Development of Multiscale Modelsfor Complex Chemical Systems
From H+H2 to Biomolecules
Do not go where the pathway leads, go instead wherethere is no path and leave a trail.
Ralph Waldo Emerson
1
“The underlying physical laws necessary for themathematical theory of a large part of physics and the wholeof chemistry are thus completely known, and the difficulty isonly that the exact application of these laws leads toequations that are much too complicated to be soluble.”
2
Quantum Mechanics of Many-ElectronSystems (Dirac ’29)
“The underlying physical laws necessary for themathematical theory of a large part of physics and the wholeof chemistry are thus completely known, and the difficulty isonly that the exact application of these laws leads toequations that are much too complicated to be soluble. Ittherefore becomes desirable that approximate practicalmethods of applying quantum mechanics should bedeveloped, which can lead to explanation of the mainfeatures of complex atomic systems without too muchcomputation.”
3
Quantum Mechanics of Many-ElectronSystems (Dirac ’29)
Development of Multiscale Models forComplex Chemical Systems
To understand the behavior of complexsystems need:
The potential surface on which the atoms move
The laws of motion for the atoms
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✦
4
The Nobel Prize focused on the developmentof multiscale models for the potential
surface.The most important approaches for representing the
potential surface of complex systems which do not usequantum mechanics (the so-called force fields) weredeveloped in the Allinger, Lifson and Scheraga groups.
To study chemical reactions, the classical force fieldswere extended to treat part of the system by quantummechanics, the so-called QM/MM method.
Since Michael Levitt and Arieh Warshel of the Lifsongroup are here, I will leave the discussion of that aspectto them.
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•
•
5
The laws of motion for the atoms
Although the laws governing the motions ofatoms are quantum mechanical, the essentialrealization that made possible the treatment ofthe dynamics of complex systems was that aclassical mechanical description of the atomicmotions is adequate in most cases
This realization was derived from simulationsof the H+H2 exchange reaction
•
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6
H+H2 Potential Surface Based on aSemiempirical Valence Bond Approximation
(Porter & K, ’64)
7
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Dynamics Based on the Integrating Newton’sClassical Equation of Motion(KPS,’65)
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9
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Dynamics Based on the Integrating Newton’sClassical Equation of Motion(KPS,’65)
HB
HA
HC
RAB
RBC
RAC
HB
HA
HC
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RBC
RAC
Accurate Quantum Dynamics Treatment of H+H2
Reaction (Kuppermann et al.;Wyatt et al.;’75)
The full QM results “agree with quasiclassicaltrajectory results of KPS within accuracy of thequantum calculation.”
If Newtonian classical mechanics works for thelightest atom, it should be valid for C, N, O, of whichmost biomolecules are composed.
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Retinal Isomerization Dynamics
11
Honig & K, ’71
Retinal Isomerization Dynamics
12
Honig & K, ’71
Warshel ’76
© N
atu
re P
ub
lish
ing
Gro
up
1976
Semiclassical trajectory approach tophotoisomerization (Warshel &K ’75)
Classical mechanical potential function based on thework of Scheraga and Lifson groups (Gelin & K ’75)
Classical mechanical dynamics based ongeneralization of the H+H2 methodology to a largenumber of atoms
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Bovine Pancreatic Trypsin Inhibitor (9.2 ps)McCammon, Gelin &K ’77
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BPTI Simulation (9.2ps)
BPTI Simulation (9.2ps)
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16
There was a sense, even at the time, ofsomething truly historic going on, of gettingthese first glimpses of how an enzyme moleculefor example, might undergo internal motions thatallow it to function as a biological catalyst.
J. A. McCammon, Oral History (1995)
Simulations of Proteins in Solution
Simulated BPTI for 210ps in a box of 2,607 watermolecules (Levitt & Sharon, ’88)
One millisecond simulation of BPTI in water (Shaw etal. 2010)
So far, no simulations of BPTI folding, though smallerprotein folding with all-atom models in explicit solventhave been performed (Shaw et al. 2011)
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“…everything that living things do canbe understood in terms of the jigglings
and wigglings of atoms.”
The Feynman Lectures in 1963
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“The atoms are eternal and always moving.Everything comes into existence simplybecause of the random movement of atoms,which, given enough time, will form andreform, constantly experimenting withdifferent configurations of matter fromwhich will eventually emerge everything weknow...”
Titus Lucretius
(99 BC - 55 BC)
19
Putting to work the“Jigglings and Wigglings”
Semirigid domains with hinges
Binding of ligand to change equilibriaamongst conformations
A.
B.
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2A-P-P A-P-P-P + A-P
Adenylate Kinase Dynamics
21
Kinesin Walks on Microtubules
Vale,2003
22
Rat Brain Dimeric Kinesin(Mandelkow1997)
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Forcegeneration
(Hwang, K et al.,2008)
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Mutant Measurements (Lane, Hwang, K et al., 2008)
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Importance of Kinesin Motors
Mitosis is inhibited.
Physiological cargoes are not deliveredappropriately (e.g.clogging of axonal transport).
Non-physiological cargoes make use of thetransport system (e.g.viruses).
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What does the future hold?
Experimentalists use simulations as a toollike any otherApplications of simulations to ever more
complex systems (viruses, ribosomes, cells,the brain, ...)
Always with cautionary realization thatsimulations, like experiments, have theirlimitations and inherent errors.
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Ivana Adamovic Qiang Cui L. Howard Holley Paul D. Lyne B. Montgomery Pettitt David J. StatesYuri Alexeev Tara Prasad Das Barry Honig Jianpeng Ma Ulrich Pezzeca Richard M. StevensDavid H. Anderson Annick Dejaegere Victor Hruby Alexander D. MacKerell, Jr. Richard N. Porter Roland StoteIoan Andricioaei Philippe Derreumaux Rod E. Hubbard Christoph Maerker Jay M. Portnow John StraubYasuhide Arata Aaron Dinner Robert P. Hurst Paul Maragkakis Carol B. Post Collin StultzGeorgios Archontis Uri Dinur Vincent B.-H. Huynh Marc Martí-Renom Lawrence R. Pratt Neena SummersGabriel G. Balint-Kurti Roland L. Dunbrack, Jr. Toshiko Ichiye Jean-Louis Martin Martine Prévost Henry SuzukawaChristian Bartels Chizuko Dutta K. K. Irikura Carla Mattos Blaise Prod'hom S. SwaminathanPaul Bash Nader Dutta Alfonso Jaramillo J. Andrew McCammon Jingzhi Pu Attila L. SzaboDonald Bashford Claus Ehrhardt Tom Jordan H. Keith McDowell Dagnija Lazdins Purins Antoine TalyMark Bathe Ron Elber Diane Joseph-McCarthy Jorge A. Medrano Lionel M. Raff Kwong-Tin TangOren M. Becker Marcus Elstner Sun-Hee Jung Morten Meeg Mario Raimondi Bruce TidorRobert Best Byung Chan Eu C. William Kern Marcus Meuwly Francesco Rao Hideaki UmeyamaAnton Beyer Jeffrey Evanseck William Kirchhoff Olivier Michielin Gene P. Reck Arjan van der VaartRobert Birge Erik Evensen Burton S. Kleinman Stephen Michnick Swarna Yeturu Reddy Wilfred van GunsterenRyan Bitetti-Putzer Jeffrey Evenson Gearld W. Koeppl Fredrick L. Minn Walter E. Reiher III Herman van VlijmenArnaud Blondel Thomas C. Farrar H. Jerrold Kolker Andrew Miranker Nathalie Reuter Michele VendruscuoloStefan Boresch Martin J. Field Yifei Kong Keiji Morokuma Bruno Robert Dennis VitkupJohn Brady Stefan Fischer Lewis M. Koppel A. Mukherji Peter J. Rossky Mark WagmanBernard Brooks David L. Freeman J. Kottalam Adrian Mulholland Benoît Roux Shunzhou WanCharles L. Brooks III Thomas Frimurer Felix Koziol David Munch Andrej Sali Iris Shih-Yung WangThomas H. Brown Kevin Gaffney Christoph Kratky Petra Munih Daniel Saltzberg Ariel WarshelRobert E. Bruccoleri Jiali Gao Sergei Krivov Robert Nagle Michael Schaefer Masakatsu WatanabePaul W. Brumer Yi Qin Gao Olga Kuchment Setsuko Nakagawa Michael Schlenkrich Kimberly WatsonAxel T. Brünger Bruce Gelin Krzysztof Kuczera Kwango Nam David M. Schrader David WeaverRafael P. Brüschweiler R. Benny Gerber John Kuriyan Eyal Neria John C. Schug Paul WeinerMatthias Buck Paula M. Getzin Joseph N. Kushick John-Thomas C. Ngo Klaus Schulten Michael A. WeissAmedeo Caflisch Debra A. Giammona Peter W. Langhoff Lennart Nilsson Eugene Shakhnovich Joanna Wiórkiewicz-K.William J. Campion Martin Godfrey Antonio C. Lasaga Dzung Nguyen Moshe Shapiro George WolkenWilliam Carlson Andrei Golosov Frankie T. K. Lau Iwao Ohmine Ramesh D. Sharma Youngdo WonDavid A. Case David M. Grant Themis Lazaridis Barry Olafson Isaiah Shavitt Yudong WuLeo Caves Daniel Grell Fabrice LeClerc Kenneth W. Olsen Henry H.-L. Shih Robert E. WyattThomas C. Caves Peter Grootenhuis Angel Wai-mun Lee Neil Ostlund Bernard Shizgal Wei YangMarco Cecchini Hong Guo Irwin Lee Victor Ovchinnikov David M. Silver Robert YelleJohn-Marc Chandonia Ogan Gurel Sangyoub Lee Emanuele Paci Manuel Simoes Darrin YorkTa-Yuan Chang Robert Harris Ming Lei Yuh-Kang Pan Balvinder Singh Hsiang-ai YuXavier Chapuisat Karen Haydock Ronald M. Levy C.S. Pangali Jeremy Smith Guishan ZhengSergei Chekmarev Russell J. Hemley Xiaoling Liang Richard W. Pastor Sung-Sau So Yaoqi ZhouRob D. Coalson Jeffrey C. Hoch Carmay Lim Lee Pedersen Michael Sommer Vincent ZoeteFrançois Colonna-Cesari Milan Hodoscek Xabier Lopez David Perahia Ojars J. SoversMichael R. Cook Gary G. Hoffman Guobin Luo Robert Petrella Martin Spichty
Karplusian: 1955-2013
ATP Synthase Picture
29
ATP Energy Currency(Use 40 kg perday)
30
ATP Actin Picture
31
Worm Movie
32
How ATP Synthase Works I
The β subunits, which synthesizeATP from ADP, Pi, interact withthe γ subunit and change theirconformations as the γ subunitrotates.
33
34
Viewed toward the membrane
35
A New Man-made Motor
36
37
38
AcknowledgementH+H2:
R. N. Porter, R. D. Sharma, K. Morokuma
Kinesin:W. Hwang, M. Lang
F1 ATPase:J. Pu, K. Nam, Y. Q. Gao, P. Maragakis, J. Ma, W. Yang, R. Marcus
Thanks to Guishan Zheng for help with preparing the slides
39
Conformation Change along γ Rotation(clock-wise) during ATP Synthesis
Gao, Yang, & Karplus Figure 3a. 40
