Whey proteins tend to interact with metal ions, which have implications in different fields related to human life quality. There are two impacts of such interactions: they can provide opportunities for applications in food and nutraceuticals, but may lead to analytical challenges related to their study and outcomes for food processing, storage, and food interactions. Moreover, interactions of whey proteins with metal ions are complicated, requiring deep understanding, leading to consequences, such as metalloproteins, metallocomplexes, nanoparticles, or aggregates, creating a biologically active system. To understand the phenomena of metal–protein interactions, it is important to develop analytical approaches combined with studies of changes in the biological activity and to analyze the impact of such interactions on different fields. The aim of this review was to discuss chemistry of β-lactoglobulin, α-lactalbumin, and lactotransferrin, their interactions with different metal ions, analytical techniques used to study them and the implications for food and nutraceuticals. The protein fraction of whey is composed of different proteins, including β-lactoglobulin (β-LG), α-lactalbumin (α-LA), lactoferrin (LTF), small amounts of immunoglobulin (IG), bovine serum albumin (BSA), and lactoperoxidase (LP) . Structuβ-Lactoglobulin is the major bovine whey protein, accounting for approximately 10% of the total protein in bovine milk and approximately 50% in ruminants , but it β-LG has eleven genetic variants . Genetic variants A and B are most common in bovine milk and differ in positions 64 and 118. Two bovine β-lactoglobulins I and J were isolated from bovine milk by isoelectric focusing by Godovac-Zimmermann et al. [Additionally, β-LG has two disulphide bonds   that mai- ions) have been reported by several authors [Heating causes changes in a protein’s structure, and subsequently, its properties, thus affecting the quality of food products. De Wit summarized the thermal behavior of β-LG up to 150 °C and concluded that thermal behavior of β-LG is dependent on pH, temperature, time of heating, and concentration . Reversi authors . In addi authors . Liu et  authors . Wijayan authors .Interestingly, Mercadante et al.  reportedα-Lactalbumin consists of 123 amino acids, except for rat α-lactalbumin, which contains 17 more amino acids and is an extension of the carboxyl end enriched with proline . α-LA coa values of individual functional ionizable groups [The native α-LA consists of two domains: a large α-helical domain and a small β-sheet domain connected by a calcium-binding loop. α-LA possesses a strong calcium-binding site with residues of Lys79, Asp82, Asp84, Asp87, and Asp88 . Calciume groups . When cae groups . The mole groups . The reme groups . Interese groups . A studye groups .α-LA is stabilized by four disulphide bonds between the cysteine residues  . The actLactoferrin (LTF) is a highly glycosylated protein of the transferrin family  that has1, C2, N1, and N2 [Lactoferrin consists of a single polypeptide chain with approximately 700 amino acids folded into two symmetrical lobes: a N-lobe and C-lobe. These are homologues with respect to each other (33%–41% homology). Each lobe consists of two domains, such as C, and N2 . Both lo, and N2 . In more, and N2 ,41.LTF can exist in two forms, apo-Lf and holo-Lf, depending on whether it binds iron (III) or not . In addiMetal ions interact with proteins, thus affecting their biological activity . The evaThe results of metal–protein interactions may include metalloproteins, metallocomplexes, and nanoparticles. Metalloprotein is primarily formed by coordination bonds between metal ions and functional groups of amino acids, for example, carboxyl, of the protein, thus embedding in the protein structure. These protein functional groups form a special binding site in a form of ‘cavity’ that is determined by protein quaternary structure and its biological activity. In addition, metalloprotein can interact with metal ions, forming either metallocomplexes (as first step) or metal/metal oxide nanoparticles. A metallocomplex is an artificial system defined by weak interactions such as electrostatic, hydrogen bonding, Wan der Waals forces, or donor–acceptor bonds, which are stronger than previously mentioned interactions. The binding affinity of metal ions to protein in the metallocomplex can be defined also by inductive  binding sites and collective strength of weak interactions. In contrast to metalloproteins, the interactions, leading to formation of metallocomplex, occur mostly via sorption or by intraparticle diffusion (modeled by Weber–Morris), while the metal ion of metalloprotein is embedded or ‘buried’ in a protein structure forming a natural system as for, e.g., hemoglobin, transferrin, etc. Interactions of a protein and metal ions with active functional groups of amino acids can be reversible and labile and lead to the formation of nanoparticles as was reported in the study of LTF and silver ions . The forBesides the formation of metallocomplexes and their nanocomposites, metal-induced protein aggregation also occurs, thus causing a loss in biological activity, protein precipitation from solution thus being detrimental for the quality of the product. Chemistry of the metal-induced protein aggregation can be explained by the Derjagin–Landau–Verwey–Overbeek (DLVO) theory of intraparticle interactions, which treats the stability of a biocolloidal system in terms of balance between attractive van der Waals forces and repulsive electrical double-layer forces . The addMoreover, such aggregation could cause (a) adsorption of proteins on metal surfaces, creating a problem with cleaning, (b) fouling of the filtration membranes by protein, complicating dairy processing by further disruption of membranes for ultra- and microfiltration, which could be explained by the increase in adhesion of proteins on the metal surface after the addition of metal ions. Interesting studies have been carried out to investigate the factors affecting whey proteins fouling. Yang et al.  reportedThe current section will be dedicated to interactions between whey proteins and metals, such as copper, zinc, silver, lanthanum, palladium, and ruthenium, as well as to the effects of iron, chromium, nickel, and calcium on the biological activity of whey proteins.First of all, the major part of metals described in this review are transition metals because the most common inorganic cofactors in biological systems are d-block metals that facilitate various functions of proteins and their complexes , thus maFinally, the increased consumption of metal–microelements as supplements to food increases the probability of their interactions with proteins because global demand for protein-rich food has increased with improved living standards  along wiThe nature of metal–protein interactions provides insights into the type and strength of the interaction as well as involvement of functional groups of a protein. For example, sorption at the surface of the protein, which is characteristic for metallocomplexes, may occur via weak non-covalent interactions that are unstable and reversible. Coordination bonds that allow embedding of a metal into the structure of protein are stronger.Polypeptide chains of proteins usually coordinate with the metal ion, and side chains with functional groups can act as an additional binding site for metals, including the imidazole group of histidine, carboxyl group of aspartate and glutamate, the phenol ring of tyrosine , and nitd value [Another factor affecting metal–protein interactions is pH. Magyar et al. reported interesting results showing potential pitfalls during metal–protein interactions studies and discussed how pH, temperature, use of different buffers, and the presence of competing ligands affect the Kd value . The effd value ,71. Furtd value . Interesd value . Anotherd value . Tang et al. also showed that glutamate and aspartate should be combined with a nitrogen donor or a sulphur donor to facilitate zinc-binding in peptides or proteins by using isothermal titration calorimetry (ITC). Whey proteins, such as lactoferrin, α-lactalbumin, and β-lactoglobulin showed strong zinc-binding affinities that were similar to each other, even though zinc binding to bovine serum albumin and lactoferrin was exothermic while binding to α-lactalbumin and β-lactoglobulin was slightly endothermic. In addition, authors suggested that zinc binds to the disulphide bonds of oxidized cysteine in LTF and to the thiol group of the cysteine (Cys34) in BSA with significant heat evolution, whereas zinc binds to histidine, aspartate, or glutamate in α-LA and β-LG .Shahraki et al. reported ultraviolet-visible spectroscopy (UV-Vis) results that showed that the interaction of the lanthanum (III)–cysteine complex with β-lactoglobulin and bovine serum albumin induces conformational changes for both proteins. In addition, the lanthanum (III)–cysteine complex strongly quenched the fluorescence of Trp fluorophore in β-LG and BSA in the static quenching mode. Hydrogen bonds and van der Waals forces stabilized the complexes for both proteins . SimilarMethods of separation of whey proteins include chromatographic , membrane-based (ultrafiltration and microfiltration), and electrophoretic methods. All these methods, except for the electrophoretic, were applied at all stages including isolation, purification, and separation, prior to analysis. Membrane-based methods are very diverse and can be applied for the isolation of whey proteins from real matrices, for the preparation of whey protein concentrate (WPC) and whey protein isolate (WPI), and for separation prior to analysis/detection. Electrophoretic techniques include capillary (CE), gel , and microchip electrophoresis (MCE). The microfluidic “lab-on-a-chip” technique for the separation of proteins has been reported as a high-throughput, automated alternative to conventional SDS-PAGE that allows the separation and quantification of many samples within 30 min. Another advantage is the low sample and material volumes required, which are usually less than 0.5 mL of the total volume chip (10 samples) . In compChromatographic techniques for separating whey proteins are also diverse. Separation in this case is based on hydrophobic, ionic, and specific (based on affinity) interactions and consists of adsorption of proteins on a solid (column or membrane) that are eluted with the liquid phase . Ion-excInstrumental techniques used for the study of the consequences of metal–protein interactions and their potential applications are summarized in Mass spectrometric methods as highly sensitive techniques that have low detection limits were applied for studying metal–protein interactions by measuring the concentrations of metal ions and protein. Inductively coupled plasma mass spectrometry (ICP-MS) is capable of detecting metal concentrations as it was reported for determination of concentration of the silver (I) ion to study the mechanism of binding of silver to LTF . Acosta In addition to mass spectrometric techniques, other methods used to understand the mechanism of binding silver to LTF have included Fourier transform infrared spectroscopy (FTIR) and Raman spectroscopy (RS). Both FTIR analysis and Raman spectroscopy have shown significant differences between LTF spectra with the addition of silver from native protein in terms of additional peaks. These techniques are complementary for the study of metal ion interactions with active functional groups of proteins. However, FTIR in comparison with RS is less specific and sensitive owing to the presence of water in the system, limiting the participation of the hydroxyl group in the interaction. Alternatively, RS is limited by the fluorescence processes of aromatic residues of LTF and requires surface-enhanced procedures, e.g., by gold or silver nanoparticle sputtering . AdditioMicroscopic techniques can serve as indirect methods for study of consequences of interaction and description of the mechanism of metal ions binding to a protein leading to the formation of nanoparticles as it was carried out previously . Kumari The matrix-assisted laser desorption ionization technique (MALDI) coupled to the time-of-flight mass spectrometry (TOF-MS) has become one of the common methods for protein characterization in addition to other MS-based approaches. The advantages of MALDI-TOF-MS include the simplicity of use, sensitivity, large mass range, and relative resistance to interferences from matrices . MoreoveMoreover, PTMs are crucial for protein biological activity, and their identification is an important analytical challenge. The MALDI-TOF-MS technique can be applied for this purpose by protein digestion to peptides and then identification of PTM sites. Although MALDI-TOF-MS is widely used for the analysis of digested proteins as well, analysis of LMW peptides can be complicated owing to the matrix interference and thus, signal suppression (<700 Da). Matrix-free approaches include many methods of analysis with the use of materials to replace the matrix. Nano-assisted laser desorption ionization (NALDI) is a promising technique. Nanomaterials assist the ionization that leads to signal enhancement owing to surface plasmon resonance. For example, Shenar et al. reported that a NALDI plate provided results with better sensitivity as compared to a DIOS chip, carbon powder, and porous silica for model peptides in the range of 519–2853 Da . InteresThus, the MALDI and NALDI techniques can be complementary to each other in terms of characterization of metal–protein interactions when coupled with other instrumental techniques in the following cases: (a) analysis and characterization of intact and digested proteins, analysis of metal–protein adducts by MALDI, (b) analysis of peptides digested from original proteins in the low molecular mass range, peptide adducts with metals and PTM sites located on the peptides with a low MW using NALDI in the mid to high range by MALDI, and (c) quantitative analysis of proteins by MALDI/NALDI. There are many publications that have reported biological claimed activities of whey proteins; however, the changes in these activities upon metal addition have not yet been deeply discussed. To the best of our knowledge, whey proteins exert antioxidant activity by forming glutathione (GSH) , which m3+ sat.) showed antitumorigenic properties; however, the apo-form showed a higher effect in inducing cytotoxicity in both cell lines (MDA-MB-231 and MCF-7) compared to Fe-bLf, which was more effective at inducing apoptosis in MCF-7 cell lines [Nevertheless, the effect of metals on anticancer activity of whey proteins can be shown by the example of LTF. It has been reported that iron-unsaturated apo-LTF inhibits the growth of cervical cancer (HeLa) cells after 48 h of treatment, whereas diferric-bLf was not effective . Additioll lines . Studiesll lines .Pseudomonas aeruginosa, Staphylococcus aureus, Escherichia coli, and Enterococcus faecalis. The growth of the drug-resistant P. aeruginosa strain was inhibited by more than 97%, which was comparable to the traditional cefotaxime antibiotic. Moreover, Komatsu et al. demonstrated that lactoferrin might be used to reduce the risk of aspiration pneumonia among elderly people for whom oral care remains difficult [LTF possesses antibacterial activity itself along with having immunomodulatory functions . Howeverifficult . Additioifficult . An interesting study by Thawari et al.  on β-LG Whey proteins as a component of milk and dairy products are a part of the everyday diet of many people. Together with the trend of uncontrolled consumption of supplements by the public, it creates a window for interactions between whey proteins and metals. Clearly, additional supplementation to food in the form of organic complexes that have metals can make up the deficiency of microelements, which has some advantages. Microelement deficiency is a serious problem that is common for developing countries, especially for infants, preschoolers, pregnant and lactating woman, and older adults , and in Another window for whey protein–metal interactions is the contact of milk products with stainless steel surfaces during storage, transport, and processing. Stainless steel alloys are of widespread use in the food industry owing to their high resistance to corrosion, good mechanical properties , and relOne more important point is whey protein–metal interactions occurring in the process of purification of whey by magnetic metal nanoparticles that is a good alternative to membrane processes. It is crucial not only for the design of functional foods and its safety but also for utilization of whey because its utilization in the purified form is more safe compared to that of the raw form . Whey proteins have a rich chemistry, thus providing interesting properties for many applications. Their natural affinity to metals has advantages as well as disadvantages in the fields of food chemistry and nutraceuticals. Advantages may include their potential applications as nutraceuticals, for the design of functional foods, whey purification, and utilization of whey wastes, while the drawbacks include their interactions with metals in food products, metals as drugs, and dietary supplements that may cause loss of the drug/supplement activity or toxic effects. This may occur with metals contact surfaces during processing, storage, and transport.Moreover, the effect of metals on their biological activity deserves attention because this also creates opportunities for new applications and is an important factor to consider in all stages of food processing, food safety, quality, and utilization. Formation of complex biocolloidal systems as a result of metal–protein interactions may occur in different ways, such as via (i) metalloproteins, (ii) metallocomplexes, (iii) nanocomposites, and (iv) aggregated systems. This review is focused on a discussion of the biological activities, interactions with metals, and analytical techniques applied for their study.


Study of interface residue pairs is important for understanding the interactions between monomers inside a trimer protein–protein complex. We developed a two-layer support vector machine (SVM) ensemble-classifier that considers physicochemical and geometric properties of amino acids and the influence of surrounding amino acids. Different descriptors and different combinations may give different prediction results. We propose feature combination engineering based on correlation coefficients and F-values. The accuracy of our method is 65.38% in independent test set, indicating biological significance. Our predictions are consistent with the experimental results. It shows the effectiveness and reliability of our method to predict interface residue pairs of protein trimers. Many protein complexes are formed by the interactions of multiple protein monomers. These complexes can carry out many biological functions, such as gene expression and regulation, signal transduction, or enzyme catalytic mechanisms . UnderstAn increasing number of computational methods have been developed to predict protein monomer binding sites and protein–protein interface residue pairs. In relation to this, Segura et al.  used a tA higher number of protein monomers implies more complex interaction mechanisms of the protein polymer. At present, there are a few methods to predict interface residue pairs of protein trimer. Zhao et al.  took theProperties of protein sequences depend on the composition and distribution of amino acids. The position and type of each amino acid in a protein sequence are unique, containing important structural and functional information. Therefore, for a specific position amino acid in the protein sequence, ideal descriptors should not only reflect the amino acid type but also structural information or the role played in the performance of the protein function. Based on previous studies on protein monomer binding sites and protein–protein interface residue pairs, we found some common properties that can allow to distinguish interface residues from the rest of the protein, using information of hydrophobicity, polarizability, solvent accessibility, and so on. We summarized these properties and divided them into two categories. The first category corresponded to amino acid physicochemical properties, including hydrophobicity ,18,19, pIn this paper, we defined an amino acid k-interval product factor to describe the influence of surrounding amino acids based on their physicochemical properties. Hence, we described a residue pair with three types of characteristics: amino acid physicochemical features, residue geometric features, and amino acid k-interval product factor. Different descriptors and different combinations may give different prediction results. We performed feature combination engineering based on correlation coefficients and F-values for all characteristics. In general, when the number of positive and negative samples in the dataset is seriously unbalanced, the accuracy and robustness of ensemble classifiers is higher than those of a single classifier (negative samples: noninterface residue pairs and positive samples: interface residue pairs). We trained a two-layer support vector machine (SVM) ensemble-classifier method to predict the interface residue pairs of protein trimers and tested it using an independent testing set. We also use different indicators to evaluate testing set results, which proves that our method is feasible.In summary, our method was divided into four parts: feature extraction, feature vector engineering, generation of a two-layer SVM ensemble-classifier, and performance evaluation, as shown in In this paper, the dataset was collected from the Protein Data Bank based on following four requirements: the number of chains is 3, the length of each chain is between 20 and 500, it is obtained by X-ray experiment, and there are physical bindings between each two chains in one protein trimer. Two chains are defined as interactors if there are interface residue pairs between the two chains.  By this way, we collect 78 protein trimers  have different physicochemical properties. These physicochemical properties, including hydrophobicity ,18,19 an1, Φ2, Φ3, Φ4, Φ5, Φ6, and Φ7 to represent the seven numerical sequences. These seven numerical sequences are the hydrophobicity number sequence 1, polarizability number sequence, polarity number sequence, secondary structure number sequence, codon diversity number sequence, hydrophobicity number sequence 2, and hydrophobicity number sequence 3.1 in formula 1,2 in formula 1, and so on. 1 in formula 1,2 in formula 1, and so on.According to the corresponding properties of each amino acid, the protein sequence P can be converted into seven different number sequences (see Formula (2)). We used ΦIn multiple protein monomers interactions, the individual behavior of the amino acid at each position is affected by the neighboring amino acids in the protein sequence. We define the amino acid k-interval product factor to describe the influence of neighboring amino acids on a given residue.The AAIPF(k) is defined as follows: the numbers at two positions with interval k are multiplied and divided by k on the amino acid number sequence. The AAIPF(k) can be divided into: amino acid forward k-interval product factor (AAFIPF(k)) and amino acid backwards k-interval product factor (AABIPF(k)) (see Formulas (3)–(5)).When exploring the individual behavior of each amino acid in a protein sequence P, as previously reported , we regaConsidering the dimensionality of descriptors, and using the experience of previous works ,29, we oWe also used as features the values of five physicochemical properties of amino acids, which we called basic first-order sequence features. Three versions of the hydrophobic values were used. Therefore, seven basic first-order sequence features were applied to describe an amino acid.1 and pK2) as features to describe the residue. The values of pK1 and pK2 were calculated by the propka3.1 software [Considering the electrostatic interaction is also one of the important factors to stabilize the protein structure. Therefore, we used the electric property values  to standardize these 128 dimensional characteristics.r and F-values. The specific process was as follows:Different characteristics and their combinations may play different roles in the prediction of interactions interface residues pairs in multiple protein monomers. Therefore, we performed feature vector engineering using two sets of feature vectors to describe a residue pair. We used the 128 dimensional characteristics extracted as the first set of feature vectors. Considering that some of the 128 dimensional characteristics have a strong correlation, we deleted 1/4 of the characteristics, and used the remaining characteristics as the second set of feature vectors. We filtered the characteristics according to the Pearson correlation coefficients r. The formula of the Pearson correlation r is as follows:In the first step, 128 dimensional characteristics were clustered according to the Pearson correlation coefficient m-th characteristic of the positive sample and the negative sample, respectively.In the second step, we used Formula (9) to calculate the F-value of each characteristic between the positive sample and the negative sample (negative sample: noninterface residue pairs and positive sample: interface residue pairs). The larger the F-value of the characteristic, the greater the difference between positive and negative samples and the greater the contribution of the characteristic to distinguish positive and negative samples.r| > 0.5, we preserved the characteristics of a relatively large F-value, with 96 characteristics in total. We used the 96 characteristics as the second set of feature vectors  were extremely imbalanced (negative classes: noninterface residue pairs and positive class: interface residue pairs). We used under-sampling to deal with the class imbalance problem. To improve the performance of the method, we used the classifier ensemble to alleviate the lack of information caused by the under-sampling. The process was as follows:Generation of balanced subset samples ):First, we randomly generated 100 subset samples of negative class from all the negative class samples in train data j. The total number of positive class was 12,687 in the entire training set. Therefore, we set the number of negative class in each subset sample to 12,687. Second, we combined each negative class subset sample with all positive class samples to generate a balanced subset sample. Finally, obtained 100 balanced subset samples for train data j .Generation of an ensemble classifier:SVM is a supervised machine learning method, which is widely used in the field of protein–protein interactions. Here, we also used SVM to predict trimer protein complexes interface residue pairs.1 and P2 through a weight ftp://202.112.126.135/pub/Trimer/code).There are 100 balance subset samples in train data j , each of which can be used to train an SVM model. We obtained 100 individual SVM predictors for train data j. We then developed an ensemble SVM classifier t predicted interface residue pairs with highest probability were used as the top t predicted interface residue pairs.The output of our model is a value between 0 and 1, showing the possibility of the residue pair to be an interface residue pair. The values were sorted from large to small. The number t predictions for each protein trimer. The first index is We used the following three measures to evaluate the performance of our method. First, we defined a three-dimensional vector The second index is The third index is index accuracy rate (see Formula (13)).t predictions, if there were z protein–protein interaction interfaces satisfying at least one positive interface residue pair, we assumed that the protein trimer was predicted correctly. SCT represents the sum of all correctly predicted trimer protein complexes. In the top There were 26 trimer protein complexes in the testing set. Each protein trimer consists of three chains, and any two chains interact to form a protein–protein interaction interface. Therefore, we obtained 78 protein–protein interaction interfaces. Through t  predictions and the two evaluation indexes corresponding to the testing set results. It can be seen from To further analyze the prediction results, we obtained the index There are 6479 pairs of interface residue pairs in the test set, of which 968 pairs are formed by residues at N- and C-terminal regions, accounting for 15% . We can accurately predict 190 interface residue pairs for all testing set protein trimers, of which 48 pairs are formed by residues at N-terminal and C-terminal, accounting for 25%.We compared the performance of our method with the previous method . When atThe analysis of the above results showed that our proposed method was able to accurately predict the interface residue pairs of trimer protein complexes. Additionally, our predicted results are consistent with the experimental results. In the experimental article of the 3ffd protein trimer , it is mt  predictions and the two evaluation indexes corresponding to the testing set 2 results. We compared the prediction results of testing set with that of testing set 2 ):We assume that the stochastic prediction of interface residue pairs of each protein–protein interaction interface in trimer protein complexes obeys a hypergeometric distribution H ; where XT predictions, the probability In order to simplify the calculation, we assumed that each protein–protein interaction interface was independently identically distributed, and T is fixed, T is 10, 15, 20, and 30, we can calculate Consideration of the complexity of the thod see .(16)P1˜T predictions, the probability When at least 2 protein–protein interaction interfaces of each protein trimer have at least one positive interface residue pair in T is fixed, T is 10, 15, 20, and 30, we can calculate Combining Formulas (15) and (18), we also enlarge thod see .(19)P2˜T predictions, the probability When 3 protein–protein interaction interfaces of each protein trimer have at least one positive interface residue pair in T was 10, 15, 20, and 30, we calculated In the same way as above, we also enlarged thod see .As can be seen from In this paper, we defined an amino acid k-interval product factor to describe the influence of neighboring amino acids on a residue. This method takes advantage of the physicochemical and geometric properties of amino acids, and also considers the influence of neighboring amino acids  as features. Finally, we developed a two-layer SVM ensemble-classifier method, based on feature vector engineering and SVM, to predict the interface residue pairs of trimer protein complexes. In our testing set, the accuracy rate of successfully predicting one interface was 84.62%, and for two interfaces, the accuracy rate was 73.08%, in the top 15 predictions, which indicates significance for biological experimentation and biomedical-related research. Moreover, our predicted results are consistent with the experimental results. This shows that our method is effective and reliable to predict interface residue pairs of trimer protein complexes. However, our accuracy rate was not high when three interfaces of one trimer are required to predict correctly. We also did not consider protein conformational changes. These are the areas where we will improve in the future.


Proteins containing intrinsically disordered regions (IDRs) are ubiquitous within biomolecular condensates, which are liquid-like compartments within cells formed through liquid–liquid phase separation (LLPS). The sequence of amino acids of a protein encodes its phase behaviour, not only by establishing the patterning and chemical nature  of the various binding sites that facilitate multivalent interactions, but also by dictating the protein conformational dynamics. Besides behaving as random coils, IDRs can exhibit a wide-range of structural behaviours, including conformational switching, where they transition between alternate conformational ensembles. Using Molecular Dynamics simulations of a minimal coarse-grained model for IDRs, we show that the role of protein conformation has a non-trivial effect in the liquid–liquid phase behaviour of IDRs. When an IDR transitions to a conformational ensemble enriched in disordered extended states, LLPS is enhanced. In contrast, IDRs that switch to ensembles that preferentially sample more compact and structured states show inhibited LLPS. This occurs because extended and disordered protein conformations facilitate LLPS-stabilising multivalent protein–protein interactions by reducing steric hindrance; thereby, such conformations maximize the molecular connectivity of the condensed liquid network. Extended protein configurations promote phase separation regardless of whether LLPS is driven by homotypic and/or heterotypic protein–protein interactions. This study sheds light on the link between the dynamic conformational plasticity of IDRs and their liquid–liquid phase behaviour. The cell interior contains thousands of different biomolecules , which need to be organized in space for the cell to function. One of the key cellular mechanisms to control the spatial organization of components is formation and dissolution of biomolecular condensates—membraneless compartments sustained by the physical chemistry of liquid–liquid phase separation (LLPS) ,2,3.Although the concept of liquid-like membraneless compartments inside cells ,5 is notMany proteins containing intrinsically disordered regions (IDRs) such as FUS ,22,23, hThe structural and dynamic behaviour of IDRs varies widely. IDRs can behave as random coils ,37, exhiExperimental advances in single molecule Förster resonance energy transfer (smFRET) have now enabled the direct observation of conformational switching in diluted conditions ,54,55. HAtomistic Molecular Dynamics (MD) simulations can characterize the conformational ensembles of single proteins and protein complexes ,57,58, pPowered by algorithmic advances and increased computer capabilities, atomistic MD simulations are now being used to investigate protein interactions within crowded environments that mimic in vivo conditions . SimultaIn this work, using MD simulations of a minimal coarse-grained protein model, we investigate the impact of modulating the conformational landscape of IDRs on their ability to form biomolecular condensates. Our results show that conformational switching enhances LLPS whenever the IDR configurational landscape is enriched in extended states. Consistently, exploring preferentially more compact and structured globular states (such as after a disorder-to-order transition) hinders LLPS by limiting the protein valency. We find that these observations are explained by a larger density of molecular connections that extended IDRs can establish within the condensed liquid. These results illustrate how beyond the amino acid sequence, the connectivity of the condensed liquid network, which governs the ability of proteins to phase separate , crucialN beads, where each bead represents a group of several amino acids  are e LAMMPS . The intbarostat ,101 withtegrator . The typtegrator ,104,105 As mentioned in the introduction, IDRs span a wide-range of different structural behaviours, including acting as fully disordered random coils ,37, servWe first focus on IDRs whose LLPS is driven by homotypic interactions. To exclude amino acid sequence and patterning effects ,85,89, wTo investigate the impact of the conformational behaviour of IDRs in their ability to phase separate, we use DC simulations  to compu109.5∘ , suggest109.5∘ ,16,17,18To further understand this observation, we evaluate the molecular connectivity  a semi-compact structure with a radius of gyration of 2.40 (in reduced units), and (2) a compact structure with radius of gyration of 1.75.The specific conformation that a protein adopts has a crucial effect on its liquid–liquid phase behaviour. As shown in If we now compare larger proteins, we observe that the impact of the structural conformation in the phase behaviour is moderately amplified. In A significant number of intrinsically disordered proteins exhibit heterotypically driven phase separation, i.e., dependent on their binding to a cognate protein or RNA . For exaWe model two binary mixtures of 20-bead IDRs with different conformational ensembles: a mixture where both types of IDRs behave as fully flexible random coils  simulations ,104,105.exponent , and s1 To quantify the number of molecular connections per protein replica, or liquid network connectivity within the condensates, we use the following procedure . For theIn this work, we investigate the impact of a protein conformational landscape in its liquid–liquid phase behaviour. Using a minimal coarse-grained model, we find that enriching the conformational ensemble of an IDR in extended configurations significantly promotes LLPS. Conversely, switching to an alternate configurational ensemble that predominantly samples compact (rigid or flexible) conformations inhibits LLPS, provided that such a structural change does not alter the binding strength among proteins.Our simulations reveal that the molecular origin of LLPS enhancement stemming from enriching an IDR conformational ensemble in extended structures is the increase in the molecular connectivity of the condensed liquid . ExtendeWe find that, within our model, fully flexible random coils and lightly extended IDRs undergo temperature-induced expansion, while IDRs more significantly constrained to sample extended states exhibit moderate temperature-induced collapse. Even though IDRs that exhibit temperature-induced expansion may have an advantage to phase separate over those exhibiting temperature-induced collapse, because of a surplus of inter-protein interactions, our CG simulations show that IDRs with a higher radius of gyration at a given temperature, irrespectively of their temperature-dependent behaviour, will have a greater ability to phase separate.Furthermore, we show that the conformational landscape of IDRs is lightly altered upon the liquid–liquid phase transition, with the more notable changes emerging at lower temperatures and higher protein–protein binding affinities. Either in homotypically or heterotypically driven LLPS, highly flexible IDRs adopt slightly more expanded conformations when transitioning from the diluted phase to the condensed phase. However, in heterotypically driven LLPS, moderately extended IDRs become more compact upon phase separation. Together this work contributes to advancing our understanding of the relationship between protein conformation and liquid–liquid phase behaviour.


Protein subcellular localization is highly regulated and critical for protein function. Spatial proteomics aims at capturing the localization dynamics of all proteins expressed in a given cell type. Among different approaches, organellar mapping through proteomic profiling stands out as the only method capable of determining the subcellular localizations of thousands of proteins in a single experiment. Importantly, it can also detect movements of proteins between subcellular compartments, providing an unbiased systems analysis tool for investigating physiological and pathological cellular processes. HighlightsOrganelle profiling maps capture localizations of 1000s of proteins in one experiment.Comparing maps +/− perturbation reveals disease mechanisms & cellular responses.A conceptual guide to planning and interpreting organellar profiling experiments.A cross-study consensus set of human organellar marker proteins. Protein subcellular localization is an essential and highly regulated determinant of protein function. Major advances in mass spectrometry and imaging have allowed the development of powerful spatial proteomics approaches for determining protein localization at the whole cell scale. Here, a brief overview of current methods is presented, followed by a detailed discussion of organellar mapping through proteomic profiling. This relatively simple yet flexible approach is rapidly gaining popularity, because of its ability to capture the localizations of thousands of proteins in a single experiment. It can be used to generate high-resolution cell maps, and as a tool for monitoring protein localization dynamics. This review highlights the strengths and limitations of the approach and provides guidance to designing and interpreting profiling experiments. Proteins must be precisely targeted to one or more subcellular localizations, to enable them to interact with other proteins, encounter substrates, become activated or inactivated, modified, degraded, secreted, or sequestered. This spatial dimension of the proteome is carefully regulated, highly dynamic, and allows much faster responses to perturbations than alteration of gene expression. Many, perhaps most, cell biological processes involve proteins transitioning between cellular locations; evidence suggests that spatial regulation of the proteome is as important and extensive as regulation of protein abundance . Support2in situ. For spatial proteomics through interaction networks, binding partners of proteins are identified by co-immunoprecipitation . The dihttps://www.proteinatlas.org/) offers an unprecedented community resource for imaging data and reagents. Proximity labeling is gradually replacing conventional affinity isolation approaches for protein interaction network analysis; the first global organellar map based on BioID data is now available  and will serve as an important framework for integrating future BioID experiments. Finally, several laboratories have applied organelle profiling to provide localization maps from diverse cell types, ranging from mammalian primary cells (https://www.uniprot.org), and Compartments (https://compartments.jensenlab.org/Search)).All three of the above fields have greatly progressed in recent years, and numerous databases with subcellular localization predictions generated with different approaches are available. High throughput imaging is now relatively fast and feasible, and there is an ever-expanding repertoire of quality-controlled antibodies and GFP cell lines , 13. Impry cells , tissuesry cells , 19 and ry cells , 20, 21 ry cells  and unicry cells , 24. Allry cells . In addiDifferent spatial proteomics approaches have pronounced strengths and drawbacks; the choice should therefore be guided by the research question, but necessarily also depends on available resources. Global approaches have intuitive appeal, but focused methods are often more appropriate, particularly if the research question only concerns a subset of the proteome, such as a single cellular compartment. Among the global mapping methods, organellar profiling is rapidly gaining popularity, for several reasons. Beyond access to mass spectrometry, it requires no special resources, and avoids the costs and potential artifacts associated with protein tagging and affinity reagents. The time commitments for a pilot study are relatively modest, and even a single experiment can reveal the localizations of thousands of proteins. Profiling also intrinsically provides protein co-fractionation data, akin to protein interaction data, allowing the detection of protein complexes (see Microclustering and Protein Complex Prediction). In addition, the approach can capture induced protein translocations, and thus provides an unbiased discovery tool to study cell biological or pharmacological processes (see Recent Applications of Comparative Organellar Profiling). Detailed protocols for mapping , 29 and e.g. the ribosome) and the actin cytoskeleton.The origins of organellar profiling date back to the seminal work of Christian De Duve in the 1950s (reviewed in ). De Duv37Beyond providing detailed static cellular maps, a strength of organellar profiling is the ability to capture induced protein translocations . Compariversus robustness and experimental simplicity. Linked to this is their suitability for static versus comparative applications.Several workflows for organellar profiling experiments have been established and well documented –21, 27. e.g. HeLa) tend to yield to Dounce (glass-on-glass) homogenization, which may be aided by prior gentle osmotic swelling of cells on ice  may be s on ice , 24. Alts on ice , it shouThere is intrinsic variability in the propensity of different organelles to be released from lysed cells. Small round organelles such as peroxisomes and lysosomes are more readily released than the ER, which is partly wrapped around the nucleus. This also means that the ER will always rupture partially during cell lysis. It is recommended to control organellar integrity by quantifying leakage of lumenal contents into the cytosolic fraction .Once cells have been lysed, organelles can be separated based on their physical properties, such as size and/or density. The most widely used methods include density equilibrium centrifugation , 29, sucRelated to the separation method is the number of collected fractions. Typical gradient fractionations generate around 10–20 fractions, whereas differential centrifugation approaches yield only 5 to 10. More fractions tend to enhance the resolution, and long profiles may even reveal multi-organellar associations , two oth37Arguably, the simplest form of a spatial proteomics experiment is to separate cell lysates by differential centrifugation into a crude nuclear fraction, a membrane fraction, and the cytosol. Quantifying the distribution of proteins across the three fractions provides a wealth of spatial information, especially in a comparative context. Pioneered by the Lamond lab , severalOrganellar profiling experiments are highly demanding with respect to mass spectrometry. Even for a single map, multiple fractions with quite different compositions need to be analyzed, and ideally, each identified protein should be quantified across most fractions. Furthermore, organelles tend to have overlapping profiles, which can be deconvolved only if the quantification is sufficiently accurate to resolve relatively subtle differences. The smaller the degree of organellar separation, the more accurate the quantification needs to be. For comparisons of organellar maps, profiles must be reproducible, requiring high precision of quantification. Fortunately, thanks to recent advances in instrumentation, data analysis and labeling based multiplexing strategies, there are several options to achieve this.e.g. using the MaxLFQ . The MaxLFQ  offers ee MaxLFQ ; the appe MaxLFQ –21, 45 ae MaxLFQ , and thue MaxLFQ , 47, bute MaxLFQ , and a Te MaxLFQ  allows nProfiling experiments are also excellent tools to evaluate the performance of MS quantification strategies . ProteinProfiling experiments typically produce high-dimensional data for thousands of proteins, which are difficult to represent in diagrammatic form. Dimensionality reduction methods compress the data down to two or three dimensions that still capture most of the information. An interpretable visual representation can be obtained by plotting the data in the reduced data space, with every protein typically displayed as a single scatter point. Proteins with similar profiles will cluster in the data map, allowing rapid discernment of resolved organelles. Software for standard visualization methods is freely available , 50.There are two families of tools for dimensionality reduction - those based on linear data transformation, such as PCA , and NMF ; and the.g. positioning between two clusters), and perhaps guide the interpretation of protein translocations. Importantly, an organellar map is not an 'image' of the cell, but reflects the resolution and underlying principles of the chosen profiling approach. Organelles that appear close in the map have similar physical properties during separation, but this does not necessarily imply that these organelles are functionally similar, or physically close in the cell. Conversely, although the map shows which organelles are separated by the method, this does not preclude that these organelles are in physical contact within the cell. In fact, most organelles make contacts with other organelles , and an analysis of organellar metadata confirmed this notion . I propose that this set may serve as a standard core reference for future organellar mapping experiments, either as an independent test set to assess the performance of classification models, or as a useful starting point for building marker sets.There are two main strategies for converting profiling data into lists of organellar proteins - supervised and unsupervised clustering. For the former, a list of 'bona fide' organellar marker proteins is used to outline areas of the profile space that correspond to individual organelles or subcellular structures. Next, machine learning algorithms , Manual curation of the marker set can be avoided using unsupervised clustering methods, allowing the profiling data first to define its own clusters, and then assigning compartments based on available external subcellular localization information of the cluster members . This apThe observed prediction accuracy of organellar profiling, as judged by recall and precision of marker predictions, is largely determined by the choice of markers, even with cross-validation. It should be regarded as an estimate of the confidence of predictions purely within the cluster boundaries defined by the given marker set, but not as an absolute measure of organellar resolution. Comparing prediction performances across studies is hence of limited value . However, F1 scores  and the corresponding “confusion matrix” of wrongly assigned marker proteins are very useful experiment-internal metrics, particularly for map optimization and interpretation, as they highlight which organellar mis-assignments are likely to occur.i.e. the relative positions of the two organelles. In the worst case, a third organelle lies in between the two clusters, and the protein is miss-assigned.Many, if not most, proteins have multiple subcellular localizations, ranging from transient movements during biosynthesis, to functional re-localizations, and genuine multi-compartment functions or even moonlighting activities . Exampleversus organellar pools of proteins independently from their compartment assignments, allowing dual localization predictions for proteins that are partly organellar and partly cytosolic . The very fact that a protein is poorly assigned has been interpreted as evidence of multiple localizations , 21. Somytosolic . Furtheric ; because profile shifts are evaluated, all profiled proteins can be included, even those lacking a confident cluster assignment.C), and greatly improves with multiple replicates.Proteins that are part of a stable complex have tightly linked fractionation profiles, resulting in visible “microcluster” formation within organellar maps , 20, 21.Fig. 2A main application of organellar mapping is to identify proteins with shifted subcellular localization following a perturbation. An intuitive approach is to focus on proteins with altered predicted compartment association, but this is rarely advisable. First, it requires that both compartment association predictions are correct, and hence may produce false positives. Second, it can only detect near complete organellar translocations; a partial (or even intra-organellar) shift is unlikely to alter the original compartment association prediction, resulting in false negatives. Evidence suggests that many translocations are partial (see for example ) and wouOf note, seven out of eight published comparative profiling studies have analyzed profile shifts to detect translocations 37, so thisi.e. to compare two sets of (untreated) replicate maps. At a given set of cut-offs, the number of hits in the mock experiment is divided by the number of hits in the perturbation experiment, yielding an FDR estimate (Because comparative profiling experiments are intrinsically noisy, FDR control for the detection of translocations is essential. A good way to calibrate the experimental system is to perform a 'mock' comparative experiment, estimate , 25. At estimate , 37.Although it would be highly desirable to estimate the sensitivity of comparative profiling experiments, this has not been possible to date. Because such experiments typically aim to uncover novel connections, the 'ground truth' is not known a priori. If possible, positive controls that are expected to shift strongly upon perturbation should be part of the experimental design. These help to gauge the sensitivity and to adjust stringency cut-offs.et al. (Profiling translocation analysis is a reductionist tool - its greatest strength is to identify from thousands of profiled proteins a relatively small set specifically responding to a perturbation. The observed shifts may be directly interpretable regarding spatial rearrangements, both by comparing organellar assignments, shifts in visual maps, and across cytosolic, membrane and nuclear fractions . Howeveret al.  identifiComparative organellar profiling promises to become a widespread systems analysis tool, with countless potential applications in cell biology, pharmacology and biomedical research. Although high quality MS instrumentation is now available to many labs, the considerable MS time requirements for profiling are still the biggest bottleneck; consequently, most profiling based publications are restricted to binary comparisons. A priority in the field should be the development of streamlined workflows that allow fast pilot experiments, more high-throughput mapping, and more complex experimental designs.The rapidly increasing number of spatial proteomics studies is exciting and shows the growing momentum of the field. A potential concern is that the current databases of protein subcellular localization cannot be easily cross-referenced. There is no central repository, and no universal data format that allows rapid comparisons of the predictions. Database curators, or perhaps the proteomic community, should tackle these issues soon, to maximize accessibility of current and future spatial proteomics datasets.


The alignment of protein-protein interaction networks was recently formulated as an integer quadratic programming problem, along with a linearization that can be solved by integer linear programming software tools. However, the resulting integer linear program has a huge number of variables and constraints, rendering it of no practical use.We present a compact integer linear programming reformulation of the protein-protein interaction network alignment problem, which can be solved using state-of-the-art mathematical modeling and integer linear programming software tools, along with empirical results showing that small biological networks, such as virus-host protein-protein interaction networks, can be aligned in a reasonable amount of time on a personal computer and the resulting alignments are structurally coherent and biologically meaningful.The implementation of the integer linear programming reformulation using current mathematical modeling and integer linear programming software tools provided biologically meaningful alignments of virus-host protein-protein interaction networks. Many meaningful questions in molecular biology have been successfully answered through their translation into alignment problems for different mathematical structures. From simple structures, such as genomic or proteomic sequences, to richer structures, such as complex networks or whole biological systems, pairwise and multiple alignment have been used to compare these structures, inferring features and new biological relations from their alignment.Several methods and software tools have been already introduced for the alignment of biological networks, including protein-protein interaction networks, metabolic pathways, and gene regulatory networks. They are addressed to solve interesting biological questions, such as the inference of protein-protein interactions and protein functions, the regulation of biological processes, and the metabolic capabilities of microorganisms. The alignment and analysis of protein-protein interaction networks has become a key ingredient to obtain functional orthologs and discover protein-protein interactions and their associated functions, as well as evolutionary conserved assembly pathways of protein complexes.In the general network setting, and hence also in the particular case of protein-protein interaction networks, an alignment between two networks is an injective, but possibly partial, mapping from the set of nodes in one network (the source network) to the set of nodes in the other network (the target network). When the mapping defining the alignment has as domain the whole set of nodes of the source network, the alignment becomes an embedding of the source into the target network. Since biological networks are large networks, with hundreds to thousands of nodes and edges, most of the techniques developed for their alignment –5 are heIn this paper, we present a compact integer linear programming reformulation of the protein-protein interaction network alignment problem, which can be solved using state-of-the-art mathematical modeling and integer linear programming software tools. We also present empirical results showing that small biological networks, such as the virus-host protein-protein interaction networks in the STRING Viruses database , can be Homo sapiens , Saccharomyces cerevisiae , and Escherichia coli . We downloaded from STRING Viruses the virus-host protein-protein interaction data for Homo sapiens and all the protein sequence data .The STRING Viruses database  containsEach of the protein-protein interactions is annotated with a combined score, an indicator of confidence ranging from 0 to 1, where a combined score of 0.5 indicates that roughly every second interaction might be a false positive. Therefore, we discarded any protein-protein interaction with a combined score under 0.510, keeping only interactions in the last 10% of the distribution of combined scores. Also, host-host protein-protein interactions were discarded since the alignment purpose in this experiment is the relation between the proteins of a virus and its host. Nevertheless, in a more general setting host-host protein-protein interactions can be also considered. Further, we discarded the smallest networks, those with 64 or less interactions, and focused our alignment experiments on the remaining 25 largest networks, which have between 56 and 735 viral and host proteins and between 65 and 957 virus-host protein-protein interactions. These networks are listed in Then, we aligned all possible pairs of these 25 networks. Due to the symmetry of the network alignment problem, we actually aligned 25·24/2=300 pairs of networks. We performed each of these 300 alignments using the compact integer linear programming formulation presented in this paper with AMPL version 2018.10.22  and GuroWhile our method is aimed at finding exact solutions to the problem of aligning protein-protein interaction networks, all of the aforementioned protein-protein interaction network alignment tools use an heuristic algorithm to obtain the final alignment. The general idea behind all of these alignment tools, is to define a node similarity measure that combine the similarity of the protein sequences with some network structure similarity. Then, the actual alignment is obtained based on node similarity. More precisely, in PINALOG, network structures are “communities,” which are scored and aligned based on a node similarity score that combines protein sequence similarity and GO terms, and aligned communities are extended to obtain the network alignment. In SPINAL, node similarity score is defined based on sequence similarity of nodes and of their neighbours, this score is iterated until some stability is reached, and the network alignment is obtained by a greedy, seed-and-extend approach. In HubAlign, network structures are “hubs” and “bottlenecks,” a score or weight is assigned to each node and edge of a network using an iterative minimum-degree heuristic algorithm to measure the topological and functional importance of a node , and the network alignment is obtained by choosing protein pairs with high alignment score by, again, a greedy, seed-and-extend approach. In L-GRAAL, node similarity is measured by considering 2-node to 4-node graphlet (connected subgraph) degree similarity and, based on node similarity, seeds are obtained using Integer Linear Programming (ILP) and Lagrangian relaxation and then extended to a network alignment using a greedy heuristic algorithm. Last, but not least, in AligNet, an overlapping clustering for every node in every network is computed. Then, all clusters pairs are aligned and scored based on sequence similarity of proteins and their neighbours. Finally, the clusters in one network are aligned with the clusters in the other network using the Hungarian algorithm, and local network alignments are first obtained as solutions to weighted bipartite hypergraph problem instances and then extended to a global network alignment.topological coherence and biological coherence measures were proposed for the comparison of protein-protein interaction network alignment methods and tools. It is shown in  that controls the balance between protein similarity scores and protein-protein interaction weights in our model  and 100 random perturbations of the Zaire ebolavirus (taxid 186538) virus-host protein-protein interaction networks. The mean and standard deviation of the EC and FC scores are 0.955413 and 0.012193 for the EC score and 0.991356 and 0.003269 for the FC score. That is, small perturbations of the virus-host protein-protein interaction networks produced small variations of the EC and FC scores.In order to measure the amount of variation or dispersion of the EC and FC scores used to evaluate the topological and biological coherence of the alignments, we introduced some noise to the virus-host protein-protein interaction networks by randomly adding and deleting 5% of the interactions. We computed 10,000 alignments between 100 random perturbations of the k-mer frequencies [k-mer frequencies, for k between 1 and 4, and normalized global alignment score), for a subset of 45 pairs of virus-host protein-protein interaction networks with λ=0.5. The higher the value of k, the lower the mean sequence similarity score, with normalized global alignment giving the lowest score, but the mean edge correctness score is unaffected by the choice of sequence similarity measure.While these results are based on a particular view of sequence similarity as correlation of amino acid composition, as mentioned above, it is possible to use the protein-protein interaction network alignment method with any measure of sequence similarity, including alignment-free measures such as the Euclidean distance between quencies  and alsoTo reinforce the statement that the integer linear programming formulation of the network alignment problem provides biologically meaningful alignments of virus-host protein-protein interaction networks, we analyzed the alignments in term of agreement on virus taxonomy. Namely, we considered the taxonomy classification of the virus in every virus-host protein-protein interaction network and assumed that the highest alignment scores must be obtained when considering closely related viruses. Indeed, Table Alphapapillomavirus 9 network is best aligned with the Human alphaherpesvirus 2 network; the Human betaherpesvirus 5 network is best aligned with the Human betaherpesvirus 6B network; the Human alphaherpesvirus 3 network is best aligned with the Human alphaherpesvirus 1 network; the Human alphaherpesvirus 1 and Human alphaherpesvirus 2 networks are best aligned with each other; and the Human betaherpesvirus 6A and Human betaherpesvirus 6B networks are also best aligned with each other.As a matter of fact, in class I (double-stranded DNA viruses), the Human coronavirus 229E network is best aligned with the SARS-related coronavirus network. In class V (negative-sense single-stranded RNA viruses), the Influenza A virus network is best aligned with the Marburg marburgvirus network; the Human orthopneumovirus, Mumps rubulavirus, and Hendra henipavirus networks are best aligned with the Human metapneumovirus network; the Marburg marburgvirus and Zaire ebolavirus networks are best aligned with each other; and the Human metapneumovirus and Measles morbillivirus networks are also best aligned with each other.In class IV (positive-sense single-stranded RNA viruses), the Human immunodeficiency virus 2 network is best aligned with the Primate T-lymphotropic virus 2 network; the Primate T-lymphotropic virus 1 network is best aligned with the Primate T-lymphotropic virus 3 network; and the Primate T-lymphotropic virus 2 and Primate T-lymphotropic virus 3 networks are also best aligned with each other.Finally, in class VI (positive-sense single-stranded RNA viruses that replicate through a DNA intermediate), the The compact integer linear programming reformulation of the protein-protein interaction network alignment problem can also be applied to similar alignment problems on graph-based representations of molecular structures, such as metabolic pathways and gene regulatory networks. The application to virus-host protein-protein interaction networks provided high scored alignments in both network topology and biological coherence, which constitutes evidence that the alignments obtained with this approach are biologically meaningful.The alignment of virus-host protein-protein interaction networks may contribute to discover the effect of viral infection to their host. New databases with virus information have been created in the last years from the analysis of new metagenomics data –16. HoweG=, where each node v∈V corresponds to a protein and each edge {u,v}∈E corresponds to an interaction between the proteins represented by the nodes u∈V and v∈V. Let G= and G′= be the two protein-protein interaction networks to be aligned, let V={v1,…,vm} and V′={v1′,…,vn′} be their respective sets of nodes and A=(aij) and B=(bkℓ) be their respective adjacency matrices. Let S=(sik) be a similarity matrix between the nodes of the two networks, with each sik the similarity score of vi∈V and vk′∈V′.The following notation will be used in this section. A protein-protein interaction network is represented by means of an undirected graph G and G′ can be represented by a binary matrix X=(xik), where xik=1 if the i-th node, vi, of the first network is aligned with the k-th node, xik=0 otherwise. Then, the protein-protein interaction network alignment problem has the following simple integer quadratic programming (IQP) formulation in terms of the binary variables xik [An alignment of Problem IQP. Objective:xik∈{0,1}, i=1,…,m, k=1,…,n(Q1) (Q2) (Q3) subject to the constraintsλ is a parameter, with 0≤λ≤1, that controls the balance between protein similarity scores and protein-protein interaction weights: only node scores are considered when λ=1, and only edge scores are taken into account when λ=0. Constraints (Q2) and (Q3) enforce that, for every i=1,…,m, at most one xik is equal to 1  defines a, possibly partial, mapping) and that, for every k=1,…,n, at most one xik is equal to 1  and hence that the matrix X defines an alignment between the networks G and G′, given by {∈V×V′:xik=1}.In this problem’s objective function, vi,vj)∈E and ∈E′ such that vi is aligned with vk′ and vj is aligned with vℓ′.The objective function above comes from the PathBLAST  idea thaO(m2n2) binary variables and constraints [O(mn) binary variables, integer variables, and constraints, along the lines of a well-known linearization of the quadratic assignment problem [This quadratic formulation has a linearization with straints , of no p problem –21.xik above, we introduce an integer variable yik for each vi∈V and each yik is intended to representi=1,…,m and k=1,…,n. In this way, if xik=0,yik=0, and if xik=1,yik is the number of edges incident to vi in G that are preserved by the alignment.In addition to the binary variables SinceProblem ILP. Objective:xik∈{0,1}, i=1,…,m, k=1,…,ni=1,…,m, k=1,…,nThis linear problem turns out to be equivalent to problem IQP, because of the following lemma:xik) is a solution to Problem IQP if, and only if, there is an integer matrix (yik) such that ((xik),(yik)) is a solution to Problem ILP. Moreover, when λ<1, if (xik) is a solution to problem IQP and (yik)is such that ((xik),(yik)) is a solution to Problem ILP, theni=1,…,m and k=1,…,n.A binary matrix  is a solution to problem IQP if, and only if, ((xik),(yik)) is a solution to problem ILP for every integer matrix (yik).If λ<1. It is clear from the problems’ objective functions that if (xik) is a solution to problem IQP, then taking for every i=1,…,m and k=1,…,n,xik),(yik)) to problem ILP.Now, assume that xik),(yik)) is a solution to problem ILP. If xik),(yik)) is a solution to problem ILP.Conversely, assume that ,(yik)) is a solution to problem ILP, theni=1,…,m and k=1,…,n. Since the constraints on (xik) are the same in both problems, we conclude that (xik) is a solution to problem IQP. □This implies that, when xik),(yik)) of the linear reformulation ILP of the alignment problem defines an alignment between the mapped proteins in the two networks via {∈V×V′:xik=1}.Therefore, a solution . (PDF 67.4 kb)