Sidues [57], gene doubling, and gene fusion. With these changes accumulated for a long period of time, many similarities between initial and resultant amino acid sequences are gradually eliminated, but the corresponding proteins may still share many common attributes, such as having basically the same biological function and residing at a same subcellular location. To incorporate this kind of sequence evolution information into the PseAAC of Eq.2, let us use the information of the PSSM (Position-Specific Scoring Matrix) [3], as described below. According to [3], the sequence evolution information of protein P with L amino acid 1454585-06-8 residues can be expressed by a 20|L 12926553 matrix, as given by 2 6 P(0) 6 PSSM 6 m(0) 1,2,2. A Novel PseAAC Feature Vector by Incorporating Sequence Evolution Information via the Grey System Anlotinib TheoryTo develop a powerful predictor for a protein system, one of the keys is to formulate the protein samples with an effective mathematical expression that can truly reflect their intrinsic6 6 m(0)m(0) 1,2 m(0) 2,2 . . . m(0) L,? ?. . . ?. 6 . 4 . m(0) L,7 m(0) 7 2,20 7 7 . 7 . 7 . 5 m(0) L,m(0) 1,3 ??where m(0) represents the original score of amino acid residue in i,jPredicting Secretory Proteins of Malaria Parasitethe i-th (i 1,2, ???,L) sequential position of the protein that is being changed to amino acid type j (j 1,2, ???,20) during the evolution process. Here, the numerical codes 1, 2, …, 20 are used to denote the 20 native amino acid types according to the alphabetical order of their single character codes [58]. The 20|L scores in Eq.3 were generated by using PSI-BLAST [3] to search the UniProtKB/Swiss-Prot database (Release 2010_04 of 23-Mar2010) through three iterations with 0.001 as the E-value cutoff for multiple sequence alignment against the sequence of the protein P. In order to make every element in Eq.3 within the range of 0?, a conversion was performed through the standard sigmoid function to make it become 2 m(1) 1,1 m(1) 1,2 m(1) 2,2 . . . m(1) L,2 ? ?. . . ?m(1) 1,20 3 ??a(1) m(1) m(1) {m(1) k,j k,j k{1,j andk{1 X i??z(1) (k)m(1) z0:5m(1) i,j k,j??In Eq.6, the coefficients aj1 and aj2 are associated with the developing coefficients, and bj the influence coefficient. Actually, aj1 , aj2 , and bj can be expressed as the components of a 3D vector as given by ?Hj aj1 aj2 bj (j 1,2, ???,20) ??6 6 m(1) 6 2,1 (1) PPSSM 6 6 . 6 . 4 . m(1) L,1 where m(1) i,j 1 1ze{m (0) i,j7 m(1) 7 2,20 7 7 . 7 . 7 . 5 m(1) L,in which the components aj1 , aj2 , and bj can be directly derived from the following equation Hj (BT B){1 BT U ?0??iL, 1j20???where 2 {m(1) 2,j {z(1) (2) {z(1) (3) . . . {z(1) (L) 1 3 ?1?Now, let us describe how to extract the useful information from Eq.4 via a grey system model. According to the grey system theory [33], if the information of a system investigated is fully known, it is called a “white system”; if completely unknown, a “black system”; if partially known, a “grey system”. The model developed based on such a theory is called “grey model”, which is a kind of nonlinear and dynamic model formulated by a differential equation. The grey model is particularly useful for solving complicated problems that are lack of sufficient information, or need to process uncertain information and reduce random effects of acquired data. In the grey system theory, an important and generally used model is called GM(1,1) [33]. It is quite effective for monotonic series, with good simulating effect a.Sidues [57], gene doubling, and gene fusion. With these changes accumulated for a long period of time, many similarities between initial and resultant amino acid sequences are gradually eliminated, but the corresponding proteins may still share many common attributes, such as having basically the same biological function and residing at a same subcellular location. To incorporate this kind of sequence evolution information into the PseAAC of Eq.2, let us use the information of the PSSM (Position-Specific Scoring Matrix) [3], as described below. According to [3], the sequence evolution information of protein P with L amino acid residues can be expressed by a 20|L 12926553 matrix, as given by 2 6 P(0) 6 PSSM 6 m(0) 1,2,2. A Novel PseAAC Feature Vector by Incorporating Sequence Evolution Information via the Grey System TheoryTo develop a powerful predictor for a protein system, one of the keys is to formulate the protein samples with an effective mathematical expression that can truly reflect their intrinsic6 6 m(0)m(0) 1,2 m(0) 2,2 . . . m(0) L,? ?. . . ?. 6 . 4 . m(0) L,7 m(0) 7 2,20 7 7 . 7 . 7 . 5 m(0) L,m(0) 1,3 ??where m(0) represents the original score of amino acid residue in i,jPredicting Secretory Proteins of Malaria Parasitethe i-th (i 1,2, ???,L) sequential position of the protein that is being changed to amino acid type j (j 1,2, ???,20) during the evolution process. Here, the numerical codes 1, 2, …, 20 are used to denote the 20 native amino acid types according to the alphabetical order of their single character codes [58]. The 20|L scores in Eq.3 were generated by using PSI-BLAST [3] to search the UniProtKB/Swiss-Prot database (Release 2010_04 of 23-Mar2010) through three iterations with 0.001 as the E-value cutoff for multiple sequence alignment against the sequence of the protein P. In order to make every element in Eq.3 within the range of 0?, a conversion was performed through the standard sigmoid function to make it become 2 m(1) 1,1 m(1) 1,2 m(1) 2,2 . . . m(1) L,2 ? ?. . . ?m(1) 1,20 3 ??a(1) m(1) m(1) {m(1) k,j k,j k{1,j andk{1 X i??z(1) (k)m(1) z0:5m(1) i,j k,j??In Eq.6, the coefficients aj1 and aj2 are associated with the developing coefficients, and bj the influence coefficient. Actually, aj1 , aj2 , and bj can be expressed as the components of a 3D vector as given by ?Hj aj1 aj2 bj (j 1,2, ???,20) ??6 6 m(1) 6 2,1 (1) PPSSM 6 6 . 6 . 4 . m(1) L,1 where m(1) i,j 1 1ze{m (0) i,j7 m(1) 7 2,20 7 7 . 7 . 7 . 5 m(1) L,in which the components aj1 , aj2 , and bj can be directly derived from the following equation Hj (BT B){1 BT U ?0??iL, 1j20???where 2 {m(1) 2,j {z(1) (2) {z(1) (3) . . . {z(1) (L) 1 3 ?1?Now, let us describe how to extract the useful information from Eq.4 via a grey system model. According to the grey system theory [33], if the information of a system investigated is fully known, it is called a “white system”; if completely unknown, a “black system”; if partially known, a “grey system”. The model developed based on such a theory is called “grey model”, which is a kind of nonlinear and dynamic model formulated by a differential equation. The grey model is particularly useful for solving complicated problems that are lack of sufficient information, or need to process uncertain information and reduce random effects of acquired data. In the grey system theory, an important and generally used model is called GM(1,1) [33]. It is quite effective for monotonic series, with good simulating effect a.

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