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9.1 Introduction

In this chapter we discuss the various structural aspects of transmembrane proteins (TMPs) and survey the tasks and methods needed for modeling their structure. The structure prediction of TMPs from the pure amino acid sequence translated from genome projects may go through the following steps: (i) remove annotated or predicted cleavable parts (transit sequences, signal peptides); (ii) determination of the protein type (TMP or not); (iii) localization of TM segments within the amino acid sequence (topography prediction, 2D prediction) and the soluble parts of the protein relative to the membrane (topology prediction, 2.5D prediction); (iv) modeling the tertiary structure (3D) of membrane embedded protein parts which, depending on the amino acid similarity to the available relatives whose structure are already solved, may be based on homology modeling ; may use the advantage of threading or may be de novo predictions including the contact prediction of amino acids of TM segments; (v) prediction of oligomerization propensity; (vi) finding the orientation in the membrane. In the following sections we guide the reader through these consecutive steps (Fig. 9.1) on how to derive the biologically active form of an unknown TMP purely computationally.

Fig. 9.1
figure 1

Summary of the prediction pipeline of transmembrane proteins

Full size image

9.2 Structural Aspects of Transmembrane Proteins

The lipid bilayer is an amphipathic slab with hydrophilic surfaces and a hydrophobic core region, from where the water molecules are excluded. Therefore the membrane segments of the polypeptide chains must adopt structures where all hydrogen donor and acceptor atoms are bound intramolecularly. This constraint leads to the formation of α-helical bundles and β-barrel secondary structures that are the most common secondary structures in the membrane spanning regions of TMPs. Therefore, based on the secondary structure of protein segments in the membrane regions, TMP can be classified into two main groups: α-helical and β-barrel. All plasma-membrane proteins are α-helical bundles with a large conformational variation, which is partly due to the water molecules penetrated into the membrane regions of the TMPs [161] forming water-filled cavities which makes the hydropathy-based topology predictions more difficult as well.

Very rarely, coil regions can be found in the membrane-embedded structure parts, mostly in re-entrant regions (that enter and exit on the same side of the membrane) or at kinks, where the translational symmetry breaks. Secondary structures do not terminate necessarily at the membrane water interface; sometimes these penetrate to the hydrophilic water phase. Often, on the membrane—water barrier interfacial helices (α-helices laying close and approximately parallel to the membrane surface) can be found, which have various (but not fully understood) functional roles, e.g. gating regulation and co-factor shielding [104].

While α-helical TMPs exist in all super-kingdoms, β-barrel TMPs can be found only in bacterial porins and in the inner membrane of mitochondria of eukaryote cells. For a long time it was believed that β-barrel TMPs always have even number of strands and in the range between 8 and 22, but this is refuted by the recently solved structure of the voltage-dependent anion channel (VDAC) [9] and the translocation domain of bacterial usher proteins [113, 150] containing 19 and 24 transmembrane (TM) β-strands, respectively.

The number of TM segments in α-helical TMPs range from 1 up to 24 (sodium channel protein type 2, α-subunit), but regarding their number in autonomous protein domains the highest known number is 15. Genome-wide analyses showed that distribution of the number of TM segments in α-helical TMPs is not random, proteins with 6 and 12 transmembrane helices (TMHs), such as small-molecule transporters, sugar transporters and ABC transporters , are predominant in uni-cellular organisms [3, 28, 67, 73, 123, 157]. In contrast, proteins with 7 TMHs are frequent in worms and human due to the high abundance of G-protein coupled receptors (GPCRs) [100]. Partly due to this abundance, the seven-helix membrane protein family members are the most important current drug targets.

9.3 Estimated Size of the Structure Space of Transmembrane Proteins

For globular/soluble proteins the total number of distinct globular folds that exist in nature is predicted to be a rather limited number [23], probably no more than 10,000 [70, 162], regardless of the astronomical number of the possible combination of structural elements. In TMPs, due to the physical constraints imposed by the lipid bilayer the number of possible folds is much smaller. Most of the TMPs adhere to one principal topology, involving one or more α-helices arranged parallel to each other and oriented about perpendicular with respect to the membrane plane. For β-barrel TMPs, they have a smaller structural diversity than α-helical ones. The short loops between helices constrain the possible folds of TMHs, therefore conformation space can be sampled effectively for small numbers of helices, and there are only about 30 possible folds for a TMP with three transmembrane helices (TMHs) [15]. However, the number of combinatorially possible folds was shown to increase exponentially with the number of TMHs to 1.5 million folds for seven helices, studies have showed that increasing number of membrane regions does not mean the exponential expansion of the fold space. Moreover structures with 8 or more transmembrane helices have less different architectures which reuse elements of folds with 3 or 4 helices [100]. Therefore the size of the fold space cannot be predicted based on combinatorial considerations. As an upper estimate of the number of different structures, the number of protein families can be used that are identifiable based on sequence similarity alone. Obviously this is a rough approximation, but provides a definite and reliable upper limit.

Liu et al. [87] showed in a study of 26 proteomes that there are about 10 times more soluble protein families than membrane protein families. Oberai et al. [107] set up a numerical experiment to estimate the number of distinct TMP folds. They found that any given residue has an 80 % chance to fall into one of about 500 families and observed a significant decrease in the number of members between the first and the second 20 most populous families. These results indicate that there are only a few very large and many very small families of membrane proteins, similarly to soluble proteins. The largest families are populated by various signaling proteins (e.g. GPCRs) and channels (e.g. potassium channels) [24, 48, 129], different transporters (secondary transporters and the ABC transporter family [32, 128, 132]), and TMPs involved in energy production ubiquinone oxidoreductases (cytochrome b and NADH ubiquinone oxidoreductases) [12, 39]. As a consequence of the rapid fall-of and the asymptotic tail of the family size distribution, Oberai et al. [107] concluded that 670 families will cover 80 % of the structured sequence space but 1,720 families are needed to cover 90 % of the structured sequence space for all extant polytopic membrane proteins. These numbers are still an upper limit, as in SCOP [2] hierarchy a family is a subset of a fold. Assuming that the distribution of folds over families is similar to the one of soluble proteins and applying a stretched exponential model [44], Oberai et al. [107] estimated that only 550 folds cover 90 % and 300 folds cover 80 % of membrane protein structured sequence space. Finally, taking into account the physical constraint that stem from the membrane bilayer environment, they expect this is still an overestimate. Currently about only a hundred distinct (good quality, X-ray) transmembrane folds are known from various organisms. Known TMP structures by now make possible to create model for 26 % of the human α-helical transmembrane proteome using homology modeling (see Sect. 9.4.2.1), this ratio could be increased up to 56 % with 100 more new evenly selected and determined structures [115].

Another interesting paper discusses the number of different helix-helix contact architectures as a function of the number of transmembrane segments [100]. They developed a method for predicting helical interaction graphs and found that membrane proteins with 8 and more helices have significantly fewer arrangements than proteins with up to 7 helices. The most striking cases are transporter proteins with either 8 or 11 transmembrane helices, which according to Neumann et al., all seem to share a common helix interaction pattern. It was observed that TMPs with 10, 12, 14 membrane segments have significantly more distinct interaction graph than TMPs with 11, 13 or 15. This implies a hypothesis, TMPs with more than 8 TM segments may originated from TMPs with 5, 6 and 7 membrane regions that themselves are distributed over many different helix interaction clusters. While odd number of regions cannot stem from gene duplication, this could be an acceptable explanation for the phenomena described above [100].

9.4 Predicting Different Levels of Structures

9.4.1 Topography and Topology Prediction

Starting structure modeling from the amino acid sequence the first task is to check the presence of signal peptides and to decide whether it codes a globular or transmembrane protein. Here we refer some recent reviews, where these problems are discussed [146].

As a second step, one has to locate membrane spanning segments within the sequence. The information refers the location of the membrane spanning regions within the sequence is called topography. While in the case of helical TMPs the transmembrane segments are formed by 15–20 hydrophobic amino acids, in case of the β-barrel TMPs the length of the TM segments are shorter and only every second amino acid has to be hydrophobic making their topography prediction harder. In this section we do not discuss topography prediction of β-barrel TMPs; instead we focus on helical transmembrane segment prediction.

Earlier topography prediction methods [35, 74] explored the fact that membrane spanning segments are more hydrophobic than other parts of the protein chain. These segments can be identified by averaging the hydrophobicity of the amino acids within a sliding window over the sequence investigated. Other statistical approaches, like the Dense Alignment Surface (DAS) algorithm [27] overcomes the difficulties caused by the different hydrophobicity scales by a special alignment procedure [26], where the unrelated TMPs recognize each other without applying any hydrophobicity scales. Later it was shown, that in the case of a properly chosen hydrophobicity scale, accuracy of topography prediction can be as high as of the best state-of-the-art prediction methods [11].

For topology prediction the next step is orienting the membrane spanning segments from outside to inside or vice versa. This is equivalent to localize the sequence segments between membrane spanning segments alternatively inside or outside. The difference between topography and topology is that topology refers the location of the non-membrane segments as well. However, there are only a few properties of TMPs that help this task. The first and most prevalent such feature of TMPs is that the positively charged amino acids are more abundant on the cytosolic part of polypeptide chain, than on the extra-cytosolic ones (positive-inside rule) [137, 151]. Most topology predictions apply this rule after the topography prediction to choose the more likely from the two possible models [126]. Some prediction methods, such as TOPPRED [137, 153], utilize this rule both for topography and for topology prediction, by generating several models with certain and possible transmembrane segments, and choosing the model where the differences of the number of lysines and arginines were the highest between the even and odd loops. The MEMSAT method [60] incorporates the positive-inside rule indirectly by maximizing the sum of log-likelihoods of amino acid preferences taken from various structural parts of membrane proteins in a model recognition approach.

By increasing the number of TMPs whose topology were experimentally proven, machine learning algorithms like hidden Markov model (HMM) [119], support vector machine (SVM) [25] and artificial neural network (ANN) [94] can provide high prediction accuracies due to the fact, that the amino acid compositions of the various structural parts of TMPs are specific and machine learning algorithms are capable of learning these compositions during supervised learning [139]. Novel machine learning methods report higher and higher prediction accuracies due to the continuously growing and more reliable training sets and combining various techniques (e.g. using SVM or ANN for residue prediction and HMM for segment identification [149]). However, as these methods usually operate with parameter sets that are hard or near-impossible to integrate biochemically we cannot learn from these methods about the topology forming rules of TMPs. Moreover, to predict the topology of novel TMPs were never seen earlier by the machine learning methods, these methods may need to be retrained.

Replacing supervised learning technique by unsupervised one for HMMs, the training phase can be eliminated and the dependence on the training set can be avoided as well. Methods, such as HMMTOP, therefore do not need to be retrained from time to time. The success of unsupervised learning is based on the fact that a polypeptide chain of a TMP goes through various spaces of a cell with different physico-chemical properties (hydrophobic, polar, negatively charged, water-lipid interface etc.), therefore, the amino acid compositions of the TMP segments will be different in each type of regions. We do not need to know and as a consequence the constructed method does not need to learn these characteristic amino acid compositions to successfully predict the topology of TMPs. According to the law of maximal probability, these structural parts can be identified by segmenting in a way, that the amino acid compositions of the various structural parts show maximal divergence. This partitioning can be found by hidden Markov models.

There are two additional possibilities to increase the prediction accuracy of topology predictions. The first one is the utilization of consensus prediction methods . In addition to getting better predictions, using the results of several prediction methods allows us to estimate the reliability of the predicted topology as well. The consensus approach was also applied to predict partial membrane topologies, i.e. the part of the sequence where the majority of the applied methods agree. The other technique to increase the prediction accuracy is the use of constrained prediction methods. These can be used if there is/are one or more experimental data about the topology and prediction method can handle these data as constraints and not only to filter results that agree with the given experimental data. Thus, given a constraint (e.g. the N-terminus is inside), a constrained prediction method gives a prediction that satisfies this criterion. In a HMM based method this is achieved by the modification of the Baum-Welch and Viterbi algorithms. The first such application was HMMTOP2 [145]. Later the two other HMM based methods, TMHMM and Phobius were also modified to include this feature [62, 139]. The mathematical details of the necessary modification can be found in Ref. [6]. The optimal placement of constraints was also investigated, and it was shown that the accuracy can be increased by 10 % if the N- or C-terminal of the polypeptide chain is constrained in the above mentioned way, and 20 % is the maximum obtainable increase if one of each loop or tail residue in turn is fixed to its experimentally annotated location [120]. Constraints can be either experimental results or bioinformatical evidence. In the first molecular biology experiments transposons were used to create random chimera proteins [52], later more specific molecular biology techniques were applied to investigate the topology of TMPs of interest (for review of these techniques see [144, 148]). The continuous development of biotechnology allows scientist to analyse the topology of all TMPs in an organism. In the topology analyses of E. coli and S. cerevisiae, the results of C-terminal fusion proteins were applied as constraints [28, 31, 67, 68, 120]. Recently high through-put techniques became available, where the surface of a living cell is labeled by chemical agents and the labeled peptides are investigated by coupled analytical technique after purification and degradation [13, 46, 93, 101]. In TOPDB more than 4,500 experimental results were collected for ~1,500 TMPs, and these constraints were applied to make constrained topology predictions for the ~1,500 TMPs. Regarding bioinformatical approaches, locations of compartment specific domains and sequence motifs can also be used as constraints. Such domains and motifs were collected into the TOPDOM database [144] from various databases such as SMART [45, 84], Pfam [36] and Prosite [136] for the purpose of constrained prediction.

9.4.2 Tertiary Structure Prediction of Transmembrane Proteins

Despite of the theoretical and computational difficulties, during the last two decades scientists have developed valuable methods to approximately model the tertiary structure of TMPs. Predicting TMP structures, at first, seems to be a relatively easy problem compared to understanding soluble protein structures. The fact that many TMPs share similar folds even with marginal sequence identities [43, 129] proves that TMPs are more structurally conserved than globular proteins. This is due to the strict conformational constraints that come from the membrane lipid bilayer, which dramatically decreases the size of the conformational space. However, the presence of an additional environment may cause previously unforeseen difficulties.

There are three main strategies to solve the tertiary structure of unknown TMP sequences. Homology modeling can be used when there is a sequential homologue with sequence identity greater than 20 %. In the case when no sequential homologue is available but (ideally) all folds are known, one can use threading methods to select the best packing of the query sequence. When neither sequential relative nor all folds are captured solely, de novo methods are still usable. It is worth mentioning that the order of this enumeration reflects the reliability of the methods as well (Fig. 9.1). Therefore it’s not surprising that—due to the fundamentally unfeasible sampling of the whole structure space while looking for native structures—de novo methods are at the end of this list.

In the following sections we go through these three main families of transmembrane tertiary structure prediction strategies, namely comparative modeling, threading and de novo methods.

9.4.2.1 Comparative Modeling Techniques

Comparative modeling (also known as homology modeling) is a structure building strategy for unknown protein structures, which can be used when at least one sequential homologue with known structure is available for a given query TMP. The 3D structure of the sequentially homologue protein are used as a template (or target). Once the template has been selected and an alignment is generated between the template and target sequences, the non-conserved residues are replaced and insertions (regions with no template structure) are modeled as loop regions using de novo methods [117]. It is important to note that as for globular proteins, the accuracy of a homology model is strongly dependent on the identity between the two sequences [38].

While this technique basically relies on sequence alignments, at first, we have to declare the sequence identity level from where two TMPs can be considered as structural homologue. It was shown for globular proteins [125] that proteins with 30 % sequence identity the probability of sharing the same fold is ~90 % (below 25 % identity this probability drops to 10 %), in alignments longer than 80 residues. Although the application of this well-known fact has become second nature for researchers in the case of globular proteins, shedding light on the twilight zone (where structural similarity starts to diverge rapidly as sequential identity decreases) of TMPs is only a recent improvement [38, 108]. This lagging is due to the difficulties in experimental structure determination methods [75] applied and its consequence, the relatively small number of known transmembrane structures.

In a recent study [108], sequence–structure relation was analyzed using TMP structures with resolution <4 Å. It was found for the membrane region of TMPs that at >35 % sequence identity the structure RMSDs (RMSD—Root Mean Square Deviation) were \( 0.89 \pm 0.43 \) Å and \( 0.80 \pm 0.32 \) Å for α-helical and β-barrel membrane proteins, respectively. In addition, at 20–30 % sequence identity RMSDs increased—as expected—to \( 1.59 \pm 0.55 \) Å and \( 1.30 \pm 0.35 \) Å. According to expectations, TMPs show lower RMSD values than globular proteins, as structure in the membrane region is more conserved or restricted than in the non-membrane regions. Consequently, in the case of membrane regions of TMPs it is possible to use structures even with low sequence identity (<20 %) for comparative modeling. Moreover, β-barrel architecture seems much more robust to sequence variations. They found that sequence–structure similarity is generally independent of the number of membrane regions. The authors [108] concluded that functional mechanisms are preserved by high structural conservation and their functional specificity is mainly determined by the variable solvent-exposed regions.

Although homology modeling of globular proteins is a tried-and-true technique to predict 3D structure of query sequences having a sequential homologue, but in the field of TMPs this approach is in its infancy. There are some examples for modeling GPCR receptors [4, 43], but there isn’t any fully automated, membrane protein specific method. Other, non-specific methods [122] are used as well, but the constraints imposed by the membrane are not utilized in the modeling, and the applied scoring functions designed for globular proteins might lead to distorted models.

Neglecting the scoring function and other technical details, a typical template-based modeling protocol can be briefly described in the following steps. At first, query protein searched against a related database containing TMP sequences with known structure and one or more homologue templates are selected based on their sequential identity. Next, query sequence is aligned to all template sequences. These steps are usually merged and performed together, while most methods for detecting templates rely on the production of sequence alignments. As known, the primary criteria of database search algorithms is speed, therefore alignments resulted in database searches may not be as accurate as alignment produced by non-searching techniques. However, these kinds of algorithms are widely used to detect, and to generate alignment for homologue templates from database, e.g. PSI-BLAST [1, 131] and HHsearch [138]. The alignment of the target to template sequence(s) is the most important step of the whole procedure. Aligning transmembrane sequences used to be a long-standing unsolved problem, but by now numerous TMP sequence aligner methods have been developed, e.g. AlignMe [140] and MP-T [53]. According to Forrest et al. [38], comparative modeling of TMPs has been estimated to obtain accuracy as high as that of soluble proteins if the alignment for TMPs achieves the accuracy of its soluble protein counterpart.

The last step is the coordinate generation based on the alignment. For predicting the conformation of loop regions one can use Loopy [163], which is one of the fastest or PLOP [57], which is one of the most accurate techniques. FREAD [22] uses environment specific scoring parameters to improve the sampling for their loop structure prediction algorithm. RAPPER [29] and FALCm4 [81] rely on fine-grained residue-specific \( \varphi /\psi \) propensity tables for conformational sampling. Recently a coarse-grained method for loop prediction [90] was also developed of which computational time scales better than others, while the accuracy was preserved.

To highly increase the accuracy of the final structure, a genetic algorithm developed by John et al. [58] can be used to iteratively build better alignment for distant homologues. This method builds target-template alignments and structure models, and after assessing generated models, the alignments of the best models are used for generating further alignments.

Here we sketched the basic principles of the homology modeling techniques, in the following we review some recent methods based on comparative modeling.

A web server for homology modeling of TMPs named Memoir [34] is a pipeline utilizing iMembrane [65], a membrane protein annotator using CGDB [21] coarse-grained database; MP-T [53] target-template aligner; Medeller [66], a coordinate generator and FREAD [22], a loop modeler. Memoir does not search for a homologue template, therefore it needs this as an input parameter and does not provide any information on the reliability of the resulting structures.

A novel method, GPCRM [79] is developed for GPCR membrane protein structure predictions with averaging of multiple template structures and profile-profile comparison. It also utilizes two distinct loop modeling techniques: Modeller [154] and Rosetta [124] and excluding models with lipid penetrated loops.

At the border of homology and de novo modeling, the SWISS-MODEL [4] 7TM interface is developed for the modeling of TMPs with 7 transmembrane helices. SWISS-MODEL 7TM performs homology modeling on experimental and theoretical templates; to use this server user needs to provide the location of TMHs in the query sequence and also a template.

9.4.2.2 Threading Algorithms

Threading becomes very useful in cases when a sequence does not have any sequential relative with a known structure. This is a common scenario in the case of TMPs, where only a highly restricted number of TMPs show significant sequence identity to any known structure. As a consequence, homology modeling techniques discussed above have serious limitations which can be bridged using threading. Nevertheless, for building an efficient and reliable pipeline first we need a representative structure set of the conformational space of TMPs.

As discussed in Sect. 9.3, only a very small ratio, about the one fifth of the TMP structure space is known. Therefore, an efficient threading algorithm must not only find the structure with the lowest energy, but it has to discriminate native and the ‘most-stable’ decoy structures as well. These structure assessing algorithms are discussed in Sect. 9.4.2.4.

Due to the significant physico-chemical differences between soluble and membrane proteins, threading methods developed for globular proteins cannot be used directly, however a few methods have been customized for TMPs.

TASSER [165] is a two-step method that threads the sequence onto parts of solved protein structures and then refines the resulting template. The method was validated on a set of 38 non-homologue TMP structures, a little fewer than half of which have the RMSDs less than 6.5 Å compared to the native structure, but in the other cases RMSDs are in excess of 10 Å. It was used systematically to predict human GPCRs and these seemed consistent with experimental data. However, when there was no significant sequential relative, it was uncertain if the results represent the native structure.

A recent method, TMFR [158] is a sequence based fold recognition algorithm and has the accuracy of 49.2 and 82.2 % for α-helical and β-barrel TMPs, respectively. It utilizes topological features which improve the fold recognition [49] and can accurately align the target sequence to the template structure and generate reliable alignment raw scores to evaluate the structural similarity between the target and template. This provides practically only a sequence alignment. Therefore, algorithm traces back structure prediction problem to something akin to homology modeling.

However, this type of approximation widen the horizon of TMP structure prediction significantly, unfortunately the lack of structural representatives limits the usability of threading henceforward. In the next subsection, de novo methods are discussed which try to get over these difficulties.

9.4.2.3 De Novo Methods

De novo modeling does not use homologue proteins of known structures to predict the structure of an unknown protein. For an effective de novo structure prediction method there are two crucial requirements: accurate energetic representation of a protein structure and an efficient sampling of conformational space [82]. While structural space expands rapidly with the sequence length, these methods are mainly applicable for small soluble proteins [16], not for TMPs, which are often large structures [158]. Although methods do not have restrictions on the number of known structures as homology modeling or threading do. However, as combinatorial approaches these require large amounts of computing time which often cannot be run on a single desktop computer, hence reducing their availability for structural biologists.

9.4.2.3.1 Contact Aided Structure Prediction

Contact prediction methods originates from the article, written by Göbel et al. [42], that describes how one could infer spatial information from multiple sequence alignments. This concept is based on the observation that the structure is more conserved than the sequence. Therefore, if a residue fulfilling structurally important role in a protein mutates, than another spatially close residue has to change to preserve both the structure and the function. Later it turned out that this assumption is a poor approximation of real proteins and their evolutionary processes.

Contact prediction methods can be classified into two main categories, namely local and global methods. The first one contains the ‘classical’ correlated mutation algorithms (CMA), which could be subdivided into further subcategories. To extract spatially close residues from multiple sequence alignments simple covariance analysis with various substitution matrices [42, 109]), \( \chi^{2} \)-test [64], information theoretic approaches [33], machine-learning [20, 103, 118], alignment perturbation (SCA [88], ELSC [30]), probabilistic and empirical matrix methods or formal language [155, 156] were used. Further on, consensus methods are developed [41], which did not succeed to significantly overcome the performance of the previous methods (Acc. ~10 %, see Ref. [55]). CASP10 [95] confirmed the need for the development of contact prediction methods. On a test set of newly identified structures the best algorithm performed at an accuracy of ~30 %. Machine learning methods (PROFcon [118], CMAPpro [20], MEMPACK [106], PhyCMAP [159]) generally outperform others based on statistical considerations. Despite of the better predictor abilities, machine learning based approaches make their results difficult to interpret biophysically. In addition, the lack of a physical model makes the limits of their usability ill-defined. A recent study [47] showed that using three representatively selected contact prediction methods, there is no such linear combination of selected local techniques which could reach a satisfiable performance level. In addition, when a consensus method was trained and tested on only two, ABC-B and ABC-C protein families, despite of a nearly over parameterized model, these techniques could not reach a satisfying performance limit.

The main problem is that the observable correlations among sites do not stem from spatial closure purely. Atchley et al. [5] formalized the sources of these correlations, that—apart from structural constraints—could came from phylogenetic noise, function and higher-order statistical non-independence of positions. In addition, random noise or uneven sampling could bias measured correlations as well. The orders of magnitude of these factors are investigated by Noivirt et al. [102]; they found that correlation from structural, functional and phylogenetic constraints are in the same order of magnitude. Therefore, using background co-evolution signal correction [33] proved to be a valuable tool to reduce phylogenetic noise and to increase precision of methods significantly albeit even these precisions remains low.

Even if we neglect the disturbingly high correlation from functional and phylogenetic sources, there still remains a significant problem, namely disentangling direct and indirect interactions [17]. Global methods can take it into account with estimating joint probabilities of multiple residues. For reliable statistics huge number of sequences is required, which is a limiting factor still could not be overcame yet. Burger and van Nimwegen [17] had developed a Bayesian-network based method, which can take into account that the probability for residues to be in contact depends on their primary sequence separation and that highly conserved residues tend to participate in a larger number of contacts [17]. With this or other methods using maximum-entropy model [77, 97], sparse inverse covariance estimating [59] approaches could break through the barriers set by indirect contacts and multiple correlations. This network-based conceptional change of view and the increased size of sequence families result in significant performance gain.

Another possibility for calculating structural constraints is the prediction of helical interaction only, instead of predicting directly residue—residue contacts. It is an easier task than identifying all individual residue contacts in an α-helical TMP. However, this does not give any information on the orientation of helices and all the helices are treated as perpendicular to the membrane plane [40, 100]. Using propensity estimation techniques, e.g. lipid exposure predictors, the precision of helix-helix interaction and orientation estimations can be improved [92, 103, 116]. It has been known for a while that the tilted orientation of transmembrane helices is a principal compensation mechanism for hydrophobic mismatch [111]. Nevertheless, spanning regions are not necessarily straight: kinked or bended helices exist as well [76, 152], which complicates helical contact prediction even further.

These methods are valuable tools in themselves, which help to get closer to the biological understanding of TMP structures, functions and their mutational processes, but unfortunately they are still not as trustworthy as e.g. topology prediction techniques.

It is worth to mention, contact predictions cannot be used to directly reconstruct the 3D structure of proteins [110] not even using perfect predictor, not even for TMPs. This is due to their contradictory results originates from the oligomerization or conformational changes of the studied proteins. In the case of oligomers we would need to distinguish between intra- and interchain contacts. Another problem arises from multiple conformations of proteins, as in the case of the open and closed conformations of the E. coli GlpT or human OCTN1 [96]. When neither conformation change nor oligomerization has an influence on the inspected protein structure, theoretically an essential set of structure determining residue contacts is enough to replicate the 3D structure [130].

If we approximate the given problem from a reverse way, we could use predicted contacts as constraints in simulated annealing simulations [54, 91] or to aid the separation of native like TMP folds from decoys [92, 103, 127]. Obviously, one could use experimental techniques, such as e.g. NMR, to earn useful structural constraints to build TMP model structures, but in this section we discussed this problem from the computational point of view only.

9.4.2.3.2 Forcefield-Based Approaches

There are many forcefield-based methods for determining the 3D structure of proteins; here we review some of those that were developed for TMPs. Given the structural simplicity observed in the β-barrel conformational space, structure prediction methods focused on estimating structures of α-helical TMPs. This imbalance will be observable in this paragraph as well.

In the early studies, such as Fleishman and Ben-Tal [37] residue environment preferences were used to predict the likely arrangement of transmembrane helices, and they were able to predict the native structure of TMP glycophorin A . Ledesma et al. [80] suggesting a model for the uncoupling protein 1 (UCP1), utilizing a computational docking method. Chen and Chen [19] used a lattice model of membrane proteins with a composite energy function to study their folding dynamics and native structures in Monte Carlo simulations. This model successfully predicts the seven helix bundle structure of sensory rhodopsin I by employing a three-stage folding. FILM [112] was developed for predicting small TMP structures based on assembling super-secondary segments taken from a protein structure library. The native structure is searched by simulated annealing. The main limitation of FILM is that the potential function is not able to reproduce the compactness of transmembrane bundles.

RosettaMembrane [164] (a derivation of Rosetta [124]) uses an all-atom physical model to describe intra-protein and protein-solvent interactions in the membrane environment. The surrounding environment is divided into 5 layers: water-exposed, polar, interface, outer and inner hydrophobic in both directions of the membrane core. Here a log-likelihood pair and environment potential were used, which penalizes steric overlap but favours packing density like characteristics of membrane proteins and strands. The method was tested on 12 membrane proteins with known structure, The length of the query sequences were between 51 and 145, which was predicted with RMSD <4 Å. However, mainly due to the technically unfeasible sampling of the conformational space this method performs poorly for large and complex proteins, independent on being soluble or transmembrane. In a newer version [7] of RosettaMembrane, experimental and predicted constraints were used to aid structure prediction. A great advantage of this method is that it can take into account cofactors, which could significantly modify structures.

BCL::MP-Fold [160] uses a three layer (solution, transition, membrane) implicit membrane representation with transition regions and a knowledge-based potential derived using Bayes’ theorem and the inverse-Boltzmann relation. The final score resulted as the linear combination of many energy terms with optimized weights. The search for the native structure starts from randomly placed helices oriented perpendicular to the membrane plane. As a next step, folding is performed with simulated annealing [63].

As GPCRs are the most common drug targets, specific methods for predicting GPCR structures, such as MembStruk [85, 147] and PREDICT [135] have been developed as well. Both methods provide full-atom models for GPCRs on the basis of physico-chemical principles. In the PREDICT algorithm a concept of structural decoys is employed to ensure that the algorithm identifies the correct structure and to avoid trapping in a local minimum.

3D-SPOT [99] is a template-free method utilizing a statistical mechanical model [98] and an empirical potential function; TMSIP [56] is to predict the 3D structure of a given β-barrel TMP. While this method is based on physical interactions and does not require template structures, it can be applied for predicting structures of novel folds. The method performs well; in a blind test it was able to generate accurate structures of the transmembrane regions with a median main chain RMSD of 3.9 Å, on a set of 23 proteins.

9.4.2.4 Validating Predicted 3D Structures

Several methods have been developed for judging the reliability of predicted structures and identifying erroneous regions. Methods like PROCHECK [78] can be used for TMPs as well, because it takes into account only fundamental properties, namely the \( \psi /\varphi \) backbone torsion angles. There are various attempts to develop a measure, like the normalized QMEAN score [10] for soluble proteins, describing absolute quality of each structure for membrane proteins too. Phatak et al. [114] described a method filtering near-native structures from decoys using low-complexity Support Vector Regression models for predicting relative lipid accessibility (RLA) . The quality assessment is based on the consistency of the predicted and observed RLA profiles. ProQM [121] utilizes SVM and membrane protein specific features, tested on GPCR structures. As it turned out, this method is capable of disentangling correct models from incorrect ones and has the ability to identify poor quality regions. IQ (Interaction-based Quality assessment) [50] incorporates four types of inter-residue interactions and achieves high prediction power on the independently constructed dataset (GPCR Dock 2008 (206 models), GPCR Dock 2010 (284 models), and HOMEP (92 models)). However, further validation of this method is needed. Recent results suggest that among conformations very dissimilar to native structures, this scoring function cannot correctly identify the best one. This is largely understandable since this scoring function relies primarily on the number of hydrophobic interactions. Lots of incorrectly formed hydrophobic interactions in decoy conformations could bias the IQ value (Li Zhijun personal communication).

9.4.3 Quaternary Structures of Membrane Proteins

As it was discussed earlier, genome-wide analysis of domain combinations of helical membrane proteins revealed that α-helical TMPs exist mostly as single domains. Oligomerization within the membrane may could be the general mechanism for membrane proteins to gain new biological functions [83, 86, 87]. Therefore, discovering principles of oligomer formation of TMPs is needed to understand theirs functions and to gain new therapeutic strategies.

For globular proteins there are various methods to predict oligomerization propensities. PQS [72] and PISA [51] can identify the biologically active oligomer from X-ray structures. However, these methods cannot be used for TMPs, therefore in the PDBTM [71, 142, 143] database a simple homology search was used for predicting oligomeric state of potentially existing novel transmembrane structures, independent on their type (α-helical or β-barrel).

Bowie [69] and coworkers predicted the structure of α-helical TMP oligomers (glycophorin A and M2 proton channel) using knowledge of the oligomer symmetry. They used a simple softened van der Waals potential and Monte Carlo minimization to pack ideal α-helices. Bordner [14] have developed a method to predict biding sites of TMPs using a Random Forest classifier, trained on residue type distributions and evolutionary conservation for individual surface residues, followed by spatial averaging of the residue scores. Random Forest predictions were first made for individual surface residues and then the resulting scores of nearby residues were averaged in order to arrive at the final prediction score. Docking based approaches for predicting oligomerization has been developed as well [18]. In a recent review, the suitability of some widely-used docking algorithms for modeling complexes of α-helical TMPs was studied and the dependence of the docking performance on the protein features discussed as well [61].

Although α-helical TMPs pose a greater challenge, the oligomerization state of β-barrel membrane proteins can be accurately predicted computationally [98]. Based on the TMSIP [56] empirical potential function and the reduced conformational state model, extensive and contiguous weakly stable regions in many β-barrel membrane proteins seem to be an indicator of oligomerization propensities of β-barrel membrane proteins. Furthermore, as structural information is not essential for such predictions, the oligomerization state can also be predicted quite successful even when only sequence information is considered [98].

As it was discussed, there are various methods to model the quaternary structure of a TMP if it is a homomer or all the different subunits are known. Cases when the other subunits are unknown cannot be solved yet.

9.5 Orientation of Membrane Proteins in the Lipid Bilayer

Neither monomeric nor oligomeric TMPs do not exist alone without the amphiphilic membrane bilayer. By removing the hydrophobic environment the native structure breaks down. For experimental structure determination special handle with detergent is needed to extract TMP from the membrane and to preserve its native structure. Accordingly during experimental structure determination of TMPs, the information on the orientation disappears. While this information is essential for understanding the biological function and the mechanism of action of TMPs, experimental methods cannot recover it and thus has to be defined using computational techniques. Orientation and burial of TMPs are very important e.g. for drug design to identify accessible parts of TMPs.

There are various attempts to predict orientation and burial of TMPs. One of the first methods was IMPALA [8], which uses amino acid propensities. TMDET [141] algorithm utilizes a geometrical algorithm to locate the most probable orientation of the given TMP in the membrane slab. OPM [89] applies a more sophisticated description of the problem, but does not outperform TMDET significantly. Senes et al. [134] have developed an empirical low-resolution potential called \( E_{z} \), for protein insertion in the lipid membrane. A recent paper describes a method for predicting membrane protein orientation using a knowledge-based statistical potential [105, 133].