140
S. Alamdari et al.
43. Sega M, Autieri E, Pederiva F (2011) Pickett angles and Cremer-Pople coordinates as collective
variables for the enhanced sampling of six-membered ring conformations. Mol Phys 109:141–
148
44. Peters B (2016) Reaction coordinates and mechanistic hypothesis tests. Annu Rev Phys Chem
67:669–690
45. Torrie GM, Valleau JP (1977) Nonphysical sampling distributions in Monte Carlo free-energy
estimation: umbrella sampling. J Comput Phys 23:187–199
46. Kumar S, Rosenberg JM, Bouzida D, Swendsen RH, Kollman PA (1992) THE weighted
histogram analysis method for free-energy calculations on biomolecules. I. The method. J
Comput Chem 13:1011–1021
47. Grossfield A. WHAM: the weighted histogram analysis method, version 2.0.10. http://mem
brane.urmc.rochester.edu/wordpress/?page_id=126
48. Shirts MR, Chodera JD (2008) Statistically optimal analysis of samples from multiple
equilibrium states. J Chem Phys 129:124105
49. Schlitter J, Engels M, Krüger P, Jacoby E, Wollmer A (1993) Targeted molecular dynamics
simulation of conformational change-application to the T ↔ R transition in insulin. Mol Simul
10:291–308
50. Wang F, Landau DP (2001) Efficient, multiple-range random walk algorithm to calculate the
density of states. Phys Rev Lett 86:2050–2053
51. Valsson O, Parrinello M (2014) Variational approach to enhanced sampling and free energy
calculations. Phys Rev Lett 113:1–5
52. Laio A, Parrinello M (2002) Escaping free-energy minima. PNAS 99:12562
53. Micheletti C, Laio A, Parrinello M (2004) Reconstructing the density of states by historydependent metadynamics. Phys Rev Lett 92:170601
54. Piana S, Laio A (2007) A bias-exchange approach to protein folding. J Phys Chem B 111
55. Vargiu AV, Ruggerone P, Magistrato A, Carloni P (2008) Dissociation of minor groove binders
from DNA: insights from metadynamics simulations. Nucleic Acids Res 36:5910–5921
56. Ensing B, De Vivo M, Liu Z, Moore P, Klein ML (2006) Metadynamics as a tool for exploring
free energy landscapes of chemical reactions. Acc Chem Res 39:73
57. Gervasio FL, Laio A, Parrinello M (2005) Flexible docking in solution using metadynamics. J
Am Chem Soc 127:2600
58. Limongelli V, Bonomi M, Parrinello M (2013) Funnel metadynamics as accurate binding
free-energy method. Proc Natl Acad Sci. https://doi.org/10.1073/pnas.1303186110
59. Martoˇ nák R et al (2005) Simulation of structural phase transitions by metadynamics. Zeitschrift
Für Krist Mater 220:489
60. Laio A, Rodriguez-Fortea A, Gervasio FL, Ceccarelli M, Parrinello M (2005) Assessing the
accuracy of metadynamics. J Phys Chem B 109:6714
61. Barducci A, Bussi G, Parrinello M (2008) Well-tempered metadynamics: a smoothly
converging and tunable free-energy method. Phys Rev Lett 100:020603
62. Dama JF, Parrinello M, Voth GA (2014) Well-tempered metadynamics converges asymptotically. Phys Rev Lett 112
63. Singh S, Chiu C-C, De Pablo JJ (2011) Flux tempered metadynamics. J Stat Phys 145:932–945
64. Bonomi M, Camilloni C, Vendruscolo M (2016) Metadynamic metainference: Enhanced
sampling of the metainference ensemble using metadynamics. Sci Rep 6:31232
65. Branduardi D, Bussi G, Parrinello M (2012) Metadynamics with adaptive gaussians. J Chem
Theory Comput 8:2247–2254
66. Dama JF, Rotskoff G, Parrinello M, Voth GA (2014) Transition-tempered metadynamics:
robust, convergent metadynamics via on-the-fly transition barrier estimation. J Chem Theory
Comput 10:3626–3633
67. Oliver WC, Pharr GM (1992) An improved technique for determining hardness and elastic
modulus using load and displacement sensing indentation experiments. J Mater Res 7:1564–
1583
68. Min D, Liu Y, Carbone I, Yang W (2007) On the convergence improvement in the metadynamics
simulations: a Wang-Landau recursion approach. J Chem Phys 126:194104
S. Alamdari et al.
43. Sega M, Autieri E, Pederiva F (2011) Pickett angles and Cremer-Pople coordinates as collective
variables for the enhanced sampling of six-membered ring conformations. Mol Phys 109:141–
148
44. Peters B (2016) Reaction coordinates and mechanistic hypothesis tests. Annu Rev Phys Chem
67:669–690
45. Torrie GM, Valleau JP (1977) Nonphysical sampling distributions in Monte Carlo free-energy
estimation: umbrella sampling. J Comput Phys 23:187–199
46. Kumar S, Rosenberg JM, Bouzida D, Swendsen RH, Kollman PA (1992) THE weighted
histogram analysis method for free-energy calculations on biomolecules. I. The method. J
Comput Chem 13:1011–1021
47. Grossfield A. WHAM: the weighted histogram analysis method, version 2.0.10. http://mem
brane.urmc.rochester.edu/wordpress/?page_id=126
48. Shirts MR, Chodera JD (2008) Statistically optimal analysis of samples from multiple
equilibrium states. J Chem Phys 129:124105
49. Schlitter J, Engels M, Krüger P, Jacoby E, Wollmer A (1993) Targeted molecular dynamics
simulation of conformational change-application to the T ↔ R transition in insulin. Mol Simul
10:291–308
50. Wang F, Landau DP (2001) Efficient, multiple-range random walk algorithm to calculate the
density of states. Phys Rev Lett 86:2050–2053
51. Valsson O, Parrinello M (2014) Variational approach to enhanced sampling and free energy
calculations. Phys Rev Lett 113:1–5
52. Laio A, Parrinello M (2002) Escaping free-energy minima. PNAS 99:12562
53. Micheletti C, Laio A, Parrinello M (2004) Reconstructing the density of states by historydependent metadynamics. Phys Rev Lett 92:170601
54. Piana S, Laio A (2007) A bias-exchange approach to protein folding. J Phys Chem B 111
55. Vargiu AV, Ruggerone P, Magistrato A, Carloni P (2008) Dissociation of minor groove binders
from DNA: insights from metadynamics simulations. Nucleic Acids Res 36:5910–5921
56. Ensing B, De Vivo M, Liu Z, Moore P, Klein ML (2006) Metadynamics as a tool for exploring
free energy landscapes of chemical reactions. Acc Chem Res 39:73
57. Gervasio FL, Laio A, Parrinello M (2005) Flexible docking in solution using metadynamics. J
Am Chem Soc 127:2600
58. Limongelli V, Bonomi M, Parrinello M (2013) Funnel metadynamics as accurate binding
free-energy method. Proc Natl Acad Sci. https://doi.org/10.1073/pnas.1303186110
59. Martoˇ nák R et al (2005) Simulation of structural phase transitions by metadynamics. Zeitschrift
Für Krist Mater 220:489
60. Laio A, Rodriguez-Fortea A, Gervasio FL, Ceccarelli M, Parrinello M (2005) Assessing the
accuracy of metadynamics. J Phys Chem B 109:6714
61. Barducci A, Bussi G, Parrinello M (2008) Well-tempered metadynamics: a smoothly
converging and tunable free-energy method. Phys Rev Lett 100:020603
62. Dama JF, Parrinello M, Voth GA (2014) Well-tempered metadynamics converges asymptotically. Phys Rev Lett 112
63. Singh S, Chiu C-C, De Pablo JJ (2011) Flux tempered metadynamics. J Stat Phys 145:932–945
64. Bonomi M, Camilloni C, Vendruscolo M (2016) Metadynamic metainference: Enhanced
sampling of the metainference ensemble using metadynamics. Sci Rep 6:31232
65. Branduardi D, Bussi G, Parrinello M (2012) Metadynamics with adaptive gaussians. J Chem
Theory Comput 8:2247–2254
66. Dama JF, Rotskoff G, Parrinello M, Voth GA (2014) Transition-tempered metadynamics:
robust, convergent metadynamics via on-the-fly transition barrier estimation. J Chem Theory
Comput 10:3626–3633
67. Oliver WC, Pharr GM (1992) An improved technique for determining hardness and elastic
modulus using load and displacement sensing indentation experiments. J Mater Res 7:1564–
1583
68. Min D, Liu Y, Carbone I, Yang W (2007) On the convergence improvement in the metadynamics
simulations: a Wang-Landau recursion approach. J Chem Phys 126:194104