pressure is a fundamental 
 thermodynamic variable that can modulate 
 protein structure , dynamics , and function . the effect of hydrostatic pressure 
 on protein stability has been studied extensively , including many 
 studies that have explored how protein denaturation occurs under high - pressure 
 conditions . an ellipse - shaped zone of stability in the temperature  pressure 
 plane has been proposed on the basis of theoretical models , molecular 
 dynamics ( md ) simulations , and experiments .
in addition 
 to studying the stability of proteins in equilibrium under high - pressure 
 conditions , pressure perturbation can also be used to study protein 
 folding kinetics .
microsecond pressure - jump ( p - jump ) 
 techniques have recently extended the range of such experiments to 
 near the folding  speed limit  .
here we ask whether such fast protein refolding from the pressure - denatured 
 state can be seen from beginning to end in a full - atom explicit solvent 
 md simulation , and whether the speed limit from the pressure - denatured 
 state has the same time scale as the 1 s speed limit 
 observed in temperature - jump ( t - jump ) experiments and single - molecule 
 experiments .
, 
 is slower than backbone torsional transitions or end - to - end contacts 
 of short loops , and attributed to either reduced diffusion on a rough 
 energy landscape , or equivalently to extremely short - lived high - free - energy 
 folding intermediates .
md simulation has been used for studying the 
 effect of pressure 
 on protein thermodynamics and protein denaturation , but kinetic refolding and the 
 molecular time scale have proved elusive so far .
recent developments 
 in both hardware and software have pushed md simulations up to the 
 millisecond time domain . at the same time , a new generation of microsecond kinetics p - jump 
 experiments can access the md time scale , and would benefit greatly from interpretation based on the atomistic 
 detail available from simulations .
so far simulations have only observed 
 the trapping process associated with non - native helix formation after 
 a p - jump , and it remains to be seen whether 
 the burst phase observed in experiments translates into fast and complete 
 refolding in silico .
we previously applied 
 the ultrafast p - jump technology to study 
 the refolding kinetics of an alanine - rich mutant of five - helix bundle 
 -repressor , *ya .
in addition to a <3 s burst 
 phase , *ya refolding exhibited a 1.5 ms  slow  

we surmised that 
 two glycines , mutated in place of alanines in helices 2 and 3 of *ya , 
 would make the protein more flexible and help it escape from traps 
 with excess helical structure , making it a good test case for complete 
 refolding upon p - jump in silico . following a t - jump 
 near its melting temperature ,
this new glycine - rich mutant of -repressor , 
 *yg , is known to fold with a rate coefficient kf  ( 22 s ) .
we computed over 33 s of explicit 
 solvent dyanmics in several 
 long trajectories to simulate a p - jump experiment .
high - pressure - denatured 
 states , generated through a high - temperature unfolding and high - pressure 
 equilibration simulation procedure , were 
 found to contain significant residual helical structure . nonetheless , 
 *yg refolded into the native state in under 20 s following 
 a pressure drop .
however , follow - up p - jump experiments on *yg 
 are in agreement 
 with previous p - jump experiments on the alanine - rich  repressor 
 mutant *ya .
we still see a small <3 s burst phase 
 and a large 1.7 ms slow phase , the latter previously attributed to 
 non - native helix formation .
thus glycine 
 substitution in helices 2 and 3 did not eliminate the slow phase . 

the microsecond folding observed here in silico therefore 
 suggests that a fraction of the proteins with native - like residual 
 helix in the unfolded state refolds very rapidly during the experimentally 
 observed microsecond burst phase , while the remaining population with 
 non - native helix content in the turns is trapped for > 1 ms .
after 18.6 s of conformational search , the simulation revealed 
 a 0.9 s stretch of productive structural assembly , bracketed 
 by three - helix alignment and loop formation motions that were almost , 
 but not quite , concerted .
this 0.9 s time scale agrees with 
 the molecular time scale of 12 s measured by t - jump 
 experiments on near - downhill folding -repressor mutants .
*yg 
 consists of the wild - type -repressor 
 sequence residues 685 , with mutations tyr22trp , gln33tyr , 
 ala37gly , and ala49gly .
it has a melting 
 temperature of tm = 55 c and a folding 
 time constant of 22 s near tm in 
 aqueous buffer . for md simulations
the 
 sequence was used without c - terminal amidation or n - terminal acetylation . 

the initial structure of the -repressor fragment was taken 
 from the protein data bank ( pdb code 1lmb ) . from a 
 crystal structure of the similar *ya mutant , we know that the 
 mutant and wild - type native structures are quite similar . for p - jump experiments ,
the protein was grown 
 in e. coli and purified and lyophilized as described 
 previously .
md simulations were 
 performed in explicit solvent using the tip3p water model and the charmm22 force field with cmap corrections 
 for protein and ions .
the force field has excess helix propensity , which may accelerate trapping 
 ( from non - native helix ) and folding ( from native helix ) .
the initial 
 protein structure was placed in a cubic box of 24  282 water 
 molecules at 55 mm nacl salinity , neutralized with extra ions employing 
 vmd . the simulated system , including 
 protein , water molecules , and ions , measured 91.1  in each dimension 
 at t = 325 k and p = 1 bar and contained 
 74  197 atoms .
all simulations were carried out with periodic 
 boundary conditions in a constant particle number , temperature , and 
 pressure ensemble ( npt ) , in five steps .
step ( 1 ) : in a p - jump simulation , 
 pressure was increased from 1 bar to 5 kbar in 0.15 s at a 
 rate of 1 bar/30 ps while maintaining the temperature at t = 325 k. step ( 2 ) : in a high - temperature and high - pressure unfolding 
 simulation , temperature was increased to 525 k while maintaining pressure 
 at p = 5 kbar , running the simulation for 0.15 s . 

step ( 3 ) : after the protein unfolded in step ( 2 ) , the temperature 
 was dropped back to 325 k and pressure was kept at p = 5 kbar while the denatured protein was equilibrated at high pressure 
 for 1 s in a high - pressure equilibrium simulation .
step ( 4 ) : 
 in a pressure - drop simulation , pressure was jumped downward from 5 
 kbar to 1 bar in 0.15 s at a rate of 1 bar/30 ps while 
 maintaining the temperature at t = 325 k. steps ( 1)(4 ) 
 were carried out on general purpose supercomputers using namd 2.9 .
step ( 5 ) : the resulting pressure - denatured state 
 under refolding conditions was employed as the initial state for a 
 refolding simulation , carried out on the special purpose supercomputer 
 anton for 32 s
. constant temperature ( t = 325 k ) and constant pressure ( p = 1 
 bar ) were maintained during the refolding simulation .
the simulation algorithm 
 and features of the namd program are described in ref ( 41 ) .
the system to be simulated 
 was first subjected to 6000 steps of conjugate gradient minimization 
 and equilibrated for 300 ps with harmonic restraints applied to all 
 the heavy atoms of the protein .
the simulation was then continued 
 for 3 ns without restraints at a constant pressure of 1 bar using 
 nos  hoover langevin piston barostat and at a constant 
 temperature of 325 k with langevin damping constant of 5.0 ps . in the subsequent simulations of steps ( 1)(4 )
, 
 constant temperature was maintained using langevin dynamics with a 
 damping constant of 1.0 ps and multiple time stepping 
 employed with an integration time step of 2.0 fs , short - range forces 
 being evaluated every time step and long - range electrostatics evaluated 
 every three time steps .
cutoff for short - range nonbonded interactions 
 was 8.0  ; long - range electrostatics was calculated using the 
 particle - mesh ewald method .
all bonds 
 involving hydrogen in the protein were constrained using rattle , while the geometries of water molecules were 
 maintained using settle .
the refolding simulation in 
 step ( 5 ) was carried out on the anton platform .
multiple time stepping was employed , with an integration time step 
 of 2.0 fs .
short - range forces were evaluated every time step and long - range 
 electrostatics every three time steps .
cutoff for the short - range 
 nonbonded interactions was 9.28  ; long - range electrostatics 
 was calculated using the k - gaussian split ewald method with a 64  64  64 grid .
refolding 
 kinetics experiments 
 were performed on a home - built p - jump apparatus as described previously .
briefly , an 810 l dimple was machined into a sapphire 
 cube with a side length of 3/8-in .
the sample consisting of 300 m protein in 50 mm phosphate buffer 
 at ph 7 with either 0 or 1 m guanidine hydrochloride ( guhcl ) was then 
 pipetted into the dimple and sealed with a double - layer of mylar - coated 
 aluminum foil to prevent mixing between the sample and the pressurization 
 fluid ( water ) .
stainless 
 steel burst membrane , to which it was connected by a pressurization 
 channel .
the sample and burst membrane were pressurized hydrostatically 
 to 1.2 kbar using a pressure pump ( high pressure equipment company , 
 erie , pa ) .
the burst membrane was ruptured by passing 10 ka 
 of current ( 95 v ) through it , releasing the sample pressure back to 
 1 bar within 23 s .
the sample was optically excited 
 with a frequency - tripled ti : sapphire laser ( kmlabs , boulder , co ) , 
 which generated femtosecond pulses of 285  3 nm light separated 
 by 12.5 ns .
fluorescence was collected and the photons were delivered 
 to a photomultiplier ( r7400u-03 , hamamatsu corp . ,
bridgewater , nj ) 
 using an optical waveguide ( oriel instruments , stratford , ct ) .
we 
 used a band - pass filter ( b370 , hoya , santa clara , ca ) to avoid interference 
 from the excitation light .
the signal was recorded and digitized at 
 100 ps time resolution using an oscilloscope with a 2.5 ghz bandwidth 
 ( dpo7254 , tektronix , beaverton , or ) .
we chose -repressor mutant *yg ( y22w / q33y / a37g / a49 g ) 
 as a model system to study complete fast protein refolding after a 
 pressure drop .
it is the largest fast - folding protein folded in silico to date by all - atom md simulations .
fast folding of various -repressor 
 mutants has been studied previously using temperature - jump , pressure - jump , and rapid microfluidic mixing techniques . in order to later 
 compare with the denatured simulation and refolding simulation
, we 
 first performed a 0.3 s md simulation of *yg at t = 325 k and p = 1 bar , starting from 
 the crystal structure .
this 0.3 s 
 simulation will be referred to hereafter as the native simulation . 

the average values of several structural characteristics , such as 
 radius of gyration ( rgyr ) , were determined 
 from the native simulation and defined as the protein s native 
 values , shown as red solid lines in figure 1 . structural characterization of the *yg unfolding trajectory . 

-content is the fraction of 
 residues that are in the -helical conformation , and rgyr is the radius of gyration .
the native values , 
 calculated from a 0.3 s equilibrium simulation of the native 
 structure at t = 325 k and p = 1 
 bar , are shown as red solid lines . the pressure applied through the 
 simulation , shown as the color background , varies from 1 bar ( white ) 
 to 5 kbar ( blue ) .
the temperature is kept at 325 k , except for the 
 time window between 0.15 and 0.3 s , where 525 k is used to 
 unfold the protein .
protein coloring runs 
 blue to red from the n - terminus to the c - terminus .
the denaturation simulation 
 followed a procedure described in a previous p - jump md simulation 
 study that did not observe refolding of the *ya mutant .
briefly , we started with the native state of 
 *yg , shown in the t = 0 s conformation 
 in figure 1 .
the pressure was gradually increased 
 from 1 bar to 5 kbar over 0.15 s , while temperature was held 
 constant at t = 325 k. in figure 1 , the value of the pressure is depicted by the background 
 color changes from white ( 1 bar ) to blue ( 5 kbar ) .
the protein remains 
 in its native conformation in the first 0.15 s of upward p - jump 
 simulation .
high pressure can unfold a protein , but 
 such high - pressure denaturation is a slow process that takes place 
 on a time scale of seconds or even longer .
therefore , 0.15 s 
 of pressurizing is too short for observing any discernible conformational 
 change . to accelerate the protein unfolding process , we heated the system 
 to t = 525 k and simulated the system for another 
 0.15 s , while keeping pressure at p = 5 kbar . 

as shown in figure 1 , the protein rapidly unfolds 
 as evidenced by the increase of c-root - mean - squared 
 deviation ( rmsd ) relative to the crystal structure ( > 20  ) . 

the 
 content of secondary structure , -helix in particular , drops 
 from the native value of 65.5% to a value in the 1030% range . 
 during the unfolding
, the protein also assumes some extended conformations 
 with rgyr of more than 30  .
the 
 high - t - p denatured state , obtained after the high - temperature and 
 high - pressure unfolding simulation , is shown in figure 1 as the conformation at t = 0.3 s .
the 
 high temperature used in the simulation unfolds the protein , 
 but also likely disrupts the protein more than when only high pressure 
 is used for denaturation . to obtain a state more representative of 
 the pressure - denatured ensemble ,
the high - t - p denatured state was 
 equilibrated for 1 s at p = 5 kbar and t = 325 k. the most striking observation in the equilibration , 
 shown in figure 1 , is that the -helix 
 content recovers from 30.0% to 60.0% , which is already 
 close to the native value of 65.5% .
the existence of high 
 -helix content at high pressure indicates that pressure denaturation 
 is mainly breaking the tertiary contacts , but does not perturb the 
 secondary structure considerably , as proposed previously .
the result is consistent with the finding that 
 pressure does not affect the helix  coil equilibrium significantly , 
 based on replica exchange md simulations of -helical peptide 
 using a different force field .
recent 
 experiments by neumaier et al . have shown that high pressure can slightly 
 stabilize a helix , which explains the frequently observed helical 
 structures in pressure - denatured proteins .
notably , the pressure - denatured state after the high - pressure equilibration , 
 shown in figure 1 as the conformation at t = 1.3 s , already contains helices 1 and 4 .
we performed a 0.15 
 s downward p - jump simulation that initiated the refolding process . 

significant amount of helical structure , resulting from the high - pressure 
 equilibration , did not change substantially during the downward jump . 

the entire 1.45 s denaturation simulation and downward p - jump 
 simulation rendered as one trajectory are shown in movie s1 in the supporting information ( si ) .
the time evolution 
 of the c-displacement per residue relative to the 
 crystal structure and the secondary structure per residue are shown 
 in figure s1 . following the downward 
 p - jump simulation
, we carried out a 32 s md simulation at p = 1 bar and t = 325 k to investigate 
 fast refolding .
the protein , except for the last helix ( helix 5 ) , 
 folded into the native state after 19 s .
the c-rmsd of the protein relative to the crystal 
 structure ( pdb code 3kz3 ) is shown in figure 2b , and the secondary 
 structure is shown in figure 2c ; see figure s2 for additional quantities of interest ) . 
 a particular mechanism by which *yg mutant folds in our trajectory 
 is punctuated by two fast events separated by a longer conformational 
 search , as shown in figure 2d .
protein refolding trajectory 
 from the simulation at t = 325 k and p = 1 bar after pressure jump .
( a ) distinct molecular rearrangements observed at the bottleneck 
 ( transition - state passage ) . at each time point , the folded residues 
 ( c displacement relative to the crystal structure 
 2  ) are colored blue .
( b ) c-rmsd values 
 for the protein core ( residues 780 ) , calculated relative to 
 the crystal structure 3kz3 . the native range is defined 
 by the mean value ( red solid line )  standard deviation ( green 
 dashed line ) from a 0.3 s equilibrium simulation of the native 
 structure at t = 325 k and p = 1 
 bar . ( c ) time evolution of the secondary structure throughout the 
 trajectory .
the secondary structure of the crystal structure is shown 
 on the left side of the panel .
( d ) time evolution of per - residue c displacements from the crystal structure throughout 
 the refolding trajectory .
( e ) the time window between 18 and 20 s 
 is enlarged to reveal the sequence of rearrangements at the bottleneck 
 ( see movie s3 in si ) .
the color bar runs 
 from blue ( close to crystal structure ) to red ( far from crystal structure ) . in a first fast step within 2 
 s of the p - jump
, helices 1 
 ( residues 727 ) and 4 ( residues 5870 ) adjusted their 
 orientation and registration to reach a near - native conformation . 

subsequently , a number of factors prolonged 
 the conformational 
 search : helix 3 did not form individually until 7 s 
 ( see figure 2c ) , and was originally shifted 
 toward the c - terminus by one full helical turn ; neither helix 2 nor 
 helix 3 acquired a native orientation ; helical overshoots were observed 
 both in helices 1 and 2 , where they eroded loop 1 between the two 
 helices as shown in figure 2c , preventing the 
 correct helix orientation from locking in .
the key bottleneck 
 was crossed in the second fast step between 
 18.6 and 19.5 s ( figure 2e ) . in 0.9 
 s
, three key rearrangements brought the protein from a compact 
 denatured state through the transition - state region into the native 
 basin ( figure 2a ) .
first , between 18.6 and 
 18.8 s , helices 2 and 3 , along with loop 2 that connects them , 
 reoriented themselves and assumed the native packing conformation 
 relative to helices 1 and 4 .
the one - helical - turn shift in helix 3 
 and the helical overshoot in loop 1 disappeared during this structural 
 transition . within the next 0.4 s , loop 1 assumed its native 
 conformation ,
finally , 
 loop 3 between helices 3 and 4 rearranged into its native structure 
 at t = 19.5 s . the whole refolding trajectory 
 is visualized in movie s2 in the si .
the 
 trajectory for the time window between 18 and 20 s is provided 
 in movie s3 in the si .
the formation 
 of helix 5 is presumably the last step of the folding process ; this 
 step is not observed in the simulation .
it is possible that the *yg 
 in solution adopts a native state that is different from the crystal 
 structure .
indeed , an unstable helix 5 
 in the native state is consistent with the high b factors in the crystal structure and 
 observed in implicit solvent md simulations .
an unstructured helix 5 has also been observed before for another 
 -repressor mutant ( d14a ) and attributed to the absence of c - terminus 
 residues from the wild - type -repressor .
previous 
 fast p - jump experiments up to 0.5 ms on *yg revealed a microsecond 
 burst phase .
we recently extended the 
 capabilities of our p - jump apparatus to collect refolding kinetic 
 data for up to 5 ms .
we used this new 
 home - built instrument to jump the pressure of the sample from 1.2 
 kbar to 1 bar ( see materials and methods ) . 

the tryptophan in position 22 ( trp22 ) was used as a fluorescence probe 
 to study folding of *yg after a microsecond pressure drop . 

tyrosine in position 33 ( tyr33 ) was introduced to quench trp22 fluorescence 
 in the folded state , enhancing the change in fluorescence lifetime 
 upon unfolding .
titration of *yg with guhcl shows an 
 unfolding midpoint concentration of 1.3 m ( figure 
 s3 ) .
equilibrium pressure denaturation of *yg was monitored 
 by fluorescence spectroscopy ( figure s4 ) .
based on these results , we expect no pressure denaturation of 
 *yg in 0 m guhcl up to 1.2 kbar , whereas in 1 m guhcl , the 
 protein is poised for unfolding when the pressure is increased above 
 1 bar . for the p - jump experiments , trp fluorescence excited 
 at 285
nm 
 was sampled every 12.5 ns and digitized with a time resolution of 
 100 ps .
the fluorescence lifetimes for nata were then normalized from 
  = 0 ( before the p - jump ) to  = 1 ( 4.7 ms after the p - jump ) 
 through a linear fitting procedure , and the 0 and 1 m protein samples 
 were analyzed on the same scale for comparison .
the dead time of the 
 instrument with a starting pressure of 1.2 kbar was determined from 
 the nata sample , fitting its step - function - like trace to a single 
 exponential rise of 3 s . in general ,  
 variants with a q33y mutation exhibit an increase 
 in fluorescence lifetime upon unfolding whether the denaturation is 
 accomplished using temperature , pressure , or a chemical denaturant . 

this response can be rationalized in terms of nonradiative quenching 
 of the tryptophan fluorescence by tyrosine in the folded state .
figure 3 shows the fluorescence - detected kinetics of nata , 
 *yg without guhcl , and *yg in 1 m guhcl from 1.2 kbar 
 to 1 bar . *yg without guhcl data is a folded control because 
 *yg without guhcl does not undergo pressure denaturation at 
 1.2 kbar . the initial lifetime increase for *yg in 1
m guhcl 
 at t = 0 is a factor of 1.4 larger than that observed 
 for *yg without guhcl .
this observation indicates that there 
 is a fast burst phase , <3 s , superimposed on the intrinsic 
 response of tryptophan to the p - jump , during which the lifetime increases . 
 in addition , a slower phase , 1.74  0.02 ms , was observed .
this 
 slow phase was not present in the control p - jumps of nata or *yg 
 without guhcl .
the absolute changes in the fluorescence decay of nata 
 and *yg without guhcl in response to a p - jump are shown in figure s5 .
pressure - jump of nata ( gray ) and *yg 
 in 1 m ( blue ) and 0 
 m ( red ) guhcl from 1.2 kbar to 1 bar probed by tryptophan fluorescence 
 decays .
tryptophan lifetime was normalized from  = 0 ( before 
 the p - jump ) to  = 1 ( 5 ms after the jump ) for nata .
p - jump 
 data of *yg were analyzed on the same lifetime scale as nata 
 data to facilitate direct comparison .
the panel on the left shows 
 the data from 20 s before the p - jump to 100 s after 
 the p - jump .
the fast phase was fitted to a single exponential function with time 
 constants of  = 2.6  0.3 ( nata ) , 2.3  0.4 ( *yg 
 with guhcl ) , and 3.7  0.5 s ( *yg without guhcl ) . 

the panel on the right shows the data from 5 s after the p - jump 
 to 4.7 ms after the p - jump .
the millisecond kinetic response 
 of *yg with guhcl was fitted to a single exponential function 
 with a time constant  = 1.74  0.02 ms ( black curve ) .
helix 
 5 does not fold in the simulation . but does that mean helix 5 is unimportant 
 for folding ?
we checked the expression of two c - terminal truncated 
 versions of *hg ( a tyr33his mutant with stability very similar 
 to that of *yg ) .
we truncated -repressor fragment after 
 either amino acid s72 or s78 . both fragments expressed poorly as compared 
 to the full - length construct .
the secondary structure content of both 
 fragments was reduced compared to the wild - type protein , as confirmed 
 by circular dichroism .
neither of the truncated proteins showed a 
 distinct thermal melting transition , as probed by circular dichroism 
 spectroscopy or fluorescence spectroscopy ( see si ) .
it appears that at least a portion of helix 5 is required 
 for successful folding of -repressor fragment , even if the 
 c - terminal helix is very flexible under conditions favoring the native 
 state .
our simulation shows 
 that refolding of a relatively large ( 80 residue ) 
 protein domain can be observed successfully after a p - jump in silico .
the computed folding process consists of two 
 very fast ( 12 s duration ) events , separated 
 by a slower ( 16 s ) conformational search . in the experiment , 
 a burst phase consistent with these fast times was observed ; there 
 was also a millisecond phase , likely due to the formation of non - native 
 helix in the pressure - denatured state , and discussed previously .
we focus our discussion on the fast refolding 
 induced by p - jump and the microsecond molecular phase which is observed 
 in our simulation .
the two fast events both occur near the  speed 
 limit  
 of folding proposed for -repressor based on t - jump experiments : 

it was previously observed that as  repressor fragment is successively 
 stabilized by mutation or lowering the temperature , a 1 s 
 fast phase appears and grows in amplitude .
this  molecular phase  was attributed to a fraction 
 of the protein population poised at the barrier top , visible to an 
 ensemble experiment only when the protein is stabilized so its folding 
 barrier approaches rt .
a similar time scale 
 has also been observed for slower folders by single - molecule experiments 
 resolving the passage of a protein across the transition state .
the molecular time scale corresponds to 
 an average over the complex 
 network of fast dynamics observed in hidden markov models .
our c-rmsd probe in figure 2b should be sensitive to events before , during , or after passage 
 through the bottleneck for folding , and indeed , the two fast events 
 we see correspond to different regions of the free energy landscape .
the first fast event observed here corresponds to relaxation in 
 the denatured basin , or downhill formation within 2 s of a 
 folding intermediate containing native secondary structure in helices 
 1 , 2 , and 4 , with 1 and 4 properly aligned .
downhill folding was first 
 invoked to rationalize the very fast appearance of folding intermediates 
 during refolding of phosphoglycerate kinase and rnase h that occurred 
 only under stabilizing conditions .
a truncated 
 version of the  repressor fragment with only helices 1 and 
 4 remaining has been shown to be stable and fold on a time scale of 
 a few microseconds , further supporting 
 the alignment of helices 1 and 4 as an important first step during 
 folding . in a simulation where these helices were incorrectly oriented
, 
 the protein remained in a trapped state for a full 60 s of 
 simulation .
the second fast event 
 can be identified with passage through the 
 bottleneck or transition - state ensemble , as it is preceded by a 16 
 s period of unproductive conformational search .
this passage 
 is not instantaneous , but takes 0.9 s during which two helices 
 rearrange and a loop forms .
this event represents the speed limit 
 of folding in the absence of unproductive conformational search , unless 
 the three motions that comprise the event can be choreographed even 
 more tightly upon further redesign of the  repressor fragment 
 sequence .
according to ref ( 20 ) , the barrier height along a one - dimensional 
 reaction coordinate 
 ( e.g. ,  = 00.5 in the experiment or c-rmsd = 28  in the simulation ) can be estimated from 
 the molecular rate km and the activated 
 rate of folding ka asalthough a single trajectory 
 lacks the statistics 
 to determine these rates , we may approximate km  ( 0.9 s ) and ka  ( 19 s ) , yielding 
 a barrier of about 3rt .
the molecular and activated 
 time scales reported here are in good agreement with measurements 
 of *yg by t - jumps at its melting temperature ( km = ( 2 s ) and ( ka = 22.5 s ) ) .
the step - by - step folding pathway reported here for 
 *yg is 
 in agreement with what has been proposed previously for wild - type 
 -repressor from theoretical studies and from implicit solvent replica - exchange md simulation on another 
 fast folding -repressor mutant .
however , the folding pathway observed here is different from what 
 we reported on the *hg mutant . for *hg , helices
helix 4 of *hg formed individually in the early folding 
 stage , but finding the correct orientation relative to other helices 
 was a slow process that involved kinetic traps .
the difference between *yg and *hg could 
 result from the point mutations altering the energy landscape , from 
 different initial structures ( pressure - denatured state vs extended 
 state ) altering the initial condition for refolding , or simply from 
 a heterogeneous ensemble of folding pathways .
it is clear from past 
 work on  repressor fragment that different mutations and different 
 solvent conditions lead to different folding pathways , but the exponential sensitivity of population to free energy ( p1/p2 = exp[g12/rt ] ) makes it rather unlikely 
 that the same sequence will fold by several equally boltzmann - weighted 
 pathways . in terms of
a funneled rough energy landscape , it is easy 
 to see how perturbations of the funnel could switch the most likely 
 path , but the random free energy variations introduced by landscape 
 roughness make it unlikely that many equally weighted paths exist . 
 indeed , relatively few cases of parallel pathway folding are known , 
 such as lysozyme , staphylococcal nuclease , or certain repeat proteins .
the same question is much more pressing for the nature of 
 the folding 
 bottleneck : how much does the timing and sequence of the three motions 
 we observed during the 0.9 s passage through the bottleneck 
 change from trajectory to trajectory ?
the answers to these questions are presently 
 unknown at an atomistic level of resolution and will require multiple 
 trajectories to provide proper sampling .
it is in our opinion a priority 
 for computational folding studies during the next several years . for both *yg and *ya ( the latter has g46a / g48a mutations 
 instead of a37g / a49 g )
, the fast p - jump experiment shows a <3 s 
 burst phase and a > 1 ms slow phase .
one of our long simulations 
 ( *ya ) 
 got trapped for the duration of the simulation , whereas the other ( *yg ) folded rapidly .
we thus 
 propose that prompt folding is roughly as likely as kinetic trapping 
 in both the p - jump experiments and simulations .
if so , this 
 raises the same question raised by lapidus and co - workers 
 in their microfluidics experiment and by pande from simulations : are there very slowly interconverting 
 denatured states ?
for example , a kinetic scheme such aswith u and t initially populated , 
 can explain 
 how some proteins ( initially in u ) reach the native state rapidly 
 whereas others ( initially in t ) reach it slowly .
if u and t bracket 
 the fluorescence lifetime of n , it is possible to observe microsecond 
 and millisecond phases of opposite sign ( figure 3 ) . it is well documented that pressure unfolding can be very slow 
 due to the positive activation volumes , and that pressure denaturation forms more compact 
 denatured states than temperature denaturation .
compact states that 
 fold more slowly than highly extended denatured states have been observed . 

for example , trpzip2 has a heterogeneous denatured population , whose 
 subpopulation with blue - shifted tryptophan fluorescence ( less solvent 
 exposed tryptophan ) folds more slowly to the native state than the 
 subpopulation with red - shifted tryptophan fluorescence ( more solvent 
 exposed tryptophan ) .
thus it remains unproven , but 
 fully consistent with our data and simulations , that the pressure - denatured 
 state of -repressor contains slowly interconverting compact 
 traps .
finally , we investigated what hinders the formation of 
 helix 5 
 in our simulation . in the native state , helix 5 is stabilized by interacting 
 with helix 4 through a small hydrophobic patch .
formation of this patch is prevented in our simulation 
 by several non - native salt bridges ( figure 4 ) .
since helix 5 has weak helix propensity and needs to form in concert 
 with its tertiary contact with helix 4 , the non - native salt bridges 
 that keep the c - terminus away from helix 4 hinder the formation in 
 helix 5 .
one should not conclude that the non - native salt bridges 
 hinder overall folding .
they form within the first 2 s after 
 the p - jump and remain stable for most of the trajectory ( figure 4 ) .
they may play a crucial role in bringing the 
 n- and c - terminus together , facilitating the formation of the main 
 hydrophobic core that involves helices 1 to 4 . particularly the bridges 
 between helix 1 and the c - terminus ( glu13-arg85 and arg17-glu83 ) , 
 may accelerate the folding reaction in its early stage , but slow it 
 down toward the end . in that regard
it is noteworthy that blue1 , a two - helix bundle containing only helices 1 and 4 , 
 folds rapidly ( the conformational search of helices 2 and 3 is eliminated ) , but truncating helix 5 in the full - length protein 
 ( results ) produces a highly unstable protein 
 with low expression level and missing secondary structure .
non - native 
 salt bridges in the refolding trajectory , monitored 
 by the distance between oxygen bridges .
the pressure jump simulation reveals key steps in 
 moving the protein 
 across the transition state during folding .
first of all , limited computational resources only allow the 
 production of a single or few trajectories , preventing one from drawing 
 a statistical conclusion , as seen in the case of the molecular rate , 
 folding rate , or the structural heterogeneity of the transition - state 
 ensemble .
second , a bias toward a certain kind of secondary structure 
 has been observed in the current generation of force fields .
although it 
 has been shown that this force field has a helical bias , we used it successfully to fold a fast folding mutant of -repressor 
 ( *hg ) , and it seems to explain 
 qualitatively both trapping and prompt refolding after a p - jump ( this 
 work ) .
the high temperature ( 325 k ) used in the current study has 
 a destabilizing effect on the helical structure , which can help in 
 balancing the helical bias to some extent .
however , the development 
 of force fields that reproduce melting temperatures and hence denatured 
 ensembles of proteins better remains an important goal .
third , a chemical 
 denaturant ( guhcl ) was used in the experiment to help unfold the protein 
 at just 1.2 kbar .
the simulations , on the other hand , utilized high 
 temperature to accelerate the unfolding process
. such differences 
 between experiment and simulation can not yet be avoided altogether , 
 but should be minimized as progress is made in both areas .
. 
 however , unfolding simulations are widely performed at very high temperature 
 ( and pressure in our case ) to generate the denatured state for refolding 
 simulation .
since the interatomic interaction strengths are much less 
 sensitive to pressure changes than temperature changes in the ranges 
 chosen for our simulations , we expect 
 that high - pressure simulation at less severe temperatures could yield 
 useful initial states for refolding .
 density 
 is an easily adjusted variable in molecular dynamics ( md ) 
 simulations . 
 thus , pressure - jump ( p - jump)-induced protein refolding , 
 if it could be made fast enough , would be ideally suited for comparison 
 with md . although pressure denaturation perturbs secondary structure 
 less than temperature denaturation , protein refolding after a fast 
 p - jump is not necessarily faster than that after a temperature jump . 
 
 recent p - jump refolding experiments on the helix bundle -repressor 
 have shown evidence of a <3 s burst phase , but also of a 
 1.5 ms  slow  phase of refolding , attributed 
 to non - native helical structure frustrating microsecond refolding . 
 
 here we show that a -repressor mutant is nonetheless capable 
 of refolding in a single explicit solvent md trajectory in about 19 
 s , indicating that the burst phase observed in experiments 
 on the same mutant could produce native protein . 
 the simulation reveals 
 that after about 18.5 s of conformational sampling , the productive 
 structural rearrangement to the native state does not occur in a single 
 swift step but is spread out over a brief series of helix and loop 
 rearrangements that take about 0.9 s . our results support the 
 molecular time scale inferred for -repressor from near - downhill 
 folding experiments , where transition - state population can be seen 
 experimentally , and also agrees with the transition - state transit 
 time observed in slower folding proteins by single - molecule spectroscopy . 
Introduction
Materials and Methods
Results
Discussion
Outlook