Documentation created by Vikram K. Mulligan (vmullig@uw.edu), Baker laboratory, on 19 April 2018. Last updated on 22 April 2018.

This code is currently unpublished. If you use it, please include Vikram K. Mulligan as a coauthor.

Note: This documentation is for the buried_unsatisfied_penalty design-centric scoreterm, which guides design to eliminate buried unsatisfied hydrogen bond donors and acceptors. For information on the BuriedUnsatHbonds filter, which is useful for post-hoc filtering of designs with buried unsatisfied hydrogen bond donors or acceptors, please see this page.

## Purpose

This scoring term, called buried_unsatisfied_penalty, is intended for use during design, to provide a penalty for buried hydrogen bond donors or acceptors that are unsatisfied. This guides design algorithms to fully satisfy or eliminate buried hydrogen bond donors and acceptors. It can be appended to the scoring function used for design, and can be used in conjunction with other design-centric terms like the voids_penalty term or the hbnet term.

While the pairwise hydrogen bonding terms can encourage residue-residue hydrogen bonding, these terms cannot penalize the absence of any hydrogen bond to a given donor or acceptor. This is because the task of determining whether a donor or acceptor is participating in zero hydrogen bonds is fundamentally non-pairwise decomposable. The buried_unsatisfied_penalty is a non-pairwise scoring term that is nonetheless compatible with the packer.

## Algorithm

The buried_unsatisfied_penalty scoreterm uses a graph representation of hydrogen bond networks that is precomputed prior to a packing trajectory. In this representation, nodes correspond to rotamers and edges correspond to hydrogen bonding interactions between rotamers. Each node stores a list of hydrogen bond donors and acceptors for that rotamer. The burial of each donor and acceptor is also pre-computed using the method of sidechain neighbours pioneered by Gabe Rocklin and stored in the node, as are the intra-residue hydrogen bonds for that rotamer. Each edge stores a list of hydrogen bonding interactions (since two rotamers may share multiple hydrogen bonds), and the donor acceptor group for each hydrogen bond is also stored in the edge. During the pre-computation, the full hydrogen bond scoring machinery is used to ensure that the definition of a hydrogen bond matches Rosetta's definition.

At each step during a packer trajectory, a sub-graph is generated from the precomputed graph, with one node per pose position. The sub-graph consists only of those nodes corresponding to the current rotamers being considered, and those edges connecting those nodes. It is then a simple matter to iterate over all hydrogen bond donors and acceptors in the nodes of the sub-graph and count, based on the connected edges to that node, the number of hydrogen bonds in which that group is participating. Once these tallies are computed, the number of groups for which the tally is zero can be determined with a second pass through the donor and acceptor groups. Although there is some computational cost to this, it is small enough that design trajectories are still quite fast.

### Definition of a hydrogen-bonding group

For the purposes of this scoreterm, hydrogen-bonding groups consist a single polar heavyatom, and possibly one or more polar hydrogen atoms that are bonded to the heavyatom. The heavyatom must either be able to accept hydrogen bonds, or must possess one or more protons that it can donate to hydrogen bonds.

### Precise rules for group satisfaction

In order to be satisfied:

• A group that can donate hydrogen bonds, but which cannot accept hydrogen bonds, must donate at least one hydrogen bond (regardless the number of protons in the group). That is, an NH2 group donating a single hydrogen bond is not considered unsatisfied.
• A group that can accept hydrogen bonds, but which cannot donate hydrogen bonds, must accept at least one hydrogen bond. That is, a carbonyl oxygen that accepts a single hydrogen bond is not considered unsatisfied.
• A group that can both donate and accept hydrogen bonds must either donate a hydrogen bond or accept a hydrogen bond. Thus, a hydroxyl group must be involved in at least one hydrogen bonding interaction in order to be considered satisfied.

### A note about oversaturated acceptors (or donors)

The pairwise-decomposability of Rosetta's default hydrogen bond terms leads to another pathology as well: oversaturated hydrogen bond acceptors (and, occasionally, donors). For example, one sometimes sees three protons hydrogen bonding to the same oxygen atom in Rosetta designs, and the software naïvely scores this very well. When counting unsatisfied hydrogen bond donors and acceptors, it is trivial to simultaneously count oversaturated donors and acceptors, and to penalize these simultaneously, with next to no additional computational cost. By default, this term penalizes both unsatisfied and oversaturated donors and acceptors.

## Usage

To use the buried_unsatisfied_penalty scoreterm in design, simply follow the following steps:

1) Turn on (reweight to a nonzero value) the buried_unsatisfied_penalty scoreterm in the scorefunction used for design. A value between 0.1 and 1.0 is recommended. Higher values will more aggressively penalize buried unsaturated polar groups at the expense of other scoreterms. Activation of the buried_unsatisfied_penalty scoreterm can be done with a weights file, or in RosettaScripts as follows:

<SCOREFXNS>
<ScoreFunction name="r15" weights="ref2015.wts" >
<Reweight scoretype="buried_unsatisfied_penalty" weight="1.0" />
</ScoreFunction>
</SCOREFXNS>

2) Design with any mover or protocol that invokes the packer, using the scorefunction defined above. Ensure that the task operations passed to the packer allow polar-containing residues at the relevant design positions (or there will be no buried hydrogen bond donors or acceptors, satisfied or otherwise). FastDesign is particularly advantageous since the rounds of minimization with the softened force field can pull hydrogen bond donors and acceptors into better hydrogen bond-forming positions.

3) (Recommended). Perform a final round of minimization or relaxation with the buried_unsatisfied_penalty scoreterm turned off. This ensures that the scoreterm is not forcing unrealistic rotamers that would not be held in place given the hydrogen bonding.

4) (Recommended). Filter based either on the buried_unsatisfied_penalty score, or using the BuriedUnsatHbonds filter. Although this scoreterm guides the packer to satisfy buried networks, it is possible that the particular backbone geometry or design settings will be incompatible with full satisfaction. For example, if the user were to design the core of a protein with aspartate as the only allowed amino acid type, it would be virtually guaranteed that there would exist no solution that would satisfy all side-chain hydrogen bond acceptors.

### Use with ligands

The buried_unsatisfied_penalty scoreterm is fully compatible with arbitrary polar ligands. If a ligand (or polymeric residue) is set not to design, the term can be very useful to coax the packer into designing polar connections to the ligand (or non-designable position) to satisfy its hydrogen bond donors and acceptors. No special setup is required.

### Use with non-canonical building blocks

The buried_unsatisfied_penalty scoreterm is fully compatible with arbitrary polymeric building-blocks, with no special setup necessary. The code is carefully written to avoid hardcoding anything that assumes (or provides special information for) the 20 canonical amino acid building-blocks.

### Use with symmetry

The buried_unsatisfied_penalty scoreterm is currently fully compatible with symmetry, with no special user configuration necessary. Symmetric poses score and pack faster than asymmetric poses with the same number of residues, since the symmetry simplifies the size of the data structures that must be stored. (The scoreterm sets up a hydrogen bonding graph only for the asymmetric unit. Hydrogen bonds between symmetry copies of the same residue are considered to be "intra-residue" hydrogen bonds, and are stored as such within nodes; hydrogen bonds between different residues in different symmetry copies are stored in the same edges. Unsatisfied counts are multiplied by the number of symmetry copies.)

The following options can be set, either globally at the commandline or on an instance-by-instance basis using <Set ... /> statements within the scorefunction definition in RosettaScripts, in order to tweak the behaviour of this scoreterm. (For example, <Set buried_unsatisfied_penalty_burial_threshold="2.5" /> within a scorefunction definition in RosettaScripts would slightly relax the criterion for considering a polar group to be buried for that particular instance of the scoreterm. The same could be achieved globally, for all instances of the scoreterm, by passing the commandline flag -buried_unsatisfied_penalty_burial_threshold 2.5.)

Option name Type Description Default
buried_unsatisfied_penalty_cone_angle_exponent Real The angle exponent for calculating burial by the method of sidechain neighbor cones, used by the BuriedUnsatPenalty energy. 2.0
buried_unsatisfied_penalty_cone_angle_shift_factor Real The angle shift factor for calculating burial by the method of sidechain neighbor cones, used by the BuriedUnsatPenalty energy. 0.25
buried_unsatisfied_penalty_cone_dist_exponent Real The distance exponent for calculating burial by the method of sidechain neighbor cones, used by the BuriedUnsatPenalty energy. 1.0
buried_unsatisfied_penalty_cone_dist_midpoint Real The distance midpoint for calculating burial by the method of sidechain neighbor cones, used by the BuriedUnsatPenalty energy. 9.0
buried_unsatisfied_penalty_burial_threshold Real The number of cones in which a point must lie to be considered buried by the method of sidechain neighbor cones, used by the BuriedUnsatPenalty energy. (Since cones have fuzzy boundaries, this is a float rather than an integer.) 5.0
buried_unsatisfied_penalty_hbond_energy_threshold Real The energy threshold above which a hydrogen bond is not counted, used by the BuriedUnsatPenalty energy. -0.25

## A companion SimpleMetric

The PolarGroupBurialPyMolStringMetric SimpleMetric exists to provide a covenient way to export, or to embed in a pose or PDB file, a list of PyMol commands to colour the polar groups in a pose based on burial. This is useful when setting the definition of burial or when debugging a protocol. See the documentation for the PolarGroupBurialPyMolStringMetric for more details.

## Organization of the code

• The scoreterm is defined in namespace core::pack::guidance_scoreterms:buried_unsat_penalty, and is located in source/src/core/pack/guidance_scoreterms/buried_unsat_penalty/BuriedUnsatPenalty.cc/hh.
• The scoreterm uses a graph class that is defined in namespace core::pack::guidance_scoreterms:buried_unsat_penalty::graph and located in source/src/core/pack/guidance_scoreterms/buried_unsat_penalty/graph/BuriedUnsatPenaltyGraph.cc/hh.
• Unit tests are located in source/test/core/pack/guidance_scoreterms/buried_unsat_penalty/BuriedUnsatPenaltyTests.cxxtest.hh and source/test/core/pack/guidance_scoreterms/buried_unsat_penalty/graph/BuriedUnsatPenaltyGraphTests.cxxtest.hh.
• Symmetric unit tests are located in source/test/core/pack/guidance_scoreterms/buried_unsat_penalty/BuriedUnsatPenaltySymmetricTests.cxxtest.hh and source/test/core/pack/guidance_scoreterms/buried_unsat_penalty/graph/BuriedUnsatPenaltyGraphSymmetricTests.cxxtest.hh.