Mi3-GPU: MCMC-based Inverse Ising Inference on GPUs for protein covariation analysis

Evolutionary sequence and structural basis for the distinct conformational landscapes of Tyr and Ser/Thr kinases

Protein kinases are molecular machines with rich sequence variation that distinguishes the two main evolutionary branches - tyrosine kinases (TKs) from serine/threonine kinases (STKs). Using a sequence co-variation Potts statistical energy model we previously concluded that TK catalytic domains are more likely than STKs to adopt an inactive conformation with the activation loop in an autoinhibitory "folded" conformation, due to intrinsic sequence effects. Here we investigated the structural basis for this phenomenon by integrating the sequence-based model with structure-based molecular dynamics (MD) to determine the effects of mutations on the free energy difference between active and inactive conformations, using a novel thermodynamic cycle involving many (n=108) protein-mutation free energy perturbation (FEP) simulations in the active and inactive conformations. The sequence and structure-based results are consistent and support the hypothesis that the inactive conformation "DFG-out Activation Loop Folded", is a functional regulatory state that has been stabilized in TKs relative to STKs over the course of their evolution via the accumulation of residue substitutions in the activation loop and catalytic loop that facilitate distinct substrate binding modes in trans and additional modes of regulation in cis for TKs.

Evolutionary sequence and structural basis for the distinct conformational landscapes of Tyr and Ser/Thr kinases

Protein kinases are molecular machines with rich sequence variation that distinguishes the two main evolutionary branches - tyrosine kinases (TKs) from serine/threonine kinases (STKs). Using a sequence co-variation Potts statistical energy model we previously concluded that TK catalytic domains are more likely than STKs to adopt an inactive conformation with the activation loop in an autoinhibitory "folded" conformation, due to intrinsic sequence effects. Here we investigated the structural basis for this phenomenon by integrating the sequence-based model with structure-based molecular dynamics (MD) to determine the effects of mutations on the free energy difference between active and inactive conformations, using a novel thermodynamic cycle involving many (n=108) protein-mutation free energy perturbation (FEP) simulations in the active and inactive conformations. The sequence and structure-based results are consistent and support the hypothesis that the inactive conformation "DFG-out Activation Loop Folded", is a functional regulatory state that has been stabilized in TKs relative to STKs over the course of their evolution via the accumulation of residue substitutions in the activation loop and catalytic loop that facilitate distinct substrate binding modes in trans and additional modes of regulation in cis for TKs.

Kinetic coevolutionary models predict the temporal emergence of HIV-1 resistance mutations under drug selection pressure

Drug resistance in HIV type 1 (HIV-1) is a pervasive problem that affects the lives of millions of people worldwide. Although records of drug-resistant mutations (DRMs) have been extensively tabulated within public repositories, our understanding of the evolutionary kinetics of DRMs and how they evolve together remains limited. Epistasis, the interaction between a DRM and other residues in HIV-1 protein sequences, is key to the temporal evolution of drug resistance. We use a Potts sequence-covariation statistical-energy model of HIV-1 protein fitness under drug selection pressure, which captures epistatic interactions between all positions, combined with kinetic Monte-Carlo simulations of sequence evolutionary trajectories, to explore the acquisition of DRMs as they arise in an ensemble of drug-naive patient protein sequences. We follow the time course of 52 DRMs in the enzymes protease, RT, and integrase, the primary targets of antiretroviral therapy. The rates at which DRMs emerge are highly correlated with their observed acquisition rates reported in the literature when drug pressure is applied. This result highlights the central role of epistasis in determining the kinetics governing DRM emergence. Whereas rapidly acquired DRMs begin to accumulate as soon as drug pressure is applied, slowly acquired DRMs are contingent on accessory mutations that appear only after prolonged drug pressure. We provide a foundation for using computational methods to determine the temporal evolution of drug resistance using Potts statistical potentials, which can be used to gain mechanistic insights into drug resistance pathways in HIV-1 and other infectious agents.

Potts Hamiltonian Models and Molecular Dynamics Free Energy Simulations for Predicting the Impact of Mutations on Protein Kinase Stability

Single-point mutations in kinase proteins can affect their stability and fitness, and computational analysis of these effects can provide insights into the relationships among protein sequence, structure, and function for this enzyme family. To assess the impact of mutations on protein stability, we used a sequence-based Potts Hamiltonian model trained on a kinase family multiple-sequence alignment (MSA) to calculate the statistical energy (fitness) effects of mutations and compared these against relative folding free energies (ΔΔGs) calculated from all-atom molecular dynamics free energy perturbation (FEP) simulations in explicit solvent. The fitness effects of mutations in the Potts model (ΔEs) showed good agreement with experimental thermostability data (Pearson r = 0.68), similar to the correlation we observed with ΔΔGs predicted from structure-based relative FEP simulations. Recognizing the possible advantages of using Potts models to rapidly estimate protein stability effects of kinase mutations seen in cancer genomics data, we used the Potts statistical energy model to estimate the stability effects of 65 conservative and nonconservative mutations across three distinct kinases (Wee1, Abl1, and Cdc7) with somatic mutations reported in the Genomic Data Commons (GDC) database. The ΔEs of these mutations calculated from the Potts model are consistent with the corresponding ΔΔGs from FEP simulations (Pearson ratio of 0.72). The agreement between these methods suggests that the Potts model may be used as a sequence-based tool for high-throughput screening of mutational effects as part of a computational pipeline for predicting the stability effects of mutations. We also demonstrate how the scalability of the fitness-based Potts model calculations permits analyses that are not easily accessed using FEP simulations. To this end, we employed site-saturation mutagenesis in the Potts model in order to investigate the relative stability effects of mutations seen in different cancer evolutionary scenarios. We used this approach to analyze the effects of drug pressure in Abl kinase by contrasting the relative fitness penalties of somatic mutations seen in miscellaneous cancer types with those calculated for mutations associated with cancer drug resistance. We observed that, in contrast to somatic mutations of Abl seen in various tumors that appear to have evolved neutrally, cancer mutations that evolved under drug pressure in Abl-targeted therapies tend to preserve enzyme stability.

In vivo functional phenotypes from a computational epistatic model of evolution

Computational models of evolution are valuable for understanding the dynamics of sequence variation, to infer phylogenetic relationships or potential evolutionary pathways and for biomedical and industrial applications. Despite these benefits, few have validated their propensities to generate outputs with in vivo functionality, which would enhance their value as accurate and interpretable evolutionary algorithms. We demonstrate the power of epistasis inferred from natural protein families to evolve sequence variants in an algorithm we developed called sequence evolution with epistatic contributions (SEEC). Utilizing the Hamiltonian of the joint probability of sequences in the family as fitness metric, we sampled and experimentally tested for in vivo [Formula: see text]-lactamase activity in Escherichia coli TEM-1 variants. These evolved proteins can have dozens of mutations dispersed across the structure while preserving sites essential for both catalysis and interactions. Remarkably, these variants retain family-like functionality while being more active than their wild-type predecessor. We found that depending on the inference method used to generate the epistatic constraints, different parameters simulate diverse selection strengths. Under weaker selection, local Hamiltonian fluctuations reliably predict relative changes to variant fitness, recapitulating neutral evolution. SEEC has the potential to explore the dynamics of neofunctionalization, characterize viral fitness landscapes, and facilitate vaccine development.

Mechanisms of HIV-1 integrase resistance to dolutegravir and potent inhibition of drug-resistant variants

HIV-1 infection depends on the integration of viral DNA into host chromatin. Integration is mediated by the viral enzyme integrase and is blocked by integrase strand transfer inhibitors (INSTIs), first-line antiretroviral therapeutics widely used in the clinic. Resistance to even the best INSTIs is a problem, and the mechanisms of resistance are poorly understood. Here, we analyze combinations of the mutations E138K, G140A/S, and Q148H/K/R, which confer resistance to INSTIs. The investigational drug 4d more effectively inhibited the mutants compared with the approved drug Dolutegravir (DTG). We present 11 new cryo-EM structures of drug-resistant HIV-1 intasomes bound to DTG or 4d, with better than 3-Å resolution. These structures, complemented with free energy simulations, virology, and enzymology, explain the mechanisms of DTG resistance involving E138K + G140A/S + Q148H/K/R and show why 4d maintains potency better than DTG. These data establish a foundation for further development of INSTIs that potently inhibit resistant forms in integrase.

Evolutionary divergence in the conformational landscapes of tyrosine vs serine/threonine kinases

Inactive conformations of protein kinase catalytic domains where the DFG motif has a "DFG-out" orientation and the activation loop is folded present a druggable binding pocket that is targeted by FDA-approved 'type-II inhibitors' in the treatment of cancers. Tyrosine kinases (TKs) typically show strong binding affinity with a wide spectrum of type-II inhibitors while serine/threonine kinases (STKs) usually bind more weakly which we suggest here is due to differences in the folded to extended conformational equilibrium of the activation loop between TKs vs. STKs. To investigate this, we use sequence covariation analysis with a Potts Hamiltonian statistical energy model to guide absolute binding free-energy molecular dynamics simulations of 74 protein-ligand complexes. Using the calculated binding free energies together with experimental values, we estimated free-energy costs for the large-scale (~17-20 Å) conformational change of the activation loop by an indirect approach, circumventing the very challenging problem of simulating the conformational change directly. We also used the Potts statistical potential to thread large sequence ensembles over active and inactive kinase states. The structure-based and sequence-based analyses are consistent; together they suggest TKs evolved to have free-energy penalties for the classical 'folded activation loop' DFG-out conformation relative to the active conformation, that is, on average, 4-6 kcal/mol smaller than the corresponding values for STKs. Potts statistical energy analysis suggests a molecular basis for this observation, wherein the activation loops of TKs are more weakly 'anchored' against the catalytic loop motif in the active conformation and form more stable substrate-mimicking interactions in the inactive conformation. These results provide insights into the molecular basis for the divergent functional properties of TKs and STKs, and have pharmacological implications for the target selectivity of type-II inhibitors.

Contingency and Entrenchment of Drug-Resistance Mutations in HIV Viral Proteins

The ability of HIV-1 to rapidly mutate leads to antiretroviral therapy (ART) failure among infected patients. Drug-resistance mutations (DRMs), which cause a fitness penalty to intrinsic viral fitness, are compensated by accessory mutations with favorable epistatic interactions which cause an evolutionary trapping effect, but the kinetics of this overall process has not been well characterized. Here, using a Potts Hamiltonian model describing epistasis combined with kinetic Monte Carlo simulations of evolutionary trajectories, we explore how epistasis modulates the evolutionary dynamics of HIV DRMs. We show how the occurrence of a drug-resistance mutation is contingent on favorable epistatic interactions with many other residues of the sequence background and that subsequent mutations entrench DRMs. We measure the time-autocorrelation of fluctuations in the likelihood of DRMs due to epistatic coupling with the sequence background, which reveals the presence of two evolutionary processes controlling DRM kinetics with two distinct time scales. Further analysis of waiting times for the evolutionary trapping effect to reverse reveals that the sequences which entrench (trap) a DRM are responsible for the slower time scale. We also quantify the overall strength of epistatic effects on the evolutionary kinetics for different mutations and show these are much larger for DRM positions than polymorphic positions, and we also show that trapping of a DRM is often caused by the collective effect of many accessory mutations, rather than a few strongly coupled ones, suggesting the importance of multiresidue sequence variations in HIV evolution. The analysis presented here provides a framework to explore the kinetic pathways through which viral proteins like HIV evolve under drug-selection pressure.

Limits to detecting epistasis in the fitness landscape of HIV

The rapid evolution of HIV is constrained by interactions between mutations which affect viral fitness. In this work, we explore the role of epistasis in determining the mutational fitness landscape of HIV for multiple drug target proteins, including Protease, Reverse Transcriptase, and Integrase. Epistatic interactions between residues modulate the mutation patterns involved in drug resistance, with unambiguous signatures of epistasis best seen in the comparison of the Potts model predicted and experimental HIV sequence “prevalences” expressed as higher-order marginals (beyond triplets) of the sequence probability distribution. In contrast, experimental measures of fitness such as viral replicative capacities generally probe fitness effects of point mutations in a single background, providing weak evidence for epistasis in viral systems. The detectable effects of epistasis are obscured by higher evolutionary conservation at sites. While double mutant cycles in principle, provide one of the best ways to probe epistatic interactions experimentally without reference to a particular background, we show that the analysis is complicated by the small dynamic range of measurements. Overall, we show that global pairwise interaction Potts models are necessary for predicting the mutational landscape of viral proteins.

Unique features of different classes of G-protein-coupled receptors revealed from sequence coevolutionary and structural analysis

G-protein-coupled receptors (GPCRs) are the largest family of human membrane proteins and represent the primary targets of about one third of currently marketed drugs. Despite the critical importance, experimental structures have been determined for only a limited portion of GPCRs and functional mechanisms of GPCRs remain poorly understood. Here, we have constructed novel sequence coevolutionary models of the A and B classes of GPCRs and compared them with residue contact frequency maps generated with available experimental structures. Significant portions of structural residue contacts were successfully detected in the sequence-based covariational models. "Exception" residue contacts predicted from sequence coevolutionary models but not available structures added missing links that were important for GPCR activation and allosteric modulation. Moreover, we identified distinct residue contacts involving different sets of functional motifs for GPCR activation, such as the Na⁺ pocket, CWxP, DRY, PIF, and NPxxY motifs in the class A and the HETx and PxxG motifs in the class B. Finally, we systematically uncovered critical residue contacts tuned by allosteric modulation in the two classes of GPCRs, including those from the activation motifs and particularly the extracellular and intracellular loops in class A GPCRs. These findings provide a promising framework for rational design of ligands to regulate GPCR activation and allosteric modulation.

The generative capacity of probabilistic protein sequence models

Potts models and variational autoencoders (VAEs) have recently gained popularity as generative protein sequence models (GPSMs) to explore fitness landscapes and predict mutation effects. Despite encouraging results, current model evaluation metrics leave unclear whether GPSMs faithfully reproduce the complex multi-residue mutational patterns observed in natural sequences due to epistasis. Here, we develop a set of sequence statistics to assess the “generative capacity” of three current GPSMs: the pairwise Potts Hamiltonian, the VAE, and the site-independent model. We show that the Potts model’s generative capacity is largest, as the higher-order mutational statistics generated by the model agree with those observed for natural sequences, while the VAE’s lies between the Potts and site-independent models. Importantly, our work provides a new framework for evaluating and interpreting GPSM accuracy which emphasizes the role of higher-order covariation and epistasis, with broader implications for probabilistic sequence models in general.

Generative models have become increasingly popular in protein design, yet rigorous metrics that allow the comparison of these models are lacking. Here, the authors propose a set of such metrics and use them to compare three popular models.

adabmDCA: adaptive Boltzmann machine learning for biological sequences

Background

Boltzmann machines are energy-based models that have been shown to provide an accurate statistical description of domains of evolutionary-related protein and RNA families. They are parametrized in terms of local biases accounting for residue conservation, and pairwise terms to model epistatic coevolution between residues. From the model parameters, it is possible to extract an accurate prediction of the three-dimensional contact map of the target domain. More recently, the accuracy of these models has been also assessed in terms of their ability in predicting mutational effects and generating in silico functional sequences.

Results

Our adaptive implementation of Boltzmann machine learning, adabmDCA, can be generally applied to both protein and RNA families and accomplishes several learning set-ups, depending on the complexity of the input data and on the user requirements. The code is fully available at https://github.com/anna-pa-m/adabmDCA. As an example, we have performed the learning of three Boltzmann machines modeling the Kunitz and Beta-lactamase2 protein domains and TPP-riboswitch RNA domain.

Conclusions

The models learned by adabmDCA are comparable to those obtained by state-of-the-art techniques for this task, in terms of the quality of the inferred contact map as well as of the synthetically generated sequences. In addition, the code implements both equilibrium and out-of-equilibrium learning, which allows for an accurate and lossless training when the equilibrium one is prohibitive in terms of computational time, and allows for pruning irrelevant parameters using an information-based criterion.

Efficient generative modeling of protein sequences using simple autoregressive models

Generative models emerge as promising candidates for novel sequence-data driven approaches to protein design, and for the extraction of structural and functional information about proteins deeply hidden in rapidly growing sequence databases. Here we propose simple autoregressive models as highly accurate but computationally efficient generative sequence models. We show that they perform similarly to existing approaches based on Boltzmann machines or deep generative models, but at a substantially lower computational cost (by a factor between 10² and 10³). Furthermore, the simple structure of our models has distinctive mathematical advantages, which translate into an improved applicability in sequence generation and evaluation. Within these models, we can easily estimate both the probability of a given sequence, and, using the model's entropy, the size of the functional sequence space related to a specific protein family. In the example of response regulators, we find a huge number of ca. 10⁶⁸ possible sequences, which nevertheless constitute only the astronomically small fraction 10^-80 of all amino-acid sequences of the same length. These findings illustrate the potential and the difficulty in exploring sequence space via generative sequence models.