I have a lot to learn from him: the creativity he shows in solving problems, the breadth and depth of his knowledge, and his boundless energy and enthusiasm. The energies do not include interaction terms between atoms that are not involved in the side chain placement calculations.
Protein Sidechain Conformation Search
Rotamers
These low-energy conformations are called 'rotamers' (see Figure 1.1 for two rotamers of the glutamine side chain), an abbreviation for rotational isomers. Amino acids such as arginine and lysine that have more torsional freedoms require more rotamers to cover the conformational space.
Placement of Sidechains
The structures of the rotamers can be derived from crystal structures in proteins or constructed according to chemical principles, such as energy minima of torsion angles. Therefore, there is a trade-off between accuracy (more rotamers) and speed (fewer rotamers) in our search problem.
Energy Expressions
Covalent Terms
For Eb, Ea, and Et, a harmonic expression is often used to capture the fact that there are structures that tend to reside in a local neighborhood around equilibrium values. Ei, the inversion term, is a special term in DREIDING that ensures that the molecules stay flat (as in benzene) or maintain the correct chirality during simulations.
Non-covalent Terms
Valence bonds are never broken in DREIDING and most other biological force fields. asymptotic behavior at large distances, reflecting the fact that its origin lies in the instantaneous but fluctuating dipole moments of neutral atoms. There are cases where we don't want this, and we will show an example in Chapter 3. The classical Coulomb interaction form is used for the electrostatic term:.
Summary
Introduction
We introduce a flat-bottom region for the van der Waals (VDW) 12-6 potential and the DREIDING hydrogen bond term (12-10 with a cosine angle term). We show in this study that the accuracy can be substantially improved by introducing a flat ground potential in a systematic manner.
Materials and Methods
- Preparation of Rotamer Libraries
- Preparation of Structures for Validation of SCREAM
- Surface Area Calculations
- Positioning of Sidechains
- Combinatorial Placement Algorithm
- The Flat-Bottom Scoring Function
The angle of the Ca-Cβ bond from the bisector of the C-Cα-N angle: 1.81∘ (from the HBPLUS protein set). The valence energies (bonds, angles, torsions, and inversion) plus the internal HB, Coulomb, and VDW energies of the rotamers were precomputed and stored in the rotamer library.
Results and Discussion
- Single Placement of Side-chains
- Effects of Buried vs. Exposed Residues
- Placement of All Sidechains on Proteins, Comparison with SCWRL
- Effects of Minimization on Structures from Different Scaling Factors
- Program Execution Performance
- Tests on the Liang Set Using the Optimized Scaling Factor
- Parameters for Other Lennard Jones Potentials
- Comparison with VDW Radii Scaling
- Extension beyond the Natural Amino Acids
In the previous sections we optimized the scale factors for the Xiang set and discussed the accuracy for the Xiang set. We also test with reduced VDW radii values on the 1.0| rotamer library for the Xiang protein set.
Conclusion
To extend the potential flat-bottom approach for ligands and non-natural amino acids, a value for Δ or σ must be determined.
Introduction
Polar Interactions
Neutralizing Amino Acids
Despite the use of counterions, they are known to cause large fluctuations in electrostatic energies59. This is despite the fact that the use of dielectric constants other than 1.0 or a modified Coulombic interaction is justified only on empirical grounds. Our approach not only reduces the source of error arising from the use of counter-ions, but also reduces the effect due to random fluctuations of charged residues far from a region of interest.
Assignment of Protons from Neutralization of Charged Residues
With the above considerations in mind, we neutralize the net charges on the normally charged amino acid residues. It has been demonstrated empirically and statistically that solvent-exposed charged side chains and exposed salt bridges contribute less than 2 kcal/mol to the self-energy of a protein63,64 due to the solvent screening effect. Clearly, with the elimination of net charges on functional groups, systems such as salt bridges are not as stable as before.
DREIDING Hydrogen Bond Term
Introduction
Because of the importance of hydrogen bonds, biomolecular calculations require an accurate description of the hydrogen bond. This hydrogen bond term consists of a 12-10 Lennard-Jones radial term and a cos4 angular term, each term being independent of the other. We investigate whether this 12-10 Lennard-Jones distance term and the cos4 angle term accurately describe the behavior of the hydrogen bond interaction.
Updating the DREIDING Hydrogen Bond Term
The well depth of the hydrogen bond term used in the fitting is based on the binding energy of the equilibrium water dimer structure in QM. As a result, we recommend using the cos2(θAHD) functional form in the angular part of the hydrogen bond expression. The new functional form we have chosen for the hydrogen bond is the product of a radial and an angular component.
Optimization of Hydrogen Bond Parameters
- Atom Types for Hydrogen Bond Donors and Acceptors
- VDW Parameters
- Hydrogen Bond Parameterization Methodology
- Parameterization of Neutral Hydrogen Bond Atom Types
- Parameterization for Neutralized Form of Charged Residues
- Validation
The same reduced off-diagonal approach is performed for each pair of a heavy hydrogen bond acceptor atom and a polar hydrogen. The position of a pair of model compounds is such that a hydrogen bond clearly forms between them (similar to the hydrogen bond structure of a water dimer, see Figure 3-3). This process is repeated until we achieve a fit within 0.1 kcal/mol in binding energy and 0.1Ǻ for both donor-acceptor hydrogen bond distances.
Applications
Protein Structure Preparation
The protein is 1isu, where both an aspartate and a lysine in minimizing charged proteins form a salt bridge when there was none before. This artificial salt bridge formation is entirely due to the strong Coulombic interaction between these two residues in the charged formulation of our force field. In the minimized neutral formulation, the two residues remained far apart as in the crystal structure.
Effect on Molecular Dynamics: An Example
The neutral system took about 50 ps to equilibrate, while the charged system took about 200 ps. We next investigate the difference in dynamics of salt bridges in the neutral system compared to the charged system. Due to the difference in interaction energies between the charged description of a salt bridge and the neutral description, we expect large differences.
Bovine Rhodopsin Helical bundle
In the case of the R152-E149 salt bridge, it is interesting to note that during the earlier part of the simulation the neutral case is bound, while the charged salt bridge is unbound. For the top 100 of the 504 results, the standard deviation in the electrostatic component of the total energy is 7.9 kcal/mol for the neutral cases, and 22.6 kcal/mol for the charged cases. A large standard deviation indicates a larger source of random error, and this could be the reason why the zero rotation case in the charged formulation does not have the best overall energy.
Conclusion
Introduction
Methods and Material
Optimization of the geometry using the conjugate gradient of the structure is then performed using MPSim73 for 100 steps. Typically the coordinate root deviation (RMSD, in !) between the optimized structure and the original crystal structure is less than 0.5.
The Design Protocol—Energy Excitation
Where EMutation is the overall stability due to the mutation, Eraw is the force field interaction energy of the mutated side chain with the rest of the protein after it. The final energy of atoms on the side chain (from Cβ to . out) and the rest of the protein is calculated from the optimized structure. This energy is the raw energy, Eraw, which includes the interaction energy between the side chain and the rest of the protein, and the internal energy of the side chain.
Design of Human Inteferon-β
Introduction
Single Mutations
At position 36, experiments with Thr, Ile and Ala mutations were performed and all mutations were found to be fully active. In fact, Thr and Tyr mutations led to mutants that were actually more active than wild-type IFN-β. The best mutation candidate is Thr for this position, but it is still 6.8 kcal/mol less favorable than the wild-type methionine.
Combinatorial Mutations of Residues around Met 62
The stability of the triple mutant I62, F40, L44 was, according to our calculations, very close to the wild-type sequence, with a difference of only 0.1 kcal/mol. Ile40 and Ile44 are identified as residues that are in direct contact with Met62 and must be mutated when changes are made to Met62.
Active Site Design of TrpRS
Introduction
PheRS (phenylalanine tRNA synthetase) and TyrRS (tyrosyl tRNA synthetase) have been used to incorporate unnatural amino acid analogues81. As a result, we perform in silico redesigns of Bacillus Stearothermophilus TrpRS and human TrpRS to recognize non-natural amino acid analogues. With the exception of the Indene amino acid analog, all of these molecules can participate in click chemistry.
Bacillus Stearothermophilus TrpRS Active Site Design
To determine which of the and 7-position of Ethinyl-Trp would be best accommodated in the active site, we constructed all four ligands and placed the ligands in the crystal structure. The ethynyl group of 4-, 6-, and 7-ethynyl-Trp would conflict with the protein backbone and is therefore eliminated from further consideration. We therefore predict that the mutations will be sufficient to distinguish related Trp from the non-natural 5- Ethinyl-Trp amino acid.
Human TrpRS Active Site Design
In the following sections, we introduce mutations at the hydrophobic lining pocket that stabilize several amino acid analogs. Ethynyl-Trp is the minimal unnatural amino acid analog that has a basic tryptophan structure and an ethynyl functional group for Click chemistry. The benzo-cyclooctyne amino acid analogue can react with an azido group without the need for a catalyst, with an activation barrier of just 7.6 kcal/mol.
Prediction of Surface Residues Prior to Sidechain Assignment
Impact of Scaling Factor s in Combinatorial Placement
Flow Network
Uncharged groups require special treatment, as we must take into account that they can "bridge" only a limited number of oppositely charged groups. To do this, these bridging groups are transformed into two virtual groups, and the capacity of the edge between these two virtual groups is defined as the maximum number of proton transfers it can handle. If there are multiple hydrogens that can be removed (eg NH3+), choose the one that does not remove an existing hydrogen bond with other atoms.
Remark on Correctness
The problem is now formally reduced to finding the maximum power of this graph we constructed, that is, the above rules are also applied to determine tie-breaks on the power network algorithm. However, according to the max-flow min-cut theorem, the value of each flow in a flow network is limited from above by the capacitance of each cut.
