Bioinformatics Advance Access originally published online on March 3, 2005
Bioinformatics 2005 21(10):2279-2286; doi:10.1093/bioinformatics/bti372
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Prediction of subcellular localization using sequence-biased recurrent networks
School of Information Technology and Electrical Engineering QLD 4072 The University of Queensland Australia
*To whom correspondence should be addressed.
 |
Abstract |
|---|
 TOP Abstract 1 INTRODUCTION2 SYSTEMS AND METHODS3 IMPLEMENTATION AND DISCUSSION4 CONCLUSIONREFERENCES |
|---|
Motivation: Targeting peptides direct nascent proteins to their specific subcellular compartment. Knowledge of targeting signals enables informed drug design and reliable annotation of gene products. However, due to the low similarity of such sequences and the dynamical nature of the sorting process, the computational prediction of subcellular localization of proteins is challenging.
Results: We contrast the use of feed forward models as employed by the popular TargetP/SignalP predictors with a sequence-biased recurrent network model. The models are evaluated in terms of performance at the residue level and at the sequence level, and demonstrate that recurrent networks improve the overall prediction performance. Compared to the original results reported for TargetP, an ensemble of the tested models increases the accuracy by 6 and 5% on non-plant and plant data, respectively.
Availability: The Protein Prowler incorporating the recurrent network predictor described in this paper is available online at http://pprowler.imb.uq.edu.au/
Contact: mikael{at}itee.uq.edu.au
|
1 INTRODUCTION |
|---|
|
TOPAbstract1 INTRODUCTION2 SYSTEMS AND METHODS3 IMPLEMENTATION AND DISCUSSION4 CONCLUSIONREFERENCES |
|---|
By holding specific protein and lipid content, distinct membrane-bound organelles maintain their functional integrity. However, proteins are usually synthesized elsewhere and thus require translocation from ribosomes to their specific organellar compartments. Subcellular protein localization is a complex, dynamic but—to prevent mixing of organellar constituents—tightly controlled process (van Vliet et al., 2003; Emanuelsson, 2002). Attesting to the importance of understanding the sorting process and the signals involved is the well-known fact that deficiencies cause numerous diseases (Aridor and Hannan, 2000), e.g. cystic fibrosis and diabetes mellitus (protein retention and degradation in the endoplasmic reticulum), Alzheimer's disease (accumulation in the endoplasmic reticulum leading to signalling and stress), Cushing's disease (mis-regulation of secretion) and autosomal recessive hyperoxaluria (kidney disease; mistargeting of peroxisomal protein to mitochondria). The knowledge of targeting signals enables sophisticated drug design, and—since subcellular localization is a major determinant of protein function—annotation of gene products.
Targeting peptides (often N-terminal) direct nascent proteins to their specific destination. However, due to low sequence similarity (Williams et al., 2000), computationally predicting subcellular localization of proteins is challenging. The prediction problem has been approached using a range of techniques including weight matrices (von Heijne, 1986), expert rules and clustering algorithms (Nakai and Horton, 1999), machine learning techniques such as support-vector machines (Park and Kanehisa, 2003; Cai et al., 2003), Bayesian classifiers (Lu et al., 2004; Drawid and Gerstein, 2000) and neural networks (Cai et al., 2002; Emanuelsson et al., 2000), using structural and evolutionary information (Nair and Rost, 2003), amino acid composition (Reinhardt and Hubbard, 1998; Hua and Sun, 2001) and order (Chou and Cai, 2003), expression data (Drawid and Gerstein, 2000) and textual data (Lu et al., 2004).
A series of neural network-based predictors have shown special abilities in handling the task of predicting biological sequence features relating to subcellular localization. SignalP, ChloroP and TargetP (Nielsen et al., 1997; Dyrlöv Bendtsen et al., 2004; Emanuelsson et al., 2000) all predict subcellular destinations and cleavage sites of proteins from the linear amino acid sequence using simple feed forward networks. The most general of the predictors, TargetP, distinguishes between proteins destined for the mitochondrion, for the chloroplast, for the secretory pathway (the endoplasmic reticulum), and proteins which lack a targeting peptide. In this paper we develop a predictor based on sequence-biased recurrent networks and contrast this predictor against TargetP's use of static feed forward networks.
By experimenting with various configurations, Emanuelsson et al. (2000) found that target-specific feed forward networks which slide over a limited window of residues can work as targeting peptide detectors, i.e. distinguish between residues that belong to the targeting peptide (to be cleaved off) and those that belong to the mature protein (or a targeting peptide directing the protein to a different organelle). The detection outputs for the first 100 residues (from each of the target specific networks) are fed into another feed forward network—the target sorting network—which makes a final decision on which subcellular compartment the protein is destined for (Fig. 1). SignalP operates in a similar manner to distinguish between proteins with and without a signal peptide, but simplifies the sorting step by employing a simple threshold criterion on the summed detection outputs (Nielsen et al., 1997).1 The first step of detecting residues as belonging to a specific targeting peptide is crucial. With highly accurate targeting peptide detection, the sorting problem reduces to a simple decision (Emanuelsson et al., 2000).
|
|
2 SYSTEMS AND METHODS |
|---|
|
TOPAbstract1 INTRODUCTION2 SYSTEMS AND METHODS3 IMPLEMENTATION AND DISCUSSION4 CONCLUSIONREFERENCES |
|---|
2.1 Recurrent networks
The properties of proteins (function, interactions, etc.) are generally difficult to characterize from linear sequence data since structurally relevant information (implied by the protein's folding) is dispersed over longer distances. A feed forward model for classification and characterization of sequence properties relies on an input window of a pre-determined size to detect discriminative sequence patterns. However, the window imposes a definite limit on the range of input signals to influence a decision. Unfortunately, increasing the size not only increases the input space (the number of possible input combinations increases exponentially) but introduces additional noise and thus compromises generalization. Alternatively, relevant high-order features can be collated and fitted in the input window—leaving us with the difficult problem of manually specifying such features.
By presenting the sequence dynamically rather than statically, we partially circumvent the input dimensionality issue. The so-called recurrent networks do not simply implement a function of the current input window to an output. Instead the mapping involves a function which is additionally based on the current state. The current state is recursively defined over the history of states and, consequently, over past inputs. The bi-directional variant of the recurrent network (Baldi et al., 1999) makes use of two states and applies two state-to-state mappings, one for residues upstream and one for residues downstream. In the variant we use, a classification for a position p is based on an upstream and a downstream state, sU(p) and sD(p) respectively. The upstream state sU(p) is defined over the current upstream input x(p – 1) and sU(p – 1). sU(p – 1) is defined over x(p – 2) and sU(p – 2), and so on (recursively). The downstream state is similarly defined over the current downstream input x(p + 1) and sD(p + 1). sD(p + 1) is defined over x(p + 2) and sD(p + 2), and so on. The final states additionally incorporate the current input x(p). The final two states can be understood as representing the context in which the current input appears. Importantly, even if the three input windows (one for the current position, one for upstream and one for downstream residues) are small, the recursive nature of generating a state imposes no hard limit on the range of intra-sequence patterns that can be captured.
Recurrent networks were used by Baldi et al. (1999) and Pollastri et al. (2002) to predict the secondary structure of proteins. Their network was equipped with a window of residues (at the point of prediction) and two context windows (one for each flank). The prediction accuracy exceeded that of feed forward networks by a few percent. More recently, Vullo and Frasconi (2004) presented promising results using yet another variant of the recurrent network for representing structural information to identify disulfide bonding patterns.
We investigate the performance of models for predicting subcellular localization using recurrent networks in contrast to feed forward networks as employed by TargetP and other predictors. More specifically, we evaluate the performance profile of the first step, targeting peptide detection, and the accuracy of the final target classification. We additionally perform simulations with the original TargetP architecture to ensure a fair comparison.
2.2 Sequence data
We use the dataset which was used to develop and evaluate TargetP (Emanuelsson et al., 2000). TargetP is able to classify sequences of eukaryotic cells. There are two versions, one for plants and one for non-plants, each trained on a specific dataset. The plant dataset consists of 940 proteins [368 with a mitochondrial targeting peptide (mTP), 141 with a chloroplast transit peptide (cTP), 269 with a signal peptides (SP) and 162 nuclear and cytosolic (other)]. The non-plant set consists of 2738 proteins (371 with a mitochondrial targeting peptide, 715 with signal peptides and 1652 nuclear and cytosolic).
Each simulation we perform is evaluated by 5-fold cross-validation: The dataset is divided into five subsets (of approximately equal size). Four are used for training the predictive model, the remaining subset is used for testing. The procedure is repeated with randomly initialized models and by shuffling the data subsets so that each of the five subsets appears as a test set exactly once (and each data sample appears as a test case exactly once). Consequently, the resulting five models are only tested on, for each individual model, unseen sequences. The score we report is the aggregate result for all five test sets (over the five models). Finally, all 5-fold cross-validated simulations are then repeated six times to ensure that final scores are significant.
2.3 Targeting peptide detection
Non-plant proteins are used to train two separate ‘non-plant’ targeting peptide detection networks: one for SP and one for mTP. A third class (other) of proteins is used as additional negatives for both networks. The detection networks are equipped with input windows of 27 and 35 residues, respectively. Each detection network is also fitted with a hidden layer consisting of four hidden nodes.
The plant proteins are used to train three ‘plant’ targeting peptide detection networks: for SP, mTP and cTP. The fourth class (other) is again used as negatives. The networks are fitted with input windows of sizes 31, 35 and 55 residues, respectively, and four hidden nodes. All networks were reportedly close to optimal with these configurations (Emanuelsson et al., 2000).
Recurrent networks are similarly used to scan and detect targeting peptides. By iteratively creating a state from the residues next to each position in the sequence, the middle residue is classified as being part of the specific targeting peptide or not (Fig. 2). We tried a few configurations and the results reported below are taken from recurrent networks with 10-residue windows for both flanks. States consist of four nodes of which all are fully recurrent (all nodes feed back to all others within the same state layer). As configurations have yet to be fully explored, we do not claim that the reported configuration is optimal. We use the same configuration for both plant and non-plant data, and for all subcellular targets.
|
All sequences are, as convention prescribes, presented to the networks as one-hot bit-strings. The element with ‘1’ is unique for the amino acid, and all other elements are set to ‘0’, resulting in a 20 bit vector for each residue in the sequence, mutually orthogonal to all others. A single bit is added to accommodate unknown residues. Preliminary trials with sequence profiles (generated by psi-BLAST) were unsuccessful due to low sequence similarities of signal peptides in particular.
Detection networks produce binomial outputs using the logistic output function. All detection networks are trained by minimizing the cross-entropy error and the error terms are propagated through the sequence both upstream and downstream as described by Baldi et al. (1999). To reduce training times the error flow is truncated after five steps. For both feed forward and recurrent networks, the learning rate is fixed to 0.01, all weight values being randomly initialized with a Gaussian distribution around 0.0 (variance 0.1). By monitoring errors throughout learning, slow convergence and minor fluctuations were noted. However, the consistency of generalization results reported below denies the presence of major learning issues.
2.4 Target sorting
In TargetP the plant sorting network has 300 input nodes (100 from each detection network), no hidden nodes and four outputs (one for each target class and one for ‘other’). The non-plant sorting network has 200 input nodes, no hidden nodes and three outputs (mTP, SP and other). We use the same sorting procedure for both feed forward and recurrent detection networks.
To ensure that the sorting networks produce a multinomial distribution over output classes, we use the softmax output function and the negative log-likelihood error function (Rumelhart et al., 1995). All other learning parameters are set as for the detection networks.
Sorting from the output of the detection networks can be done in many ways. To evaluate the criticality of this step, we also test k-nearest neighbours: the detection output of a test sequence is compared with all detection outputs of training sequences. The probability distribution over targets of the k = 3 nearest sequences is used as the model's classification output.
Matthews' correlation coefficient (Matthews, 1975) takes into account the numbers of true positives (tp), true negatives (tn), false positives (fp) and false negatives (fn) of a class [Equation (1)]:
 | (1) |
 | (2) |
 | (3) |
|
3 IMPLEMENTATION AND DISCUSSION |
|---|
|
TOPAbstract1 INTRODUCTION2 SYSTEMS AND METHODS3 IMPLEMENTATION AND DISCUSSION4 CONCLUSIONREFERENCES |
|---|
Training is performed by presenting each detection network with a sequence randomly drawn from the training subsets (uniformly over the target classes). The sequence is processed by training the network to classify each residue as ‘1’ or ‘0’, in the same manner as TargetP (Emanuelsson et al., 2000). After 30 000 training sequences have been presented,2 the actual output of each of the detection networks for each position in each test sequence is recorded. Moreover, the squared difference between the target output (‘1’ or ‘0’) and the actual output is used to assess the classification ability of the network. As the cleavage site determines the end of the string of 1s, the error indicates the success of both the classification of the peptide and the identification of the cleavage point.
The outputs of the detection networks produced for each of the training sequences are used to train the target sorting network (alternatively, used for k-nearest neighbour classification). The sorting networks are trained for 10 000 sequences to output the correct classification of each.
3.1 Non-plant proteins
In Table 1 the mean errors are shown for both feed forward and recurrent targeting peptide detection networks. Residues within signal peptides are generally easy to detect for both network types. On average, the recurrent network is 24% better than the feed forward SP detection network. Results from mitochondrial targeting peptides also demonstrate an advantage for recurrent networks (15%).
|
To understand the strengths and weaknesses of each technique in terms of sequence components, we collected the outputs produced by the SP detection networks for all test sequences that are known to have a signal peptide. The position-specific errors are shown in Figure 3. The cleavage site of signal peptides is usually located at position 15–30 of the nascent protein relative to the N-terminus (mean = 23, SD = 6, in the dataset). The classification error is generally higher around the cleavage site. As the relevant biological signals are located here, this observation is rather unsurprising. Notably, the error is relatively higher for the feed forward network (as employed by TargetP) for most residues preceding the cleavage site. Moreover, there is a sharp upturn in error after position 13. Position 14 is the first position which is classified using a window fully populated with real amino acids (when the window ranges over non-existing sequence positions a nil-pattern pads out the window). It is thus quite likely that the TargetP detection network uses such weak, encoding-specific indicators. The recurrent network—partially avoiding the pre-fixed window approach—shows no dramatic changes in performance. After the cleavage site, where relevant signals are scarce, both network types perform equally well.
|
The errors for mitochondrial test sequences were similarly analyzed. The performance of recurrent targeting peptide detection networks is considerably better before and around the cleavage sites of the nascent protein sequence. The cleavage sites of matrix mitochondrial processing peptidases occur further along the nascent protein (mean = 34, SD = 16, in the data). Being very close to their mean, the error profiles of individual networks show little variation.
The outputs of targeting peptide detection networks for test data are presented to the target sorters (both feed forward networks and k-nearest neighbour models) to assess their ability to make use of the first step. For non-plant data, the classification accuracy is shown in Table 2.
|
The improvement noted for the first detection step is not apparent in the accuracy of the final classification. All of the tested configurations seem to result in the same overall performance. On a more detailed look, we see that compared to the k-nearest neighbour model, a network sorter has higher sensitivity, traded for lower specificity on mTP sequences.
3.2 Plant proteins
The ‘plant’ targeting peptide detection networks are evaluated in the same way as the ‘non-plant’ networks. There are three targets, and recurrent networks demonstrate superior detection ability for SP and mTP sequences. cTP sequences are better handled by the original feed forward detection networks. However, this advantage is only present in the latter end of the sequence (after position 55, coinciding with the mean cleavage site) where any signals are likely to be less relevant to the task at hand. See Table 3 for the overall performance and Figure 4 for the position-specific error profiles.
|
|
The errors are generally higher for the mTP detection network when trained on plant proteins (compared to when trained on non-plant proteins). This may seem odd at first—considering that the same set of proteins is re-used for the plant-version of TargetP (Emanuelsson et al., 2000). However, since other plant-specific proteins (including cTP sequences) are used as negatives, the discriminative task of the plant-specific mTP detector is fundamentally different.
The classification accuracy of the target sorters for test data is specified in Table 4. Here, the advantage indicated by the detection networks seems to carry over to the sorting. As reflected by Matthews' correlation coefficient, recurrent models (with network and k-nearest neighbour sorters) demonstrate a general improvement on SP, mTP and ‘other’ sequences. The cTP sequences are handled equally well by all configurations, though a slightly higher sensitivity is noted for network sorters at the expense of lower specificity. The latter also holds for ‘other’ sequences. As a matter of fact, viewed over all simulations, network sorters tend to exhibit higher sensitivity and lower specificity in general compared to k-nearest neighbour sorters.
|
3.3 Further analysis
Computationally, recurrent networks have been shown to be extremely powerful. Carefully hand-crafted recurrent networks level with Turing machines (Siegelmann, 1999). We have demonstrated elsewhere that recurrent networks have an inherent ability to make accessible sequence patterns with a biological flavour exceeding that of feed forward architectures (Bodén and Hawkins, 2005). A burst of papers recently suggested that the networks exhibit intrinsic properties that naturally lend themselves to sequential prediction tasks (Hammer and Tino, 2003; Tino et al., 2004). With small weights, the recurrent feedback realizes a contractive state function inherently sensitive to past states (and therefore previous inputs). When states are grouped, transitions between groups over time abstractly resemble those of a finite Markovian model (Tino et al., 2004). As a note, hidden Markov models have proven useful when sequences follow a general and known pattern, e.g. membrane protein topology (Käll et al., 2004). Even before the training of recurrent networks—by virtue of their architecture—sequences sharing a sequence pattern are separated in state space from those without (Bodén and Hawkins, 2005). The recurrent network is, in other words, biased toward sequence recognition tasks.
According to our simulations the accuracy of ‘recurrent’ targeting peptide detection seems to correlate with putative signal sites. However, the general improvement offered by recurrent networks is not completely evident in target sorting accuracy. The observation prompts a better characterization of the intermediate targeting peptide detection output space. From the sorting module's point of view, ideally, the inter-class detection outputs need to be distinct, whereas the intra-class outputs should be grouped. The detection networks are only indirectly trained to enforce this relative constraint, and the classification error realized by the sorter has no impact on the organization of its inputs. To address the performance of detection networks from a sorting point of view, we calculated the relative differences between outputs for different targets. We calculated the mean outputs for each of the three (or four) classes. The differences (shown in Tables 5 and 6) were squared (per residue) and averaged. Using this method the classes were consistently more separated by the recurrent networks. The variation of the detection output within a class has of course an impact on the simplicity by which sorting occurs. The means and standard deviations are shown for one feed forward and one recurrent non-plant model in Figure 5. The deviations were generally lower for all recurrent detection networks.3
|
|
|
Overall, no specific reason was found as to why only the plant model improved its sorting accuracy when using recurrent networks.
|
4 CONCLUSION |
|---|
|
TOPAbstract1 INTRODUCTION2 SYSTEMS AND METHODS3 IMPLEMENTATION AND DISCUSSION4 CONCLUSIONREFERENCES |
|---|
We note that recurrent networks are better than the feed forward networks used by TargetP at classifying residues as belonging to a targeting peptide. The advantage is particularly clear within the window believed to exhibit the strongest signals used by the translocation machinery (Emanuelsson, 2002). The reason for the success lies partly in the fact that recurrent networks are naturally biased towards detecting sequential patterns (Bodén and Hawkins, 2005; Tino et al., 2004). The co-occurrence with improved detection accuracy and putative signal sites supports that recurrent networks base their generalization on regions relevant to the task at hand.
We conclude that in cases where marginal improvements in accuracy are crucial, recurrent neural networks are well worth exploring. In a recent review, Emanuelsson (2002) illustrated at length the superiority of TargetP compared to a representative set of alternative localization predictors. The average sensitivity of the combined model is 0.919 for non-plant and 0.880 for plant proteins. The average specificity for the combined model is 0.908 for non-plant and 0.866 for plant proteins. By improving on TargetP our approach represents—at least for the main organelles—the most accurate prediction model to date.
However, our study also flags that the two-step process, involving targeting peptide detection and then classification on the basis of detection output, fails to fully exploit the increased accuracy provided by recurrent networks and that more effective sequence–target mappings should be pursued for even better prediction of subcellular localization.
|
Acknowledgments |
|---|
The authors would like to thank Dr Zheng Yuan for generating profile data, and James Watson and Mark Wakabayashi for contributions to the simulation software.
|
Footnotes |
|---|
1In SignalP version 3.0 a new score incorporating a cleavage site prediction is used to determine whether a sequence has a signal peptide or not (Dyrlöv Bendtsen et al., 2004).
2The number of training sequences was set to ensure convergence to a low training error for both types of networks.
3The only exception to this was the recurrent plant mTP detection network which produced a slightly higher variation in the output but-on the other hand-had a significantly lower mean.
Received on November 18, 2004; revised on January 24, 2005; accepted on March 1, 2005
|
REFERENCES |
|---|
|
TOPAbstract1 INTRODUCTION2 SYSTEMS AND METHODS3 IMPLEMENTATION AND DISCUSSION4 CONCLUSIONREFERENCES |
|---|
Aridor, M. and Hannan, L.A. (2000) Traffic jam: a compendium of human diseases that affect intracellular transport processes. Traffic, 1, 836–851[CrossRef][Web of Science][Medline].
Baldi, P., et al. (1999) Exploiting the past and the future in protein secondary structure prediction. Bioinformatics, 15, 937–946
Bodén, M. and Hawkins, J. (2005) Improved access to sequential motifs: a note on the architectural bias of recurrent networks. IEEE Trans. Neural Networks, 16, .
Cai, Y.-D., et al. (2002) Artificial neural network model for predicting protein subcellular location. Comput. Chem., 26, 179–182[CrossRef][Web of Science][Medline].
Cai, Y.-D., et al. (2003) Support vector machines for prediction of protein signal sequences and their cleavage sites. Peptides, 24, 159–161[CrossRef][Web of Science][Medline].
Chou, K.C. and Cai, Y.D. (2003) Prediction and classification of protein subcellular location-sequence-order effect and pseudo amino acid composition. J. Cell. Biochem., 90, 1250–1260[CrossRef][Web of Science][Medline].
Drawid, A. and Gerstein, M. (2000) A Bayesian system integrating expression data with sequence patterns for localizing proteins: comprehensive application to the yeast genome. J. Mol. Biol., 301, 1059–1075[CrossRef][Web of Science][Medline].
Dyrlöv Bendtsen, J., et al. (2004) Improved prediction of signal peptides: SignalP 3.0. J. Mol. Biol., 340, 783–795[CrossRef][Web of Science][Medline].
Emanuelsson, O. (2002) Predicting protein subcellular localisation from amino acid sequence information. Brief. Bioinform., 3, 361–376
Emanuelsson, O., et al. (2000) Predicting subcellular localization of proteins based on their N-terminal amino acid sequence. J. Mol. Biol., 300, 1005–1016[CrossRef][Web of Science][Medline].
Hammer, B. and Tino, P. (2003) Recurrent neural networks with small weights implement definite memory machines. Neural Comp., 15, 1897–1929[CrossRef][Web of Science].
Hua, S. and Sun, Z. (2001) Support vector machine approach for protein subcellular localization prediction. Bioinformatics, 17, 721–728
Käll, L., et al. (2004) A combined transmembrane topology and signal peptide prediction method. J. Mol. Biol., 338, 1027–1036[CrossRef][Web of Science][Medline].
Lu, Z., et al. (2004) Predicting subcellular localization of proteins using machine-learned classifiers. Bioinformatics, 20, 547–556
Matthews, B.W. (1975) Comparison of predicted and observed secondary structure of t4 phage lysozyme. Biochim. Biophys. Acta, 405, 442–451[Medline].
Nair, R. and Rost, B. (2003) Better prediction of sub-cellular localization by combining evolutionary and structural information. Proteins, 53, 917–930[CrossRef][Web of Science][Medline].
Nakai, K. and Horton, P. (1999) PSORT: a program for detecting sorting signals in proteins and predicting their subcellular localization. Trend. Biochem. Sci., 24, 34–35[CrossRef][Web of Science][Medline].
Nielsen, H., et al. (1997) Identification of prokaryotic and eukaryotic signal peptides and prediction of their cleavage sites. Protein Eng., 10, 1–6
Park, K. and -J. and Kanehisa, M. (2003) Prediction of protein subcellular locations by support vector machines using compositions of amino acids and amino acid pairs. Bioinformatics, 19, 1656–1663
Pollastri, G., et al. (2002) Improving the prediction of protein secondary strucure in three and eight classes using recurrent neural networks and profiles. Proteins, 47, 228–235[CrossRef][Web of Science][Medline].
Reinhardt, A. and Hubbard, T. (1998) Using neural networks for prediction of the subcellular location of proteins. Nucleic Acids Res., 26, 2230–2236
Rumelhart, D.E., Durbin, R., Golden, R., Chauvin, Y. (1995) Backpropagation: the basic theory. In Chauvin, Y. and Rumelhart, D.E. (Eds.). Backpropagation: Theory, Architectures, and Applications, , Hillsdale, NJ Lawrence Erlbaum, pp. 1–34.
Siegelmann, H.T. Neural Networks and Analog Computation: Beyond the Turing Limit, (1999) , Basel Birkhäuser.
Tino, P., et al. (2004) Markovian architectural bias of recurrent neural networks. IEEE Trans. Neural Networks, 15, 6–15[CrossRef].
van Vliet, C., et al. (2003) Intracellular sorting and transport of proteins. Progr. Biophys. Mol. Biol., 83, 1–45[CrossRef][Web of Science][Medline].
von Heijne, G. (1986) A new method for predicting signal sequence cleavage sites. Nucleic Acids Res., 14, 4683–4690
Vullo, A. and Frasconi, P. (2004) Disulfide connectivity prediction using recursive neural networks and evolutionary information. Bioinformatics, 20, 653–659
Williams, E.J.B., et al. (2000) The molecular evolution of signal peptides. Gene, 253, 313–322[CrossRef][Web of Science][Medline].
CiteULike 
Connotea 
Del.icio.us What's this?
This article has been cited by other articles:
|
|
 |
|
  Y.-Q. Shen, B. F. Lang, and G. Burger Diversity and dispersal of a ubiquitous protein family: acyl-CoA dehydrogenases Nucleic Acids Res., September 1, 2009; 37(17): 5619 - 5631. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 K. A. Howell, R. Narsai, A. Carroll, A. Ivanova, M. Lohse, B. Usadel, A. H. Millar, and J. Whelan Mapping Metabolic and Transcript Temporal Switches during Germination in Rice Highlights Specific Transcription Factors and the Role of RNA Instability in the Germination Process Plant Physiology, February 1, 2009; 149(2): 961 - 980. [Abstract] [Full Text] [PDF]
|
|
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||