Pseudo amino acid composition
伪氨基酸组成

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In molecular biology, pseudo amino acid composition (PseACC) is a method introduced by Kuo-Chen Chou to convert the protein sequence into a numerical vector for enhancing pattern recognition techniques, such as during discrimination between classes of proteins based on their sequences (e.g. between membrane proteins, transmembrane proteins, cytosolic proteins, and other types).^[1] This method represented an advance beyond using the immediate amino acid composition (AAC). Instead, the protein is characterized into a matrix of amino-acid frequencies. This matrix incorporates not only amino acid composition, but can also incorporate information from local features of the protein sequence.^[2]
在分子生物学中，伪氨基酸组成（PseACC）是由 Kuo-Chen Chou 提出的一种方法，旨在将蛋白质序列转化为数值向量，以增强模式识别技术，例如基于序列区分不同类别的蛋白质（如膜蛋白、跨膜蛋白、胞质蛋白及其他类型）。 ^[1] 该方法超越了直接使用氨基酸组成（AAC）的传统方式，转而将蛋白质特征化为氨基酸频率矩阵。此矩阵不仅包含氨基酸组成信息，还能整合蛋白质序列局部特征的相关数据。 ^[2]

Due to the success and widespread application of the PseACC method, it was extended to address sequence-order effects in nucleotide compositions, giving rise to a comparative method called PseKNC.^[3]
鉴于 PseACC 方法的成功与广泛应用，其被进一步扩展以解决核苷酸组成中的序列顺序效应，由此诞生了名为 PseKNC 的对比方法。 ^[3]

Two kinds of models are usually used to represent protein samples: the sequential and the discrete (or non-sequential) models.^[4] The most elementary sequential model is to use the entire amino acid sequence, as expressed by:
通常用于表示蛋白质样本的模型有两类：序列模型和离散（或非序列）模型。 ^[4] 最基础的序列模型是直接使用完整的氨基酸序列，其表达式如下：

• ${\displaystyle \mathbf {P} ={\begin{bmatrix}\mathrm {R} _{1}\mathrm {R} _{2}\mathrm {R} _{3}\mathrm {R} _{4}\mathrm {R} _{5}\mathrm {R} _{6}\mathrm {R} _{7}\cdots \mathrm {R} _{L}\end{bmatrix}}\qquad {\text{(1)}}}$

where, P represents the amino acid sequence, ${\displaystyle L}$ is the number of amino acid residues, R₁ is the first residue of the protein P, R₂ is the second residue, and so forth.
其中，P 代表氨基酸序列， ${\displaystyle L}$ 为氨基酸残基数量，R ₁ 是蛋白质 P 的第一个残基，R ₂ 为第二个残基，依此类推。

The problem with this approach was that in some sequence-similarity-search-based tools, the query protein often lacked significant homology (or sequence similarity) with any other known protein in the database. To resolve this problem, discrete models for representing protein samples were proposed. The simplest discrete model is using the amino acid composition (AAC) to represent protein samples. Under the AAC model, the protein P of Eq.1 can also be expressed by
这种方法的问题在于，在某些基于序列相似性搜索的工具中，查询蛋白质往往与数据库中任何已知蛋白质缺乏显著同源性（或序列相似性）。为解决此问题，研究者提出了表示蛋白质样本的离散模型。最简单的离散模型是利用氨基酸组成（AAC）来表征蛋白质样本。在 AAC 模型下，公式 1 中的蛋白质 P 也可表示为：

• ${\displaystyle \mathbf {P} ={\begin{bmatrix}f_{1}&f_{2}&\cdots &f_{20}\end{bmatrix}}^{\mathbf {T} }\qquad {\text{(2)}}}$

where ${\displaystyle \,f_{u}\,(u=1,2,\cdots ,20)}$ are the normalized occurrence frequencies of the 20 native amino acids in P, and T is the transposing operator.^[4]
其中 ${\displaystyle \,f_{u}\,(u=1,2,\cdots ,20)}$ 代表蛋白质 P 中 20 种天然氨基酸的归一化出现频率，T 为转置运算符。 ^[4]

The primary weakness of the discrete model that relies on the amino acid composition (AAC) is that the information on the frequencies of each amino acid from the sample alone involves a loss of sequence-order information, or information obtained by the order of the amino acid residues. To avoid this information loss, the concept of PseAAC (pseudo amino acid composition) was proposed.^[1]
基于氨基酸组成(AAC)的离散模型主要弱点在于，仅从样本中获取各氨基酸频率信息会导致序列顺序信息或氨基酸残基排列顺序所蕴含的信息丢失。为避免这种信息损失，研究者提出了伪氨基酸组成(PseAAC)的概念。 ^[1]

Under this new model, the first 20 discrete factors represent amino acid frequencies are retained, but additional discrete factors are included that also ascertain information about sequence order. The sequence order information is represented by what are called "pseudo components". The number of additional components, beyond the first 20 frequencies, is called λ (or upper-case Λ), and so 20+λ components are included in the model. The upper limit for λ is one less than the length of the shortest protein sample in the dataset.^[1] The total number of components (20+λ) may be denoted Ω. Any additional factors can be incorporated so long as they, in some way, obtain or represent information about the sequence-order. Typically, these are a series of rank-different correlation factors along the protein chain.^[4]
在这一新模型下，前 20 个代表氨基酸频率的离散因子被保留，同时引入了额外的离散因子以捕获序列顺序信息。序列顺序信息通过所谓的“伪组分”来体现。超出前 20 个频率的额外组分数目记为λ（或大写Λ），因此模型中包含 20+λ个组分。λ的上限为数据集中最短蛋白质样本长度减一。 ^[1] 组分的总数（20+λ）可用Ω表示。只要这些额外因子能以某种方式获取或表征序列顺序信息，均可被纳入模型。通常，这些是一系列沿蛋白质链的等级差异相关因子。 ^[4]

The additional factors are a series of rank-different correlation factors along a protein chain, but they can also be any combinations of other factors so long as they can reflect some sorts of sequence-order effects one way or the other. Therefore, the essence of PseAAC is that on one hand it covers the AA composition, but on the other hand it contains the information beyond the AA composition and hence can better reflect the feature of a protein sequence through a discrete model.
这些额外因素是一系列沿蛋白质链的等级差异相关性因子，但它们也可以是其他因素的任意组合，只要这些组合能以某种方式反映序列顺序效应。因此，伪氨基酸组成（PseAAC）的本质在于，它一方面涵盖了氨基酸组成信息，另一方面又包含了超出氨基酸组成的信息，从而能通过离散模型更好地反映蛋白质序列的特征。

Meanwhile, various modes to formulate the PseAAC vector have also been developed, as summarized in a 2009 review article.^[2]
同时，如 2009 年的一篇综述文章所述，人们还开发了多种构建 PseAAC 向量的模式。 ^[2]

According to the PseAAC model, the protein P of Eq.1 can be formulated as
根据 PseAAC 模型，蛋白质 P 的 Eq.1 可表述为

• ${\displaystyle \mathbf {P} ={\begin{bmatrix}p_{1},\,p_{2},\,\ldots ,\,p_{20},\,p_{20+1},\,\ldots ,\,p_{20+\lambda }\end{bmatrix}}^{\mathbf {T} },\,\,\,(\lambda <L)\qquad {\text{(3)}}}$

where the (${\displaystyle 20+\lambda }$) components are given by
其中 ( ${\displaystyle 20+\lambda }$ ) 分量由下式给出

• ${\displaystyle p_{u}={\begin{cases}{\dfrac {f_{u}}{\sum _{i=1}^{20}f_{i}\,+\,w\sum _{k=1}^{\lambda }\tau _{k}}},&(1\leq u\leq 20)\\[10pt]{\dfrac {w\tau _{u-20}}{\sum _{i=1}^{20}f_{i}\,+\,w\sum _{k=1}^{\lambda }\tau _{k}}},&(20+1\leq u\leq 20+\lambda )\end{cases}}\qquad {\text{(4)}}}$

where ${\displaystyle w}$ is the weight factor, and ${\displaystyle \tau _{k}}$ the ${\displaystyle k}$-th tier correlation factor that reflects the sequence order correlation between all the ${\displaystyle k}$-th most contiguous residues as formulated by
其中 ${\displaystyle w}$ 为权重因子， ${\displaystyle \tau _{k}}$ 为反映所有第 ${\displaystyle k}$ 个最邻近残基间序列顺序相关性的第 ${\displaystyle k}$ 层相关系数，其公式表达为

• ${\displaystyle \tau _{k}={\frac {1}{L-k}}\sum _{i=1}^{L-k}\,\mathrm {J} _{i,i+k},\,\,\,(k<L)\qquad {\text{(5)}}}$

with   与

• ${\displaystyle \mathrm {J} _{i,i+k}={\frac {1}{\Gamma }}\sum _{q=1}^{\Gamma }\left[\Phi _{q}\left(\mathrm {R} _{i+k}\right)-\Phi _{q}\left(\mathrm {R} _{i}\right)\right]^{2}\qquad {\text{(6)}}}$

where ${\displaystyle \Phi _{q}\left(\mathrm {R} _{i}\right)}$ is the ${\displaystyle {q}}$-th function of the amino acid ${\displaystyle \mathrm {R} _{i}\,}$, and ${\displaystyle \Gamma \,}$ the total number of the functions considered. For example, in the original paper by Chou,^[1] ${\displaystyle \Phi _{1}\left(\mathrm {R} _{i}\right)}$, ${\displaystyle \Phi _{2}\left(\mathrm {R} _{i}\right)}$ and ${\displaystyle \Phi _{3}\left(\mathrm {R} _{i}\right)}$ are respectively the hydrophobicity value, hydrophilicity value, and side chain mass of amino acid ${\displaystyle \mathrm {R} _{i}\,}$; while ${\displaystyle \Phi _{1}\left(\mathrm {R} _{i+1}\right)}$, ${\displaystyle \Phi _{2}\left(\mathrm {R} _{i+1}\right)}$ and ${\displaystyle \Phi _{3}\left(\mathrm {R} _{i+1}\right)}$ the corresponding values for the amino acid ${\displaystyle \mathrm {R} _{i+1}\,}$. Therefore, the total number of functions considered there is ${\displaystyle \Gamma =3\,}$. It can be seen from Eq.3 that the first 20 components, i.e. ${\displaystyle p_{1},\,p_{2},\,\cdots ,\,p_{20}}$ are associated with the conventional AA composition of protein, while the remaining components ${\displaystyle p_{20+1},\,\cdots ,\,p_{20+\lambda }}$ are the correlation factors that reflect the 1st tier, 2nd tier, ..., and the ${\displaystyle \lambda \,}$-th tier sequence order correlation patterns (Figure 1). It is through these additional ${\displaystyle \lambda \,}$ factors that some important sequence-order effects are incorporated.
其中， ${\displaystyle \Phi _{q}\left(\mathrm {R} _{i}\right)}$ 代表氨基酸 ${\displaystyle \mathrm {R} _{i}\,}$ 的第 ${\displaystyle {q}}$ 种功能属性，而 ${\displaystyle \Gamma \,}$ 则是所考虑功能的总数。举例来说，在 Chou 的原始论文中， ^[1] 、 ${\displaystyle \Phi _{1}\left(\mathrm {R} _{i}\right)}$ 、 ${\displaystyle \Phi _{2}\left(\mathrm {R} _{i}\right)}$ 和 ${\displaystyle \Phi _{3}\left(\mathrm {R} _{i}\right)}$ 分别对应氨基酸 ${\displaystyle \mathrm {R} _{i}\,}$ 的疏水性值、亲水性值及侧链质量；而 ${\displaystyle \Phi _{1}\left(\mathrm {R} _{i+1}\right)}$ 、 ${\displaystyle \Phi _{2}\left(\mathrm {R} _{i+1}\right)}$ 和 ${\displaystyle \Phi _{3}\left(\mathrm {R} _{i+1}\right)}$ 则为氨基酸 ${\displaystyle \mathrm {R} _{i+1}\,}$ 的相应属性值。因此，该研究考虑的功能总数为 ${\displaystyle \Gamma =3\,}$ 。由式 3 可见，前 20 个组分（即 ${\displaystyle p_{1},\,p_{2},\,\cdots ,\,p_{20}}$ ）与蛋白质的传统氨基酸组成相关，其余组分 ${\displaystyle p_{20+1},\,\cdots ,\,p_{20+\lambda }}$ 则反映了一级、二级直至第 ${\displaystyle \lambda \,}$ 级序列顺序相关模式（图 1）。正是通过这些额外的 ${\displaystyle \lambda \,}$ 个因子，一些关键的序列顺序效应得以纳入考量。

${\displaystyle \lambda \,}$ in Eq.3 is a parameter of integer and that choosing a different integer for ${\displaystyle \lambda \,}$ will lead to a dimension-different PseAA composition.^[5]
式 3 中的 ${\displaystyle \lambda \,}$ 是一个整数参数，选择不同的 ${\displaystyle \lambda \,}$ 将导致维度不同的伪氨基酸组成 ^[5] 。

Using Eq.6 is just one of the many modes for deriving the correlation factors in PseAAC or its components. The others, such as the physicochemical distance mode^[6] and amphiphilic pattern mode,^[7] can also be used to derive different types of PseAAC, as summarized in a 2009 review article.^[2] In 2011, the formulation of PseAAC (Eq.3) was extended to a form of the general PseAAC as given by:^[8]
使用方程 6 仅是推导 PseAAC 或其组分中相关性因子的众多模式之一。其他方法，如物理化学距离模式 ^[6] 和两亲性模式 ^[7] ，也可用于推导不同类型的 PseAAC，正如 2009 年的一篇综述文章中所总结的那样。 ^[2] 2011 年，PseAAC 的公式（方程 3）被扩展为一般 PseAAC 的形式，如下所示： ^[8]

• ${\displaystyle \mathbf {P} ={\begin{bmatrix}\psi _{1},\,\psi _{2},\,\ldots ,\,\psi _{u},\,\ldots ,\psi _{\Omega }\end{bmatrix}}^{\mathbf {T} }\,\,\,\qquad {\text{(7)}}}$

where the subscript ${\displaystyle \Omega }$ is an integer, and its value and the components ${\displaystyle \psi _{1},\,\psi _{2},\,\ldots }$ will depend on how to extract the desired information from the amino acid sequence of P in Eq.1.
其中下标 ${\displaystyle \Omega }$ 为整数，其值及分量 ${\displaystyle \psi _{1},\,\psi _{2},\,\ldots }$ 将取决于如何从方程 1 中 P 的氨基酸序列提取所需信息。

The general PseAAC can be used to reflect any desired features according to the targets of research, including those core features such as functional domain, sequential evolution, and gene ontology to improve the prediction quality for the subcellular localization of proteins.^[9][10] as well as their many other important attributes.
通用伪氨基酸组成(PseAAC)可依据研究目标反映任何所需特征，包括功能域、序列进化和基因本体等核心特征，以提升蛋白质亚细胞定位预测质量 ^{[9] [10]} ，以及它们的许多其他重要属性。

• PseAAC web server  PseAAC 网络服务器
• Pse-in-One web server  Pse-in-One 网络服务器