peerj_json_files/PeerJ_Json_1.json

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    "v1_text": "how long is a piece of loop? : Loops are irregular structures which connect two secondary structure elements in proteins. They often play important roles in function, including enzyme reactions and ligand binding. Despite their importance, their structure remains difficult to predict. Most protein loop structure prediction methods sample local loop segments and score them. In particular protein loop classifications and database search methods depend heavily on local properties of loops. Here we examine the distance between a loop's end points (span). We find that the distribution of loop span appears to be independent of the number of residues in the loop, in other words the separation between the anchors of a loop does not increase with an increase in the number of loop residues. Loop span is also unaffected by the secondary structures at the end points, unless the two anchors are part of an anti-parallel beta sheet. As loop span appears to be independent of global properties of the protein we suggest that its distribution can be described by a random fluctuation model based on the Maxwell-Boltzmann distribution. It is believed that the primary difficulty in protein loop structure prediction comes from the number of residues in the loop. Following the idea that loop span is an independent local property, we investigate its effect on protein loop structure prediction and show how normalised span (loop stretch) is related to the structural complexity of loops. Highly contracted loops are more difficult to predict than stretched loops. Pre Prin ts Pre Prin ts Introduction1 Protein loops are patternless regions which connect two regular secondary2 structures. They are generally located on the protein\u2019s surface in solvent3 exposed areas and often play important roles, such as interacting with4 other biological objects.5 Despite the lack of patterns, loops are not completely random struc-6 tures. Early studies of short turns and hairpins showed that these peptide7 fragments could be clustered into structural classes (Richardson 1981;8 Sibanda & Thorton 1985). Such classifications have also been made9 across all loops (Burke, Deane & Blundell 2000; Chothia & Lesk 1987;10 Donate et al. 1996; Espadaler et al. 2004; Oliva et al. 1997; Vanhee11 et al. 2011) or within specific protein families such as antibody comple-12 mentarity determining regions (CDRs) (Al-Lazikani, Lesk & Chothia 1997;13 Chothia & Lesk 1987; Chothia et al. 1989). Loop classifications are gener-14 ally based on local properties such as sequence, the secondary structures15 from which the loop starts and finishes (anchor region), the distance be-16 tween the anchors, and the geometrical shape along the loop structure17 (Kwasigroch, Chomilier & Mornon 1996; Leszczynski & Rose 1986; Ring18 et al. 1992; Wojcik, Mornon & Chomilier 1999).19 Loops can also be classified in terms of function. There is some ev-20 idence that a loop can have local functionality. Experiments have been21 carried out which support the idea that swapping a local loop sequence for22 1 Pre Prin ts Pre Prin ts a different functional loop sequence enables the new function to be taken23 on (Pardon et al. 1995; Toma et al. 1991; Wolfson et al. 1991). One24 important example of functional loop exchange is in the development of25 humanised antibodies (Queen et al. 1989; Riechmann et al. 1988).26 Accurate protein loop structure prediction remains an open question.27 Protein loop predictors have dealt with the problem as a case of local pro-28 tein structure prediction. Protein structures are hypothesised to be in ther-29 modynamic equilibrium with their environment (Anfinsen 1973). Thus the30 primary determinant of a protein structure is considered to be its atomic31 interactions, i.e. its amino acid sequence. An analogous conjecture has32 arisen at the local scale where environment other than loop structure is33 fixed. Thus the modelling of protein loops is often considered a mini pro-34 tein folding problem (Fiser, Do & Sali 2000; Nagi & Regan 1997). Although35 most loop structure prediction methods are based on this conjecture, ap-36 parently loop sequence alone is not the complete determinant of the loop37 structure as even identical loop sequences can take multiple structural38 conformations depending on external environmental factors such as sol-39 vent and ligand binding (Fernandez-Fuentes & Fiser 2006). Quintessen-40 tial examples of such multiple loop structure conformations can be found41 in antibody CDR loops upon antigen binding (Choi & Deane 2011).42 Database search methods have been successful in the realm of loop43 structure prediction (Verschueren et al. 2011). They depend upon the44 assumption that similarity between local properties may suggest similar45 2 Pre Prin ts Pre Prin ts local structures. All database search methods work in an analogous fash-46 ion using either a complete set or a classified set of loops and selecting47 predictions using local features including sequence similarity and anchor48 geometry (Choi & Deane 2010; Fernandez-Fuentes, Oliva & Fiser 2006;49 Hildebrand et al. 2009; Peng & Yang 2007; Wojcik, Mornon & Chomi-50 lier 1999). Ab initio loop modelling methods aim to predict peptide frag-51 ments that do not exist in homology modelling templates without structure52 databases. Generally, ab initio methods generate large local structure con-53 formation sets and select predictions (de Bakker et al. 2003; Fiser, Do &54 Sali 2000; Jacobson et al. 2004; Mandell, Coutsias & Kortemme 2009;55 Soto et al. 2008). The generated loop candidates are optimised against56 scoring functions. In all loop modelling procedures anchor regions are57 often problematic and the accuracy of loop modelling depends upon the58 distance between the anchors (Xiang, 2006).59 Here, we focus on a specific local property of protein loop structure: the60 distance between the two terminal C\u03b1 atoms of the loop, which we refer to61 as its span. The nature of the span distribution is broadly similar across dif-62 ferent protein classes or anchor types, except for loops linking anti-parallel63 strands (anti-parallel \u03b2 loops). In particular, the most highly frequent span64 appears to stay the same irrespective of the number of residues. This sug-65 gests that the span is distributed independently of other local properties66 and global structures. We demonstrate that the observed span distribution67 can largely be explained by a simple model of random fluctuations with a68 3 Pre Prin ts Pre Prin ts given length scale, based on the Maxwell-Boltzmann distribution.69 It is widely believed that the accuracy of loop structure prediction de-70 pends on the number of residues, i.e. the larger the number of residues,71 the more difficult a loop is to predict (Choi & Deane 2010; Karen et al.72 2007). We introduce the normalised span which indicates how stretched73 a loop is (loop stretch \u03bb). Fully stretched loops (\u03bb ' 1) are almost always74 predicted accurately, whereas contracted loops (\u03bb 1) are harder to pre-75 dict. In fact, shorter loops tend to be more stretched whereas longer loops76 are likely to be highly contracted. We suggest that loop stretch should be77 addressed in practical modelling situations and loop structure prediction78 should be concerned with predicting highly contracted loops.79 Materials and Methods80 Loop Definition81 In each of the sets of protein structures loops, were identified using the fol-82 lowing protocol. Secondary structures were annotated using JOY (Mizuguchi83 et al. 1998). A loop structure was defined as any region between two84 regular secondary structures that was at least three residues in length85 (Donate et al. 1996). Short (less than 4 residues in length) loops were86 discarded. Redundancy was removed using sequence identity. If a pair87 of loops shares over 40% sequence identity (Fernandez-Fuentes & Fiser88 4 Pre Prin ts Pre Prin ts 2006), the loop which has a higher average B-factor was discarded.89 Membrane Protein Structures90 Membrane proteins (3, 789 chains) were extracted from PDBTM (Tusnady,91 Dosztanyi & Simon 2004). The membrane layer was defined as being92 from \u221220 to +20A\u030a (Scott et al. 2008) from the centre of the protein and93 loops whose two end C\u03b1 atom coordinates were outside the layer were94 discarded. A total of 1, 027 non-redundant membrane loops were defined.95 Soluble Protein Structures96 All protein chains determined by X-ray crystallography which share less97 than 99% sequence identity (< 3.0A\u030a resolution and < 0.3 R-factor) were98 collected using PISCES (Wang & Dunbrack Jr. 2005) and all of our 3, 78999 membrane chains were removed. In order to get rid of any potential mem-100 brane chains in the list, PSI-BLAST (Altschul et al. 1997) was then used to101 compare the 3, 789 membrane chains against the soluble set. Any chains102 found during 5 iterations with an E-value cut-off of 0.001 were removed from103 the list of soluble protein chains. A total of 25, 191 non-redundant soluble104 loops were identified from 27, 717 soluble protein chains.105 5 Pre Prin ts Pre Prin ts Loop Span and Loop Stretch106 The loop span (l) is the distance between the two terminal C\u03b1 atoms of a107 loop (Figure 1).108 The maximum span lmax is a function of the number of residues n and109 calculated as follows.110 lmax(n) = \u03b3 \u00b7 (n/2\u2212 1) + \u03b4 if n is even\u03b3 \u00b7 (n\u2212 1) /2 if n is odd where \u03b3 = 6.046A\u030a and \u03b4 = 3.46A\u030a (Flory 1998; Tastan, Klein-Seetharaman111 & Meirovitch 2009). If the distance between two terminal C\u03b1 atoms in the112 loop (i.e. the span) is l, the loop stretch (\u03bb) of the loop is defined as a113 normalised span.114 \u03bb \u2261 l lmax (1) Note that the values of \u03b3 and \u03b4 are theoretical approximations so the115 \u03bb of some loops may occasionally be larger than 1. Similar notations are116 found in (Ring et al. 1992) and (Tastan, Klein-Seetharaman & Meirovitch117 2009).118 6 Pre Prin ts Pre Prin ts Protein Structure Prediction and Loop Stretch119 Loop Modelling Test Sets120 There are two modelling test sets. The first set includes loops of 8 residues.121 The loops were binned every 0.1 loop stretch. In each bin, 40 test loops122 were randomly selected. A total of 320 test loops from 0.2 to 1 in loop123 stretch were used (A full list is given in Table S1).124 The second set consists of loops of between 6 and 10 residues in125 length. Two classes of loops were collected at each length: contracted126 loops (\u03bb < 0.4) and stretched loops (\u03bb > 0.95); an identical number of127 loops was kept in each of these classes at each length. A total of 346128 test loops were identified (58, 72, 110, 58 and 48 loops respectively, See Ta-129 ble S2 and S3). For example, there are 55 contracted test loops and 55130 stretched loops for loops of 8 residues.131 The measurement of accuracy is loop RMSD of all backbone atoms (N,132 C\u03b1, C and O) after superimposing anchor structures.133 MODELLER Setting134 The default loop refinement script was used. One hundred loop models135 were sampled under the molecular dynamics level of slow. The DOPE po-136 tential energy (Shen & Sali 2006) was used for model quality assessment.137 7 Pre Prin ts Pre Prin ts FREAD Setting138 A database was constructed using the 27, 717 soluble protein chains de-139 fined above. All the parameters were set as default (the environment sub-140 stitution score cut-off value \u2265 25). Any results from self-prediction were141 eliminated.142 Results143 Nomenclature144 In this paper, proteins are divided into two main classes: membrane and145 soluble proteins. Loops from membrane protein structures are called \u201cmem-146 brane loops\u201d and those from soluble protein structures are referred to as147 \u201csoluble loops\u201d. Loops are also described by their secondary structure148 types: for example, loops connecting anti-parallel \u03b2 sheets are termed149 \u201canti-parallel \u03b2 loops\u201d. The physical spatial distance between the two end150 C\u03b1 atoms of a loop is referred to as \u201cspan\u201d (l). Maximum loop span (lmax)151 is the furthest that a set of residues can spread. \u201cLoop stretch\u201d (\u03bb) is the152 normalised loop span: the observed span between two C\u03b1 atoms at each153 end of a loop in a protein structure over the loops maximum span (Figure154 1).155 8 Pre Prin ts Pre Prin ts Loop Span Distribution156 The number of residues in a loop is distributed in a similar fashion regard-157 less of anchor types except for the loops linking anti-parallel \u03b2 sheets due158 to the constraint of hydrogen bonds between adjacent \u03b2 strands (Figure159 2A). Figure 2B displays how loop spans are distributed for different anchor160 types. Again, apart from anti-parallel \u03b2 loops, the loop span distributions161 do not change with anchor structures.162 The loop span distribution also does not alter when considering differ-163 ent protein classes. Figures 2C\u20132G show how the loop spans of mem-164 brane loops and soluble loops are distributed in a similar manner.165 Essentially a loop span value reflects how distant the end tips of the166 two secondary structures that the loop connects are. These observations167 suggest that the loop span may be distributed independently of local an-168 chor structures and protein types, i.e. anchor distances do not depend on169 local secondary structure elements or global protein structures.170 The modes of loop span distributions are roughly constant (Figure 2B),171 even if we split the loops in terms of the number of residues (Figure 3A).172 We fit our data using the Gaussian kernel density estimation. The esti-173 mated distributions show a nearly constant mode (' 13A\u030a on average, Fig-174 ure 3B). This constant span value may be due to protein packing. Folded175 proteins tend to be tightly packed and thus secondary structures are placed176 close to one another while avoiding side chain steric clashes. This packing177 9 Pre Prin ts Pre Prin ts effect may mean that the end points of two secondary structures (i.e. span)178 will lie within a constant span value regardless of the number of residues179 in a loop.180 Maxwell-Boltzmann Distribution for Loop Span181 From the above observations, it appears that loop span is distributed in-182 dependently of local anchor structures or global protein classes. Here we183 assume that a protein loop is an independent unit of the protein structure184 and the span is determined regardless of any other effects including se-185 quence or the rest of the structure.186 Here a model for the loop span distribution is established under the187 hypothesis that the two end points of a loop fluctuate in three dimensional188 space, following the Maxwell-Boltzmann distribution. Two constraints are189 imposed in this model: the minimum span lmin and the maximum span190 as a function of the number of residues lmax(n). Within these constraints,191 the span oscillates according to a normal distribution N (\u00b5, \u03c32) with a given192 length-scale lmode in three dimensional space.193 The underlying assumptions are that the end points cannot approach194 each other too closely, and that there is a maximum span achievable for195 a loop with a given number of residues (n). Within these constraints, the196 span is allowed to fluctuate around the given length-scale lmode in three197 dimensional space. Thus, in this model, the loop span l of n residues is198 10 Pre Prin ts Pre Prin ts distributed as199 l = \u221a l2x + l 2 y + l 2 z lx, ly, lz \u223c N ( 0, l2mode 2 ) (2) subject to the constraints that l \u2265 lmin and l \u2264 lmax(n), as stated above.200 The variance of l2mode/2 corresponds to a modal span of lmode. Thus there201 are two parameters to be determined in our model: lmin and lmode. We set202 lmin to 3.8A\u030a, which is the typical distance between two neighbouring C\u03b1203 atoms in a protein chain. lmode is set to an estimate of the empirical mode204 using the Gaussian kernel density estimation (12.7A\u030a).205 As there are not many longer loops in the data set, loops longer than206 20 residues were discarded. In addition, all anti-parallel \u03b2 loops were elim-207 inated due to their physical constraints. These eliminations left 21, 597208 soluble loops (The frequency distribution for each number of residues is in209 Figure S2). Having set the two parameters lmin and lmode, loop spans were210 generated 10 times per model in accordance with the Maxwell-Boltzmann211 distribution, preserving the observed distribution of the number of residues212 (i.e. 10 simulated loop spans were generated for each real loop in the data213 set). The simulation outcome is depicted in Figure 4A. The two distri-214 butions show the same shape and the quantile comparison in Figure 4B215 indicates that they are statistically similar except for the tail region.216 There are apparent anomalies between the simulated and real span217 distributions towards the extremes. The model seems to predict more218 11 Pre Prin ts Pre Prin ts short-span loops than observed. Our model imposes a sharp lower thresh-219 old at lmin = 3.8A\u030a, whereas in reality we expect a smoother transition. In220 other words, we expect our assumption of free fluctuation to break down221 when the span gets close to the lower bound and the physical constraints222 begin to become relevant. On the other side of the distribution, we see a223 substantially higher number of long-span loops (> 20A\u030a) than predicted by224 the model. The mismatches in the long-span region tend to become more225 prominent as the number of residues is increased. When we examined226 which loops tend to have exceptionally long spans, we found that some of227 these \u201cloops\u201d are domain linkers between independent folding units and228 therefore likely to be under different constraints. Others appear to have229 been misclassified, as the loop definition used here is based only on the230 anchors containing at least three consecutive residues of secondary struc-231 tures and the loop containing none. This allows segments such as termini232 structures to be included if there happen to be very short helical segments233 at a protein structure\u2019s terminus (Figure S1).234 Protein Structure Prediction and Loop Stretch235 The number of residues in loops is known to be related to the protein236 stability (Nagi & Regan 1997) and the accuracy of most loop modelling237 techniques. Based on our observation that the loop span is independent238 of other properties, we examine its effects on protein loop structure pre-239 12 Pre Prin ts Pre Prin ts diction. Here we introduce loop stretch, the normalised loop span (Eq.240 1). Loop stretch values take on a range of 0 to 1, which indicates how241 stretched a loop is (1: fully stretched).242 Figure 5 displays how loop stretch frequencies are distributed for dif-243 ferent numbers of residues, demonstrating that the number of residues is244 negatively correlated with loop stretch, i.e. the longer a loop is, the more245 likely it is to be contracted. This may suggest that, instead of the stan-246 dard belief that loop modelling performs worse as the number of residues247 in the loop increases, it may be that the real problem is better described248 by considering how stretched the loop to be predicted is. For example, if249 a loop contains many residues but is highly stretched, it will be predicted250 relatively accurately, as it can take on only a small number of different251 conformations.252 In order to check the relationship between accuracy and loop stretch253 we used a test set containing only 8 residue loops with 40 non-redundant254 loops in every 0.1 loop stretch bin. Two loop modelling methods, which255 use two different sampling methods, were tested. MODELLER (Fiser, Do256 & Sali 2000) is a popular protein structure prediction programme which has257 a built-in ab initio loop modelling module. FREAD (Choi & Deane 2010)258 is a database search method which samples candidate loops depending259 on local properties and ranks predictions based on local loop sequence260 similarity and anchor geometry matches.261 The average accuracy of MODELLER shows a negative linear corre-262 13 Pre Prin ts Pre Prin ts lation against loop stretch for the first test set (Figure 6A). In the case of263 fully stretched loops (\u03bb > 0.95), MODELLER can produce consistently ac-264 curate predictions, but its predictions worsen as the target loops are less265 stretched. FREAD produces more accurate predictions than MODELLER266 in general. However its predictions also begin to disperse as the loops267 become more contracted (Figure 6B). FREAD generates candidate loops268 based on anchor matches and sequence similarity for a given loop target.269 This may imply that contracted loops tend to have multiple structural con-270 formations or stringent sequence identity is required to predict such highly271 contracted loops. It should be noted that FREAD is not able to predict272 all the target loops due to the incompleteness of the structure database it273 uses (Figure 6C).274 In order to further assess the effect of loop stretch in loop structure275 prediction, MODELLER was re-examined on a second set. The second276 test set consists of loops from 6 to 10 residues in length. In this set, for277 each number of residues, the same numbers of loops (See Materials and278 Methods) were selected for both contracted (\u03bb < 0.4) and fully stretched279 loops (\u03bb > 0.95). MODELLER produces consistently accurate results for280 fully stretched loops regardless of the number of residues, but fails to ac-281 curately predict contracted loops (Figure 6D).282 We calculated the partial correlations (Spearman\u2019s rank correlation)283 between accuracy, and the number of residues and loop stretch on the284 second test set. so as to investigate what affects the prediction accuracy285 14 Pre Prin ts Pre Prin ts more (the number of residues or loop stretch). The partial correlation be-286 tween loop stretch and RMSD is larger than that between the number of287 residues and RMSD (\u22120.465 and 0.367 respectively). Loop stretch, just like288 the number of residues is something that can be calculated without knowl-289 edge of loop conformation and therefore can be used in the design of loop290 structure prediction software.291 Discussion292 In this paper, we focus on a specific local property (span) and demonstrate293 that the modes of loop span distribution appear to be independent of the294 number of residues. Loop span shows a distinct frequency distribution295 which does not depend on anchor types or protein classes. From these296 observations, we hypothesised that loop span is independent of the other297 effects and showed how the loop span distribution appears to correspond298 to a truncated Maxwell-Boltzmann distribution.299 The reason behind the independence of loop span from the number300 of loop residues or secondary structure type is not known. 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Advances in Homology Protein Structure Modeling.422 Curr Protein Pept Sci, 7: 217-227.423 19 Pre Prin ts Pre Prin ts Figure 1 The definition of loop span and loop stretch Loop span is the separation of the two C\u03b1s at either end of the loop. In this example, 2J9O Chain A (198-205) has a span of 13.7\u00c5 and contains 8 residues. Maximum span can be calculated from the number of residues in the loop to be 21.6\u00c5. Loop stretch is the normalised span (13.7/21.6 0.63).\u2243 Pre Prin ts Pre Prin ts Figure 2 statistics of protein loops : (A) The frequency distribution of loops containing different numbers of residues. Anti-parallel \u03b2 loops tend to have fewer residues. (B) The loop span distribution in terms of the anchor secondary structure do not show differences except for anti-parallel \u03b2 loops. The upper part of the anti-parallel \u03b2 loop span distribution is omitted in the figure. (C) The distributions of soluble loop span and membrane loop span appear to be similar. (D)-(G) Q\u2013Q plots showing that the membrane and soluble loop span distributions are from the same probability distribution. Pre Prin ts Pre Prin ts Figure 3 The span distributions for loops containing different numbers of residues (A) These appear to show a constant mode. Data here is soluble loops excluding anti-parallel beta loops. (B) The modes for the span distributions for loops containing different numbers of residues compared to the maximum span for that length. The span modes were estimated using the Gaussian kernel density estimation. Note that the estimated mode of loops of 4 residues is close to its maximum span. Pre Prin ts Pre Prin ts Pre Prin ts Pre Prin ts Figure 4 Maxwell-Boltzmann distribution and loop span distribution (A) The loop span distribution (black) from soluble loops and that of the Maxwell-Boltzmann distribution (red). (B) The Q-Q plot suggesting that they follow the same distribution. Pre Prin ts Pre Prin ts Pre Prin ts Pre Prin ts Figure 5 Loop stretch of long and short loops Loop stretch distributions for loops containing different numbers of residues Shorter loops tend to be more stretched whereas longer loops are likely to be more contracted. Only soluble loops excluding anti-parallel \u03b2 loops are plotted. Pre Prin ts Pre Prin ts Figure 6 Protein loop structure prediction and loop stretch Accuracy of protein loop structure prediction methods do not only depend on the number of residues, but also on loop stretch. MODELLER (A) and FREAD (B) both show accurate results when the target loop is stretched on the first set (including loops of 8 residues in length only). MODELLER shows worse prediction as loop stretch decreases whereas FREAD gives consistent accuracy on loop stretch. However both fail to predict very contracted loops (\u03bb &lt; 0.4) (C) The coverage of FREAD predictions in terms of loop stretch. (D) The second test set (contracted (\u03bb &lt; 0.4) and stretched (\u03bb &gt; 0.95) loops). The test loops are also split by the number of residues. For fully stretched loops (\u03bb &gt; 0.95), regardless of the number of residues, MODELLER predicts accurately.Pre Prin ts Pre Prin ts",
    "v2_text": "how long is a piece of loop? : Loops are irregular structures which connect two secondary structure elements in proteins. They often play important roles in function, including enzyme reactions and ligand binding. Despite their importance, their structure remains difficult to predict. Most protein loop structure prediction methods sample local loop segments and score them. In particular protein loop classifications and database search methods depend heavily on local properties of loops. Here we examine the distance between a loop's end points (span). We find that the distribution of loop span appears to be independent of the number of residues in the loop, in other words the separation between the anchors of a loop does not increase with an increase in the number of loop residues. Loop span is also unaffected by the secondary structures at the end points, unless the two anchors are part of an anti-parallel beta sheet. As loop span appears to be independent of global properties of the protein we suggest that its distribution can be described by a random fluctuation model based on the Maxwell-Boltzmann distribution. It is believed that the primary difficulty in protein loop structure prediction comes from the number of residues in the loop. Following the idea that loop span is an independent local property, we investigate its effect on protein loop structure prediction and show how normalised span (loop stretch) is related to the structural complexity of loops. Highly contracted loops are more difficult to predict than stretched loops. Pre Prin ts Pre Prin ts Introduction1 Protein loops are patternless regions which connect two regular secondary2 structures. They are generally located on the protein\u2019s surface in solvent3 exposed areas and often play important roles, such as interacting with4 other biological objects.5 Despite the lack of patterns, loops are not completely random struc-6 tures. Early studies of short turns and hairpins showed that these peptide7 fragments could be clustered into structural classes (Richardson 1981;8 Sibanda & Thorton 1985). Such classifications have also been made9 across all loops (Burke, Deane & Blundell 2000; Chothia & Lesk 1987;10 Donate et al. 1996; Espadaler et al. 2004; Oliva et al. 1997; Vanhee et al.11 2011) or within specific protein families such as antibody complementarity12 determining regions (Al-Lazikani, Lesk & Chothia 1997; Chothia & Lesk13 1987; Chothia et al. 1989). Loop classifications are generally based on14 local properties such as sequence, the secondary structures from which15 the loop starts and finishes (anchor region), the distance between the an-16 chors, and the geometrical shape along the loop structure (Kwasigroch,17 Chomilier & Mornon 1996; Leszczynski & Rose 1986; Ring et al. 1992;18 Wojcik, Mornon & Chomilier 1999).19 Loops can also be classified in terms of function. There is some ev-20 idence that a loop can have local functionality. Experiments have been21 carried out which support the idea that swapping a local loop sequence for22 1 Pre Prin ts Pre Prin ts a different functional loop sequence enables the new function to be taken23 on (Pardon et al. 1995; Toma et al. 1991; Wolfson et al. 1991). One24 important example of functional loop exchange is in the development of25 humanised antibodies (Queen et al. 1989; Riechmann et al. 1988).26 Accurate protein loop structure prediction remains an open question.27 Protein loop predictors have dealt with the problem as a case of local pro-28 tein structure prediction. Protein structures are hypothesised to be in ther-29 modynamic equilibrium with their environment (Anfinsen 1973). Thus the30 primary determinant of a protein structure is considered to be its atomic31 interactions, i.e. its amino acid sequence. An analogous conjecture has32 arisen at the local scale. The modelling of protein loops is often consid-33 ered a mini protein folding problem (Fiser, Do & Sali 2000; Nagi & Regan34 1997). In fact, most loop structure prediction methods are based on this35 conjecture.36 Database search methods have been successful in the realm of loop37 structure prediction (Verschueren et al. 2011). They depend upon the38 assumption that similarity between local properties may suggest similar39 local structures. All database search methods work in an analogous fash-40 ion using either a complete set or a classified set of loops and selecting41 predictions using local features including sequence similarity and anchor42 geometry (Choi & Deane 2010; Fernandez-Fuentes, Oliva & Fiser 2006;43 Hildebrand et al. 2009; Peng & Yang 2007; Wojcik, Mornon & Chomi-44 lier 1999). Ab initio loop modelling methods aim to predict peptide frag-45 2 Pre Prin ts Pre Prin ts ments that do not exist in homology modelling templates without structure46 databases. Generally, ab initio methods generate large local structure con-47 formation sets and select predictions (de Bakker et al. 2003; Fiser, Do &48 Sali 2000; Jacobson et al. 2004; Mandell, Coutsias & Kortemme 2009;49 Soto et al. 2008). The generated loop candidates are optimised against50 scoring functions. In all loop modelling procedures anchor regions are51 often problematic and the accuracy of loop modelling depends upon the52 distance between the anchors (Xiang, 2006).53 Here, we focus on a specific local property of protein loop structure: the54 distance between the two terminal C\u03b1 atoms of the loop, which we refer to55 as its span. The nature of the span distribution is broadly similar across dif-56 ferent protein classes or anchor types, except for loops linking anti-parallel57 strands (anti-parallel \u03b2 loops). In particular, the most highly frequent span58 appears to stay the same irrespective of the number of residues. This sug-59 gests that the span is distributed independently of other local properties60 and global structures. We demonstrate that the observed span distribution61 can largely be explained by a simple model of random fluctuations with a62 given length scale, based on the Maxwell-Boltzmann distribution.63 It is widely believed that the accuracy of loop structure prediction de-64 pends on the number of residues, i.e. the larger the number of residues,65 the more difficult a loop is to predict (Choi & Deane 2010; Karen et al.66 2007). We introduce the normalised span which indicates how stretched67 a loop is (loop stretch \u03bb). Fully stretched loops (\u03bb \u2243 1) are almost always68 3 Pre Prin ts Pre Prin ts predicted accurately, whereas contracted loops (\u03bb \u226a 1) are harder to pre-69 dict. In fact, shorter loops tend to be more stretched whereas longer loops70 are likely to be highly contracted. We suggest that loop stretch should be71 addressed in practical modelling situations and loop structure prediction72 should be concerned with predicting highly contracted loops.73 Materials and Methods74 Loop Definition75 In each of the sets of protein structures loops, were identified using the fol-76 lowing protocol. Secondary structures were annotated using JOY (Mizuguchi77 et al. 1998). A loop structure was defined as any region between two78 regular secondary structures that was at least three residues in length79 (Donate et al. 1996). Short (less than 4 residues in length) loops were80 discarded. Redundancy was removed using sequence identity. If a pair81 of loops shares over 40% sequence identity (Fernandez-Fuentes & Fiser82 2006), the loop which has a higher average B-factor was discarded. Mem-83 brane Protein Structures84 Membrane proteins (3, 789 chains) were extracted from PDBTM (Tus-85 nady, Dosztanyi & Simon 2004). The membrane layer was defined as86 being from \u221220 to +20A\u030a (Scott et al. 2008) from the centre of the protein87 and loops whose two end C atom coordinates were outside the layer were88 4 Pre Prin ts Pre Prin ts discarded. A total of 1, 027 non-redundant membrane loops were defined.89 Soluble Protein Structures90 All protein chains determined by X-ray crystallography which share less91 than 99% sequence identity (< 3.0A\u030a resolution and < 0.3 R-factor) were92 collected using PISCES (Wang & Dunbrack Jr. 2005) and all of our 3, 78993 membrane chains were removed. In order to get rid of any potential mem-94 brane chains in the list, PSI-BLAST (Altschul et al. 1997) was then used to95 compare the 3, 789 membrane chains against the soluble set. Any chains96 found during 5 iterations with an E-value cut-off of 0.001 were removed97 from the soluble chains list. A total of 25, 191 non-redundant soluble loops98 were identified from 27, 717 soluble protein chains.99 Loop Span and Loop Stretch100 The loop span (l) is the distance between the two terminal C\u03b1 atoms of a101 loop (Figure 1).102 The maximum span lmax is a function of the number of residues n and103 calculated as follows.104 lmax(n) = \u03b3 \u00b7 (n/2\u2212 1) + \u03b4 if n is even\u03b3 \u00b7 (n\u2212 1) /2 if n is odd where \u03b3 = 6.046A\u030a and \u03b4 = 3.46A\u030a (Flory 1998; Tastan, Klein-Seetharaman105 5 Pre Prin ts Pre Prin ts & Meirovitch 2009). If the distance between two terminal C\u03b1 atoms in the106 loop (i.e. the span) is l, the loop stretch (\u03bb) of the loop is defined as a107 normalised span.108 \u03bb \u2261 l lmax (1) Note that the values of \u03b3 and \u03b4 are theoretical approximations so the109 \u03bb of some loops may occasionally be larger than 1. Similar notations are110 found in (Ring et al. 1992) and (Tastan, Klein-Seetharaman & Meirovitch111 2009).112 Loop Modelling Test Sets113 There are two modelling test sets. The first set includes loops of 8 residues.114 The loops were binned every 0.1 loop stretch. In each bin, 40 test loops115 were randomly selected. A total of 320 test loops from 0.2 to 1 in loop116 stretch were used (A full list is given in Table S1).117 The second set consists of loops of between 6 and 10 residues in118 length. Two classes of loops were collected at each length: contracted119 loops (\u03bb < 0.4) and stretched loops (\u03bb > 0.95); an identical number of120 loops was kept in each of these classes at each length. A total of 346121 test loops were identified (58, 72, 110, 58 and 48 loops respectively, See Ta-122 ble S2 and S3). For example, there are 55 contracted test loops and 55123 stretched loops for loops of 8 residues.124 6 Pre Prin ts Pre Prin ts The measurement of accuracy is loop RMSD of all backbone atoms (N,125 C\u03b1, C and O) after superimposing anchor structures.126 MODELLER Setting127 The default loop refinement script was used. One hundred loop models128 were sampled under the molecular dynamics level of slow. The DOPE po-129 tential energy (Shen & Sali 2006) was used for model quality assessment.130 Results131 Nomenclature132 In this paper, proteins are divided into two main classes: membrane and133 soluble proteins. Loops from membrane protein structures are called \u201cmem-134 brane loops\u201d and those from soluble protein structures are referred to as135 \u201csoluble loops\u201d. Loops are also described by their secondary structure136 types: for example, loops connecting anti-parallel \u03b2 sheets are termed137 \u201canti-parallel \u03b2 loops\u201d. The physical spatial distance between the two end138 C atoms of a loop is referred to as \u201cspan\u201d (l). Maximum loop span (lmax)139 is the furthest that a set of residues can spread. \u201cLoop stretch\u201d (\u03bb) is the140 normalised loop span: the observed span between two C\u03b1 atoms at each141 end of a loop in a protein structure over the loops maximum span (Figure142 1).143 7 Pre Prin ts Pre Prin ts Loop Span Distribution144 The number of residues in a loop is distributed in a similar fashion regard-145 less of anchor types except for the loops linking anti-parallel \u03b2 sheets due146 to the constraint of hydrogen bonds between adjacent \u03b2 strands (Figure147 2A). Figure 2B displays how loop spans are distributed for different anchor148 types. Again, apart from anti-parallel \u03b2 loops, the loop span distributions149 do not change with anchor structures.150 The loop span distribution also does not alter when considering dif-151 ferent protein classes. Figures 2C and D show how the loop spans of152 membrane loops and soluble loops are distributed in a similar manner.153 Essentially a loop span value reflects how distant the end tips of the154 two secondary structures that the loop connects are. These observations155 suggest that the loop span may be distributed independently of local an-156 chor structures and protein types, i.e. anchor distances do not depend on157 local secondary structure elements or global protein structures.158 The modes of loop span distributions are roughly constant (Figure 2B),159 even if we split the loops in terms of the number of residues (Figure 3A).160 We fit our data using the Gaussian kernel density estimation. The es-161 timated distributions show a nearly constant mode (\u2243 13A\u030a on average,162 Figure 3B). On the face of it the fact that the mode is a constant inde-163 pendent of the number of residues in the loop is surprising. However it164 might be due to protein structural features. Apart from long loops linking165 8 Pre Prin ts Pre Prin ts two remote anchors (e.g. Figure S1), the secondary structures tend to be166 packed against one another. Due to the sizes of side chains the anchors167 are not able to approach too closely, but it may be that they pack against168 one another potentially leading to a constant value.169 Maxwell-Boltzmann Distribution for Loop Span170 From the above observations, it appears that loop span is distributed in-171 dependently of local anchor structures or global protein classes. Here we172 assume that a protein loop is an independent unit of the protein structure173 and the span is determined regardless of any other effects including se-174 quence or the rest of the structure.175 Here a model for the loop span distribution is established under the176 hypothesis that the two end points of a loop fluctuate in three dimensional177 space, following the Maxwell-Boltzmann distribution. Two constraints are178 imposed in this model: the minimum span lmin and the maximum span179 as a function of the number of residues lmax(n). Within these constraints,180 the span oscillates according to a normal distribution N (\u00b5, \u03c32) with a given181 length-scale lmode in three dimensional space.182 The underlying assumptions are that the end points cannot approach183 each other too closely, and that there is a maximum span achievable for184 a loop with a given number of residues (n). Within these constraints, the185 span is allowed to fluctuate around the given length-scale lmode in three186 9 Pre Prin ts Pre Prin ts dimensional space. Thus, in this model, the loop span l of n residues is187 distributed as188 l = \u221a l2x + l 2 y + l 2 z lx, ly, lz \u223c N ( 0, l2mode 2 ) (2) subject to the constraints that l \u2265 lmin and l \u2264 lmax(n), as stated above.189 The variance of l2mode/2 corresponds to a modal span of lmode. Thus there190 are two parameters to be determined in our model: lmin and lmode. We set191 lmin to 3.8A\u030a, which is the typical distance between two neighbouring C\u03b1192 atoms in a protein chain. lmode is set to an estimate of the empirical mode193 using the Gaussian kernel density estimation (12.7A\u030a).194 As there are not many longer loops in the data set, loops longer than195 20 residues were discarded. In addition, all anti-parallel \u03b2 loops were elim-196 inated due to their physical constraints. These eliminations left 21, 597197 soluble loops (The frequency distribution for each number of residues is in198 Figure S2). Having set the two parameters lmin and lmode, loop spans were199 generated 10 times per model in accordance with the Maxwell-Boltzmann200 distribution, preserving the observed distribution of the number of residues201 (i.e. 10 simulated loop spans were generated for each real loop in the data202 set). The simulation outcome is depicted in Figure 4A. The two distri-203 butions show the same shape and the quantile comparison in Figure 4B204 indicates that they are statistically similar except for the tail region.205 There are apparent anomalies between the simulated and real span206 10 Pre Prin ts Pre Prin ts distributions towards the extremes. The model seems to predict more207 short-span loops than observed. Our model imposes a sharp lower thresh-208 old at lmin = 3.8A\u030a, whereas in reality we expect a smoother transition. In209 other words, we expect our assumption of free fluctuation to break down210 when the span gets close to the lower bound and the physical constraints211 begin to become relevant. On the other side of the distribution, we see a212 substantially higher number of long-span loops (> 20A\u030a) than predicted by213 the model. The mismatches in the long-span region tend to become more214 prominent as the number of residues is increased. When we examined215 which loops tend to have exceptionally long spans, we found that some of216 these \u201cloops\u201d are domain linkers between independent folding units and217 therefore likely to be under different constraints. Others appear to have218 been misclassified, as the loop definition used here is based only on the219 anchors containing at least three consecutive residues of secondary struc-220 tures and the loop containing none. This allows segments such as termini221 structures to be included if there happen to be very short helical segments222 at a protein structure\u2019s terminus (Figure S1).223 Protein Structure Prediction and Loop Stretch224 The number of residues in loops is known to be related to the protein225 stability (Nagi & Regan 1997) and the accuracy of most loop modelling226 techniques. Based on our observation that the loop span is independent227 11 Pre Prin ts Pre Prin ts of other properties, we examine its effects on protein loop structure pre-228 diction. Here we introduce loop stretch, the normalised loop span (Eq.229 1). Loop stretch values take on a range of 0 to 1, which indicates how230 stretched a loop is (1: fully stretched).231 Figure 5 displays how loop stretch frequencies are distributed for dif-232 ferent numbers of residues, demonstrating that the number of residues is233 negatively correlated with loop stretch, i.e. the longer a loop is, the more234 likely it is to be contracted. This may suggest that, instead of the stan-235 dard belief that loop modelling performs worse as the number of residues236 in the loop increases, it may be that the real problem is better described237 by considering how stretched the loop to be predicted is. For example, if238 a loop contains many residues but is highly stretched, it will be predicted239 relatively accurately, as it can take on only a small number of different240 conformations.241 In order to check the relationship between accuracy and loop stretch,242 we use the ab initio loop modelling programme, MODELLER (Fiser, Do243 & Sali 2000). MODELLER is a popular protein structure prediction pro-244 gramme which has a built-in ab initio loop modelling module. Two test sets245 were prepared. The first test set contains loops of only 8 residues in length246 and 40 non-redundant loops in every 0.1 loop stretch bin. The second test247 set consists of loops from 6 to 10 residues in length. In this set, for each248 number of residues, the same numbers of loops (See Materials and Meth-249 ods) were selected for both contracted (\u03bb < 0.4) and fully stretched loops250 12 Pre Prin ts Pre Prin ts (\u03bb > 0.95).251 The average accuracy of MODELLER shows a negative linear corre-252 lation against loop stretch for the first test set (Figure 6A). In the case of253 fully stretched loops (\u03bb > 0.95), MODELLER can produce consistently ac-254 curate predictions, but its predictions worsen as the target loops are less255 stretched. Fully stretched loops are predicted accurately regardless of the256 number of residues (Figure 6B).257 However MODELLER failed to accurately predict contracted loops (Fig-258 ure 6A). In order to investigate what affects the prediction accuracy more259 (the number of residues or loop stretch), we calculated the partial cor-260 relations (Spearman\u2019s rank correlation) between accuracy, and the num-261 ber of residues and loop stretch. The partial correlation between loop262 stretch and RMSD is larger than that between the number of residues and263 RMSD (\u22120.465 and 0.367 respectively). Loop stretch, just like the number264 of residues is something that can be calculated without knowledge of loop265 conformation and therefore can be used in the design of loop structure266 prediction software.267 Discussion268 In this paper, we focus on a specific local property (span) and demonstrate269 that the modes of loop span distribution appear to be independent of the270 number of residues. Loop span shows a distinct frequency distribution271 13 Pre Prin ts Pre Prin ts which does not depend on anchor types or protein classes. 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Insertion of an elastase-394 binding loop into interleukin-1 beta. Protein Eng, 4: 313-317.395 Xiang Z. 2006. Advances in Homology Protein Structure Modeling.396 Curr Protein Pept Sci, 7: 217-227.397 17 Pre Prin ts Pre Prin ts Figure 1 The definition of loop span and loop stretch Loop span is the separation of the two C\u03b1s at either end of the loop. In this example, 2J9O Chain A (198-205) has a span of 13.7\u00c5 and contains 8 residues. Maximum span can be calculated from the number of residues in the loop to be 21.6\u00c5. Loop stretch is the normalised span (13.7/21.6 0.63).\u2243 Pre Prin ts Pre Prin ts Figure 2 statistics of protein loops : (A) The frequency distribution of loops containing different numbers of residues. Anti-parallel \u03b2 loops tend to have fewer residues. (B) The loop span distribution in terms of the anchor secondary structure do not show differences except for anti-parallel \u03b2 loops. The upper part of the anti-parallel \u03b2 loop span distribution is omitted in the figure. (C) The distributions of soluble loop span and membrane loop span appear to be similar. (D) A Q\u2013Q plot showing that the membrane and soluble loop span distributions are from the same probability distribution. Pre Prin ts Pre Prin ts Figure 3 The span distributions for loops containing different numbers of residues (A) These appear to show a constant mode. Data here is soluble loops excluding anti-parallel beta loops. (B) The modes for the span distributions for loops containing different numbers of residues compared to the maximum span for that length. The span modes were estimated using the Gaussian kernel density estimation. Note that the estimated mode of loops of 4 residues is close to its maximum span. Pre Prin ts Pre Prin ts Pre Prin ts Pre Prin ts Figure 4 Maxwell-Boltzmann distribution and loop span distribution (A) The loop span distribution (black) from soluble loops and that of the Maxwell-Boltzmann distribution (red). (B) The Q-Q plot suggesting that they follow the same distribution. Pre Prin ts Pre Prin ts Pre Prin ts Pre Prin ts Figure 5 Loop stretch of long and short loops Loop stretch distributions for loops containing different numbers of residues Shorter loops tend to be more stretched whereas longer loops are likely to be more contracted. Only soluble loops excluding anti-parallel \u03b2 loops are plotted. Pre Prin ts Pre Prin ts Figure 6 Protein loop structure prediction and loop stretch Accuracy of protein loop structure prediction methods do not only depend on the number of residues, but also on loop stretch. (A) The accuracy of loop prediction by MODELLER for loops which contain 8 residues with different values of loop stretch. there are 40 loops in each 0.1 split of loop stretch. a : moving average is shown. As loop stretch decreases prediction accuracy decreases. (B) Two sets of loops one contracted (\u03bb < 0.4) and one stretched (\u03bb > 0.95). Loops are also split by number of residues. For fully stretched loops (\u03bb > 0.95), regardless of the number of residues, MODELLER predicts accurately. Pre Prin ts Pre Prin ts Pre Prin ts Pre Prin ts",
    "url": "https://peerj.com/articles/1/reviews/",
    "review_1": "Walter de Azevedo Jr. \u00b7 Nov 21, 2012 \u00b7 Academic Editor\nACCEPT\nPaper accepted after modifications.",
    "review_2": "Walter de Azevedo Jr. \u00b7 Nov 15, 2012 \u00b7 Academic Editor\nMINOR REVISIONS\nYou manuscript needs minor revision.",
    "review_3": "Andras Fiser \u00b7 Nov 14, 2012\nBasic reporting\nNo comments\nExperimental design\nNo comments\nValidity of the findings\nNo comments\nAdditional comments\nThe manuscript of Choi et al. explores a specific property of protein loops: their span. It observes that loops with very different lengths (number of residues) can be fitted roughly to the same spans. They also describe a metric to asses the loop stretch, which in turn is informative to the quality of prediction: the more compact a loop, the more difficult to model it properly. As a consequence the authors argue that loop modeling methods should be tested and should be more focused on highly contracted loops, irrespectively of loop length, because these are much more challenging to model. Overall I found this work interesting and useful, the analysis is well done. I have a few minor comments:\n\n(1) The Introduction describing the loop modeling approaches is slightly misleading. It is important to stress that loop conformations -once the modeling is treated as a mini protein problem - do not depend on the loop sequence only. As in case of full length proteins a given sequence folds in its native fold under physiological conditions. In case of full length proteins the physiological environment is the solvent (and temperature etc), while in case of loop it is the solvent AND the rest of the protein spanning it. As a consequence, as it was described by us (BMC Struct Biol. 2006 Jul 4;6:15.Saturating representation of loop conformational fragments in structure databanks. Fernandez-Fuentes N, Fiser A.) and others, loops with identical sequences can have different conformations depending on the protein they show up.\n\n(2) In Fig 2C, I would guess that probably almost all membrane loops come from helix-helix connections, and this would require a comparison to helix-helix connected soluble loops and not to a mixed class, as it is now. In Fig2B helix-helix soluble loops spans are slightly shifted right for longer spans and on Fig2C membrane ones to the left, to shorter spans and therefore it is possible that once properly compared there will be a small but possibly significant difference.\n\n(3) There might be some trivial explanation for the roughly constant span of loops: tightly packed proteins cannot afford large cavities and therefore the typical anchor distances of ends of secondary structures will be under strong thermodynamic selection. All loops , irrespectively of length will have to be accommodated within that given span. There are some references to it in the text, but I think it might be a driving effect.\n\n(4) Fig. 6 illustrates one of the main points of the work that loop prediction accuracy is negatively correlated with loop span. While I do not doubt this effect, it seems that among compacted loops a few outliers contribute disproportionally to the worsening performance. I would suggest to use mean instead of average to account for the non-gaussian distribution more accurately.\nCite this review as\nFiser A (2013) Peer Review #1 of \"How long is a piece of loop? (v0.1)\". PeerJ https://doi.org/10.7287/peerj.1v0.1/reviews/1",
    "review_4": "Joost Schymkowitz \u00b7 Nov 13, 2012\nBasic reporting\nThe paper meets all the criteria of PeerJ, it is sound, well written and it represents an important intelectual contribution to the field of loop structure prediction.\nExperimental design\nThe authors do two things: they analyse some test sets of loops in terms of the stretch and span parameters and then evaluate loop prediction accuracy of the ab initio method Modeller to try to get an idea of difficulty of the structure prediction problem (judged by the accuracy of modeller's performance).\n\nI like the concept a lot and it makes a lot of sense, complicated loop folds are essentially harder to predict - which still allows for longer loops to be harder than shorter ones, but length in not in itself the key determinant.\n\nAs an adept of database-based methods, I would have liked to see the same analysis using eg our freely available loopbrix method (http://brix.switchlab.org/), since this would tell if DB methods somehow have a different accuracy profile.\nValidity of the findings\nI think the study is well done and the results are clearly presented, the conclusions are supported by the data.\nAdditional comments\nCool paper.\nCite this review as\nSchymkowitz J (2013) Peer Review #2 of \"How long is a piece of loop? (v0.1)\". PeerJ https://doi.org/10.7287/peerj.1v0.1/reviews/2",
    "pdf_1": "https://peerj.com/articles/1v0.2/submission",
    "pdf_2": "https://peerj.com/articles/1v0.1/submission",
    "all_reviews": "Review 1: Walter de Azevedo Jr. \u00b7 Nov 21, 2012 \u00b7 Academic Editor\nACCEPT\nPaper accepted after modifications.\nReview 2: Walter de Azevedo Jr. \u00b7 Nov 15, 2012 \u00b7 Academic Editor\nMINOR REVISIONS\nYou manuscript needs minor revision.\nReview 3: Andras Fiser \u00b7 Nov 14, 2012\nBasic reporting\nNo comments\nExperimental design\nNo comments\nValidity of the findings\nNo comments\nAdditional comments\nThe manuscript of Choi et al. explores a specific property of protein loops: their span. It observes that loops with very different lengths (number of residues) can be fitted roughly to the same spans. They also describe a metric to asses the loop stretch, which in turn is informative to the quality of prediction: the more compact a loop, the more difficult to model it properly. As a consequence the authors argue that loop modeling methods should be tested and should be more focused on highly contracted loops, irrespectively of loop length, because these are much more challenging to model. Overall I found this work interesting and useful, the analysis is well done. I have a few minor comments:\n\n(1) The Introduction describing the loop modeling approaches is slightly misleading. It is important to stress that loop conformations -once the modeling is treated as a mini protein problem - do not depend on the loop sequence only. As in case of full length proteins a given sequence folds in its native fold under physiological conditions. In case of full length proteins the physiological environment is the solvent (and temperature etc), while in case of loop it is the solvent AND the rest of the protein spanning it. As a consequence, as it was described by us (BMC Struct Biol. 2006 Jul 4;6:15.Saturating representation of loop conformational fragments in structure databanks. Fernandez-Fuentes N, Fiser A.) and others, loops with identical sequences can have different conformations depending on the protein they show up.\n\n(2) In Fig 2C, I would guess that probably almost all membrane loops come from helix-helix connections, and this would require a comparison to helix-helix connected soluble loops and not to a mixed class, as it is now. In Fig2B helix-helix soluble loops spans are slightly shifted right for longer spans and on Fig2C membrane ones to the left, to shorter spans and therefore it is possible that once properly compared there will be a small but possibly significant difference.\n\n(3) There might be some trivial explanation for the roughly constant span of loops: tightly packed proteins cannot afford large cavities and therefore the typical anchor distances of ends of secondary structures will be under strong thermodynamic selection. All loops , irrespectively of length will have to be accommodated within that given span. There are some references to it in the text, but I think it might be a driving effect.\n\n(4) Fig. 6 illustrates one of the main points of the work that loop prediction accuracy is negatively correlated with loop span. While I do not doubt this effect, it seems that among compacted loops a few outliers contribute disproportionally to the worsening performance. I would suggest to use mean instead of average to account for the non-gaussian distribution more accurately.\nCite this review as\nFiser A (2013) Peer Review #1 of \"How long is a piece of loop? (v0.1)\". PeerJ https://doi.org/10.7287/peerj.1v0.1/reviews/1\nReview 4: Joost Schymkowitz \u00b7 Nov 13, 2012\nBasic reporting\nThe paper meets all the criteria of PeerJ, it is sound, well written and it represents an important intelectual contribution to the field of loop structure prediction.\nExperimental design\nThe authors do two things: they analyse some test sets of loops in terms of the stretch and span parameters and then evaluate loop prediction accuracy of the ab initio method Modeller to try to get an idea of difficulty of the structure prediction problem (judged by the accuracy of modeller's performance).\n\nI like the concept a lot and it makes a lot of sense, complicated loop folds are essentially harder to predict - which still allows for longer loops to be harder than shorter ones, but length in not in itself the key determinant.\n\nAs an adept of database-based methods, I would have liked to see the same analysis using eg our freely available loopbrix method (http://brix.switchlab.org/), since this would tell if DB methods somehow have a different accuracy profile.\nValidity of the findings\nI think the study is well done and the results are clearly presented, the conclusions are supported by the data.\nAdditional comments\nCool paper.\nCite this review as\nSchymkowitz J (2013) Peer Review #2 of \"How long is a piece of loop? (v0.1)\". PeerJ https://doi.org/10.7287/peerj.1v0.1/reviews/2\nReview 5: nan\nReview 6: \n",
    "LLM_extracted_review": "['Review 1: Paper accepted after modifications.\\n\\nReview 2: Your manuscript needs minor revision.\\n\\nReview 3: \\n(1) The Introduction describing the loop modeling approaches is slightly misleading. It is important to stress that loop conformations do not depend on the loop sequence only; they also depend on the rest of the protein spanning it.\\n(2) In Fig 2C, almost all membrane loops likely come from helix-helix connections, requiring a comparison to helix-helix connected soluble loops rather than a mixed class.\\n(3) There might be a trivial explanation for the roughly constant span of loops: tightly packed proteins cannot afford large cavities, leading to strong thermodynamic selection on anchor distances.\\n(4) Fig. 6 illustrates that loop prediction accuracy is negatively correlated with loop span, but a few outliers among compacted loops may disproportionately worsen performance. It is suggested to use mean instead of average for a more accurate representation.\\n\\nReview 4: \\nThe paper meets all the criteria of PeerJ, is sound, well written, and represents an important intellectual contribution to the field of loop structure prediction. \\nThe authors analyze test sets of loops in terms of stretch and span parameters and evaluate loop prediction accuracy of the ab initio method Modeller. The concept makes sense, as complicated loop folds are harder to predict. \\nIt would be beneficial to see the same analysis using the loopbrix method to determine if database methods have a different accuracy profile. \\nThe study is well done, results are clearly presented, and conclusions are supported by the data. \\nCool paper.']"
}