Mazur J, Jernigan R L
Frederick Biomedical Super Computing Laboratory, Program Resources, Inc./DYNCORP, National Cancer Institute/Frederick Cancer Research Foundation, National Institutes of Health 20892, USA.
Biophys J. 1995 Apr;68(4):1472-89. doi: 10.1016/S0006-3495(95)80320-6.
A new method, based on a space-fixed rotation axis, or local helix axis, is proposed for the calculation of the relative orientation variables for a sequence of base pairs. With this method, orientation variables are determined through the rotation of a base pair about this axis. These variables uniquely determine a set of helical variables, similar to the roll, tilt, and twist, commonly used for a description of spatial orientations of internally rigid base pairs. The proposed identification of roll and tilt with the direction cosines of the space-fixed rotation axis agrees well with their customary definitions as the openings of the angles between adjoining base pairs toward the minor groove and toward the ascending (5' to 3') backbone strand, respectively. These new variables permit a more direct physical comprehension of DNA conformations and also the behavior of self-complementary sequences. These direction cosines, together with the rotation angle about the space-fixed axis, form a set of three independent orientation variables of the bases that afford some advantages over the variously defined twist, roll, and tilt angles, either for static or average forms. An example for the static form of these variables is shown through their use to interpret crystal coordinates. An example for the average of orientation variables is based on statistical calculations. In this example, the orientation variables, together with the translational variables that describe the relative displacements of a pair of adjacent base pairs, form a canonically distributed ensemble in phase space spanned by these variables. Two sets of conformational variables are generated by using two different methods for performing rotation operations on the sequences of base pairs. The first method is based on the new single rotation about a space-fixed axis of rotation. This space-fixed axis of rotation is, in fact, the local helical axis as constructed previously by others. The second method is based on three consecutive rotations by Euler angles. Because of large flexibilities and anisotropies along various conformational variables of DNA base pairs, the two sets of generated conformational variables, based on these two different methods of performing rotation operations, lead to slightly different sets of structurally different, but energetically equivalent, spatial arrangements of the base pairs.
提出了一种基于空间固定旋转轴或局部螺旋轴的新方法，用于计算碱基对序列的相对取向变量。使用该方法，通过碱基对绕此轴的旋转来确定取向变量。这些变量唯一地确定一组螺旋变量，类似于通常用于描述内部刚性碱基对空间取向的滚动、倾斜和扭转。所提出的用空间固定旋转轴的方向余弦来识别滚动和倾斜，与它们作为相邻碱基对之间朝向小沟和朝向上升（5'至3'）主链的角度开口的惯常定义非常吻合。这些新变量允许对DNA构象以及自互补序列的行为有更直接的物理理解。这些方向余弦与绕空间固定轴的旋转角一起，形成了一组碱基的三个独立取向变量，无论是对于静态形式还是平均形式，都比各种定义的扭转、滚动和倾斜角具有一些优势。通过使用这些变量来解释晶体坐标，展示了这些变量静态形式的一个例子。取向变量平均值的一个例子基于统计计算。在这个例子中，取向变量与描述一对相邻碱基对相对位移的平移变量一起，在由这些变量跨越的相空间中形成一个正则分布的系综。通过对碱基对序列执行旋转操作使用两种不同方法生成了两组构象变量。第一种方法基于绕空间固定旋转轴的新单次旋转。实际上，这个空间固定旋转轴就是其他人先前构建的局部螺旋轴。第二种方法基于通过欧拉角的三次连续旋转。由于DNA碱基对沿各种构象变量具有很大的灵活性和各向异性，基于这两种不同旋转操作方法生成的两组构象变量，导致碱基对的结构不同但能量等效的空间排列略有不同。
