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Protein Sci. Apr 2001; 10(4): 779–787.
PMCID: PMC2373968

Prediction of the transmembrane regions of β-barrel membrane proteins with a neural network-based predictor


A method based on neural networks is trained and tested on a nonredundant set of β-barrel membrane proteins known at atomic resolution with a jackknife procedure. The method predicts the topography of transmembrane β strands with residue accuracy as high as 78% when evolutionary information is used as input to the network. Of the transmembrane β-strands included in the training set, 93% are correctly assigned. The predictor includes an algorithm of model optimization, based on dynamic programming, that correctly models eight out of the 11 proteins present in the training/testing set. In addition, protein topology is assigned on the basis of the location of the longest loops in the models. We propose this as a general method to fill the gap of the prediction of β-barrel membrane proteins.

Keywords: Neural networks, secondary structure predictions, multiple sequence alignment, pattern recognition, membrane β strands, prediction of membrane porins

At present, two types of membrane proteins have been characterized: The first includes all the proteins that to a different extent interact with the lipid bilayer of the cytosplamic membrane of all cells (White and Wimley 1999); the second group includes those proteins that during the last ~10 yr have been discovered in the outer membrane of bacteria, chloroplasts, and mitochondria (Schulz 2000). A major distinguishing feature of membrane proteins of the first type is that they span the cytoplasmic membrane with α-helixes, whereas those of the second type interact with the outer membrane with antiparallel β-strands forming barrels, existing as monomers and oligomers (Cowan and Rosenbusch 1994). These chains, referred to as β-barrel membrane proteins (Gouaux 1998; Schulz 2000), comprise the archetypal trimeric porins of Gram-negative bacteria consisting of water-filled channels that nonspecifically mediate the passive transport of ions and small hydrophilic molecules (<6 kD) or select for certain molecules such as malto-oligosaccharides (Schulz 1996). In addition, more recently, other β-barrel membrane proteins have been characterized, and their functions are quite diverse from that of archetypal porins. After the recent atomic resolution of some proteins from enteric bacteria (FepA, Buchanan et al. 1999; and Fuha, Ferguson et al. 1998), it became evident that high-affinity outer membrane receptors that actively translocate large nutrient molecules like iron-siderophore complexes and vitamin B12 span the outer membrane with a β-barrel structure. This architecture is also the outer membrane's interacting part of export protein systems for small antibacterial drugs and large protein toxins (TolC in Escherichia coli; Koronakis et al. 2000) and that part of the enzyme phospholipase A (OmplA; Snijder et al. 1999) participating in secretion of colicins in E. coli and implied in virulence in Helicobacter pylori. The structure of Staphyloccal α-hemolysin highlights the fact that the lytic outer transmembrane domain comprises the lower half of a 14-strand antiparallel barrel containing seven homoprotomers (Song et al. 1996). In addition, membrane β-barrels also have been found in OmpA (Pautsch and Schulz 1998) and OmpX (Vogt and Schulz 1999) from E. coli, proteins that participate in bacterial conjugation, function as receptors for bacteriophages and colicins, and mediate virulence and pathogenicity. Finally, in eukaryotes, β-barrels are thought to be the functional structure of voltage-dependent anion channels present in the outer membrane of chloroplasts and mitochondria (for review, see Mannella 1998). It seems, therefore, that the β-barrel structure is associated with functions that are more and more relevant to the entire cell metabolism and that are as diverse as active ion transport, passive nutrient intake, membrane anchors, membrane-bound enzymes, and defense against attack proteins. In addition, it is now evident that the different functions are associated with different barrel sizes (ranging from small eight-stranded to large 22-stranded β-barrels) and with different topologies and aggregation number (Schulz 2000).

Although after a decade of analysis the construction principles of β-barrel membrane proteins are known (Sansom and Kerr 1995; Schulz 2000), it is almost impossible to derive three-dimensional models for proteins of the outer membrane. This is because of the fact that unless they belong to the same family, β-barrel membrane proteins share little sequence identity within each other even in the transmembrane spanning regions. It is well documented that in this case, methods based on homology building and threading cannot be successful (Sternberg et al. 1999). It is therefore necessary to be able to locate correctly the transmembrane regions in a sequence to assign the correct barrel topology and eventually build a three-dimensional model on the basis of the existing templates.

This task, however, appears to be more difficult than predicting the topography and topology of all-helical membrane proteins, whose transmembrane domains can be well detected (Jones et al. 1994; Rost et al. 1995, 1996).

When only the archetypal porins were known, it was suggested that strands along the protein sequence could be located using the evaluation of the chemico-physical properties, such as the hydrophobic moment, associated with the transmembrane region (Paul and Rosenbusch 1985; Welte et al. 1991). However, these methods were successful only if used in combination with experimental information (Schirmer and Cowan 1993). Moreover, amphipathicity of β-membrane strands is generally more complex than simple alternating patterns of hydrophobic and hydrophilic residues (Schulz 2000).

Gibbs sampling provides some hints on the alignment of local regions partially overlapping with transmembrane strands (Neuwald et al. 1995), and Hidden Markov models of different porin families can be used to produce alignments that are useful for structure prediction, provided that a given sequence fit the alignment and that a crystallized counterpart is present in the family (Bateman et al. 1999).

An alternative to alignment methods is predictors of β-membrane spanning regions specific for outer-membrane proteins. A rule-based approach for identifying transmembrane β-strands was described and successfully applied to predict a limited number of archetypal porins (Gromiha et al. 1997). More recently, a neural network predictor became available for locating residues along the Z-axis of the pores (Diederichs et al. 1998).

In this article, we will use prototypes of the β-barrel membrane proteins crystallized so far for training and testing a neural network-based predictor to locate strands along the protein sequence. The method with a jackknife procedure, using evolutionary information as input, reaches an overall accuracy per residue as high as 78%. In addition, with a model optimization method using a dynamic programming algorithm, eight topological models out of the 11 proteins included in the testing set are correctly predicted. We analyze the results in terms of the network's capability of extracting characteristic features common to the different β-barrel membrane proteins representative of the different barrel architectures (and functions) and propose models for outer membrane proteins not yet solved at atomic level.

Results and Discussion

The database of β-barrel proteins

We use a database including 11 β-barrel membrane proteins. They were selected from the PDB database (after clustering the porins and porin-like proteins into homologous families). From each group, we considered one solved structure with a sequence identity <23% to all the other structures in the different families and with the highest crystal resolution within the group. In this way, the database includes 11 proteins. Among these, five porins are active as canonical homotrimers of β-barrels: the integral membrane protein porin from Rhodobacter capsulatus (2por; Weiss and Schulz 1992), its counterpart from Rhodopseudomonas blastica (1prn; Kreusch and Schulz 1994), the matrix Ompf porin (2omf; Cowan et al. 1995), maltoporin from Salmonella typhimurium (2mpr; Meyer et al. 1997), and the sucrose-specific porin ScrY from the same bacterium (1a0s; Forst et al. 1998). The first three porins contain 16 β-strands in the barrel, the second two contain 18 strands. The remaining six proteins of the database act as monomers with one barrel: The outer membrane transporters FepA (1fep; Buchanan et al. 1999) and FhuA (1fcp; Ferguson et al. 1998) from E. coli (both with 22 β-strands in the barrel); the integral outer membrane protein X from E. coli (OmpX; 1qj8; Vogt and Shulz 1999) and the transmembrane region of the outer membrane protein A from E. coli (OmpA; 1bxw; Pautsch and Schultz 1998; both with 8 β-strands in the barrel); the integral membrane phospholipase from E. coli (1qd5; Snijder et al. 1999; with 12 β-strands in the barrel); and one subunit of the heptameric transmembrane pore of Staphyloccal α-hemolysin (7ahl; Song et al. 1996; assembling two β-strands to the barrel).

The database, therefore, contains prototypes of all the β-barrel membrane proteins known so far with atomic resolution (Schulz 2000), and in this, it differs from smaller sets of porins used in previous studies (Diederichs et al. 1998). The number of total residues is 3773, 1909 of which are included in 158 β-strands. Figure 1A [triangle] shows the length distribution of the β-strands of the database and also the different length distribution of the inner and outer loops of the β-barrels in the selected database. It is evident that the length of the transmembrane β-strands ranges from a minimum of six residues to a maximum of 22 residues, with the highest frequency of occurrence centered at 12 residues. Also, it is noticeable that the longest loops in the different barrels are exposed to the external medium (Fig. 1B [triangle]). These characteristics are taken into account when implementing the predictor (see below).

Fig. 1.
Characteristic feature of the β-barrels of the outer membrane proteins of the training set. (A) Bar plot of the length distribution of the β strands contained in the barrels. (B) Bar plot of the length distribution of the inner (black ...

The predictor at work

A neural network is trained and tested on the selected database with a jackknife procedure. In this way, each protein at the time is tested while the remaining 10 are used to train the network (the level of identity among the different proteins used ranges from 4% to 22% at the most). It is evident (Table 11)) that the network performance is significantly improved when the evolutionary profile is used as input, as compared to single sequence. This is particularly true when a nonredundant database of sequences is used to perform the alignment. Sequence profiles are derived using the HSSP files (Dodge et al. 1998) or a program implemented in-house that computes profiles directly from the alignments performed by PSI-BLAST on a nonredundant database including a number of sequences greater (~500,000) than Swiss-Prot (90,000). For the sake of comparison, the accuracy of the best-performing neural network–based predictors available on the web (PHD and PSIpred) and those using PSI-BLAST is also shown. As described by the authors at their Web sites, PHD and PSIpred were trained on training sets containing a subset of our selected β-barrel membrane proteins. For this reason, we list their performance under "Training" in Table 11.. It appears that in spite of this, the three-output predictors are performing with efficiency lower than that of the predictor specific for β barrel membrane proteins, both in training and in testing.

Table 1.
Statistical analysis of the predictive performance

If we consider that our selected database contains ~50% of the residues with β-strand structures, we can estimate that random prediction would give an average accuracy equal to 50%. It is evident from the data shown in Table 11 that even using single sequence as input to the network, the accuracy is 19 points better than random. This value further improves of another 9 points when evolutionary information is extracted from the nonredundant database (for a total of 28 points better than random). The observation that the predictive performance improves when using a large database to extract profiles is in agreement with what was recently observed on the prediction of secondary structure of proteins (Cuff and Barton 2000).

If the base line to score predictive performance is the accuracy of the random predictor, the performance that we obtain in predicting transmembrane β-strands is similar to that of other predictors based on neural networks and developed for the prediction of transmembrane all-helical regions (Rost et al. 1995; Casadio et al. 1996). The rate of false positives (equal to ~1−P[β]) is in the range of 20% and is somewhat higher than that noticed before for the all-helical transmembrane domains (16%; Rost et al. 1995), suggesting that transmembrane β-strands are endowed with less representative patterns that the all-helical transmembrane domains.

This finding prompted us to develop an algorithm based on dynamic programming (Needleman and Wunsch 1970) and implementing constraints derived from the models of the transmembrane β-barrel proteins known at atomic resolution (Fig. 1A,B [triangle]). Network outputs are used to evaluate the score relating the compatibility of a given sequence with a given architectural model of transmembrane β-barrels. For computing this, we rely on a model optimization approach (see Materials and Methods).

This method should, in principle, correct for all the false positives that fall in regions along the protein sequence that do not meet the constraints used to describe β-barrel models present in the database. In Figure 2 [triangle], two examples of predictions are shown: one is that of the porin chain from Rhodopesudomonas blastica (1prn; Fig. 2A [triangle]), and the other is that of OmpA from E. coli (1bxw; Fig. 2B [triangle]). Network outputs obtained in testing (the protein is not included in the database used for training) are plotted along the protein sequence together with the expected transmembrane β-strands (segments in black), and the results are computed after regularizing outputs with the algorithm based on model optimization (segments in gray). It is evident that both the 16 and 8 β-strands of 1prn and 1bxw are correctly located (see, also, Table 22).). This last protein, whose crystal structure became available only recently (Pautsch and Schulz 1998) was predicted with 16 β-strands with other methods mainly relying on comparative modeling (Stathopoulos 1996) and also by a neural network previously described and trained on a set of transmembrane β-barrel proteins smaller than that described in this article (Diederichs et al. 1998). This last predictor was trained using single sequence and provides only network outputs, without minimizing false positives (http://strucbio.biologie.uni-konstanz.de/~kay).

Table 2.
Observed and predicted transmembrane β-strands for the selected data base of β-barrel transmembrane proteins
Fig. 2.
The predictor at work. Outputs of the neural network predictor are plotted along the protein sequence and originate a pattern whose peaks correspond to regions of high propensity for the membrane β strand structure. A model optimization algorithm ...

All the models predicted with our procedure (outlined above) are presented in Table 22 and compared to the expected structures. Of the β-strands, 93% are correctly located, and eight out of 11 models are also correctly assigned (73%). Evidently, in some cases the model optimization algorithm is not sufficient to cancel out false positives (the presence of a β-strand in a wrong position in the sequence), or alternatively, network outputs are not enough strong to originate a transmembrane segment (the absence of a β-strand in the correct position). Our predictor fails in correctly locating one transmembrane strand in 1fcpA, 2mprA and 2por. In all the remaining proteins of the testing set, transmembrane β-strands are correctly located, although with not a perfect overlapping with the observed corresponding regions.

After selecting the optimal model, the predictor gives also the protein topology. In the case of membrane proteins, topology refers to the protein organization with respect to the membrane phase. On the basis of the observation that in bacterial porins the longest loops are facing the extracellular space, topology is assigned after computing which side of the barrel is endowed with the longest loops. In this way, and considering the predicted models listed in Table 22,, the topology of all the 11 proteins of the database is also correctly assigned. It should be noticed, however, that this rule might not hold for β-barrel membrane proteins of mitochondria and chloroplasts, for which data are not yet available.

Predicting other β-barrel transmembrane proteins

While this work was in progress, the crystal of TolC became available (Koronakis et al. 2000). The complex has a channel–tunnel structure spanning the region from the outer membrane up to the inner membrane and is assembled as a trimer of 428-residue identical protomers. Spanning the outer membrane, the protomers form a transmembrane β-barrel of 12 β-strands. We tested one protomer in the transmembrane region, and the results are listed in Table 33.. It is evident that our predictor correctly locates the four transmembrane β-strands of the protomer.

Table 3.
Prediction of β-barrel transmembrane β-regions of TolC and OMP32

The second prediction that we show is that of Omp32, an anion selective porin from Comamonas acidovorans, whose crystal structure is announced for June 2001 (Zeth et al. 2000) and was already a target (target 70) during the last CASP3 competition (Orengo et al. 1999). The sequence shows a 23% level of identity with ompf_ecoli, and as soon as it will be available, it can be included in the database. At present, we tested our results by comparing them with the model that scored the less root mean square deviation (RSMD = 0.35 nm; http://predictioncenter.llnl.gov/casp3/results) to the crystal structure (Venclovas et al. 1999). As shown in Table 33,, our predictor indicates a putative 16-stranded transmembrane β-barrel, with the location of 14 out of 16 strands in agreement with the computed model. These results confirm that the predictor is endowed with a generalization capability sufficient to predict with good accuracy transmembrane segments even in proteins distantly related to those of the training set.

Is the predictor of transmembrane β-barrel proteins necessary?

At present, the accuracy of secondary structure prediction is quite high (Cuff and Barton 1999). So one may wonder to which extent neural networks are capable of capturing and generalizing the characteristic features of transmembrane β-strands as compared to those of globular ones.

We trained and tested by cross validation a two-output network for discriminating globular β-strands from coil structure in all-β globular proteins. The overall accuracy of the network reaches 74% with a correlation coefficient equal to 0.49. When, with this network, the transmembrane β-strands are predicted, the accuracy is 69%, compared with that of 78% obtained when the specific network is used on the same testing set (Table 44).). This tells us that the predictor trained on β-barrel transmembrane proteins captures distinguished features of transmembrane β-strands that are not included in the same structural type of globular proteins.

Table 4.
Efficiency of different predictors on transmembrane and globular β-strands

In addition, we may ask whether different functions are requiring distinct features. We divided our testing (and training set) in two subsets containing, respectively, trimeric porins and monomeric β-barrel ones, performing different functions (see above). Each subset was used to train a network, and the other was predicted. The results (Table 55)) indicate that the predictive efficiency is rather similar in both cases, suggesting that β-barrel architectures are endowed with the same characteristic patterns independent of the function. This adds to the network capability of extracting general features common to all the β-barrel transmembrane proteins.

Table 5.
Predicting β-barrel transmembrane proteins with different functions


We propose the use of the predictor described in this work to locate putative transmembrane β-strands in β-barrel-containing membrane proteins. This method may help to build the three-dimensional model of β-barrel membrane proteins by threading on templates of similar architecture.

Our predictor implements an algorithm based on model optimization, which selects network predictions on the basis of the transmembrane β-barrel architectures presently known at atomic resolution. For this and for using evolutionary information, it is presently the only one that is implemented and based on neural network that is capable of correctly assigning 93% of the transmembrane β-strands known at atomic resolution. In addition, our analysis highlights that a neural network is capable of capturing features that are characteristic of transmembrane β-strands, as compared to globular ones, and that these features are shared by the transmembrane β-barrels performing different functions. It is therefore feasible that when new examples will be known at atomic resolution, this method will be potentiated.

The predictor is presently available on request at http://www.biocomp.unibo.it.

Materials and methods

The neural network–based predictor

A feed-forward neural network is implemented and trained with the back-propagation algorithm (Rumelhart et al. 1986) to discriminate membrane β-strands from extra membrane regions in the β-barrel membrane proteins of the database. The network architecture basically consists of perceptrons with one hidden layer containing five hidden nodes and an input window spanning nine residues. Two output nodes are considered ("β" and "not β"). The architecture of the predictor is extended to include a second cascaded network to filter out spurious assignments. Other network architectures (a smaller or greater number of neurons in the hidden layer) and lengths of the input window (from five to 15) were also tried, and the one described above was found to give the best predictive performance.

Evolutionary information is given as input in the form of sequence profiles after multiple sequence alignments. Sequence alignments were derived from the HSSP database (Dodge et al. 1998) in which alignments were constructed using BLAST (Altschul et al. 1990) to search the sequence database and MAXHOM (Sander and Schneider 1991) to align the sequences. Moreover, we used PSI-BLAST (Altschul et al. 1997; one round with threshold equal to 0.001) to search a nonredundant database (available at http://www.ncbi.nlm.nih.gov/BLAST). We generated sequence profiles from its outputs by means of a newly implemented program. This is based on the notion that the PSI-BLAST complete outputs contain the local pairwise alignments of the query sequence with all the extracted sequences. From this, it is possible to compute a profile by merging each local pairwise alignment.

β-barrel membrane proteins taken from the PDB database were clustered into different homology groups using CLUSTALW (Thompson et al. 1994).

Selecting the model

An algorithm based on dynamic programming uses the network outputs to locate the transmembrane β-strands along the protein sequence by model optimization. A similar algorithm was previously used to locate transmembrane α-helices (Jones et al. 1994). The one we implement takes advantage of the notion that transmembrane β-strands in the prototypes of β-barrel membrane proteins are even in number and range from two to 22 in the sequence (Fig. 1 [triangle]). A recursive algorithm generates a scoring matrix for each predicted sequence by evaluating the total sum of the output differences along a segment of fixed length. Minimal and maximal lengths are derived from the database of selected proteins (Fig. 1A [triangle]). A model is selected by evaluating the optimal score among those satisfying the observed constraints in the crystals.

For a given sequence position j and for a given model i (i is the number of β-strands), the scoring matrix S is computed as

equation M1

where L and n are the minimum length of a loop segment and the protein length, respectively; slj is the score associated with a transmembrane strand of length l at position j in the sequence.

Topology is then predicted by simply comparing the length of the loops of the two sides of the barrel and labeling as extra-cellular the barrel side with the longest loops.

Scoring the prediction

The efficiency of the predictors is scored using the statistical indexes defined in the following.

The network accuracy is

equation M2

where P is the total number of correct membrane β-strand predictions and N is the total number of possible predictions.

The correlation coefficient C is defined as

equation M3

where, for each class β, p(β), and n(β) are, respectively, the total number of correct predictions and correctly rejected assignments, whereas u(β) and o(β) are the numbers of under and over predictions.

The accuracy for each discriminated structure s is evaluated as

equation M4

where p(β) and u(β) are the same as in Equation (3).

The probability of correct predictions P(β) is computed as

equation M5

where p(β) and o(β) are the same as in Equation 3.

The segment-based measure (Sov) of the assessment of transmembrane β-strands is computed as previously described (Zemla et al. 1999).


This work was partially supported by a grant of the Ministero della Universitá e della Ricerca Scientifica e Tecnologica (MURST) for the project "Structural, Functional and Applicative Prospects of Proteins from Termophiles," and by a grant for a target project in Biotechnology of the Italian Centro Nazionale delle Ricerche (CNR), both delivered to R.C.

The publication costs of this article were defrayed in part by payment of page charges. This article must therefore be hereby marked "advertisement" in accordance with 18 USC section 1734 solely to indicate this fact.


Article and publication are at www.proteinscience.org/cgi/doi/10.1110/ps.37201.


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