Euclidean sections of protein conformation space and their implications in dimensionality reduction.
Euclidean sections of protein conformation space and their implications in dimensionality reduction.
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DOI：
10.1002/prot.24622
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发表时间：
2014-10
影响因子：
2.9
通讯作者：
Huo, Shuanghong
中科院分区：
文献类型：
--
作者：
Duan, Mojie;Li, Minghai;Han, Li;Huo, Shuanghong
关键词：
构象约化被广泛应用于寻找蛋白质构象变化的内在反应坐标。我们发现使用成对均方根偏差作为局部距离度量的降维方法面临挑战。我们使用Isomap作为例子来说明这个问题。我们认为，降维方法存在一个隐含的假设，旨在保留对象之间的几何关系：原始空间和降维空间都具有相同类型的几何，例如欧几里得几何与欧几里得几何或球面几何与球面几何。当蛋白质自由能景观映射到二维平面或三维空间时，约化的空间是欧氏空间，因此原始空间也应该是欧氏空间。对于具有N个原子的蛋白质，其构象空间是3 N维欧几里得空间R3 N的子集。利用刚体运动的等价关系，将蛋白质构象空间形式化地定义为R3 N的商空间。商空间是否是欧几里得空间取决于它是如何被参数化的。当采用成对均方根偏差作为局部距离度量时，隐式表示用于蛋白质构象空间，导致与欧几里得集没有直接对应。我们已经证明，蛋白质构象空间的显式欧几里得表示和与之相关的局部距离度量提高了四肽和β-发夹系统的降维质量。
Dimensionality reduction is widely used in searching for the intrinsic reaction coordinates for protein conformational changes. We find the dimensionality–reduction methods using the pairwise root–mean–square deviation as the local distance metric face a challenge. We use Isomap as an example to illustrate the problem. We believe that there is an implied assumption for the dimensionality–reduction approaches that aim to preserve the geometric relations between the objects: both the original space and the reduced space have the same kind of geometry, such as Euclidean geometry vs. Euclidean geometry or spherical geometry vs. spherical geometry. When the protein free energy landscape is mapped onto a 2D plane or 3D space, the reduced space is Euclidean, thus the original space should also be Euclidean. For a protein with N atoms, its conformation space is a subset of the 3N-dimensional Euclidean space R3N. We formally define the protein conformation space as the quotient space of R3N by the equivalence relation of rigid motions. Whether the quotient space is Euclidean or not depends on how it is parameterized. When the pairwise root–mean–square deviation is employed as the local distance metric, implicit representations are used for the protein conformation space, leading to no direct correspondence to a Euclidean set. We have demonstrated that an explicit Euclidean-based representation of protein conformation space and the local distance metric associated to it improve the quality of dimensionality reduction in the tetra-peptide and β–hairpin systems.
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DOI：
10.1002/prot.340110305
发表时间：
1991-01-01
期刊：
PROTEINS-STRUCTURE FUNCTION AND GENETICS
影响因子：
--
作者：
ICHIYE, T;KARPLUS, M
通讯作者：
KARPLUS, M
影响因子：
4.4
作者：
Becker, OM;Karplus, M
通讯作者：
Karplus, M
DOI：
10.1137/0109047
发表时间：
1961-01-01
期刊：
JOURNAL OF THE SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS
影响因子：
--
作者：
GOMORY, RE;HU, TC
通讯作者：
HU, TC
影响因子：
3.7
作者：
Kentsis A;Gindin T;Mezei M;Osman R
通讯作者：
Osman R
影响因子：
3.3
作者：
Li, Da-Wei;Han, Li;Huo, Shuanghong
通讯作者：
Huo, Shuanghong