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Advances in Molecular Simulation

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Abstract and Figures

In the past decade molecular simulations have become mainstream tools. They are routinely used to help improve and refine working hypotheses that link structure and function of proteins and other macromolecules. In addition, they are increasingly being employed in various aspects of drug discovery, from the discovery of cryptic binding sites through to free energy predictions. The popularity and success of molecular simulation, in our view, can be attributed to three main areas that have seen significant developments in recent years. These are (i) hardware and related software advances, (ii) force field development, and (iii) the development of advanced algorithms that in particular aim to address one of the central issues surrounding molecular simulations, namely the sampling problem. The combination of significant developments in all three of these key areas means that molecular simulation of biomolecules is not only a mature research field in its own right, but also a valuable, if not an essential component for medicinal chemistry research. In this chapter we review the recent progress in these areas and highlight some of the more significant advances.
Schematic representation of an MSM. A 2000-state Markov State Model (MSM) was built using a lag time of 12 ns. Shown is the superposition of the top 10 folding fluxes, calculated by a greedy backtracking algorithm. These pathways account for only ∼25% of the total flux and transit only 14 of the 2000 macrostates (shown labeled a−n, for convenient discussion). The visual size of each state is proportional to its free energy, and arrow size is proportional to the interstate flux. Reprinted with permission from "Unfolded-state dynamics and structure of protein L characterized by simulation and experiment". Voelz VA, Singh VR, Wedemeyer WJ, Lapidus LJ, Pande VS. J Am Chem Soc. 2010 132:4702-9. Copyright 2010 American Chemical Society. Overall, the use of MSM results in a number of benefits for molecular simulations. First of all, as mentioned previously, the approach provides a means to perfect parallelization, and also takes advantage of the direction of recent hardware trends towards higher number of cores on chips rather than increased speeds of single processors. Moreover, adaptive sampling coupled with MSM should provide more effective sampling of rare events. In fact, many biological systems are characterized by rugged energy landscapes that result in the presence of several metastable states separated by high-energy barriers. As a consequence, most of the time during a conventional MD simulation is spent sampling a few low energy states due to kinetic bottlenecks, and the exploration of transition events or other metastable states is limited. Adaptive sampling would allow one to focus the computational effort into phase space areas that have not been extensively sampled yet by the simulations. In addition, it provides a framework for the study of the kinetics of molecular events such as drug binding and protein conformational change. Last but not least, MSMs allow a human-readable interpretation of large amounts of data thanks to the kinetic clustering and coarse-graining procedures.
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Advances)in)Molecular)Simulation)
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Matteo!Aldeghi!and!Philip!C.!Biggin*!
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Department!of!Biochemistry!
University!of!Oxford!
South!Parks!Road!
Oxford!
OX1!3QU!
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In:$Comprehensive$Medicinal$Chemistry$III$(Ed.$S.$Chackalamannil,$D.$Rotella,$S.$Ward)$
Reference!Module!in!Chemistry,!Molecular!Sciences!and!Chemical!
Engineering.!Elsevier!2017,!Vol.!3,!Chap.!2,!14-33!
http://www.sciencedirect.com/science/article/pii/B9780124095472123431!
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This!document!is!the!preprint!of!the!above!referenced!article.!
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*Corresponding!author.!
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Email:!!Philip.biggin@bioch.ox.ac.uk!
Tel:!!01865!613305!
Fax:!!01865!613201!
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Keywords:!!Molecular!dynamics,!graphical!processing!units,!force-fields,!cloud!computing,!
simulations,!long!timescales.!
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Advances in Molecular Simulation - Comprehensive Medicinal Chemistry III Aldeghi and Biggin
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Abstract)
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In! the! past! decade! molecular! simulations! have! become! mainstream! tools.! ! They! are!
routinely!used!to!help!improve!and!refine!working!hypotheses!that!make!the!link!between!
structure! and! function! of! proteins! and! other! macromolecules.! ! ! In! addition,! they! are!
increasingly! being! employed! in! various! aspects! of! drug! discovery,! from! the! discovery! of!
cryptic! binding! sites! through! to! free! energy! predictions.! ! The! popularity! and! success! of!
molecular! simulation,! in! our! view,! can! be! attributed! to! three! main! areas! that! have! seen!
significant! developments! in! recent! years.! ! These! are! i)! hardware! and! related! software!
advances,!ii)!!force-field!development!and!iii)!the!development!of!advanced!algorithms!that!
in! particular! aim! to! address! one! of! the! central! issues! surrounding! molecular! simulations,!
namely!the!sampling!problem.!!!The!combination!of!significant!developments!in!all!three!of!
these! key! areas! means! that! molecular! simulation! of! biomolecules! is! not! only! a! mature!
research!field!in!its!own!right,!but!also!a!valuable,!if!not!essential!component!for!medicinal!
chemistry! research.! ! In! this! chapter! we! review! the! recent! progress! in! these! areas! and!
highlight!some!of!the!more!significant!advances.!
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Advances in Molecular Simulation - Comprehensive Medicinal Chemistry III Aldeghi and Biggin
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1.)Hardware)and)software)advances)
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The!main!obstacles!to!the!progress!in! the!application!of!molecular!dynamics!(MD)!to!drug!
discovery! have! been! the! computational! cost! of! the! simulations,! leading! to! precision! and!
convergence!issues,!and!inaccuracies!of!the!underlying!physical!model!used.!Problems!with!
convergence! arise! from! incomplete! sampling! of! all! accessible! configurations.! As! the!
properties!of!interest!often!depend!on!an!average!of!all!ensemble!conformations,!it!will!not!
be! possible! to! have! a! converged! estimate! of! those! properties! until! the! simulation! has!
sampled!all,!or!at!least!many,!such!conformations.!!Issues!with!the!physical!model!arise!on!
the!other!hand!from!the!assumptions!and!simplifications!made!with!respect!to!the!classical!
treatment!of!atoms!and!molecules,!as!well!as!inaccuracies!in!the!derivation!of!parameters.!!
The!two! problems! are! however!interconnected,! because! in! order!to! be! able! to!rigorously!
test! a! physical! model! and! improve! upon! it,! it! is! necessary! to! be! able! to! compute! the!
quantities!of!interest!with!a!precision!similar!to!the!experimental!counterpart.!!For!the!most!
part!this!necessitates!access!to!the!relevant!space-!and!time-scales.!
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There!has,!however,!been!a!steady!increase!in!the!scales!accessible!by!molecular!dynamics!
simulations! over! the! past! few! decades.! ! This! has! arisen,! at! least! in! part,! from! a! direct!
consequence!of!Moore’s! Law!for! semiconductors!and!computing,!which!observes! that!the!
number!of!transistors!on!CPUs!and!the!consequent!computer!power!approximately!doubles!
every! two! years.1! However,! algorithmic! advances! have! also! played! an! important! role! in!
expanding!simulations!capabilities,!in!particular!by!maximizing!the!opportunities!presented!
by!new! hardware! technologies! such! as! graphical! processing! units! (GPUs)!for! example.! ! In!
fact,! simulation! speed! has! been! growing! faster! than! Moore’s! Law,2! suggesting! that!
hardware! and! software! innovations! have! worked! in! synchrony! to! deliver! necessary!
improvements!in!simulation!performance!as!witnessed!by!both!the!scale3!and!timescales4!of!
simulation!now!achievable.!!!
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1.1 ))Special-purpose)machines)
Among! the! most! notable! hardware! advances! since! the! turning! of! the! century! was! the!
development! of! Anton,! a! specialised! machine! designed! specifically! to! accelerate! MD!
simulations,!by!D.E.!Shaw!Research.5!Previous!efforts!in!this!direction!were!not!particularly!
successful! due! to! the! fact! the! production! of! specialized! chips! is! demanding! and,! without!
adequate!resources,!too!slow!to!keep!up!with!the!pace!of!general-purpose!processors.!Yet,!
D.E.!Shaw!Research!managed!to!develop!a!parallel!machine,!based!on!512!specialized!nodes!
that!interact! in! a! tightly! coupled! manner! through! a! dedicated! high-speed! communication!
network,! which! performs! simulations! at! about! two! orders! of! magnitude! the! speed! of!
standard! hardware.5!!In! the! years! following! its! release,! Anton! allowed! ground-breaking!
simulations!of! milliseconds! in! length,! two! orders! of! magnitude! longer! than! the! lengthiest!
simulation!performed!before,6!which!permitted!the!observation!of!phenomena!such!as!the!
folding!of!small!proteins!into!their!native!structure,7!or!the!unbiased!binding!of!a!drug!into!a!
binding!pocket.8!!
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Lindorff-Larsen!et$al.9!reported!the! folding!of!12!diverse! small!proteins!through!simulation!
on!the!Anton!chip.!The!authors!observed!at!least!ten!folding!and!unfolding!events!for!each!
of!these! proteins! using! simulations! of! length! between! 0.1! and! 1! ms.! ! Other!than! proving!
Advances in Molecular Simulation - Comprehensive Medicinal Chemistry III Aldeghi and Biggin
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how! relatively! simple! physics-based! models! are! able! to! fold! proteins! into! their! native!
structure,!the!work! suggested!the! existence!of! a!preferential!folding! route!for! the!studied!
systems.! The! ability! to! simulate! and! study! protein! folding! pathways! will! impact! on! our!
understanding!of!misfolding! diseases!such!as! Alzheimer’s!and!Parkinson’s,! and!possibly! on!
our!ability!to!develop!strategies!to!tackle!such!illnesses.!!!
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The! same! year,! Shan! et$ al.10! showed! how! long! unbiased! molecular! dynamics! simulations!
were!able!to!capture! the!binding!process! and!final!! (crystallographically!observed)!pose! of!
two! Src! kinase! inhibitors;! PP1! and! dasatinib.! ! These! results! are! potentially! significant! for!
drug!discovery,! as! the! methodology!does!not! assume! any! prior! knowledge!of! the! binding!
location! and! pose.! ! Thus! it! is! conceivable! that! this! approach! might! be! applied! to! the!
discovery! of! allosteric! inhibitors! targeting! previously! unknown! binding! sites.! Moreover,! it!
allows! the! elucidation! of! the! binding! pathway,! which! can! affect! significantly! the! binding!
kinetics.!Longer!time!scales!not!only!allow!us!to!access!biologically!relevant!time!scales,!but!
also!provide!the!fundamental!framework!necessary!in!order!to!test!the!validity!of!the!force!
fields,!as!it!will!be!discussed!later.11-13!!
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Currently,!an! upgraded!version! of!this!machine! (Anton-2)!is! in! use!at! D.E.!Shaw! Research,!
while!the! previous!version! was! donated!to! the! Pittsburgh!Supercomputer! Centre! for!non-
commercial!use.!! This!new! machine!achieves!the! impressive!performance! of!85!µs/day! on!
dihydrofolate!reductase!(DHFR),!a!standard!benchmark!system!of!23,558!atoms,!and!breaks!
the! 1! µs/day! barrier! on! million-atom! systems;! for! instance,! using! all! 512! nodes! (33,792!
processors)!a!performance!of!3.6!µs/day!is!achievable!for!a!ribosome!system!containing!2.2!
million!atoms.14!
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1.2 )Graphics)processing)units)
While! special-purpose! architectures! can! deliver! extraordinary! performances! as! described!
above,! they! are! not! widely! available! as! a! significant! investment! in! human! and! financial!
resources! is! necessary! for! their! continuous! development.! ! Recently! however,! another!
avenue! for! simulation! acceleration! has! become! available! that! is! much! cheaper,! namely!
graphics! processing! units! (GPUs).! ! Driven! by! a! $100! billion! interactive! entertainment!
industry,! large! and! sustained! investments! in! GPU! development! have! resulted! in! steady!
increases!in!performance!alongside!decreasing!costs.15!
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When!rendering!graphics,!many!of!the!operations!required!are!simple!but!large!amounts!of!
data!need!to!be!handled.!!GPUs!have!thus!been!designed!with!a!large!number!(hundreds!or!
thousands)! of! simple! processors! that! work! in! parallel.! ! GPUs! are! basically! a! specialised!
circuit,!built!in!order!to!perform!a!large!number!of!floating-point!operations!per!video!frame!
(Fig.) 1).!! Some! of! the! calculations! performed!during! a! molecular! simulation! are! of!similar!
nature!to!the!ones!that!GPUs!can!accelerate,!such!as!the!computing!of!the!non-bonded!pair!
interactions! between! a! large! number! of! atoms,! which! is! typically! the! most! expensive!
calculation!during!a!simulation.15,16!!It!thus!became!clear! that!such!computations! could!be!
solved!faster!with!the!use!of!GPUs,!improving!the!simulation!throughput.16,17!!
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In!the!late!2000s,!comprehensive!MD!engines!such! as!ACEMD18!!and!OpenMM19!had!been!
developed! specifically! to! take! advantage! of! the! acceleration! provided! by! widely! available!
Advances in Molecular Simulation - Comprehensive Medicinal Chemistry III Aldeghi and Biggin
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GPUs.!!At!the!time!of!publication,!in!2009,!ACEMD!using!3!GPUs!and!3!CPU!cores!showed!a!
performance!on!the!DHFR!benchmark!that!was!roughly!equivalent!to!that!of!GROMACS!on!
20!CPU!cores.18!!Using!ACEMD!and! a!GPU!cluster,!Buch!et$ al.20!(2011)!carried!out!50!µs! of!
aggregate!simulated!time!and!reconstructed!the!binding!of!benzamidine!to!trypsin.!!In!2015,!
the!same!group! carried!out! similar!unbiased!simulations! for!42! fragments!and!the! protein!
serine!protease!factor!Xa,!for!a!total!of!2.1!ms!simulated!time!and!managed!to!recapitulate!
binding!poses,!affinities!and!kinetics!for!a!number!of!the!ligands!studied.21!!In!both!cases!the!
use!of!GPUs!enabled!such!extensive!sampling.!
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Nowadays,! most! widely! used! MD! software! can! take! advantage! of! available! GPUs! to!
significantly! improve! simulation! throughput! and! cost-efficiency.! Some! packages,! such! as!
GROMACS,! CHARMM! and! NAMD,! use! GPUs! in! an! off-loading! approach! where! the! short-
range! non-bonded! interactions! are! sent! to! the! GPU,! while! the! rest! of! the! calculation! is!
borne!by!the!CPU,! while!other!packages,! such!as!ACEMD!or! AMBER,!perform!almost! all!of!
the! computation! on! the! GPU.! ! Kutzner! et$ al.22! recently! evaluated! a! number! of! hardware!
setups!with!GROMACS!4.6!in!terms!of!pure!simulation!performance,!but!also!performance-
to-price!ratio,! taking! also! into!account! the! energy! consumption! of!the! hardware.! ! From! a!
purely! performance! perspective,! they! noted! that! GPUs! increase! the! speed! of! a! compute!
node!by!a!factor!of!1.7-3.8,! with!inexpensive!GeForce!consumer!cards! also!providing!a!2-3!
factor!increase!in!performance-to-price!ratio.!As!an!example,!a!single!node!comprising!two!
Intel! Xeon! E5-2680v2! processors! (10! cores! each)! offered! 26.8! ns/day! of! simulation! on! a!
membrane!protein! system! of! 81,743! atoms.! At!the! time! of! their! study! in! 2014!this! setup!
would! have! cost! about! 4400€.! ! However,! when! adding! a! single! Nvidia! GeForce! GTX! 980!
card,!the!performance!doubled!to!52.0!ns/day,!in!face!of! an!extra!cost! of!only!~450€.! The!
peak!performance!of! 66.9!ns/day!was! obtained!with!four!GTX!980! cards,!however,!adding!
the!third!and!fourth!GPU!improved!performance!only!marginally!as!the!simulation!became!
CPU-bound,!consequently!not!improving!the!cost-efficiency!of!the!setup.!!When!considering!
energy! consumption,! nodes! with! one! or! two! GPUs! have! an! increased! power! draw! and!
energy!cost,!yet!still!produce!from!1.5!to!2!times!the!MD!trajectory!per!€!invested!than!CPU-
only! nodes.! The! authors! also! remarked! that! the! energy! efficiency! improvement! of! the!
newer!Maxwell!architecture!as!compared!to!the!Kepler!one,!results!in!a!~20%!reduction!of!
trajectory!costs.!!With!AMBER14,!a!soluble!test!system!of!90,906!atoms!provided!an!output!
of!4.5!ns/day!on!two!E5-2650v3!processors!(10!cores!each),!going!to!34.6!ns/day!when!using!
one!GTX!980!card!(almost!a!8x!speedup)!and!up!to!50.2!ns/day!with!two!GTX!980!cards.!!It!is!
interesting! to! note! that! since! the! code! barely! uses! the! CPU,! the! performance! does! not!
become!CPU-bound!when!using!more!GPUs,!reaching!an!output!of!90.0!ns/day!when!using!
four!GTX!Titan!X!cards.!
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Advances in Molecular Simulation - Comprehensive Medicinal Chemistry III Aldeghi and Biggin
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Fig.!1.$Performance$improvements$of$CPUs$and$GPUs$in$the$last$decade.$$The$plot$compares$
the$GeForce$series$of$Nvidia$consumer$graphics$card$with$high-end$Intel$Xeon$processors$by$
launch$year.$Performance$for$GPUs$was$taken$from$
https://en.wikipedia.org/wiki/List_of_Nvidia_graphics_processing_units,$and$for$CPU$was$
calculated$from$data$available$at$
https://en.wikipedia.org/wiki/List_of_Intel_Xeon_microprocessors$and$http://ark.intel.com.$
$
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1.3 )Cloud)and)distributed)computing)
In!addition!to!new!hardware,!and!faster!and!larger!supercomputers,!recent!years!have!seen!
the!rising!of!cloud!and!distributed!computing23-25!!Cloud!computing!involves!the!use!of! a!
network!of! remote!servers! to! process!and! store! the!data23! and! allows!the!access! to!large!
computer!power!with!flexible!pay-as-you-go!pricing!schemes.!!Some!private!vendors!such!as!
Amazon! Elastic! Compute! Cloud! (EC2;! https://aws.amazon.com/ec2/)! or! IBM! Platform!
Computing! (http://www-
03.ibm.com/systems/uk/platformcomputing/solutions/hpccloud.html)! have! started!
providing! services!on!the!cloud!specifically!for!HPC.!!Google!have! instead! been! supplying!
computing!facilities!for!academic!research!for!free,!but!based!on!a!competitive!application!
process.!!In!its!first!year!in!2013,!it!provided!about!1!billion!core-hours!for!projects!covering!
a! wide! range! of! science! and! engineering! challenges! including! antibiotic! resistance,! drug!
discovery,26!and! protein! structure!prediction! and! design.!! As! a!consequence! of! this! trend,!
software! to! facilitate! the! execution! of! ensemble! of! simulation! on! remote! cloud! services!
have!been!developed.27!!
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Distributed!computing! projects! such! as! Folding@Home!or!Rosetta@Home! rely! instead! on!
the! unused! power! of! volunteers’! personal! computers,! where! anyone! can! contribute! by!
downloading!a!client!software.25,28!!This!creates!a!large!network!of!heterogeneous!hardware!
that! is! available! to! the! researcher! for! performing! molecular! dynamics! simulations.!!
Presently,! more! than! 100,000! users! are! contributing! to! the! Folding@Home! project,!
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providing!over! 20!petaflops! of!computing! power,!comparable! to!the! peak!performance!of!
IBM! Sequoia,! the! third! most! powerful! supercomputer! as! of! late! 2015! (see!
www.top500.org).! ! Since! the! early! 2000s,! such! computing! power! has! been! employed! for!
many! important! computational! studies! on! protein! folding! and! design.29-37!!Similarly,!
GPUGRID.net! was! released! in! 2007! and! uses! the! graphics! cards! of! volunteers! in! order! to!
pursue! scientific! research! in! cancer,! HIV,! and! neural! disorders! through! the! use! of!
simulations.38-41!
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Cloud!and!distributed!computing!provide!much!raw!power!at!low!cost.!!!However,!they!do!
not! provide! the! same! communication! and! I/O! performance! as! supercomputing.! The!
strength!of!distributed!systems!is!that!they!are!cheaper!than!supercomputers,!as!they!tend!
to! use! off-the-shelf! computers! for! processors! and! memory,! which! also! require! minimal!
cooling! costs.! However,! high-speed! network! and! storage,! and! tight! connections! between!
nodes,!mean!that!many! nodes!of!supercomputers!such!as!Tianhe-2,!Titan,! or!Sequoia,!can!
work! together! on! the! same! tasks! since! data! can! move! between! processors! rapidly.!!
Supercomputers! are! therefore! still! more! suited! for! highly-complex,! real-time! applications!
for!instance.!!For!molecular!dynamics!simulations!specifically,!it! means!that!running!a!very!
large!simulation!consisting!of!millions!of!atoms!would!perform!better!on!an!HPC!facility.!!On!
the! other! hand,! running! thousands! of! small! simulations! on! cloud/distributed! computing!
would! be! more! cost! effective! without! suffering! much! performance! loss.! ! Moreover,! the!
analysis!of!large!amounts!of!data!also!benefits!from!the!communication!hardware!provided!
by!HPC! facilities.! ! The! data! need! to! be! read! in! (often! as! whole! data!sets)!and! processed.!!
Consequently,! aspects! such! as! data! I/O,! CPU! speed,! and! node! communication! become!
important!factors.!
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1.4 )Novel)algorithms)and)parallelization)
Hardware!advances!need!to!be!combined!with!new!and!improved!software!and!algorithms!
in!order! to! maximize! any! potential!benefits! that! arise.! ! GPUs!have! provided! probably! the!
most! significant! step! change! in! recent! years;! since! the! introduction! of! general! GPU!
programming!platforms,!such!as!NVIDIA’s!CUDA!in!2006!or!OpenCL!in!2009,!the!use!of!the!
new!hardware!for!scientific!applications!has!become!much!more!accessible.!!!Prior!to!those!
developments,!graphics! specific! APIs! such! as!OpenGL! had! to! be! used!in! order! to! perform!
calculations! that! were! not! related! to! the! rendering! of! vector! graphics,! making! the!
development!of!new!code!time! consuming.!!Similarly,!the!availability!of!tools!like!MPI! and!
OpenMP!have!allowed!the! implementation! of! parallel! algorithms! for! multicore! machines,!
including!large! supercomputing! clusters,!greatly! increasing! the!performance! of! MD!codes.!!
As!a!result,!all!widely!used!MD!codes!have!substantially!improved!their!parallel!performance!
in!the! last! decade.! ! For!instance,! as! part! of! the!Blue!Gene! project,! scientists! at! IBM!have!
been! exploring! parallel! strategies! in! order! to! achieve! strong! scaling! for! their! Blue! Matter!
simulation!code;!in!2006!they!reported!continued!speed-up!to!fewer!than!three!atoms!per!
node.42!!Scaling!is! important! as! the! number! of! cores!available! increases! there! will! be! the!
issue!of!using!efficiently!a!large!number!of!cores!for!small!and!medium!size!systems.!
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MD! algorithms! have! been! constantly! refined! in! order! to! decrease! the! communication!
requirements! between! processors,! resulting! in! decreased! latency.! ! Inter-processor!
communication! is! necessary! on! parallel! machines! when! evaluating! forces! on! interacting!
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particles.!!In!early!designs,!because!of!its!simplicity!and!the!fact!it!was!fairly!efficient!over!a!
limited! number! of! cores,! particle! decomposition! was! the! main! method! employed! to!
distribute!the!computation!of!near!interactions!across!the!available!processors!43,44.!!In!this!
scheme,! at! the! beginning! of! the! simulation! each! particle! in! the! box! is! assigned! to! a!
processor,!which!then!computes! its!interactions!at!each! time!step.!!However,! this!method!
does!not!scale!well!with!system!size!and!number!of!cores:!since!the!decomposition!is!static,!
but!the! particles! diffuse!through! the! simulation! box,!the! interaction! partners!of! a! specific!
particle!will!be! distributed!across!the! whole!box! and!many!of! the!CPUs!will! be!involved! in!
the!computation,!resulting!in!a!large!communication!volume.43!!
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Spatial!decomposition!methods!on!the!other!hand!can!really!take!advantage!of!the!locality!
of! the! interactions,! by! dividing! the! space! of! the! simulation! into! a! number! of! cells! and!
dynamically!assigning!particles!to!processors!based!on! the!location!of!each!particle.!In!this!
way,! particles! in! a! cell! will! interact! only! with! other! ones! in! the! same! cell! or! in! the!
neighbouring!cells,! improving! data! locality! and! minimising! inter-processor! communication!
requirements! despite! the! additional! book-keeping! necessary! to! keep! track! of! particles!
moving!between! cells.! In! addition,! many!modern! parallel! machines! (e.g.! Blue! Gene/L!and!
Cray’s! T3D,! T3E,! and! XT3! systems)! have! networks! with! toroidal! topology,! so! that! spatial!
decomposition!allows!to!match!the!box!grid!to!the!network!grid!for!faster!data!exchange.45!!
!
A! number! of! spatial! decomposition! methods! have! been! developed! during! the! years,! but!
more!recently!so-called!“neural!territory”!methods!have!provided!a!significant!reduction!of!
the! amount! of! data! that! needs! to! be! exchanged! between! cores.45-47!!Due! to! particle!
diffusion! across! spatial! domains! of! inhomogeneous! systems,! load! imbalance! between!
processors!can!be!an!issue!as!the!number! and!type!of!particles! in!each!domain!determine!
the!load.!!The!issue!is!however!easily!solved!by!dynamically!balancing!the!load!on!the!cores!
by!shifting! the!boundaries! of!the!domains.43!!For! a!more! in!depth! review! on!a! number!of!
decomposition!methods!see!these!refs.43-45!
!
Other! algorithmic! advances! have! been! related! to! the! acceleration! of! floating-point!
calculations,! for! instance! by! the! development! of! custom! math! functions:! Enenkel! et! al.!
reported! a! number! of! functions! optimised! for! MD,! improving! floating-point! efficiency.48!!
Alternatives!to!the!widely!used!Particle!Mesh!Ewald!(PME)!method!for!the!computation!of!
long-range! electrostatic! interactions! have! been! proposed:! the! multilevel! (or! multigrid)!
summation!method!provides! similar!speed!and! accuracy!to!the! traditional!PME,!but!it!can!
also!be!used! for!semi-! and!non-periodic! systems.49-52!!Semi-periodicity!might! be!useful!for!
the! simulation! of! different! solvent! conditions! across! a! membrane! for! instance.! Such! a!
method! has! been! also! shown! to! provide! improved! parallel! scalability! over! PME! as!
implemented!in!NAMD!for!a!system!of!size!<100K!atoms!simulated!over!a!thousand!cores.50!!
A!number!of!improved!implementations!of!the!traditional!bonds!constraint!method!SHAKE!
have! been! proposed,53-56! as! well! as! alternative! methodologies! that! are! more! easily!
parallelizable!for!global!constraints!such!as!LINCS.57,58!!
!
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2. Force)field)advances)
In! the! last! decade! the! trend! of! force! field! improvement! has! continued.! ! While! their!
functional!forms!have!remained!unvaried,!their!parameters!have!been!modified!in!order!to!
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better! match! experimental! and! quantum! mechanical! data.! ! One! concern,! that! has! only!
recently! become! addressable,! is! to! what! extent! force-field! parameters! reproduce! longer-
timescale!properties.! !In! 2012,! Lindorf-Larsen!et$ al.11!used! Anton! to!access! long!timescale!
simulations! and! assess! the! performance! of! a! number! of! modern! force! fields! from! the!
Amber,! OPLS! and! CHARMM! families! through! comparison! to! experimental! data.! ! The! test!
evaluated! the! ability! of! the! force! fields! to! reproduce! folded! protein! structure! and!
fluctuations! from! NMR! data,! secondary! structure! content,! and! to! correctly! fold! small!
proteins! into! their! native! structure.! ! The! results! indicated! the! force! fields! considered!
showed! steady! improvement! during! the! previous! decade,! with! the! most! recent! versions!
providing! the! most! accurate! descriptions! of! different! protein! structural! and! dynamical!
properties.!
!
Despite! years! of! optimisation! and! steady! improvement,! current! models! are! still! far! from!
perfect! and! there! is! still! plenty! of! room! for! improvement.! ! In! fact,! the! same! study!
mentioned! above! also! identified! some! deficiencies;! in! particular,! the! force! fields! did! not!
manage!to! capture! the! temperature!dependency! of! the! secondary! structure!propensities.!
Piana!et$al.13!used! the!fast!folding!variant! of!the!villin! headpiece!as!a!test! case!in!order!to!
assess!the!ability!of!four!force!fields!to!fold!the!protein!into!its!native!structure.!!While!they!
observed! that! all! force! fields! correctly! folded! the! protein! with! rates! in! agreement! to!
experiment,!it!was!noticed!that!the! folding!mechanism!and!the!properties! of!the!unfolded!
states! strongly! depended! on! the! force! field! employed.! ! Rauscher! et$ al.59! have! instead!
recently! studied! the! structural! ensembles! generated! with! µs-long! simulations! for!
intrinsically!disordered!proteins!(IDPs).!!The!group!compared!eight!different!force!fields!for!
a!total!simulation!time!of!almost!a!millisecond,!and!found!that!different!force!fields!yielded!
markedly! different! ensembles! that! differed! in! chain! dimensions,! hydrogen! bonding,! and!
secondary!structure!content.!!While!IDPs!are!highly!sensitive!to!force!field!parameters!given!
their!rugged! energy! landscape,! the! observation! that! changing! the! force! field!had! a! larger!
effect!on!secondary!structure!content!than!changing!the!entire!peptide!sequence!points!to!
clear!limitations!in!the!physical!model.!
!
Here,!we!will!focus!mainly!on!some! of!the!most!popular!fixed-charge!all-atom! force!fields,!
while! also! an! overview! of! recent! developments! on! polarizable! and! coarse-grained! force!
fields!will! be!given! too.! Notable!exclusions! from!this! review! are!improvements! on!united-
atom!force!fields!(such!as!the!improvements!to! the!GROMOS!force-field60),!universal!force!
fields,61,62!reactive!force!fields,63,64!and!force!fields!with!more!complex!functional!form!such!
as!the!Merck!Molecular!Force!Fields.65!
!
2.1. Protein)force)fields)
A!number!of! researchers!noticed!that! the!Amber! ff94!and!ff99! energy!functions!produced!
an! imbalanced! proportion! of! secondary! structure! elements! with! over-stabilization! of! α-
helices.!! In! 2006! the! backbone! dihedrals! of! the! Amber! ff99! force! field! were! improved! by!
fitting!the! energies!of! multiple! conformation!of! glycine! and!alanine! tetra-peptides!to!high!
level!ab$ initio!quantum! mechanical!data.66! !Additional! backbone!torsion! improvements! by!
Best!and!Hummer!to! correct!the!α-helical! propensity!of!the! model!resulted!in! the!ff99SB*!
and!ff03*!force!fields!in!2009.67!!Lindorff-Larsen!and! co-workers!introduced!ff99SB-ILDN!in!
2010,! which! improved! side! chain! torsions,! by! fitting! energies! to! QM! calculations! and!
comparing!microsecond-long! MD!simulations! to! NMR!data.12! !Other! enhanced! versions!of!
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ff99SB! were! the! ff99SB-nmr!by! Li! and! Brüschweiler68! and! ff99SB-phi!by! Nerenberg! and!
Head-Gordon.69!At!the!time!of!writing,!the!latest!Amber!force!field!available!is!ff14SB,!which!
is!a!result!of!a!complete!refit!of!all!amino!acid!side!chain!torsions.!!The!work!also!included!
multidimensional! dihedrals! scans! to! improve! the! parameter! transferability.! Additional!
empirical! adjustments! were! made! to! protein! backbone! dihedral! parameters! in! order! to!
better!reproduce!NMR!scalar!coupling!data.70!!
!
Analogous! backbone! dihedral! issues! have! been! found! for! other! force! fields! too.! ! In! 2004!
MacKerrel! and! co-workers! used! QM! and! crystallographic! data! in! order! to! improve! the!
peptide-backbone! parameters! of! CHARMM22,! introducing! the! CHARM22/CMAP71!force!
field.! ! Despite! some! degree! of! success! for! protein! folding! applications,72! flaws! were! still!
present!as!indicated!by!the!misfolding!observed!in!long!simulations!of!the!fast-folding!WW!
domain73,74!and!the!discrepancy!of!the!folding!mechanism!of!the!villin!headpiece!subdomain!
between! simulations! and! experiment.72! ! Piana! et$ al.13! tackled! the! issue! of! α-helical! over-
stabilisation75!by! replacing! the! CMAP! correction! with! new! backbone! torsion! terms,!which!
resulted! in! a! force! field! they! named! CHARM22*.! !A! substantial! revision! of! the! CHARMM!
force! field! parameters! by! the! MacKerell! lab,! trying! to! address! the! above! shortcomings,!
resulted!in!2012!in!the!improved!CHARMM36!force!field.76!!
!
Another! popular! protein! force! field! that! has! undergone! constant! refinement! in! the! last!
twenty! years! since! its! initial! introduction! is! the! OPLS-AA! force! field.77!!The!non-bonded!
interactions!in!OPLS-AA!are!parameterised!in!order!to!reproduce!properties!of!pure!organic!
liquids,!such!as!heat! of!vaporization,!densities! and!hydration!free!energies,! while!torsional!
parameters!are!fit!to!available!experimental!or!QM!data.!!The!original!torsion!scans!where!
performed! at! the! Hartee-Fock! (HF)! level! of! theory! with! a! small! basis! set! due! to! the!
computational! limitations! at! the! time,! but! a! revised! OPLS-AA/L! was! presented! in! 2001!
where!single!point!energies!of!HF!geometry!optimised!structures!were!obtained!using!local!
MP2!calculations!and! a!larger!basis! set.78!!In! 2015,!the!torsional! parameters!were!revised,!
performing!torsional!scans!with!modern!hybrid!density!functionals79,80!which!has!resulted!in!
the!latest!OPLS-AA/M!force!field.81!
)
)
2.2. Organic)molecule)force)fields)
If! simulations! are! to! be! used! for! drug! discovery,! it! is! necessary! to! have! a! good! physical!
model! for! small! organic! molecules! in! addition! to! proteins.! ! However,! while! the! chemical!
space!covered! by!polypeptides! has!clear! boundaries,! this!is! not!the! case! for!small! organic!
molecules.!!The!drug-like!space!is!vast!with!a!huge!number!of!possible!atom!combinations.!!
Even! though! there! are! many! stable! chemical! groups! in! which! a! molecule! can! be! broken!
down!in! to,! the! properties! of! such! groups! can! change! drastically! depending! on! the!
neighbouring!chemical! moieties.! !For! instance,! the! electrostatic!properties! of! an! aromatic!
ring!such!as!benzene!depend!strongly!on!its! substituents!and!their!relative!positions.!!As! a!
consequence,!the! development!of! a! general!yet! accurate! organic!molecule! force! field!is! a!
difficult!task.!
!
Due! to! the! increasing! interest! in! the! use! of! modelling! and! simulation! for! drug-discovery,!
since! the! mid-2000s! there! has! been! increasing! effort! in! developing! organic! molecule!
parameter!sets!that!are!consistent!with!existing!(typically!protein)!force!fields.!!While!OPLS!
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was!thought!from!the! beginning!as!a!force! field!for!both!organic! and!biological!molecules,!
others!such!as!AMBER!or!CHARMM!had!mainly!focussed!on!proteins.!!In!2004,!the!General!
AMBER!Force!Field!(GAFF)!was!introduced!by! Wang!et$al.82!and!is!meant!to! be!compatible!
with!the!AMBER!family!of!protein!force!fields.!!!Since!then,!the!force!field!has!been!regularly!
updated!to! improve!many! of! the!parameters,! with!these! improvements! incorporated!into!
each!new!release!(see!www.ambermd.org).!
!
Following! a! philosophy! that! focuses! on! quality! at! the! expense! of! transferability,!
Vanommeslaeghe! et! al.! developed! a! CHARMM-compatible! organic! molecule! force! field,!
named! the! general! CHARMM! force! field! (CGenFF).83! CGenFF! too! is! currently! actively!
maintained! and! constantly! being! improved.84! ! As! manual! assignment! of! parameters! is! a!
cumbersome! task,! prone! to! errors! and! preventing! automation,! algorithms! for! automated!
atom!typing!have!been!developed!for!both!the!general!Amber!and!CHARMM!force!fields.85-
87!!In! addition,! due! to! the! fact! that! encountering! missing!or! imprecise! parameters! is!
relatively!common!given!the!diversity!of!existing!drug-like!species,!tools!to!aid!the!users!in!
the!derivation!of!new!parameters!have!been!developed.88-91!!!
!
Also!of!note! is!the! proprietary!OPLS!force! field!developed!by! Schrödinger!Inc.!for! proteins!
and! organic! molecules.! ! OPLS_2005,! OPLS2.1! and! the! most! recent! OPLS3! have! been!
developed! in! order! to! have! a! broader! coverage! of! medicinal! chemical! space! and! support!
their! free! energy! perturbation! suite! for! binding! affinity! prediction.92,93! ! In! OPLS3,! the!
reparameterisation!of!peptide!dihedral!angles!and!the!inclusion!of!off-atom!charge!sites!to!
better! represent! halogen! bonding! and! aryl! nitrogen! lone! pairs! resulted! in! more! accurate!
binding!free!energy! calculations.92!! The!work!reminds!us!how! it!is!not! only!the! ligand,!but!
also! the! protein! parameters,! and! how! they! interplay! with! each! other,! that! have! a!
substantial!effect!on! modelling!approaches! to!drug! design.!!Overall,! it!appears! that!across!
the! different! small! molecule! force! fields! there! has! been! a! focus! on! the! improvement! of!
dihedrals!parameter!and!partial!charges!due!to!their!limited!transferability!across!different!
chemical!species.94-97!
!
2.3. Force)fields)for)other)species:)nucleic)acids,)lipids,)sugars,)and)water)
While!proteins!represent!the!majority!of!current!drug!targets,!there!is!clearly!an!interest!to!
model! and! simulate! nucleic! acids! too.! ! Nucleic! acid! force! fields! have! historically! lagged!
behind! protein! force! fields;! nonetheless,! in! the! last! decade! there! had! been! significant!
improvements!in!the! availability!of!force! fields!for!DNA! and!RNA!simulations.! !In!the! early!
2000s! the! CHARMM27! force! field! for! nucleic! acids! was! released! and! has! been! recently!
updated.98,99! ! At! the! same! time,! when! 50-100ns! long! simulation! times! became! available,!
deficiencies!in! the! AMBER! force! field! for!nucleic! acids! were! observed,! in! particular! in!the!
sampling! of! backbone! populations.100,101!!Pérez! et! al.! have! provided! an! improved! set! of!
parameters!ff99-bsc0!102!and!work!by!Yildirim!and!co-workers!focussed!on!reparametrizing!
the! RNA! chi! torsional! angles.103-105! ! Additional! recent! work! focussed! on! the! derivation! of!
specific!improved!parameters!for!both!RNA!106,107!and!DNA.108,109!!Testing!and!benchmarking!
of!all!these!parameter!modifications!and!extensions!is!still!very!much!an!on-going!exercise.!
!
With!increasing! interest!in! the!study! of!membrane! properties!and! the!role! of!lipids!in! the!
modulation! of! protein! functions,! dedicated! lipid! parameter! sets! that! are! compatible! with!
other!protein!force!fields!are!increasingly!becoming!more!available!and!accurate.!!In!2005,!a!
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revised!version!of!CHARMM27! with!optimised!parameters! for!aliphatic!tails!was! published!
and! termed! CHARMM27r.110!!Later! in! 2010,! the! CHARMM! 36! lipid! FF! was! developed! by!
improving!the!parameters!of!the!headgroups!and!ester!links.111!!On!the!other!hand,!AMBER!
had! not! had! support! for! lipid! parameters! until! 2012,! when! Lipid11! and! GAFFlipid! were!
released.112,113!!Lipid14!was!later!released!in!2014!as!a!significant!advance!over!the!previous!
AMBER! lipid! force! fields!114! and! allowed! the! artificial! surface! tension! term! that! was!
previously!required!to!keep!the!correct!phase!to!be!dropped.!!Lipid14!compared!favourably!
with!a!number!of!experimental!properties,!such!as!area/volume!per!lipid,!bilayer!thickness,!
NMR! order! parameters,! scattering! data,! and! lipid! lateral! diffusion.! ! In! 2015,! the! first!
example!of! spontaneous! lipid! bilayer! formation! during! unbiased! all-atom! simulations! was!
presented!using!both!the!CHARMM36!lipid!FF!and!AMBER!Lipid14.115!
Carbohydrates!are!fundamental!building!blocks!in!biology!and!have!important!roles!in!many!
cellular!processes.!!Moreover,!carbohydrate-based!structures!are!of!interest!for!drug!design!
purposes.116,117!!However,!the!modelling!of!carbohydrates!presents!a!set!of!challenges!due!
to!their!particular!structural! and!electronic!properties.! !The!high! number!of!chiral! centres,!
rotatable! bonds,! and! linkages! between! units,! results! in! a! large! number! of! complex!
structures.! ! In! addition! to! the! high! number! of! polar! groups,! peculiarities! such! as! the!
anomeric!effect!cause!complex!charge!distributions!around!the!molecule!contributing!to!the!
difficulty!to! derive! adequate! fixed! partial!charges.! ! As! a! consequence,!carbohydrate! force!
fields!are!currently!not!as!mature!as!force!fields!for!other!biological!small!molecules!such!as!
lipids!and!it!may! well!be!that!more! complex!functional!forms!are! required!to!fully!capture!
the! properties! of! carbohydrates! properly.118,119! ! ! The! main! carbohydrates! atomistic! force!
fields! currently! available! are! GLYCAM06! 120,121,! and! CHARMM36.122-125! ! In! particular!
GLYCAM06,!which!is!compatible! with!the!AMBER! force!field,!supports! a!large!collection!of!
carbohydrates! with! parameters! for! both! anomeric! and! enantiomeric! forms! of! the!
compounds.!!An!OPLS!version!for!carbohydrates!dates!back!to!2002!126,!and!there!have!also!
been!contributions!to!the!GROMOS!force-field.127!
!
The! quality! of! the! solvent! model! is! fundamental! too,! as! properties! such! as! partition!
coefficients!and!binding!affinities!depend!strongly!on!the!solute-solvent!interactions.!Water!
models!are!thus! also!deeply! entrenched!in! the!fabric! of!all! solute!force!fields,! so!that! it!is!
difficult!to!replace!water!models!straightforwardly.!However,!the!prevalent!models!of!liquid!
water! were! developed! decades! ago128! despite! computational! advances! and! larger!
availability!of!experimental!data.!!This!motivates!the!development!of!new!models!showing!
better!agreement!with!experiment.129!!Among!recent!developments!on!fixed-charge!water!
models,! there! is! the! 4-point! Optimal! Point! Charge! (OPC)! water! model,! which! showed! an!
improved! performance! for! a! number! of! different! bulk! properties! as! compared! to! other!
popular!models!such!as!TIP3P,!SPC/E,!TIP4P-Ew,!TIP4P-ew,!and!TIP5P.129!!!The!authors!also!
suggest! an! improved! performance! in! the! results! of! hydration! free! energy! calculation! for!
small!molecules.!! Similarly,!new! TIP3P!and! TIP4P!parameters!(termed! TIP3P-FB!and! TIP4P-
FB)!were!derived!using!an! automated!force!field! optimisation!program,!and! showed!much!
better!agreement!with!bulk!properties!than!the!original!water!model.130!
!
2.4. Polarizable)force)fields)
The! lack! of! explicit! polarization! has! long! been! recognized! as! one! of! the! crudest!
simplifications! of! traditional! fixed-charge! force! fields.131,132!!Indeed,! it! is! known! that! the!
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environment!has!a!large!effect!of!the!electronic!distribution!of!a!molecule;!for!instance,!the!
charge!distribution!around!a!peptide!depends!upon!its!conformation133!and!that!of!a!ligand!
changes!between!the!bound!and!unbound!states.134!!Such!effects!cannot!be!captured!with!a!
fixed-charge!model.! !There! have!therefore! been!efforts! to!develop! polarizable!force! fields!
for! decades! now.! ! However,! it! has! only! been! recently! that! there! has! been! an! increased!
interest!in!these!models,!facilitated!by!the!computer!power!now!available!along!with!efforts!
to!include!them!in!widely!used!simulation!software!such!as!GROMACS,!NAMD,!AMBER!and!
CHARMM.!!A!few!different!theoretical!methods!with!different!degrees!of!rigour!have!been!
explored!in!order!to!model!atom!polarization!during!molecular!simulations.!!
!
One! such! approach! is! the! ‘fluctuating! charge’! model,! in! which! the! partial! charge! of! each!
atom!is! placed! on!their! nucleus! but! the!magnitude! of! each! charge!can! change! during! the!
simulation.135!!Charges! are! transferred! between! atoms! in! a! way! that! equalizes! the!
electronegativities,! where! the! instantaneous! electronegativity! on! an! atomic! site! depends!
upon! the! atom’s! type,! charge,! and! the! electrostatic! potential! it! experiences! due! to! its!
neighbouring! particles.135! ! Whilst! it! does! not! require! any! more! interaction! terms! than!
classical! force! fields,! it! can! easily! represent! polarization! that! occurs! in! the! direction! of!
atomic!bonds.131!!The!most!extensively!applied!fluctuating!charge!model!so!far!has!been!the!
charge!equilibration!(CHEQ)!force!field!developed!within!the!CHARMM!program.136,137!
!
Another! popular! method! is! based! on! classical! Drude! oscillators,! where! a! pair! of! point!
charges! represents! each! polarizable! atom.! ! While! the! first! charge! is! positioned! on! the!
nucleus!like!in!typical!fixed-charge!force!fields,!the!second!charge!is!attached!to!the!nucleus!
via!a!spring!as!a!massless!(Drude)!particle.!!The!two!particles!can!therefore!be!considered!as!
representing!the!nucleus!and!electron!cloud!of!the!atom,!and!the!total!partial!charge!for!the!
atom!is!the!sum!of!the!charges!of!these!two!particles.!!The!mimicking!of!polarization!is!due!
to! the! fact! the! second! particle! is! free! to! move! around! the! nucleus! responding! to! the!
external!field!and!creating!an!induced!dipole!moment.138-140!
!
This!approach!too!is!easily!implemented!within!already! existing!force!fields!and!simulation!
codes.!!On!the!other!hand!it!involves!a!substantially!larger!amount!of!charges!present!in!the!
system,! so! that! many! more! interactions! need! to! be! calculated! at! each! time! step.! ! The!
Drude-2013!model!by!MacKerell,!Roux!and!co-workers,!where!Drude!particles!are!added!to!
all! non-hydrogen! atoms,! is! currently! the! most! widely! adopted! for! simulation! of!
biomolecules.141-144!!Extra!point!charges,!representing!lone!pairs!and!an!anisotropic!form!of!
polarizability,! have! been! introduced! in! order! to! better! represent! hydrogen-bond!
acceptors.145!!Lemkul! et$ al.145! have! recently! published! a! comprehensive! review! on! this!
model!and!we!redirect!the!readers!to!it!for!a!more!in-depth!treatment!of!the!subject.!!
!
In! the! inducible! dipole! methodology,! inducible! point! dipoles! are! assigned! to! each! atomic!
site.! ! The! field! due! to! the! explicit! charges! alone! is! calculated! first,! and! then! dipoles! are!
calculated!as!the!field! multiplied!by!the!local! polarizability,!resulting!in!a! new!electric!field!
133.! ! Dipoles! are! therefore! usually! calculated! with! an! iterative! procedure! to! convergence,!
and!the! electrostatic!energy!derived! from!charge-charge,! charge-dipole,! and!dipole-dipole!
interactions.145,146!!Such!an!approach!was!used!with!the!AMBER!ff02!force!field!and!AMBER!
simulation! package.82,147! A! more! rigorous! approach! that! includes! multipoles! up! to!
quadrupoles! is! employed! in! the! AMOEBA! force! field.148-152! Contrary! to! all! the! other!
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approaches!discussed!above,! AMOEBA!takes! into!account! anisotropic!polarisation! through!
permanent! multipole! moments! and! does! not! need! additional! point! charges! in! order! to!
represent!anisotropy!due!to!lone!pairs.!!In!addition,!other!instances!of!anisotropy!such!as!pi-
clouds!or!sigma-holes!are!naturally!taken!into!account!too.131,153-156!
!
Most!parameterization!efforts!for!polarizable!force!fields!for!biomolecules!have!focussed!on!
proteins!(indeed,!all!of! the!above-mentioned!force! fields!include!parameters!for! proteins).!
Polarizability!is!also!expected!to!have!a!strong!impact!on!nucleic!acids,!firstly!because!they!
are!highly!charged!and!contain!a!large!number!of!hydrogen!bonds,!but! secondly!their!high!
charge!density! means! they!are! highly! polarising!themselves.! ! Amber! ff02!and! Drude-2013!
both!contain!parameters!for!nucleic!acids.!!Parameters!for!lipids! and!carbohydrates,!while!
highly!desirable,!are! still!limited,!with! the!CHARMM! Drude!and!CHEQ! force!field!providing!
only!partial!coverage! for!these!species.131!!A! broad!set!of! parameters!for!arbitrary! organic!
molecules! is! not! available! yet,! but! would! be! extremely! desirable! in! the! context! of! drug-
design.!! At! present,! it! is! clear!that! there! is! huge! potential! for!polarizable! force-fields,! but!
much!work!is!still!needed!to!develop!and!validate!them.!!!Consequently,!fixed-charge!force!
fields! are! still! very! much! the! standard! for! molecular! simulations! of! protein-ligand!
complexes.!
!
While!simulations!using!polarizable! force!fields!tend! to!be!computationally! more!intensive!
and!used!to!be!limited!to!very!short!timescales,!there!are!now!instances!of!simulations!with!
lengths!in! the! tens!to! hundreds! of!nanosecond! in! length.!! The! Drude-2013!force! field! has!
been!used!for!simulations!of!proteins!with!up!to!224!residues!and!for!100-200!ns,144!while!
for!smaller!proteins!simulations!of!even!up!to!the!microsecond!timescale!have!been!run.157!!
The!more!expensive! AMOEBA!force! field!was! used!in! 2013!with! optimized!parameters! for!
30!ns!long!simulations!of!10!different!proteins!in!solution.!!The!simulations!showed!how!the!
structures!were!stable!with!good!agreement!of!the!calculated!order!parameters!with!NMR!
data.!!In!addition,!the!force!field!showed!a!correlation!coefficient!of!0.998!between!the!x,y!
and!z!components!of!the!gas!phase!dipole!moments!obtained!with!AMOEBA!and!high-level!
QM! calculation! for! each! amino! acid! dipeptide! at! multiple! conformations,! which! is! an!
unprecedented! level! of! accuracy! in! reproducing! the! electrostatic! properties! of! peptides!
using!a!molecular!mechanics!based!force!field.148!!Jiao!et!al.!using!the!same!force!field!also!
found! good! quantitative! agreement! between! calculated! and! experimental! binding! free!
energies!for!a!series!of!benzamidine-like!ligands!binding!to!trypsin.158,159!!Often,!polarizable!
force! fields! are! found! to! perform! just! as! well! as! classical! force! fields.! ! However,! classical!
force! fields! have! gone! through! much! more! extensive! optimisation.! ! Assuming! the! same!
extent!of!scrutiny!and!development!will!be!achieved!for!polarizable!force!fields!within!a!few!
years,! we! can! expect! these! to! yield! a! more! accurate! representation! of! molecular!
interactions!in!the!near!future.!
!
One!of!the!perceived!disadvantages!of!polarizable!force!field!is!the!fact!they!are!slower!than!
fixed-charge! force! fields.! ! However,! this! is! expected! given! the! higher! complexity! of! the!
functional!form,!and!once!fully!developed!the!more!appropriate!question!will!probably!be:!
what!level!of!physical!detail!of!the!system!do!I!need!in!order!to!study!the!process/property!I!
am! interested! in?! ! Conventional! additive! force! fields! will! likely! always! provide! longer!
trajectories!given!the!same!amount!of!computation,!trading-off!accuracy!in!the!electrostatic!
description! of! interactions! for! speed.! ! Therefore,! researchers! will! have! to! weigh! the!
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advantages! of! a! longer! timescale! versus! greater! accuracy! and! decide! which! one! is! more!
important! for! the! problem! at! hand.! ! Similar! considerations! already! apply! when! deciding!
whether! to! use! an! all-atom! force! field! versus! a! coarse-grained! model,! or! even! versus! a!
quantum!mechanical! treatment! of! the!system.! ! Computational! demands! notwithstanding,!
advances! in! polarizable! force! fields! are! among! the! most! promising! developments! toward!
the!goal!of!more!accurate!force!fields.!
!
2.5. Coarse)grained)force)fields)
Despite! the! increase! of! computational! power! available! and! efficiency! of! simulation!
algorithms,! the! large! spatiotemporal! jump! between! the! atomistic! and! mesoscopic! scales!
calls!for!coarser!physical!models!in!order!to!describe!many!biologically!relevant!properties.!
In!fact,!important!phenomena,!such!as!complex!self-assembly!or!macromolecular!crowding,!
only! start! to! emerge! at! the! mesoscale,! where! systems! are! typically! of! µm! in! length! and!
several!seconds!in!time.!!In!addition,!depending!on!the!scientific!question!asked,!the!level!of!
detail!provided! by!atomistic! simulations!might! not!be! necessary,!and! sometimes!not! even!
desirable!considering!the!computational!burden.!!With!access!to!longer!simulation!time!and!
space!scales!we! can!begin! to!address!more! biologically!relevant! scales,!and!to! have!broad!
overlap!with!experiments!which!is!important!not!only!for!validation!but!also!for!prospective!
use! of! such! simulations.! ! Coarse-grained! (CG)! models! therefore! provide! a! much-needed!
representation! of! biological! and! chemical! systems! that! bridge! the! gap! between! atomistic!
and!continuum!models.!
!
In!most!forms!of!coarse-graining,!groups!of!atoms!are!clustered!into!a!lower!number!of!CG!
beads.! ! There! are! therefore! many! different! levels! of! coarse-graining,! from! models! that!
cluster!only! a! few!atoms! into! one!bead,! to! ones!that! represent! a!whole! protein! with!one!
bead.!!One!challenge!when!developing!a!coarse!grained!model!is!therefore!to!determine!the!
appropriate! mapping! of! atoms! on! the! CG! sites! for! the! problem! to! be! studied;! too! much!
detail! might! result! in! useless! additional! computation! and! thus! limit! accessible!
spatiotemporal!scales,!while!too!little!detail!might!average!out!useful!information!about!the!
properties! of! the! systems! we! are! interested! into.! ! Thus,! Einstein’s! advice! to! “make!
everything! as! simple! as! possible,! but! not! simpler”! applies! here! too.! !The! other! chief!
challenge! in! the! development! of! CG! models! in! general,! is! to! obtain! a! potential! energy!
function!that! is! able! to! approximate! the! atomistic!one.160!! Coarse-graining! is! effectively! a!
dimensionality! reduction! process,! in! which! atomic! interactions! are! renormalized! into! a!
coarser!representation.!!This!process!results!in!a!smoother!free!energy!landscape!where!the!
kinetics!is!typically!accelerated,!yet!as!much!of!the!underlying!physics!as!possible!has!been!
retained.!
!
While!Levitt!and!Warshel!performed!possibly!the!first!CG!simulation!of!protein!folding!over!
forty!years!ago,161!it!is!in!the!last!ten!years!or!so!that!the!CG!field!started!expanding!rapidly!
and!allowing!the!application!of!MD!to!a!number!of!new!biological!problems.!!One!CG!force!
field! that! has! become! popular! is! the! MARTINI! model.162-166! ! This! force! field! is! based! on!
relatively!high-resolution!models! where!typically! four!heavy! atoms!are!mapped! to!one! CG!
particle,!allowing!computational!efficiency!while!retaining!some!chemical!relevance!(see!Fig.)
2).!!The!CG!beads!are!of!four!types!(polar,!non-polar,!apolar,!and!charged),!where!each!type!
can! have! different! hydrogen-bonding! capabilities! (donor,! acceptor,! both,! or! none)! and!
degree! of! polarity! (from! 1! =! low! to! 5! =! high! polarity),! forming! a! total! of! 18! fundamental!
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bead!types.!!The!non-bonded!interaction!for!the!CG!particles!are!based!on!the!standard!12-
6!Lennard-Jones!potential,!with!Coulombic!interaction!too!for!the!charged!bead!type,!where!
parameters! are! derived! empirically! from! experimental! thermodynamic! data! such! as! free!
energies!of!hydration,!vaporization,!and!partitioning!between!water!and!organic!phases.167!!
Such! a! top-down! approach,! where! the! model! is! calibrated! based! on! experimental!
properties,!coupled!with!the!high-resolution!of!the!model,!means!that!MARTINI!manages!to!
be!quite!transferable!between!different!systems.!!Such!transferability!and!the!availability!in!
a! number! of! simulation! packages! (GROMACS,! NAMD,! GROMOS,! Desmond)! have! made!
MARTINI!one!of!the!most!popular!CG!models!for!the!simulation!of!biological!systems.167-179!
!
!
!
!
Fig.! 2.$ Martini$ mapping$ examples$ of$ selected$ molecules.$ (A)$ Standard$ water$ particle$
representing$four$water$molecules.$(B)$Polarizable$water$molecule$with$embedded$charges.$
(C)$DMPC$lipid.$(D)$Polysaccharide$fragment.$(E)$Peptide.$(F)$DNA$fragment.$(G)$Polystyrene$
fragment.$ (H)$ Fullerene$ molecule.$ In$ all$ cases$ Martini$ CG$ beads$ are$ shown$ as$ cyan$
transparent$beads$ overlaying$ the$ atomistic$structure.$$From$Marrink$&$Tieleman,$Chem$Soc$
Rev,$2013,$reproduced$with$permission$from$the$Royal$Society$of$Chemistry.$
!
Voth!and!co-workers!adopted!a!different!philosophy!for!the!development!of!their!multiscale!
coarse-graining!(MS-CG)!methodology.!!!In!this!bottom-up!approach,!forces! from!atomistic!
simulations!are!variationally!mapped!onto!the!CG!potential,!with!no!fitting!to!experimental!
data.160,180-182!!! Since!the! approach!relies! on!a!variational! principle,!it! allows!for! a!rigorous!
derivation!of!CG! force!field!parameters! from!a!corresponding!all-atom!system.! !The!broad!
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applicability!of!the!approach! has!resulted!in! its!use!for!a!number!of!different! applications;!
from!the!study!of!simple!and!complex!liquids183!to!nanoparticles,184!lipid!bilayers,185,186!and!
proteins.187,188!!On!the!other!hand,!being!derived!for!specific!systems!and!conditions,!MS-CG!
potentials!might!not!be!easily!transferred!to!others.!!However,!transferability!is,!in!general,!
inherently!reduced!in!all!coarse-graining!procedures,!due!to!the!simplified!representation!of!
a!system!that!causes!loss!of!information.!
!
Multi-scale!methods!that!integrate!atomistic!and!CG!models!in!a!single!simulation!are!now!
starting!to!appear,!either!in!a!static189!or!adaptive!fashion,190-193!where!the!resolution!of!the!
molecule!depends!on!its!position!in!space.!!Some!of!the!main!challenges!in!this!case!are!the!
parameterisation! of! the! interaction! between! atomistic! and! CG! particles,! and! the!
appropriate!mapping!between!all-atom!and!CG! representations.160,194-196!!!! An! alternative!
approach,!termed!resolution!exchange,!is!based!on!the!replica!exchange!methodology! and!
allows! Monte! Carlo! swaps! between! replicas! at! different! resolutions.197,198! ! While! this!
approach!avoids!the!problem!of!interactions!between!all-atom!and!CG!particles,!the!on-the-
fly! mapping! between! the! two! resolutions! still! needs! to! be! addressed! efficiently.! ! So! far,!
however,!the!most!common!approach!to!mix!CG!and!atomistic!scales!has!been!to!use!CG!for!
enhanced!sampling!and!then!to!convert!certain!configurations!to!an!all-atom!representation
199!that!is!a!reasonable! starting!point! for!additional,! more!detailed,! simulations.194,200-206!A!
few!tools! to! back-map! all-atoms! particles! onto! CG! beads! have! been!developed.! Stansfeld!
and!Sansom199!described!a!fragment-based!protocol!for!the!conversion!of!lipid!and!proteins!
from! CG! to! all-atom! resolution! in! 2011.! Wassenaar! et! al.207! later! proposed! a! general!
approach!based!on!a!geometric!projection!followed!by!force!field-based!relaxation.!!
!
!
3. Novel)simulation)approaches)and)trends)
The! hardware! and! force-field! advances! have! been! complemented! in! recent! years! by! the!
development!and!application!of!new!simulation!approaches,!some!of!which!we!highlight!in!
this!final!section.!!We!also! draw!attention!to!the!types!of! problems!that!these!approaches!
can!begin!to!address!that!were!conceivable!just!ten!years!ago.!
!
3.1 Parallel)and)enhanced)sampling))
With!increasing!availability!of!a!large!number!of!processors!to!the!researcher!through!large-
scale!facilities!or!distributed!computing,!the!question!of!how!to!exploit!most!efficiently!such!
computing!power!arises.!In! fact,!in!recent! years,!while!Moore’s! law!still!applied,!there!has!
been! a! barrier! to! increased! clock! speed! due! to! heat! dissipation! issues! and! vendors! have!
rather!focussed! on! increasing!the! number! of! cores!on! chips.208,209!!This! means!that! larger!
and! larger! systems! can! be! studied,! however! a! point! might! be! reached! where! ‘standard’!
systems!of!up!to!100K!atoms!will!not!benefit!any!more!from!a!larger!number!of!cores!due!to!
limits!in!parallelization.!!In!addition,!since!during!an!MD!simulation!a!large!amount!of!time!is!
spent!sampling! the! low! energy!states,! the! relevant!states!and! transition! the! researcher!is!
interested! in! might! not! be! sampled! within! the! timescales! currently! achievable! with! MD.!!
Therefore,! a! number! of! techniques! that! aim! at! accelerating! the! sampling! of! a! single!
simulation,!or! at! combining! information!from! parallel! independent! simulations! have!been!
pursued.! ! Here! we! review! some! of! these! approaches! that! in! our! opinion! have! made!
significant!progress!in!the! last!decade!and!have! started!being!adopted! by!the!broader!MD!
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community.!!Due!to!the!limitation!in!space!we!are!not! reviewing!comprehensively!all!such!
methods;!we!apologise!in!advance!for!the!inevitable!omissions!in!that!regard.!
!
3.1.1 Markov)state)models)
Perfect!parallelism!that!would!make!an!efficient!use!of!a!large!number!of!processors!could!
be!achieved!by!running!multiple!independent!simulations.!!However,!the!process!of!interest!
might! often! occur! on! timescales! longer! than! the! individual! simulations.! ! Therefore,! the!
challenge!becomes!to!meaningfully!combine!the!data!so!as!to!correctly!extract!information!
about! the! long! timescale! dynamics! of! the! system.! ! For! instance,! while! one! might! run!
efficiently! a! thousand! 1! µs! long! simulations! on! a! supercomputer! with! enough! CPU/GPU!
power,! can! we! extrapolate! information! about! events! happening! in! the! millisecond! time!
scale?!!Another!question!that!follows!immediately!is!how!to!process!the!data!in!such!a!way!
that! the! results! are! easily! interpretable.! ! Discrete! state! kinetic! models,! such! as! Markov!
Models,!are!statistical!approaches!that!have!recently!been!very!successful!at!addressing!the!
above!challenges.210-212!!While!the!theoretical!framework!has!been!available!for!many!years,!
application! to! biological! systems! has! only! really! appeared! in! the! last! 10-15! years.! ! The!
increase!in!popularity!in!Markov!state!models!(MSM)!and!hidden!MSMs!is!in!part!due!to!the!
development! of! freely! available! tools213,214! that! allow! the! user! to! build! such! models! in! a!
relatively! straightforward! manner,! despite! the! complexity! of! the! underlying! statistical!
methods.!
!
The!idea!behind!such!analysis!is!to! cluster!an!ensemble!of!structures!from!MD!simulations!
based!on!kinetic!rather!than!on!geometric!distance,!and!to!derive!transition!rates!between!
all!these!states!from!the!simulation!data.210,213,214!!In!practice,!a!typical!workflow!would!start!
with! the! definition! of! a! set! of! observables! that! will! be! used! for! analysis.! However,! in!
contrast!to!other!techniques!we!will!describe!in!the!next!sections,!this!set!does!not!need!to!
be!system-specific,! so!that!there! is!no!need! to!know!a$ priori!the!reaction! coordinate!that!
best! describe,! for! instance,! the! opening! of! a! channel! or! the! loop! movement! of! a! kinase.!!
These!variables!could!be!the!Cartesian!coordinates!of!a!group!of!atoms,!certain!angles!and!
torsions,!as!well! as!the! distance!between!all! Cα!atoms,! or!contacts!between! any!residues.
213!!!
!
Since!a! large!number! of!variables! can!be!selected! in!such! a!way,! some!of! which! might!be!
redundant,! potentially! resulting! in! an! inefficient! discretization! of! the! high-dimensional!
space,! a! dimensionality! reduction! is! generally! performed! first.! ! The! time-lagged!
independent!component!analysis!(TICA)!has!become!the!standard!dimensionality!reduction!
technique!employed!for!the!constructing!of!MSM.!!This!is!because!as!opposed!to! methods!
using! orthogonal! transformations! such! as! PCA,! which! maximise! the! variance! of! the!
transformed! coordinates,! TICA! maximises! their! autocorrelation,! i.e.! it! finds! the! slowest-
relaxing!degrees!of!freedom.215-218!!This!is!important!because!we!are!interested!in!studying!
the!kinetics!of!the!system,!identifying,!for!example,!metastable!states!and!rare!transitions,!
rather!than!finding!the!most!similar/different!conformations.!!The!transformed!input!is!then!
discretised! into! a! number! of! microstates! using! clustering! methods! such! as! k-means,! and!
conditional!probabilities! of! transitioning!between! these!microstates! within! a!certain! time-
lag! are! estimated! from! the! MD! data.213,219,220! ! Such! probabilities! are! the! basis! for! the!
estimation!of!the!MSM!(or!the!hidden!MSM).!!Using!the!MSM!model!one!can!then!estimate!
equilibrium!expectations!of!an!observable,!free!energy!surfaces!(FES),!relaxation!time!scales!
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that! can! be! compared! to! experiment,! or! metastable! states.! ! In! addition,! using! transition!
path!theory!one!can!compute!fluxes!between!sets!of!states!and!recover!the!mechanism!and!
kinetics! of! going! from! state! A! to! state! B.221-223! ! Since! thousands! of! states! are! hard! to!
visualise!and!hardly!comprehensible,!kinetically!related!microstates!can!be!clustered!into!a!
few! relevant! macrostates! in! order! to! have! a! coarser,! more! interpretable,! view! of! the!
configurational!space!and!its!kinetics.224!
!
MSMs!have!rapidly!become!widespread!and!their!application!to!diverse!biological!problems!
has!been!demonstrated!in!a!number!of!noteworthy!studies.!!Voelz!et$al.225!employed!MSM!
to! study! the! folding! pathway! of! the! millisecond! folder! NTL9(1-39).! ! The! authors! used!
adaptive!resampling!techniques!in!order!to!improve!the!sampling!of!metastable!basins!and!
transitions! between! them.! ! The! simulations,! revealing! a! network! of! possible! paths! with!
different!likelihoods,!identified!numerous!folding!pathways!(see!Fig.)3).!!!
!
Kohlhoff!et!al. 26!used!Google! servers!in!order!to!run! a!large!number!of!simulations! of!the!
active!and!inactive!structures!of!the!β2-adrenergic!receptor!for!a!total!of!2.15!ms!of!MD,!and!
then!used!MSM!in!order!to!combine!all!the!trajectories!and!study!the!activation!mechanism!
of! the! GPCR.! ! Again,! many! parallel! pathways! rather! than! a! single! dominant! one! were!
observed.!!In! addition,!it! was!shown! how!ligands! modulate!the! activity!of! the!receptor! by!
affecting!its!probability!of!accessing!the!active!state.!!Finally,!different!receptor!states!along!
the! activation! pathways! were! used! for! docking,! resulting! in! the! enrichment! of! different!
chemotypes! for! different! receptor! conformations,! showing! how! the! use! of! intermediate!
states!might!be!beneficial!for!hit!discovery.!!!
!
Shukla! et$ al.226! used! MSMs,! transition! pathways,! and! adaptive! sampling! techniques! on!
distributed!computing!in!order!to!study!the!activation!pathways!of!Src!kinase.!In!such!a!way!
they!provided!a!thermodynamic!and!kinetic!description!of!the!activation!mechanism!of!the!
kinase!at!atomistic!detail.!In!addition,!novel!intermediates!states!that!could!be!targeted!by!
allosteric!inhibitors!have!been!identified.!!Plattner!and!Noé227!have!instead!employed!MSMs!
to! study! the! binding! mechanism! of! benzamidine! to! trypsin,! and! in! particular! the! role! of!
protein! conformational! plasticity! in! ligand! binding.! Six! different! slowly-interconverting! (of!
the! order! of! tens! of! microseconds)! apo-state! conformations! have! been! found,! with! one!
additional!conformation!that! was!accessible!only! to!the! bound!state.!! The!binding!kinetics!
observed! exhibited! both! conformational! selection! and! induced! fit! features.! ! The! study!
showed!how!conformation!and!binding!kinetics!are!closely!coupled,!and!how!various!trypsin!
conformations!can!be!accessed!and!stabilized!both!by!ligand!binding!or!protein!mutations.!
!
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!
Fig.!3.$$$Schematic$representation$of$an$MSM.$$A$2000-state$Markov$State$Model$(MSM)$was$
built$ using$ a$ lag$ time$ of$ 12$ ns.$ $ Shown$ is$ the$ superposition$ of$ the$ top$ 10$ folding$ fluxes,$
calculated$by$a$greedy$backtracking$algorithm.$ $ $ These$pathways$account$for$only$
25%$of$
the$total$flux$and$transit$only$14$of$the$2000$macrostates$(shown$labeled$a−n,$for$convenient$
discussion).$The$visual$size$of$each$ state$ is$ proportional$ to$ its$ free$ energy,$ and$ arrow$ size$is$
proportional$ to$ the$ interstate$ flux.$ $ Reprinted$ with$ permission$ from$ “Unfolded-state$
dynamics$and$structure$of$protein$L$characterized$by$simulation$and$experiment”.$$Voelz$VA,$
Singh$ VR,$ Wedemeyer$ WJ,$ Lapidus$ LJ,$ Pande$ VS.$ J$ Am$ Chem$ Soc.$2010$$ 132:4702-9.$
Copyright$2010$American$Chemical$Society.$
$
$
Overall,!the!use!of!MSM!results!in!a!number!of!benefits!for!molecular!simulations.!!First!of!
all,!as!mentioned!previously,!the!approach!provides!a!means!to!perfect!parallelization,!and!
also!takes!advantage!of!the!direction!of!recent!hardware!trends!towards!higher!number!of!
cores! on! chips! rather! than! increased! speeds! of! single! processors.! ! Moreover,! adaptive!
sampling!coupled!with!MSM!should!provide!more!effective!sampling!of!rare!events.!!In!fact,!
many!biological! systems! are! characterized! by! rugged! energy!landscapes!that! result! in! the!
presence!of!several!metastable!states!separated!by!high-energy!barriers.!!As!a!consequence,!
most!of!the!time!during!a! conventional!MD!simulation!is!spent! sampling!a!few!low!energy!
states! due! to! kinetic! bottlenecks,! and! the! exploration! of! transition! events! or! other!
metastable!states!is!limited.!!Adaptive!sampling!would!allow!one!to!focus!the!computational!
effort! into! phase! space! areas! that! have! not! been! extensively! sampled! yet! by! the!
simulations.!!In!addition,!it!provides!a!framework!for!the!study!of!the!kinetics!of!molecular!
events!such!as!drug!binding!and!protein!conformational!change.!!Last!but! not!least,!MSMs!
allow! a! human-readable! interpretation! of! large! amounts! of! data! thanks! to! the! kinetic!
clustering!and!coarse-graining!procedures.!
!
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3.1.2)Replica)exchange)methods)
Replica! exchange! molecular! dynamics! (REMD)! methods! enhance! sampling! by! running!
multiple!simulations! of!the! same!system! in!parallel! at!different!thermodynamic! states.!! In!
the! first! use! of! the! method,! Swendsen! and! Wang! used! multiple! Monte! Carlo! replicas! at!
different! temperatures! to! speed-up! sampling.228! ! Sugita! and! Okamoto! later! proposed! a!
similar! framework! for! MD.229! ! This! is! often! called! “parallel! tempering”! or! “temperature!
replica!exchange”!(T-REMD),!and!the!idea!is!to!run!simulations!at!higher!temperatures!than!
the! one! of! interest! in! order! to! explore! larger! volumes! of! phase! space! thanks! to! the!
Arrhenius!law. 230-232!!
!
A!set!of!simulations!with!increasing!temperatures!T0!<!T1!<!T2!<!TM!is!prepared,!where!T0!is!
the!thermodynamic!state!we! are!interested!in.! !All!the!simulations!are!run!in! parallel,!and!
the!system!configurations!(i.e.!the!positions!of!the! particles)!are!allowed!to!swap!between!
replicas!according!to!a!Metropolis!criterion!that!depends!on!the!potential!energy!difference!
between!replicas.!!The!exchange!probability!between!replicas!i!and!j!is$p(i$->$j)$=$min(1,$eΔij),!
where! for! parallel! tempering! Δij! =! [(βi$ –$ βj)(U(ri)$ –$ U(rj))],! with! β!being! 1/kT,! and! U! the!
potential! energy! of! the! configuration! r.232,233! ! In! such! a! way,! energetic! barriers! are! more!
easily!overcome!thanks!to!the!larger!kinetic!energy!at!higher!temperatures,!while!providing!
a! correct! ensemble! of! conformations! at! T0.! ! The! acceptance! criterion! implies! that! swaps!
between! replicas! occur! frequently! only! if! the! energetic! overlap! between! replicas! is!
sufficient,! which! affects! the! number! and! temperatures! of! replicas! needed! for! a! specific!
system.232!!Typically,!swaps! are!allowed!only! between!neighbouring!replicas! (e.g.!between!
T0! and! T1,! or! T1! and! T2),! however,! it! is! possible! to! swap! configurations! across! all! replicas!
leading!to!improved!mixing!between!states.234!!More!generally,!replica!exchange!belongs!to!
the! group! of! techniques! referred! to! as! generalized$ ensembles,! among! which! are! also!
expanded$ensemble!methods,!a!serial!equivalent!of!replica!exchange.235-237!
!
It!soon!became!clear!that!temperature!is!not!the!only!alteration!between!replicas!that!can!
be!used,! and! several! variants! of! the! original! T-REMD! have! been!implemented! and! widely!
used!in!the!last!decade.!!Hamiltonian!replica!exchange!(H-REMD)!is!a!more!general!form!of!
REMD! where! it! is! possible! to! enhance! sampling! by! using! parameters! other! than!
temperature. 238-241!!Interaction! energies!can!be! scaled!between!replicas! for!example,! and!
as!such!H-REMD!can!be!used!for!free!energy!perturbation!calculations,!where!two!systems!
(e.g.!two!protein! mutants,! or! the! apo! and! holo! forms! of! a! protein)! are! interpolated! by! a!
coupling!parameter!λ,!and!the!replicas!correspond!to!the!two! end!states!plus!a!number!of!
intermediate!ones.242-245!!Replica!exchange!with!solute!tempering!(REST)!was!developed!to!
remove! the! dependence! of! the! acceptance! probability! on! the! number! of! waters! in! the!
system,! so! that! fewer! replicas! are! needed! to! explore! a! certain! temperature! range.246! ! In!
addition,!different!flavours!of!multidimensional!REMD!where!replicas!are!swapped!in!more!
than!one!dimension!have!been!developed,!and!have!been!successfully!applied,!for!instance,!
in!free!energy!calculations.247-249!!
!
Thanks!to!its!robust!implementation!in!mainstream!MD!packages,239,250-252!!replica-exchange!
has!become!a!standard!technique!to!accelerate!sampling!and!aid!convergence.!!It!has!found!
many! applications! for! the! study! of! protein! dynamics! and! folding,253-263!free! energy!
calculations,242,264-268! as! well! as! ligand! binding! site! and! pose! identification,269,270! and!
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constant! pH! simulations. 271-275! ! The! computational! cost! of! replica! exchange! grows!
proportionally! with! the! number! of! replicas,! however,! it! has! become! accepted! that! the!
sampling!obtained!is!more!efficient!than!can!be!obtained!from!a!single!(long)!simulation.!!In!
addition,! the! computational! overhead! due! to! the! swaps! and! the! Monte! Carlo! move! is!
negligible,!considering!that!the!potential!energies!of!the!systems!are!evaluated!anyway!for!
the! calculation! of! the! forces.! ! These! facts! have! contributed! in! making! replica! exchange!
methods!a!standard!instrument!in!the!modeller’s!current!toolbox.!
!
3.1.3)Bias)potential)methods:)metadynamics)
Bias!potential!methods!facilitate!the! exploration!of! the!free-energy! surface!by! introducing!
additional! potential! energy! terms! that! encourage! the! system! to! move! out! of! free! energy!
minima.233!!!Typically,!such! methods! act!on!a! small! number!of! degrees! of! freedom,!often!
called! collective$ variables!(CVs).! ! Many! methods! that! fall! in! this! category! have! been!
developed,! including! umbrella! sampling,276! local! elevation,277! adaptive! force! bias,278!
accelerated! molecular! dynamics,279,280! conformational! flooding,281,282! and! steered! MD.283!!
Here,! however,! we! will! focus! only! on! metadynamics,284-287! one! of! the! most! popular! bias!
potential! approaches,! thanks! in! part! to! its! availability! across! multiple! MD! packages!
(Amber,288!Gromacs,251!NAMD,252!LAMMPS289)!through!the!PLUMED!code.290,291!
!
Metadynamics!allows!accelerated!exploration!of!phase!space!and!reconstruction!of!the!free!
energy! surface! (FES)! along! selected! CVs! by! adding! a! history-dependent! bias! potential.284-
287,292!Such!bias!is!a!function!of!the!chosen!CVs.!!Therefore,!the!choice!of!CVs!is!an!important!
step! in! the! setup! of! the! simulations! and! has! important! consequences! on! the! ability! to!
enhance!sampling!and!the!convergence!of!the!free!energy!estimates.!!A!CV!is!a!function!of!
the! microscopic! coordinates! of! the! system,! and! a! wide! choice! of! CVs! is! available! to! the!
researcher.! ! Typical! CVs! are! distances,! angles,! or! dihedrals,! as! well! as! the! number! of!
hydrogen!bonds,! radius! of! gyration,!or! dipole! moments.290,291! !The! CVs! that! best!describe!
the! reaction! coordinate! of! interest! should! be! chosen! for! the! bias! potential! to! be! added.!!
Broadly! speaking,! CVs! should! allow! one! to! distinguish! between! the! initial! and! final! state,!
describe! all! relevant! intermediates,! and! include! all! the! slow! modes! of! the! system.!!
Moreover,! it! is! suggested! that! the! number! of! CVs!is! kept! as! low! as! possible! (usually! not!
more!than!three),!since!higher!dimensionality!comes!with!considerable!computational!cost,!
in! addition! to! the! fact! that! the! interpretation! of! high-dimensional! surfaces! can! become!
difficult.284-287!!The!a$ priori! choice! of! CVs! is! far! from! trivial.! ! Often,! machine! learning! or!
dimensionality! reduction! are! performed! on! preliminary! MD! runs,! in! order! to! identify! the!
most! relevant! degrees! of! freedom! for! the! process! of! interest.293-298! ! Knowledge! of! the!
physical!and!chemical!behaviour!of!the!system!can!go!a!long!way!in!the!identification!of!the!
most!suitable!CVs!for!the!problem!at!hand.!
!
Once!a!set!of!CVs!is!determined,!the!metadynamics!simulation!biases!the!potential!energy!
function! along! the! chosen! CVs! so! that! configurations! that! have! been! visited! already! are!
discouraged.!!The!bias!potential!that!is!added!to!the!force!field!based!potential!energy!can!
be! described! by! a! sum! of! Gaussians.284-287,292! ! Fig.! 4,! adapted! from! the! original!
metadynamics!paper,287!exemplifies!the!basic!idea!behind!the!approach.!!In!this!example!a!
one!dimensional!potential!energy!surface!(PES)!with!three!minima!is!considered.!!The!thick!
black! line! represents! the! shape! of! the! potential! surface! along! a! general! CV,! which! is!
unknown,! and! the! simulation! is! in! fact! used! to! explore! it.! ! However,! if! we! start! a!
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conventional!MD!simulation!from!basin!B,!the!system!would!remain!stuck!in!this!minimum!if!
the! barriers! are! larger! than! thermal! fluctuations.! On! the! other! hand,! adding! the! bias!
potential!during!the!course!of!the! simulation!we!modify!the!shape! of!the!potential!energy!
surface.!!At!step!=!10,!the!depth!of!the!basin!is!reduced,!but!a!minimum!is!still!present;!at!
step!=!20!the!energy!minimum!is!filled!by!the!bias!potential!and!the!system!can!fall!into!the!
local! minimum! A;! at! step! =! 40! the! bias! potential! now! starts! filling! basin! A;! continuing! to!
deposit!Gaussian-shaped!potentials!along!the!CV,!the!point!where!the!global!minimum!C!is!
explored!is!reached!at!step!=!160;!eventually,!the!potential!energy!surface!becomes!flat!and!
the!system!evolution!resembles!a!random!walk!after!step!=!320.!Once!a!flat!PES!is!obtained,!
the! bias! potential! can! be! used! to! recover! the! negative! image! of! the! underlying! free!
energy.287,292,299!!!Since!in! a! single! run!the!bias! potential! tends! to! oscillate!around! (rather!
than!converge!to)!the!free!energy,!the!well-tempered!variant!of!metadynamics!method,!in!
which! the! bias! deposition! rate! decreases! over! time,! has! been! developed! to! address! the!
issue.300,301!
!
!
Fig.! 4.!!Time$ evolution$ of$ the$ sum$ of$ a$ one-dimensional$ model$ potential$V(σ)$ and$
accumulating$Gaussian$terms.$$The$dynamic$evolution$(thin$lines)$is$labeled$by$the$number$of$
dynamical$iterations.$$The$starting$potential$(thick$ line)$has$three$minima$and$the$dynamics$
is$ initiated$ in$ the$ second$ minimum.$ $ $ Adapted$ from$ “Escaping$free-energy$minima”$ Laio$ A$
and$Parrinello$M.$(2002)$$Proc$Natl$Acad$Sci$USA.$99:12562-6.!!
!
!
As!compared!to!replica!exchange!approaches,! metadynamics!allows!us!to!overcome!larger!
energy!barriers.!On!the!other!hand,!it!acts!only!on!a!few!selected!CVs,!which,!if!inadequate,!
might! provide! non-converged! or! misleading! estimates! of! the! energy! barriers! between!
"
#
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minima.285,301! ! The! two! methods! are! therefore! complementary! and! can! in! fact! be!
combined.302! ! In! such! a! way,! while! parallel! tempering! allows! us! to! cross! moderate! free!
energy!barriers!on!all!degrees!of!freedom,!metadynamics! allows!us!to!cross!larger!barriers!
on! the! specified! CVs.303,304! ! Alternatively,! replica! exchange! can! be! used! in! order! to! bias!
different!sets!of!CVs!in!a!number!of!parallel!simulations!while!allowing!exchanges!between!
them,!in!a!paradigm!called!bias$ exchange.!!A!reweighting!procedure!that!is!specific!to!bias!
exchange!can!be!used!in!order!to!recover!the!free!energy!surface!as!a!function!of!part!of!the!
set!of!CVs.305,306!
!
Metadynamics!has!been!used!quite!extensively!in!biomolecular!dynamics!and!protein-ligand!
association.303,307-321!!As! an! example! applied! to! drug! discovery,! Limongelli! et$ al.318! have!
studied!the!full!dissociation!process! of!SC-558,!a!highly!selective!cyclooxygenase-2! (COX-2)!
inhibitor,!through!the!use!of!metadynamics!calculations!based!on!a!distance!and!a!torsional!
angle!as!the! two!collective! variables.!!They! discovered!an! alternative!binding! mode!to!the!
one!observed! experimentally,! and!suggested! this! as!the! reason! behind!the!selectivity! and!
the! long! residence! time! of! the! inhibitor! for! this! isoform.! ! In! fact,! when! simulating! the!
dissociation!of! SC-558!from!COX-1,! only! one! energy!minimum,! i.e.! a! single!binding!mode,!
was! observed! in! the! protein! binding! site.!!This! binding! mode! was! very! close! to! the!
crystallographically!observed!pose!in!COX-2!for!the!same!inhibitor.!!On!the!other!hand,!the!
simulations!with!COX-2!revealed!a!second!energy!minimum!in!the!binding!site,!in!which!the!
ligand!also!engages!in!additional!hydrophobic!contacts!with!the!protein.!Lanzo!et!al.322!had!
previously! shown! with! fluorescence! quenching! experiments! that! an! analogue! of! SC-558!
would!bind!to!COX-1!in!a!two-step!process,!but!an!additional!unidentified!step!was!required!
to! bind! to! COX-2.! The! authors! also! reported! slower! dissociation! kinetics! from!COX-2! as!
compared!to! COX-1! (several! hours! versus! one! minute).! Limongelli!et! al.318! suggested! that!
the!alternative!binding!pose!observed!in!their!simulation!is!what!causes!the!detection!of!an!
additional!binding!step!in!the!fluorescence!experiments.!
!
Grazioso!et$al.316!used! a!similar!method! to!study!glutamate! uptake!from!the!synaptic! cleft!
and!its!release!into!the!intracellular!medium.!The!authors!managed!to!describe!the!opening!
mechanism,! which! involved! a! large-scale! hairpin! motion,! and! the! associated! free! energy!
profile.! ! Herbert! et$ al.315! ! reported! the! discovery! of! the! first! extracellular! inhibitor! of! the!
fibroblast!growth!factor!receptor!(FGFR),!a!tyrosine!kinase!receptor!involved!in!cell!growth,!
proliferation,!and!survival.!!In!this!study,!bias!exchange!metadynamics!was!used!in!order!to!
study!the!ligand’s!mode!of!action.!!Experimental!methods!had!hitherto!been!unsuccessful!in!
identifying!the!inhibitor’s!binding!site.!!The!simulations!correctly!predicted!the!dissociation!
constant!of!the!inhibitor,!as! well! as! for! other! lower! potency! analogues,! validating! the! in-
silico!analysis.!
!
3.2 Simulation)of)large)systems)
As!we!enter!an!era!of!exascale!computing!with!highly!optimised!MD!codes,!larger!and!larger!
systems!are!starting!to!be!studied!through!simulation,!both!in!all-atom!and!coarse-grained!
detail.! ! Accessing! greater! spatial! scales! is! important! in! order! to! probe! the! function! of!
biological!machineries,!which!often!operate!on!scales!spanning!hundreds!of!nanometers!to!
micrometres.3! Simulations! of! viruses,323! the! ribosome,324! large! membranes,325! and! small!
organelles326!contain!millions!of!atoms!and!require!highly!scalable!software. 3!!Such!systems!
present! both! opportunities! and! challenges! for! high-performing! computing! and! molecular!
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modelling,!and!hold!the! promise!to!contribute!to! a!deeper!level!of! understanding!of!living!
organisms!and!their! behaviour!at! the!mesoscale.!This,! in!turn,! would!enable! the!design!of!
new! therapeutics! based! on! small! molecules! and! engineered! biologics! with! the! aid! of!
computation.!
!
Due!to!the!large! size!of!viruses! for!MD!simulations,! most!initial!studies! on!viruses!focused!
on!isolated!proteins!or!fragments!of!the!viral!capsid.327!!However,!in!2006,!Freddolino!et!al.
328!simulated!for!the!first!time!a!complete!virion!(capsid!and!genetic!material)!atomistically,!
despite! some! approximations! in! the! RNA! genome! structure.! ! The! authors! simulated! the!
entire!virion!and!both! the!capsid!and! RNA!core!alone! of!the!satellite!tobacco! mosaic!virus!
(STMV)!for!a!total! of!50!ns!of! MD.!!The!systems!contained!about!1! million!atoms,!and!the!
simulations!demonstrated!the!stability!of!the!virion!and!RNA!core,!while!showing!instability!
for!the!capsid!without!RNA.!!Since!then,!other!large!and!complex!viral!components!of,!for!
instance,! Poliovirus, 329!Dengue,330! influenza, 331! and! HIV-1, 201,332! have! been! studied! by!
means! of! simulation.!!Reddy! et$ al.331! reported! the! microsecond-long! CG! (Martini)!
simulations!of!an!influenza!A!virion.!!The!authors!showed!how!the!presence!of!the!Forssman!
glycolipid!altered!the!mobility!of!bilayer!species,!and!suggested!that!the!viral!spike!proteins!
do!not! aggregate! and!are! thus! competent! for!IgG! antibody! binding.!! In! other! studies,!the!
spontaneous!assembly!of!the!viral!capsid,!a!fundamental!step!in!the!replication!cycle!of!the!
virus,!has!been!studied!by!simulation!at!different!levels!of!coarse!graining.329,333-336!
!
Through!Brownian!dynamics,!it!was!shown!how!the!optimal!configuration!of!viral!genome!is!
essential! for! the! correct! assembly! of! the! capsid.333,334!!Recently,! electron! microscopy! has!
been!integrated!with!molecular!dynamics!flexible!fitting!(MDFF)337!in!order!to!elucidate!the!
structure!of!complex!viral!capsids!in!atomic!detail!and!in!their!native!environments.!!Zhao!et$
al.332!obtained!an!8!! cryo-EM!structure!of!the!mature!HIV-1!native!capsid,!a!polymorphic!
capsid!with!no! apparent!symmetry;!they! then!docked! atomic!NMR!and! x-ray!structures!of!
capsid! proteins! into! the! density! map,! modelled! the! linker! and! missing! loops,! and! finally!
refined! the! model! by! MDFF! to! obtain! an! atomistic! representation! of! the! virus.! ! The! final!
model! contained! 64! million! atoms! and! was! simulated! in! explicit! solvent! for! 100! ns,! and!
demonstrated! the! importance! of! the! placement! of! capsid! protein! pentamers! in! the!
structure.! ! Other! multi-million! simulations! of! viral! structures,! such! as! in! the! case! of! the!
Rabbit! hemorrhagic! disease! virus! (RHDV),338! have! been! successfully! employed! in! the!
refinement!of!crystal!structures!fitting!into!cryo-EM!densities.339,340!!
!
The!ribosome!is!an!obvious!antibacterial!target,!and!in!the!last!decade!an!increasing!amount!
of! experimental! data! has! become! available.! Consequently,! a! number! of! researchers! have!
started!simulating!the!ribosome!with!MD,!trying!to!bridge!the!gap!between!its!structure!and!
dynamics.324! ! Similarly! to! viruses,! the! first! ribosome! simulations! focussed! on! selected!
regions!due!to!the!computational!expense!of!million-atom!simulations.341,342!However,!with!
increasing!computing!power!available,!simulations!of!the!entire!ribosome!became!viable.343!
Recently,!Bock!et$al.344!performed!MD!simulations!of!13!intermediate!translocation!states!of!
an! entire! bacterial! ribosome.! ! Such! systems! comprised! ~2.2! million! atoms! and! were!
simulated! for! a! total! of! more! than! 1.8! µs,! revealing! a! description! of! the! time-resolved!
translocation!in!atomic!detail.!!Kinetic!information!was!extracted!from!the!simulations!and!it!
was! found! that! tRNA! motions! govern! the! transition! rates! within! the! pre-! and! post-
translocation!states.! ! On! the!other! hand,! faster! sub-microsecond!rates! were! observed! for!
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inter-subunit!rotations!and!L1-stalk!motion.!!Overall,!the!results!added!the!time!dimension!
to!the!structural!data!available,!providing!information!on!transition!rates,!molecular!forces,!
and!correlated!functional!motions!that!could!have!not!been!obtained!otherwise.!!
!
Whitford! et$ al.345! also! carried! out! microsecond! MD! simulations! of! a! complete! ribosome,!
identifying! reaction! coordinates! for! the! subunit! rotation! that! were! used! to! estimate! free!
energy!barriers!associated!with!the!translocation.!!Given!its!role!as!a!pharmaceutical!target,!
a! number! of! MD! simulations! of! the! ribosome! in! the! presence! of! antibiotics! have! been!
performed!in!order!to!elucidate!the!mode!of!action!of!small!molecules.346-350!!For!instance,!
Sothiselvam!et$al.346!used!both!biochemical!methods!and!molecular!dynamics!to!show!how!
erythromycin,!a!macrolide!antibiotic,!allosterically!predisposes!the!ribosome!to!translational!
arrest,!without!necessarily!forming!extensive! contacts!with!the!nascent! peptide!in!the!exit!
tunnel!as!previously!suggested.!!MD,!in!particular,!hypothesised!the!base!flipping!of!specific!
nucleotides!in!the!catalytic!centre,!which!were!later!confirmed!by!cryo-EM!data.346,351!!With!
the! increasing! availability! of! ribosome! structures,! including! human! ribosomes,352-354! ! and!
computer! power,! molecular! simulations! have! the! opportunity! to! significantly! contribute!
towards!the! understanding! of!drug! action! on!the! ribosome! and! to!the! next! generation!of!
much!needed!antibiotics.355-357!
!
Large!membrane!bilayers!have!been!simulated!at!increasing!degrees!of!chemical!detail!and!
complexity,! trying! to! include! as! many! lipid! species! as! possible! in! order! to! reproduce!
compositions! found! in! living! cells.3,170,325,358-360!!Marrink! and! co-workers! used! the! Martini!
coarse-grained! model! to! simulate! a! large! plasma! membrane! containing! 63! different! lipid!
species.325! ! The! 71x71! nm! patch! included! about! 20,000! lipids,! which! with! water! and! ion!
beads! totalled! almost! half! a! million! particles,! and! was! simulated! for! 40! µs.! ! The! study!
provided! a! high-resolution! view! of! the! cell! membrane! and! showed! an! asymmetrical!
distribution! of! cholesterol! with! enrichment! in! the! outer! leaflet.! ! Moreover,! transient!
domains! with! liquid-ordered! character! were! observed! to! appear! and! disappear! in! the!
microsecond!time-scale.325! Similarly,!Koldsø! and!Sansom170! simulated!a!complex! and!large!
(>100! nm)! plasma! membrane! also! using! CG! MD,! where! they! introduced! two! types! of!
crowded!membrane!proteins!in!order!to!study!the!interplay!between!lipids!and!proteins!in!
determining!mesoscale!fluctuations! of!the! bilayer!and! clustering!of!receptors.! !Closing! the!
gap! between! experiments! and! simulations! in! terms! of! membrane! complexity! and! spatial!
scales,!the!study!showed!good!agreement!with!the!dynamical!behaviour!of!lipids!observed!
in!living!cells.361,362!
!
!
4. Conclusion)
In!this! chapter! we! have!tried! to! summarize! the!main! advances! in! molecular!simulation! in!
the!past!decade!or!so.!!Progress!in!both!hardware!and!algorithm!design!have!construed!to!
make! it! possible! to! explore! length! and! timescales! that! are! now! within! the! regimen! of!
several!experimental!techniques.!!During!the!next!decade!we!can!expect!this!overlap!to!be!
extended.! ! The! resulting! integration! between! experiment! and! simulation! will! become! a!
powerful!way!to!understand!many!underlying!biophysical!principles!as!well!as!improve!our!
prospects!for!the!design!of!new!therapeutic!approaches.!
!
!
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... Slater described the usefulness of this idea into long range aids to navigation [20] . Also, this concept has some applications in chemistry for representing chemical compounds [14,15] and in problems of pattern recognition and image processing, some of which involve the use of hierarchical data structures [18] . Other applications of this concept to navigation of robots in networks and other areas appear in [4, 10,16]. ...
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