New and Notable
When Computer Simulation Excels Experiment Alexander Vologodskii1,* 1
New York University, New York, New York
For many biophysical problems we have, in general, two approaches. A problem can be studied experimentally, or the corresponding system can be simulated. So far, for the great majority of problems, simulation cannot compete with experiment. Still, simulation seems very attractive because if we solve a problem this way, we can obtain much more interesting additional information about the system. This can be seen in the field of largescale conformational properties of DNA where simulation and experiment compete successfully and, of course, complement each other. This is well demonstrated in the study by Ivenso and Lillian (1) published in this issue of the Biophysical Journal. Ivenso and Lillian studied relaxation of a supercoiled DNA molecule extended by force (Fig. 1). If the force is not too large and the degree of supercoiling is sufficiently high, the molecule can form plectonemic branches distributed along its contour. Of course, to create and preserve the supercoiling, the ends of the molecule have to be torsionally constrained. Experimentally this is achieved by attaching both DNA strands to a surface at one end, to a magnetic bead at the other end, and then rotating the bead. The torsional constraint can be eliminated by a single-stranded nick in the
Submitted April 1, 2016, and accepted for publication April 14, 2016. *Correspondence: [email protected] Editor: Nathan Baker.
DNA molecule, allowing the DNA on either side of the nick to rotate independently. The supercoiling disappears and the extension of the molecule increases. There have been a few attempts to study the dynamics of this process experimentally (2,3). DNA extension, the only parameter monitored in the experiments, was determined by the bead position. The bead was sufficiently large, 1–3 mm in diameter, so that it could be observed in an optical microscope. It turned out, however, that the bead was too large: Crut et al. (2) convincingly showed that the movement of the bead after DNA nicking (or changing the pulling force) was the rate-limiting factor in the relaxation of DNA extension, making it possible to estimate only a lower limit of the DNA relaxation rate. Thus, the necessity of the bead limited the time resolution in the experimental setup. In the study by Ivenso and Lillian, the system was simulated with Brownian dynamics, a method that is capable of reliably reproducing largescale dynamic properties of DNA without any adjustable parameters (reviewed in Vologodskii (4)). In this method, for which the application to DNA was mainly developed by Allison (5,6), the double helix is modeled as a chain of straight segments. The number of basepairs represented by a single segment is a simulation parameter but usually close to 30. The model properly accounts for DNA bending and torsional rigidity and the forces of hydrodynamic friction on the chain
http://dx.doi.org/10.1016/j.bpj.2016.04.016 Ó 2016 Biophysical Society.
2136 Biophysical Journal 110, 2136–2137, May 24, 2016
segments. Over the years, Brownian dynamics has been used to study many dynamic properties of DNA molecules. It is very suitable for studying relaxation of torsionally constrained extended DNA. Its key advantage over the experiment is that the bead at the chain end can be eliminated in the simulated system, and this is what Ivenso and Lillian did. They found that after removing the torsional constraint, the extension relaxation of 21 kb DNA increases on the timescale of 10 ms. This is ~10 times faster than the corresponding displacement of the bead observed experimentally for DNA of the same length (2). Ivenso and Lillian simultaneously monitored the relaxation of both the DNA extension and supercoiling. Unexpectedly, they found that the relaxation time of the supercoiling, t s , is ~10 times smaller than the relaxation time of the extension, t e . Thus, even in the absence of the bead, monitoring the relaxation of DNA extension is not a good way to study the relaxation of supercoiling. It is not clear how general this conclusion is, because t e strongly depends on the DNA length (7). Also, t s can increase at higher degrees of plectonemic supercoiling. Even more puzzling is the finding that t s was reduced 15-fold when the researchers performed the simulation for a shorter DNA, 5 kb in length. Indeed, the torsional stress disappears very fast after removing the torsional constraint (8), so each plectonemic branch should relax to an achiral loop independently of the others. Assuming
New and Notable
FIGURE 1 Linear supercoiled DNA extended by force. The conformation shown (simulated by A.V. as described in Vologodskii and Marko (9)) corresponds to DNA with a superhelix density of 0:043 under an extending force F of 1.6 pN, the parameters used by Ivenso and Lillian in their simulation. Under these conditions, 80% of supercoiling takes the form of torsional deformation of the double helix (DTw), and only 20% as writhe (Wr) of the DNA axis. This is why only one small plectonemic branch is seen in the conformation. More branches are formed at higher degrees of supercoiling. The conformation corresponds to 5-kb DNA, while Ivenso and Lillian (1) performed the simulation for 21-kb DNA molecules.
that the average size of plectonemic branches does not depend on DNA length, the origin of such strong dependence of t s on DNA length remains unclear. Thus, there are unanswered questions about the properties of the system. Also, the simulations were performed without accounting for the hydrodynamic interaction between the chain segments, although some estimates of the effect of this factor are given in Ivenso and Lillian’s Supporting Material (1). However, the approach definitely allows one to study all of these issues in detail.
REFERENCES 1. Ivenso, I. D., and T. D. Lillian. 2016. Simulation of DNA supercoil relaxation. Biophys. J. 110:2176–2184. 2. Crut, A., D. A. Koster, ., N. H. Dekker. 2007. Fast dynamics of supercoiled DNA revealed by single-molecule experiments. Proc. Natl. Acad. Sci. USA. 104:11957–11962. 3. Bai, H., J. E. Kath, ., J. F. Marko. 2012. Remote control of DNA-acting enzymes by varying the Brownian dynamics of a distant DNA end. Proc. Natl. Acad. Sci. USA. 109:16546–16551. 4. Vologodskii, A. 2006. Simulation of equilibrium and dynamic properties of large DNA molecules. In Computational studies of DNA and RNA. F. Lankas and J. Sponer, editors. Springer, Dordrecht, The Netherlands, pp. 579–604.
5. Allison, S. A. 1983. Torsion dynamics in linear macromolecules: exact inclusion of hydrodynamic interaction. Macromolecules. 16:421–425. 6. Allison, S. A. 1986. Brownian dynamics simulation of wormlike chains. Fluorescence depolarization and depolarized light scattering. Macromolecules. 19:118–124. 7. Perkins, T. T., S. R. Quake, ., S. Chu. 1994. Relaxation of a single DNA molecule observed by optical microscopy. Science. 264:822–826. 8. Wada, H., and R. Netz. 2009. Rotational friction of a semiflexible polymer far from equilibrium. Europhys. Lett. 87:38001. 9. Vologodskii, A. V., and J. F. Marko. 1997. Extension of torsionally stressed DNA by external force. Biophys. J. 73:123–132.
Biophysical Journal 110, 2136–2137, May 24, 2016 2137
When Computer Simulation Excels Experiment Alexander Vologodskii1,* 1
New York University, New York, New York
For many biophysical problems we have, in general, two approaches. A problem can be studied experimentally, or the corresponding system can be simulated. So far, for the great majority of problems, simulation cannot compete with experiment. Still, simulation seems very attractive because if we solve a problem this way, we can obtain much more interesting additional information about the system. This can be seen in the field of largescale conformational properties of DNA where simulation and experiment compete successfully and, of course, complement each other. This is well demonstrated in the study by Ivenso and Lillian (1) published in this issue of the Biophysical Journal. Ivenso and Lillian studied relaxation of a supercoiled DNA molecule extended by force (Fig. 1). If the force is not too large and the degree of supercoiling is sufficiently high, the molecule can form plectonemic branches distributed along its contour. Of course, to create and preserve the supercoiling, the ends of the molecule have to be torsionally constrained. Experimentally this is achieved by attaching both DNA strands to a surface at one end, to a magnetic bead at the other end, and then rotating the bead. The torsional constraint can be eliminated by a single-stranded nick in the
Submitted April 1, 2016, and accepted for publication April 14, 2016. *Correspondence: [email protected] Editor: Nathan Baker.
DNA molecule, allowing the DNA on either side of the nick to rotate independently. The supercoiling disappears and the extension of the molecule increases. There have been a few attempts to study the dynamics of this process experimentally (2,3). DNA extension, the only parameter monitored in the experiments, was determined by the bead position. The bead was sufficiently large, 1–3 mm in diameter, so that it could be observed in an optical microscope. It turned out, however, that the bead was too large: Crut et al. (2) convincingly showed that the movement of the bead after DNA nicking (or changing the pulling force) was the rate-limiting factor in the relaxation of DNA extension, making it possible to estimate only a lower limit of the DNA relaxation rate. Thus, the necessity of the bead limited the time resolution in the experimental setup. In the study by Ivenso and Lillian, the system was simulated with Brownian dynamics, a method that is capable of reliably reproducing largescale dynamic properties of DNA without any adjustable parameters (reviewed in Vologodskii (4)). In this method, for which the application to DNA was mainly developed by Allison (5,6), the double helix is modeled as a chain of straight segments. The number of basepairs represented by a single segment is a simulation parameter but usually close to 30. The model properly accounts for DNA bending and torsional rigidity and the forces of hydrodynamic friction on the chain
http://dx.doi.org/10.1016/j.bpj.2016.04.016 Ó 2016 Biophysical Society.
2136 Biophysical Journal 110, 2136–2137, May 24, 2016
segments. Over the years, Brownian dynamics has been used to study many dynamic properties of DNA molecules. It is very suitable for studying relaxation of torsionally constrained extended DNA. Its key advantage over the experiment is that the bead at the chain end can be eliminated in the simulated system, and this is what Ivenso and Lillian did. They found that after removing the torsional constraint, the extension relaxation of 21 kb DNA increases on the timescale of 10 ms. This is ~10 times faster than the corresponding displacement of the bead observed experimentally for DNA of the same length (2). Ivenso and Lillian simultaneously monitored the relaxation of both the DNA extension and supercoiling. Unexpectedly, they found that the relaxation time of the supercoiling, t s , is ~10 times smaller than the relaxation time of the extension, t e . Thus, even in the absence of the bead, monitoring the relaxation of DNA extension is not a good way to study the relaxation of supercoiling. It is not clear how general this conclusion is, because t e strongly depends on the DNA length (7). Also, t s can increase at higher degrees of plectonemic supercoiling. Even more puzzling is the finding that t s was reduced 15-fold when the researchers performed the simulation for a shorter DNA, 5 kb in length. Indeed, the torsional stress disappears very fast after removing the torsional constraint (8), so each plectonemic branch should relax to an achiral loop independently of the others. Assuming
New and Notable
FIGURE 1 Linear supercoiled DNA extended by force. The conformation shown (simulated by A.V. as described in Vologodskii and Marko (9)) corresponds to DNA with a superhelix density of 0:043 under an extending force F of 1.6 pN, the parameters used by Ivenso and Lillian in their simulation. Under these conditions, 80% of supercoiling takes the form of torsional deformation of the double helix (DTw), and only 20% as writhe (Wr) of the DNA axis. This is why only one small plectonemic branch is seen in the conformation. More branches are formed at higher degrees of supercoiling. The conformation corresponds to 5-kb DNA, while Ivenso and Lillian (1) performed the simulation for 21-kb DNA molecules.
that the average size of plectonemic branches does not depend on DNA length, the origin of such strong dependence of t s on DNA length remains unclear. Thus, there are unanswered questions about the properties of the system. Also, the simulations were performed without accounting for the hydrodynamic interaction between the chain segments, although some estimates of the effect of this factor are given in Ivenso and Lillian’s Supporting Material (1). However, the approach definitely allows one to study all of these issues in detail.
REFERENCES 1. Ivenso, I. D., and T. D. Lillian. 2016. Simulation of DNA supercoil relaxation. Biophys. J. 110:2176–2184. 2. Crut, A., D. A. Koster, ., N. H. Dekker. 2007. Fast dynamics of supercoiled DNA revealed by single-molecule experiments. Proc. Natl. Acad. Sci. USA. 104:11957–11962. 3. Bai, H., J. E. Kath, ., J. F. Marko. 2012. Remote control of DNA-acting enzymes by varying the Brownian dynamics of a distant DNA end. Proc. Natl. Acad. Sci. USA. 109:16546–16551. 4. Vologodskii, A. 2006. Simulation of equilibrium and dynamic properties of large DNA molecules. In Computational studies of DNA and RNA. F. Lankas and J. Sponer, editors. Springer, Dordrecht, The Netherlands, pp. 579–604.
5. Allison, S. A. 1983. Torsion dynamics in linear macromolecules: exact inclusion of hydrodynamic interaction. Macromolecules. 16:421–425. 6. Allison, S. A. 1986. Brownian dynamics simulation of wormlike chains. Fluorescence depolarization and depolarized light scattering. Macromolecules. 19:118–124. 7. Perkins, T. T., S. R. Quake, ., S. Chu. 1994. Relaxation of a single DNA molecule observed by optical microscopy. Science. 264:822–826. 8. Wada, H., and R. Netz. 2009. Rotational friction of a semiflexible polymer far from equilibrium. Europhys. Lett. 87:38001. 9. Vologodskii, A. V., and J. F. Marko. 1997. Extension of torsionally stressed DNA by external force. Biophys. J. 73:123–132.
Biophysical Journal 110, 2136–2137, May 24, 2016 2137
