Rēs ipSAE loquuntur : What’s wrong with AlphaFold’s ipTM score and how to fix it

Rēs ipSAE loquuntur: What’s wrong with AlphaFold’s ipTM score and how to fix it | bioRxiv /* */ /* */ <!-- <!-- /*! * yepnope1.5.4 * (c) WTFPL, GPLv2 */ (function(a,b,c){function d(a){return"[object Function]"==o.call(a)}function e(a){return"string"==typeof a}function f(){}function g(a){return!a||"loaded"==a||"complete"==a||"uninitialized"==a}function h(){var a=p.shift();q=1,a?a.t?m(function(){("c"==a.t?B.injectCss:B.injectJs)(a.s,0,a.a,a.x,a.e,1)},0):(a(),h()):q=0}function i(a,c,d,e,f,i,j){function k(b){if(!o&&g(l.readyState)&&(u.r=o=1,!q&&h(),l.onload=l.onreadystatechange=null,b)){"img"!=a&&m(function(){t.removeChild(l)},50);for(var d in y[c])y[c].hasOwnProperty(d)&&y[c][d].onload()}}var j=j||B.errorTimeout,l=b.createElement(a),o=0,r=0,u={t:d,s:c,e:f,a:i,x:j};1===y[c]&&(r=1,y[c]=[]),"object"==a?l.data=c:(l.src=c,l.type=a),l.width=l.height="0",l.onerror=l.onload=l.onreadystatechange=function(){k.call(this,r)},p.splice(e,0,u),"img"!=a&&(r||2===y[c]?(t.insertBefore(l,s?null:n),m(k,j)):y[c].push(l))}function j(a,b,c,d,f){return q=0,b=b||"j",e(a)?i("c"==b?v:u,a,b,this.i++,c,d,f):(p.splice(this.i++,0,a),1==p.length&&h()),this}function k(){var a=B;return a.loader={load:j,i:0},a}var l=b.documentElement,m=a.setTimeout,n=b.getElementsByTagName("script")[0],o={}.toString,p=[],q=0,r="MozAppearance"in l.style,s=r&&!!b.createRange().compareNode,t=s?l:n.parentNode,l=a.opera&&"[object Opera]"==o.call(a.opera),l=!!b.attachEvent&&!l,u=r?"object":l?"script":"img",v=l?"script":u,w=Array.isArray||function(a){return"[object Array]"==o.call(a)},x=[],y={},z={timeout:function(a,b){return b.length&&(a.timeout=b[0]),a}},A,B;B=function(a){function b(a){var a=a.split("!"),b=x.length,c=a.pop(),d=a.length,c={url:c,origUrl:c,prefixes:a},e,f,g;for(f=0;f<d;f++)g=a[f].split("="),(e=z[g.shift()])&&(c=e(c,g));for(f=0;f<b;f++)c=x[f](c);return c}function g(a,e,f,g,h){var i=b(a),j=i.autoCallback;i.url.split(".").pop().split("?").shift(),i.bypass||(e&&(e=d(e)?e:e[a]||e[g]||e[a.split("/").pop().split("?")[0]]),i.instead?i.instead(a,e,f,g,h):(y[i.url]?i.noexec=!0:y[i.url]=1,f.load(i.url,i.forceCSS||!i.forceJS&&"css"==i.url.split(".").pop().split("?").shift()?"c":c,i.noexec,i.attrs,i.timeout),(d(e)||d(j))&&f.load(function(){k(),e&&e(i.origUrl,h,g),j&&j(i.origUrl,h,g),y[i.url]=2})))}function h(a,b){function c(a,c){if(a){if(e(a))c||(j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}),g(a,j,b,0,h);else if(Object(a)===a)for(n in m=function(){var b=0,c;for(c in a)a.hasOwnProperty(c)&&b++;return b}(),a)a.hasOwnProperty(n)&&(!c&&!--m&&(d(j)?j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}:j[n]=function(a){return function(){var b=[].slice.call(arguments);a&&a.apply(this,b),l()}}(k[n])),g(a[n],j,b,n,h))}else!c&&l()}var h=!!a.test,i=a.load||a.both,j=a.callback||f,k=j,l=a.complete||f,m,n;c(h?a.yep:a.nope,!!i),i&&c(i)}var i,j,l=this.yepnope.loader;if(e(a))g(a,0,l,0);else if(w(a))for(i=0;i (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0];var j=d.createElement(s);var dl=l!='dataLayer'?'&l='+l:'';j.src='//www.googletagmanager.com/gtm.js?id='+i+dl;j.type='text/javascript';j.async=true;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-M677548'); Skip to main content Home About Submit ALERTS / RSS Search for this keyword Advanced Search New Results Rēs ipSAE loquuntur : What’s wrong with AlphaFold’s ipTM score and how to fix it View ORCID Profile Roland L. Dunbrack Jr. doi: https://doi.org/10.1101/2025.02.10.637595 Roland L. Dunbrack Jr. 1 Institute for Cancer Research, Fox Chase Cancer Center , Philadelphia, PA 19111 USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Roland L. Dunbrack Jr. For correspondence: Roland.Dunbrack{at}fccc.edu Abstract Full Text Info/History Metrics Data/Code Preview PDF Abstract AlphaFold’s ipTM metric is used to predict the accuracy of structural predictions of protein-protein interactions (PPIs) and the probability that two proteins interact. Many AF2/AF3 users have experienced the phenomenon that if they trim full-length sequence constructs (e.g. from UniProt) to the interacting domains (or domain+peptide), their ipTM scores change, even though the structure prediction of the interaction is unchanged. The reason this happens is due to the mathematical formulation of ipTM in AF2/AF3, which scores the interactions of whole chains. When one chain is a single ordered domain but the other contains lots of disorder or irrelevant domains, ipTM is higher in the presence of those residues than it is when they are trimmed. If both chains in a PPI complex contain large amounts of disorder or accessory domains that do not form the primary domain-domain or domain/peptide interaction, the ipTM score can be significantly lower in the presence of those regions than when they are trimmed. The score then does not accurately represent the accuracy of the structure prediction nor whether the two proteins actually interact. We have solved this problem by: 1) including only residue pairs in the ipTM metric that have good predicted aligned error ( PAE ) scores; 2) by adjusting the d 0 parameter (a function of the length of the query sequences) in the TM score equation to include only the number of residues with good interchain PAE s to the aligned residue; and 3) using the PAE value itself and not the probability distributions over the aligned error to calculate the pairwise residue-residue pTM values that go into the ipTM calculation. The first two are crucial in calculating high ipTM s for domain-domain and domain-peptide interactions even in the presence of many hundreds of residues in disordered regions and/or accessory domains. The third allows us to require only the common output json files of AF2 and AF3 (including the server output) without having to change the AlphaFold code and without affecting the accuracy. It also works on npz file output from Boltz. We show in a benchmark that the new score, called ipSAE (interaction prediction Score from Aligned Errors), is able to separate true from false complexes more efficiently than AlphaFold2’s ipTM score. The resulting program is freely available at https://github.com/dunbracklab/IPSAE . Introduction The AlphaFold programs ( 1 - 3 ) have had a profound impact on the structure prediction of proteins and protein complexes. AlphaFold-Multimer (v2.3) has enjoyed the widest use in predicting the structures of protein-protein interactions (PPIs), which are critical to essentially all biological processes. Since AlphaFold-Multimer code has been available for download since late 2021 (and v2.3 since December 2022), these programs have been extensively benchmarked for their ability to predict the structures of protein complexes accurately and their ability to predict whether two proteins interact. These benchmarks have utilized the scoring output from the AlphaFold programs, including residue-specific predicted local distance difference tests ( pLDDT s), predicted aligned errors ( PAE s) for residue pairs, and predicted template-modeling scores ( pTM ) and interface predicted template modeling scores ( ipTM s) for the whole modeled system. Typically, benchmarks have been constructed from Protein Data Bank (PDB) structures, and use the sequences provided for each PDB entry (e.g., the CASP competitions ( 4 , 5 ) and others ( 6 , 7 )). That is, they do not use the full UniProt sequences, which may contain disordered sequences and domains that do not form part of the interaction. PDB constructs are mostly fully ordered, save for some loops or short N and C terminal tails. In these cases, the ipTM score generally works well in assessing the accuracy of the structure prediction ( 8 ). However, in real-world situations where the interacting regions may not be known, structure predictions usually start with full-length protein sequences from UniProt. Then after observing which domains interact in the model with good PAE scores, it can be productive to input shorter sequence constructs to AlphaFold. Many studies have noted that different sequence constructs produce different ipTM scores, even though the predicted interface contacts are unchanged ( 9 - 13 ). For example, Danneskiold-Samsøe et al. compared AlphaFold-Multimer v2.2 models produced from either full-length sequences of single-pass transmembrane receptors and their full-length unprocessed ligands, or various truncations of the proteins (e.g., the extracellular domains only and the proteolytically processed secreted ligand proteins) ( 14 ). ipTM scores were higher and more predictive for the shorter constructs comprising only the interacting domains. In a comprehensive study, Lee et al. found shorter fragments of peptides binding to protein domains often scored better than longer fragments or full-length proteins ( 15 ). Bret et al. developed a scanning approach to search through disordered sequence regions for protein domain binders, because the ipTM score was not successful on full-length sequences ( 9 ). Some reports have shown that ipTM s, which are calculated over whole chains, are less predictive than other measures. These measures include pLDDT values of interface residues (as in the pDockQ score) ( 16 , 17 ), interface PAE values ( iPAE ’s) calculated over only interchain residue pairs within various cutoff distances ( 18 , 19 ), or combinations of AlphaFold metrics and energy functions to evaluate interfaces ( 7 ). In this paper, we investigate the origin of the behavior of AlphaFold’s pTM and ipTM scores based on their mathematical descriptions in the AlphaFold papers. We then use this analysis to identify alternative formulations that are not sensitive to disordered regions or non-interacting accessory domains in either or both chains of pairwise interactions in AlphaFold models. We show that using only interchain residue pairs with good PAE scores in the evaluation of ipTM and evaluating the TM formula’s d 0 parameter (which is based on sequence length) according to the number of such pairs, we can produce good ipTM -like values for true interactions even in the presence of large amounts of disorder and accessory domains. The resulting code, which is freely available, works only on the PAE matrix provided in the default output of both AlphaFold2 and AlphaFold3. We have named the metric ipSAE for “interaction prediction score from aligned errors.” The word is a play on the Latin phrase “ Rēs ipsae loquuntur ,” meaning “The things speak for themselves ,” referring to the AlphaFold output scores. Derivation of the ipTM and ipSAE scores The TM score was developed by Zhang and Skolnick to assess the accuracy of predicted models of protein structures compared to experimental structures of the same proteins ( 20 ). It is defined as: Each d j is a distance between the predicted position of the Cα atom of residue j in the model and residue j in the experimental structure for a given superposition. A model of a protein can be superimposed in various ways on an experimental structure, and the maximum is taken over all possible alignments. In practice, the maximum is taken over only a subset of such alignments (e.g., by running different structure alignment programs or with different parameters). d 0 is a scaling factor that reduces or eliminates the length dependence of the TM score for alignments of unrelated proteins ( 20 ). It has a fitted value of If L target is 500 residues, d 0 has a value of about 8 ( Figure 1 ). The original TM score was used in development of protein structure prediction methods, when the sequence length of the experimental structure (the target) might be longer than the sequence length of the model (e.g., if only a single domain of the target could be modeled using templates). Thus, a partial model (or template) was heavily penalized. In some cases, the experimental structure might be missing some residues due to poor electron density. The sum is therefore over the number of residues the model and experimental structure have in common ( L common ). Download figure Open in new tab Figure 1. The d 0 parameter in the TM score equation as a function of sequence length L AlphaFold2 and AlphaFold3 use the concept of “aligned error” to generate predicted accuracy metrics for output models ( Figure 2 ). After superposing the N, Cα, and C atoms of residue i of a model onto the N, Cα, and C atoms of the same residue i in the experimental structure, the aligned error (AE) of residue j is the distance between the Cα atom of residue j in the model and Cα of residue j in the experimental structure. During training, the experimental structure is known, and the network is trained to predict a probability distribution over the aligned error distance when the experimental structure is not known (i.e., during inference). The probability distribution is defined over the AE ij distance in 64 bins of width 0.5 Å (0Å-0.5Å, 0.5Å-1.0Å, …, 31.5-32Å), where the last bin also includes distances larger than 32 Å. The predicted aligned error, PAE ij , for each pair of residues is calculated from the predicted probability distribution over the aligned error with the equation ( Eq. 11 in AF3 paper supplemental): where Δ b = ( b − 0.5)⁄2 is the center of each bin (0.25Å, 0.75Å, …, 31.75Å), of bin b , and . Download figure Open in new tab Figure 2. Definition of aligned error (AE) in AlphaFold2 and AlphaFold3 For a single chain (or a whole protein complex), the PAE ij values can be substituted into Equation 1 for the TM score to provide an equation for the pTM score (predicted template modeling score): The role of residue i in this equation is to create a set of alignments used to calculate the TM score, one for each residue in the chain (or complex) The value of pTM is then calculated from the highest scoring of these alignments, just as in Equation 1 for the original TM score In the AlphaFold papers, the expression under the sum is instead calculated as an expectation value from the probability distribution of the aligned error used in Eq. 3 (AF3 paper supplemental Eq 17): For simplicity, we define the pairwise pTM matrix from the aligned error probability distribution as: or alternatively (as an approximation) from the PAE value. The pSAE ij can be used anywhere pTM ij can be used. The residue-specific mean value of pTM ij , based on the alignment of residue i is given by: And . From these equations, we can generalize the expression for pTM by specifying the residue sets for the alignments (set S 1 , residues i ) and those for the residue displacements between modeled structure and experimental structure, if it were known ( S 2 : residues j ): For a complex of two protein chains, A and B, we can perform the residue-residue structure superpositions over one chain (e.g., S 1 =chain A) and calculate the TM score over the other chain ( S 2 =chain B), which would then contain a rotation-translation component as well as the accuracy of the structural model of chain B. So When AlphaFold2 or AlphaFold3 provides a value of ipTM for a pair of chains, it provides a single value which is the maximum of the two asymmetric values (or equivalently the maximum over all residues in both chains of the interchain pTM i ): AlphaFold2 and AlphaFold3 use a value for d 0 based on the sum of the lengths of the two chains. AlphaFold3 provides an ipTM for each chain where the maximum is taken over all residues i in that chain and the mean is over all residues in all other chains. In AlphaFold2 and AlphaFold3, the overall ipTM of any multiprotein complex is calculated from the maximum over all residues of the mean ipTM ij , where the mean is taken over all residues in all other chains that do not contain residue i . The value of d 0 is the sum of all protein chain lengths in the model. Our experience, and that of many others ( 14 ), demonstrates problems in the calculation of ipTM in the presence of disordered residues and other domains in the sequence constructs that do not interact between the chains. Frequently, users of AlphaFold2 and AlphaFold3 have to repeat calculations with different protein constructs that remove the disordered regions and observe a large change (up or down) in ipTM , even though the interacting domain-domain or domain-peptide complex structure remains the same. There are two scenarios to consider, one in which the ipTM score is artificially high and one in which it is artificially low. The reasons for both are clear from the equations presented above as follows. If one chain is held fixed in sequence, while the other is extended to include disordered regions or additional domains that do not interact with the fixed sequence chain, the ipTM score goes up . This is because the Δ b values in Eq. 5 (or PAE ij values in Eq. 7 if PAE s are used directly) are scaled down by the larger value of d 0 (calculated from the sum of the two chain lengths, as in Eq. 2 ). This causes an artifact in the calculation of ipTM , artificially raising the score when the user adds sequence to one of the chains. Removing these regions in one chain lowers the score to more realistic values. The opposite occurs when both chains contain non-interacting regions (disorder or non-interacting domains). For a protein-protein complex, ipTM is a mean value of pTM ij over all residues j in one of the chains, after superposition on one residue i in the other chain (after taking the maximum over all residues i ). It therefore includes many very low pTM ij values because of the high PAE ij values (>30) between ordered residues in one chain and disordered residues in the other. Any mobile domains that do not interact also lower the score, because they also contribute low pTM ij from low PAE ij . In practice, both effects are operative and compete unpredictably: raising ipTM due to an increase in sequence length and consequently d 0 in Eq. 5 , and lowering ipTM due to the inclusion of many poor PAE values for non-interacting sequence in both chains. As an example, we take the interaction between KRAS and the RAS-binding domain of RAF1 ( Figure 3 ). When only the ordered domain sequences are input to AlphaFold-Multimer (v2.3), the ipTM is 0.85. When 120 residues of disorder are added to only one chain (the blue RAF1 in Example 2), the ipTM rises to 0.90 (since the ipTM is already quite high, it cannot raise significantly). This occurs because a residue in RAF1 (marked by a red asterisk) has high pTM ij values with all residues in the fully ordered KRAS chain (magenta) and the value of d 0 is higher in Example 2 than it is in Example 1. But when disorder is present in both chains (Examples 3 and 4 in Fig. 3 ), the ipTM is decreased because every residue in each chain has some low pTM ij values with residues in the other chain. The decrease is proportional to the relative amount of disorder to order in the chain with less disorder. For example, with 120 disordered residues in each chain (Example 4), RAF1-RBD and KRAS are 61% and 41% disordered respectively. The ipTM value is due to residue T68 of RAF1, which sits in the interface with KRAS. Its pairwise pTM ij values with KRAS residues are 59% ordered (at ∼0.9 each) and 41% disordered (at ∼0.2 each), or approximately 0.59 * 0.9 + 0.41 * 0.2 = 0.61 (the AF2 output value is 0.56). Download figure Open in new tab Figure 3. AlphaFold2 models of the complex of KRAS (magenta) and the RAS-binding domain of RAF1 (blue). Disordered residues (15 repeats of the sequence GGGS) were added to the N or C terminus (or both) of one or both chains, which increases the ipTM when this occurs in one chain (Example 2) and decreases it when it occurs in both chains (Examples 3 and 4). There are several ways of dealing with this. In the ipTM expressions, we could skip residue pairs where one (or both) residues have pLDDT values less than some cutoff value (e.g. pLDDT <50). This does not always work: auxiliary domains in one or both of the proteins that do not contribute to the protein-protein interaction will have good pLDDT s but poor intermolecular pTM ij , thus lowering the ipTM . The ipTM could be calculated over only contacting residues in the model within some cutoff distance. This can also be a problem because disordered residues or auxiliary domains in one or both chains can contact the other chain and contribute poor pTM ij to the ipTM evaluation, Varga et al recently proposed using the predicted distance distograms produced by the AlphaFold2 network to restrict the calculation of ipTM to interchain residue pairs that are predicted to be in contact ( 21 ). This method excludes disordered regions and auxiliary domains that do not have a strongly predicted interaction, even if they are in contact in the models. Their score, called actifpTM , is calculated over the subsets of residues that make up the interface of two chains but only those that AlphaFold2 is confident about. actifpTM is now implemented within the ColabFold framework ( 22 ). We propose another alternative, where we use the PAE ij values to restrict the ipTM calculation to interchain residue pairs that have well predicted aligned error distances, regardless of whether they are in or near the protein-protein interface. In contrast to actifpTM , we adjust the value of d 0 in the asymmetric ipTM expression to the number of residues in the chain under the mean expression with good interchain PAE values ( Equation 10 ). This is critical, because a small number of interchain residue pairs with spuriously good PAE ij and consequently good pTM ij values may produce an unrealistically ipTM if d 0 is not adjusted. We define the ipSAE score ( i nterface p redicted TM S core based on A ligned Errors) for two chains (A and B) as follows: And Here, L PAE < cutoff is the number of unique residues in chain B that have PAE ij < cutoff given the identity of the aligned residue i . We use a minimum value of 1 for d 0 , since Yang and Skolnick did not test the fit for proteins shorter than 30 amino acids ( d 0 =1 for L∼26.5), and the denominator in Eq. 14 starts to blow up for values << 1.0, which may not be realistic or helpful. In the AlphaFold code, the minimum value is set to 19, since L =18 produces a negative number. For a given chain pair, the ipSAE score is the maximum of the two asymmetric values: ipSAE can be calculated for every pair of chains in a multi-chain complex from the PAE matrices from the AlphaFold2 or AlphaFold3 output json files. Results RAF1 complexes The TKL family kinase, RAF1, contains three domains: a RAS-binding domain (RBD: residues 56-131), an immediately adjacent cysteine-rich domain (CRD: residues 138-184), and a protein kinase domain (PK: residues 340-614). The rest of the chain of length 648 residues is intrinsically disordered (residues 1-55, 185-339, and 615-648). As noted above, AlphaFold-Multimer models of the RAF1-RBD with KRAS result in ipTM values that are lowered in the presence of artificial disordered sequences when they are present in both chains ( Figure 3 ). The ipSAE value of 0.8 for Example 4 eliminates most of the disorder effect. RAF1 interacts with the TKL family pseudokinase KSR1, facilitating the activation of RAF1 and its translocation to the membrane ( 23 ). KSR1 also contains three domains: the coiled-coil/Sterile-α-motif domain (CC-SAM: residues 30-172), a cysteine-rich domain, homologous to the CRD of RAF1 (CRD: residues 347-391), and a protein pseudokinase domain (pPK: residues 599-833). There is no experimental structure of a RAF1-KSR1 complex, but it has been hypothesized that the two kinase domains bind in a mode similar to the well-known BRAF homodimer ( 24 ). AlphaFold-Multimer models of the heterodimer sequences of full-length RAF1 and full-length KSR1 show a kinase/pseudokinase heterodimer that is very similar to the BRAF homodimer ( 24 ) with ipTM values between 0.38 and 0.41 across 25 models (5 seeds by all 5 sets of AF2 model weights, without templates). The other folded domains and disordered regions of both proteins are not in fixed position relative to the kinase domains across the 25 models, and do not show any key interprotein interactions ( Figure 4A ). Download figure Open in new tab Figure 4. RAF1-KSR1 models. A. AlphaFold2 models of full-length RAF1 and KSR1 . RAF1 RBD-CRD domains in pink and kinase domain in magenta. KSR1 CC-SAM domains in green, CRD in yellow, and pseudokinase domain in blue. The 25 models are aligned on the kinase domain of RAF1. The non-kinase domains are not fixed relative to the two kinase domains. B. Scatterplot of interchain pSAE ij vs pTM ij values for RAF1-KSR1 complex . pTM ij was calculated from the pTM matrix output by AlphaFold2 (from a modified version of ColabFold). It uses a d 0 from the combined length of both proteins. pSAE ij was calculated with no PAE cutoff and with a d 0 also based on the combined length of both protein chains. As described above, we can use the PAE values to calculate ipTM -like scores over specified interprotein residue pairs. AF2 calculates the full pTM matrix with a value of d 0 that is the combined length of the two proteins. If we calculate pTM with the PAE values instead and use the same d 0 , the interchain pSAE ij and pTM ij are highly correlated ( Figure 4B ). AlphaFold-Multimer calculates the ipTM via Equations 10 and 11 by calculating the pTM i for each residue in both chains ( Figure 5 ). The two kinase domains are responsible for the high scoring regions, while the accessory domains in each protein are visible as small bumps in the plots. The maximum value in the curve in Figure 5 occurs for residue W632 of KSR1, which is in the interface between the kinase domains. If we use the pSAE ij value to calculate pSAE i for each aligned residue i of the complex and adjust d 0 for the number of residues that have a good PAE for the aligned, we see higher scores for the kinase domains in RAF1 and KSR1 and zero for the accessory domains. AlphaFold2’s ipTM for the top-ranking complex is 0.41, while the ipSAE score is 0.73. Download figure Open in new tab Figure 5. Per-residue ipTM and ipSAE scores for the RAF1-KSR1 complex. ipTM (top) was calculated from the pairwise pTM matrix from AlphaFold-Multimer v2.3 (ColabFold). It uses a d 0 from the combined length of the two proteins (1571 amino acids; d 0 =12.57). ipSAE with a PAE cutoff of 15.0 and the same value of d 0 (middle figure). A cutoff for the PAE score of 15.0 Å was used to produce the ipSAE scores (bottom figure). The maximum occurs for W632 of KSR1 for both scores (green arrows) with a value of d 0 of 6.32 (286 residues in RAF1 with PAE <15 Å). The TKL family kinase, RIPK1, is not known to bind to RAF1. RIPK1 has a kinase domain (PK: residues 8-324), a RIP homotypic interaction motif (RHIM: residues 531-547), and a Death domain (DD: residues 567-671). ipTM and ipSAE plots by residue are shown in Figure 6 , demonstrating the effects of using the PAE cutoff and the evaluation of d 0 based on the number of residues with PAE less than a cutoff of 15 Å. The top plot shows the per-residue ipTM scores from AlphaFold2 (by averaging each row of the interchain pTM ij values output from a modified version of ColabFold). AF2 uses a d 0 based on the sum of the two chain lengths (in this case 648 + 671 = 1319 residues, d 0 =11.75). In the middle plot, the PAE matrix is used to limit the number of pTM ij used for each residue. It uses the same value of d 0 (11.75) as in the top plot. The resulting residue-specific ipSAE values are much higher than the ipTM values, with an overall ipSAE value of 0.459 from the alignment on residue L433. This is expected because residue pairs with good PAE values will have high pairwise ipTM (or ipSAE ) values. But the number of such pairs in truly non-interacting proteins is quite low, if AlphaFold is working as expected. In the bottom plot, the combined effect of the PAE cutoff of 15 Å and the residue-specific d 0 values bring the residue ipSAE values way down. The overall value of ipSAE is now 0.044, indicating that the proteins are not likely to interact. The value of d 0 was 3.05 from 75 residues below the PAE cutoff. Download figure Open in new tab Figure 6. Per-residue ipTM (top) and ipSAE scores (middle and bottom) for the RAF1-RIPK1 pseudocomplex. A cutoff for the PAE score of 15.0 Å was used to produce the ipSAE scores. The ipTM score per residue scores (top plot) show a modest interaction between the chains with a maximum value at residue D380 of RIPK1, ipTM =0.290. AF2 uses d 0 from the sum of the full chain lengths. A PAE cutoff using the same d 0 (middle plot) (from the sum of both chain lengths) raises the ipSAE values compared to the ipTM values. But adjusting d 0 to account for the number of residues in the mean pTM ij calculation (e.g. for each residue in RAF1, this is the number of residues in RIPK1 that have PAE < PAEcutoff ) significantly lowers the score of the non-interacting proteins to a value of 0.044. The TKL family kinase, RIPK1, is not known to bind to RAF1. RIPK1 has a kinase domain (PK: residues 8-324), a RIP homotypic interaction motif (RHIM: residues 531-547), and a Death domain (DD: residues 567-671). ipTM and ipSAE plots by residue are shown in Figure 6 , demonstrating the effects of using the PAE cutoff and the evaluation of d 0 based on the number of residues with PAE less than a cutoff of 15 Å. The top plot shows the per-residue ipTM scores from AlphaFold2 (by averaging each row of the interchain pTM ij values output from a modified version of ColabFold). AF2 uses a d 0 based on the sum of the two chain lengths (in this case 648 + 671 = 1319 residues, d 0 =11.75). In the middle plot, the PAE matrix is used to limit the number of pTM ij used for each residue. It uses the same value of d 0 (11.75) as in the top plot. The resulting residue-specific ipSAE values are much higher than the ipTM values, with an overall ipSAE value of 0.459 from the alignment on residue L433. This is expected because residue pairs with good PAE values will have high pairwise ipTM (or ipSAE ) values. But the number of such pairs in truly non-interacting proteins is quite low, if AlphaFold is working as expected. In the bottom plot, the combined effect of the PAE cutoff of 15 Å and the residue-specific d 0 values bring the residue ipSAE values way down. The overall value of ipSAE is now 0.044, indicating that the proteins are not likely to interact. The value of d 0 was 3.05 from 75 residues below the PAE cutoff. Benchmark of recent PDB entries We identified a set of 40 PDB entries that share at most 40% identity with any chain present in the PDB prior to the AlphaFold-Multimer v2.3 cutoff date of Sept. 30, 2021. The entries had to have exactly two unique sequences and have a biological assembly consistent with a pairwise interaction of the two unique sequences (e.g., we excluded assemblies larger than octamers and chose entries where the shorter sequence interacted with only one copy of the longer sequence). Each sequence had to have at least 12 amino acids in the coordinates of the PDB file. Sequence identities were obtained from the PISCES webserver ( 25 ). We ran AlphaFold-Multimer v2.3 on the PDB sequences themselves and from the full-length Uniprot sequences, as identified from SIFTS ( 26 ) (as given in the PISCES sequence files). We also created a set of 70 AlphaFold jobs by randomly creating heterodimer pairs by mixing sequences from different entries in the set of 40 PDB entries. These were run with the full-length Uniprot sequences only. The results of the ipTM and ipSAE scores are shown in Figure 7 . The top left panel shows the ipTM values calculated from the pTM matrix in ColabFold. AF2 uses a value of d 0 calculated from the sum of the lengths of the two sequences in each query. Our values of ipTM agree exactly with the ipTM values present in the AF2 json output files. If we use the PAE values in the ipTM expression (but no PAE cutoff), instead of the AF2 pTM matrix, we get quite similar distributions (top right panel). In both panels, there is overlap in the density between values of ipTM or ipSAE from 0.3 to 0.7 for the true dimers (full-length Uniprot sequences, blue curves and data points) and false dimers (full-length Uniprot sequences, magenta curves and data points). Download figure Open in new tab Figure 7. Benchmark of recent PDB heterodimers. A set of 40 heterodimer PDB entries with less than 40% sequence identity to any sequences in the PDB prior to October 1, 2021 were identified. The PDB sequences were used as queries to AlphaFold-Multimer v2.3 (green curves). The full-length Uniprot sequences for these chains were also used as a second set of 40 target complexes for AF-Multimer v2.3 (blue curves). A third set of 70 targets was built from mixing the Uniprot sequences from different entries (magenta curves). The plots show kernel density estimates of ipTM and ipSAE for the top 10 ranked complexes (AF2 ranking based on 0.8 * ipTM + 0.2 * pTM ) out of 25 models (5 seeds x 5 AF2 weight-sets with no templates used). The top left panel shows ipTM based on the pTM matrix from AF2. The top right panel shows ipTM calculated from the PAE matrix instead of the pTM matrix (the PAE value is used in the denominator of the pTM expression instead of the sum over probabilities). The remaining rows show ipSAE values with different PAE cutoffs used in the mean value calculation. d 0 for these calculations was based on the PAE cutoff. The set of 40 PDB entries is: 7f4p, 7qii, 7sck, 7t5p, 7tj4, 7wmv, 7wwq, 7ytu, 7zd5, 8a51, 8a82, 8bfj, 8blw, 8cdp, 8dqv, 8fbd, 8fzz, 8g0p, 8gs1, 8guo, 8hi7, 8hk0, 8ir4, 8jj9, 8jmq, 8jzd, 8orn, 8ows, 8q4h, 8qvc, 8r5i, 8s2m, 8vjl, 8vx9, 8wx5, 8xfb, 8y2n, 8ypu, 8zlz, 9dk1. Download figure Open in new tab Figure 8. Top-ranked ColabFold AlphaFold-Multimer v2.3 models of protein complexes from full-length Uniprot sequences. PDB entries 1YCR, 2A25, 3ZGC, and 4H3B were used as examples in the preprint of Varga et al. RAF1 kinase domain plus chicken Lysozyme C and full-length RAF1 with RIPK1 are examples of non-interacting proteins and their resulting scores. In the next three rows, kernel density plots of ipSAE values are shown for all three sets of targets with different values of the PAE cutoff in descending order (32 = no cutoff, 25, 20, 15, 10, and 5 Å). As the PAE cutoff decreases, the density in the mid-range of ipSAE decreases, separating true from false dimers more effectively than the ipTM values from AlphaFold (top left panel). The true dimers with Uniprot sequences have significantly improved ipSAE values at lower cutoffs, because they contain disorder and accessory domains that do not form part of the interaction between the two proteins. The PDB sequences (green curves), conversely, do not change that much with the PAE cutoff since they do not usually contain disordered regions or mobile domains that do not form part of the interaction. The overall results indicate that the ipSAE score may be better at separating true from false interactions even in the presence of disordered sequences and/or accessory domains in both sequences. Cutoffs of 10 or 15 Å may be most suitable . Comparison with actifpTM Varga et al. ( 21 ) identified the same problem with the ipTM score as we have discussed above – that disordered regions depress the ipTM score when they are not part of the binding interface between two proteins. They gave four example systems of protein-peptide complexes: PDB entries 1ycr (MDM2 and P53 peptide), 2a25 (E3 ubiquitin ligase SIAH1 and Calcyclin binding protein peptide), 3zgc (KEAP1 and NF2L2 peptide), and 4h3b (MAPK10 and SH3 domain-binding protein 5 peptide). We ran AlphaFold-Multimer v2.3 on the Colabfold Jupyter notebook, which calculates the actifpTM values, using the full-length Uniprot sequences of both chains (instead of the PDB constructs or short elongations of these, used in the actifpTM preprint). The calculations were performed with two seeds, no templates, and 3 recycles. We calculated ipSAE at different PAE cutoffs on the rank001 models from Colabfold. The results are shown in Table 1 . For three of the targets, AlphaFold produces good models where the binding peptide is correctly placed on the folded domain, even though the full-length Uniprot sequence was provided to Colabfold. After superposition onto the folded domain from the PDB structure (chain A in all cases), the RMSDs were 1.32, 0.72, and 1.12 Å for entries 1ycr, 2a25, and 3zgc. For these three entries, the actifpTM values were quite high, ranging from 0.93 to 0.97. The ipSAE values were lower with values around 0.68, 0.55, and 0.73 Å respectively (at PAE cutoff 10 Å). View this table: View inline View popup Download powerpoint Table 1. Comparison of actifpTM targets with their ipTM and ipSAE values The 4h3b structure is quite different. AlphaFold places the wrong peptide from SH3BP5 into the inhibitory binding site on the kinase domain MAPK10. In the PDB structure, residues 341-350 bind to the kinase domain. But in the model from full-length Uniprot sequences, the 341-350 segment is 100 Å away. Instead, residues 425-439 bind to the kinase domain in the SH3BP5 binding site. The ipTM from AlphaFold is 0.443, and the actifpTM value is 0.690, while the ipSAE values range from 0.0 (no PAE pairs less then 5 Å) to 0.20 ( PAE cutoff 25 Å). We also ran Colabfold calculations of the RAF1 kinase domain with a presumably non-interacting protein, chicken lysozyme C (LYSC_HUMAN), and full-length RAF1 with RIPK1. For LYSC, The ipTM value was 0.388 and the actifpTM was 0.467. The ipSAE scores successfully identify the non-interaction with ipSAE values from 0.0 to 0.1 ( Table 1 , last column). For RIPK1, ipTM was 0.277, actifpTM was 0.462, and ipSAE was 0.0 ( PAE cutoffs ≤ 15 Å). Structure prediction benchmark of Genz et al Genz et al recently published a benchmark of 223 heterodimeric complexes absent from the training data of AlphaFold2 and AlphaFold3 ( 6 ). They ran ColabFold with and without templates (labeled CF-T and CF-F respectively) and AlphaFold3 (AF3) and assessed the correlation of various metrics with structural accuracy as measured by DockQ. The sequences used in these computations were those from the constructs in the PDB structures. While the main advantage of the ipSAE score may be in handling sequences with high amounts of disorder or non-interacting domains in one or both proteins, we wanted to assess whether ipSAE had good correlation with structure prediction accuracy. Luca Genz was kind enough to run their benchmark with the ipSAE score and compare it to the other metrics in their published paper. The results are shown in Fig. 9 . ipSAE performs slightly better than the next best metrics on the ColabFold models and equivalently on the AF3 models. Download figure Open in new tab Figure 9. Benchmark of Genz et al. for correlation of various scoring metrics with structure prediction accuracy as measured by DockQ. The set of targets comprised 223 heterodimers from the PDB not in the training data of AlphaFold2 and AlphaFold3. CF-T and CF-F indicate template-based and template-free modeling with ColabFold. Discussion We have proposed an ipTM -like score based on the output of AlphaFold2. The code has been modified to work on AlphaFold3 output, both from the AlphaFold3 server and AlphaFold3 run locally, as well as Boltz1. It works on modified amino acids as well as protein/nucleic acid interactions. The ipSAE score is calculated over interchain residue pairs that pass a PAE cutoff, thus eliminating the effect of disordered regions in both chains and/or accessory domains that AlphaFold2 does not predict to be part of the binding interface. On a benchmark of 40 heterodimer complexes in the PDB not very similar (at 40% sequence identity) in the AlphaFold2 training set and 70 non-interacting sequence pairs from the same set, models based on full-length Uniprot sequences showed greater discrimination between true and false dimers with the ipSAE score compared to ipTM . We also showed that in some cases, our score behaves better at discrimination true than false interactions than the recently proposed actifpTM score of Varga et al. A true comparison would require a much larger set of targets. Like ipTM in AlphaFold3 output and the actifpTM score, the ipSAE score can be calculated for every pair of chains in a multi-chain complex from AlphaFold2 output. We calculate the asymmetric values (A⟶B is different from B⟶A, where the first chain contains the aligned residues and the second chain contains the scored residues in the PAE values), as well as the maximum over all residues in both chains. It is possible there is insight to be gained in considering both values, rather than just the maximum, particularly for protein-peptide complexes. Further comparison is needed to other scores presented in the literature that account for the flaws in ipTM in various ways. We made a few comparisons to the actifpTM score ( 21 ), which like ipSAE limits (and weights) the contribution of pairwise ipTM matrix elements to the resulting score. Kim et al. presented to the Local Interaction Score ( 27 ), which is obtained from the by converting PAE scores to a score from 0 to 1.0 and averaging over all interchain residue pairs with PAE ≤ 12 Å. The pDockQ ( 28 ) and pDockQ2 ( 18 ) scores are based on the pLDDT and PAE scores of interface residues, and also attempt to improve on the ipTM score from AlphaFold. In addition to its ability to distinguish true from false interacting pairs, even in the presence of substantial disorder and non-interacting accessory domains, a recent benchmark from Genz et al. demonstrate that ipSAE performs as well or slightly better than ipTM as demonstrated by correlation with DockQ scores. The d 0 parameter in the TM expressions presents challenges for short peptides. In the original TM score paper, no individual structures were compared that were shorter than 40 amino acids. d 0 becomes negative when the protein length is less than 19 amino acids, with a resulting d 0 value of 0.17 when the length is 19. But in that case, the denominator of the pTM expression blows up and becomes very low, not matter how accurately the position of a peptide bound to a folded domain is predicted. To avoid this, we chose to set a minimum value of d 0 to 1.0, which is a peptide length of approximately 27 amino acids. But this is somewhat arbitrary and needs to be investigated further. Finally, the method for calculating the ipTM in the AlphaFold programs relies on the maximum ipTM over the residues in both chains. But many protein pairs have multiple domain-domain interactions separated by disordered regions. In these cases, the ipTM only scores one domain-domain pair (which ever scores highest) and the other(s) do not contribute. Examination of the PAE plot is helpful in identifying such cases. Models can then be produced with shorter constructs to estimate the ipTM s of each domain-domain interaction. Outputting ipSAE values from different aligned residues (not just the maximum value) may be useful in deriving a more useful metric than the methods described here and elsewhere. Our script, described below, outputs a file with the by-residue values of ipSAE which may be used for this purpose. Recently, several papers have utilized the ipSAE score in protein binder design and structure prediction of protein complexes. Overath et al assembled a set of more than 3,700 designed binders with experimental data, comprising 436 binders and 3,324 non-binders, from studies on 15 different targets from various labs ( 29 ). The minimum of the two asymmetric AlphaFold3 ipSAE scores (target⟶binder and binder⟶target) was found to have 1.4 times the precision of iPAE used for binder design in the RFDiffusion program ( 30 ). It was the single best predictor of binding compared to ipTM, iPAE, actifpTM , and pDock Q. Chow et al. ( 31 ) designed 1,589 novel protein binders targeting BCMA, CD19, and CD22 with BindCraft ( 32 ) and RFDiffusion. They found that ipSAE was a better metric for identifying binders than ipTM and iPAE , and correlated well with kD. Moriwaki et al found that ipSAE had a greater discriminatory power than ipTM in predicting known true complexes from mismatched pairs of proteins in biosynthetic gene clusters ( 33 ). Usage and Output The code is written in Python3 and takes as input a json file from AlphaFold2 or AlphaFold3 and corresponding PDB-format or mmCIF-format files for the coordinates respectively. The commands to use are: python ipsae.py python ipsae.py For example: python ipsae.py RAF1_KSR1_scores_rank_001_alphafold2_multimer_v3_model_4_seed_003.json \ RAF1_KSR1_unrelaxed_rank_001_alphafold2_multimer_v3_model_4_seed_003.pdb 15 15 python ipsae.py fold_raf1_ksr1_mek1_full_data_0.json fold_raf1_ksr1_mek1_model_0.cif 15 15 The output from the second command is given in Figure 10 . Download figure Open in new tab Figure 10. Output of ipsae.py on an AlphaFold3 model of a ternary complex of full-length human RAF1, KSR1, and MEK1 (Uniprots: RAF1_HUMAN, KSR1_HUMAN, MP2K1_HUMAN). The asymmetric values of the ipSAE metrics are given in rows with type equal to “asym.” The maximum value of each metric (over X⟶Y and Y⟶X asymmetric values) is given in the row labeled “max” (shown in bold type). Bottom: (left) top ranked AlphaFold3 model with chains labeled by color: RAF1 (chain A: magenta), KSR1 (chain B: blue), MEK1 (chain C: green). Middle: After coloring all three chains gray, PyMOL script alias “color_A_B” colors magenta and blue all residues in chains A and B respectively that have one or more interchain PAE values less than the cutoff (15 Å). Right: color B_C colors residues blue and green if they have interchain PAE values less than the same cutoff. The code reads the overall ipTM from the AlphaFold2 json file, which has one value for any size protein complex. Given the name of the AlphaFold3 “full_data” json file, the code will read the chain_pair_iptm from the corresponding “summary_confidences” json file, if it exists. In this example, that would be named fold_raf1_ksr1_mek1_summary_confidences_0.json . In the output, these scores are called ipTM_af . For AlphaFold2, all chain pairs have the same value of ipTM_af . For the example in Figure 10 , AlphaFold3 calculate ipTM pairwise values for 0.46 for RAF1-KSR1 (chains A and B), 0.51 for RAF1-MEK1 (chains A and C), and 0.77 for KSR1-MEK1 (chains B and C). To calculate the ipSAE and other metrics, the code reads the PAE values from the respective json files. AlphaFold2 provides a square PAE matrix with row and column dimensions of the length of the combined protein sequences. The rows are aligned residues and the columns are scored residues. AlphaFold3 structure predictions may include post-translationally modified amino acids as well as ligands. The standard amino acids have single tokens and therefore single rows or columns in the PAE matrix in the json file. Modified amino acids, however, have one token per atom (e.g., phosphoserine, residue type SEP, has 10 tokens). We use the Cα atom as the appropriate token for the PAE matrix, so we can construct a square PAE matrix covering only one row or column per amino acid (whether modified or not). Ligands are excluded (label_seq_id=“.”). Since AlphaFold2 does not calculate pairwise ipTM scores for multi-protein complexes and AlphaFold3 provides only the symmetric (maximum) pairwise ipTM scores, we use the PAE matrix to calculate pairwise ipTM scores. To calculate d 0 for the ipTM calculation, we use the sum of the full-length protein sequences for each sequence pair, as AlphaFold2 does (for dimer complexes) and AlphaFold3 does for all chain pairs. This metric is called ipTM_d0chn , where d0chn indicates that d 0 is calculated from the chain lengths. The values for the complex in Figure 10 are 0.443, 0.429, and 0.752 respectively (compare the ipTM_af values of 0.46, 0.51, 0.77 respectively).The small differences arise from using the PAE values in the pairwise pTM matrix ( Equation 7 ), instead of the expectation value over the probability distribution of PAE ( Equation 6 ). With the PAE matrix and PAEcutoff value, we can calculate the asymmetric ipSAE scores ( Equation 14 ) and the overall ipSAE score ( Equation 16 ), which is the maximum value of the two asymmetric scores for each chain pair. For the regular ipSAE score, we use d 0 based on the number of residues in the scored chain that have PAE < PAEcutoff , given the aligned residue in the aligned chain. The number of residues ( n0res ) and the value of d 0 ( d0res ) are given in the output. For the example in Figure 10 , the ipSAE values are: 0.563, 0.261, and 0.636. The columns nres1 and nres2 provide the number of residues in the first and second chains that have interchain PAE values (for the same pair of chains) less than the cutoff (15 Å in this case). In the asym lines, these are for the aligned residues and scored residues respectively. In the “max” lines, they are the maximum of the two asymmetric values. Thus, RAF1 and KSR1 have maximum values (scored or aligned) with PAE less than the cutoff of 280 and 292 residues respectively. The next two columns, dist1 and dist2 , provide the number of residues with PAE less than the cutoff and Cα-Cα distance less than the distance cutoff set by the user (15 Å in this case). RAF1 does not contact MEK1 in the model, and the dist1 and dist2 values are both 0 for chains A+C. The ipSAE value is correspondingly only 0.261, while the ipTM_af value is 0.51 (probably because RAF1 can also interact with MEK1 but does not do so in this model). The ipsae.py script outputs a PyMOL script with aliases to color residues in each pair of chains with PAE less than the cutoff. These residues are highlighted in magenta and blue in the middle structural figure in Figure 10 for RAF1+KSR1 and the right-side structural figure in blue and green for KSR1+MEK1. The script also calculates two other forms of ipSAE for comparison purposes: ipSAE_d0chn and ipSAE_d0dom. ipSAE_d0chn uses the same PAE cutoff as ipSAE but calculates d 0 from the sum of the two full-length sequence lengths ( n0chn, d0chn ). ipSAE_d0dom uses a value of d 0 from the number of residues in the two chains that have any interchain PAE values less than the PAEcutoff ( nres1, nres2 ). Finally, for plotting figures like Figures 5 and 6 (e.g., the residue- and chain-pair specific values for ipSAE ), the script outputs a file with name like: fold_raf1_ksr1_mek1_model_0_15_15_byres.txt with columns: i, AlignChn, ScoredChain, AlignResNum, AlignResType, AlignRespLDDT, n0chn, n0dom, n0res, d0chn, d0dom, d0res, ipTM_pae, ipSAE_d0chn, ipSAE_d0dom, ipSAE. The value i is the residue number across all chains (from 1 to total number of residues in model). The aligned chain refers to the chain with residues i in the pTM expressions, the scored chain covers residues j. n0res and d0res are residue-specific values for the number of residues with PAE less than the chosen cutoff and the corresponding d 0 value. The other values are all chain-pair specific. Code availability A python3 script is available at github.com/dunbracklab/IPSAE . Acknowledgments I thank my lab members and members of the Fox Chase Cancer Center Molecular Modeling Facility for helpful discussions, including Mark Andrake, Sven Miller, Qifang Xu, Joan Gizzio, Pragya Priyadarshini, Brianna Trankle, and Xiyao Long. This work was funded by NIH grants R35 GM122517 (R.L.D.) and P30 CA006927 (Fox Chase Cancer Center). I thank Luca Genz and Maya Topf for running their benchmark on structure prediction accuracy of protein complexes and providing me with the results, as well as permission to use the figure they provided ( Fig. 9 ). Funder Information Declared NIH , R35-GM122517 , P30-CA006927 Footnotes The title changed loquunt into the correct Latin loquuntur. Added text about the effect of d0 in artificially increasing ipTM in some circumstances. Added a figure from benchmark data on structure prediction accuracy provided by Luca Genz (with permission: not previously published). https://github.com/DunbrackLab/IPSAE/ References 1. ↵ R. Evans et al. 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