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1 生物信息学蛋白质结构预测吴凌云中国科学院数学与系统科学研究院

2 目录蛋白质的三维结构蛋白质结构预测的重要性蛋白质二级结构预测方法蛋白质三级结构预测方法研究趋势

3 蛋白质的结构 structure medicine sequence function

4 蛋白质的三维结构蛋白质三维结构 Turn or coil Alpha-helix Beta-sheet Loop and Turn

5 蛋白质的结构层次 CUHK 5

6 蛋白质二级结构 α-helix (30-35%) α- 螺旋 β-sheet / β-strand (20-25%) β- 折叠 Coil (40-50%) 无规则卷曲 Loop 环 β-turn β- 转角

7 蛋白质结构分类法 Class (<10) 结构类 Folds (<1000) 折叠子 Superfamily 超家族序列或结构相似 Family 家族序列相似性 > 25% 30% 同源 Homology

8 蛋白质结构类

9 目录蛋白质的三维结构蛋白质结构预测的重要性蛋白质二级结构预测方法蛋白质三级结构预测方法研究趋势

10 蛋白质结构与功能 Hemoglobin ( 血红蛋白 ) 运输氧气

11 蛋白质结构与功能 Porin ( 孔蛋白 ) 穿透细胞膜的运输

12 蛋白质三维结构的测定 X- 射线衍射法核磁共振法费用昂贵速度慢对某些蛋白质无法使用

13 蛋白质结构预测从蛋白质一级序列 ( 氨基酸 ) 序列预测蛋白质三维结构序列二级结构三维结构功能

14 必要性与可行性必要性 DNA 序列数据 >> 蛋白质序列数据 >> 蛋白质结构数据序列 (Swiss-Prot) 40,000 68, , , ,203 结构 (PDB) 4,045 7,000 18,838 32,434 64,500 意义重大 : 蛋白质功能预测药物设计可行性蛋白质的序列信息唯一地决定三维结构序列相似性意味着结构相似性

15 序列结构功能左边的 Bacteriocin 是 CASP-4 测试中的 T0102 试题中间的结果是 Baker 研究小组用从头预测方法 Rosetta 获得的右边是用中间的结构在数据库中进行搜索得到的最相似的蛋白质结构

16 目录蛋白质的三维结构蛋白质结构预测的重要性蛋白质二级结构预测方法蛋白质三级结构预测方法研究趋势

17 二级结构预测 Given a protein sequence a 1 a 2 a N, secondary structure prediction aims at defining the state of each amino acid a i as being either H (helix), E (extended=strand), or O (other) (Some methods have 4 states: H, E, T for turns, and O for other). The quality of secondary structure prediction is measured with a 3-state accuracy score, or Q3. Q3 is the percent of residues that match reality (X-ray structure).

18 二级结构的确定 Determine Secondary Structure positions in known protein structures using DSSP or STRIDE: Kabsch and Sander. Dictionary of Secondary Structure in Proteins: pattern recognition of hydrogen-bonded and geometrical features. Biopolymer 22: (1983) (DSSP) Frischman and Argos. Knowledge-based secondary structure assignments. Proteins, 23: (1995) (STRIDE)

19 Q3 ALHEASGPSVILFGSDVTVPPASNAEQAK hhhhhooooeeeeoooeeeooooohhhhh ohhhooooeeeeoooooeeeooohhhhhh (useful prediction) hhhhhoooohhhhooohhhooooohhhhh (terrible prediction) Amino acid sequence Actual Secondary Structure Q3=22/29=76% Q3=22/29=76% Q3 for random prediction is 33% Secondary structure assignment in real proteins is uncertain to about 10%; Therefore, a perfect prediction would have Q3=90%.

20 早期的二级结构预测方法 Chou and Fasman Chou and Fasman. Prediction of protein conformation. Biochemistry, 13: , 1974 GOR Garnier, Osguthorpe and Robson. Analysis of the accuracy and implications of simple methods for predicting the secondary structure of globular proteins. J. Mol. Biol., 120:97-120, 1978

21 Chou and Fasman Start by computing amino acids propensities to belong to a given type of secondary structure: P( i Helix) P( i Beta) P( i Turn) Pi () Pi () Pi () Propensities > 1 mean that the residue type i is likely to be found in the corresponding secondary structure type.

22 Amino Acids Propensity Amino Acid α-helix β-sheet Turn Ala Cys Leu Met Glu Gln His Lys Val Ile Phe Tyr Trp Thr Gly Ser Asp Asn Pro Arg Favors α-helix Favors β-strand Favors turn

23 Chou and Fasman Predicting helices: find nucleation site: 4 out of 6 contiguous residues with P(α)>1 extension: extend helix in both directions until a set of 4 contiguous residues has an average P(α) < 1 (breaker) if average P(α) over whole region is >1, it is predicted to be helical

24 Chou and Fasman Predicting strands: find nucleation site: 3 out of 5 contiguous residues with P(β)>1 extension: extend strand in both directions until a set of 4 contiguous residues has an average P(β) < 1 (breaker) if average P(β) over whole region is >1, it is predicted to be a strand

25 Chou and Fasman Position-specific parameters for turn: Each position has distinct amino acid preferences. f(i) f(i+1) f(i+2) f(i+3) Examples: -At position 2, Pro is highly preferred; Trp is disfavored -At position 3, Asp, Asn and Gly are preferred -At position 4, Trp, Gly and Cys preferred

26 Chou and Fasman Predicting turns: for each tetrapeptide starting at residue i, compute: P Turn (average propensity over all 4 residues) F = f(i)*f(i+1)*f(i+2)*f(i+3) if P Turn > P α and P Turn > P β and P Turn > 1 and F> tetrapeptide is considered a turn.

27 Position-dependent propensities for helix, sheet or turn is calculated for each amino acid. For each position j in the sequence, eight residues on either side are considered. j A helix propensity table contains information about propensity for residues at 17 positions when the conformation of residue j is helical. The helix propensity tables have 20 x 17 entries. Build similar tables for strands and turns. The predicted state of AA j is calculated as the sum of the position-dependent propensities of all residues around AA j. GOR can be used at : (GOR5, 2005)

28 二级结构预测方法的发展基于碱基的统计信息 Chou-Fasman, GOR 复杂统计信息 GOR3, Qian-Sejnowski 同源序列信息 PHD, PREDATOR

29 神经元的数学模型模型假设 : 每个神经元都是一个多输入单输出的信息处理单元 ; 神经元输入分兴奋性输入和抑制性输入两种类型 ; 神经元具有空间整合特性和阈值特性 ; 神经元输入与输出间有固定的时滞, 主要取决于突触延搁 ; 忽略时间整合作用和不应期 ; 神经元本身是非时变的, 即其突触时延和突触强度均为常数

30 x 1 x 1 w 1j o j w ij o j x i x n x i w nj x n (a) 多输入单输出 (b) 输入加权 x 1 w 1j x 1 w 1j w ij o j w ij o j x I x I f w nj x n w nj x n (c) 输入加权求和 (d) 输入 - 输出函数

31 神经元函数

32 神经网络的分类前向神经网络 (BP 网 ) 回馈神经网络 (Hopfield 网 ) 自组织神经网络 (SOM)

33 BP 神经网络

35 PHD: 输入 For each residue, consider a window of size 13: 13x20=260 values

36 PHD: Network 1( 序列结构 ) 13x20 values 3 values Network1 P α (i) P β (i) P c (i)

37 PHD: Network 2( 结构结构 ) For each residue, consider a window of size 17: 3 values 17x3=51 values 3 values Network2 P α (i) P β (i) P c (i) P α (i) P β (i) P c (i)

38 二级预测服务器 Available servers: Chou and Fasman: GOR: PHD: JPRED : PSIPRED: NNPREDICT:

39 目录蛋白质的三维结构蛋白质结构预测的重要性蛋白质二级结构预测方法蛋白质三级结构预测方法研究趋势

40 Lattice Models Modeling protein folding Simple exact model + approximate algorithm

41 HP Model Twenty amino acids can be divided into two classes: Hydrophobic/Non-polar (H) ( 疏水 ) Hydrophilic/Polar (P) ( 亲水 ) The contacts between H points are favorable hydrophobic amino acid hydrophilic amino acid Covalent bond H-H contact Goal: maximize the number of H-H contacts

42 HP Model Reduce computation by limiting degrees of freedom Limit α-carbon (Cα) atoms to positions on 2D or 3D lattice Protein sequence represented as path through lattice points Emphasis on forming hydrophobic core

43 Complexity A combinatorial optimization problem NP-hard problem Long range interaction + global optimization GA MC SA time consumed How Bad are NP-Complete Problems? Length=20

44 SOM Approach Existed SOM solution Motivated by SOM for TSP Incorporation of HP Information Compact lattice

45 New SOM Approach Motivation Consider a big lattice Multiple map of SOM Feasibility of solutions Equivalent to PCTSP Properly define the lattice distance TSP force + H-H force

46 New SOM Approach Approachs Initialization Learning sample set partition strategy Learning sample set reduction strategy Local search procedure

47 Numerical Results 1. Constructed HP sequences 2. HP benchmark (up to 36 amino acids)

48 Unique Optimal Folding Problem What proteins in the two dimensional HP model have unique optimal (minimum energy) folding? (Brian Hayes, 1998) Oswin Aichholzer proved that in square lattice There are closed chains of monomers with this property for all even lengths. There are open monomer chains with this property for all lengths divisible by four.

49 Square Lattice and Triangular Lattice

50 Our Results For any n = 18k (k is a positive integer), there exists an n-node (open or closed) chain with at least 3^O(n) optimal foldings all with isomorphic contact graphs of size n/2. On 2D triangular lattice, for any integer n> 19, there exist both closed and open chains of n nodes with unique optimal folding.

51 Examples of Optimal Foldings

52 三级结构预测方法 Comparative (homology) modeling ( 比较建模法 ) 通过与已知结构蛋白质的序列比对来预测 ( 序列 - 序列比对 ) 适用于 >50% 的未知结构蛋白质 Threading (fold recognition) ( 折叠识别法 ) 从已知的结构类中找到最适合的 ( 序列 - 结构比对 ) 适用于 30% 左右的未知结构蛋白质 Ab initio / de novo methods ( 从头预测法 ) 不使用已知的结构信息, 仅仅利用序列信息来预测适用于全新结构的蛋白质

53 RMSD 蛋白质的空间坐标表示定义氨基酸 ( 原子 ) 对应关系 : 计算 RMSD:

54 比较建模法原理序列相似性 >25% 的蛋白质具有相似的结构基本步骤将目标序列和模板序列进行比对 ( 关键步骤 ) 构造主干 (backbone) 的三维模型用二级结构预测和手工预测等方法来填补一些空隙构造环 (loops) 和卷曲 (coils) 安装侧链搜索侧链数据库, 使用分子动力学优化 / 检验模型关键方法序列 - 序列比对

55 折叠识别法原理蛋白质具有很少的折叠类型 (<1000) 基本步骤将目标蛋白质序列与已知的折叠进行比对将目标序列安装到选择的模板结构上对模型进行优化调整检验模型的合理性关键方法序列 - 结构比对

56 折叠识别法

57 折叠识别法动态规划人工神经网络分支定界法线性规划 Monte Carlo 方法

58 从头预测法理论基础蛋白质的天然构象是热力学最稳定构象也是能量最低构象能量函数通过原子间作用力计算出的热力学能量精确, 但难以计算伪能量函数根据已知的三维结构知识得到的势能函数常见的结构低能量不常见的结构高能量极罕见的结构极高能量

59 原子间作用力

60 蛋白质的势能

61 蛋白质的势能

62 能量函数

63 基于能量最小化的从头预测法基本步骤选择蛋白质能量函数模型选择三维结构的表示方法选择三维结构的评价函数选择寻找最优结构的优化方法关键问题大规模非线性规划大量的局部极小点在计算时间和准确度之间寻找平衡

64 非线性规划最速下降法牛顿法共轭梯度法全局优化方法遗传算法分解 - 结合法离散化方法最优化方法

65 Monte Carlo 方法 Metropolis 算法基本步骤选择一个初始结构 A 随机产生一个新的结构 B 如果 EB < E, A 接受 B 否则产生一个 [0,1] 之间的随机数 r ( EB EA)/ KT 如果 r < e, 接受 B, 否则拒绝重复以上步骤温度 T 的修改模拟退火方法

66 分子动力学 ( 动力系统 ) 方法对蛋白质中原子间的作用力进行建模用动力学方程跟踪蛋白质折叠时每个原子的位置求解这些方程的解析解是极其困难的用离散动力系统的方法来确定数值解问题模拟蛋白质折叠过程是非常消耗时间的模拟 10-9 秒的蛋白质折叠过程大约需要一天时间蛋白质的实际折叠时间大约在 10-4 秒的数量级或者更多需要超级计算机

67 预测结果 E. Eskow, B. Bader, R. Byrd, et al. An optimization approach to the problem of protein structure prediction. Mathematical Programming, Vol. 101, No. 3, pp , 2004.

68 预测结果 E. Eskow, B. Bader, R. Byrd, et al. An optimization approach to the problem of protein structure prediction. Mathematical Programming, Vol. 101, No. 3, pp , 2004.

69 目录蛋白质的三维结构蛋白质结构预测的重要性蛋白质二级结构预测方法蛋白质三级结构预测方法研究趋势

70 新的趋势混合预测方法在比较建模法和折叠识别法中使用从头预测法来预测部分难以找到模板的片断在从头预测法中使用二级结构预测的结果和其他已知结构信息辅助建模 Meta-predictor 使用多个预测方法对收集的结果进行综合比较和分析改进收集的结果

71 ROSETTA at CASP (David Baker) Homology modeling Ab initio prediction Simultaneous modeling of the target and 2 homologs Secondary structure prediction Fragment based approach to generate decoys Most successful Method at CASP, for fold recognition and ab initio prediction Select 5 decoys For prediction Rosetta predictions in CASP5: Successes, failures, and prospect for complete automation. Baker et all, Proteins, 53: (2003)

72 参考文献 1. K. Ginalski, N. V. Grishin, A. Godzik and L. Rychlewski. Practical lessons from protein structure prediction. Nucleic Acids Research, Vol. 33, No. 6, pp , Jinbo Xu, Ming Li, Dongsup Kim and Ying Xu. Raptor: optimal protein threading by linear programming. J. of Bioinformatics and Computational Biology, Vol. 1, No. 1, pp , E. Eskow, B. Bader, R. Byrd, et al. An optimization approach to the problem of protein structure prediction. Mathematical Programming, Vol. 101, No. 3, pp , 2004.

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i i ii 1 2 3 4 % N) 5 50.0 AMINO ACID #64 [modified by Administrator] IntAmp_1 nc 40.0 30.0 20.0 10.0 0.0-10.0 1 - ala - 10.483 2 - thr - 11.107 3 - gly - 11.872 4 - val - 13.458 5 - ser - 14.903 6 - pro