Alchemical free energy simulations without speed limits. A generic framework to calculate free energy differences independent of the underlying molecular dynamics program.

We describe the theory of the so-called common-core/serial-atom-insertion (CC/SAI) approach to compute alchemical free energy differences and its practical implementation in a Python package called Transformato. CC/SAI is not tied to a specific biomolecular simulation program and does not rely on special purpose code for alchemical transformations. To calculate the alchemical free energy difference between several small molecules, the physical end-states are mutated into a suitable common core. Since this only requires turning off interactions, the setup of intermediate states is straightforward to automate. Transformato currently supports CHARMM and OpenMM as back ends to carry out the necessary molecular dynamics simulations, as well as post-processing calculations. We validate the method by computing a series of relative solvation free energy differences.

Dummy Atoms in Alchemical Free Energy Calculations.

In calculations of relative free energy differences, the number of atoms of the initial and final states is rarely the same. This necessitates the introduction of dummy atoms. These placeholders interact with the physical system only by bonded energy terms. We investigate the conditions necessary so that the presence of dummy atoms does not influence the result of a relative free energy calculation. On the one hand, one has to ensure that dummy atoms only give a multiplicative contribution to the partition function so that their contribution cancels from double-free energy differences. On the other hand, the bonded terms used to attach a dummy atom (or group of dummy atoms) to the physical system have to maintain it in a well-defined position and orientation relative to the physical system. A detailed theoretical analysis of both aspects is provided, illustrated by 24 calculations of relative solvation free energy differences, for which all four legs of the underlying thermodynamic cycle were computed. Cycle closure (or lack thereof) was used as a sensitive indicator to probing the effects of dummy atom treatment on the resulting free energy differences. We find that a naive (but often practiced) treatment of dummy atoms results in errors of up to kBT when calculating the relative solvation free energy difference between two small solutes, such as methane and ammonia. While our analysis focuses on the so-called single topology approach to set up alchemical transformations, similar considerations apply to dual topology, at least many widely used variants thereof.

Constraints on the Coupling between Axionlike Dark Matter and Photons Using an Antiproton Superconducting Tuned Detection Circuit in a Cryogenic Penning Trap.

We constrain the coupling between axionlike particles (ALPs) and photons, measured with the superconducting resonant detection circuit of a cryogenic Penning trap. By searching the noise spectrum of our fixed-frequency resonant circuit for peaks caused by dark matter ALPs converting into photons in the strong magnetic field of the Penning-trap magnet, we are able to constrain the coupling of ALPs with masses around 2.7906-2.7914 neV/c^{2} to g_{aγ}<1×10^{-11} GeV^{-1}. This is more than one order of magnitude lower than the best laboratory haloscope and approximately 5 times lower than the CERN axion solar telescope (CAST), setting limits in a mass and coupling range which is not constrained by astrophysical observations. Our approach can be extended to many other Penning-trap experiments and has the potential to provide broad limits in the low ALP mass range.

Configurational Entropy Components and Their Contribution to Biomolecular Complex Formation.

Configurational entropy change is a central constituent of the free energy change in noncovalent interactions between biomolecules. Due to both experimental and computational limitations, however, the impact of individual contributions to configurational entropy change remains underexplored. Here, we develop a novel, fully analytical framework to dissect the configurational entropy change of binding into contributions coming from molecular internal and external degrees of freedom. Importantly, this framework accounts for all coupled and uncoupled contributions in the absence of an external field. We employ our parallel implementation of the maximum information spanning tree algorithm to provide a comprehensive numerical analysis of the importance of the individual contributions to configurational entropy change on an extensive set of molecular dynamics simulations of protein binding processes. Contrary to commonly accepted assumptions, we show that different coupling terms contribute significantly to the overall configurational entropy change. Finally, while the magnitude of individual terms may be largely unpredictable a priori, the total configurational entropy change can be well approximated by rescaling the sum of uncoupled contributions from internal degrees of freedom only, providing support for NMR-based approaches for configurational entropy change estimation.

Toward Prediction of Electrostatic Parameters for Force Fields That Explicitly Treat Electronic Polarization.

The derivation of atomic polarizabilities for polarizable force field development has been a long-standing problem. Atomic polarizabilities were often refined manually starting from tabulated values, rendering an automated assignment of parameters difficult and hampering reproducibility and transferability of the obtained values. To overcome this, we trained both a linear increment scheme and a multilayer perceptron neural network on a large number of high-quality quantum mechanical atomic polarizabilities and partial atomic charges, where only the type of each atom and its connectivity were used as input. The predicted atomic polarizabilities and charges had average errors of 0.023 Å3 and 0.019 e using the neural net and 0.063 Å3 and 0.069 e using the simple increment scheme. As the algorithm relies only on the connectivities of the atoms within a molecule, thus omitting dependencies on the three-dimensional conformation, the approach naturally assigns like charges and polarizabilities to symmetrical groups. Accordingly, a convenient utility is presented for generating the partial atomic charges and atomic polarizabilities for organic molecules as needed in polarizable force field development.

Self-Consistent Framework Connecting Experimental Proxies of Protein Dynamics with Configurational Entropy.

The recently developed NMR techniques enable estimation of protein configurational entropy change from the change in the average methyl order parameters. This experimental observable, however, does not directly measure the contribution of intramolecular couplings, protein main-chain motions, or angular dynamics. Here, we carry out a self-consistent computational analysis of the impact of these missing contributions on an extensive set of molecular dynamics simulations of different proteins undergoing binding. Specifically, we compare the configurational entropy change in protein complex formation as obtained by the maximum information spanning tree approximation (MIST), which treats the above entropy contributions directly, and the change in the average NMR methyl and NH order parameters. Our parallel implementation of MIST allows us to treat hard angular degrees of freedom as well as couplings up to full pairwise order explicitly, while still involving a high degree of sampling and tackling molecules of biologically relevant sizes. First, we demonstrate a remarkably strong linear relationship between the total configurational entropy change and the average change in both methyl and backbone-NH order parameters. Second, in contrast to canonical assumptions, we show that the main-chain and angular terms contribute significantly to the overall configurational entropy change and also scale linearly with it. Consequently, linear models starting from the average methyl order parameters are able to capture the contribution of main-chain and angular terms well. After applying the quantum-mechanical harmonic oscillator entropy formalism, we establish a similarly strong linear relationship for X-ray crystallographic B-factors. Finally, we demonstrate that the observed linear relationships remain robust against drastic undersampling and argue that they reflect an intrinsic property of compact proteins. Despite their remarkable strength, however, the above linear relationships yield estimates of configurational entropy change whose accuracy appears to be sufficient for qualitative applications only.

PARENT: A Parallel Software Suite for the Calculation of Configurational Entropy in Biomolecular Systems.

Accurate estimation of configurational entropy from the in silico-generated biomolecular ensembles, e.g., from molecular dynamics (MD) trajectories, is dependent strongly on exhaustive sampling for physical reasons. This, however, creates a major computational problem for the subsequent estimation of configurational entropy using the Maximum Information Spanning Tree (MIST) or Mutual Information Expansion (MIE) approaches for internal molecular coordinates. In particular, the available software for such estimation exhibits serious limitations when it comes to molecules with hundreds or thousands of atoms, because of its reliance on a serial program architecture. To overcome this problem, we have developed a parallel, hybrid MPI/openMP C++ implementation of MIST and MIE, called PARENT, which is particularly optimized for high-performance computing and provides efficient estimation of configurational entropy in different biological processes (e.g., protein-protein interactions). In addition, PARENT also allows for a detailed mapping of intramolecular allosteric networks. Here, we benchmark the program on a set of 1-µs-long MD trajectories of 10 different protein complexes and their components, demonstrating robustness and good scalability. A direct comparison between MIST and MIE on the same dataset demonstrates a superior convergence behavior for the former approach, when it comes to total simulation length and configurational-space binning.

Adaptable Lipid Matrix Promotes Protein-Protein Association in Membranes.

The cell membrane is "stuffed" with proteins, whose transmembrane (TM) helical domains spontaneously associate to form functionally active complexes. For a number of membrane receptors, a modulation of TM domains' oligomerization has been shown to contribute to the development of severe pathological states, thus calling for detailed studies of the atomistic aspects of the process. Despite considerable progress achieved so far, several crucial questions still remain: How do the helices recognize each other in the membrane? What is the driving force of their association? Here, we assess the dimerization free energy of TM helices along with a careful consideration of the interplay between the structure and dynamics of protein and lipids using atomistic molecular dynamics simulations in the hydrated lipid bilayer for three different model systems - TM fragments of glycophorin A, polyalanine and polyleucine peptides. We observe that the membrane driven association of TM helices exhibits a prominent entropic character, which depends on the peptide sequence. Thus, a single TM peptide of a given composition induces strong and characteristic perturbations in the hydrophobic core of the bilayer, which may facilitate the initial "communication" between TM helices even at the distances of 20-30 Å. Upon tight helix-helix association, the immobilized lipids accommodate near the peripheral surfaces of the dimer, thus disturbing the packing of the surrounding. The dimerization free energy of the modeled peptides corresponds to the strength of their interactions with lipids inside the membrane being the lowest for glycophorin A and similarly higher for both homopolymers. We propose that the ability to accommodate lipid tails determines the dimerization strength of TM peptides and that the lipid matrix directly governs their association.