基于盒维数原理计算蛋白质的分形维数汇总

2010年第68卷

化学学报

V ol. 68, 2010 第11期, 1143~1147

ACTA CHIMICA SINICA

No. 11, 1143~1147

* E-mail: qiwei@

Received September 4, 2009; revised December 2, 2009; accepted January 25, 2010.

国家自然科学基金(No. 20976125、863(No. 2008AA10Z318、教育部新世纪优秀人才(2008和科学技术研究重点(No. 108031资助项目.

·研究简报·

基于盒维数原理计算蛋白质的分形维数

彭鑫a 张雨薇a 齐崴*,a ,b 苏荣欣a ,b

吴少敏a ,b 何志敏a ,b

(a 天津大学化工学院化学工程研究所天津 300072 (b 天津大学化学工程联合国家重点实验室天津 300072

摘要蛋白质表面的粗糙性和内部结构的不规则性具有明显的分形特征. 依据直观的盒维数原理对PDB 库中收录的典型酶蛋白、球蛋白和膜蛋白共72种蛋白质的分形维数进行了简洁地模拟计算. 数据表明: 蛋白质的分形维数(D f 介于1~3之间; 分形方法可定量描述蛋白质分子结构的复杂性, 即D f 值越大, 蛋白结构越复杂; D f 与残基数的不同步性证明蛋白质分子并不是简单的肽段堆积, 而是存在特定的空间结构; 同功能酶蛋白具有相近的D f 值表明分维是区别于各种宏观参量而对蛋白质

微观结构与功能进行表征的有用工具. 关键词分形; 蛋白质; 盒维数; 模拟; 计算; 结构

Fractal Analysis of Proteins Based on Box Dimension

Peng, Xin a Zhang, Yuwei a Qi, Wei *,a ,b Su, Rongxin a ,b

Wu, Shaomin a ,b He, Zhimin a ,b

(a Chemical Engineering Research Center , School of Chemical Engineering and Technology , Tianjin 300072

(b State Key Laboratory of Chemical Engineering , Tianjin University , Tianjin 300072

Abstract Proteins with rough surfaces and irregular structures are characteristic of fractal nature. Fractal dimensions of a set of 72 proteins including typical enzyme, globulin and membrane protein selected from PDB database were calculated based on the principle of intuitive box dimension. The results showed that fractal dimensions of proteins were between 1 and 3, and the more complicated structure a protein has, the larger value of fractal dimension the protein is, so the fractal theory could be used to quantitatively describe the complexity of proteins structure. The discordance between fractal dimensions and the number of residues demonstrated that proteins not only were composed of peptide chains, but also had the specifically spatial structure. The close D f values of the enzymes with similar function indicated that D f , differed from a variety of macro-parameters, was a useful tool for the characterization of micro-structure and function of proteins. Keywords fractal; protein; box dimension; simulation; calculation; structure

蛋白质是生物体内各种生命活动的主要参与者. 为体现不同的生理功能, 蛋白质的空间结构极为独特复杂, 并在一定标度范围内表现出明显的分形(Fractal特征

[1~3], 这是由其自身组成规律与结构特点所决定的, 例如: 从蛋白质的链结构分析, 其链段是一条弯曲的折

线, 而弯曲的形态不随观测尺度的变化而改变, 这是一种统计意义上的相似性或称标度不变性, 属分形分析研究的对象; 又如: 从蛋白质空间立体结构分析, 其分子内具有各种不规则的“洞穴”、“缝隙”和“折皱”, 进一步观测发现这些微观结构内部也是凹凸不平、极不规

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化学学报 V ol. 68, 2010

则的, 即蛋白质具有极强的局部与整体相似性, 这是明显的分形特征, 属分形理论研究的范畴. 同时计算科学的飞速发展, 为分形维数的模拟计算提供了可能, 部分学者[1~3]通过蛋白质分子链长L(M与测量残基数M 之间的幂函数关系1(D L M M ∝f -(D f 为链分形维数, 求得许多蛋白质分子的分形维数, 结果大多介于1~3之间