RESUMO
Computing free energy differences between metastable states characterized by nonoverlapping Boltzmann distributions is often a computationally intensive endeavor, usually requiring chains of intermediate states to connect them. Targeted free energy perturbation (TFEP) can significantly lower the computational cost of FEP calculations by choosing a set of invertible maps used to directly connect the distributions of interest, achieving the necessary statistically significant overlaps without sampling any intermediate states. Probabilistic generative models (PGMs) based on normalizing flow architectures can make it much easier via machine learning to train invertible maps needed for TFEP. However, the accuracy and applicability of approaches based on empirically learned maps depend crucially on the choice of reweighting method adopted to estimate the free energy differences. In this work, we assess the accuracy, rate of convergence, and data efficiency of different free energy estimators, including exponential averaging, Bennett acceptance ratio (BAR), and multistate Bennett acceptance ratio (MBAR), in reweighting PGMs trained by maximum likelihood on limited amounts of molecular dynamics data sampled only from end-states of interest. We carry out the comparisons on a set of simple but representative case studies, including conformational ensembles of alanine dipeptide and ibuprofen. Our results indicate that BAR and MBAR are both data efficient and robust, even in the presence of significant model overfitting in the generation of invertible maps. This analysis can serve as a stepping stone for the deployment of efficient and quantitatively accurate ML-based free energy calculation methods in complex systems.
RESUMO
Class A ß-lactamases are known for being able to rapidly gain broad spectrum catalytic efficiency against most ß-lactamase inhibitor combinations as a result of elusively minor point mutations. The evolution in class A ß-lactamases occurs through optimisation of their dynamic phenotypes at different timescales. At long-timescales, certain conformations are more catalytically permissive than others while at the short timescales, fine-grained optimisation of free energy barriers can improve efficiency in ligand processing by the active site. Free energy barriers, which define all coordinated movements, depend on the flexibility of the secondary structural elements. The most highly conserved residues in class A ß-lactamases are hydrophobic nodes that stabilize the core. To assess how the stable hydrophobic core is linked to the structural dynamics of the active site, we carried out adaptively sampled molecular dynamics (MD) simulations in four representative class A ß-lactamases (KPC-2, SME-1, TEM-1, and SHV-1). Using Markov State Models (MSM) and unsupervised deep learning, we show that the dynamics of the hydrophobic nodes is used as a metastable relay of kinetic information within the core and is coupled with the catalytically permissive conformation of the active site environment. Our results collectively demonstrate that the class A enzymes described here, share several important dynamic similarities and the hydrophobic nodes comprise of an informative set of dynamic variables in representative class A ß-lactamases.
RESUMO
Understanding allostery in enzymes and tools to identify it offer promising alternative strategies to inhibitor development. Through a combination of equilibrium and nonequilibrium molecular dynamics simulations, we identify allosteric effects and communication pathways in two prototypical class A ß-lactamases, TEM-1 and KPC-2, which are important determinants of antibiotic resistance. The nonequilibrium simulations reveal pathways of communication operating over distances of 30 Å or more. Propagation of the signal occurs through cooperative coupling of loop dynamics. Notably, 50% or more of clinically relevant amino acid substitutions map onto the identified signal transduction pathways. This suggests that clinically important variation may affect, or be driven by, differences in allosteric behavior, providing a mechanism by which amino acid substitutions may affect the relationship between spectrum of activity, catalytic turnover, and potential allosteric behavior in this clinically important enzyme family. Simulations of the type presented here will help in identifying and analyzing such differences.
Antibiotics are crucial drugs for treating and preventing bacterial infections, but some bacteria are evolving ways to resist their effects. This 'antibiotic resistance' threatens lives and livelihoods worldwide. ß-lactam antibiotics, like penicillin, are some of the most commonly used, but some bacteria can now make enzymes called ß-lactamases, which destroy these antibiotics. Dozens of different types of ß-lactamases now exist, each with different properties. Two of the most medically important are TEM-1 and KPC-2. One way to counteract ß-lactamases is with drugs called inhibitors that stop the activity of these enzymes. The approved ß-lactamase inhibitors work by blocking the part of the enzyme that binds and destroys antibiotics, known as the 'active site'. The ß-lactamases have evolved, some of which have the ability to resist the effects of known inhibitors. It is possible that targeting parts of ß-lactamases far from the active site, known as 'allosteric sites', might get around these new bacterial defences. A molecule that binds to an allosteric site might alter the enzyme's shape, or restrict its movement, making it unable to do its job. Galdadas, Qu et al. used simulations to understand how molecules binding at allosteric sites affect enzyme movement. The experiments examined the structures of both TEM-1 and KPC-2, looking at how their shapes changed as molecules were removed from the allosteric site. This revealed how the allosteric sites and the active site are linked together. When molecules were taken out of the allosteric sites, they triggered ripples of shape change that travelled via loop-like structures across the surface of the enzyme. These loops contain over half of the known differences between the different types of ß-lactamases, suggesting mutations here may be responsible for changing which antibiotics each enzyme can destroy. In other words, changes in the 'ripples' may be related to the ability of the enzymes to resist particular antibiotics. Understanding how changes in one part of a ß-lactamase enzyme reach the active site could help in the design of new inhibitors. It might also help to explain how ß-lactamases evolve new properties. Further work could show why different enzymes are more or less active against different antibiotics.
