BSDB: the biomolecule stretching database

Abstract

We describe the Biomolecule Stretching Data Base that has been recently set up at http://www.ifpan.edu.pl/BSDB/. It provides information about mechanostability of proteins. Its core is based on simulations of stretching of 17 134 proteins within a structure-based model. The primary information is about the heights of the maximal force peaks, the force–displacement patterns, and the sequencing of the contact-rupturing events. We also summarize the possible types of the mechanical clamps, i.e. the motifs which are responsible for a protein's resistance to stretching.

INTRODUCTION

Despite more than a decade of experiments on single biomolecule manipulation, mechanical properties of only several scores of proteins have been measured. A characteristic scale of the force of resistance to stretching, F_max, has been found to range between ∼10 and 480 pN. The Biomolecule Stretching Data Base (BSDB) described here provides information about expected values of F_max for, currently, 17 134 proteins. The values and other characteristics of the unfolding process, including the nature of identified mechanical clamps, are available at http://www.ifpan.edu.pl/BSDB/. They have been obtained through simulations within a structure-based model which correlates satisfactorily with the available experimental data on stretching. BSDB also lists experimental data and results of the existing all atom simulations. It is intended to be updated internally, through users input, and by making requests for needed calculations. The database offers a Protein-Data-Bank-wide guide to mechano-stability of proteins.

Functioning of a biological cell involves conversion of chemical energy into conformational changes of proteins, nucleic acids and their complexes. Understanding of mechanical processes in the cell requires information about mechanical properties of the constituting biomolecules. One way to obtain it is through single-molecule manipulation such as stretching by a tip of an atomic force microscope (1,2). The scope of such studies is very limited compared to the number of the kinds of the molecules that are present in the cell. There is then a need to have estimates of mechanical parameters for a much larger set of molecules. These estimates are necessary to provide guidance when selecting targets for experimental studies and when making theoretical models.

Recently, we have provided such estimates for 17 134 proteins (3) by performing molecular dynamics simulations within a coarse-grained, structure-based model. We have considered all proteins comprising up to 250 amino acids and having structures deposited in the Protein Data Bank (PDB) (4). The cutoff size well exceeds a typical single domain size which is of order 100–150 residues. This data set includes also proteins with knots of type 3₁ and one slipknotted protein (5,6). Reference (3) presents a summary of the results and lists proteins with particularly large values of F_max. One of these proteins, scaffoldin c7A with the PDB structure code 1aoh, has been confirmed experimentally to be highly resistant to stretching. Its measured is equal to 480 pN (7). Here, we describe the Biomolecule Stretching Database (BSDB) in which results for all studied proteins are deposited. Initially, it is based on the results derived for ref. (3) but it is intended to grow. A synthetic discussion of the results is contained in (3). It includes presenting probability distributions of the values of F_max for the whole set and for various structural categories of proteins. In particular, it identifies categories which are likely to yield large forces. It also discusses the nature of possible mechanical clamps—structural regions which generate the most significant resistance to stretching. Usually, resistance arises through shear between parallel or antiparallel β-strands (8–10). However, it should attain its top strength if formation of the cysteine slipknot motif is operational dynamically (3). This novel mechanism of strength has been discovered as a result of making the PDB-wide survey. It involves pulling a piece of the backbone through a cysteine knot as explained in the Discussion section where we also provide classification of all types of mechanical clamps found so far.

MATERIALS AND METHODS

The theoretical model used in the survey

An input to structure-based models of proteins comes from the PDB. Such models are defined by requirement that the ground state of the system coincides with the native structure. They usually come with an implicit solvent and are coarse-grained. The simplest choice is to represent residues by C^α atoms. There is no unique prescription for a good structure-based model. A total of 62 possible variants have been analyzed in (11). Their mechanical and folding properties differ substantially. Several of them are optimal and we use the simplest of them as described in references (10,12–14).

An attractive native contact between C^α atoms in residues i and j (at distance r_ij) is declared to arise if van der Waals spheres (enlarged to account for attraction) associated with the heavy atoms overlap (15). Non-native contacts are considered repulsive. In the first survey (10), all native contacts were included in the energy function. Here, we remove the i, i + 2 contacts as they are usually dispersive and weak (16).

The potential energy of the system of N amino acids is given by . The harmonic tethers consecutive beads at the equilibrium bond length and k = 100 ε/Å⁻², where ε is defined below. A similar potential is used to describe the disulphide bonds. The native contacts are described by the Lennard-Jones potentials with the uniform energy parameter ε:

(1)

The length parameters, σ_ij, are selected so that the minima of the potentials agree with the native distances between the C^α atoms in the contact. V^NON, the potential in the non-native contacts, is similar to V^NON but it has purely repulsive terms.

The model also contains a four-body chirality term that favors the native sense of chirality (17), where and C_i^NAT is the chirality of residue i in the native conformation and κ = 1. Here, . A positive C_i corresponds to right-handed chirality. V^CHIR favors native values of the dihedral angles (11). The model considered here has similar properties (18) to the model with the 10–12 contact potentials of Clementi et al. (19).

In our stretching simulations, both termini are attached to harmonic springs of elastic constant k = 0.12ε/Å. The choice of k affects mostly the location of the force peaks. One end of the spring is pulled at a constant speed, v_p, along the initial end-to-end position vector. We consider v_p = 0.005 Å/τ, where τ is of order 1 ns since this is a characteristic time to cover a typical distance of 5 Å through diffusion in the implicit solvent. The experimental results are obtained at various speeds that are all at least two orders of magnitude slower (<10⁴ nm/s). Using one speed for all proteins facilitates making comparisons. We monitor F as a function of d and record F_max.

The value of ε should be within 800–2300 K since it averages over of all non-covalent interactions in proteins. Our previous simulations of folding (13,20) were optimal with the dimensionless temperature of order 0.3 which corresponds to room temperature if ε is ∼900 K (k_B is the Boltzmann constant and T is temperature). Our simulations are performed at . Our latest estimate of ε is about 110 pNÅ or 1.5 kcal/mole (3).

Thermal fluctuations are introduced by random Gaussian forces together with a velocity dependent damping. This noise mimics the random effects of the solvent and provides thermostating. The equation of motion for each C^α reads where F_C is the net force due to the molecular potentials. The damping constant Γ is taken to be equal to 2m/τ and the dispersion of the random forces is equal to . This choice of Γ corresponds to a situation in which the inertial effects are negligible (13) but the damping action is not yet as strong as in water. Larger values of γ have only a minor effect on the F–d curves. The equations of motion are solved by a fifth order Gear predictor-corrector scheme (21). Due to the overdamping, our results are equivalent to those obtained by the Brownian dynamics algorithm (22). The F–d curves are averaged over a pulling distance of 0.5 Å.

Proteins with non-trivial topology

The BSDB includes proteins with knots which were recognized by the KMT algorithm (23) as implemented in (24,25). These proteins were stretched to a maximal distance defined as the end-to-end distance along the backbone from which the sequential size of the maximally tightened knot (of order 12 residues for the trefoil knot) is subtracted. Currently, the BSDB does not include other types of knots since the corresponding proteins contain more than the cutoff value of 250 residues. BSDB includes one slip knotted protein which was recognized by the technique described in (26).

The force peak recognition

An automated detection of F_max poses difficulties due to existence of fluctuations and a need to discard the final indefinite growth in F when the resistance to pulling is provided only by the unbreakable couplings. There is no absolute prescription as to when it starts. The strongest proteins often give rise to isolated force peaks on such ‘final’ slopes. In our procedure, a trajectory is split into 100 parts in which we determine the maximum and time averaged values of F. The maximum arises in the l’th partition provided . The value of F_max is then read off as in this partition. Mistaken calls are due to large fluctuations in the final ascent and they occur with a probability of ∼1%. Thus peaks signaled as arising toward the end of the process are examined separately. If no isolated force peak is detected, F_max is declared to be 0.

For each molecule, at least two trajectories have been studied to get a measure of errors. If the two trajectories are significantly distinct, the statistics is raised to 10 trajectories to identify various pathways (e.g. for 1qu0). The F_max specified in the data base is then given by the weighted average over the pathways. The experimentally studied 1aoh has small pieces of its contact map incomplete (due to missing locations of some atoms in the side chains). This contact map was completed (7) by calculating the C^α – C^α distances in the affected regions and accepting distances smaller that 7.5 Å as corresponding to the missing native contacts.

RESULTS

Stretching protocol

The stretching protocol used in the survey involves anchoring one terminus to an immobile substrate and pulling another terminus by an elastic spring which moves at a constant speed. There is a huge number of other possibilities to choose pairs of amino acids as attachment points. Some of the available experimental data correspond to such non-terminal manipulation. This fact has been taken into account when comparing experimental to theoretical values of F_max to relate the effective unit of the calculated force to measurements. This unit is equal to ε/Å, where the energy parameter ε denotes the depth of the attractive potential well in native contacts between the C^α atoms. We estimate ε/Å to be equal to 110 ± 30 pN (3). The estimation procedure involves making extrapolations to the experimental pulling speeds used. The existing studies (9,27–32) indicate that it is only for protein GFP (33) that non-terminal pulling may result in a larger F_max than the terminal pulling. It is thus expected that the values of F_max provided by the BSDB are usually the upper bounds for the various choices of the manipulation. The data for non-terminal pulling can be calculated upon request.

The BSDB also provides other information about stretching. In particular, it displays two calculated force, F, versus displacement, d, curves. If the two curves display noticeable differences then at least two distinct unfolding pathways are possible. The corresponding values of F_max usually do not differ much. Larger statistics of trajectories were obtained only for a small number of proteins. The F – d curves can be used, for example, to identify mechanically stable intermediates along the unfolding pathway. These intermediates correspond to the force peaks and the associated conformations can be determined upon request. It has been shown (34) that such intermediates in FN-III are responsible for exposure of cryptic binding sites that allow for fibrillogenesis.

The BSDB also presents findings obtained through literature search. Specifically, it lists available experimental data on F_max, together with the pulling speed used, and theoretical results that have been obtained by other methods, especially by all-atom simulations. It should be emphasized, however, that the literature data refer only to several tens of proteins.

Selection of structures from the PDB

PDB entries include proteins, nucleic acids, carbohydrates, and their complexes. We have downloaded all 54 807 structures that were available on 17 December 2008 by establishing a local mirror of the ftp://ftp.rcsb.org/pdb/ site and utilizing GNU wget program with an option preserving the database tree structure. We have restricted the survey to proteins of not more than 250 amino acids. We have used a script that eliminates entries containing words like DNA DUPLEX, RIBOSYME, OLIGONUCLEOTIDE, etc. in their HEADER and TITLE sections. Other keywords are detailed in the Database description presented online. However, special attention has been paid to files containing keywords like DNA as they may still refer to proteins, like the DNA ribonuclease.

Despite the thorough validation of structures in the PDB, not all structure files are readily available for molecular dynamics simulations, as they may have either missing residues or insufficiently resolved segments. Generally, such gap containing structures have been eliminated from our studies. We have also rejected structures in which some distances between consecutive C^α atoms are outside of the (3.6–3.95) Å range. This rule does not apply if one of the amino acids is proline as the corresponding distances fall then in the range (2.8–3.85) Å. In case of proteins that occur in multimeric or multi-protein complexes, we examine only the first chain and neglect any disulphide bridges to other units. We do not eliminate structures with artificial or modified amino acids. If there are multiple structures assigned to a protein (especially for structures determined through NMR), we take the first one. If there are alternative local placements, we take the first one if the distances between the C^α atoms are proper, otherwise we try the alternative. However, we reject files with ambiguous definitions of alternative local placements.

The disulfide bonds in our model cannot break and thus behave differently than contacts due to hydrogen bonds or ionic bridges. We detect such bonds using the information contained in the ‘SSBOND’ section of the PDB file.

Databases used in BSDB

The BSDB relates to four external databases: PDB (4), CATH (35), SCOP (36) and Gene Ontology database (37). The first of these is the source of structures for which the calculations were made. The next two assign a symbol of structure classification to a protein. The assignment based on CATH is algorithmic whereas the one on SCOP relies on human judgment. The fourth database provides description of biological function. The very strongest protein is currently predicted to be the extracellular bone morphogenic protein 1 bmp for which F_max could be around 1 nN. Its mechanical clamp is that of the cysteine slipknot. It should be noted that there is a website, www.p-found.org, which allows for making and depositing all-atom simulation of protein stretching (38).

The Structural Classification of Proteins (SCOP) (36), accessible at http://scop.mrc-lmb.cam.ac.uk/scop, is a hierarchical scheme that classifies proteins according to features that relate to both structural and sequential features. The scheme is accessible either by name of a hierarchical level (Domain, Family, etc.), or it's ascension number (39) in the form of [a–k].xx.yy.zz where a–k stands for class of proteins, and xx, yy, zz for lower levels of hierarchy. The numbers are not immutable and change between releases of the SCOP, thus they are presented along with the corresponding names.

The Class, Architecture, Topology, Homology (CATH) (35,14) scheme is also hierarchical, but it considers four classes (α, β, α–β and no-structure). Each entry in our database is presented with the corresponding ascension number and name.

One should note, that a given PDB code may come with none, one or more SCOP or CATH entries, since a protein may be unclassified or contain two or more domains. When studying correlations between the dynamics and structure, we use classified structures and take the first assignment. In the 1.73 version of SCOP (11), there are 92 972 entries that relate to 34 495 pdb structures. These entries are divided into 3464 families, 1777 superfamilies and 1086 unique folds. The 3.2 version of CATH contains 114 215 domains, 2178 homologous superfamilies and 1110-fold groups (12).

Information provided

The structure-based data are presented in four lists: one ranked by the value of F_max, another by the number of amino acids in the structure, the remaining two by the structure classification codes that come with the CATH and SCOP schemes. One can also access the results by providing the PDB code of a protein. An example of data available for a given protein is shown in Figure 1 for the scaffoldin 1aoh. They start with the chain used, value of F_max in ε/Å together with the corresponding standard deviation, ΔF_max, based on several trajectories, and the value of F_max converted to pN. They also specify value of the tip displacement, D_max, at which the maximal peak force arises for v_p = 0.005 Å/τ, where τ is of order 1 ns, and the corresponding end-to-end distance, L_max. The force peak position is also described in terms of the dimensionless parameter λ defined as (L_max − L_n)/(L_f − L_n), where L_n is the native end-to-end distance and L_f is the full backbone length. Small values of λ indicate that the force peak arises at the beginning of the pulling process. L_f is close to the end-to-end distance at full extension only provided there are no disulphide bridges that require significantly larger forces to get ruptured. The number of the disulphide bridges is given by the parameter nSS. In this example, there are no such bridges.

Figure 1.

Example of a screenshot from the BSDB for protein 1aoh.

The entry also specifies the related structure codes and corresponding names, if available, and all GO numbers that specify molecular function, biological process, and cellular component. In addition, it shows examples of two stretching trajectories in the F–d plots. Such plots indicate whether the force peaks are multiple or not. The arrow locates the displacement at which the biggest force maximum arises.

A simultaneous display of data for several proteins is implemented through the ‘add this protein to compare’ hyperlink and then using ‘compare’. It allows for an analysis of data with a common characteristic such as the system size, the value of F_max or function. The F–d curves for the selected proteins are displayed in a column, where they can be inspected visually. Results can be sorted according to various properties, for example by the CATH or SCOP number. In this way, the user can inspect changes in extension curves within the same family, or between proteins with relatively low homology, allowing one to correlate the peak pattern with a degree of relationship.

An important feature of the BSDB is that it provides information about the microscopic nature of the unravelling process. It is contained in the so called scenario diagrams (14) which specify the pulling distances at which particular native contacts are seen as operational for the last time (i.e. distances between amino acids i and j do not exceed a threshold value). For each protein, the BSDB gives a listing of the breaking distances, d_u, for each native contact. A scenario diagram can be obtained if |j − i| is plotted against d_u as in (14). We provide examples of such diagrams for 1aoh (one of the strongest proteins) and 1j85 (a protein with a knot).

We provide hyperlinks to several other databases, such as CSU (16), that facilitate understanding of contacts and of identification of secondary structures to interpret the scenario diagrams.

DISCUSSION

The information contained in the scenario diagrams can be used to determine the nature of the relevant mechanical clamp. Accumulation of rupture events around a specific value of d_u signifies occurrence of a force peak. Some of the rupture events belonging to a peak are crucial dynamically—removal of the corresponding contacts reduces F_max significantly. Such contacts identify the mechanical clamp. The remaining rupture events are just concurrent. It is hard to identify the mechanical clamps in an automated way since one needs to determine structurally relevant groups of contacts and then redo the simulation with various groups removed. We have accomplished this task for selected proteins, including the 64 strongest (results are listed in BSDB). Taking it together with discussions in the literature we can identify typical motifs which are associated with mechanical clamps. We divide these motifs into two groups: (i) involving strain in localized regions and (ii) involving a larger motion of a loop or two loops that are made of segments of the backbone.

Figure 2 shows examples of mechanical clamps belonging to the first group. The β-strands are indicated as black arrows in the figure. The simplest motifs are denoted by S, SA and Z. The first of these corresponds to shearing between parallel β-strands, similar to what takes place in a stretched titin (8,9). The longer the strand, the bigger the number of bonds that are sheared simultaneously and then the bigger the value of F_max. It should be noted that F_max is also affected by the direction of the stretching force relative to the orientation of the clamp. The second of these corresponds to shearing between antiparallel strands (10). For a given length of the strand, SA yields a smaller F_max than S. The third motif is a zipper (40) which is the most fragile of them all since the contacts get ruptured one at a time. The elementary motifs S and Z can also arise with helices (in which case the arrows in Figure 2 would represent helices) but the corresponding values of F_max then are expected to be smaller than for the β strands of a similar length. Another possibility is U—an unstructured clamp seen in 1qp1 and 1tum (10). It is similar to S except that two nearby β-strands are replaced by unstructured segments of the backbone (non-typical strands).

Figure 2.

Mechanical clamps involving shear or zipping in localized regions. Except for the zipper motif, all other motifs involve shear between secondary structures. The black arrows indicate β-strands. More generically, however, they may also depict α-helices. The lighter arrows indicate the sense of motion that is induced by pulling. The ‘delocalized’ clamp consists of multiple local shearing regions. Unlike the motifs shown in Figure 3, its operation does not rely on motion of any backbone loops. This is the reason why motif D is lamped together with the clamps displayed in the current Figure 3.

The elementary motifs S and SA can combine to form shear composite motifs shown in the middle line of the panels in Figure 2. Examples of these include disconnected shear motifs SD1 and SD2 and a supported shear motif SS. In SD1, discussed in (10) and observed in 1aoh (7), one S motif is followed by another S motif, separated by an essentially shear free region. SD2 is similar but it involves two SA motifs in a row. The panel illustrating SD2 is drawn in a particular fashion that indicates the geometry of fibronectin (8) in a schematic way. For this protein, the constituting SA motifs correspond to the β-hairpin. The SD2 motif is also found in proteins L and G (41). One can also consider a variant, SD3, in which S is combined with SA. It arises in GPF when pulled by residues 3 and 212 (33).

In SS characterizing 1cp4 (10), the main S motif is flanked by neighboring β-strands which stabilize it. Shearing the main S results also in a shear with the flanking β-strands. We have found a few examples of still other possibilities in group I. One of them is SB—a shear box in protein 1pav as discussed in (10). It involves a sheared two-strand β-sheet that is placed below a sheared two-helix ‘sheet’ so that a shear in one strand induces a shear on the helix above (not shown). Still another possibility is D—a delocalized clamp with multiple elementary clamps exerting comparable resistances to pulling. This happens, e.g. in 1lsl. Its schematic representation shown at the bottom of Figure 2 indicates that some of the contributing strands may be unstructured.

Figure 2 shows one more shearing motif denoted by T for torsion. It has been argued to be operational in polyankyrin (42). It combines shear in multiple S-like motifs with undoing of the overall horseshoe shape of the protein. This shape seems to result from a combination of steric stiffness and some contacts in the loop-like linkers. The reported experimental value of F_max for 12 domains is larger than that of 1aoh (42), however for six domains is much smaller (∼50 ± 20 pN) (43). Our simulations for 12 and 3 domains have yielded F_max of only of order 140 and 60 pN respectively (J.I. Sułkowska, unpublished data). A small force for a single domain has been also derived through all-atom simulations (44) [see also ref. (45)].

Figure 3 illustrates another category of mechanical clamps belonging to the second group in which topological loops matter. In four of these, CK, CL1, CL2 and CSK, the loops arise due to the presence of between one and three relevant disulphide bonds (indicated by short solid lines) between pairs of cysteines. The cysteine knot, CK, corresponds to shearing taking place inside a cysteine knot (3)—a loop that is created by two disulphide bonds.

Figure 3.

Types of the force clamps that involve backbone loops.

CL1 and CL2 are cysteine loops. In CL1 shearing results because one branch of § is pulled by a cysteine loop (3). CL2 is similar but the motion of the cysteine loop also drags another piece of the backbone that transmits shear to the other branch of the S motif (3). CSK is the cysteine slipknot motif (3), it involves three disulfide bridges which generate two loops: knot-loop (which is an example of a cysteine knot) and a slip-loop. The mechanical resistance to pulling comes from pulling the slip-loop through the knot-loop. The fifth motif shown in Figure 3 is SK—the slipknot motif (26) that is observed, for instance, in protein 2j85. It is created by two interacting loops, the slip-loop and the knot-loop, that move simultaneously on pulling. If the knot loops shrinks faster than the knot loop then the slipknot gets tightened temporarily and a ‘catch bond’ (46) is formed. This intermediate and metastable configuration eventually gets untied upon further stretching. The existence of such a metastable conformation where the slipknot is jammed (26) is responsible for lengthening of unravelling times at a higher velocity or force.

When we rank order the proteins according to the value of F_max, as calculated in our model, and ask in what order particular mechanical clamps are seen for the first time on reducing F_max, then their strengths can be rank ordered in the following succession: CSK, SS, SK, S, SD1, CL1, CL2, SD2 and Z. However, the strengths of various types of clamps intermix when going down the ranking ladder because they are influenced by dynamical details such as the length of a strand. In the case of CSK and SK, F_max depends on the relationship between sizes of the cysteine- and knot-loops in a strong way.

We plan to expand and improve the database. In particular, we intend to implement a possibility of self-submitted calculations for desired pulling directions and speeds. Currently, the requests for data should be sent to bsdb@ifpan.edu.pl. In particular a structure file which is not in the PDB can also be submitted. The resulting data are added to the database (which may affect ranking of the proteins).

FUNDING

Funding for open access charge: Grant N N202 0852 33 from the Ministry of Science and Higher Education in Poland; EC FUNMOL project under FP7-NMP-2007-SMALL-1; European Union within European Regional Development Fund, through grant Innovative Economy (POIG.01.01.02-00-008/08); Center for Theoretical Biological Physics sponsored by the NSF (Grant PHY-0822283); NSF-MCB-0543906 (to J.I.S.).

Conflict of interest statement. None declared.