Transition state searching for complex biomolecules: Algorithms and machine learning

Yang Jian-Yu; Xi Kun; Zhu Li-Zhe

doi:10.7498/aps.72.20231319

Abstract

Transition state is a key concept for chemists to understand and fine-tune the conformational changes of large biomolecules. Due to its short residence time, it is difficult to capture a transition state via experimental techniques. Characterizing transition states for a conformational change therefore is only achievable via physics-driven molecular dynamics simulations. However, unlike chemical reactions which involve only a small number of atoms, conformational changes of biomolecules depend on numerous atoms and therefore the number of their coordinates in our 3D space. The searching for their transition states will inevitably encounter the curse of dimensionality, i.e. the reaction coordinate problem, which invokes the invention of various algorithms for solution. Recent years, new machine learning techniques and the incorporation of some of them into the transition state searching methods emerged. Here, we first review the design principle of representative transition state searching algorithms, including the collective-variable (CV)-dependent gentlest ascent dynamics, finite temperature string, fast tomographic, travelling-salesman based automated path searching, and the CV-independent transition path sampling. Then, we focus on the new version of TPS that incorporates reinforcement learning for efficient sampling, and we also clarify the suitable situation for its application. Finally, we propose a new paradigm for transition state searching, a new dimensionality reduction technique that preserves transition state information and combines gentlest ascent dynamics.

Keywords:

Authors and contacts

Warshel Institute for Computational Biology, School of Medicine, The Chinese University of Hong Kong, Shenzhen 518172, China

Corresponding author: Zhu Li-Zhe, zhulizhe@cuhk.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 31971179) and the Science Technology and Innovation Commission of Shenzhen Municipality, China (Grant Nos. JCYJ20200109150003938, RCYX20200714114645019).

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References

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图 1 (a)依赖集合变量的过渡态搜索示意图, 需由生物分子(以丙戊酸二肽为例)体系所在的高维相空间(phase space)选取少量集合变量CV强行“定向降维”, 后在此低维CV空间利用非路径类方法或路径方法, 找到过渡态(Transition State), 并给出微观机制解释(mechanism interpretation); (b)非路径类的GAD算法原理示意图; (c), (d)两类路径类搜索算法原理示意图

Figure 1. (a) Illustration of the flow-chart of the collective variables (CVs) based transition state searching. A low dimensional space must be constructed with the CVs, which are arbitrary a priori guess about the mechanism. The transition state(s) is then determined by either the non-path or path methods. (b) The non-path method GAD. Path methods of (c) finite temperature string and (d) fast tomographic.

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图 2 (a) PCV构建^[120]和TAPS Method^{[91–95,121]}算法原理示意图; (b)基于伞形采样方法得到的TAPS算法确定的MEK1由Loop-Out到达Loop-In转变过程最小自由能路径(MFEP)的自由能图景及相应的微观转变机制^[92]

Figure 2. (a) Illustration for the construction of PCV and the flow-chart of the TAPS method; (b) TAPS revealed the free energy landscape and the transition states for the transition from the Loop-Out state of MEK1 to its Loop-In state^[92].

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图 3 路径采样算法的基本原理示意图　(a)路径采样中生成新相空间路径的shooting move; (b)传统过渡路径采样(左侧)的随机蒙特卡罗采样与过渡态分析原理^[98–101], 融合强化学习的路径采样(右侧)在学习过程中不断促进采样起始点选择向过渡态集中^[113]

Figure 3. Schematics of path sampling methods. (a) Shooting move: select a phase space point on the current path, make a small perturbation to this point (redraw random initial velocities) and perform a set of simulations. (b) Path sampling is built upon the committor probability $ {p}_{{\mathrm{B}}} $. The traditional transition path sampling (left)^[98–101] selects shooting points randomly and uses Monte Carlo for sampling; the transition state is characterized through post-analysis: choosing the CVs with the highest and narrowest distribution of P(TP|CV); the new reinforcement path sampling (right)^[113] chooses shooting points adaptively and directly learns the committor probability $ {p}_{{\mathrm{B}}} $ with maximized P(TP|x). Symbolic regression of $ {p}_{{\mathrm{B}}} $ is used for mechanism interpretation.

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图 4 物理化学家需要怎样的降维算法　(a)现有降维算法范式不保留过渡态信息, 不利于机制解析; (b)可能的替代范式, 基于生成模型研发可保留过渡态信息的可逆降维算法, 并与低维空间搜索过渡态的GAD联用

Figure 4. Requirements on dimensionality reduction algorithms by physical chemists. (a) Current paradigm for dimensionality reduction and the main difficulties for the transition state searching. (b) Proposed alternative paradigm for transition state searching: combine dimensionality reduction that preserves transition state information with GAD.

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表 1 主要过渡态搜索算法的总结分类

Table 1. Classification of the algorithms for transition state searching.

过渡态搜索算法分类		代表性算法	参考文献	备注
传统方法	依赖CV	Gentlest ascent dynamics (GAD)	[79—81]	非路径方法
	依赖CV	Finite temperature string	[82—87]	路径方法
	预设低维	Fast tomographic	[88—90]
	空间搜索	基于旅行商的路径搜索 TAPS	[91—95]
融合AI	不依赖CV 高维空间搜索	Transition path sampling	[98—101]
	不依赖CV 高维空间搜索	Reinforcement path sampling	[113]
	保留过渡态信息的降维低维空间搜索	融合生成模型及GAD 的过渡态搜索(待研发)	无	非路径方法

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[2]	Evenäs J, Malmendal A, Thulin E, Carlstrӧm G, Forsén S 1998 Biochemistry 37 13744 Google Scholar
[3]	Hanson J A, Duderstadt K, Watkins L P, Bhattacharyya S, Brokaw J B, Chu J W, Yang H 2007 Proc. Natl. Acad. Sci. USA 104 18055 Google Scholar
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[5]	Huang C, Kalodimos C G 2017 Annu. Rev. Biophys. 46 317 Google Scholar
[6]	Weissenberger G, Henderikx R J M, Peters P J 2021 Nat. Methods 18 463 Google Scholar
[7]	Clegg R M 1995 Curr. Opin. Biotechnol. 6 103 Google Scholar
[8]	Karplus M, McCammon J A 2002 Nat. Struct. Biol. 9 646 Google Scholar
[9]	Hollingsworth S A, Dror R O 2018 Neuron 99 1129 Google Scholar
[10]	Bernèche S, Roux B 2001 Nature 414 73 Google Scholar
[11]	Khafizov K, Perez C, Koshy C, Quick M, Fendler K, Ziegler C, Forrest L R 2012 Proc. Natl. Acad. Sci. USA 109 E3035 Google Scholar
[12]	Li J, Shaikh S A, Enkavi G, Wen P C, Huang Z, Tajkhorshid E 2013 Proc. Natl. Acad. Sci. USA 110 7696 Google Scholar
[13]	Dror, R O, Green H F, Valant C, Borhani D W, Valcourt J R, Pan A C, Arlow D H, Canals M, Lane J R, Rahmani R, Baell J B, Sexton P M, Christopoulos A, Shaw D E 2013 Nature 503 295 Google Scholar
[14]	Wacker D, Stevens R C, Roth B L 2017 a Cell 170 414 Google Scholar
[15]	Wacker D, Wang S, McCorvy J D, Betz R M, Venkatakrishnan A J, Levit A, Lansu K, Schools Z L, Che T, Nichols D E, Dror R O, Roth B L 2017 Cell 168 377 Google Scholar
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[20]	Groban E S, Narayanan A, Jacobson M P 2006 PLoS Comput. Biol. 2 e32 Google Scholar
[21]	Liu Y, Ke M, Gong H 2015 Biophys. J. 109 542 Google Scholar
[22]	Delemotte L, Tarek M, Klein M L, Amaral C, Treptow W 2011 Proc. Natl. Acad. Sci. USA 108 6109 Google Scholar
[23]	Lindorff-Larsen K, Piana S, Dror R O, Shaw D E 2011 Science 334 517 Google Scholar
[24]	Snow C D, Nguyen H, Pande V S, Gruebele M 2002 Nature 420 102 Google Scholar
[25]	Dror R O, Arlow D H, Maragakis P, Mildorf T J, Pan A C, Xu H, Borhani D W, Shaw D E 2011 Proc. Natl. Acad. Sci. USA 108 18684 Google Scholar
[26]	Dror R O, Pan A C, Arlow D H, Borhani D W, Maragakis P, Shan Y, Xu H, Shaw D E 2011 Proc. Natl. Acad. Sci. USA 108 13118 Google Scholar
[27]	Gu Y, Shrivastava I H, Amara S G, Bahar I 2009 Proc. Natl. Acad. Sci. USA 106 2589 Google Scholar
[28]	Latorraca N R, Fastman N M, Venkatakrishnan A J, Frommer W B, Dror R O, Feng L 2017 Cell 169 96 Google Scholar
[29]	Stelzl L S, Fowler P W, Sansom M S, Beckstein O 2014 J. Mol. Biol. 426 735 Google Scholar
[30]	Buch I, Giorgino T, De Fabritiis G 2011 Proc. Natl. Acad. Sci. USA 108 10184 Google Scholar
[31]	Liang R, Swanson J M J, Madsen J J, Hong M, DeGrado W F, Voth G A 2016 Proc. Natl. Acad. Sci. USA 113 E6955 Google Scholar
[32]	Suomivuori C M, Gamiz-Hernandez A P, Sundholm D, Kaila V R I 2017 Proc. Natl. Acad. Sci. USA 114 7043 Google Scholar
[33]	Tajkhorshid E, Nollert P, Jensen M Ø, Miercke L J W, O’Connell J, Stroud R M, Schulten K 2002 Science 296 525 Google Scholar
[34]	Watanabe A, Choe S, Chaptal V, Rosenberg J M, Wright E M, Grabe M, Abramson J 2010 Nature 468 988 Google Scholar
[35]	Dedmon M M, Lindorff-Larsen K, Christodoulou J, Vendruscolo M, Dobson C M 2005 J. Am. Chem. Soc. 127 476 Google Scholar
[36]	Nguyen H D, Hall C K 2004 Proc. Natl. Acad. Sci. USA 101 16180 Google Scholar
[37]	Levitt M 1983 J. Mol. Biol. 168 595 Google Scholar
[38]	Sugita Y, Okamoto Y 1999 Chem. Phys. Lett. 314 141 Google Scholar
[39]	Rhee Y M, Pande V S 2003 Biophys. J. 84 775 Google Scholar
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