conventional molecular dynamics allows 
 one to access time scales 
 on the order of tens to hundreds of nanoseconds ; however , many biological 
 processes of interest occur on longer time scales of up to milliseconds 
 or more .
efforts to explore these long time scales have led to the development 
 of several advanced sampling techniques such as conformational flooding , hyperdynamics , metadynamics , and the adaptive 
 biasing force method . inspired by voter , accelerated molecular dynamics 
 ( amd ) is an additional enhanced conformational sampling method that 
 provides access to events beyond those obtainable with conventional 
 molecular dynamics ( cmd ) . here , we emphasize 
 one of the great advantages of amd , which is that no prior knowledge 
 of the potential energy landscape needs to be known and , consequently , 
 no reaction coordinate needs to be defined prior to running the simulation .
in addition to advances in algorithms to achieve dynamics on longer 
 time scales , recent efforts by d. e. shaw research have focused on 
 building a specialized computer , anton , with the sole purpose of simulating 
 protein dynamics . with this great engineering 
 achievement ,
simulation time scales have been pushed into the range 
 of hundreds of microseconds to milliseconds using unbiased brute force 
 cmd .
while time on an anton machine has been 
 generously granted to the scientific community , access is still limited , 
 and many researchers are stuck waiting in queues on crowded super 
 computers or local clusters . recently , the advancement of computational 
 science on conventional graphic processing units ( gpu ) has allowed 
 researchers efficient and inexpensive access to microseconds of simulation 
 time on just a single desktop computer . by combining the advanced sampling method 
 of amd and the inherent power of the gpu
, we present the synthesis 
 of a tool that allows researchers access to inexpensive efficient 
 exploration of long time scale events . here , we point out that a time 
 scale can not be directly determined from an amd simulation , but we 
 can correlate events which occur on long time scales from either experimental 
 results or long conventional molecular dynamics simulations
. however , 
 future work using the conformational space explored by amd as a seed 
 for other methods , namely , markov models , would allow one access to time dependent properties , such as nmr 
 relaxation data , which was shown can be computed directly from the 
 anton millisecond trajectory . in 
 its original form
, the amd method modifies the potential energy 
 landscape by raising energy minima that lie below a defined threshold 
 level , while leaving those areas lying above the threshold unmodified . 
 as a result ,
barriers separating adjacent energy basins are effectively 
 reduced , providing the simulation access to conformational space that 
 can not be easily accessed in a cmd simulation .
historically , amd was 
 first implemented by hamelberg et al . within the framework of the 
 sander module in the amber 7 package and used to study several small 
 peptide and protein systems . since the original 
 implementation
, there have been several notable variations of the 
 amd method , but no official implementation has been released . 
 however , wang et al .
recently ported the amd method to namd , and following this approach , we have ported 
 amd to the three main md engines included in amber 12 : the cpu versions sander and pmemd and the gpu version pmemd.cuda . 

the performance enhancements for cmd on gpus obtained with pmemd.cuda 
 alone are remarkable and can be found on the amber web site ( ambermd.org ) 
 and in the following publications . for this work
, 
 we have used our implementation of amd in the pmemd.cuda md engine 
 and will refer to it simply as amd .
bovine pancreatic trypsin 
 inhibitor ( bpti ) is a small protein with 
 58 residues that has been extensively studied experimentally , being 
 the first subject of nmr experiments to characterize individual hydration 
 water molecules in proteins , and also 
 the first protein to be simulated with molecular dynamics .
d. e. shaw research reported in 2010 a remarkable 
 1.03 ms md simulation of bpti in explicit water . using our amd implementation in pmemd.cuda
, we have performed 
 a 500 ns amd simulation of bpti in explicit water , maintaining the 
 same conditions as the simulation on anton . in order to mimic the 
 force field used in the anton simulation
, we modified the ff99sb - ildn 
 force field removing the modifications to leucine , aspartic acid , 
 and asparagine , which we refer to as ff99sb - i . using the 1.03 
 ms simulation of bpti provided by d. e. shaw research 
 throughout our analysis
additionally , we performed a 500 ns 
 cmd simulation to use as a measure of the amount of sampling attainable 
 by conventional md with the same computational effort . to the best 
 of our knowledge ,
our amd implementation is the first to support gpu 
 acceleration , and the work presented here represents the longest single 
 amd simulation of a biomolecule run to date .
both amber simulations 
 were completed in two weeks on individual desktop computers containing 
 single $ 500 gtx580 gpus .
in the millisecond anton simulation , 
 five long - lived structural states were identified that persisted for 
 626 s with deviations of up to 3.5  from the 
 crystal structure , 5pti . using these same five 
 structures and the crystal structure as references , we calculated 
 rmsd values ( heavy backbone atoms ) along our 500 ns amd simulation , 
 shown in figure 1 .
we color each point according 
 to which of the five structures it is closest to in terms of rmsd , 
 allowing one to see the transitions from the different structural 
 states .
rmsd results show we sample structures from all five states 
 but spend the majority of the time near the blue state and the least 
 amount of time close to the green state .
the rmsd with respect to 
 the x - ray structure shows that the protein moves away from the crystal 
 structure 49 ns into the simulation and achieves a maximum rmsd of 
 2.7  before coming back to within 0.89  , emphasizing that 
 the system is sampling states both far from and near to the crystal 
 structure , as was seen in the long 1 ms cmd simulation .
the largest 
 deviation from the crystal structure is 3.29  , which occurs 
 at 195 ns .
red , blue , 
 green , purple , and black colors correspond to the kinetic clusters 
 identified in the 1 ms cmd bpti simulation . for each frame
only a handful of transitions to the green state were 
 observed , and we highlight them with diamond markers . to characterize the conformational states explored 
 in more detail , 

figure 2a displays the two - dimensional representation of the structural 
 data set as a projection of the boltzmann reweighted distribution 
 onto the subspace defined by the first and second principal component 
 vectors ( pc1 and pc2 ) built from the c- atoms spanning residues 
 4 to 54 . in this analysis , pc1 and pc2 describe 35% and 21% , respectively , 
 of the total variance of the motions in the simulation ( movies s1 and s2 ) .
the five long - lived structures 
 and the crystal structure were then projected into this space .
the 
 500 ns cmd control simulation and the 500 ns amd simulation were also 
 projected into the subspace defined by the 1 ms simulation ( figure 2b , c ) .
it is clear from figure 2b that the 500 ns cmd control simulation does not explore the amount 
 of conformational space that the amd simulation does and remains trapped 
 in the basin localized around the crystal structure .
the free energy principal 
 component projection of ( a ) 1 ms simulation , 
 ( b ) 500 ns cmd ff99sb - i simulation , and ( c ) 500 ns amd ff99sb - i simulation 
 onto ( pc1 , pc2 ) defined by the 1 ms simulation .
the long - lived structures 
 are projected onto the free energy surface and are labeled as red , 
 blue , green , purple , and black triangles .
the crystal structure , 5pti , 
 is demarked by the red diamond ( see also movies 
 s1 and s2 ) . the amd simulation ( figure 2c ) exhibits 
 a rather broad pathway from the crystallographic basin ( 0.0 , 5.0 ) 
 to the region ( 10.0 , 5.0 ) which is not present in 
 the 1 ms simulation ( figure 2a ) .
flattening 
 of the potential energy surface in the two basins could promote transitions 
 over a large barrier separating them , but the 1 ms simulation may 
 also not have sampled these regions frequently enough to explore this 
 pathway .
the 1 ms simulation spent the majority of the time in the 
 basin around ( 2.5 , 1.0 ) which is ultimately responsible for the observed 
 populations in the 1 ms cmd simulation differing substantially from 
 experiment . in the shaw et al .
paper , this is attributed to inaccuracies 
 in the underlying force field , and indeed we also spend a considerable 
 amount of our 500 ns simulation in the same basin , as one would expect 
 using the same force field . in future work , to determine accurately 
 the conformational changes mapped out by the pc space using an amd 
 simulation , one could use the technique employed by wereszczynski 
 and mccammon . the recent analysis carried out by 
 xue et al .
examined in detail the 1 , 2 , and 3 dihedral angles associated with 
 the disulfide bond formed between cysteine 14 and cysteine 38 during 
 the course of the 1 ms cmd bpti simulation . in this manuscript ,
figure 3c shows the boltzmann reweighted 1(c14 ) vs 1(c38 ) free energy surface explored throughout 
 the 500 ns amd simulation . in contrast , the 500 ns control cmd simulation 
 never visits the minima explored by the amd simulation and remains 
 trapped in a state close to the crystal structure ( figure 3b ) , as was seen in the pc projections . comparing 
 the free energy surface explored by the 1 ms cmd simulation ( figure 3a ) to that of our amd simulation , it is clear the 
 amd simulation explores the same states as the unbiased simulation .
the 1c14 vs 1c38 
 dihedral angle free energy surfaces of ( a ) 1 ms cmd simulation , ( b ) 
 500 ns cmd ff99sb - i simulation , and ( c ) 500 ns amd ff99sb - i simulation . 

the long - lived stable states are plotted onto the free energy surface 
 and are labeled as red , blue , green , purple , and black triangles . 
 the crystal structure , 5pti , is demarked by the red diamond .
the major 
 state m is labeled along with the minor states mc14 and 
 mc38 .
the 2 and 3 dihedral angles 
 associated with cys14 and cys38 can be used to further describe isomerization 
 configurations of the disulfide bond : the major state m , which consists 
 of three substates ( m1 , m2 , and m3 ) , and the two minor or excited 
 states mc38 and mc14 . a detailed description of these states is included in the supporting information ( figure s1 ) , which can 
 be compared to those analyzed by xue et al . for the 1 ms cmd simulation . 

in contrast with the 1 ms cmd simulation , which predicts the excited 
 state mc14 to be the most populated , we find the major 
 state m to be the most populated in the amd simulations after boltzmann 
 reweighting our distribution ( table s1 ) ; 
 however , to fully converge the population distribution would require 
 a longer simulation than was used in this study .
structures 
 from states m1 , mc38 , and mc14 were extracted 
 from the trajectory by using the lowest energy structure 
 in the m1 state as a reference to select an ensemble of structures 
 with similar energy from each of the three basins for performing the 
 chemical shift analysis . using the shiftx2 software package ,
chemical shift differences were computed between 
 the ensembles representing the different substates ( table 1 ) . a rms deviation of 2.1 ppm was obtained from 
 the ff99sb - i amd simulation ( computed for the shifts with known sign ) 
 compared to 2.7 ppm computed from the 1 ms cmd simulation . in general , 
 good agreement is achieved from the amd simulation compared to values 
 calculated from the 1 ms cmd simulation and the experimental values .
we would like to highlight the fact that one can not compute these 
 differences using only 500 ns of cmd since the simulation never explores 
 the excited states during the course of such a short simulation ( figure 3b ) .
examination of the water occupancy 
 throughout the amd simulation correctly identifies the four long - lived 
 waters in agreement with experimental results .
the longest - lived water , w122 , is identified by the 1 ms 
 cmd simulation as having a lifetime of 14 s . during the course 
 of the amd simulation ,
several exchange events are captured at this 
 location and an interesting  revolving door 
mechanism 
 is identified , whereby the disulfide bond rotates around and pushes 
 the water out of the pocket ( highlighted in movie 
 s3 ) .
the longest binding events of water molecules at this 
 site occur when in the crystallographic basin of the amd simulation , 
 consistent with the 1 ms cmd simulation .
this work shows that , using conventional 
 off the shelf gpu hardware 
 combined with an enhanced sampling algorithm , events taking place 
 on the millisecond time scale can be effectively sampled with dynamics 
 simulations orders of magnitude shorter ( 2000 ) than those time 
 scales . the implementation is validated in this work by comparison 
 with a long unbiased cmd simulation and experimental data .
structurally , 
 we show the long - lived states identified by the 1 ms cmd simulation 
 have been sampled both in terms of rmsd and coverage in pc space . 
 we demonstrate that access to these states can not be obtained with 
 the same length of simulation carried out using conventional md .
important 
 structural waters were preserved and found to exhibit the same occupancies 
 as those experimentally .
chemical shift differences computed from 
 the amd simulations were found to be in agreement with those calculated 
 from the long 1 ms cmd simulation , and similar dihedral populations 
 were also observed .
however , we point out that , while amd is great 
 for exploration of conformational space , it does not reproduce the 
 exact dynamics of the system .
we conclude by emphasizing never before 
 has the amd been benchmarked against a long cmd simulation , and we 
 commend d. e. shaw research for providing their data to the community .
 in this work , we critically assess the ability of the 
 all - atom 
 enhanced sampling method accelerated molecular dynamics ( amd ) to investigate 
 conformational changes in proteins that typically occur on the millisecond 
 time scale . 
 we combine amd with the inherent power of graphics processor 
 units ( gpus ) and apply the implementation to the bovine pancreatic 
 trypsin inhibitor ( bpti ) . 
 a 500 ns amd simulation is compared to a 
 previous millisecond unbiased brute force md simulation carried out 
 on bpti , showing that the same conformational space is sampled by 
 both approaches . to our knowledge , this represents the first implementation 
 of amd on gpus and also the longest amd simulation of a biomolecule 
 run to date . 
 our implementation is available to the community in the 
 latest release of the amber software suite ( v12 ) , providing routine 
 access to millisecond events sampled from dynamics simulations using 
 off the shelf hardware . 
Introduction
Results
Conclusion