Accurate Calculations of Rotationally Inelastic Scattering Cross Sections Using Mixed Quantum/Classical Theory

For computational treatment of rotationally inelastic scattering of molecules, we propose to use the mixed quantum/classical theory, MQCT. The old idea of treating translational motion classically, while quantum mechanics is used for rotational degrees of freedom, is developed to the new level and is applied to Na + N2 collisions in a broad range of energies. Comparison with full-quantum calculations shows that MQCT accurately reproduces all, even minor, features of energy dependence of cross sections, except scattering resonances at very low energies. The remarkable success of MQCT opens up wide opportunities for computational predictions of inelastic scattering cross sections at higher temperatures and/or for polyatomic molecules and heavier quenchers, which is computationally close to impossible within the full-quantum framework

Multi-state design of flexible proteins predicts sequences optimal for conformational change.

Computational protein design of an ensemble of conformations for one protein-i.e., multi-state design-determines the side chain identity by optimizing the energetic contributions of that side chain in each of the backbone conformations. Sampling the resulting large sequence-structure search space limits the number of conformations and the size of proteins in multi-state design algorithms. Here, we demonstrated that the REstrained CONvergence (RECON) algorithm can simultaneously evaluate the sequence of large proteins that undergo substantial conformational changes. Simultaneous optimization of side chain conformations across all conformations increased sequence conservation when compared to single-state designs in all cases. More importantly, the sequence space sampled by RECON MSD resembled the evolutionary sequence space of flexible proteins, particularly when confined to predicting the mutational preferences of limited common ancestral descent, such as in the case of influenza type A hemagglutinin. Additionally, we found that sequence positions which require substantial changes in their local environment across an ensemble of conformations are more likely to be conserved. These increased conservation rates are better captured by RECON MSD over multiple conformations and thus multiple local residue environments during design. To quantify this rewiring of contacts at a certain position in sequence and structure, we introduced a new metric designated 'contact proximity deviation' that enumerates contact map changes. This measure allows mapping of global conformational changes into local side chain proximity adjustments, a property not captured by traditional global similarity metrics such as RMSD or local similarity metrics such as changes in φ and ψ angles

Design of Protein Multi-specificity Using an Independent Sequence Search Reduces the Barrier to Low Energy Sequences

<div><p>Computational protein design has found great success in engineering proteins for thermodynamic stability, binding specificity, or enzymatic activity in a ‘single state’ design (SSD) paradigm. Multi-specificity design (MSD), on the other hand, involves considering the stability of multiple protein states simultaneously. We have developed a novel MSD algorithm, which we refer to as REstrained CONvergence in multi-specificity design (RECON). The algorithm allows each state to adopt its own sequence throughout the design process rather than enforcing a single sequence on all states. Convergence to a single sequence is encouraged through an incrementally increasing convergence restraint for corresponding positions. Compared to MSD algorithms that enforce (constrain) an identical sequence on all states the energy landscape is simplified, which accelerates the search drastically. As a result, RECON can readily be used in simulations with a flexible protein backbone. We have benchmarked RECON on two design tasks. First, we designed antibodies derived from a common germline gene against their diverse targets to assess recovery of the germline, polyspecific sequence. Second, we design “promiscuous”, polyspecific proteins against all binding partners and measure recovery of the native sequence. We show that RECON is able to efficiently recover native-like, biologically relevant sequences in this diverse set of protein complexes.</p></div

Complexes used in common germline antibody benchmark.

<p>RECON was benchmarked on three sets of mature antibodies derived from the same V_H gene. Effective MSD should result in reversion of mature antibodies to the polyspecific germline sequence.</p><p>^aGermline sequence and positions varying from germline are inferred from IMGT/3D Structure-DB [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004300#pcbi.1004300.ref021" target="_blank">21</a>].</p><p>Complexes used in common germline antibody benchmark.</p

Results of common germline gene multi-specificity design benchmark.

<p>Three sets of antibodies encoded by a common germline gene were designed against their targets using RECON, both by fixed backbone (FBB) and backbone minimized (BBM) designs, and MPI_MSD algorithms. Designs were evaluated by recovery of the germline sequence and the fitness of designed models.</p><p>^aFitness is defined as the sum of the Rosetta score of all input complexes, in Rosetta Energy Units (REU). Fitness was reported for the top ten complexes generated by each design method.</p><p>Results of common germline gene multi-specificity design benchmark.</p

Incorporation of backbone motion into RECON recapitulates evolutionary sequence profiles in un-minimized structures.

<p>Multi-specificity design using RECON was repeated on structures that had not been previously energy minimized to evaluate the benefit of incorporating backbone movements. Designs were generated using either a fixed backbone protocol (Fixed BB), alternating rounds of φ, ψ, and χ angle minimization (Minimize), or using backrub motions (Backrub). P values were calculated by a paired two-tailed t test.</p

Complexes used in promiscuous protein benchmark.

<p>RECON was benchmarked on a set of promiscuous proteins that have been crystallized in complex with multiple partners. As the native sequence is near optimal for binding of all partners, MSD should recover the native sequence at a high rate.</p><p>^aResidues determined to be at the interface with all binding partners. See <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004300#sec031" target="_blank">methods</a> for details on interface residue calculations.</p><p>Complexes used in promiscuous protein benchmark.</p

Encouraging sequence convergence in RECON can avoid high-energy sequence intermediates.

<p>A. An example design trajectory of RECON in the FI6v3 benchmark through four design rounds is shown. Sequences tend to diverge in early rounds when convergence restraints are kept low, whereas in later rounds when restraints are increased states are encouraged to adopt a single solution. The figure displays one example from the fixed backbone design protocol, with convergence restraints removed before reporting fitness. The two states showed different preferences for residues highlighted in red. B. Residues highlighted in panel A were applied to the opposing state to analyze the energetic barrier of forced sequence convergence. The energy of these three residues was analyzed when the sequence favored by state 1 (TSY) was applied to state 2, and vice versa with the sequence QQW (intermediate sequence, black/red lines). This was compared to the three-residue fitness when each state was allowed to adopt its own preferred sequence (intermediate sequence, blue line). Energies were compared to the final, “compromised” sequence (QQY). These three amino acids occurred at positions 28, 30, and 53, respectively.</p

Native/germline sequence recovery of designed complexes.

<p>100 designs were generated using RECON, with both fixed backbone (FBB) and backbone minimized (BBM) protocols, and MPI_MSD. Sequences of the top 10% of models were compared to either the native sequence or, in the case of common germline-derived antibodies, to the germline sequence. See <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004300#sec031" target="_blank">methods</a> for details of native sequence recovery calculations.</p

Pseudocode describing the implementation of the RECON algorithm.

<p>Pseudocode describing the implementation of the RECON algorithm.</p