1932

Abstract

Friction is a phenomenon that manifests across all spatial and temporal scales, from the molecular to the macroscopic scale. It describes the dissipation of energy from the motion of particles or abstract reaction coordinates and arises in the transition from a detailed molecular-level description to a simplified, coarse-grained model. It has long been understood that time-dependent (non-Markovian) friction effects are critical for describing the dynamics of many systems, but that they are notoriously difficult to evaluate for complex physical, chemical, and biological systems. In recent years, the development of advanced numerical friction extraction techniques and methods to simulate the generalized Langevin equation has enabled exploration of the role of time-dependent friction across all scales. We discuss recent applications of these friction extraction techniques and the growing understanding of the role of friction in complex equilibrium and nonequilibrium dynamic many-body systems.

Loading

Article metrics loading...

/content/journals/10.1146/annurev-physchem-082423-031037
2025-04-21
2025-06-15
Loading full text...

Full text loading...

/deliver/fulltext/physchem/76/1/annurev-physchem-082423-031037.html?itemId=/content/journals/10.1146/annurev-physchem-082423-031037&mimeType=html&fmt=ahah

Literature Cited

  1. 1.
    Zwanzig R, Bixon M. 1970.. Hydrodynamic theory of the velocity correlation function. . Phys. Rev. A 2:(5):200512
    [Crossref] [Google Scholar]
  2. 2.
    Español P, Zúñiga I. 1993.. Force autocorrelation function in Brownian motion theory. . J. Chem. Phys. 98:(1):57480
    [Crossref] [Google Scholar]
  3. 3.
    Bocquet L, Piasecki J, Hansen JP. 1994.. On the Brownian motion of a massive sphere suspended in a hard-sphere fluid. I. Multiple-time-scale analysis and microscopic expression for the friction coefficient. . J. Stat. Phys. 76:(1):50526
    [Crossref] [Google Scholar]
  4. 4.
    Mason TG, Weitz DA. 1995.. Optical measurements of frequency-dependent linear viscoelastic moduli of complex fluids. . Phys. Rev. Lett. 74:(7):125053
    [Crossref] [Google Scholar]
  5. 5.
    Crocker JC, Valentine MT, Weeks ER, Gisler T, Kaplan PD, et al. 2000.. Two-point microrheology of inhomogeneous soft materials. . Phys. Rev. Lett. 85:(4):88891
    [Crossref] [Google Scholar]
  6. 6.
    Lesnicki D, Vuilleumier R, Carof A, Rotenberg B. 2016.. Molecular hydrodynamics from memory kernels. . Phys. Rev. Lett. 116:(14):147804
    [Crossref] [Google Scholar]
  7. 7.
    Straub JE, Borkovec M, Berne BJ. 1987.. Calculation of dynamic friction on intramolecular degrees of freedom. . J. Phys. Chem. 91:(19):499598
    [Crossref] [Google Scholar]
  8. 8.
    Berne BJ, Tuckerman ME, Straub JE, Bug ALR. 1990.. Dynamic friction on rigid and flexible bonds. . J. Chem. Phys. 93:(7):508495
    [Crossref] [Google Scholar]
  9. 9.
    Tuckerman M, Berne BJ. 1993.. Vibrational relaxation in simple fluids: comparison of theory and simulation. . J. Chem. Phys. 98:(9):730118
    [Crossref] [Google Scholar]
  10. 10.
    Heyden M, Sun J, Funkner S, Mathias G, Forbert H, et al. 2010.. Dissecting the THz spectrum of liquid water from first principles via correlations in time and space. . PNAS 107:(27):1206873
    [Crossref] [Google Scholar]
  11. 11.
    Lesnicki D, Sulpizi M. 2018.. A microscopic interpretation of pump-probe vibrational spectroscopy using ab initio molecular dynamics. . J. Phys. Chem. B 122:(25):66049
    [Crossref] [Google Scholar]
  12. 12.
    Carlson S, Brünig FN, Loche P, Bonthuis DJ, Netz RR. 2020.. Exploring the absorption spectrum of simulated water from MHz to infrared. . J. Phys. Chem. A 124:(27):5599605
    [Crossref] [Google Scholar]
  13. 13.
    Furst EM, Squires TM. 2017.. Microrheology. Oxford, UK:: Oxford Univ. Press
    [Google Scholar]
  14. 14.
    Schmidt RF, Kiefer H, Dalgliesh R, Gradzielski M, Netz RR. 2024.. Nanoscopic interfacial hydrogel viscoelasticity revealed from comparison of macroscopic and microscopic rheology. . Nano Lett. 24:(16):475865
    [Google Scholar]
  15. 15.
    Schuler B, Eaton WA. 2008.. Protein folding studied by single-molecule FRET. . Curr. Opin. Struct. Biol. 18:(1):1626
    [Crossref] [Google Scholar]
  16. 16.
    Chung HS, McHale K, Louis JM, Eaton WA. 2012.. Single-molecule fluorescence experiments determine protein folding transition path times. . Science 335:(6071):98184
    [Crossref] [Google Scholar]
  17. 17.
    Chung HS, Eaton WA. 2013.. Single-molecule fluorescence probes dynamics of barrier crossing. . Nature 502:(7473):68588
    [Crossref] [Google Scholar]
  18. 18.
    Neupane K, Foster DAN, Dee DR, Yu H, Wang F, Woodside MT. 2016.. Direct observation of transition paths during the folding of proteins and nucleic acids. . Science 352:(6282):23942
    [Crossref] [Google Scholar]
  19. 19.
    Neupane K, Manuel AP, Woodside MT. 2016.. Protein folding trajectories can be described quantitatively by one-dimensional diffusion over measured energy landscapes. . Nat. Phys. 12:(7):7003
    [Crossref] [Google Scholar]
  20. 20.
    Ridley AJ, Schwartz MA, Burridge K, Firtel RA, Ginsberg MH, et al. 2003.. Cell migration: integrating signals from front to back. . Science 302:(5651):17049
    [Crossref] [Google Scholar]
  21. 21.
    Maiuri P, Terriac E, Paul-Gilloteaux P, Vignaud T, McNally K, et al. 2012.. The first World Cell Race. . Curr. Biol. 22:(17):R67375
    [Crossref] [Google Scholar]
  22. 22.
    Mitterwallner BG, Schreiber C, Daldrop JO, Rädler JO, Netz RR. 2020.. Non-Markovian data-driven modeling of single-cell motility. . Phys. Rev. E 101:(3):032408
    [Crossref] [Google Scholar]
  23. 23.
    Klimek A, Mondal D, Block S, Sharma P, Netz RR. 2024.. Data-driven classification of individual cells by their non-Markovian motion. . Biophys. J. 123:(10):117383
    [Crossref] [Google Scholar]
  24. 24.
    Nakajima S. 1958.. On quantum theory of transport phenomena: steady diffusion. . Prog. Theor. Phys. 20:(6):94859
    [Crossref] [Google Scholar]
  25. 25.
    Mori H. 1965.. Transport, collective motion, and Brownian motion. . Prog. Theor. Phys. 33:(3):42355
    [Crossref] [Google Scholar]
  26. 26.
    Mori H. 1965.. A continued-fraction representation of the time-correlation functions. . Prog. Theor. Phys. 34:(3):399416
    [Crossref] [Google Scholar]
  27. 27.
    Zwanzig R. 1961.. Memory effects in irreversible thermodynamics. . Phys. Rev. 124:(4):98392
    [Crossref] [Google Scholar]
  28. 28.
    Carof A, Vuilleumier R, Rotenberg B. 2014.. Two algorithms to compute projected correlation functions in molecular dynamics simulations. . J. Chem. Phys. 140:(12):124103
    [Crossref] [Google Scholar]
  29. 29.
    Ayaz C, Scalfi L, Dalton BA, Netz RR. 2022.. Generalized Langevin equation with a nonlinear potential of mean force and nonlinear memory friction from a hybrid projection scheme. . Phys. Rev. E 105:(5):054138
    [Crossref] [Google Scholar]
  30. 30.
    Vroylandt H. 2022.. On the derivation of the generalized Langevin equation and the fluctuation-dissipation theorem. . Europhys. Lett. 140:(6):62003
    [Crossref] [Google Scholar]
  31. 31.
    Vroylandt H, Monmarché P. 2022.. Position-dependent memory kernel in generalized Langevin equations: theory and numerical estimation. . J. Chem. Phys. 156:(24):244105
    [Crossref] [Google Scholar]
  32. 32.
    Vroylandt H, Goudenège L, Monmarché P, Pietrucci F, Rotenberg B. 2022.. Likelihood-based non-Markovian models from molecular dynamics. . PNAS 119:(13):e2117586119
    [Crossref] [Google Scholar]
  33. 33.
    Berne BJ, Harp GD. 1970.. On the calculation of time correlation functions. . Adv. Chem. Phys. 17::63227
    [Google Scholar]
  34. 34.
    Lange OF, Grubmüller H. 2006.. Collective Langevin dynamics of conformational motions in proteins. . J. Chem. Phys. 124:(21):214903
    [Crossref] [Google Scholar]
  35. 35.
    Jung G, Hanke M, Schmid F. 2017.. Iterative reconstruction of memory kernels. . J. Chem. Theory Comput. 13:(6):248188
    [Crossref] [Google Scholar]
  36. 36.
    Daldrop JO, Kappler J, Brünig FN, Netz RR. 2018.. Butane dihedral angle dynamics in water is dominated by internal friction. . PNAS 115:(20):516974
    [Crossref] [Google Scholar]
  37. 37.
    Tepper L, Dalton B, Netz RR. 2024.. Accurate memory kernel extraction from discretized time-series data. . J. Chem. Theory Comput. 20:(8):306168
    [Crossref] [Google Scholar]
  38. 38.
    Chorin AJ, Hald OH, Kupferman R. 2000.. Optimal prediction and the Mori–Zwanzig representation of irreversible processes. . PNAS 97:(7):296873
    [Crossref] [Google Scholar]
  39. 39.
    Darve E, Solomon J, Kia A. 2009.. Computing generalized Langevin equations and generalized Fokker–Planck equations. . PNAS 106:(27):1088489
    [Crossref] [Google Scholar]
  40. 40.
    Straube AV, Kowalik BG, Netz RR, Höfling F. 2020.. Rapid onset of molecular friction in liquids bridging between the atomistic and hydrodynamic pictures. . Commun. Phys. 3:(1):126
    [Crossref] [Google Scholar]
  41. 41.
    Schilling T. 2022.. Coarse-grained modelling out of equilibrium. . Phys. Rep. 972::145
    [Crossref] [Google Scholar]
  42. 42.
    Ayaz C, Tepper L, Brünig FN, Kappler J, Daldrop JO, Netz RR. 2021.. Non-Markovian modeling of protein folding. . PNAS 118:(31):e2023856118
    [Crossref] [Google Scholar]
  43. 43.
    Brünig FN, Daldrop JO, Netz RR. 2022.. Pair-reaction dynamics in water: competition of memory, potential shape, and inertial effects. . J. Phys. Chem. B 126:(49):10295304
    [Crossref] [Google Scholar]
  44. 44.
    Lau AWC, Hoffman BD, Davies A, Crocker JC, Lubensky TC. 2003.. Microrheology, stress fluctuations, and active behavior of living cells. . Phys. Rev. Lett. 91:(19):198101
    [Crossref] [Google Scholar]
  45. 45.
    Gnesotto FS, Mura F, Gladrow J, Broedersz CP. 2018.. Broken detailed balance and non-equilibrium dynamics in living systems: a review. . Rep. Prog. Phys. 81:(6):66601
    [Crossref] [Google Scholar]
  46. 46.
    Abbasi A, Netz RR, Naji A. 2023.. Non-Markovian modeling of nonequilibrium fluctuations and dissipation in active viscoelastic biomatter. . Phys. Rev. Lett. 131:(22):228202
    [Crossref] [Google Scholar]
  47. 47.
    Meyer H, Wolf S, Stock G, Schilling T. 2021.. A numerical procedure to evaluate memory effects in non-equilibrium coarse-grained models. . Adv. Theory Simul. 4:(4):2000197
    [Crossref] [Google Scholar]
  48. 48.
    Netz RR. 2024.. Derivation of the nonequilibrium generalized Langevin equation from a time-dependent many-body Hamiltonian. . Phys. Rev. E 110:(1):014123
    [Crossref] [Google Scholar]
  49. 49.
    Brünig FN, Hillmann P, Kim WK, Daldrop JO, Netz RR. 2022.. Proton-transfer spectroscopy beyond the normal-mode scenario. . J. Chem. Phys. 157:(17):174116
    [Crossref] [Google Scholar]
  50. 50.
    Dalton BA, Kiefer H, Netz RR. 2024.. The role of memory-dependent friction and solvent viscosity in isomerization kinetics in viscogenic media. . Nat. Commun. 15:(1):3761
    [Crossref] [Google Scholar]
  51. 51.
    Kiefer H, Furtel D, Ayaz C, Klimek A, Daldrop JO, Netz RR. 2024.. Predictability analysis and prediction of discrete weather and financial time-series data with a Hamiltonian-based filter-projection approach. . arXiv:2409.15026 [physics.data-an]
  52. 52.
    Dalton BA, Ayaz C, Kiefer H, Klimek A, Tepper L, Netz RR. 2023.. Fast protein folding is governed by memory-dependent friction. . PNAS 120:(31):e2220068120
    [Crossref] [Google Scholar]
  53. 53.
    Wraight CA. 2006.. Chance and design—proton transfer in water, channels and bioenergetic proteins. . Biochim. Biophys. Acta Bioenerg. 1757:(8):886912
    [Crossref] [Google Scholar]
  54. 54.
    Agmon N, Bakker HJ, Campen RK, Henchman RH, Pohl P, et al. 2016.. Protons and hydroxide ions in aqueous systems. . Chem. Rev. 116:(13):764272
    [Crossref] [Google Scholar]
  55. 55.
    Agmon N. 1995.. The Grotthuss mechanism. . Chem. Phys. Lett. 244:(5–6):45662
    [Crossref] [Google Scholar]
  56. 56.
    Marx D. 2006.. Proton transfer 200 years after von Grotthuss: insights from ab initio simulations. . ChemPhysChem 7:(9):184870
    [Crossref] [Google Scholar]
  57. 57.
    Thämer M, De Marco L, Ramasesha K, Mandal A, Tokmakoff A. 2015.. Ultrafast 2D IR spectroscopy of the excess proton in liquid water. . Science 350:(6256):7882
    [Crossref] [Google Scholar]
  58. 58.
    Dahms F, Fingerhut BP, Nibbering ETJ, Pines E, Elsaesser T. 2017.. Large-amplitude transfer motion of hydrated excess protons mapped by ultrafast 2D IR spectroscopy. . Science 357:(6350):49195
    [Crossref] [Google Scholar]
  59. 59.
    Roy S, Schenter GK, Napoli JA, Baer MD, Markland TE, Mundy CJ. 2020.. Resolving heterogeneous dynamics of excess protons in aqueous solution with rate theory. . J. Phys. Chem. B 124:(27):566575
    [Crossref] [Google Scholar]
  60. 60.
    Brünig FN, Rammler M, Adams EM, Havenith M, Netz RR. 2022.. Spectral signatures of excess-proton waiting and transfer-path dynamics in aqueous hydrochloric acid solutions. . Nat. Commun. 13:(1):4210
    [Crossref] [Google Scholar]
  61. 61.
    Kowalik B, Daldrop JO, Kappler J, Schulz JCF, Schlaich A, Netz RR. 2019.. Memory-kernel extraction for different molecular solutes in solvents of varying viscosity in confinement. . Phys. Rev. E 100:(1):012126
    [Crossref] [Google Scholar]
  62. 62.
    Scalfi L, Vitali D, Kiefer H, Netz RR. 2023.. Frequency-dependent hydrodynamic finite size correction in molecular simulations reveals the long-time hydrodynamic tail. . J. Chem. Phys. 158:(19):191101
    [Crossref] [Google Scholar]
  63. 63.
    Yamaguchi T. 2021.. Molecular dynamics simulation study on the isomerization reaction in a solvent with slow structural relaxation. . Chem. Phys. 542::111056
    [Crossref] [Google Scholar]
  64. 64.
    Lindorff-Larsen K, Piana S, Dror RO, Shaw DE. 2011.. How fast-folding proteins fold. . Science 334:(6055):51720
    [Crossref] [Google Scholar]
  65. 65.
    Shaw DE, Dror RO, Salmon JK, Grossman JP, Mackenzie KM, et al. 2009.. Millisecond-scale molecular dynamics simulations on Anton. . In Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis, pp. 111. New York:: Assoc. Comput. Mach.
    [Google Scholar]
  66. 66.
    Beece D, Eisenstein L, Frauenfelder H, Good D, Marden MC, et al. 1980.. Solvent viscosity and protein dynamics. . Biochemistry 19:(23):514757
    [Crossref] [Google Scholar]
  67. 67.
    Doster W. 1983.. Viscosity scaling and protein dynamics. . Biophys. Chem. 17:(2):97103
    [Crossref] [Google Scholar]
  68. 68.
    Ansari A, Jones CM, Henry ER, Hofrichter J, Eaton WA. 1992.. The role of solvent viscosity in the dynamics of protein conformational changes. . Science 256:(5065):179698
    [Crossref] [Google Scholar]
  69. 69.
    Jas GS, Eaton WA, Hofrichter J. 2001.. Effect of viscosity on the kinetics of ∝-helix and β-hairpin formation. . J. Phys. Chem. B 105:(1):26172
    [Crossref] [Google Scholar]
  70. 70.
    Hagen SJ. 2010.. Solvent viscosity and friction in protein folding dynamics. . Curr. Protein Peptid. Sci. 11:(5):38595
    [Crossref] [Google Scholar]
  71. 71.
    Soranno A, Buchli B, Nettels D, Cheng RR, Müller-Späth S, et al. 2012.. Quantifying internal friction in unfolded and intrinsically disordered proteins with single-molecule spectroscopy. . PNAS 109:(44):178006
    [Crossref] [Google Scholar]
  72. 72.
    Borgia A, Wensley BG, Soranno A, Nettels D, Borgia MB, et al. 2012.. Localizing internal friction along the reaction coordinate of protein folding by combining ensemble and single-molecule fluorescence spectroscopy. . Nat. Commun. 3:(1):1195
    [Crossref] [Google Scholar]
  73. 73.
    Klafter J, Sokolov IM. 2005.. Anomalous diffusion spreads its wings. . Phys. World 18:(8):29
    [Crossref] [Google Scholar]
  74. 74.
    Bartumeus F, da Luz MGE, Viswanathan GM, Catalan J. 2005.. Animal search strategies: a quantitative random-walk analysis. . Ecology 86:(11):307887
    [Crossref] [Google Scholar]
  75. 75.
    Johnson DS, London JM, Lea MA, Durban JW. 2008.. Continuous-time correlated random walk model for animal telemetry data. . Ecology 89:(5):120815
    [Crossref] [Google Scholar]
  76. 76.
    Dieterich P, Klages R, Preuss R, Schwab A. 2008.. Anomalous dynamics of cell migration. . PNAS 105:(2):45963
    [Crossref] [Google Scholar]
  77. 77.
    Viswanathan GM, Da Luz MGE, Raposo EP, Stanley HE. 2011.. The Physics of Foraging: An Introduction to Random Searches and Biological Encounters. Cambridge, UK:: Cambridge Univ. Press
    [Google Scholar]
  78. 78.
    Viswanathan GM, Afanasyev V, Buldyrev SV, Murphy EJ, Prince PA, Stanley HE. 1996.. Lévy flight search patterns of wandering albatrosses. . Nature 381:(6581):41315
    [Crossref] [Google Scholar]
  79. 79.
    Edwards AM, Phillips RA, Watkins NW, Freeman MP, Murphy EJ, et al. 2007.. Revisiting Lévy flight search patterns of wandering albatrosses, bumblebees and deer. . Nature 449:(7165):104448
    [Crossref] [Google Scholar]
  80. 80.
    Klimek A, Netz RR. 2022.. Optimal non-Markovian composite search algorithms for spatially correlated targets. . Europhys. Lett. 139:(3):32003
    [Crossref] [Google Scholar]
  81. 81.
    Ayaz C, Tepper L, Netz RR. 2022.. Self-consistent Markovian embedding of generalized Langevin equations with configuration-dependent mass and a nonlinear friction kernel. . Turkish J. Phys. 46:(6):194205
    [Crossref] [Google Scholar]
  82. 82.
    Brünig FN, Geburtig O, von Canal A, Kappler J, Netz RR. 2022.. Time-dependent friction effects on vibrational infrared frequencies and line shapes of liquid water. . J. Phys. Chem. B 126:(7):157989
    [Crossref] [Google Scholar]
  83. 83.
    Risken H. 1996.. The Fokker-Planck Equation: Methods of Solution and Applications. Berlin:: Springer
    [Google Scholar]
  84. 84.
    Ceriotti M, Bussi G, Parrinello M. 2010.. Colored-noise thermostats à la carte. . J. Chem. Theory Comput. 6:(4):117080
    [Crossref] [Google Scholar]
  85. 85.
    Zwanzig R. 1973.. Nonlinear generalized Langevin equations. . J. Stat. Phys. 9:(3):21520
    [Crossref] [Google Scholar]
  86. 86.
    Kappler J, Hinrichsen VB, Netz RR. 2019.. Non-Markovian barrier crossing with two-time-scale memory is dominated by the faster memory component. . Eur. Phys. J. E 42:(9):119
    [Crossref] [Google Scholar]
  87. 87.
    Kou SC, Xie XS. 2004.. Generalized Langevin equation with fractional Gaussian noise: subdiffusion within a single protein molecule. . Phys. Rev. Lett. 93::180603
    [Crossref] [Google Scholar]
  88. 88.
    Goychuk I. 2009.. Viscoelastic subdiffusion: from anomalous to normal. . Phys. Rev. E 80:(4):046125
    [Crossref] [Google Scholar]
  89. 89.
    Goychuk I. 2012.. Viscoelastic subdiffusion: generalized Langevin equation approach. . Adv. Chem. Phys. 150::187253
    [Google Scholar]
  90. 90.
    Schrader B, ed. 1995.. Infrared and Raman Spectroscopy: Methods and Applications. New York:: Wiley-VCH
    [Google Scholar]
  91. 91.
    Bakker HJ, Skinner JL. 2010.. Vibrational spectroscopy as a probe of structure and dynamics in liquid water. . Chem. Rev. 110:(3):1498517
    [Crossref] [Google Scholar]
  92. 92.
    Kubo R. 1966.. The fluctuation-dissipation theorem. . Rep. Prog. Phys. 29:(1):25584
    [Crossref] [Google Scholar]
  93. 93.
    Auer BM, Skinner JL. 2008.. IR and Raman spectra of liquid water: theory and interpretation. . J. Chem. Phys. 128:(22):224511
    [Crossref] [Google Scholar]
  94. 94.
    Perakis F, De Marco L, Shalit A, Tang F, Kann ZR, et al. 2016.. Vibrational spectroscopy and dynamics of water. . Chem. Rev. 116:(13):7590607
    [Crossref] [Google Scholar]
  95. 95.
    Metiu H, Oxtoby DW, Freed KF. 1977.. Hydrodynamic theory for vibrational relaxation in liquids. . Phys. Rev. A 15:(1):36171
    [Crossref] [Google Scholar]
  96. 96.
    Oxtoby DW. 1981.. Vibrational relaxation in liquids. . Annu. Rev. Phys. Chem. 32::77101
    [Crossref] [Google Scholar]
  97. 97.
    Adelman SA, Stote RH. 1988.. Theory of vibrational energy relaxation in liquids: construction of the generalized Langevin equation for solute vibrational dynamics in monatomic solvents. . J. Chem. Phys. 88:(7):4397414
    [Crossref] [Google Scholar]
  98. 98.
    Smith DE, Harris CB. 1990.. Generalized Brownian dynamics. II. Vibrational relaxation of diatomic molecules in solution. . J. Chem. Phys. 92:(2):131219
    [Crossref] [Google Scholar]
  99. 99.
    Bader JS, Berne BJ, Pollak E, Hänggi P. 1996.. The energy relaxation of a nonlinear oscillator coupled to a linear bath. . J. Chem. Phys. 104:(3):111119
    [Crossref] [Google Scholar]
  100. 100.
    Gottwald F, Ivanov SD, Kühn O. 2016.. Vibrational spectroscopy via the Caldeira-Leggett model with anharmonic system potentials. . J. Chem. Phys. 144:(16):164102
    [Crossref] [Google Scholar]
  101. 101.
    Kramers HA. 1940.. Brownian motion in a field of force and the diffusion model of chemical reactions. . Physica 7:(4):284304
    [Crossref] [Google Scholar]
  102. 102.
    Kappler J, Daldrop JO, Brünig FN, Boehle MD, Netz RR. 2018.. Memory-induced acceleration and slowdown of barrier crossing. . J. Chem. Phys. 148:(1):014903
    [Crossref] [Google Scholar]
  103. 103.
    Zhou Q, Netz RR, Dalton BA. 2024.. Rapid state-recrossing kinetics in non-Markovian systems. . arXiv:2403.06604 [cond-mat.stat-mech]
  104. 104.
    Grote RF, Hynes JT. 1980.. The stable states picture of chemical reactions. II. Rate constants for condensed and gas phase reaction models. . J. Chem. Phys. 73:(6):271532
    [Crossref] [Google Scholar]
  105. 105.
    Dalton BA, Netz RR. 2024.. pH modulates friction memory effects in protein folding. . arXiv:2401.12027 [physics.bio-ph]
  106. 106.
    Straub JE, Borkovec M, Berne BJ. 1986.. Non-Markovian activated rate processes: comparison of current theories with numerical simulation data. . J. Chem. Phys. 84:(3):178894
    [Crossref] [Google Scholar]
  107. 107.
    Pollak E, Grabert H, Hänggi P. 1989.. Theory of activated rate processes for arbitrary frequency dependent friction: solution of the turnover problem. . J. Chem. Phys. 91:(7):407387
    [Crossref] [Google Scholar]
  108. 108.
    Lavacchi L, Kappler J, Netz RR. 2020.. Barrier crossing in the presence of multi-exponential memory functions with unequal friction amplitudes and memory times. . Europhys. Lett. 131:(4):40004
    [Crossref] [Google Scholar]
  109. 109.
    Lavacchi L, Daldrop JO, Netz RR. 2022.. Non-Arrhenius barrier crossing dynamics of non-equilibrium non-Markovian systems. . Europhys. Lett. 139:(5):51001
    [Crossref] [Google Scholar]
  110. 110.
    Plotkin SS, Wolynes PG. 1998.. Non-Markovian configurational diffusion and reaction coordinates for protein folding. . Phys. Rev. Lett. 80:(22):501518
    [Crossref] [Google Scholar]
  111. 111.
    Schulz JCF, Schmidt L, Best RB, Dzubiella J, Netz RR. 2012.. Peptide chain dynamics in light and heavy water: zooming in on internal friction. . J. Am. Chem. Soc. 134:(14):627379
    [Crossref] [Google Scholar]
  112. 112.
    Echeverria I, Makarov DE, Papoian GA. 2014.. Concerted dihedral rotations give rise to internal friction in unfolded proteins. . J. Am. Chem. Soc. 136:(24):870813
    [Crossref] [Google Scholar]
  113. 113.
    de Sancho D, Sirur A, Best RB. 2014.. Molecular origins of internal friction effects on protein-folding rates. . Nat. Commun. 5::4307
    [Crossref] [Google Scholar]
  114. 114.
    Zheng W, De Sancho D, Hoppe T, Best RB. 2015.. Dependence of internal friction on folding mechanism. . J. Am. Chem. Soc. 137:(9):328390
    [Crossref] [Google Scholar]
  115. 115.
    Best RB, Hummer G. 2005.. Reaction coordinates and rates from transition paths. . PNAS 102:(19):673237
    [Crossref] [Google Scholar]
  116. 116.
    Hummer G. 2005.. Position-dependent diffusion coefficients and free energies from Bayesian analysis of equilibrium and replica molecular dynamics simulations. . New J. Phys. 7:(1):34
    [Crossref] [Google Scholar]
  117. 117.
    Gopich IV, Szabo A. 2009.. Decoding the pattern of photon colors in single-molecule FRET. . J. Phys. Chem. B 113:(31):1096573
    [Crossref] [Google Scholar]
  118. 118.
    Muñoz V, Eaton WA. 1999.. A simple model for calculating the kinetics of protein folding from three-dimensional structures. . PNAS 96:(20):1131116
    [Crossref] [Google Scholar]
  119. 119.
    Best RB, Hummer G. 2006.. Diffusive model of protein folding dynamics with Kramers turnover in rate. . Phys. Rev. Lett. 96:(22):228104
    [Crossref] [Google Scholar]
  120. 120.
    Best RB, Hummer G. 2010.. Coordinate-dependent diffusion in protein folding. . PNAS 107:(3):108893
    [Crossref] [Google Scholar]
  121. 121.
    Zheng W, Best RB. 2015.. Reduction of all-atom protein folding dynamics to one-dimensional diffusion. . J. Phys. Chem. B 119:(49):1524755
    [Crossref] [Google Scholar]
  122. 122.
    Chung HS, Piana-Agostinetti S, Shaw DE, Eaton WA. 2015.. Structural origin of slow diffusion in protein folding. . Science 349:(6255):150410
    [Crossref] [Google Scholar]
  123. 123.
    Best RB, Hummer G, Eaton WA. 2013.. Native contacts determine protein folding mechanisms in atomistic simulations. . PNAS 110:(44):1787479
    [Crossref] [Google Scholar]
  124. 124.
    Berezhkovskii AM, Makarov DE. 2018.. Single-molecule test for Markovianity of the dynamics along a reaction coordinate. . J. Phys. Chem. Lett. 9:(9):219095
    [Crossref] [Google Scholar]
  125. 125.
    Tailleur J, Cates ME. 2008.. Statistical mechanics of interacting run-and-tumble bacteria. . Phys. Rev. Lett. 100:(21):218103
    [Crossref] [Google Scholar]
  126. 126.
    Martin D, O'Byrne J, Cates ME, Fodor É, Nardini C, et al. 2021.. Statistical mechanics of active Ornstein-Uhlenbeck particles. . Phys. Rev. E 103:(3):032607
    [Crossref] [Google Scholar]
  127. 127.
    Mitterwallner BG, Lavacchi L, Netz RR. 2020.. Negative friction memory induces persistent motion. . Eur. Phys. J. E 43::67
    [Crossref] [Google Scholar]
  128. 128.
    Li L, Cox EC, Flyvbjerg H. 2011.. ` Dicty dynamics': Dictyostelium motility as persistent random motion. . Phys. Biol. 8:(4):046006
    [Crossref] [Google Scholar]
  129. 129.
    Gail MH, Boone CW. 1970.. The locomotion of mouse fibroblasts in tissue culture. . Biophys. J. 10:(10):98093
    [Crossref] [Google Scholar]
  130. 130.
    Wright A, Li YH, Zhu C. 2008.. The differential effect of endothelial cell factors on in vitro motility of malignant and non-malignant cells. . Ann. Biomed. Eng. 36::95869
    [Crossref] [Google Scholar]
  131. 131.
    Mondal D, Prabhune AG, Ramaswamy S, Sharma P. 2021.. Strong confinement of active microalgae leads to inversion of vortex flow and enhanced mixing. . eLife 10::e67663
    [Crossref] [Google Scholar]
  132. 132.
    Lorenc AC. 1986.. Analysis methods for numerical weather prediction. . Q. J. R. Meteorol. Soc. 112:(474):117794
    [Crossref] [Google Scholar]
  133. 133.
    Franzke CLE, O'Kane TJ, Berner J, Williams PD, Lucarini V. 2015.. Stochastic climate theory and modeling. . WIREs Clim. Change 6:(1):6378
    [Crossref] [Google Scholar]
  134. 134.
    Watkins NW, Chapman SC, Chechkin A, Ford I, Klages R, Stainforth DA. 2021.. On generalized Langevin dynamics and the modelling of global mean temperature. . In Unifying Themes in Complex Systems X: Proceedings of the Tenth International Conference on Complex Systems, pp. 43341. Cham, Switz:.: Springer
    [Google Scholar]
  135. 135.
    Hochreiter S, Schmidhuber J. 1997.. Long short-term memory. . Neural Comput. 9:(8):173580
    [Crossref] [Google Scholar]
  136. 136.
    Zhang GP. 2003.. Time series forecasting using a hybrid ARIMA and neural network model. . Neurocomputing 50::15975
    [Crossref] [Google Scholar]
  137. 137.
    Tseng FM, Yu HC, Tzeng GH. 2002.. Combining neural network model with seasonal time series ARIMA model. . Technol. Forecast. Soc. Change 69:(1):7187
    [Crossref] [Google Scholar]
  138. 138.
    Pathak J, Hunt B, Girvan M, Lu Z, Ott E. 2018.. Model-free prediction of large spatiotemporally chaotic systems from data: a reservoir computing approach. . Phys. Rev. Lett. 120:(2):024102
    [Crossref] [Google Scholar]
  139. 139.
    Raissi M, Karniadakis GE. 2018.. Hidden physics models: machine learning of nonlinear partial differential equations. . J. Comput. Phys. 357::12541
    [Crossref] [Google Scholar]
  140. 140.
    Han J, Jentzen A, Weinan E. 2018.. Solving high-dimensional partial differential equations using deep learning. . PNAS 115:(34):850510
    [Crossref] [Google Scholar]
  141. 141.
    Blum AL, Langley P. 1997.. Selection of relevant features and examples in machine learning. . Artif. Intel. 97:(1–2):24571
    [Crossref] [Google Scholar]
  142. 142.
    Al-Jarrah OY, Yoo PD, Muhaidat S, Karagiannidis GK, Taha K. 2015.. Efficient machine learning for big data: a review. . Big Data Res. 2:(3):8793
    [Crossref] [Google Scholar]
  143. 143.
    Schmitt DT, Schulz M. 2006.. Analyzing memory effects of complex systems from time series. . Phys. Rev. E 73:(5):056204
    [Crossref] [Google Scholar]
  144. 144.
    Hassanibesheli F, Boers N, Kurths J. 2020.. Reconstructing complex system dynamics from time series: a method comparison. . New J. Phys. 22:(7):73053
    [Crossref] [Google Scholar]
  145. 145.
    Petropoulos F, Apiletti D, Assimakopoulos V, Babai MZ, Barrow DK, et al. 2022.. Forecasting: theory and practice. . Int. J. Forecast. 38::705871
    [Crossref] [Google Scholar]
  146. 146.
    Netz RR. 2024.. Temporal coarse-graining and elimination of slow dynamics with the generalized Langevin equation for time-filtered observables. . arXiv:2409.12429 [cond-mat.stat-mech]
  147. 147.
    Netz RR. 2023.. Multi-point distribution for Gaussian non-equilibrium non-Markovian observables. . arXiv:2310.08886 [cond-mat.stat-mech]
/content/journals/10.1146/annurev-physchem-082423-031037
Loading
/content/journals/10.1146/annurev-physchem-082423-031037
Loading

Data & Media loading...

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error