Recently, the study of protein structures using angular representations has attracted much attention among structural biologists. The main challenge is how to efficiently model the continuous conformational space of the protein structures based on the differences and similarities between different Ramachandran plots. Despite the presence of statistical methods for modeling angular data of proteins, there is still a substantial need for more sophisticated and faster statistical tools to model the large-scale circular datasets. To address this need, we have developed a nonparametric method for collective estimation of multiple bivariate density functions for a collection of populations of protein backbone angles. The proposed method takes into account the circular nature of the angular data using trigonometric spline which is more efficient compared to existing methods. This collective density estimation approach is widely applicable when there is a need to estimate multiple density functions from different populations with common features. Moreover, the coefficients of adaptive basis expansion for the fitted densities provide a low-dimensional representation that is useful for visualization, clustering, and classification of the densities. The proposed method provides a novel and unique perspective to two important and challenging problems in protein structure research: structure-based protein classification and angular-sampling-based protein loop structure prediction. Depending on the amino acid sequence  and interactions with their environment, proteins fold into a three-dimensional structure, which allows them to interact with other proteins and molecules to perform their function. Hence, an important topic in the field of structural biology is the determination of the three-dimensional (3D) structure of a protein. In a protein, each amino acid is called a residue and the chain of carbon, nitrogen and oxygen atoms are referred to as the backbone. While the side-chain structures determine local structures and interactions of the amino acids of the protein, the backbone structure determines the overall shape of the protein and is the focus of much research.Proteins are large biomolecules or macromolecules that perform a vast array of functions for the biological processes within the cell of organisms. A protein is a linear chain of amino acids, each of which is composed of an amino group , and ω, with the assumption of standard bond lengths and angles. Moreover, the global folds of proteins can be equivalently represented by either the Cartesian coordinates of Cα traces or the 2 pseudo-angles  between the two consecutive planes formed by 4 successive Cα. The Ramachandran plot, a scatter plot of ϕ vs. ψ, can reflect the allowed regions of conformational space available to protein chains. By analogy to Ramachandran's concept of dihedral angles, the pseudo-Ramachandran plot, a scatter plot of θ vs. τ, can provide a distinctive classification of protein structures and largely contribute to different applications The backbone conformation of proteins can be represented equivalently by Cartesian coordinates of carbon, nitrogen and oxygen atoms, or the backbone dihedral angles  is too small, and that makes it challenging to obtain reliable bivariate densities using techniques that estimate each Ramachandran distribution separately. An intuitive solution to this problem is to borrow information from a group of Ramachandran plots that has some common features. To this end, Lennox et al. Comparing to other competitive approaches, PSCDE is more efficient in estimating the densities in the sparse regions by incorporating the shared information among the distributions. In this technique, the bivariate log-densities are represented using a common set of basis functions. Each log-density has its own coefficient vector in the basis expansion, and it can be used for clustering and classification of the densities. Furthermore, using a common set of basis functions significantly reduces the number of parameters to be estimated. This method has been applied to estimate the neighbor-dependent Ramachandran distributions to make the angular-sampling-based protein structure prediction more accurate. In this paper, we make an innovative and constructive development over the PSCDE method.The PSCDE method is constructed based on Bernstein-Bézier spline basis functions defined over triangles to estimate the log-densities in a complex domain The PSCDE method is originally applied to the protein loop modeling problem. Here, we focus on a new application and use an extension of PSCDE to the protein structure classification problem. There is a large literature on the classification of the protein structures in the Protein Data Bank (PDB) Specifically, the estimated angular density corresponding to a protein structure has a basis expansion whose coefficients can be used as an input to a clustering algorithm. Furthermore, most of the existing techniques for protein classification are using sequence and/or 3D structure comparison to classify the proteins based on some (dis)similarity scores obtained after pairwise alignments. The proposed method is an alignment-free procedure that provides a vector of coefficients (i.e. features), associated with each structure (density), that can be directly used to classify the proteins.We also applied the proposed method to the loop modeling problem and compared the result with the other methods in the online supplementary. In this application, we trained the neighbor-dependent distributions of the backbone dihedral angles  using the new collective density estimation approach and fed the results into the Rosetta loop modeling procedure to study the accuracy and efficiency of the Rosetta server in predicting the loop regions. The main concern of using the neighbor-dependent Ramachandran distributions is that we are partitioning the data into smaller groups, some partitions may end up with a limited number of observations, and therefore we may lose accuracy in estimating the Ramachandran distributions due to the data sparsity. The proposed collective estimation procedure can overcome this difficulty and thereby improve the accuracy of the estimated densities. We encourage the interested readers to read the online supplementary materials for the implementation of the proposed method on loop-modeling application.The rest of the paper is organized as follows. 2m bivariate probability distributions with the density functions fi, i = 1,⋯ ,m. We assume that each log-density can be represented by a set of common basis functions. Therefore we write each log-density function asωi(x) is a linear combination of the basis functions {ϕk,k = 1,…,K} such that ci is a normalizing constant fi is a valid density function. In our setting, the value of K and the basis functions (ϕk’s) are not pre-specified and will be determined based on data. We assume that ϕk’s fall in a low-dimensional subspace of a function space spanned by a rich family of fixed basis functions, {bℓ(x),ℓ = 1,…,L},(L ≫ K), such that In this section, we review and extend a procedure for estimating the multiple probability density functions, known as the PSCDE αik, k = 1,…,K, which can be used as an excellent feature for comparison, assessment and classification of the densities. Furthermore, similar to the scree plot in principal component analysis (PCA), one may plot the sum of square of the component coefficients K, e.g. see This framework provides a common set of basis functions to represent the log-densities. Also, each density in this model is represented with a set of coefficients ϕ(x) = (ϕ1(x),ϕ2(x),…,ϕK(x))⊤, αi = ⊤, b(x) = (b1(x),b2(x),…,bL(x))⊤, θk = T and Θ = , then ωi(x) given in Eq.  in the circular plane, we may further simplify the presentation of the densities in an n × m matrix: Ω ={ωi(xj)}⊤. Specifically, let B = (b(x1),b(x2),…,b(xn))⊤, and A = ⊤, then Eq. . To address the identifiability issue raised by the product of two matrices , we follow the remedy given in If we evaluate the densities on common regular grids  and λ > 0 is the tuning parameter. We then use the alternating blockwise Newton–Raphson algorithm in Maadooliat et al. To obtain smooth densities, the parameters can be estimated by introducing the roughness penalty λ, that minimizes the Akaike Information Criterion (AIC) ℓ is the log likelihood function and df(λ) is the degrees of freedom, defined as: There are different well-known methods to select the tuning parameter. A commonly used technique is to choose the tuning parameter, λ’s and then pick the one that minimizes the criterion function, which can be very expensive in time. Instead, we present an alternative procedure that updates the value of the tuning parameter within the Newton–Raphson iterations. This idea has been used in generalized mixture model to iteratively update the smoothing parameter ith step to update the tuning parameter, a is the order of the differences used in the penalty matrix D .2.1There are a variety of basis functions that can come in handy depend on the dimensionality of the problem and the data structure. In this context, the circular nature of the protein angles is an obstacle that prevents us from using the standard B-spline functions. Maadooliat et al. A frequently used basis functions for Euclidean space is the tensor product of standard B-spline functions which is appealing and very easy to use in the real world applications bℓ(X),ℓ = 1,…,L}, that is required for estimating the Ramachandran or pseudo-Ramachandran distributions, over the support set (Ω or Ω′) which can be defined asWe need to develop rich set of basis functions {′ represents the surface of a sphere with fixed radius. In fact, the existing parametric models take into account the topology and develop a parametric framework on surfaces of a torus or sphere with some fixed radiuses to model the bivariate densities From a geometric point of view, Ω resembles the surface of a torus with some fixed minor/major radiuses and Ωϕ,ψ) defined over Ω. One may proceed with a similar procedure based on the Kronecker product of a trigonometric spline and a standard B-spline to obtain the bivariate basis representation for the pair of dihedral, planar angles  defined over Ω′.Here we present the tensor product of two sets of trigonometric basis functions and construct the bivariate bases that can be used to represent the space for two dihedral angles , and order of ν, can be represented recursively as a periodic spline on a circle; see Schumaker  the spline functions are defined as A univariate normalized trigonometric spline with chumaker , ch. 8 fψ. The main advantage of using these linearly independent basis functions over the standard B-spline choice is that the continuity of the tangent plane for any smooth function on surface of a sphere is the result of the former one. Therefore, there is no need to introduce any periodic constraints for the trigonometric spline functions , as the following: The positive definite penalty matrix used to control the smoothness in the We now have the required tools to proceed with the estimation procedure. The minimization of the penalized likelihood function (Eq. ) can be 3In this section, we introduce an application of collective density estimation in protein structural comparison. To evaluate the proposed method, we designed four protein clustering tasks from the Structural Classification of Proteins (SCOP) database, and then try to cluster the proteins in each task without knowing their labels in the SCOP tree. The final clustering result of PSCDE(T) is compared with seven competitive approaches using two external measures  in different datasets, we designed four SCOP tasks with “Easy”, “Somewhat Hard”, “Hard” and “Challenging” level of difficulty, that we call them SCOP.1 to SCOP.4, respectively:1.Classes in SCOP. The constituents of the collection of protein domains and the details of this SCOP tree are available in the online supplementary materials.SCOP.1 (Easy Task): In this task, we considered an easy protein classification. The goal is to classify 63 protein domains that were randomly selected from three remote Protein 2.Species under the same Protein subclass that belongs to the “all-alpha protein” Class. The constituents of the collection of domains and the details of the SCOP tree involving these domains are available in the online supplementary materials. This classification task is considered somewhat harder than the easy task, because the domains are very similar both sequentially and structurally—they are very close in the SCOP tree and depart only at the bottom  of the SCOP hierarchy.SCOP.2 (Somewhat Hard Task): We considered a protein classification task for which 33 domains were extracted from four 3.Fold/Superfamily levels, where all chains belong to the “Alpha and beta proteins (a+b)” Class. The constituents of the collection of domains and the details of the SCOP tree involving these domains are available in the online supplementary materials. This classification task is considered harder than the SCOP.2, because the similarities within a group of chains branched out from a specific Superfamily level is not as strong as branching out at a specific Species levels. This task can be used to evaluate different methods in detecting the remote homology relationship at the Superfamily level.SCOP.3 (Hard Task): We considered a protein classification task for which 40 protein chains were randomly selected from three different 4.Class within three different Folds. This classification task is considered the hardest task in this paper, which is also indicated in SCOP.4 : Fischer et al. θ,τ) angles from the PDB files for each task. We observed that θ angles are within the range  and τ’s are within .After choosing the protein domains from the SCOP database, the complete information of the proteins were obtained from the Protein Data Bank (PDB). The PDB record of each protein structure contains its 3D atomic coordinates, secondary structure assignments, as well as atomic connectivity. While different types of dihedral/planar angles can be obtained using the atomic coordinates, we used the R package PRESS 3.3Due to the tree based structure of the SCOP database, we use the agglomerative hierarchical clustering technique to group the protein structures. In order to do this, we need to feed in a pairwise (dis)similarity matrix as an input to the clustering algorithm. In this subsection, we illustrate how to obtain such (dis)similarity matrices to compare five non-density based and three density based approaches, respectively.•Needleman–Wunsch (NW) algorithm for global sequence alignment •Smith–Waterman (SW) algorithm for local sequence alignment •http://zhanglab.ccmb.med.umich.edu/TM-align/;TM-align •http://bioserv.rpbs.jussieu.fr/Yakusa/download/index.html;Yakusa •http://ekhidna.biocenter.helsinki.fi/dali_lite/downloads/v3/.Dali Since clustering cannot be directly performed on 3D protein structures, a protein structure or sequence comparison algorithm is usually applied to generate (dis)similarity scores between any pair of structures and such scores are then used for clustering The first two methods are based on sequence comparison, and the other three methods are based on structure comparison. After we apply these five algorithms, we follow Sam et al. We also considered three density based approaches: Kernel Density Estimator (KDE), PSCDE and PSCDE(T) for protein classification. We used Symmetric Kullback–Leibler Divergence (SKLD) between Ramachandran distributions to obtain pairwise distance matrices between proteins θ direction and the cubic trigonometric B-spline basis functions with 15 degrees of freedom in the τ direction. The final tensor product basis functions are obtained and evaluated over 90 gird points in each direction. Furthermore, we selected the number of common basis to be equal to the number of classes in the gold standard associated to each task . In general, one may use scree plot based on the initial estimates (obtained by mapping the kernel density estimators to the column space of the basis expansion) or other approaches available in the literature to select the number of common basis. After estimating the parameters  using the Newton–Raphson algorithm, the densities can be obtained using Eq.  domain to 64 similar right triangles with cubic bivariate B-spline basis functions over each triangle (see In the PSCDE(T) method, we initialized the algorithm with the cubic B-spline basis functions with 5 degrees of freedom in the The distance matrices obtained for the above eight approaches: NW, SW, TM-align, Yakusa, Dali, KDE, PSCDE and PSCDE(T) are used as an input to the hierarchical clustering algorithm, implemented in the hclust function with option {method=”ward.D”} in the R package stats to obtain dendrograms 3.4A and B be two clusterings of a dataset consisting of N records. Let A cluster the data in r clusters and define ai as the size of cluster i = 1,…,r, and let B cluster the data in c clusters of size bj for each cluster j = 1,…,c . Given that A and B are partitions of the same data it is possible to count the elements that belong both to cluster i and j. Let nij denote the number of records shared between cluster i and j. The overlap between two clusterings can be represented in matrix form by a r × c contingency table M such as the one in Consider 1.Normalized Mutual Information (NMI): In the information theory, the mutual information of two random variables is a measure of the mutual dependence between the two variables. The concept of mutual information is intricately linked to that of entropy of a random variable. The entropy in clustering is defined as the expected value of its information content if it is seen as a random variable. We can therefore define entropy for clustering A and B asH(A),H(B)} to normalize the MI as follows: The mutual information has many possible upper bounds that might be used to obtain the Normalized Mutual Information. Here, we have used max{2.Adjusted Rand Index (ARI): The Rand index in data clustering is a measure of the similarity between two data clusterings. The adjusted Rand Index (ARI) is defined to adjust the chance grouping of elements Here, we have used two external measures as follows: Both NMI and ARI indices change between 0 to 1, with 0 indicating that the two clusters do not agree on any pairs and 1 indicating that the clusters are exactly the same. In the following subsection, we present and compare the clustering results for the eight approaches given in 3.5We implemented the eight approaches introduced in λ) within each iteration while PSCDE runs independent Newton–Raphson iterations for each tuning parameters separately and pick the one that minimizes the AIC Furthermore, SCOP.1 (Easy Task): As it is expected, SCOP.2 (Somewhat Hard Task): The results shown in In the remaining of this section, we emphasize some important outcomes of each task and refer the readers to the online supplementary materials for further details. The difference between the results of PSCDE and PSCDE(T) in SCOP.2 makes it interesting to further compare the associated results in more details and illustrate their properties. In a similar framework, SCOP.3 (Hard Task): The results shown in SCOP.4 : The results shown in By comparing the results of 4λ, which could be very expensive in time.This paper develops an extension to a recent technique for collective estimation of multiple bivariate densities. The proposed method develops a new set of bivariate spline functions, using a tensor product approach, which can replace the bivariate B-spline functions (based on triangulation) implemented in PSCDE. The construction of the new bivariate basis function is simpler, more appealing, and can be easily extended to handle cases with more than two dimensions. While PSCDE handles the circular nature of the angular data with some artificial constraints (that extend the notion of adjacent triangles to the triangles in boundaries), the proposed method simply uses the trigonometric spline functions, that are naturally periodic. Another advantage of the new procedure is to speed up the process by updating the smoothness parameter within the Newton–Raphson iterations and avoid a grid search over the space of smoothing parameter, The estimated coefficients of the basis expansion based on PSCDE(T) provide a low-dimensional representation of the densities that can be used for visualization and clustering the densities. In general, the PSCDE(T) algorithm is faster, more appealing and interpretable in comparison to the previous approach, PSCDE.We have applied the proposed method to four protein structural comparison tasks with different levels of difficulties. The results of these tasks show that PSCDE(T) is a new competitive method compared with existing approaches. Furthermore, the last two tasks illustrate that the PSCDE(T) can improve the efficiency of the estimated densities by borrowing strength across distributions while the non-collective estimation method of KDE does not have such ability. This improvement directly influenced the efficiency of clustering in the last two harder tasks.We also used this method in estimating the neighbor-dependent Ramachandran distributions , and fed those estimates into Rosetta for loop modeling application. The ultimate results showed that PSCDE(T) is competitive with other similar methods and occasionally improve the results for some hard cases. We also included, in our web application tool, the corresponding input file that contains the 800 neighbor-dependent Ramachandran densities. This can be used by the scientific community to test the quality and applicability of PSCDE(T) approach in loop modeling or any other applications that use the neighbor-dependent Ramachandran distributions (e.g. backbone-dependent rotamer library In summary, since the angular density is only a summary statistics and ignores many aspects of the protein structure, we do not expect that it always gives the best results in an arbitrary dataset. This new methodology can be used independently or as a supplement to the existing methods.


Since in general there is no conclusive evidence about the absence of proteins in the groups, protein groups need to be linked across different runs in subsequent statistical analyses. We propose an algorithm, called Protein Group Code Algorithm (PGCA), to link groups from multiple experimental runs by forming global protein groups from connected local groups. The algorithm is computationally inexpensive and enables the connection and analysis of lists of protein groups across runs needed in biomarkers studies. We illustrate the identification problem and the stability of the PGCA mapping using 65 iTRAQ experimental runs. Further, we use two biomarker studies to show how PGCA enables the discovery of relevant candidate protein group markers with similar but non-identical compositions in different runs.The quantitation of proteins using shotgun proteomics has gained popularity in the last decades, simplifying sample handling procedures, removing extensive protein separation steps and achieving a relatively high throughput readout. The process starts with the digestion of the protein mixture into peptides, which are then separated by liquid chromatography and sequenced by tandem mass spectrometry (MS/MS). At the end of the workflow, recovering the identity of the proteins originally present in the sample is often a difficult and ambiguous process, because more than one protein identifier may match a set of peptides identified from the MS/MS spectra. To address this identification problem, many MS/MS data processing software tools combine all plausible protein identifiers matching a common set of peptides into a protein group. However, this solution introduces new challenges in studies with multiple experimental runs, which can be characterized by three main factors:  Shotgun proteomic techniques have gained popularity in the last decades allowing a global and relatively high throughput identification and quantitation of proteins in complex samples such as plasma or total cell/tissue extracts , 2. The ™ [Many software tools have been developed to process MS/MS data addressing the protein identification problem, such as ProteinPilot™ , Protein™ , Scaffol™ , Protein™ , Protein™ , TRIC [1™ , DBParse™ , and X!T™ . Althoug™ , this st™ software v4.0 with the integrated Paragon™ Search and ProGroup™ algorithms [gorithms  and searProtein groups with more than one identifier contain, in general, proteins with a high degree of sequence similarity, including multiple entries for one gene product, and isoforms or multiple members of a protein family. Some tools assign a probability or a score to each protein in the group estimating the likelihood that the corresponding protein was present in the sample  each protein group has only a local identifier per experimental run , ii) the composition of each group may change across runs, and iii) the supporting evidence of proteins within each group may also change across runs. For example, the local protein groups in In general, the identification problem in a multi-experiment setting can be characterized by three main factors: In this paper, we propose a computationally inexpensive algorithm, called Protein Group Code Algorithm (PGCA), to merge protein summaries from multiple experimental quantitative proteomics data. The goal of PGCA is to enable the analysis of quantitative data available for protein groups instead of unique protein identifiers. Although this strategy does not directly address the protein inference problem that resulted in the identification of protein groups, it enables the user to maintain the information available in the groups for subsequent analyses. PGCA creates a mapping (or dictionary) of local into global protein groups and assigns a protein group code (PGC) to each global group in the resulting list. The global PGC can then be used to link lists of protein groups across different experimental runs. We use three datasets to characterize the problem, to examine in detail the mapping created by PGCA, as well as to carefully evaluate the impact of its application in two biomarker studies.In this section we describe the algorithm we developed to merge proteomic data files containing protein groups that resulted from processing MS/MS data. We then use the algorithm to characterize the composition of typical protein summaries containing groups of protein identifications and evaluate the reproducibility of the groups among multiple experimental runs. Further, we illustrate how the protein inference problem may impact on a subsequent statistical analysis. Finally, we demonstrate two useful properties of PGCA: the proposed method is order invariant  and incremental . Technical details about the datasets used and the algorithm are presented Materials and methods.CreateLocalGroups, UpdateDictionary, and CodingProteinGroups.PGCA can be decomposed into three algorithms: CreateLocalGroups algorithm creates a set of local or intra-experimental protein groups  from the protein groups available within each input file. Examples of local protein groups include the top-protein of a group, the set of proteins matching to the top gene, or the whole protein group. We can think of this step as a potential refinement of the groups created from MS/MS data to determine the amount of information contained in each group that will be kept for comparisons across multiple runs.UpdateDictionary merges sets of local protein groups from different experimental runs creating a set of global or inter-experimental protein groups . Each global protein group is built from the union of connected local groups across multiple runs. A protein group code (PGC) is then assigned to each global group creating a mapping or dictionary.D2. In the third step, a new protein is added to one of the local groups, and thus to the existing global group. The last panel shows the corresponding dictionaries, created by the UpdateDictionary algorithm, as files are being processed.CodingProteinGroups uses the created dictionary to translate protein identities into protein group codes (PGC) within each protein summary. The assigned PGCs can be used to link the groups across different experimental runs and analyze the quantitative value of each group across experiments.Continuing with the previous example, after processing all 3 files, a new column is added to each file in the top panel with the resulting PGC, e.g., PGC 20 in this example.i)PGCA-All links the raw protein groups identified within each experimental run, ii)PGCA-topGene links subsets of proteins matching to the gene of the top protein, and iii)PGCA-topIdentifier links groups by their top-proteins across different experimental runs. This last option was included in the algorithm for completion. However, we note that there are different ways of doing this without PGCA and that the UpdateDictionary step becomes trivial in this case since all local groups are singletons.PGCA offers three different approaches enabling the user to tune the degree of similarity among linked protein groups: Although some of the groups change their composition and/or ordering of the proteins, in general they contain some common proteins that allow the connection of the detected groups through all runs. PGCA-All assigns a unique and common protein group code (PGC) to all connected proteins, which can then be used to link and analyze this group across runs. Noteworthy, the statistical analysis of some groups can be lost if only the top-identifier is used to link the identified groups across runs. In the example illustrated in Dataset A consists of 4 lists of protein groups generated by ProteinPilot from 4 iTRAQ experiments used to process technical replicates of a pool of plasma from healthy individuals see . IdeallyDataset B consists of 12 lists of protein groups generated by Proteome Discoverer from 12 spectral count-based experiments used to process plasma samples from 12 healthy individuals. Thus, with this dataset, we examine the effect of technical and biological variation in protein identification see . Fig 4 iWe first compare the raw protein groups created by Proteome Discoverer  with the corresponding global groups in the dictionary created by PGCA. If a global group in the dictionary is not identified in an individual experiment, the intersection between the global and the local group is empty and the Dice coefficient is 0  all experimental runs are analyzed to compare protein levels from different subject groups . As previously discussed, two main tasks are required before starting this discovery analysis. First, the protein identifiers in each identified group (or a selected subset of these) need to be translated into a unique protein group code (PGC) identifier for each experimental run. Second, the assigned group code is used to link the groups among runs and to retain those consistently detected in all  runs for subsequent statistical analyses. Importantly, these steps are required even if only the top-protein in each group will be retained, since the lists of top-proteins also vary, both in content and order, across runs. Using different criteria to link the lists of identified proteins results in different sets of proteins to be analyzed. For example, the group illustrated in codes that are consistently identified in different experimental runs of the heart transplantation study (dataset C in The Biomarkers in Transplantation (BiT) team conducted a large biomarker study seeking protein markers of acute rejection in cardiac and renal transplantation using plasma samples , 20. FigOne goal of this biomarker study was to identify potential proteomic markers of acute cardiac allograph rejection. A total of 17 iTRAQ experiments were used to process 6 plasma samples from patients with acute heart rejection (AR) and 12 from patients without rejection (NR). Using PGCA-All in this study to link the protein groups identified across different runs enabled the analysis of 127 protein groups, of which 61 were not represented by the same top-identifier in all runs. Some of the candidate markers with statistically significant differential protein levels between AR and NR groups were represented by different top-proteins across the 17 iTRAQ runs and would have been missed if only the top-protein was used to represent each protein group. For example, Isoform 1 of Sex hormone-binding globulin protein (SHBG) was the top-protein in 13 out of 17 iTRAQ experiments in the study and Isoform 2 of the same protein was the top-protein in the 4 remaining experiments. In particular this candidate marker  was validated using multiple reaction monitoring coupled with mass spectrometry (MRM assay) showing differential protein levels between the AR and NR groups . All data from this study is available in The Jain Foundation with MRM Proteomics and PROOF Centre of Excellence is conducting a proteomics discovery study of blood-based biomarkers associated with skeletal muscle function. Using PGCA-All to link the protein groups identified across different runs enabled the analysis of 131 protein groups identified in more than 75% of the samples, of which 26 were not represented by the same top-identifier in all runs. Of the 26 that would have been missed if only the top-protein were used to link the identified groups, 9 had a false discovery rate (FDR) below 10% in a statistical analysis that compares the protein levels of LGMD2B (n = 50) versus control samples (n = 25). The difference in groups identifications are shown in i) new global protein groups are added, ii) new protein identities are added to existing global protein groups, and iii) existing global protein groups are merged due to the incorporation of connecting groups in the mapping.PGCA creates a mapping of local to global protein groups by comparing the composition of the local protein groups identified within each experimental run. Using a unique global protein group code to represent all the proteins identified in connected local groups enables linking related groups from multiple experimental runs, even if these groups slightly change their composition across runs. Noteworthy, the mapping created by PGCA is data driven and depends on the list of local protein groups identified within each experimental run. Thus, if new experiments are added to a study, the current mapping needs to be updated accordingly see . To studA complementary measure examined is the growth in the total number of global protein groups in the mappings for different ranges of group sizes . SimilarThis Section presents some properties of PGCA with proof outlines given in Each time a new file is processed, the updated mapping results in a comprehensive list of global protein groups, each with a protein group code, that can be used to link groups across experimental runs. The following results demonstrate that the global groups in the mapping are disjoint and that each was derived from connected local groups. The corollaries at the end of this Section show two results with important practical utility. First, the same mapping is obtained regardless of the order in which files are processed . Second, a current mapping can be easily updated every time that new files are incorporated into a study without the need of reprocessing all the data .Definition 1Letbe a set of protein groups. Given two groupsandB1andB2are connected if either B1 ∩ B2 ≠ ∅ or there exist a connector setwith all Bjinsuch that:fori = 1, 2, andcan not be partitioned into two disjoint collections of sets inFurther, is connected if all groupsare connected.Lemma 1Let L be the set of local groups from a file F ), G be the set of global groups from a dictionary D, andLetbe the output dictionary from the UdpdateDictionary algorithm. Given B, a set of accession numbers from those inandB is a global group inif and only ifis non-empty and connected, andB in B.From Lemma 1, it easily follows that any global group Theorem 1i be the set of local groups from an input file Fi ) for iLet L = 1, …, nFiles, andbe the universe of all these local groups. Starting from an empty dictionary D0, nFiles = PGCAlet D be the output dictionary from input files Fi, i = 1, …, nFiles. Given B a set of accession numbers from those inandB is a global group in DnFilesif and only ifis non-empty and connected, andCorollary 1PGCA is order invariant, i.e., the order in which the files F1, …, FnFilesare input in PGCA do not change the general groups in the output DnFiles.Corollary 2PGCA is incremental, i.e., using the same notation as in Theorem 1,This section describes the datasets used to demonstrate the properties of our algorithm. We also present all formal details of PGCA (see Algorithm 1) and its three main algorithms, CreateLocalGroups, UpdateDictionary, and CodingProteinGroups .™ Search and Pro Group™ algorithms [http://www.r-project.org). A library with an associated Vignette to implement PGCA algorithm is publicly available from Bioconductor (http://www.bioconductor.org).We use 4 different datasets to examine the protein inference problem when multiple experimental runs are required to process all samples in a study. Dataset A consists of 4 experimental runs used to process 16 technical replicates of a pool of plasma from 16 healthy individuals processed by iTRAQ-MALDI-TOF/TOF methodology see . Datasetgorithms , searchigorithms . DatasetA ∩ B|/(|A| + |B|), where |.| denotes the number of elements in the set. Note that if the sets A and B do not share any elements, then the Dice coefficient equals 0. If the sets A and B have the same elements, then the dice measure equals 1. However, this measure can not capture differences in the order of the elements of the sets. For example, if two protein groups contain the same set of protein identifiers then the Dice coefficient equals 1, even if each group is represented by a different top-protein in different experiments.Hesse et al.  proposedF1, …, FnFiles, with nFiles being the total number of input files. PGCA works on the assumption that the following variables are available within each protein summary, or easily generated as a result of processing MS/MS data:As a result of processing MS/MS data, most proteomics software generate protein summaries containing quantitative and qualitative information of the sample(s) analyzed within each run. PGCA uses these protein summaries as input files, here named Group identifier (N): an integer used to define  protein groups within each experimental runTop-protein identifier (TopID): an identifier of the top protein identification within each protein groupAccession number (Acc): an identifier from a proteomic database for each identified proteinProtein name (Prot): the protein name in the database matching to the accession numberGene symbol (Gene): gene(s) matching to the identified proteinFk has entries <N, TopID, Acc, Prot, Gene, Further, we assume that each input file has the variables defined above as columns, i.e., DnFiles, adding a protein group code (PGC) to each global group created from F1, …, FnFiles. The subscript nFiles is used to indicate how many files were used to create the dictionary. In practice, the set of files used can range from the total number of files in a study to specific files used to process data to answer a particular question.PGCA creates a dictionary, F1, …, FnFiles and thus generate nFiles output files, denoted as CF1, …, CFnFiles. Each entry in CFk is of the form <PGC, N, TopID, Acc, Prot, Gene, The resulting dictionary is used to recode each entry of j-th local group Fk as the set of Fk with identical group identifier j, i.e., nLocalGroups the total number of distinct Ns in Fk. Similarly, The j-th global group GGj in D is defined as the set of mj accession numbers from entries in a dictionary D with identical PGC identifier j, i.e., GGj = {Acci ∈ D: PGCi = j}; and nGlobalGroups the total number of distinct PGCs in D. To simplify the notation, we assume that all groups are numbered in consecutive order, since one can always re-name existing groups.In PGCA, we define the f(x) = y, to state that the algorithm f transforms the input file x into the output object y.Each algorithm is presented as a mathematical function, i.e., We only present PGCA-All in detail since PGCA-topGene and PGCA-topIdentifier only differ from it in the CreateLocalGroups algorithm within each. In particular, each local group in the LocalGroupSet created by the CreateLocalGroups algorithm in PGCA-topGene retains only those entries from the full local group with identical rank and Gene element as those of the top protein identification. Similarly, CreateLocalGroups algorithm in PGCA-topIdentifier retains only the top entry. Thus, the local groups created by these algorithms are subsets of those created by the PGCA-All see .Algorithm 1: PGCAInput:F1, …, FnFiles Output:DnFiles, CF1, …, CFnFiles D0 be an empty dictionary1 Let for 1 ≤ k ≤ nFilesdo2 Fk) = LocalGroupSetk3  CreateLocalGroups = Dk4  UpdateDictionary = CFk. ∎6  CodingProteinGroups the information contained in the groups maintaining the lists of non-redundant protein identities created within runs. In most cases, the comparison of these proteins is supported by the similarity of their sequences and the overlap among the lists of identified peptides from multiple experimental runs. Although the protein inference problem is well understood in the proteomics community, in this paper we characterize this problem and quantify its impact in subsequent quantitative and qualitative analyses based on multiple experimental runs.S1 Figi. Protein IPI00215894.1 is in IPI.HUMAN.v3.87 database (last version of IPI), its accession number in UniProt is P01042-2, and is the isoform of LMW of Kininogen-1 (KNG1). Protein IPI00797833.3 differs from IPI00215894.1 by only one amino acid and was removed from IPI.HUMAN.v3.87; ii. Protein IPI00032328.2 (in IPI.HUMAN.v3.87) corresponds to P01042-1 in UniProt, and is the isoform HMW of KNG1; iii. Alignment of the 3 disRnct proteins in the protein group by Clustal Omega v1.2.2.(PDF)Click here for additional data file.S2 FigAlignment of the 4 distinct proteins in the protein group by Clustal Omega v1.2.2.(PDF)Click here for additional data file.S1 Appendix(PDF)Click here for additional data file.S1 File4 iTRAQ experiments with technical replicates.(ZIP)Click here for additional data file.S2 File12 spectral count-based experiments from 12 plasma samples.(ZIP)Click here for additional data file.S3 File65 iTRAQ experiments used to process samples from the BiT Heart Cohort.(ZIP)Click here for additional data file.S4 FileSubset from dataset C.(ZIP)Click here for additional data file.S5 FileProtein identification information from the muscular dystrophy biomarkers study.(ZIP)Click here for additional data file.


Fusarium oxysporum f. sp. cubense (Foc) is one of the major disease constraints of banana production. Previously, we reported the disease resistance Musa paradisiaca cv. puttabale clones developed from Ethylmethanesulfonate and Foc culture filtrate against Foc inoculation. Here, the same resistant clones and susceptible clones were used for the study of protein accumulation against Foc inoculation by two-dimensional gel electrophoresis (2-DE), their expression pattern and an in silico approach. The present investigation revealed mass-spectrometry identified 16 proteins that were over accumulated and 5 proteins that were under accumulated as compared to the control. The polyphosphoinositide binding protein ssh2p (PBPssh2p) and Indoleacetic acid-induced-like (IAA) protein showed significant up-regulation and down-regulation. The docking of the pathogenesis-related protein (PR) with the fungal protein endopolygalacturonase (PG) exemplify the three ionic interactions and seven hydrophobic residues that tends to good interaction at the active site of PG with free energy of assembly dissociation . The protein-ligand docking of the Peptide methionine sulfoxide reductase chloroplastic-like protein (PMSRc) with the ligand β-1,3 glucan showed minimum binding energy  and docking energy  with an interaction of nine amino-acid residues. These explorations accelerate the research in designing the host pathogen interaction studies for the better management of diseases.Panama wilt caused by  Musa paradisiaca (L) cv. puttabale is an indigenous banana cultivar belongs to the AB genome  primers. About 2 μg of total RNA in a single 20 μL reaction was quantitatively converted to single-stranded cDNA. The primer pairs were designed to gene sequences of software  and crosde novo Rosetta method by using Robetta server [ab initio and comparative models of protein domains. Domains without a detectable protein homology were modeled with the Rosetta de novo protocol. The structure analysis and verification server v4  was used for assessing the modeled protein structures. The energy profiles of the modeled proteins were evaluated by using a ProSA server [The differentially accumulated proteins namely, PR, PBPssh2p, PMSRc and IAA were searched against the PDB by BLASTP for the presence of similar three-dimensional protein structures. The structure predictions were made using the a server  which prA server .P with the radius set to 1.4 Å [The quality of the computational models of protein structure was assessed by a MetaMQAPII server . The absto 1.4 Å . The constructed refined model of the PR, PBPssh2p, PMSRc and IAA proteins were used for the MDS studies. The simulation was performed using the Groningen Machine for the Chemical Simulation (GROMACS) program  running A GRAMM-X web server  was utilA protein Interaction Calculator was used to determine the ionic and hydrophobic interaction between the protein complexes . A Coil The molecular docking of identified and modeled defense related proteins namely, PR, PBPssh2p, PMSRc and the IAA protein with the ligand molecules β-1,3 glucan and chitin of fungi with using place an AutoDock 4.0 program . The thrFusarium wilt disease and validated through a qRT-PCR analysis. Homology modeling and in silico protein-protein docking of the modeled proteins with target fungal proteins can open new avenue for computer aided drug designing to better understand the potential proteins that acts against the molecules of the fungal pathogen. The protein-protein docking of all predicted structures with the fungal protein endopolygalacturonase resulted in a stable complex because of their positive ∆GDiss values. Exploring protein-protein docking within defense related proteins and target fungal proteins can open the new avenues for computer-aided drug designing to better identify the potential proteins that act against the molecules of the fungal pathogen. The protein ligand docking study revealed that both the PBPssh2p and IAA proteins showed a better interaction with chitin and β-1, 3 glucan. With this data, the PBPssh2p and IAA proteins have been shown to have the potential to break down the fungal cell wall constituents of chitin and β-1, 3 glucan. This investigation accelerates the research in designing strategies to control the Fusarium wilt diseases of the banana plants.The application of novel proteomic and genetic engineering techniques will extend the possibilities of developing disease-resistant plants. Protein profiling using 2-DE studies revealed the accumulation of 21 differentially accumulated proteins in Foc-inoculated samples. Among these, PR protein, PMSRc, PBPssh2p and IAA proteins were predominantly related to the


For non-synonymous mutations in structured proteins, one of these is the protein stability change, which can lead to loss of protein structure or function. We developed a stability-driven knowledge-based classifier that uses protein structure, artificial neural networks and solvent accessibility-dependent combinations of statistical potentials to predict whether destabilizing or stabilizing mutations are disease-causing. Our predictor yields a balanced accuracy of 71% in cross validation. As expected, it has a very high positive predictive value of 89%: it predicts with high accuracy the subset of mutations that are deleterious because of stability issues, but is by construction unable of classifying variants that are deleterious for other reasons. Its combination with an evolutionary-based predictor increases the balanced accuracy up to 75%, and allowed predicting more than 1/4 of the variants with 95% positive predictive value. Our method, called SNPMuSiC, can be used with both experimental and modeled structures and compares favorably with other prediction tools on several independent test sets. It constitutes a step towards interpreting variant effects at the molecular scale. SNPMuSiC is freely available at  Non-synonymous mutations that change both the codon and the associated amino acid can modify the biophysical properties of the encoded protein, such as its thermodynamic stability or solubility, or its functional properties by affecting the active site or the binding affinity for ligands and proteins partners. Moreover, the impact of a given variant crucially depends on its context within the genome: its deleteriousness can depend on the presence of other variants in the same or in other genes. Its effect also varies according to the cellular context. Indeed, some variants occur in proteins that play an essential role for the cell or the organism, which cannot be performed by any other protein. In such case, even a slightly destabilizing variant can be strongly deleterious. In contrast, some proteins perform functions that can very well be performed by other proteins, so that inactivating mutations do not cause diseases.Despite the large amounts of genomic data collected in the last decade and the multiple efforts to elucidate their links with phenotypic traits, an accurate and interpretative classification of the effects of genetic variants on various disorders remains a difficult goal to achieve. The high complexity of the problem is mainly due to the heterogeneity of the molecular mechanisms underlying the diseases, most of which have still to be deeper understood to be useful at the clinical level. For example, a change in a single DNA base pair that occurs in a coding region can be synonymous, 1. They are directly related to a wide range of pathological conditions among which Parkinson’s and Alzheimer’s diseases, and are involved in complex diseases such as cancers, in which the accumulation of different types of genetic variants determine the tumor initiation and progression2.Among all the possible types of variants, the non-synonymous single nucleotide variants in coding genes (SNV) play an important role since they constitute more than half of the mutations known to be associated in human inherited disorders4, SIFT5 or the Evolutionary Action method7, use as sole ingredient the evolutionary conservation in homologous proteins at the mutated position and in the neighborhood along the sequence. Though this information is represented by a single score, it corresponds to a mixture of several molecular effects, among which protein stability, solubility, function, and interactions. Understanding why a residue is conserved is impossible on the basis of the evolutionary data only. Other methods add further layers of information on top of this data, by considering for example structural alterations in the biophysical characteristics of proteins, which are usually predicted from the sequence and sometimes derived from the structure when available; these methods include Mutation Tasser8, Mutation Assessor9, CADD10, Polyphen-211, and VIPUR12. The addition of contextual information about the protein-protein interaction networks, the protein essentiality index, and the pathway in which the protein is involved appear to significantly improve the performances, as shown in DEOGEN14 and SuSPect15. These various computational tools use machine learning techniques to predict from the considered features the effect of missense mutations.It is thus of primary interest, especially in the context of personalized medicine, to have computational methods to classify SNVs and identify those that are disease causing. Classification methods developed in the literature usually integrate different kinds of biological data in view of gathering the complexity of the phenomenon, and require only the amino acid sequence as input. Some of them, such as Provean16. Frequently moreover, the computational methods only focus on reaching the highest variant classification accuracy on a given dataset rather than predicting and understanding the modifications that occur at the molecular scale and are responsible for the altered phenotype; yet this information is a prerequisite for the rational design of drugs or treatments. As a matter of fact, although protein structure can help getting insight into in the molecular impact of mutations, it is rarely (fully) exploited by variant classification methods, except in a few cases19.Unfortunately, the accuracy of the prediction methods remain limited, with often a quite high false-positive rate with the detrimental consequence that many of the predicted deleterious variants observed in clinical whole-exome sequencing turn out to be neutralThe present analysis aims at deepening the understanding of the relation between protein structural stability and variant deleteriousness. To evaluate the stability of a given protein structure and its change upon single-site mutations, we used knowledge-based statistical mean-force potentials derived from a dataset of three-dimensional (3D) protein structures. Combinations of these potentials, performed with the help of different artificial and probabilistic neural network architectures that include the solvent accessibility of the mutated residue to modulate the importance of the energetic terms, were used to classify SNVs into neutral and deleterious. Note that the primary goal of this analysis is not to reach the highest prediction accuracy but rather to get insight into the functional and stability characteristics of protein variants and their relation with the phenotypic traits. Our objective also involves predicting with high accuracy the subset of mutations that are deleterious due to stability problems.20, SwissVar21 and HumSaVar22. In a first stage, we combined all SNVs while avoiding repeats. Note that variants occurring in more than one database with different neutral/deleterious annotation were discarded. The SNVs were characterized in these databases by the protein’s UniProt code22 and the variant’s residue number, without any reference to a possible 3D structure. We had thus, in a second stage, to identify the subset of variants introduced in proteins that have an experimental structure, using the SIFTS webserver23. We only considered the subset of mutations introduced in:globular proteins, or cytoplasmic or extracellular domains of membrane proteins;24 (PDB) of resolution of 2.5 Å at most.proteins with an X-ray structure available in the Protein DataBankThe training dataset was built by combining the annotated, non-synonymous SNV data from three different databases: DbSNPα distance of 10 Å at least, to avoid direct interactions between them. The final dataset is referred to as S and is reported in Table Some of the PDB protein structures have not exactly the same sequence as the corresponding entry in the UniProt database, but contain one or several mutations. We only retained the subset of SNVs of residues that are far from all these additional mutations by an inter-C12: SH (variants in Human proteins), SNH (in Non-Human proteins), SCV (from the ClinVar dataset25) and SSSC (from the Simon Simplex Collection26). They are described in Supplementary Material , where s and c are sequence and structure elements respectively, is obtained from the inverse Boltzmann law as:kB is the Boltzmann constant, T the absolute temperature, and P, P(c) and P(s) are the probabilities of observing , (c) or (s) elements. These probabilities are approximated in terms of the number of occurrences of these elements in a reference dataset of protein structures. The sequence elements s are amino acid types and the structural motifs c can be interresidue distances, torsion angle domains or solvent accessibilities. Higher order potentials, in which different combinations of sequence and structure elements are considered, have also been utilized in this investigation. For example, a 3-term potential describing the association between one structure and two sequence elements is defined as:We used the statistical potential formalism to evaluate the stability of a protein and its change caused by non-synonymous SNVs, and to understand the link with their polymorphic or pathogenic effect. These potentials are knowledge-driven mean force potentials that are extracted from a dataset of well-resolved X-ray protein structures32.For sake of simplicity, such potentials are referred to as c: (1) distance potentials describing tertiary interactions, in which c is the distance d between the average side chain geometric centers of two amino acids; (2) solvent accessibility potentials, in which c is the solvent accessibility a of a given residue; (3) torsion potentials describing local interactions along the sequence, in which c is the main chain torsion angle domain t of a residue. Several combinations of these basic descriptors were also used. Besides these potentials, we also considered two biophysical characteristics: the solvent accessibility A of the mutated residues and the difference in volume ΔV between the wild type and the mutated residues32.We used here 13 statistical potentials, listed in Table S, the corresponding change in volume ΔV and in folding free energy ΔΔWi, with Wi, A and ΔV were compared between deleterious and neutral variants from S, in view of getting insight into the relation between the structure and stability characteristics and the pathogenicity of the variants. In a second stage, all the potentials and features were combined to set up a predictor of variant deleteriousness.These potentials and structural features were used to estimate, for each mutation of our SNV dataset 32 and HoTMuSiC33 algorithms, which predict changes in thermodynamic and thermal stabilities upon single-site mutations from protein 3D structures. More precisely, PoPMuSiC uses a combination of the 13 statistical potentials and the two structural features listed in Table V+ and ΔV− are two volume terms defined as: A of the mutated residues:Gs; note that this dataset has a negligible overlap with S (one mutation). For further technical details about the choice of parameters or the construction of the model, see the original PoPMuSiC papers34.The first approach for predicting on a structural basis which variants are disease-causing and which are not consists in using our PoPMuSiCS dataset into deleterious and neutral was performed on the basis of the computed ΔΔG values: SNVs with a predicted ΔΔG higher than a threshold value, which correspond to the most destabilizing mutations, were predicted as deleterious, whereas those with lower ΔΔG were predicted as neutral. The value of the threshold was identified so as to optimize the values of the balanced accuracy (BACC):The classification of the variants of the 33 for deleterious/neutral classification. This algorithm predicts changes in melting temperature ΔTm upon mutations rather than changes in folding free energy ΔΔG. These two quantities are anti-correlated only in a first approximation, and yield two different informations about protein stability35. HoTMuSiC uses a distinct combination of the statistical potentials:a and b, where identified using as cost function the mean square deviation between experimental and predicted ΔTm s on a dataset of characterized mutants, that displays only a very small intersection with S (3 mutations only). Note that the number of energy terms has been restricted to nine because of the smaller size of the ΔTm learning dataset, to avoid overfitting.Similarly, we also used the thermal stability predictor HoTMuSiCd in Eq. , and \doG predictions, a given variant of the S dataset is considered as deleterious if its ΔTm value is smaller than a given threshold, which means that the variant provokes a strong thermal destabilization; otherwise it is predicted as neutral. Again, the threshold value was identified using the BACC score as cost function.Using a similar procedure as for the ΔΔ37. To take this into account, we considered the stabilizing and destabilizing statistical potential contributions separately, and separated the potential terms into their positive and negative parts:I:Using a different combination of the same potentials and two structural features listed in Table The functions m of Eq. . The numm of Eq. .S dataset and as cost function the mean square deviation between I and the annotated variant effect, with deleterious defined as 1 and neutral as 0. The mutations were then considered as deleterious when the pathogenicity index is larger than a given threshold value ψ and neutral otherwise. The threshold value was optimized so as to maximize the BACC score  schematically depicted in Fig. ore (Eq. ) of the By construction, this new model allows predicting as deleterious both stabilizing and destabilizing mutations. It is a striking illustration that elucidating the biophysical mechanisms underlying the variant effects can be used to guide the model architecture and contribute to improve the classification performances and the understanding of the data.38 have architectures that are very different from ANNs, and are utilized for classification purposes. The idea behind their construction consists in a Bayes classification strategy through the estimation of the probability density function (PDF) for each considered category, based on a number of characteristics of the elements to be classified. PNNs are composed of four layers, as shown in Fig. j, contains a probability value computed from the comparison between the feature vectors of the input variant Structural stability and evolutionary information are entangled but distinct notions. On the one hand, biophysical constraints, including stability but also solubility, aggregation propensity, interactions and function, act on natural selection, thus affecting the evolution of proteins, while on the other hand, natural selection guides mutations, which in turn have an impact on the biophysical properties of proteins.In our last predictor, both types of information are joined to obtain a more complete picture of the variant effects. We would like to stress that, in contrast to the black-box machine learning approach usually employed in variant classification, we tested concretely whether the stability change due to a residue substitution impacts directly on the variant’s deleteriousness, taking also into account the role of the evolutionary pressure.4 score, noted PRO, with the pathogenicity index I defined in Eq.  have a higher probability to be deleterious, and so are, albeit to a much smaller extent, the substitutions from larger into smaller amino acids (negative ΔV s), as shown in Fig. A > 60%, mutations from smaller to larger residues still have a higher probability to be disease-causing, but less than in the core  and HoTTo take into account that both stabilizing and destabilizing mutations can cause diseases, we set up two new classifiers that use the same structural features and statistical potentials as PoPMuSiC and HoTMuSiC but are based on two different neural network architectures, an ANN (Eq. ) and a P4 reaches the same score as our ANN and PNN models (0.07 higher), though the former is based on evolutionary information that mixes stability with other biophysical characteristics such as solubility and activity while the latter purely exploits stability information. The variant distributions obtained with this predictor are depicted in Fig. Quite interestingly, the Provean classifierI of the ANN model , i.e. 0.83. The associated distributions of neutral and deleterious variants are quite well separated as shown in Fig. −4 using a bootstrap test). It performs even better than more complete classification methods, based on a whole range of sequence and structural features, such as Polyphen-211. Strikingly, SNPMuSiC increases the sensitivity of the ANN and PNN models up to 0.79, and almost maintains their high specificity value (0.71)  with thdex (Eq. ). This mmentclass2pt{minimSH, SNH, SCV and SSSC taken from12 and specified in Tables 11, Provean4, CADD10, SIFT5 and VIPUR12, which use sequence and sometimes structural features but no contextual (or systems biology) information. The results of these predictors were taken from VIPUR’s article12.To analyze in more detail the performances of our predictors, we applied them to four different test sets 11 and to non-human variants, respectively. We excluded from the former set the variants present in the training sets of our method and of Polyphen-2, as well as the proteins whose 3D structure was modeled from templates that have less than 30% identity with respect to the target sequence to avoid incorrectly modeled structures. The results are shown in Table SNH. In contrast, Polyphen-2, Provean and VIPUR have better sensitivity and NPV.The first two test sets correspond to human variants from HumVarSCV and SSSC, which contain neutral and disease-causing human variants from ClinVar25 and de novo missense mutations of the Simon Simplex Collection (SSC)26, respectively. The results are shown in Table SCV. In spite of this, the specificity and PPV scores of SNPMuSiC are the highest on both sets.We also evaluated the performances on the two other sets This leads us to the conclusion that SNPMuSiC is also applicable to mutations in proteins with low-resolution (modeled) structures, which drastically increases its application possibilities. Its strength is rooted in its high PPV and specificity for all test sets analyzed, compared to other commonly used sequence- or structure-based classification tools. Hence, the deleterious mutations predicted by SNPMuSiC have a large chance of being so. This is in accordance with its construction: it only predicts mutations that are deleterious because of stability reasons, and misses some other deleterious mutations that are instead caused by other biophysical mechanisms.S that are predicted to be the most thermodynamically stabilizing by PoPMuSiC; they are reported in Table 35 is reflected in the imperfect anticorrelation between PoPMuSiC’s ΔΔG and HoTMuSiC’s While destabilizing mutations can clearly be deleterious as they are likely to cause structural modification which can negatively impact on protein function, it is less obvious that variants with a stabilizing effect can also be disease causing. To clarify this point we analyzed the ten deleterious mutations of the variant dataset Obviously, the PoPMuSiC and HoTMuSiC-based classifiers wrongly predict these ten mutations as neutral, since only destabilizing mutations have a chance to be classified as deleterious by these two models. In contrast, both our ANN-based predictor and SNPMuSiC, which are designed to be able to predict stabilizing disease-causing mutations, correctly classify all ten mutations as deleterious.22. As shown in Table 41 or affect post-translational modifications sites42.It is instructive to briefly analyze the biophysical mechanisms that are involved in the pathogenic phenotype of these SNVs caused by protein stabilization. These are taken from the annotations of the variants reported in the Uniprot databaseIn summary, this investigation shows that biophysical knowledge at the molecular level - in this case, the fact that both strongly stabilizing and destabilizing mutations are likely to cause diseases - can guide the design of the model structures, improve the classification performances and lead to a deeper understanding of the variant effects.Our SNPMuSiC method reaches the very high positive predicted value (PPV) of 89%, as shown in Table The idea here is thus to identify a subset of mutations, whose pathogenicity index S set. Here we can be almost sure of the deleteriousness of the mutations and of its molecular cause. Indeed, combining the SNPMuSiC prediction with the outputs of PoPMuSiC and HoTMuSiC, we can determine if they are deleterious due to thermodynamic or thermal stabilization or destabilization.Setting the S set. For these mutations, we have a good indication of their neutral impact on the phenotype.With the S set, is also significantly improved and reaches 0.87. The SNPMuSiC distribution for deleterious and neutral variants at both sides of the confidence thresholds are shown in Fig. The BACC score computed on the subsets characterized by Here we made a further step towards the prediction of the biophysical causes of the deleteriousness of non-synonymous SNVs. We focused on protein stability which guides a series of crucial biophysical mechanisms that encompass folding, interactions, and function. Our analysis can be extended and generalized to all other types of biophysical characteristics that play a role at the protein level and could be at the basis of deleteriousness, such as solubility, aggregation, allostery, flexibility, and catalytic activity. This will lead to a complete view of the relation between the effect of SNVs at the molecular level and disease, and pave the way towards personalized medecine.43 even though they are frequently considered as correlated. Other factors that we will add to this analysis is the SNV effect on protein activity and on protein-protein interaction networks44, which are undoubtedly important factors in the initiation of diseases.Let us give a flavor of the next stages of our quest. We will include the changes caused by mutations on the protein aggregation properties, which are not directly related to protein stability45. We would like to end by stressing the broad applicability of structure-based predictors, as it has been estimated that almost half of all structured proteins have either an experimental or reliably modeled structure46.Finally we would like to underline the importance of using the 3D structures of the proteins in which SNV occur to predict and interpret their biophysical and disease-causing effects. This data is essentially overlooked in most commonly used deleteriousness classification methods, which drastically limits their interpretative power. Two reasons can be invoked to explain this shortcoming. On the one hand, protein sequences are much easier to handle than protein structures, and on the other hand, many proteins have no available experimental structure. This last issue has, however, to be relativized, as many protein structures can be obtained through comparative modeling. Given that our methods use coarse-grained representations of protein structure, they can be applied on protein models with only a small loss of accuracySupplementary InformationTable S1 - SNV training setTable S2 - Human variant datasetTable S3 - Non-Human variant datasetTable S4 - ClinVar datasetTable S5 - Simon Simplex dataset


Uncovering the signaling architecture in protein-protein interaction (PPI) can certainly benefit the understanding of disease mechanisms and promise to facilitate the therapeutic interventions. Therefore, it is important to reveal the signaling relationship from one protein to another in terms of activation and inhibition. In this study, we propose a new measurement to characterize the regulation relationship of a PPI pair. By utilizing both Gene Ontology (GO) functional annotation and protein domain information, we developed a tool called Prediction of Activation/Inhibition Regulation Signaling Pathway (PAIRS) that takes protein interaction pairs as input and gives both known and predicted result of the human protein regulation relationship in terms of activation and inhibition. It helps to give prognostic regulation information for further signaling pathway reconstruction. The rapid increase in genomic information requires new techniques to infer protein function and predict protein-protein interactions. To properly understand normal cellular responses and their potential dysregulation in disease, a global multivariate approach is required . Many stIn this paper, we first integrated GO and protein domain information. Then we proposed the enrichment ratio (ER) score for each GO term or domain term interaction pair; for one activation/inhibition relationship of a protein interaction pair, the ER score was treated as the feature to distinguish the regulation relationship in terms of activation/inhibition. By using the ER score as new feature, we developed a web tool, PAIRS, to give extensive prediction of protein pathway regulation relationship. The workflow of PAIRS is shown in http://geneontology.org/page/downloads.As a standard terminology in genome research, Gene Ontology (GO)  covers tConsidered as the conserved part of a protein, domains are independently stable. One domain may appear in a variety of different proteins. Different domain combinations give rise to the diverse range of proteins found in nature. Therefore, protein domain information is also an important data source to infer new regulation relationships in a signaling pathway. Here, the PFAM database  was usedN is the protein interactions number in the whole standard dataset and M is the protein interactions number in the activation/inhibition dataset. For a specific pair of domains, n is defined as the number of protein interactions containing this pair in the whole standard dataset and m is the number of protein interactions containing this pair in the activation/inhibition dataset.The enrichment ratio was first posed by Liu and Xie . It was P value is calculated as the probability of randomly drawing m′ or more successes from the population in n total draws. For ER ≥ 1 the p value is defined asp value is defined asThe hypergeometric test was adopted to measure the statistical significance of ER. The hypothesis test was designed to investigate the overrepresentation of GO or domain pairs appearing in the activation/inhibition dataset. The hypergeometric All signaling networks were extracted from KEGG (Kyoto Encyclopedia of Genes and Genomes) . The regOther protein interactions with activation/inhibition regulation information were obtained from Liu et al. . There ax is explanatory variable as the vectors of significant ER in GO or domain pairs. F(x) is confined to values between 0 and 1 and hence is interpretable as a probability of regulation relationship being activation (or inhibition). Then the other regulation relationship inhibition (or activation) is 1 − F(x). Here, β0 is the intercept from the linear regression equation and β1 is the regression coefficient multiplied by some value of the predictor. β0 and β1 are the regression coefficients. In the binomial logistic regression model with L1 regulation, the beta 1 is the sparse vector with more than 73689 dimensions. The WEKA package [https://fengyanghe.github.io/). It can be used to identify the regulation relationships by estimating the ER score of GO or domain pairs.Several machine learning techniques have been adopted for prediction in the domain of bioinformatics , 15–18.  package  was usedBefore PAIRS predicts the regulation relationship of the input protein-protein interaction pair, it will check if regulation relationship of the input pair is already known. If it is known, then PAIRS will output the known regulation directly.After the ER is computed, in a certain pathway some of the GO or domain interaction pairs may be correlated. For example, in the known apoptosis pathway as shown in Only the nonredundant interactions with corresponding Entrez Gene ID and not reported in protein complex were extracted from the human proteome-wide interaction dataset, which is mentioned before. The total number of protein interactions is 45,238. As shown in We developed a web tool, called PAIRS, to identify the regulation relationships. The input of PAIRS is protein interaction pair. After GO or PFAM was chosen, the ER score of GO or domain pairs are computed by PAIRS to construct the feature vector for each protein-protein interaction pair. Then, the trained classifier was used to predict the regulation relationship of the protein interaction pairs. As shown in For a certain protein-protein interaction, PAIRS outputs the interaction type and it also gives the significant ER scores of GO or domain pairs that was used.The challenge of systematic approach requires the protein networks involving all protein-protein interactions and the metabolic networks involving all enzymes and pathways. Bioinformatics methods can be used to accelerate the discovery of regulation relationship between protein interactions and distinguish the activation relations from inhibition relations. Reconstruction of signaling networks from protein interactions might be applied to understanding signaling transduction process, complex drug actions, and dysfunctional signaling in diseased cells . In thisThe limit of PAIRS lies in that if the interacting proteins do not contain either domain or GO interaction pairs, PAIRS cannot give any results. And if the inputs contain a large amount of protein interactions, the prediction computational time by the classifier will increase. With the development of efficient machine learning method and comprehensive biological data sources, PAIRS can be improved.


What is poorly appreciated, however, is that by localizing to membranes, proteins search in a reduced space that effectively drives up concentration. Here we derive an accurate and practical analytical theory to quantify the significance of this dimensionality reduction in regulating protein assembly on membranes. We define a simple metric, an effective equilibrium constant, that allows for quantitative comparison of protein-protein interactions with and without membrane present. To test the importance of membrane localization for driving protein assembly, we collected the protein-protein and protein-lipid affinities, protein and lipid concentrations, and volume-to-surface-area ratios for 46 interactions between 37 membrane-targeting proteins in human and yeast cells. We find that many of the protein-protein interactions between pairs of proteins involved in clathrin-mediated endocytosis in human and yeast cells can experience enormous increases in effective protein-protein affinity (10–1000 fold) due to membrane localization. Localization of binding partners thus triggers robust protein complexation, suggesting that it can play an important role in controlling the timing of endocytic protein coat formation. Our analysis shows that several other proteins involved in membrane remodeling at various organelles have similar potential to exploit localization. The theory highlights the master role of phosphoinositide lipid concentration, the volume-to-surface-area ratio, and the ratio of 3D to 2D equilibrium constants in triggering (or preventing) constitutive assembly on membranes. Our simple model provides a novel quantitative framework for interpreting or designing  in vitro binding data and cellular concentrations of proteins and lipids involved in pathways including clathrin-mediated endocytosis to demonstrate how cellular proteins could exploit membrane localization to regulate assembly.In a multitude of cellular processes, including cell division and endocytosis, proteins must bind to one another to form large multi-protein complexes. To initiate the formation of these critical multi-protein assemblies at the right time and the right place, the constituent proteins must be present at sufficient concentrations. We show here that membrane localization offers a powerful way of controlling protein concentrations by reducing the dimensionality of the protein’s search space. We present a simple and practical analytical theory that determines the significance of membrane localization for triggering protein-protein interactions. We show that protein binding partners will often form substantially more complexes when both partners can localize to surfaces, and thus localization can regulate the timing of multi-protein assembly. We collect  Despite the wide-ranging cellular processes such as cell division and viral budding that could exploit this phenomenon, it has so far lacked a predictive theoretical framework. Hence while the concept that membrane localization can enhance binding may be familiar or intuitive, we here make that concept quantitative for soluble binding partners. In contrast, theory for understanding reduction of dimensionality in chemoreception and receptor mediated signaling , self-assembles into multi-protein cages, the same protein-protein contacts are used regardless of whether clathrin is in solution or on the membrane –3. Howevnificant ) has beenificant , 6. Membnificant –9 and innificant –10. Howenificant , membrannificant , 13, or in vitro. Without accounting for the complex array of factors present in vivo, such as variability in membrane composition, competition for protein and lipid binding from diverse proteins, spatial distributions of proteins or lipids, and non-equilibrium dynamics, we can only speculate about the behavior in the cell. However, the theory provides a novel and valuable metric for interpreting how important membrane localization can be given the concentrations and binding properties of component proteins, and it isolates the role of membrane localization from other factors. Since even most in vitro experiments contain more components and complexity than is captured in our simple model, we discuss how it can still be used as a quantitative guide for estimating how membrane heterogeneity, competition for binding, and mutations would influence the parameters of the model  and thus the proteins’ subsequent response to localization. We specifically address in our results how lipids such as PIP2 can be targeted by many proteins at any time 0 = [P1P2] + [P1] and same for [P2]0. If these proteins can also reversibly bind to membranes via targeting a specific lipid M, and continue to bind one another, their binding equilibrium will shift as a total of nine distinct species can form -1. All species copy numbers, whether on or off the membrane, however, can be solved for in volume units when the appropriate Solution volume/Membrane surface Area (V/A) conversion factor scales the 2D binding constants, so we always report volume units for concentrations. To quantify the change in bound protein-protein complexes as a function of membrane localization we will define an effective equilibrium constantaeff and initial protein concentrations [P1]0 and [P2]0, one can immediately solve for bound complex concentration using aeff will revert to the solution bound value, KaPP, and thus the ratio of Kaeff / KaPP determines the extent to which membrane localization either enhances or diminishes protein-protein complex formation. As we discuss further below, in the extreme limits where all proteins are either in solution or on the membrane, Kaeff reduces to a true equilibrium constant. The strength of Kaeff is that it also quantitatively describes all the conditions in between these limits. Thus, our Kaeff definition offers a valuable metric for quantifying the equilibrium of the model in In our primary model, we consider two proteins Pcan form , Methodsrvations  even of rvations . Each ofaeff based on the 10 individual equilibrium relations for each reversible binding reaction  are different from the corresponding 3D values, but they are related through Ka2D = Ka3D/(2σ). The variable σ, with units of length, is a thermodynamic property of each binding pair that captures changes to binding free energy as a result of surface restriction and changes in standard state units. Changes to free energy are largely entropic, due to altered rotational freedom and protein flexibility eq is the unbound lipid concentration at equilibrium, and all equilibrium constants (including Kaeff) and concentrations are in volume units ; we therefore derive an additional approximate analytical equation for [M]eq described below  constitutive assembly on membranes. The right-hand side of aPP values (a2D) from experiments where binding occurs both on membranes and in solution. This practical application of our result should help simplify the relatively rare experimental characterization of protein-protein affinities on surfaces, as the proteins need not be restricted to the surface for it to work. The condition of excess lipids can be satisfied even with a lipid recruiter such as PIP2, present at 2.5x104μm-2 in the plasma membrane [Our main result is then a surprisingly simple and exact analytical relationship that quantifies the equilibrium solution of our model  via Kaefme units . [M]eq ied below . Howeverf lipids . Criticaproteins  and whicP values . In this2M[M]eq),where γ membrane , or ~1% membrane  Fig 2A)aeff and eq to provide a complete equilibrium theory of complex formation applicable to all experimental regimes, and we validate this equilibrium theory through extensive simulations of ordinary differential equations (ODEs) (aPP = 0), giving aPP = ∞), giving aPP. We can continuously interpolate between them  that smoothly interpolates between them  , MethodsM]eqCoop . These teen them  using thaeff, we first ask: are there any cases where membrane binding will reduce protein complexation, i.e. Kaeff<KaPP? To answer this, we consider the case where all proteins are on the membrane . V and A thus also control the initial copy numbers of proteins and lipids separately, such that large values of V/A have a great excess of proteins over lipids. This drives Kaeff⟶KaPP  at equilibrium. As is clear from aPM[M]eq for all γ>1 geometries. Hence with either stronger affinity for the membrane (KaPM) or a higher concentration of target lipids ([M]0), localization to the membrane and thus enhancement will increase. aPM[M]eq exceeds values of ~10, maximum enhancement is reached and increasing the stickiness of the membrane does not change the resulting binding. In the aPM[M]eq, as well as the corresponding critical value for lipid concentration, [M]c  and V = 37.2 μm3 (yeast). Performing RD simulations at these dimensions would produce slower relaxation times, particularly for human cells, due to the time required to reach the surface. Crowding would also lower effective diffusion constants of proteins, although the decrease in time-scales to equilibrate would be negligible unless binding rates were strongly diffusion-influenced (Methods).Our theory  only des binding , S4 Fig. binding  were per binding : V = 1202 eq[P2]eq gives:1 and P2 target distinct lipids, the [M] concentrations will be subscripted accordingly. Thus eq is needed that will be approximate.Inputting Eqs eq, is a function of two limiting cases for protein localization to the membrane with a smooth interpolation in between defined via aPP = 0), we solve for unbound lipids at equilibrium based solely on protein-lipid interactions, M+P⇋MP, giving the familiar quadratic rooteq~[M]0, the initial concentration of lipids, when [M]0>>[Ptot]0 = [P1]0+[P2]0. The KaPM,av is the average from both proteins. For significant differences between affinities and protein populations, the weighted average is most accurate, 1]eq’s rather than [P1]0 is more accurate. For the second extreme, (KaPP = ∞) we now treat all proteins as bound in complex, creating an equilibrium between proteins with two lipid binding sites and the membrane. This gives us aPP), using the function λ. The λ function is the fraction of proteins that are bound to one another (based on P1+P2⇋P1P2 with Kaeff) out of the maximum possible,aeff, which can be calculated based on plugging aeff dependent on λ can also be then fed back into this aeff.Our equation for the unbound lipids at equilibrium, [M]aPP is large. We note that the relative error in the full An important feature of To simulate the systems of ordinary differential equations (ODEs) for a is the intrinsic association rate that captures the barrier to complex formation for species in contact at binding radius σ, and Dtot is the sum of both species’ diffusion constants. The macroscopic off-rate can be defined in all dimensions viab is defined via the corresponding equation, kb = ka/Ka, with all off-rates having the same units in all dimensions of s-1. In 2D, there is no single macroscopic rate constant independent of the system size or concentrations eq is nearly exactly predicted by our approximate theory. In (b), the error increases now that lipids are outnumbered. Error is highest for moderate KaPP values, because here the predicted value of [M]eq is farthest from either of the limiting (and exact) predictions of −3 and 10−2 near these limits. c,d) From aeff, we can directly calculate the concentration of bound protein-protein complexes, as Kaeff = [Complex]eq/(([P1]0-[Complex]eq)([P2]0-[Complex]eq)). Simulation (red) vs theory (black). c) V/A = 0.76, KaPM = 104M-1, [P1]0 = [P2]0 = 0.1 μM, [M]0 = 2.5104μm−2. (d) Same as (c) except [P1]0 = [P2]0 = 2 μM and [M]0 = 103μm−2 e,f) The fraction of these complexes that are specifically on the membrane (Eq. S7). g) Network of reactions between all states. States with black outline all contain protein-protein complexes. Reactions in 2D are in green text. Protein-protein binding is otherwise in navy text, and protein-lipid binding in orange text.a,b) The relative error of the theoretically predicted K(TIF)Click here for additional data file.S2 Figa) Proteins in the cytosol can localize to membranes by binding specific lipids (yellow). Peripheral membrane proteins that do not bind directly can be bridged by a scaffold protein (green/gray) b) We collected the solution volumes (V) and membrane surface areas (A) for both plasma and organellar membranes in a variety of cell types . Only wh(TIF)Click here for additional data file.S3 FigaPM. b) This critical lipid concentration, [M]c, beyond which no further changes are observed in binding is derived in aeff = γKaPP, with results here shown for ε = 0.01. c) Protein interactions between proteins with weak solution binding (low KaPP) or d) low protein concentrations benefit more widely from recruitment. This is because these systems will form minimal complexes in solution (with (KaPP)-1>[P]0/2, fewer than half of proteins are in complex). Increased concentrations on the membrane can then substantially increase complex formation. e) Similar to aPP. Here we used KaPM = 104M-1 and [P]0 = 1μM. f) Enhancement increases with smaller σ as is clear from aPM  to a new value, KaPM*, would result in a change from Kaeff to Kaeff*. Here we set KaPP = 106M-1 and [P]0 = 1μM. For systems with higher [M]0, only significant (>factor of 50) decreases in affinity due to mutation affect the enhancement. h) For Epsin and AP180, the effect of pH and mutations on lipid binding affinity have been measured experimentally[2 at [M]0 = 2.5x104 μm-2, these up to 10-fold changes in affinity have relatively minor impact on enhancement.a) Once the enhancement due to membrane localization is near to the maximum value, the addition of more lipids changes the binding equilibrium imperceptibly. Even a relatively low concentration of lipids is needed to trigger the maximum binding interactions, particularly with strong Kimentally. We illu(TIF)Click here for additional data file.S4 Figoff = 1s-1 were used, and diffusion was only captured implicitly in binding rates, as ODEs have no spatial resolution. We started with V = 50μm3 and A = 65.63μm2, and then kept the volume constant and varied the area. KaPP = 106M-1, KaPM = 106M-1 b) For the CME binding pairs, many binding reactions are ultimately slowed by membrane localization. For human proteins, V = 1200μm3 and A = 767μm2 and for yeast proteins, V = 37.2μm3 and A = 75.8μm2  In purely 2D simulations, we also verify that the ODE (black lines) and RD simulations (colors) give the same equilibrium, as expected. The surface area was set to of 0.467x0.467μm for the RD simulations, and the equivalent area (0.218μm2) for the ODEs. Time-dependence is also similar to reach that equilibrium. These results are used to define the average time-scales to equilibrate in part (f) [P1]0 = [P2]0 = 458.92μm-2 koff = 1s-1 f) Pure 2D binding (green-RD or blue-ODE) is generally faster than 3D (red) despite slow-downs (factor of 100 here) in diffusion. Only for very strong (diffusion-limited) binding reactions does the impact of the diffusional search make a dominant impact on binding. V/A = 0.762, and same copy numbers in 3D and 2D, with solution concentrations of [P1]0 = [P2]0 = 1μM. Data on 2D timescales is defined from results of part (e). ODE system sizes and RD box sizes are the same as for part (d-e). Theory in black dashed (3D) and gray (2D). (g) Equilibrium values of all species for the system studied in part (d). For the stochastic FPR simulations, standard deviations from 24 trajectories are shown. Theory values are derived from a) ODE simulations show how localization can produce relative speed-ups and slow-downs to reach equilibrium relative to pure solution binding. The dashed line is a theoretical maximum estimated from comparing time-scales of pure 2D binding to pure 3D binding (Methods and Supplementary Text). Values of k 75.8μm2 . c) The  75.8μm2  Datasets(TIF)Click here for additional data file.S5 FigaPM. Notably, when AP-2 binds cargo (light green relative to dark green bars), KaPM is 40 times higher. The consequence of this stronger KaPM in (c) is marginal, but with limited lipids in (d), it drives significantly larger increases in complex formation. All results in a) If we increase σ from 1nm to 10nm, the maximal enhancement decreases by a factor of 10. b) If we reduce the lipid concentration by a factor of 10 (with σ = 1nm), enhancement again decreases relative to (TIF)Click here for additional data file.S6 FigaPM and two different KaPP for binding to AP-2 to show how the ability to bind other proteins will help stabilize the lipid binding FCHo1 on membranes, where we estimated [M]0 as 25000μm-2. b) The same effect is possible if the protein pairs can bind through multiple domains. Because AP-2 can use both its α and β appendages to bind epsin, it can form more complexes and stay tethered more strongly to the membrane. Results here used 10 times less PIP2. Other model inputs are based on in vivo measurements and are collected in a) We compare FCHo1’s localization to the membrane by itself (gray bars) or with help from protein-protein interactions (colors). We consider a range of possible values for K(TIF)Click here for additional data file.S7 Fig3, P4, S) and a membrane lipid (M). The two peripheral membrane proteins P3 and P4 do not directly bind one another, but both can bind to a scaffold protein S. The scaffold protein thus has two binding sites, one for P3 and one for P4. Only P3 and P4 can bind the lipid, not S. a) Binding interactions occurring purely in solution (3D) are shown in this box. b) All the orange boxed interactions involve the localization of a protein or protein complex from solution to the membrane via binding a lipid or membrane localized protein. Hence these are all 3D interactions. In panels c-f we show all the 2D interactions that can thus exploit membrane localization to enhance complex formation.We show all the possible interactions for a system with three cytosolic proteins (P(TIF)Click here for additional data file.S8 Figa values from simulation). Inset shows how the enhancement at a fixed V/A increases with increasing scaffold to peripheral protein. Black dashed line is maximal enhancement of Kaeff,SP/KaSol,SP = γ. b) We simulated a system of clathrin and the adaptor AP-2 to mimic in vitro experiment [-2 from the study, and used clathrin and AP-2 concentrations of 0.4μM each. Stronger Ka (= Kd-1) values for the clathrin-clathrin (CC) interaction produce more polymerization, particularly with membrane localization included (green lines). Yellow pie is percent clathrin on the membrane for simulations with AP-2. The enhancement is not limited by the AP-2:PIP2 interaction, but rather because the recruitment of clathrin to the membrane requires AP-2, which is only at 0.4μM (~25 times lower than lipid at this V/A = 9.46μm). c) Clathrin binds moderately to AP-2 (22μM). However, because clathrin has three leg domains that can each bind AP-2, once on the membrane, it will quickly bind multiple AP-2s. d) Time-scales to reach equilibrium are slowed (relative to pure solution in red) due to the time needed to bind AP-2 to the membrane, and then clathrin. Simulation inputs in a) For scaffold-mediated interactions , the twoperiment  using ru(TIF)Click here for additional data file.S9 FigaPP values are not known for these interactions, so we estimate a range (0.1–100μM: error bars). Since the protein-lipid affinity is only known to be >100μM (26), we compare values of 100μM and weaker binding of 300μM. We compare dimerization without membrane (gray bars) and with (dark red). When assisted by an (putative) interaction between SNX3 and VPS17, more complexation occurs of the now 3-protein complexes (light red). Because SNX3 binds strongly to PI(3)P, it will drive more complexation even without VPS5 (right bars). b) VPS17 is more effectively recruited to the endosome when it also interacts with SNX3. Pink is VPS17 by itself, dark red is with dimer formation allowed, and light red is with the third protein added . Although this direct interaction between SNX3 and VPS17 is not physiological, SNX3 does bind the full 5-protein retromer complex [a) Retromer components VPS17 and VPS5 bind weakly to PI(3)P on endosomes. K complex . These r(TIF)Click here for additional data file.S10 Fig2, PI(3)P, PI(4)P, and PIP2 at distinct organelles are reported in Yeast proteins that can also bind lipids including PIP(TIF)Click here for additional data file.