In order to test the performance of our lifelong learning model, we experimentally selected two membrane protein datasets for testing, Data 1 and Data 2. The specifics of the two datasets are shown in Table 1. Data 1 and Data 2 include eight membrane protein types. Data 1 is from the work of Chou (Chou and Shen, 2007) et al. The training and test sets were randomly obtained from Swiss-Prot (Boeckmann et al., 2003) by percentage assignment, which ensured that the quantities of these two sequences are consistent. Data 2 is from the work of Chen (Chen and Li, 2013) et al. where they used the CD-hit (Li and Godzik, 2006) method to remove redundant sequences from dataset 1 so that no two-by-two sequences would have less than 40% identity.

The PSSM used in this experiment is the “Position-Specific Scoring Matrix.” This scoring matrix stores the sequence information of membrane proteins. We use the PSSM matrix (Shen et al., 2017; Ding et al., 2017; Shen et al., 2019) for membrane protein prediction because it reflects the evolutionary information of membrane proteins very well. For any membrane protein sequence, such as Q, the PSSM can be derived by PSI-BLAST (Altschul et al., 1997), after several iterations. First it forms the PSSM based on the first search result, then it performs the next step which is the second search based on the first search result, then it continues with the second search result for another time and repeats this process until the target is searched for the best result. As the performance of the experimental results is best after three iterations, we generally adopt three iterations as the setting. The value of its E is 0.001. Assume that the sequence Q = q 1 q 2 q 3 ...   .   q L , whose length is L. This is followed by storing the PSSM containing the membrane protein evolution information inside a matrix with a size-area of L × 20. The matrix is represented as follows: PSS M original = [ p 1,1 p 1,2 p 2,1 p 2,2 ⋮ ⋮ … p 1,20 … p 2,20 ⋱ ⋮ p i , 1 p i , 2 ⋮ ⋮ p L , 1 p L , 2 … p i , 20 ⋱ ⋮ … p L , 20 ] L× 20 (1)

In addition, the expression below shows the representation of   P S S M o r i g i n a l ( i , j ) : PSS M original ( i,j ) = ∑ k=1 20 ω ( i,k ) ×D ( k,j ) , i=1, …,L .  j=1,…,20 (2) where ω ( i , k ) is the frequencies of the k-th type of amino acid at the i-th position and D ( k , j ) is the mutation percentage of the substitution matrix from the k-th molecular substances into the sequence of the protein. The larger the value, the more conserved the position is. If this is not present, the contrary will be achieved.

Lifelong learning (Thrun and Mitchell, 1995), like machine learning, can be divided into the directions of lifelong supervised learning, lifelong unsupervised learning and lifelong reinforcement learning. The lifelong machine learning part of the study focuses on whether the model can be extended when new categories of categories are added to the model. When the current model has been classified into n categories, if a new class of data is added, the model can somehow be adaptively expanded to classify n + 1 category. Multi-task learning models and lifelong machine learning are easily translatable to each other if we have all the original data. Whenever a new category is added to the original category and needs to be classified, only one new category needs to be added and then all the training data can be trained again to expand the new category. One obvious disadvantage of this strategy is that it wastes a lot of computational time to compute each new class, and if too many new classes are added, it may lead to changes in the model architecture for multi-task learning. This model therefore uses a dynamically scalable network to better perform incremental learning of the added tasks. Assume that the current model has successfully classified Class 1, Class 2, ... , Class n. When the new data class Class-new is added, the model does not need to train all the data from scratch, but only needs to expand the overall model by adding n new binary classification models. The simple flow of the lifelong learning model is shown in Figure 4.

Dynamically scalable networks are incremental training of deep neural networks for lifelong learning, for which there will be an unknown amount and unknown distribution of data to be trained fed into our model in turn. To expand on this, there are now T a sequence of task learning models, t = 1, .... , t, .... , T is unbounded T in which the tasks at time point t carry training data D t = { x i , y i } i = 1 N t . It is important to note that each subtask can be a single or a group of tasks. For simplicity, even though our approach is general for any kind of task, we only consider the two-classification problem. That is, input features x   ∈   R d of y   ∈   { 0 ,   1 } . One challenge with lifelong learning is that at the current time t, all previous training datasets are unavailable (if any, only from previous model parameters). The lifelong learning agent learns the model parameters W t by solving the following problem in a reasonable amount of time t: minimiz e W t L ( W t  ; W t- 1 , D t ) + λ Ω ( W t   ) , t = 1 1 , … (11) where L is task specific loss function, W t is the parameter for task t, and Ω ( W t ) is the regularization (e.g. element-wise ℓ 2 norm) to enforce our model W t appropriately. In case of a neural network which is our primary interest, W t = { W l } l = 1 L is the weight tensor.

To counter these problems that arise in the course of lifelong learning, we allow the knowledge generated in previous tasks to be used to the maximum extent possible. At the same time, it is allowed to dynamically extend its capabilities when mechanically accumulated knowledge does not explain well for emerging tasks. Figure 5 and Algorithm 1 illustrate our progressive learning process.

To evaluate our lifelong learning model better, we chose several parameters: sample all-prediction accuracy (ACC), single sample specificity (SP), single sample sensitivity (SN), and Mathews correlation coefficient. These metrics are widely used in the analysis of biological sequence information: { SN= TP TP+FN SP= TN TN+FP ACC= TP+TN TP+FP+TN+FN MCC= TP×TN-FP×FN ( TP+FN ) × ( TN+FP ) × ( TP+FP ) × ( TN+FN )     (12)

For the above equation, true trueness (TP) refers to the number of true samples correctly predicted; false positivity (FP) refers to the number of true samples incorrectly predicted; true negativity (TN) refers to the number of negative samples correctly predicted; and false negativity (FN) refers to the number of negative samples erroneously predicted (Chou et al., 2011a; Chou et al., 2011b; Chou, 2013).

The lengths of the datasets used in our experiments are shown in Figure 6. Most of the membrane proteins in dataset 1 and dataset 2 have a similar length distribution because of their specific type. To better demonstrate the superiority of lifelong learning for membrane protein classification, we calculated the amino acid frequencies for all protein types in the experiment, as shown in Figure 7.

The PSSM sequence matrix contains important genetic information required for protein prediction. Many elements of biological evolution, such as the stability of the three-dimensional structure and the aggregation of proteins, can have an impact on the storage and alteration of sequences. These elements demonstrate that PSSM captures important information about ligand binding. Thus, proving the validity of the PSSM characterization method.

We will compare the model methods we used in this use with other existing methods in terms of prediction accuracy on dataset 1. The methods involved in the comparison are MemType-2L (Chou and Shen, 2007) and predMPT (Chen and Li, 2013). Details can be found in Table 2, where it is clear that our model approach has an overall ACC of 95.3%. 3.7% higher than MemType-2L’s 91.6%, 2.7% higher than predMPT’s 92.6%, and 2.4% higher than Average weights’ 92.7%. In the independent test set, our method was superior for membrane protein type 2 (88.4%), type 4 (83.3%), type 5 (96.3%) and type 7 (100%).

As a solution to the possible problem of untimely updates in Data 1, Chen and Li (Chen and Li, 2013) used the Swissprot annotation method to update Data Set 1, resulting in a new dataset of membrane proteins (Data Set 2). The results of the comparison using Dataset 2 are presented in Table 3. The overall average accuracy of our models was 3.2% higher than the predMPT method (90.3%). Even though they added features such as 3D structure to the predMPT prediction session, our model performance was clearly higher than it. We outperformed it by 2.6% in terms of prediction accuracy for type 1 (94.1 vs. 91.5%). In contrast, analog 5 outperformed it by 1.3% (94.1 vs. 92.8%).