Using self-consistent fields to bias Monte Carlo methods with applications to designing and sampling protein sequences

Mapping the energy landscape of PROTAC-mediated protein-protein interactions

A principal challenge in computational modeling of macromolecules is the vast conformational space that arises out of large numbers of atomic degrees of freedom. Recently, growing interest in building predictive models of complexes mediated by Proteolysis Targeting Chimeras (PROTACs) has led to the application of state-of-the-art computational techniques to tackle this problem. However, repurposing existing tools to carry out protein-protein docking and linker conformer generation independently results in extensive sampling of structures incompatible with PROTAC-mediated complex formation. Here we show that it is possible to restrict the search to the space of protein-protein conformations that can be bridged by a PROTAC molecule with a given linker composition by using a cyclic coordinate descent algorithm to position PROTACs into complex-bound configurations. We use this methodology to construct potential energy and solvation energy landscapes of PROTAC-mediated interactions. Our results suggest that desolvation of amino acids at interfaces could play a dominant role in PROTAC-mediated complex formation.

Lattice protein design using Bayesian learning

Protein design is the inverse approach of the three-dimensional (3D) structure prediction for elucidating the relationship between the 3D structures and amino acid sequences. In general, the computation of the protein design involves a double loop: A loop for amino acid sequence changes and a loop for an exhaustive conformational search for each amino acid sequence. Herein, we propose a novel statistical mechanical design method using Bayesian learning, which can design lattice proteins without the exhaustive conformational search. We consider a thermodynamic hypothesis of the evolution of proteins and apply it to the prior distribution of amino acid sequences. Furthermore, we take the water effect into account in view of the grand canonical picture. As a result, on applying the 2D lattice hydrophobic-polar (HP) model, our design method successfully finds an amino acid sequence for which the target conformation has a unique ground state. However, the performance was not as good for the 3D lattice HP models compared to the 2D models. The performance of the 3D model improves on using a 20-letter lattice proteins. Furthermore, we find a strong linearity between the chemical potential of water and the number of surface residues, thereby revealing the relationship between protein structure and the effect of water molecules. The advantage of our method is that it greatly reduces computation time, because it does not require long calculations for the partition function corresponding to an exhaustive conformational search. As our method uses a general form of Bayesian learning and statistical mechanics and is not limited to lattice proteins, the results presented here elucidate some heuristics used successfully in previous protein design methods.

Comparing three stochastic search algorithms for computational protein design: Monte Carlo, replica exchange Monte Carlo, and a multistart, steepest-descent heuristic

Computational protein design depends on an energy function and an algorithm to search the sequence/conformation space. We compare three stochastic search algorithms: a heuristic, Monte Carlo (MC), and a Replica Exchange Monte Carlo method (REMC). The heuristic performs a steepest-descent minimization starting from thousands of random starting points. The methods are applied to nine test proteins from three structural families, with a fixed backbone structure, a molecular mechanics energy function, and with 1, 5, 10, 20, 30, or all amino acids allowed to mutate. Results are compared to an exact, "Cost Function Network" method that identifies the global minimum energy conformation (GMEC) in favorable cases. The designed sequences accurately reproduce experimental sequences in the hydrophobic core. The heuristic and REMC agree closely and reproduce the GMEC when it is known, with a few exceptions. Plain MC performs well for most cases, occasionally departing from the GMEC by 3-4 kcal/mol. With REMC, the diversity of the sequences sampled agrees with exact enumeration where the latter is possible: up to 2 kcal/mol above the GMEC. Beyond, room temperature replicas sample sequences up to 10 kcal/mol above the GMEC, providing thermal averages and a solution to the inverse protein folding problem. © 2016 Wiley Periodicals, Inc.

Designing pH induced fold switch in proteins

This work investigates the computational design of a pH induced protein fold switch based on a self-consistent mean-field approach by identifying the ensemble averaged characteristics of sequences that encode a fold switch. The primary challenge to balance the alternative sets of interactions present in both target structures is overcome by simultaneously optimizing two foldability criteria corresponding to two target structures. The change in pH is modeled by altering the residual charge on the amino acids. The energy landscape of the fold switch protein is found to be double funneled. The fold switch sequences stabilize the interactions of the sites with similar relative surface accessibility in both target structures. Fold switch sequences have low sequence complexity and hence lower sequence entropy. The pH induced fold switch is mediated by attractive electrostatic interactions rather than hydrophobic-hydrophobic contacts. This study may provide valuable insights to the design of fold switch proteins.

Protein:Ligand binding free energies: A stringent test for computational protein design

A computational protein design method is extended to allow Monte Carlo simulations where two ligands are titrated into a protein binding pocket, yielding binding free energy differences. These provide a stringent test of the physical model, including the energy surface and sidechain rotamer definition. As a test, we consider tyrosyl-tRNA synthetase (TyrRS), which has been extensively redesigned experimentally. We consider its specificity for its substrate l-tyrosine (l-Tyr), compared to the analogs d-Tyr, p-acetyl-, and p-azido-phenylalanine (ac-Phe, az-Phe). We simulate l- and d-Tyr binding to TyrRS and six mutants, and compare the structures and binding free energies to a more rigorous "MD/GBSA" procedure: molecular dynamics with explicit solvent for structures and a Generalized Born + Surface Area model for binding free energies. Next, we consider l-Tyr, ac- and az-Phe binding to six other TyrRS variants. The titration results are sensitive to the precise rotamer definition, which involves a short energy minimization for each sidechain pair to help relax bad contacts induced by the discrete rotamer set. However, when designed mutant structures are rescored with a standard GBSA energy model, results agree well with the more rigorous MD/GBSA. As a third test, we redesign three amino acid positions in the substrate coordination sphere, with either l-Tyr or d-Tyr as the ligand. For two, we obtain good agreement with experiment, recovering the wildtype residue when l-Tyr is the ligand and a d-Tyr specific mutant when d-Tyr is the ligand. For the third, we recover His with either ligand, instead of wildtype Gln.

De novo design and experimental characterization of ultrashort self-associating peptides

Self-association is a common phenomenon in biology and one that can have positive and negative impacts, from the construction of the architectural cytoskeleton of cells to the formation of fibrils in amyloid diseases. Understanding the nature and mechanisms of self-association is important for modulating these systems and in creating biologically-inspired materials. Here, we present a two-stage de novo peptide design framework that can generate novel self-associating peptide systems. The first stage uses a simulated multimeric template structure as input into the optimization-based Sequence Selection to generate low potential energy sequences. The second stage is a computational validation procedure that calculates Fold Specificity and/or Approximate Association Affinity (K*association) based on metrics that we have devised for multimeric systems. This framework was applied to the design of self-associating tripeptides using the known self-associating tripeptide, Ac-IVD, as a structural template. Six computationally predicted tripeptides (Ac-LVE, Ac-YYD, Ac-LLE, Ac-YLD, Ac-MYD, Ac-VIE) were chosen for experimental validation in order to illustrate the self-association outcomes predicted by the three metrics. Self-association and electron microscopy studies revealed that Ac-LLE formed bead-like microstructures, Ac-LVE and Ac-YYD formed fibrillar aggregates, Ac-VIE and Ac-MYD formed hydrogels, and Ac-YLD crystallized under ambient conditions. An X-ray crystallographic study was carried out on a single crystal of Ac-YLD, which revealed that each molecule adopts a β-strand conformation that stack together to form parallel β-sheets. As an additional validation of the approach, the hydrogel-forming sequences of Ac-MYD and Ac-VIE were shuffled. The shuffled sequences were computationally predicted to have lower K*association values and were experimentally verified to not form hydrogels. This illustrates the robustness of the framework in predicting self-associating tripeptides. We expect that this enhanced multimeric de novo peptide design framework will find future application in creating novel self-associating peptides based on unnatural amino acids, and inhibitor peptides of detrimental self-aggregating biological proteins.

Computational protein design: the Proteus software and selected applications

We describe an automated procedure for protein design, implemented in a flexible software package, called Proteus. System setup and calculation of an energy matrix are done with the XPLOR modeling program and its sophisticated command language, supporting several force fields and solvent models. A second program provides algorithms to search sequence space. It allows a decomposition of the system into groups, which can be combined in different ways in the energy function, for both positive and negative design. The whole procedure can be controlled by editing 2-4 scripts. Two applications consider the tyrosyl-tRNA synthetase enzyme and its successful redesign to bind both O-methyl-tyrosine and D-tyrosine. For the latter, we present Monte Carlo simulations where the D-tyrosine concentration is gradually increased, displacing L-tyrosine from the binding pocket and yielding the binding free energy difference, in good agreement with experiment. Complete redesign of the Crk SH3 domain is presented. The top 10000 sequences are all assigned to the correct fold by the SUPERFAMILY library of Hidden Markov Models. Finally, we report the acid/base behavior of the SNase protein. Sidechain protonation is treated as a form of mutation; it is then straightforward to perform constant-pH Monte Carlo simulations, which yield good agreement with experiment. Overall, the software can be used for a wide range of application, producing not only native-like sequences but also thermodynamic properties with errors that appear comparable to other current software packages.

Dynamics in Sequence Space for RNA Secondary Structure Design

We have implemented a method for the design of RNA sequences that should fold to arbitrary secondary structures. A popular energy model allows one to take the derivative with respect to composition, which can then be interpreted as a force and used for Newtonian dynamics in sequence space. Combined with a negative design term, one can rapidly sample sequences which are compatible with a desired secondary structure via simulated annealing. Results for 360 structures were compared with those from another nucleic acid design program using measures such as the probability of the target structure and an ensemble-weighted distance to the target structure.

Discovery of entry inhibitors for HIV-1 via a new de novo protein design framework

A new (to our knowledge) de novo design framework with a ranking metric based on approximate binding affinity calculations is introduced and applied to the discovery of what we believe are novel HIV-1 entry inhibitors. The framework consists of two stages: a sequence selection stage and a validation stage. The sequence selection stage produces a rank-ordered list of amino-acid sequences by solving an integer programming sequence selection model. The validation stage consists of fold specificity and approximate binding affinity calculations. The designed peptidic inhibitors are 12-amino-acids-long and target the hydrophobic core of gp41. A number of the best-predicted sequences were synthesized and their inhibition of HIV-1 was tested in cell culture. All peptides examined showed inhibitory activity when compared with no drug present, and the novel peptide sequences outperformed the native template sequence used for the design. The best sequence showed micromolar inhibition, which is a 3-15-fold improvement over the native sequence, depending on the donor. In addition, the best sequence equally inhibited wild-type and Enfuvirtide-resistant virus strains.

Neutrality and evolvability of designed protein sequences

The effect of foldability on protein's evolvability is analyzed by a two-prong approach consisting of a self-consistent mean-field theory and Monte Carlo simulations. Theory and simulation models representing protein sequences with binary patterning of amino acid residues compatible with a particular foldability criteria are used. This generalized foldability criterion is derived using the high temperature cumulant expansion approximating the free energy of folding. The effect of cumulative point mutations on these designed proteins is studied under neutral condition. The robustness, protein's ability to tolerate random point mutations is determined with a selective pressure of stability (ΔΔG) for the theory designed sequences, which are found to be more robust than that of Monte Carlo and mean-field-biased Monte Carlo generated sequences. The results show that this foldability criterion selects viable protein sequences more effectively compared to the Monte Carlo method, which has a marked effect on how the selective pressure shapes the evolutionary sequence space. These observations may impact de novo sequence design and its applications in protein engineering.

Toward full-sequence de novo protein design with flexible templates for human beta-defensin-2

In this article, we introduce and apply our de novo protein design framework, which observes true backbone flexibility, to the redesign of human beta-defensin-2, a 41-residue cationic antimicrobial peptide of the innate immune system. The flexible design templates are generated using molecular dynamics simulations with both Generalized Born implicit solvation and explicit water molecules. These backbone templates were employed in addition to the x-ray crystal structure for designing human beta-defensin-2. The computational efficiency of our framework was demonstrated with the full-sequence design of the peptide with flexible backbone templates, corresponding to the mutation of all positions except the native cysteines.

Advances in computational protein design

Computational protein design continues to experience a variety of methodological advances. Several improvements have been suggested for the objective functions used to quantify sequence/structure compatibility. Disparate design strategies based upon dead-end elimination, simulated annealing and statistical design have each recently yielded striking successes involving de novo designed proteins with sizes on the order of 100 residues or greater. Such methods may be used to design new proteins, as well as to redesign natural proteins to facilitate structural and biophysical studies.

Computational design and characterization of a monomeric helical dinuclear metalloprotein

The de novo design of di-iron proteins is an important step towards understanding the diversity of function among this complex family of metalloenzymes. Previous designs of due ferro (DF) proteins have resulted in tetrameric and dimeric four-helix bundles having crystallographically well-defined structures and active-site geometries. Here, the design and characterization of DFsc, a 114 residue monomeric four-helix bundle, is presented. The backbone was modeled using previous oligomeric structures and appropriate inter-helical turns. The identities of 26 residues were predetermined, including the primary and secondary ligands in the active site, residues involved in active site accessibility, and the gamma beta gamma beta turn between helices 2 and 3. The remaining 88 amino acid residues were determined using statistical computer aided design, which is based upon a recent statistical theory of protein sequences. Rather than sampling sequences, the theory directly provides the site-specific amino acid probabilities, which are then used to guide sequence design. The resulting sequence (DFsc) expresses well in Escherichia coli and is highly soluble. Sedimentation studies confirm that the protein is monomeric in solution. Circular dichroism spectra are consistent with the helical content of the target structure. The protein is structured in both the apo and the holo forms, with the metal-bound form exhibiting increased stability. DFsc stoichiometrically binds a variety of divalent metal ions, including Zn(II), Co(II), Fe(II), and Mn(II), with micromolar affinities. 15N HSQC NMR spectra of both the apo and Zn(II) proteins reveal excellent dispersion with evidence of a significant structural change upon metal binding. DFsc is then a realization of complete de novo design, where backbone structure, activity, and sequence are specified in the design process.