Methods to calculate reaction paths in chemical and biochemical systems

Main Research line: Protein dynamics and enzyme catalysis
Main Researcher: Ramon Crehuet

The study of chemical reactions requires the use of methods to describe reaction paths and characterize energy barriers. Chemical reactions are rare events, so that running molecular dynamics and expecting to see a chemical reaction is a very inefficient approach.

In small molecules, Transition State Theory and reaction paths give an accurate picture of reaction mechanisms. In biomolecules or other large systems, the degrees of freedom increase and the number of simultaneous similar pathways makes their characterization impossible. In this situation, free energy calculations sample all degrees of freedom orthogonal to the selected reaction coordinate.

The choice of a reaction coordinate is not trivial for complex reaction mechanisms. Methods that only rely on the structures of reactants or products become a better alternative. They are computationally efficient because they do not require the second derivative matrix of the energy (the Hessian) which is very expensive to calculate for such large systems. These methods can produce both free energy profile and potential energy profile, albeit at a different computational cost.

What we do
In collaboration with Josep Maria Bofill we have implemented several methods to locate transition states and characterize reaction paths. The application of the Hamilton-Jacobi equation resulted in a tool to determine reactions paths.[1] We have also explored the use of reduced gradients to characterize paths. [2,3]

The study of biomolecular systems prompted us to implement and improve chain-of-state methods in an QM/MM environment.[4] We also explored Transition Path Sampling techniques –which do not require any definition of a reaction coordinate—to study enzyme mechsnisms.[5]

We have implemented a method to obtain free energies from a chain-of-state profile. This method was developed by the Roux lab, and we did its first applications to enzymes. This method will allow us to explore enzyme mechanisms that cannot be described by a simple combination of reaction coordinates.[6]

Software
In this line of research, we mainly use pDynamo and code our algorithms with Python and Fortran.

Swarms of trajectories direct the evolution of the path and produce free energy profiles for reactions described by a set of collective coordinates

Swarms of trajectories direct the evolution of the path and produce free energy profiles for reactions described by a set of collective coordinates

Related publications

Crehuet, R.; Bofill, J. M, The Reaction Path Intrinsic Reaction Coordinate Method and the Hamilton-Jacobi Theory, J. Phys. Chem. B, 2005, 122 (23), 234105

Crehuet, R.; Bofill, J. M.; Anglada, J. M, A New Look at the Reduced-Gradient-Following Path., Theor. Chem. Accounts Theory, Comput. Model. (Theoretica Chim. Acta), 2002, 107 (3), 130–139

Anglada, J. M.; Besalú, E.; Bofill, J. M.; Crehuet, R, On the Quadratic Reaction Path Evaluated in a Reduced Potential Energy Surface Model and the Problem to Locate Transition States, J. Comput. Chem, 2001, 22 (4), 387–406

Crehuet, R.; Field, M. J, A Temperature-Dependent Nudged-Elastic-Band Algorithm, J. Chem. Phys, 2003, 118 (21), 9563–9571

Crehuet, R.; Field, M. J, A Transition Path Sampling Study of the Reaction Catalyzed by the Enzyme Chorismate Mutase, J. Phys. Chem. B, 2007, 111 (20), 5708–5718

Sanchez-Martinez, M.; Field, M.; Crehuet, R, Enzymatic Minimum Free Energy Path Calculations Using Swarms of Trajectories, J. Phys. Chem. B, 2015, 119 (3), 1103–1113

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