Albrecht Goez and Johannes Neugebauer

Contributed by Christoph Jacob

Fragment-based methods nowadays make it possible to perform quantum-chemical calculations for rather large biomolecules, for instance light-harvesting protein systems [1]. Such methods are based on the idea of splitting a protein into smaller fragments, such as its constituting amino acids. This leads to a linear scaling of the computational effort with the size of protein. Popular examples of fragment-based electronic structure methods include the fragment molecular orbital (FMO) method [2] and a generalization of the frozen-density embedding scheme (3-FDE) [3].

In a recent article in JCTC, Goez and Neugebauer from the University of Münster (Germany) address an additional bottleneck that appears in such calculations. Usually, it is necessary to include a solvent environment in the calculations, in particular if charged amino-acid side chains are present. The simplest way of doing so are continuum solvation models, such as COSMO or PCM. These models represent the solvent in terms of apparent charges on the surface of a cavity enclosing the protein. However, for proteins the number of apparent surfaces charges becomes rather large - for ubiquitin, a protein with only 78 amino acids, already 20,000 charges are needed. Updating these apparent surface charges involves solving a linear system of equations of size 20,000 x 20,000. When doing so in each SCF cycle for each of the fragments, the continuum solvation model will become the bottleneck of the calculation.

To solve this problem, Goez and Neugebauer developed a local variant of the COSMO model (LocCOSMO). In each fragment calculation, they update only those apparent surface charges that are close to this fragment. This reduces the computational effort significantly, but because every fragment is updated at some point it will eventually result in the same final result. This is demonstrated by the authors for several test cases. They can reduce the computational time required for a 3-FDE calculation of ubiquitin in a solvent environment by a factor of 30, without compromising the quality of the result.

The efficient combination of fragment-based quantum chemistry with continuum solvation models provides an important tool for studies of biomolecules. It will make such calculations more robust by alleviating convergence problems for charged amino acids and will allow for a more realistic inclusion of protein environments in studies of spectroscopic properties of chromophores in biomolecular systems.

[2] D. G. Fedorov, K. Kitaura, “Extending the Power of Quantum Chemistry to Large Systems with the Fragment Molecular Orbital Method”,

[3] Ch. R. Jacob, L. Visscher, “A subsystem density-functional theory approach for the quantum chemical treatment of proteins”,

*J. Chem. Theory Comput*., Article ASAP, DOI: 10.1021/acs.jctc.5b00832Contributed by Christoph Jacob

Fragment-based methods nowadays make it possible to perform quantum-chemical calculations for rather large biomolecules, for instance light-harvesting protein systems [1]. Such methods are based on the idea of splitting a protein into smaller fragments, such as its constituting amino acids. This leads to a linear scaling of the computational effort with the size of protein. Popular examples of fragment-based electronic structure methods include the fragment molecular orbital (FMO) method [2] and a generalization of the frozen-density embedding scheme (3-FDE) [3].

In a recent article in JCTC, Goez and Neugebauer from the University of Münster (Germany) address an additional bottleneck that appears in such calculations. Usually, it is necessary to include a solvent environment in the calculations, in particular if charged amino-acid side chains are present. The simplest way of doing so are continuum solvation models, such as COSMO or PCM. These models represent the solvent in terms of apparent charges on the surface of a cavity enclosing the protein. However, for proteins the number of apparent surfaces charges becomes rather large - for ubiquitin, a protein with only 78 amino acids, already 20,000 charges are needed. Updating these apparent surface charges involves solving a linear system of equations of size 20,000 x 20,000. When doing so in each SCF cycle for each of the fragments, the continuum solvation model will become the bottleneck of the calculation.

To solve this problem, Goez and Neugebauer developed a local variant of the COSMO model (LocCOSMO). In each fragment calculation, they update only those apparent surface charges that are close to this fragment. This reduces the computational effort significantly, but because every fragment is updated at some point it will eventually result in the same final result. This is demonstrated by the authors for several test cases. They can reduce the computational time required for a 3-FDE calculation of ubiquitin in a solvent environment by a factor of 30, without compromising the quality of the result.

The efficient combination of fragment-based quantum chemistry with continuum solvation models provides an important tool for studies of biomolecules. It will make such calculations more robust by alleviating convergence problems for charged amino acids and will allow for a more realistic inclusion of protein environments in studies of spectroscopic properties of chromophores in biomolecular systems.

### References:

[1] A. Goez, Ch. R. Jacob, J. Neugebauer, “Modeling environment effects on pigment site energies: Frozen density embedding with fully quantum-chemical protein densities”,*Comput. Theor. Chem.***1040–1041**, 347–359 (2014).[2] D. G. Fedorov, K. Kitaura, “Extending the Power of Quantum Chemistry to Large Systems with the Fragment Molecular Orbital Method”,

*J. Phys. Chem. A***111**, 6904–6914 (2007).[3] Ch. R. Jacob, L. Visscher, “A subsystem density-functional theory approach for the quantum chemical treatment of proteins”,

*J. Chem. Phys.***128**, 155102 (2008).
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