# Workshops

## From trajectories to reaction coordinates: making sense of molecular simulation data

### Organisers

- Christoph Dellago
*(University of Vienna, Austria)* - Peter Bolhuis
*(University of Amsterdam, The Netherlands)* - Gerhard Hummer
*(Max Planck Institute of Biophysics, Germany)*

### Supports

CECAM

ESI - Erwin Schrödinger Institute

### Description

The goal of this workshop is to define and advance the state of the art in constructing reliable and meaningful models from complex data, and in using such models to gain mechanistic insight as a guide for applications and further study.

Having appropriate reaction coordinates is key for the efficient sampling both in space and in time. Knowledge of the relevant degrees of freedom for transition between metastable states helps improve the efficiency in free energy calculations. Exploring the system along these most slowly relaxing degrees of freedom minimizes the hysteresis effects associated with unresolved slow degrees of freedom [Rosta 2009]. One can also use the reaction coordinates to increase the efficiency of the dynamic sampling of rare events in methods such as forward-flux sampling [Allen 2009] or string methods [E 2005], where the appropriate choice of coordinates is critical. Even for methods that do not rely on prior knowledge of reaction coordinates such as transition path sampling [Dellago 2002] and transition-interface sampling [van Erp 2003], improved coordinates are beneficial.

The identification of reliable order parameters and reaction coordinates also constitutes a key step in the construction of mechanistic models. They help define both the state space in a coarse-grained manner more accessible to humans (e.g., reducing the protein folding problem to transitions between just two states), and the dynamics in state space. By contrast, if one has only poor order parameters and reaction coordinates, the resulting models will not accurately capture the populations and their dynamics, since the metastable states will be mixed to together and the transitions between them poorly resolved.

A key element of the workshop will also be the interpretation and use of reaction coordinate information in areas such as control. An emerging practical application is in the design of novel pharmaceuticals that no longer aim to inhibit enzyme binding and function directly, in part to avoid cross-reactivity. Instead, often-critical allosteric couplings are targeted that relay the effects of distal binding and conformational dynamics [D’Abramo 2012]. Understanding the relevant reaction coordinates of associated conformational changes should aid in rational design approaches for allosteric inhibitors.

We expect much progress from adaptively optimized reaction coordinates in simulation applications such as targeted molecular dynamics [Ovchinnikov 2012] and ratchet-and-pawl simulations [Marchi 1999], where large-scale conformational changes are induced through time-dependent biases. Similarly, the efficient use of information about slow degrees of freedom in free energy calculations will be a major theme, with relevance in all areas of molecular simulation, from simple physical systems to biomolecules and complex materials. Importantly, the exploration of free energy surfaces and the sampling of rare events should benefit greatly from having good coordinates. How the expected gains can be realized will be an important theme of the workshop.

As much work has been done the development and use of Markov state models to describe complex processes, we expect a lively discussion on whether and when one should try identifying a single (possibly complicated) reaction coordinate, or try to construct an MSM using many metastable states. The development and application of transition path theory [Vanden-Eijnden 2006] plays a key role in this discussion.

Another important topic that will be discussed during the workshop is the use of reaction coordinates for dynamical coarse-graining. Since reaction coordinates (often) constitute the slow variables of a process, a natural coarse-graining of the dynamics would be to replace the many-particle system by a diffusive (overdamped Langevin) process on the reaction coordinate. When and how this procedure is allowed is hotly debated. Several novel developments in this area address these issues [Peters2013, Berezhkovskii 2013, Lu2014], and hence we expect a lively discussion about this topic.

With reaction coordinates being at the center of a wide range of problems, it will be important to pool the cumulative knowledge of diverse but related fields. Applied mathematicians interested in areas such as transition path theory, computer scientists in areas such as machine learning, physicists interested in dynamical systems and phase transitions, chemists working on reaction mechanisms, and biologists elucidating the function of molecules and cellular networks are representative of the many fields having contributed to and benefiting from an improved understanding of reaction coordinates. While the focus is mainly on theory and simulation, the discussion will also benefit from exchange with experimentalists. As the time and space resolution of experiments reaches the single-particle level (atoms, molecules, or colloids), experimentalist face the same problems as computer simulators in gaining insight from their data. A main goal of the meeting is to enhance communication in the community, with the hope of developing new ideas and computational approaches.

### References

[Allen 2009] R. J. Allen, C. Valeriani and P. R. ten Wolde, Forward flux sampling for rare event simulations, J. Phys.: Condens. Matter 21, 463102 (2009).

[Best 2005] R. B. Best and G. Hummer, Reaction coordinates and rates from transition paths, Proc. Natl. Acad. Sci. USA 102, 6732-6737 (2005).

[Best 2013] R. B. Best, G. Hummer, W. A. Eaton, Native contacts determine protein folding mechanisms in atomistic simulations, Proc. Natl. Acad. Sci. USA 110, 17874-17879 (2013).

[Buchete 2008] N.V. Buchete, G. Hummer, Coarse master equations for peptide folding dynamics, J. Phys. Chem. B 112, 6057-6069 (2008).

[Berezhkovskii 2009] A. Berezhkovskii, G. Hummer, and A. Szabo, Reactive flux and folding pathways in network models of coarse-grained protein dynamics, J. Chem Phys. 130, 205102 (2009).

[Berezhkovskii 2013] A. M. Berezhkovskii, A. Szabo Diffusion along the Splitting/ Commitment Probability Reaction CoordinateJ. Phys. Chem. B 117,13115-13119 (2013)

[Chipot 2007] C. Chipot and A. Pohorille (Eds.), Free Energy Calculations, Springer (2007)

[Chodera 2014] J. D. Chodera, and F. Noé, Markov state models of biomolecular conformational dynamics, Curr. Opin. Struct. Biol., 25 . 135-144 (2014).

[D. Abramo 2012] M. D Abramo, O. Rabal, J. Oyarzabal, and F. Gervasio, Conformational Selection versus Induced Fit in Kinases: The Case of PI3K-γ, Angew. Chem. Int. Ed. 51, 642-646 (2012).

[Dellago 2002] C. Dellago, Peter G. Bolhuis, Phillip L. Geissler, Transition Path Sampling, Adv. Chem. Phys. 123, 1 (2002).

[Dellago 2008] C. Dellago and P. G. Bolhuis, "Transition Path Sampling and other Advanced Simulation Techniques for Rare Events", pp. 167-233, Adv. Poly. Sci. 221, Springer (2008).

[E 2005] W. E, W. Ren, and E. Vanden-Eijnden, Finite temperature string method for the study of rare events, J. Phys. Chem. B: 109, 6688-6693(2005).

[Jungblut 2011] S. Jungblut and C. Dellago, Heterogeneous crystallization on tiny clusters, Europhys. Lett. 96, 56006 (2011).

[Jungblut 2013] S. Jungblut, A. Singraber, and C. Dellago, Optimizing reaction coordinates for crystallization by tuning the crystallinity definition, Mol. Phys. 111, 3527-3533 (2013).

[Krivov 2013] S. V. Krivov, On reaction coordinate optimality, J. Chem. Theo. Comput. 9 135-146 (2013).

[Lechner 2010] W. Lechner, J. Rogal, J. Juraszek, B. Ensing and P. G. Bolhuis, Non-linear reaction coordinate analysis in the reweighted path ensemble, J. Chem. Phys. 133, 174110 (2010).

[Lechner 2011] W. Lechner, C. Dellago and P. G. Bolhuis, Role of the prestructured surface cloud in crystal nucleation, Phys. Rev. Lett. 106, 085701 (2011).

[Lu2014] J. Lu and E. Vanden-Eijnden, Exact dynamical coarse-graining without time-scale separation ArXiv:1404.4729 (2014).

[Ma 2005] A. Ma and A.R. Dinner, An automatic method for identifying reaction coordinates in complex systems. J. Phys. Chem B 109, 6769-6779 (2005).

[Marchi 1999] M. Marchi and P. Ballone, Adiabatic bias molecular dynamics: A method to navigate the conformational space of complex molecular systems, J. Chem. Phys., 110, 3697 (1999).

[Onsager 1938] L. Onsager, Initial Recombination of Ions, Phys. Rev. 54, 554 (1938).

[Ovchinnikov 2012] V. Ovchinnikov, M. Karplus, Analysis and elimination of a bias in targeted molecular dynamics simulations of conformational transitions: application fo calmodulin, J. Phys. Chem. B 116, 8584-603 (2012).

[Peters 2006] B. Peters, B. L. Trout, "Obtaining reaction coordinates by likelihood maximization," J. Chem. Phys. 125, 054108 (2006).

[Peters 2013] Peters, B, P.G. Bolhuis, R.G. Mullen, J-E. Shea Reaction coordinates, one-dimensional Smoluchowski equations, and a test for dynamical self-consistency," J. Chem. Phys 138, 054106 (2013).

[Rohrdanz 2013] M. A. Rohrdanz, W. Zheng, M. Maggioni, C. Clementi, Determination of reaction coordinates via locally scaled diffusion map, J. Chem. Phys. 134, 124116 (2011)

[Rosta 2009] E. Rosta, H.L. Woodcock, B.R. Brooks, G. Hummer, Artificial reaction coordinate tunneling in free energy calculations: the catalytic reaction of RNase H, J. Comput. Chem. 30, 1634-1641 (2009).

[Tribello 2011] G. A. Tribello, M. Ceriotti and M. Parrinello, Using sketch-map coordinates to analyze and bias molecular dynamics simulations, Proc. Natl. Acad. Sci. USA 109, 5196 (2012).

[Tribello 2012] G. A. Tribello, J. Cuny, H. Eshet, M. Parrinello, Exploring the free energy surfaces of clusters using reconnaissance metadynamics, J. Chem. Phys. 135, 114109 (2011).

[Vanden-Eijnden 2006] E. Vanden-Eijnden, Transition Path Theory, Springer Lecture Notes in Physics 703, 453-493 (2006).

[van Erp 2003] T. S. van Erp, D. Moroni and P. G. Bolhuis, "A Novel Path Sampling Method for the Calculation of Rate Constants", J. Chem. Phys. 118, 7762-7774 (2003).