Efficient Sampling of High-Dimensional …
141
69. Raiteri P, Laio A, Gervasio FL, Micheletti C, Parrinello M (2006) Efficient reconstruction of
complex free energy landscapes by multiple walkers metadynamics †. J Phys Chem B 110:3533
70. Singh S, Chopra M, de Pablo JJ (2012) Density of states-based molecular simulations. Annu
Rev Chem Biomol Eng 3:369–394
71. Valsson O, Tiwary P, Parrinello M (2016) Enhancing important fluctuations: rare events and
metadynamics from a conceptual viewpoint. Annu Rev Phys Chem 67:159–184
72. Zhang Y, Voth GA (2011) Combined metadynamics and umbrella sampling method for the
calculation of ion permeation free energy profiles. J Chem Theory Comput 7:2277–2283
73. White AD, Dama JF, Voth GA (2015) Designing free energy surfaces that match experimental
data with metadynamics. J Chem Theory Comput 11:2451–2460
74. Pfaendtner J (2018) Biomolecular simulations: methods in molecular biology. In: Bonomi M,
Camilloni C (eds) In Press, Springer
75. Bussi G, Gervasio FL, Laio A, Parrinello M (2006) Free-energy landscape for hairpin folding
from combined parallel tempering and metadynamics. J Am Chem Soc 128:13435
76. Bonomi M, Parrinello M (2010) Enhanced sampling in the well-tempered ensemble. Phys Rev
Lett 104:1–4
77. Gil-Ley A, Bussi G (2015) Enhanced conformational sampling using replica exchange with
collective-variable tempering. J Chem Theory Comput 11:1077
78. Pfaendtner J, Bonomi M (2015) Efficient sampling of high-dimensional free-energy landscapes
with parallel bias metadynamics. J Chem Theory Comput 11:5062–5067
79. Prakash A, Fu CD, Bonomi M, Pfaendtner J (2018) Biasing smarter, not harder, by partitioning
collective variables into families. J Chem Theory Comput. doi:https://doi.org/10.1021/acs.jctc.
8b00448
80. Prakash A, Baer MD, Mundy CJ, Pfaendtner J (2018) Peptoid backbone flexibilility dictates
its interaction with water and surfaces: a molecular dynamics investigation. Biomacromol
19:1006–1015
81. Tiwary P, Parrinello M (2015) A time-independent free energy estimator for metadynamics. J
Phys Chem B 119:14
82. Fu CD, Pfaendtner J (2018) Lifting the curse of dimensionality on enhanced sampling of
reaction networks with parallel bias metadynamics. J Chem Theory Comput 14:2516–2525
83. Pietrucci F, Andreoni W (2011) Graph theory meets Ab initio molecular dynamics: atomic
structures and transformations at the nanoscale. Phys Rev Lett 107:085504
84. Arsiccio A, McCarty JJ, Pisano R, Shea J-E (2018) The effect of surfactants on surface-induced
denaturation of proteins: evidence of an orientation-dependent mechanism. J Phys Chem B.
doi:https://doi.org/10.1021/acs.jpcb.8b07368
85. Prakash A, Sprenger KG, Pfaendtner J (2018) Essential slow degrees of freedom in proteinsurface simulations: a metadynamics investigation. Biochem Biophys Res Commun 498:274–
281
86. Löhr T, Jussupow A, Camilloni C (2017) Metadynamic metainference: Convergence towards
force field independent structural ensembles of a disordered peptide. J Chem Phys 146:165102
87. Nava M, Palazzesi F, Perego C, Parrinello M (2017) DImer metadynamics. J Chem Theory
Comput 13:425–430
88. Tribello GA, Ceriotti M, Parrinello M (2010) A self-learning algorithm for biased molecular
dynamics. Proc Natl Acad Sci USA 107:17509–17514
89. Tiwary P, Berne BJ (2016) Spectral gap optimization of order parameters for sampling complex
molecular systems. Proc Natl Acad Sci 113:2839 LP-2844
141
69. Raiteri P, Laio A, Gervasio FL, Micheletti C, Parrinello M (2006) Efficient reconstruction of
complex free energy landscapes by multiple walkers metadynamics †. J Phys Chem B 110:3533
70. Singh S, Chopra M, de Pablo JJ (2012) Density of states-based molecular simulations. Annu
Rev Chem Biomol Eng 3:369–394
71. Valsson O, Tiwary P, Parrinello M (2016) Enhancing important fluctuations: rare events and
metadynamics from a conceptual viewpoint. Annu Rev Phys Chem 67:159–184
72. Zhang Y, Voth GA (2011) Combined metadynamics and umbrella sampling method for the
calculation of ion permeation free energy profiles. J Chem Theory Comput 7:2277–2283
73. White AD, Dama JF, Voth GA (2015) Designing free energy surfaces that match experimental
data with metadynamics. J Chem Theory Comput 11:2451–2460
74. Pfaendtner J (2018) Biomolecular simulations: methods in molecular biology. In: Bonomi M,
Camilloni C (eds) In Press, Springer
75. Bussi G, Gervasio FL, Laio A, Parrinello M (2006) Free-energy landscape for hairpin folding
from combined parallel tempering and metadynamics. J Am Chem Soc 128:13435
76. Bonomi M, Parrinello M (2010) Enhanced sampling in the well-tempered ensemble. Phys Rev
Lett 104:1–4
77. Gil-Ley A, Bussi G (2015) Enhanced conformational sampling using replica exchange with
collective-variable tempering. J Chem Theory Comput 11:1077
78. Pfaendtner J, Bonomi M (2015) Efficient sampling of high-dimensional free-energy landscapes
with parallel bias metadynamics. J Chem Theory Comput 11:5062–5067
79. Prakash A, Fu CD, Bonomi M, Pfaendtner J (2018) Biasing smarter, not harder, by partitioning
collective variables into families. J Chem Theory Comput. doi:https://doi.org/10.1021/acs.jctc.
8b00448
80. Prakash A, Baer MD, Mundy CJ, Pfaendtner J (2018) Peptoid backbone flexibilility dictates
its interaction with water and surfaces: a molecular dynamics investigation. Biomacromol
19:1006–1015
81. Tiwary P, Parrinello M (2015) A time-independent free energy estimator for metadynamics. J
Phys Chem B 119:14
82. Fu CD, Pfaendtner J (2018) Lifting the curse of dimensionality on enhanced sampling of
reaction networks with parallel bias metadynamics. J Chem Theory Comput 14:2516–2525
83. Pietrucci F, Andreoni W (2011) Graph theory meets Ab initio molecular dynamics: atomic
structures and transformations at the nanoscale. Phys Rev Lett 107:085504
84. Arsiccio A, McCarty JJ, Pisano R, Shea J-E (2018) The effect of surfactants on surface-induced
denaturation of proteins: evidence of an orientation-dependent mechanism. J Phys Chem B.
doi:https://doi.org/10.1021/acs.jpcb.8b07368
85. Prakash A, Sprenger KG, Pfaendtner J (2018) Essential slow degrees of freedom in proteinsurface simulations: a metadynamics investigation. Biochem Biophys Res Commun 498:274–
281
86. Löhr T, Jussupow A, Camilloni C (2017) Metadynamic metainference: Convergence towards
force field independent structural ensembles of a disordered peptide. J Chem Phys 146:165102
87. Nava M, Palazzesi F, Perego C, Parrinello M (2017) DImer metadynamics. J Chem Theory
Comput 13:425–430
88. Tribello GA, Ceriotti M, Parrinello M (2010) A self-learning algorithm for biased molecular
dynamics. Proc Natl Acad Sci USA 107:17509–17514
89. Tiwary P, Berne BJ (2016) Spectral gap optimization of order parameters for sampling complex
molecular systems. Proc Natl Acad Sci 113:2839 LP-2844