BACKGROUND
the central dogma of structural biology asserts that the aminoacid sequence has all the information needed for a protein to adopt a structure, and that structure determines function.
the connection between sequence and structure has centered a great amount of work and detailed theories of protein folding exist  <cit> , but still predicting structure or function from sequence is a extremely complex task except in cases of high sequence identity between the target protein and a well annotated homolog  <cit> .
there are many cases of non-homologous proteins sharing a given fold or function as well as proteins with reasonably similar sequences having quite different structures.
flexibility seems to play an important role in protein function, as in many cases movements are key for activity.
unfortunately, still less information exists on this connection between flexibility and function and, specifically, regarding the conformational changes that need to happen in a protein to perform its biological function  <cit> .
in the very same way as structures that are able to perform a specific function are conserved by evolution by not tolerating mutations that seriously modify that structure, it is plausible to think that mutations disrupting the flexibility pattern of a given protein are not going to be accepted either  <cit> .
inspection of structural databases such as scop  <cit> , cath  <cit>  or fssp  <cit>  shows the existence of superfamilies of proteins which display very similar folds and are evolutionary related.
analysis of these superfamilies allows us to determine the structural variation within a common fold  <cit> , thus defining the flexibility of that fold.
other works, using mostly coarse-grained models  <cit> , suggest that, at least for some proteins, the most important deformation modes are preserved within superfamilies, supporting the idea that structural flexibility patterns tend to be conserved.
however, these findings immediately raise a new question: are flexibility patterns conserved because if disrupted, the function would be lost, or instead, are they conserved because these are the ones better tolerant to change?
in more precise terms, the following two extreme scenarios, equally reasonable a priori, are possible:
i) if physical deformability is crucial to protein function, conformational changes introduced by sequence modifications will happen as orthogonal as possible to the physical deformation pattern.
ii) the physical deformation pattern traces movements that allow quite significant conformational changes without disruption of the function associated to a fold.
mutations leading to conformational changes along this pattern of flexibility are going to be better tolerated, as they won't affect the function.
this would suggest a good overlap between the physical space studied by md and the conformational space explored by the members of a superfamily.
following pioneering work by ortiz and others  <cit> , here we have performed a thorough comparison of the space of protein domain flexibility shown by the members of a cath superfamily  with the space of protein flexibility sampled by one reference member of the superfamily by molecular dynamics , aiming at investigating the potential overlap between both spaces and consequently, testing the possibility of using them in a combined way for applications that require protein deformation exploration.
the dataset used in this work includes  <dig> different superfamilies selected to cover all topologies, a good distribution of domain size and presenting enough number of non-redundant members.
a satisfactory reference domain to perform md was chosen for each superfamily based on having enough sequence percentage in the core of the alignment and providing good alignments to define such as core with at least  <dig> members .
the md-space was obtained using atomistic md simulations in explicit water  <cit>  and the sf-space was derived from alignment of experimental structures.
both ensembles were subjected to decomposition algorithms such as single value decomposition  and incremental singular value decomposition , to capture and compare the essential components of their spaces .
the use of isvd when treating the sf-space  <cit>  allowed us to consider regions only partially aligned within the members of the superfamily, consequently increasing the number of residues incorporated in the analysis.
our results show that the relative flexibility among domains of a given superfamily is restricted to just a few "directions of change" , which overlap only partially with the "directions of change" indicated by md .
for technical purposes, the conclusion is that both spaces can be combined to increase the dimensionality of the search space when performing any kind of computational-biology task that requires the exploration of possible protein deformations.
RESULTS
to study the relative size of the md- and sf-spaces, we computed their variance after matrix decomposition  by summing the squares of all the singular values .
we clearly observe that, in general, the sf-space of deformation is larger, having a variance between  <dig> and  <dig> times  bigger than the md-space.
these results do not seem to be influenced by the fact that the md-space is defined using many more structures than the sf-space, since the basic trend is kept when we restrict the calculations to a partial md-space  with just as many snapshots as experimental structures in the superfamily.
there are only  <dig> cases among the  <dig> superfamilies analyzed in which this pattern is, without any clear reason, different .
we have not found any apparent correlation between these three cases, neither structurally  nor functionally .
interestingly, we do not find any relationship between the variance of the md-space and the number of aminoacids of the domain, which can be explained considering that the factors producing more structural variability, such as flexible loops, are not affected by the size of a domain.
on the contrary, the variance of the sf-space increases with the number of aminoacids of the protein , which is reasonable given the linear relationship between protein length and possibilities of variation in composition through mutation.
as a consequence of this different behavior of variance versus size, a rough increase in the ratio between sf- and md-space variances with protein size is found , and the same incremental tendency is observed for the variance ratio plotted against the number of superfamily members .
again, a similar reasoning explains it: a greater size of the superfamily implies a parallel increase in the possibilities of sequence variation, while it does not affect the variance of the md-space.
quite surprisingly, we found that the sf-space is less complex  than the md one: i.e., it requires a smaller number of singular vectors to explain a given threshold  of the variance.
the difference in complexity  can be partly explained as a natural consequence of the fact that microstates that are accessible to md are not present among the experimentally resolved structures that form a superfamily.
however, when we calculate the complexity of mdp, we still see that it is larger than the complexity of sf-space , indicating that is a defined characteristic between the two spaces.
as expected, the unbalance in complexity between md- and sf-spaces generally decreases when the number of members in the superfamily increases .
however, we observe the existence of a threshold around 40– <dig> members after which the ratio of complexities remains approximately  <dig>  we interpret this fact as an indication that the superfamily has saturated its possibilities to gain complexity in the md-space with a reasonably small number of structures, in other words the "evolutionary" deformation space of the superfamily seems to be saturated rather quickly.
the other types of deformation movements present in the md trajectories seem physically possible, but they are not well populated within the experimental ensembles of the superfamilies, meaning that they have not been tolerated by evolution.
we employed a complementary way to analyze the ability of a superfamily to cover the md-space, determining the coverage of its domains on the essential md-space, the subspace defined by the first two md singular vectors .
the results in figure  <dig> show that the structures in the superfamilies do not cover well the essential md-space, with 70% of them showing  <dig>  coverage or lower, and a total average value of  <dig> .
the limited number of elements in the superfamilies is not responsible for this moderate coverage, since mdp covers 80% of the essential md-space.
finally, it is worth noting that larger number of elements in the superfamily does not lead to better absolute  or relative  coverage , confirming that larger superfamilies do not necessarily sample better than the smaller ones the physical deformation space.
to study the overlap between the sf- and md-spaces, we computed the hess metric employing as many vectors as members in the superfamily .
in the superfamilies studied in this work, the hess metric ranges from  <dig>  to  <dig> , with mean equal to  <dig>  .
the best overlaps are found for class α and β proteins, which are explained by their simple dynamics  or intrinsic rigidity  when compared to class α+β.
we found that the hess metric values are statistically significant and not due to simple chance  when the results are compared to a pure random background model.
large z-scores were also obtained when the background protein model is obtained by forcing the random trajectory to maintain covalent connectivity  and to avoid steric clashes.
we interpret this low, but statistically significant overlap of the sf- and md-spaces, as a proof that proteins sharing the same fold conserve at least some part of their physical deformability pattern in order to conserve function.
the rest of the deformations happening inside a superfamily by modification of the composition occur orthogonally to the deformations in the md-space.
putting together all the analysis commented above, we conclude that there appear to be many deformation patterns that are physically possible but are not explored within a superfamily and that the overlap between md- and sf-spaces is only partial.
the reasons for these findings could be related to the bias of the sf-space towards insertions, deletions, and changes of aminoacids leading to bigger deformations in the structure than the simple variation of the torsion angles explored in the physical space.
others reasons are probably related to the inability of the sf-space to explore movements that might challenge protein functionality.
the structural changes inside a superfamily can be severe in extension but are easily represented by a few essential movements.
we cannot completely rule out the possibility that when the structures of more members of a given superfamily were solved, the overlap between spaces increased, but according to our results it seems to be an inherent limit.
in summary, as suggested in the complexity analysis, the sf-space is quickly saturated.
after analyzing the global deformability patterns, we turned our attention to local residue flexibility.
we computed the b-factor  for each residue using the same data sources as before: the structural alignment of the superfamily members, and the md trajectory of a reference domain.
as expected from the previous global variance calculations, much larger b-factors are obtained from the superfamily data than from the md trajectory .
variations in sequence composition introduce dramatic local changes in a fold that would be difficult to obtain modifying the physical deformation pattern alone.
we, however, observe some cases of residues with b-factors derived from md larger than those obtained considering superfamily variation.
typically they correspond to regions involved in interactions with other macromolecules.
for example, the loops  of the anticodon-binding domain of methionyl-trna synthetase from thermus thermophilus  are very flexible in our md simulations performed in the absence of rna, but they are frozen in the biologically-relevant rna-bound form  <cit> .
similarly, the c-terminal region of germin from hordeum vulgare , required for dimer formation  <cit> , is exposed and flexible in the md trajectory of the monomer while in the dimer the contacts trap it.
taking into account local and global behavior together, we distinguish three groups among the  <dig> studied superfamilies:
i) superfamilies  showing poor overlap between sf- and md-spaces  and low correspondence between b-factor plots .
this group is largely enriched in enzymes of the α+β structural class.
we can expect that flexibility will be a crucial issue in these proteins and accordingly the deformation pattern should be very well preserved, which means that changes in the sf-space happen as orthogonal as possible to the functionally relevant md-space  <cit> .
ii) superfamilies with high number of members , good overlap of sf- and md-spaces  and relatively good correspondence between the b-factor plots .
here we find domains with structural or binding roles and fewer enzymes, with preference for α and β motives.
in this group the superfamilies have been able to explore many physically-available deformation modes of the md-space which do not interfere with function.
iii) superfamilies with low number of members , some overlap in the deformation spaces  and poor correspondence between b-factor plots .
this group shows diverse families both in structural and functional terms.
the physical deformability space has been explored to a little extent, but the residues that are not essential for function introduce large local structural changes reflected in poor b-factor correspondence.
CONCLUSIONS
our technical analysis comparing the spaces of structural variation within superfamilies  and along atomistic md simulations  sheds light on the connection between physical flexibility and conformational variation with compositional change in the aminoacid sequence.
the overall picture showed a more complex scenario than we originally thought, in part due to the fact that we are comparing a set of different structures in a sf with the md of just one of them.
first, we have observed that when the sequence of a protein changes to become another member of the superfamily, the change is produced following a way that does not completely overlap with that expected from the intrinsic physical deformability of the protein, which suggests that functional restriction limits the access to some flexibility patterns to evolution.
this effect is especially clear for enzymes, where there is the worst overlap between sf- and md-spaces.
second, our analysis shows that conformational changes resulting from sequence variation tend to be larger and much simpler than those allowed by individual physical flexibility.
interestingly, the threshold for achieving the maximum overlap between the sf and md-spaces seems to be situated around  <dig> superfamily members , suggesting some saturation in the deformation along the superfamily when compared to the physical space.
md and sf spaces are comparable, but they also have important differences, and some words of caution are necessary.
since superfamily members vary in sequence, in some cases quite dramatically, and they will be expected to have different structures, while md simulation samples the flexibility of a single sequence, it is not surprising that md does not explain instances where there are specific chemical interactions.
the strength of our analysis relies in its interesting methodological implications.
as the deformation spaces have different size and complexity and do not fully overlap, they can be considered as complementary.
flexibility analysis derived from the study of the structural variation along superfamilies can provide easy to manage and useful descriptions  <cit> , although they will have a limit in the physical complexity that they can describe.
in much the same way, physical descriptions of isolated domains without considering their possible interactions have a limited capability to predict their flexibility in the context of protein-protein complexes, and variation along domains in a superfamily is a good way of obtaining that information.
in other words, taking together sf and md spaces we enrich our view on the conformational freedom of proteins.
this is expected to be of especial interest in the areas of 3d-em/x-ray hybrid models or ab initio protein folding, where the exploration of the physical conformational space exclusively with high dimensionality methods such as molecular dynamics or normal mode analysis could be over-conservative.
we suggest that the use of the most important singular vectors of the sf-space  will provide a complementary deformation space that can be very useful in sampling  <cit> , since it will attract to the common fold quite distant structures.
a combination of both spaces in a sequential way can help to improve these areas of protein structure prediction.

 the central dogma of structural biology asserts that the aminoacid sequence has all the information needed for a protein to adopt a structure, and that structure determines function. the connection between sequence and structure has centered a great amount of work and detailed theories of protein folding exist, but still predicting structure or function from sequence is a extremely complex task except in cases of high sequence identity between the target protein and a well annotated homolog. there are many cases of non-homologous proteins sharing a given fold or function as well as proteins with reasonably similar sequences having quite different structures. flexibility seems to play an important role in protein function, as in many cases movements are key for activity. unfortunately, still less information exists on this connection between flexibility and function and, specifically, regarding the conformational changes that need to happen in a protein to perform its biological function. in the very same way as structures that are able to perform a specific function are conserved by evolution by not tolerating mutations that seriously modify that structure, it is plausible to think that mutations disrupting the flexibility pattern of a given protein are not going to be accepted either. inspection of structural databases such as scop, cath or fssp shows the existence of superfamilies of proteins which display very similar folds and are evolutionary related. analysis of these superfamilies allows us to determine the structural variation within a common fold, thus defining the flexibility of that fold. other works, using mostly coarse-grained models, suggest that, at least for some proteins, the most important deformation modes are preserved within superfamilies, supporting the idea that structural flexibility patterns tend to be conserved. however, these findings immediately raise a new question: are flexibility patterns conserved because if disrupted, the function would be lost, or instead, are they conserved because these are the ones better tolerant to change? in more precise terms, the following two extreme scenarios, equally reasonable a priori, are possible: i) if physical deformability is crucial to protein function, conformational changes introduced by sequence modifications will happen as orthogonal as possible to the physical deformation pattern. ii) the physical deformation pattern traces movements that allow quite significant conformational changes without disruption of the function associated to a fold. mutations leading to conformational changes along this pattern of flexibility are going to be better tolerated, as they won't affect the function. this would suggest a good overlap between the physical space studied by md and the conformational space explored by the members of a superfamily. following pioneering work by ortiz and others, here we have performed a thorough comparison of the space of protein domain flexibility shown by the members of a cath superfamily with the space of protein flexibility sampled by one reference member of the superfamily by molecular dynamics, aiming at investigating the potential overlap between both spaces and consequently, testing the possibility of using them in a combined way for applications that require protein deformation exploration. the dataset used in this work includes different superfamilies selected to cover all topologies, a good distribution of domain size and presenting enough number of non-redundant members. a satisfactory reference domain to perform md was chosen for each superfamily based on having enough sequence percentage in the core of the alignment and providing good alignments to define such as core with at least members. the md-space was obtained using atomistic md simulations in explicit water and the sf-space was derived from alignment of experimental structures. both ensembles were subjected to decomposition algorithms such as single value decomposition and incremental singular value decomposition, to capture and compare the essential components of their spaces. the use of isvd when treating the sf-space allowed us to consider regions only partially aligned within the members of the superfamily, consequently increasing the number of residues incorporated in the analysis. our results show that the relative flexibility among domains of a given superfamily is restricted to just a few "directions of change", which overlap only partially with the "directions of change" indicated by md. for technical purposes, the conclusion is that both spaces can be combined to increase the dimensionality of the search space when performing any kind of computational-biology task that requires the exploration of possible protein deformations.  to study the relative size of the md- and sf-spaces, we computed their variance after matrix decomposition by summing the squares of all the singular values. we clearly observe that, in general, the sf-space of deformation is larger, having a variance between and times bigger than the md-space. these results do not seem to be influenced by the fact that the md-space is defined using many more structures than the sf-space, since the basic trend is kept when we restrict the calculations to a partial md-space with just as many snapshots as experimental structures in the superfamily. there are only cases among the superfamilies analyzed in which this pattern is, without any clear reason, different. we have not found any apparent correlation between these three cases, neither structurally nor functionally. interestingly, we do not find any relationship between the variance of the md-space and the number of aminoacids of the domain, which can be explained considering that the factors producing more structural variability, such as flexible loops, are not affected by the size of a domain. on the contrary, the variance of the sf-space increases with the number of aminoacids of the protein, which is reasonable given the linear relationship between protein length and possibilities of variation in composition through mutation. as a consequence of this different behavior of variance versus size, a rough increase in the ratio between sf- and md-space variances with protein size is found, and the same incremental tendency is observed for the variance ratio plotted against the number of superfamily members. again, a similar reasoning explains it: a greater size of the superfamily implies a parallel increase in the possibilities of sequence variation, while it does not affect the variance of the md-space. quite surprisingly, we found that the sf-space is less complex than the md one: i.e., it requires a smaller number of singular vectors to explain a given threshold of the variance. the difference in complexity can be partly explained as a natural consequence of the fact that microstates that are accessible to md are not present among the experimentally resolved structures that form a superfamily. however, when we calculate the complexity of mdp, we still see that it is larger than the complexity of sf-space, indicating that is a defined characteristic between the two spaces. as expected, the unbalance in complexity between md- and sf-spaces generally decreases when the number of members in the superfamily increases. however, we observe the existence of a threshold around 40– members after which the ratio of complexities remains approximately we interpret this fact as an indication that the superfamily has saturated its possibilities to gain complexity in the md-space with a reasonably small number of structures, in other words the "evolutionary" deformation space of the superfamily seems to be saturated rather quickly. the other types of deformation movements present in the md trajectories seem physically possible, but they are not well populated within the experimental ensembles of the superfamilies, meaning that they have not been tolerated by evolution. we employed a complementary way to analyze the ability of a superfamily to cover the md-space, determining the coverage of its domains on the essential md-space, the subspace defined by the first two md singular vectors. the results in figure show that the structures in the superfamilies do not cover well the essential md-space, with 70% of them showing coverage or lower, and a total average value of. the limited number of elements in the superfamilies is not responsible for this moderate coverage, since mdp covers 80% of the essential md-space. finally, it is worth noting that larger number of elements in the superfamily does not lead to better absolute or relative coverage, confirming that larger superfamilies do not necessarily sample better than the smaller ones the physical deformation space. to study the overlap between the sf- and md-spaces, we computed the hess metric employing as many vectors as members in the superfamily. in the superfamilies studied in this work, the hess metric ranges from to, with mean equal to. the best overlaps are found for class α and β proteins, which are explained by their simple dynamics or intrinsic rigidity when compared to class α+β. we found that the hess metric values are statistically significant and not due to simple chance when the results are compared to a pure random background model. large z-scores were also obtained when the background protein model is obtained by forcing the random trajectory to maintain covalent connectivity and to avoid steric clashes. we interpret this low, but statistically significant overlap of the sf- and md-spaces, as a proof that proteins sharing the same fold conserve at least some part of their physical deformability pattern in order to conserve function. the rest of the deformations happening inside a superfamily by modification of the composition occur orthogonally to the deformations in the md-space. putting together all the analysis commented above, we conclude that there appear to be many deformation patterns that are physically possible but are not explored within a superfamily and that the overlap between md- and sf-spaces is only partial. the reasons for these findings could be related to the bias of the sf-space towards insertions, deletions, and changes of aminoacids leading to bigger deformations in the structure than the simple variation of the torsion angles explored in the physical space. others reasons are probably related to the inability of the sf-space to explore movements that might challenge protein functionality. the structural changes inside a superfamily can be severe in extension but are easily represented by a few essential movements. we cannot completely rule out the possibility that when the structures of more members of a given superfamily were solved, the overlap between spaces increased, but according to our results it seems to be an inherent limit. in summary, as suggested in the complexity analysis, the sf-space is quickly saturated. after analyzing the global deformability patterns, we turned our attention to local residue flexibility. we computed the b-factor for each residue using the same data sources as before: the structural alignment of the superfamily members, and the md trajectory of a reference domain. as expected from the previous global variance calculations, much larger b-factors are obtained from the superfamily data than from the md trajectory. variations in sequence composition introduce dramatic local changes in a fold that would be difficult to obtain modifying the physical deformation pattern alone. we, however, observe some cases of residues with b-factors derived from md larger than those obtained considering superfamily variation. typically they correspond to regions involved in interactions with other macromolecules. for example, the loops of the anticodon-binding domain of methionyl-trna synthetase from thermus thermophilus are very flexible in our md simulations performed in the absence of rna, but they are frozen in the biologically-relevant rna-bound form. similarly, the c-terminal region of germin from hordeum vulgare, required for dimer formation, is exposed and flexible in the md trajectory of the monomer while in the dimer the contacts trap it. taking into account local and global behavior together, we distinguish three groups among the studied superfamilies: i) superfamilies showing poor overlap between sf- and md-spaces and low correspondence between b-factor plots. this group is largely enriched in enzymes of the α+β structural class. we can expect that flexibility will be a crucial issue in these proteins and accordingly the deformation pattern should be very well preserved, which means that changes in the sf-space happen as orthogonal as possible to the functionally relevant md-space. ii) superfamilies with high number of members, good overlap of sf- and md-spaces and relatively good correspondence between the b-factor plots. here we find domains with structural or binding roles and fewer enzymes, with preference for α and β motives. in this group the superfamilies have been able to explore many physically-available deformation modes of the md-space which do not interfere with function. iii) superfamilies with low number of members, some overlap in the deformation spaces and poor correspondence between b-factor plots. this group shows diverse families both in structural and functional terms. the physical deformability space has been explored to a little extent, but the residues that are not essential for function introduce large local structural changes reflected in poor b-factor correspondence.  our technical analysis comparing the spaces of structural variation within superfamilies and along atomistic md simulations sheds light on the connection between physical flexibility and conformational variation with compositional change in the aminoacid sequence. the overall picture showed a more complex scenario than we originally thought, in part due to the fact that we are comparing a set of different structures in a sf with the md of just one of them. first, we have observed that when the sequence of a protein changes to become another member of the superfamily, the change is produced following a way that does not completely overlap with that expected from the intrinsic physical deformability of the protein, which suggests that functional restriction limits the access to some flexibility patterns to evolution. this effect is especially clear for enzymes, where there is the worst overlap between sf- and md-spaces. second, our analysis shows that conformational changes resulting from sequence variation tend to be larger and much simpler than those allowed by individual physical flexibility. interestingly, the threshold for achieving the maximum overlap between the sf and md-spaces seems to be situated around superfamily members, suggesting some saturation in the deformation along the superfamily when compared to the physical space. md and sf spaces are comparable, but they also have important differences, and some words of caution are necessary. since superfamily members vary in sequence, in some cases quite dramatically, and they will be expected to have different structures, while md simulation samples the flexibility of a single sequence, it is not surprising that md does not explain instances where there are specific chemical interactions. the strength of our analysis relies in its interesting methodological implications. as the deformation spaces have different size and complexity and do not fully overlap, they can be considered as complementary. flexibility analysis derived from the study of the structural variation along superfamilies can provide easy to manage and useful descriptions, although they will have a limit in the physical complexity that they can describe. in much the same way, physical descriptions of isolated domains without considering their possible interactions have a limited capability to predict their flexibility in the context of protein-protein complexes, and variation along domains in a superfamily is a good way of obtaining that information. in other words, taking together sf and md spaces we enrich our view on the conformational freedom of proteins. this is expected to be of especial interest in the areas of 3d-em/x-ray hybrid models or ab initio protein folding, where the exploration of the physical conformational space exclusively with high dimensionality methods such as molecular dynamics or normal mode analysis could be over-conservative. we suggest that the use of the most important singular vectors of the sf-space will provide a complementary deformation space that can be very useful in sampling, since it will attract to the common fold quite distant structures. a combination of both spaces in a sequential way can help to improve these areas of protein structure prediction. 
second, that conformational changes from variation in a superfamily are larger and much simpler than those allowed by physical deformability. in this contribution we have compared two different approaches to explore the flexibility space of protein domains: i) molecular dynamics, and ii) the study of the structural changes within superfamily. we expect this fact to have application in fields as 3d-em/x-ray hybrid models or ab initio protein folding. first, that function restricts the access to some flexibility patterns to evolution, as we observe that when a superfamily member changes to become another, the path does not completely overlap with the physical deformability. methodologically, the conclusion is that both spaces studied are complementary, and have different size and complexity. technically, protein flexibility exploration is an essential task in many applications, such as protein structure prediction and modeling. our analysis indicates that the md-space and the sf-space display a significant overlap, but are still different enough to be considered as complementary.
 it is well known the strong relationship between protein structure and flexibility, on one hand, and biological protein function, on the other hand. technically, protein flexibility exploration is an essential task in many applications, such as protein structure prediction and modeling. in this contribution we have compared two different approaches to explore the flexibility space of protein domains: i) molecular dynamics, and ii) the study of the structural changes within superfamily.  our analysis indicates that the md-space and the sf-space display a significant overlap, but are still different enough to be considered as complementary. the sf-space space is wider but less complex than the md-space, irrespective of the number of members in the superfamily. also, the sf-space does not sample all possibilities offered by the md-space, but often introduces very large changes along just a few deformation modes, whose number tend to a plateau as the number of related folds in the superfamily increases.  theoretically, we obtained two conclusions. first, that function restricts the access to some flexibility patterns to evolution, as we observe that when a superfamily member changes to become another, the path does not completely overlap with the physical deformability. second, that conformational changes from variation in a superfamily are larger and much simpler than those allowed by physical deformability. methodologically, the conclusion is that both spaces studied are complementary, and have different size and complexity. we expect this fact to have application in fields as 3d-em/x-ray hybrid models or ab initio protein folding. 