protein folding occurs in vivo in the environment quite unlike that under experimental , in vitro conditions . a large fraction of newly synthesized protein chains do not fold spontaneously , but are assisted by molecular chaperones.(1 ) chaperonins , a class of hollow cylindrical chaperones , are responsible for binding and encapsulating substrate proteins ( sp ) in their non - native conformations by enabling them to reach their native states . the observation of protein dynamics in the presence of or inside the chaperonin by means of experimental techniques is extremely difficult and lacks sufficient detail . a number of models have been proposed for the chaperonin mechanism related to either direction of the chaperonin cage role : passive ( aggregation prevention without altering the folding mechanism or kinetics ) or active ( folding promotion ) . the two major active models are iterative annealing mechanism ( iam ) , where the chaperonin promotes folding by unfolding from misfolding traps , and the active cage model exploring the role of the chaperonin interior microenvironment on sp folding promotion . there is evidence for either of these mechanisms , both experimental and theoretical , and none of them is mutually exclusive.(2 ) the presence of more than one mechanism may be important for the ability to serve a great variety of different sps , which may require different supportive mechanisms . probably the earliest and most popular explanation of the chaperonin active role is the iam model . the first theoretically driven iam concepts were followed by simple kinetic models and simulations of chaperonin - assisted folding . the earliest simulations involved highly simplistic protein - like models and later less simplified real protein models , recently reviewed in refs ( 2,3 ) . the common interaction model for the chaperonin - assisted folding simulation of real proteins is the simplified potential known as the go - model employed in most , if not all , simulation studies.(2 ) go - like models favor native interactions , assuring the lowest energy for the native conformation a priori , and ignore non - native interactions , assuming their low importance in folding mechanisms . for many proteins , non - native interactions could be important as shown , for instance , in the b1 domain of protein g ( gb1 ) folding studies.(6 ) in this respect , the present results differ from the other iam models . the simulations presented here rely on the predictive power of the model , rather than on biasing the interactions toward the native ones . that is because the cabs force field , derived from statistical regularities seen in experimentally determined protein structures , describes molecular interactions common for all globular proteins , and not for a single structure as assumed in the go - like models . therefore , cabs simulations do not preclude different from  down the hill  folding pathways , as it has been demonstrated in our earlier work . this work is a continuation of in silico studies of protein folding pathways by means of stochastic dynamics , coarse - grained representation , and knowledge - based potentials ( the cabs model ) . the folding mechanisms observed in simulations ( for the paradigm systems : chymotrypsin inhibitor 2 and barnase(7 ) or gb1(8 ) ) showed high consistency with the experimental findings on the level of individual residues . in this work , we apply a similar strategy to characterize the equilibrium folding of b domain of protein a ( bdpa ) . following one of the most popular theoretical pictures of the nonspecific mechanism of chaperonin action , it is assumed that the protein inside the chaperonin cage is subject to periodic swelling caused by hydrophobic interactions with the cage walls . thus , the present simulations could be considered as a computational test of such an iam model , describing its consequences on the molecular level , and thereby providing some additional hints for designing new experiments . bdpa and gb1 are not natural chaperonin sps as their small size and spontaneous , fast folding process make them very good folders . importantly , their folding process is particularly well reproduced in the cabs model as we show here for bdpa and already described for gb1.(8 ) the cabs simulation of both proteins offers a possibility to observe multiple transitions from a highly denatured ensemble ( perfectly matching experimental data ) to a native - like ensemble , around 2  from the native , in a short time . because the simulation accurately describes the ground and transition states , we expect correct prediction of the changes introduced by the chaperonin protocol . the simple chaperonin - like protocol was implemented within the cabs algorithm.(9 ) cabs proved very accurate in protein folding and protein structure predictions ( ranked as best , or one of the best , among other approaches in casp6 blind prediction experiments).(10 ) a detailed description of cabs , the ca - cb - side - chain protein modeling tool , can be found elsewhere.(9 ) here , we provide a concise outline only of the most important features of this modeling tool . cabs coarse grained representation of polypeptide chains uses up to four united atoms per residue . these are  carbon ,  carbon , a virtual united atom placed at the center of mass of a side group ( where applicable ) , and a virtual atom placed in the center of the cc virtual bond . the c-trace is restricted to a high resolution ( 0.61  spacing ) cubic lattice . allowing some fluctuations of the cc distances leads to 800 possible orientations of cc virtual bonds . positions of the remaining united atoms are not restricted to the lattice , being defined in the local cartesian coordinates determined by the c-trace . the lattice representation enables very fast computation of local conformational transitions , making cabs simulations about 100 times faster in respect to otherwise similar continuous models . the stochastic dynamics of the cabs chains is simulated as a long series of small conformational updates controlled by an appropriately designed ( pseudo)random mechanism . except for very short times ( corresponding to the characteristic time of the local conformational transitions ) , the cabs monte carlo dynamics is equivalent to brownian dynamics of analogous continuous space coarse - grained models . the force field of cabs is knowledge - based , and the parameters of the constituent potentials are derived via boltzmann inversion applied to the statistics of structural regularities seen in experimentally solved protein structures . the interaction scheme consists of sequence - dependent short - range conformational propensities , a model of main - chain hydrogen bonds , and context - dependent potential of pairwise interactions of side groups . the averaged solvent effect is accounted for in an implicit fashion in the statistics used in the derivation of the cabs potentials . thus , at present , the model can not be used for straightforward simulations of  atypical  ph or ionic strength effects on protein structure and dynamics . the average hydrophobic effects are well accounted for , and it has been proven that the model is capable of reproducing complex details of protein folding mechanisms . the sizes and shapes tested included spherical small ( r = 2rg ) , spherical medium ( r = 2.33rg ) , spherical large ( r = 3rg ) , and cylindrical ( r = 2rg ) models , where r is the radius of a sphere or a tube ( cylindrical ) and rg is the estimated , native radius of gyration of a given protein . during the hydrophobic disruption cycle ( see below ) , the walls of the model chaperonin attract the polypeptide segments with a strength set to 1ktb , and a thickness of the attractive wall equal to 1rg . for each chaperonin model , we performed a set of long isothermal simulations at reduced temperatures from 2.52 to 2.90 for gb1 and 3.10 for bdpa with the 0.02 increment . only the first interval of a cycle refers to the chaperonin hydrophobic attraction phase ; in the remaining nine intervals , the chaperone is inert with respect to the encapsulated protein ( see also figure 4a ) . each run simulated 1000 chaperonin cycles , and each cycle lapsed with 20  000 arbitrary time units , where the time unit of monte carlo dynamics corresponded to several ( range of 10 ) attempts at various local random micromodifications of the model chain per residue ( see a detailed description of the cabs modeling tool ) . because the sequence of local micromodifications is controlled by a pseudorandom mechanism , the evolution of the model chain follows a coarse - grained brownian motion . every simulation started from a random conformation prepared in a separate , short , high temperature run . the number of folding transitions ( figure 3 ) was estimated as a number of transitions between low root - mean - square deviation ( rmsd ) structures ( below 5  ) and high rmsd structures ( above 9 and 10  , for bdpa and gb1 , respectively ) , using the averaged rmsd values over the trajectory frames spanning one - half of the chaperonin cycle . tse structures where defined as those having 5.5 < rmsd < 8.5  for bdpa , and 6 < rmsd < 9  for gb1 , respectively . these tses contributed to about one - fourth of bdpa and one - half of gb1 trajectory snapshots ( bdpa exhibits more two - state - like behavior ) . simulation analysis was done with a bioshell tool - set  utility library for structural bioinformatics . secondary structure assignments ( helix , strand , coil ) , presented in table 1 and figure 6 , were done using the p - sea algorithm.(13 ) average number of residues with helix secondary structure assignment in the bulk and the small chaperonin simulations for all the trajectory snapshots ( 10  000 snapshots ) and the most expanded only ( with radius of gyration larger than 11  , constituting 5% of the bulk and 18% of chaperonin simulation ) . chaperonin - assisted simulations of bdpa and gb1 were performed independently with several size and shape chaperonin types ( see materials and methods ) and compared to the results of equilibrium folding simulations for a protein only ( bulk ) model . temperature - dependent compactness analysis ( see figure 1 ) and other characteristics showed the most significant impact for a small and a medium - size spherical chaperonin , and for clarity only these types are presented here . mean radius of gyration ( in  ) and its standard deviation as a function of reduced dimensionless temperature for two types of chaperonins ( small and medium ) as compared to chaperonin - free ( bulk ) simulations . chaperonin - assisted simulations produce , on average , less compact structures , although with significantly larger structural variability . bdpa is a three - helical protein ( pdb code : 1bdd ) , 46 residues long ( when the n - terminal unstructured fragment is truncated ) , which folds according to simple two - state kinetics.(14 ) the folding pathway of bdpa is one of the most systematically studied by computer simulation because of the short folding time scale , close to current simulation capabilities . not long ago , it was also thoroughly examined by the phi value analysis,(15 ) the only extensive experimental technique sufficiently close to atomic resolution . as experimentally assessed , many of the simulation predictions captured important folding features ; however , none was entirely consistent with the experimental data , especially with respect to the observed order of folding events . as summarized by wolynes,(16 ) the transition state ensemble ( tse ) structures seen in simulations broadly fall into two classes , those suggesting an h1 and h2 helices dominant role , and those highlighting an h3 helix role and its interactions with h2 . these inconsistencies may be due to the existence of multiple transition states and pathways of bdpa , as inferred from the statistical mechanical folding model(25 ) ( discussed in more detail in the next section ) . the phi value analysis suggested the following:(15 ) tse is constructed around a nearly fully formed h2 stabilized by hydrophobic interactions with h1 , which is only weakly structured . some structure was noted within the turn connecting h2 and h3 and the n - terminus of h3 . h3 was found to contribute to stabilizing hydrophobic interactions by its n - terminal side chains , while c - terminal interactions are less important . in general , the folding follows the nucleation condensation mechanism with the secondary structure well formed ( mainly h2 ) and with a stabilizing contribution of hydrophobic interactions . the cabs energy landscape for bdpa seems to be the least rugged among the paradigm systems we have described so far . the average picture of the transitional , between - the - basins ( native and denatured ) conformers is amazingly consistent with the phi value observations ( see figure 2a ) . the most persistent cluster of contacts , forming an unstable network of tertiary interactions ( contact probability  0.20.3 ; involving 14 residues : 14 , 15 , 17 , 18 , 20 , 23 , 28 , 31 , 32 , 35 , 45 , 46 , 49 , 52 ) , belongs to the extended hydrophobic core identified in the phi value analysis ( except for r28 and w15 , for which phi values have not been estimated ) . the most persistent contacts were those between h1 and h2 with f14 , l18 , f31 , i32 , l35 playing a central role ( and all having high phi values ; see table 3 in ref ( 15 ) ) . the next group ( about 1/4 from the most persistent ) are h2h3 contacts , with l45 as the dominant h3 residue ( the highest phi value among the h3 residues : 0.6 ) interacting most notably with f31 and l35 ( also heavily involved in h1h2 contacts ) . the rest of the most persistent ones are individual contacts of turn 1 ( t1 ) with all of the helices and h1h3 contacts formed mostly by l18 , l45 and i13 , a49 , l52 ( moderate phi values ) . analyzing the secondary structure formation , the 3135 region of h2 is the best structured thanks to the stabilizing tertiary interactions ( see figure 2 ) , h3 does have some structure , and h1 is only weakly structured ( see also the average secondary structure content in table 1 ) . phi value analysis suggests a similar picture , although with a somewhat more stable h2 secondary structure and weaker h3 . interestingly , h3 early formation agrees with experimental measurements of isolated helices stability and the general picture emerging from the simulation studies.(16 ) recently , a very detailed computational study of bdpa , using a different coarse - grained model of protein folding , unres , has been published . the overall picture emerging from these studies is very similar to the findings of the present work . in particular , the identified set of residues responsible for nucleation of folding , the order of the secondary structure , and tertiary network formation are almost the same , despite qualitatively different philosophy and design of cabs and unres . unres is a continuous space model with its force field being physics - based ( in contrast to the knowledge - based potentials of cabs ) and classical molecular dynamics used in simulations . this provides yet additional justification of the applicability of knowledge - based models not only to structure prediction but also to the prediction of dynamics ( folding / assembly pathways ) of proteins . ( a ) averaged side - chain contact map ( with 7  cutoff ) of the bdpa nucleation core from bulk simulation at t = 3.0 ( below the diagonal ) . short - range contacts ( up to i , i+3 ) are omitted for clarity . native distance map ( above the diagonal ) is shown in gray scale , indicating pairwise distances . native helices and extended hydrophobic core residues in the tse , inferred from phi value analysis,(15 ) are marked at the borders of the map . ( b ) examples of bdpa tse structures ( percentages are explained in table 2 ) as compared to the native . the highest frequency of interconversions between native - like and denatured ensembles is observed for the small chaperonin ( see figure 3a ) . therefore , the small variant was chosen for more detailed analysis ( figure 3b , c ) . the time - averaged side - chain contact maps from the chaperonin and the bulk system were used to calculate difference contact maps ( see figure 3c ) . the most pronounced differences were observed at chaperonin maximum yields ( t = 2.62 ; 2.64 ; 2.66 ) and indicated the weakening of the folding nucleus , most significant in the key contacts between h2h3 ( l45 with f31 , l35 , the most distinct at t = 2.64 , and a49f31 ) together with individual contacts between h3 ( l52 , a49 ) and h1 ( i18 ) or t1 ( l20 ) . this suggests a chaperonin - induced shift toward a nucleus centered more on h1h2 than on h2h3 . ( a ) number of folding transitions between denatured and native - like ensembles , see also materials and methods , as a function of temperature . ( b ) the rmsd ( from native ) flowcharts at selected temperatures for small chaperonin and bulk systems . ( c ) difference contact maps ( below the diagonal ) show the weakening of folding nuclei by the chaperonin ( see the text ) . the maps were obtained by subtracting side - chain contact ( 7  cutoff ) frequencies from chaperonin and corresponding ( at the same temperature ) bulk system simulations ( preceded by the normalization over the number of tse snapshots ) and were shaded gray to show meaningful differences only . native distance maps ( above the diagonals ) are given for reference . to measure protein chain mobility , the autocorrelation function ( time - averaged mean - square displacement , msd ) was calculated as a function of time lapse and residue position in the sequence ( figure 4 ) according to the following formula : msd = g(t ) = (ri(t + t ) ri(t ) )  where ri(t ) are cartesian coordinates ( in angstroms ) of the ith side chain at time t , and  denotes averaging over a long trajectory . ( a ) illustration of the chaperonin cycle and the time frame used for measuring chain mobility . ( b ) profiles of the mean square displacement ( msd , measured in  ) for bdpa bulk and small chaperonin simulations calculated for all of the simulation snapshots . ( c ) comparison of residue mobility ( plotted as : 1  msd/300 ) with phi values measured for 0 and 2 m gdmcl ( denaturant ) concentration ( 10 ) . it means that on the microscopic level the experimental phi values measure not only the structural stability in the neighborhood of selected residues ( see the correlation of the high phi values with frequency of ternary contacts during the folding demonstrated in figure 2a ) but also the residues local mobility along the folding pathways . as demonstrated in figure 4c , where the mobility profiles are arbitrarily rescaled using a linear function , high phi values imply low mobility , and vice versa . mobility analysis shows that the chaperonin action significantly alters h1 and h3 ( with h3 being slightly more stable ) . thus , more efficient sampling of h1 and h3 around the folding nucleus center ( h2 ) occurs , and h2 remains the most stable region under the chaperonin disruption cycles . interestingly , the calculations of time - averaged secondary structure content show slight additional stabilization of h1 and h2 in the most expanded structures , as compared to bulk folding ( table 1 ) . according to the statistical mechanical model of folding analysis,(25 ) the bdpa nucleation process can proceed through many pathways , and most of them should pass through two distinct tses : centered at h1h2 or h2h3 ( ts1 and ts2 , respectively ) . moreover , the tses and pathways are sensitively dependent on temperature and denaturant concentration , which may be the key to resolving the inconsistency among simulation and experiment ( thus , comparing simulation and experiment , one has to ensure that they are conducted in the same conditions ) . the effect is a consequence of broken symmetry pathways in a nearly symmetrical protein : the ts1 interface involves a larger number of native interactions than that of ts2 , which makes ts1 more sensitive to weakening upon denaturant addition or temperature increase . itoh and sasai(25 ) showed that under physiological conditions , bdpa should fold through ts1 , while at high temperature and high denaturant concentration , pathways passing ts2s are more important . consequently , the prediction of phi values in the unfolding process for high denaturant concentration(25 ) showed higher values in h3 , low in h1 , and highest in h2 . contrary to the denaturing environment effect , the iam employed here leads to ts2 rather than ts1 pathway destabilization as compared to the bulk system , which is not surprising as the environmental conditions remain the same and ts1 involves more contacts . the changes are small , on the border of statistical significance , although the overall destabilization of the pathways involving either of the two transition states typical for the bulk folding is significant , as evidenced by the statistics given in column 2 of table 2 ( 31% pathways seen in the chaperonin - assisted folding simulations do not pass through any of the well - defined transition states of the bulk folding ) . the modulation is shown by the percentage of four kinds of tse structures for which ts1 and ts2 are well formed , or none of them , or ts1 only , or ts2 only . tse structures were parsed as ts1 or ts2 well - formed if the number of long - range side - chain contacts within ts1 or ts2 , native or non - native , was above an average from the entire simulation ( measured in the bulk and given temperature ) . the average number of contact threshold values were 9.3  3.1 * ( ts1 ) , 6.1  2.5 ( ts2 ) at t = 3.0 and 10.6  3.3 * ( ts1 ) , 6.4  2.5 ( ts2 ) at t = 2.82 ( * note that the ts1 threshold is much larger at lower temperature ) . gb1 is a 56 residue , / protein ( -helix tightly packed against four - stranded -sheet , pdb code : 2gb1 ) . recently , using the same ab initio modeling approach as here , we described its folding process in detail.(8 ) interestingly , the simulations clearly showed a subset of native interactions driving the nucleation condensation process from highly expanded conformations , with the observed folding nucleus perfectly matching the experimental data . as compared with the bulk system , simulations within the chaperonin - like protocol produced notably more - expanded structures with a higher level of size and compactness variability , similarly to bdpa ( see figure 1 ) . as in the case of bdpa , chaperonin - mediated iterative unfolding leads to gb1 destabilization and temperature decrease where the largest number of transitions is observed ( see figure 3 ) . because the frequency of transitions should be the largest near the folding temperature , this indicated a decrease of the folding temperature , evident also from the observed shift of the heat capacity peaks ( not displayed here ) . the result is contrary to the simulation of the confinement effect only for gb1 ( and other sps ) folding showing significant sp stabilization and increase in denaturation temperature.(28 ) as can be seen in figure 5 , the chaperonin action leads to a more diffuse and less cooperative transition as compared to the simulation in the bulk . the native and unfolded basins are less separated ( shallow near - native and unfolded basins ) during the chaperonin - assisted folding . distribution of structures according to their energy ( cabs model ) and rmsd values for the bulk system ( upper panel ) and small chaperonin ( lower panel ) . histograms were calculated at the same temperature ( 2.82 ) , for all simulation snapshots ( 10  000 ) , with bin sizes of 10 for energy and 0.25 for rmsd values . colors denote frequencies of occurrence from black ( 6.5  10 ) , through blue and red , to white ( 0 ) . the maximum number of transitions for the small spherical chaperonin type is almost twice as high as in the bulk , as in the bdpa case . as seen in trajectory fragments shown in figure 3b , gb1 two - state behavior is much less pronounced than for bdpa ( reflected also in a nearly 5-fold difference in the maximum number of transitions for the same simulation length ) . on the residue contact level , the most relevant difference between the bulk and the chaperonin system appears to be where the largest difference in transition yields occurs ( t = 2.64 ) . given the relevancy criteria , no difference is observed in other temperatures . as seen in figure 3c , chaperonin - mediated simulation differs almost exclusively in a smaller number of non - native 23 interactions ( being in the native at the edges of the 4-stranded  sheet ) together with a notable decrease in f30w43 contacts , belonging to the folding nucleus ( the same at t = 2.62 ) . going down with the relevancy cutoff ( applied in figure 3 ) , we observed an interesting feature at t = 2.62 : one of the largest drops in the contact number ( about 6% ) for f30w43 is accompanied by the largest increase ( about 3% ) for another folding nucleus contact , l5w30 ( together with other drops : notable in native - like 34 contacts , less significant in 23 , and minor increase for native - like 12 ) . in summary , the observed nucleation mechanism appears to be similar to that in the bulk , but the sequence of events in the nucleation process is less emphasized ; nucleus growth is more simultaneous . we also examined all of the structures with the least resemblance to the native , the misfolders ( see figure 6 ) . the misfolders from the bulk and the chaperonin system have similar secondary structure content ; however , some of the bulk are notably more compact , reaching an radius of gyration ( rg ) of the native structure ( 10.8  ) or even slightly smaller . most of those densely packed misfolders have secondary structure patterns similar to the native but with secondary structure elements assembled in non - native supersecondary configurations . plot of secondary structure content ( number of residues assigned as helices or strands ) in the most misfolded structures ( rmsd > 12 ) against their radii of gyration ( in  ) for the bulk simulations ( green  and example structures on the left ) and small chaperonin (  and example structures on the right ) , respectively . so far , the simulation studies of the iam suggested essentially the same mechanistic concept : binding to the hydrophobic walls of the open chaperonin helps to pull out kinetically trapped sps from their misfolded conformations.(2 ) we demonstrate that periodical disrupting can also have an effect on a folding pathway modulation toward the more efficient exploration of the folding landscape and avoiding the kinetic traps . the iterative relaxation of the tertiary structure together with stabilization of the preformed secondary structure elements results in the folding mechanism shifted from nucleation  condensation toward the framework . the shift of the folding mechanism manifests itself by a similar secondary structure content with and without a chaperonin effect ( see table 1 and figure 6 , confirmed also by rmsd of the native measurements of single bdpa helices ) accompanied by the chaperonin - induced increased volume of structures and significantly larger structural variability ( see figures 1 , 4 , and 6 ) . when taken at face value , the changes in the secondary structure alone suggest a slight shift toward the framework - like mechanism ( table 1 ) ; however , the small differences observed are statistically insignificant . our observations remain in agreement with recent experimental evidence on chaperonin bound sp structure and indicate an ensemble of compact and locally expanded states which lack stable tertiary interactions . framework and nucleation-condensation mechanisms of protein folding are extreme manifestations of an underlying common mechanism . the former is favored by a highly stable secondary structure , while the latter is the concomitant secondary and tertiary structure formation . a shift between the two extremes is not unusual upon condition changes or even by a single mutation . more generally , our results illustrate the power of the reduced protein models of interactions , motion , and chain representation employed . combining experiment and simulation has already become a powerful method for describing protein folding pathways(33 ) and atomic details involved in the dynamic processes of macromolecular machines.(34 ) the future of accessing most of the molecular machineries of life would require new tools combining all - atom and coarse - grained schemes .
the iterative annealing mechanism ( iam ) of chaperonin - assisted protein folding is explored in a framework of a well - established coarse - grained protein modeling tool , which enables the study of protein dynamics in a time - scale well beyond classical all - atom molecular mechanics . 
 the chaperonin mechanism of action is simulated for two paradigm systems of protein folding , b domain of protein a ( bdpa ) and b1 domain of protein g ( gb1 ) , and compared to chaperonin - free simulations presented here for bdpa and recently published for gb1 . 
 the prediction of the bdpa transition state ensemble ( tse ) is in perfect agreement with experimental findings . 
 it is shown that periodic distortion of the polypeptide chains by hydrophobic chaperonin interactions can promote rapid folding and leads to a decrease in folding temperature . 
 it is also demonstrated how chaperonin action prevents kinetically trapped conformations and modulates the observed folding mechanisms from nucleation  condensation to a more framework - like .