ Repressor-Operator Complex The preceding series of M D simulations on D N A as well as several previously published M D simulations on proteins (12,14) demonstrate that M D models based on the GROMOS force field are reasonably accurate when applied to these systems independently. A logical next step is to apply these models for studying the intricate interactions involved in the formation of a protein-DNA complex. Protein-DNA complexes present an additional level of complexity to M D simulation methods, since the intermolecular interactions are likely to be governed by a highly subtle balance of forces. We seek to evaluate the accuracy with which calculations on interacting macromolecules can be carried out, using the λ repressor-operator complex as a prototype case. A number of characteristic structural elements have now been recognized in proteins interacting with D N A , including the helix-turn-helix (HTH) motif, zinc fingers and leucine zippers (44). The modus operandi of binding motifs involving recognition and regulation of genetic biochemical processes have been found to vary from one complex to another (2). Further, regions of protein structure that are contiguous to the above motifs, some dynamically labile, have been found to contribute significantly to the binding. There is no clear indication of the structural changes, particularly in the D N A , that occur on complex formation. Collective efforts in the fields of molecular biology, biochemistry and molecular biophysics are now directed towards determining the relationship between the structural details of protein-DNA complexes and the origin of the remarkable specificity of their interactions.



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S T R U C T U R E A N D R E A C T I V I T Y IN A Q U E O U S S O L U T I O N

Understanding the specificity of a regulatory protein to it's various cognate operator sequences involves interpretive knowledge of the relative contributions of all significant factors to the free energy of binding relative to each other and to random sequence D N A . Genetic and chemical protection experiments at the molecular level and crystallography at or near the atomic level provide a knowledge of the direct interactions involved, but not the energetics (beyond the idea that if a structure occurs, it must have a favorable free energy). Direct measurement of free energy via equilibrium binding studies provides information on the energetics, but unequivocally linking the energetics to structure is difficult, especially when subtle non-local changes are involved. Theoretical methods can, in principle, provide the link between structure and energetics. In addition, the dynamical aspects of proteinD N A complexes, not accessible to experiment, can be explored via M D studies, forming a basis for interpretation of experimental results. However, M D simulations are still limited by assumptions inherent in the underlying molecular force field, the sensitivity of results to simulation protocols and truncation of potentials, and the limited time frame that can be reasonably simulated on systems of this size. Detailed study of a prototype system is necessary to determine the capabilities and limitations of M D applied to protein-DNA interactions. We describe herein separate M D studies of the repressor protein from the bacteriophage λ, its cognate duplex D N A O L 1 , of sequence d(TATCACCGCCAGTGGTA), and the repressor-operator complex. This system is of historic interest in the elucidation of the 'genetic switch' from lysogenic to lytic phases of the phage (45) and has been studied extensively from diverse points of view. The availability of crystal structures of the complex (46,47) and that of the unbound protein (48) makes this system ideally suited for inquiring into the overall accuracy and utility of M D simulation applied to a regulatory protein-DNA complex. A l l three simulations were carried out with water included explicitly. For the simulation of the free D N A and the complex an hexagonal prism cell was employed and the simulation of the protein employed a simple cubic cell. Simulation of the free D N A , free protein and the complex required 4411, 6576 and 7133 waters, respectively, which provided at least 9.0 Â solvation in all systems. The effect of counterions was introduced via the use of a reduced charge of -0.24 on phosphates fully exposed to solvent. Sequestered phosphates are set to -1.0, and partially exposed phosphates have their charges scaled proportional to their solvent accessibility. A l l other protocols were similar to that of the preceding three simulations on the dodecamer duplex D N A . The results are analyzed with respect to the intrinsic stability of the model system, the dynamical structure of the protein-DNA interface, adaptive changes in structure on complex formation, and solvent effects. The initial structure for the protein, D N A , and the complex are taken from crystal structure data (46,47). We consider our M D results from this study thus far to be quite preliminary, especially in the light of the results presented in the previous section of this article. A combined 2-D RMS plot comparing the calculated dynamical structure of the uncomplexed protein and that of the protein in the



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Figure 3. 2D RMS map comparing structures from the M D trajectory of the free and complexed protein, in solution. Both axes represent structures from the M D trajectory at 1.0 ps intervals and averaged over 5.0 ps blocks. Simulation of the free protein in solution was carried out for 230 ps and that of the complex for 100 ps. Cross peaks indicate similarity between two structures either from a given trajectory or between the two trajectories and the shading reflects the extent of similarity (RMS deviation over backbone atoms). For each simulation, the starting structure and four snapshots from the M D trajectory, at equally spaced intervals, are overlaid to indicate the dynamical flexibility. The gray scaling varies from light to dark as the simulation progresses.



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complex is shown in Figure 3. A n α carbon overlay of five snapshots from each trajectory indicate the dynamic range covered by the M D . Although the overall structure of the proteins in the two simulations are similar, the absence of RMS cross peaks within 3.0 Â indicate the structures are diverging, as the simulation progresses. The M D structures of the uncomplexed protein also indicate that the C-terminal helices, located at the protein dimer interface in the complex, are substantially destabilized. This result is consistent with the experimental observation that the free repressor does not form dimers in solution (48). Despite the unwinding of the C-terminal helices, the calculated % helicity for the uncomplexed protein is in good agreement with experimental measurements (49). Also, both the N-terminal arms of the dimer show significant changes with respect to the crystal conformation and appear to flop back on the protein. In the simulation of the complex, the dimer interface is more stable than in the uncomplexed protein, and the structural rearrangement of the arms remain localized within the major groove area. A comparison of structures from the trajectory of the uncomplexed D N A and that of the D N A in complex with the protein is presented in Figure 4. The simulation on the uncomplexed D N A was carried out to a trajectory length of 320 ps and the simulation of the protein-DNA complex to about 100 ps at the time of this writing. The isolated D N A remains within the Β family of structures, although there appears to be some slight fraying at the ends. In general, a slight expansion of the major groove and a compression of the minor groove at all base steps is evident, except for a three base pair region in the middle segment of the D N A . The overall dynamics of the complex is shown in Figure 5. The calculations indicate the complex to be stable up to this point. The dynamical structure features a compression of the major groove, beginning at both ends of the D N A , and an expansion in the base steps between the two D N A binding pockets. In the minor groove, there is an expansion in the protein binding regions and at the ends. We now plan to extend each of these simulations as far as is necessary to characterize the dynamical stability, and then analyze the dynamical structures and the molecular motions in detail. Summary and Conclusion We have reviewed herein M D simulations on D N A oligonucleotides and a proteinD N A complex recently performed in this laboratory. M D simulation is a potentially powerful approach to the study of problems in this area, since full details of the molecular motions are obtained at a level inaccessible to any other method, theoretical or experimental. However, due to the empirical nature of the underlying molecular force field, the methods require extensive independent validations before the results obtained can be considered reliable and accurate. The results to date are encouraging but suggest a significantly new dynamical behavior in the ns regime. This may be a consequence of the particular flexibility of the D N A double helix, but more likely due to relaxation processes occurring over a longer time scale. Further investigations are clearly necessary to delineate the capabilities and limitations of M D methodology applied to this class of problems.



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Figure 4. 2D RMS map comparing structures from the M D trajectory of the free and complexed D N A , in solution. Simulation of the uncomplexed D N A was carried out for 320 ps. See legend of Figure 3 for additional details.



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Figure 5. Overlay of the stick figure of the D N A and α-carbon drawing of the protein from the simulation of the complex. The crystal structure and four snapshots from the M D trajectory, taken at equally spaced intervals, are shown. The gray scaling varies from light to dark as the simulation progresses. Acknowledgments This project is supported by NIH Grants # G M 37909 from the National Institutes of General Medical Sciences, and RR 07885 from the Division of Research Resources. K. J. McConnell is supported by an NIH Molecular Biophysics Training Grant # G M 08271. Cray C90 and Y M P computer facilities for this project were made available to us by the Pittsburgh Supercomputer Center and the NCI Frederick Cancer Research and Development Center of NIH. Literature Cited (1)

Beveridge, D. L.; Swaminathan, S.; Ravishanker, G.; Withka, J. M . ; Srinivasan, J.; Prevost, C.; Louise-May, S.; LAngley, D. R.; DiCapua, F. M.; Bolton, P. H. In Water and Biological Molecules; E. Westhof, Ed.; The Macmillan Press, Ltd: London, 1993; pp 165. In Structure and Reactivity in Aqueous Solution; Cramer, Christopher J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1994.

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(2) (3) (4)


(5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22) (23) (24) (25) (26) (27) (28) (29)

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Steitz, T. A. Quart. Rev. Biophys. 1990, 23, 205. Westhof, E.; Beveridge, D. L. In Water Science Reviews; F. Franks, Ed.; Cambridge University Press: Cambridge, 1990, Vol. 5; pp 24. Subramanian, P. S.; Ravishanker, G.; Beveridge, D. L. Proc. Natl. Acad. Sci. (USA) 1988,85,1836. Subramanian, P. S.; Beveridge, D. L.J.Biomol. Struct. & Dyn. 1989, 6, 1093. Swaminathan, S.; Ravishanker, G.; Beveridge, D. L. J. Am. Chem. Soc. 1991, 113, 5027. Pohorille, Α.; Ross, W. S.; Tinoco Jr., I. Int. J. Supercomp. App. 1990, 4, 81. Ravishanker, G.; Nirmala, R.; McConnell, K. J.; Young, M. Α.; Beveridge, D. L. 1994, manuscript in preparation. van Gunsteren, W. F.; Berendsen, H. J. C. GROMOS, University of Groningen: Groningen, The Netherlands, 1986. van Gunsteren, W. F.; Berendsen, H. J. C. Angew. Chem. Int. Ed. Engl. 1990, 29, 992. Berendsen, H. J. C.; Postma, J. P. M.; van Gunsteren, W. F.; Hermans, J. In Intermolecular Forces; B. Pullman, Ed.; D. Reidel: Dordrecht, 1981; pp 331. Harte Jr., W. E.; Swaminathan, S.; Beveridge, D. L. Proteins: Structure, Function and Energetics 1992, 13, 175. Vijayakumar, S.; Visveshwara, S.; Ravishanker, G.; Beveridge, D. L. BiophysicalJ.1993, 65, 2304. van Gunsteren, W. F. Curr. Opin. Struct. Biol. 1993, 3, 277. Hermans, J.; Berendsen, H. J. C.; van Gunsteren, W. F.; Postma, J. P. M . Biopolymers 1984, 23, 1513. Berendsen, H. J. C.; van Gunsteren, W. F.; Swinderman, H. R.J.;Geurtsen, R. G. Ann. N. Y. Acad. Sci. 1986, 482, 269. Brunne, R. M.; van Gunsteren, W. F.; Bruschweiler, R.; Ernst, R. R. J. Am. Chem. Soc. 1993, 115, 4764. Berendsen, H. J. C.; Grigera, J. R.; Straatsma, T. P. J. Phys. Chem. 1987, 91, 6269. Levitt, M.; Sharon, R. Proc.Natl.Acad. Sci. (USA) 1988, 85, 7557. Jorgensen, W. L.J.Am. Chem. Soc. 1981, 103, 335. Jorgensen, W. L.; Chandrasekar, J.; Madura, J.; Impey, R.; Klein, M . L. J. Chem. Phys. 1983, 79, 926. Daggett, V.; Levitt, M. Ann. Rev. Biophys.Biomol.Struct. 1993, 22, 353. Miaskiewicz, K.; Osman, R.; Weinstein, H. J. Am. Chem. Soc. 1992, 115, 1526. Hirshberg, M.; Sharon, R.; Sussman, J. L.J.Biomol. Struct. Dyn. 1988, 5, 965. Van de Ven, J. M.; Hilbers, C. W. Eur. J. Biochem. 1988, 178, 1. Withka, J. M.; Swaminathan, S.; Beveridge, D. L.; Bolton, P. H. Science 1991, 225, 597. Withka, J. M.; Swaminathan, S.; Beveridge, D. L.; Bolton, P. H. J. Am. Chem. Soc. 1991, 113, 5041. Tung, C. S.; Harvey, S.C.;McCammon, A. J. Biopolymers 1984, 23, 2173. Auffinger, P.; Nirmala, R.; Ravishanker, G.; Beveridge, D. L. 1994, manuscript in preparation.



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Molecular Dynamics Simulations of DNA and ProteinâDNA

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